[
    {
        "image_filename": "designv10_10_0001598_j.ijmecsci.2006.06.013-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001598_j.ijmecsci.2006.06.013-Figure2-1.png",
        "caption": "Fig. 2. Kinematic inversion.",
        "texts": [
            " To determine the external gear, its profile must be determined geometrically by parts xe(age),ye(age) \u00bc f(R2,S,G,Z), which is in turn the function of four geometrical parameters. Both profiles are shown in the reference, set forth in Fig. 1. For any other position of the gear set, profiles can be generated by the applying rotation equation, xr;j\u00f0oj\u00de \u00bc xj agj cos oj yj agj sin oj, yr;j\u00f0oj\u00de \u00bc xj agj cos oj \u00fe yj agj sin oj, \u00f02\u00de where j \u00bc i for the internal gear and j \u00bc e for the external gear [4]. Fig. 2 shows a kinematic inversion in which the entire system has been given a counter clockwise rotation of (Z 1)c, where c is the counter clockwise rotation of the external gear relative to the internal gear. Once the coordinates of the contact points are known at any position of the gear set, the idea behind this method is to bring all the contact points to the first quadrant of the external gear reference through a kinematic inversion. Thus, contact points are studied at the position illustrated P.J. Gamez-Montero et al. / International Journal of Mechanical Sciences 48 (2006) 1471\u20131480 1473 in Fig. 2. The external gear is then brought back to its original position by the angle oe \u00bc (Z 1)c. The internal gear will now have its centre O1 rotated a counter clockwise rotation of (Z 1)c and a clockwise rotation of c over itself. Hence, if a point Pk,i of the internal gear touches the external gear at Pk,e, then the normal to the external gear at Pk,e must pass through the instantaneous centre of relative motion I. By using this property, the relation between the radii of curvature of conjugate shapes was derived by L\u2019Ho\u0302pital and quoted by Hartenberg and Denavit [5] as 1 IQk;e 1 IQk;i \u00bc 1 r2 1 r1 1 sin fk , (3) where Qk,e and Qk,i are the centres of curvature of the external and internal gears at the contact point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003464_we.1940-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003464_we.1940-Figure5-1.png",
        "caption": "Figure 5. Notional sketch of a PGB structure.",
        "texts": [
            " The driving motor is a three-phase 10HP induction motor with a motor controller. The output shaft of the gearbox is connected to a generator and a grid tie which serves as a load generator. The structure of the PGB test rig is similar to those used in a wind turbine. During the test, commercially available single-stage PGBs with a 5:1 speed reduction ratio were used. Wind Energ. (2015) \u00a9 2015 John Wiley & Sons, Ltd. DOI: 10.1002/we Amongst the three different PGB operational types, a specific PGB with the fixed ring gear was used in this paper. Figure 5 shows a notional sketch of the PGB structure with the fixed ring gear. For this type of PGB, the number of teeth is linear to the radius of each gears pitch circle. This indicates that the input to output velocity ratio is also related to the angular velocity (\u03c9) of the gears. The gear ratio can be defined as R \u00bc \u03c9sun \u03c9carrier \u00bc 1\u00fe zring zsun (11) where \u03c9i is the angular velocities on gear component i and zj is the number of teeth on gear component j; The planet carrier rotation speed (i.e. output speed) in frequency could be obtained as f carrier \u00bc f sun R (12) where fi is the rotation speed in frequency at gear component i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002455_fuce.201000114-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002455_fuce.201000114-Figure2-1.png",
        "caption": "Fig. 2 Sample holder assemblies: (A) shows a sectional view of the assembly used for single layer fuel cell to realise a cathode to anode area proportion of 1:1. (B) shows the assembly of the fuel cells in depletion design [24]. Here silicon with KOH-etched feedholes serves as glucose permeable substrate for the cathode. Feedholes occupy 8% of the projected cathode area. Cathode and anode are separated by an additional filter membrane.",
        "texts": [
            "0% correspond to the lower and upper limits of the physiological oxygen concentration range estimated for tissue fluid [30]. Between two measurements at different oxygen concentrations the anodes were regenerated to ensure comparability between the individual experiments. This was done by cyclic voltammetry conducted under nitrogen atmosphere (10 cycles between \u20130.9 and 1.4 V vs. SCE, scan speed 10 mV s\u20131, final value: \u20130.5 V vs. SCE). For fuel cell experiments the individual electrodes were contacted with two platinum wires, and mounted in sample holders as shown in Figure 2A. For cathode to anode proportions differing from the case of equally sized cathode and anode the windows in the sample holder structure defining the accessible electrode area were varied in size according to Table 1. For comparison Figure 2B shows the according setup for the previously published fuel cell realised in depletion O R IG IN A L R ES EA R C H P A P ER 318 \u00a9 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim FUEL CELLS 11, 2011, No. 2, 316\u2013326www.fuelcells.wiley-vch.de design. As depicted in Figure 2 a Supor\u2013450 membrane filter (0.45 lm pore size, Pall Life Sciences, East Hills, New York, USA) was placed on top of each electrode in single layer design and on top of the cathode in depletion design. This was done to experimentally simulate the diffusion resistance for glucose through a tissue capsule which is expected to form around the fuel cell device after implantation as indicated in Figure 1 [27, 31]. In depletion design an identical membrane filter was additionally placed between cathode and anode to guarantee electrical insulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003309_1475921717727700-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003309_1475921717727700-Figure3-1.png",
        "caption": "Figure 3. Gears with different tooth removal.",
        "texts": [
            " The chipped tooth is the rapture of material at a point on the working tip of gear. Chipped tooth is very common in many industrial applications.20 In this work, depth-wise damage is simulated on the spur gear tooth by grinding the tooth in steps based on percent removal of teeth depth. A total of seven conditions of the gear are investigated: healthy gear and gear with six stages of depth-wise tooth removal, that is, 10%, 20%, 30%, 50%, 70%, and 100% tooth removal across the tooth width as shown in Figure 3. The notation of all running conditions is listed in Table 3. For all simulated gear conditions, both vibration and acoustic signals are acquired. The sampling frequency of the system is 12.8 kHz, and 30,000 data points were collected for each case at 900 r/min. Each test is repeated five times for every fault conditions in order to have sufficient number of signals for the training and testing of the classifier in classification stage. Data consists of four vibration and acoustic files for healthy condition and 10 files for each kind of fault"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001730_j.cirp.2007.05.092-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001730_j.cirp.2007.05.092-Figure6-1.png",
        "caption": "Figure 6: Test stand.",
        "texts": [
            " The theoretical analysis of the multipoint(4P)-bearing with internal spring preload shows that the elastic arrangement of the two halves of the inner ring can prevent the bearing from jamming. The negative effects which result from inner ring excess temperatures can be reduced. In the following, experimental results regarding the operating behaviour of multipoint(4P)-bearings under the influence of an excess temperature are presented. The test stand used for the experimental investigations is shown in Figure 6. The direct drive can realise maximum rotational speeds of up to 40,000 rpm. The nominal torque amounts to 4.2 Nm for a nominal speed of 23,000 rpm. The test spindle and the drive are connected by a jaw clutch. The test bearings can be loaded axially by a hydraulic piston. A tempering of the outer ring is realised by a water circulation in the flange. Thereby, the heating of the outer ring caused by the additional rolling contact can be reduced. The inner bearing temperature is measured by a non-contacting sensor positioned closely to the rotating inner ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002792_36007-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002792_36007-Figure2-1.png",
        "caption": "Fig. 2: (Colour on-line) (a) A solid nematic torus shell with inner and outer radii ri, ro and internal radius rc with the director aligned along the long circumference. (b) A discrete torus with lines of concentrated Gaussian curvature. (c) After deformation the radii ri and ro need to increase by \u03bb to produce the correct new circumferences, but their material lengths decrease by \u03bb\u2212\u03bd since they are in directions perpendicular to n\u0302. The adoption of the angle \u03b8 < \u03c0/2 resolves this conflict.",
        "texts": [
            " Incompatibility arises purely from changing the topology and enforcing a periodic boundary condition. It is noteworthy, however, that if the material under consideration were a nematic elastomer, instead of a glass, then the soft-mode director rotation [5] unique to the elastomeric case allows for the availability of a compatible, stress-free deformation and the possibility of a torsional actuator. On a torus the topologically-induced incompatibility exists even when n\u0302 is along a principal direction, for instance along a long circumference, see fig. 2(a). The radii ri and ro must increase by \u03bb in order to generate the circumferences that have been increased by \u03bb. The sectional radius rc = 1 2 (ro\u2212 ri)\u2192 \u03bbrc increases in this way too and would then give a circumference of 2\u03c0\u03bbrc. But the initial sectional circumference 2\u03c0rc takes a new natural length \u03bb\u2212\u03bd2\u03c0rc which is inconsistent with the new inner radius \u03bbrc. Again we have an incompatibility arising from a uniform director field on a surface of non-trivial topology. However topology and curvature determine elastic compatibility in a subtle manner. Consider a discrete surface with the topology of a torus, but with its regions of positive and negative Gaussian curvature now confined to lines, fig. 2(b). It can easily be seen that with circumferential directors (that is, azimuthal on the cylinders) a transformation to the surface of fig. 2(c) has no areas of extension/contraction with respect to the new natural dimensions of the body if the angle of distortion is \u03b8= sin\u22121(\u03bb1+\u03bd) (see the right triangle with \u03b8 in (c). The argument is analogous to that for the opening angle of a cone, and the result is the same [2]. Spherical shells. \u2013 Spherical shells of nematic solid represent another reference geometry with non-trivial topology of potential interest. Unlike in the case of cylindrical shells, the initial intrinsic geometry is no longer flat and we must calculate the effect on the local curvature of the spontaneous strain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003470_s12206-015-0901-8-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003470_s12206-015-0901-8-Figure1-1.png",
        "caption": "Fig. 1. Structure and principle of a high-power wind turbine gearbox\u2019s transmission system.",
        "texts": [
            "cn \u2020 Recommended by Associate Editor Cheolung Cheong \u00a9 KSME & Springer 2015 between the inner gear and planetary gear, a coupled dynamic model for high-power wind turbine gearbox transmission system, which consists of two-stage helical planetary gears and one helical gear stage, was established using the lumped parameter method, and the dynamic characteristics for the wind turbine gear transmission system were studied. The gear transmission system for the high-power wind turbine gearbox consists of three transmission stages: 1st planetary transmission stage with five helical planet gears, one ring gear, one carrier and one sun gear, 2nd planetary transmission stage with three helical planet gears, one ring gear, one carrier and one sun gear, 3rd parallel transmission stage with two helical gears. The structure and principle of the gear transmission system is shown in Fig. 1. As shown in Fig. 1, an input with low rotation velocity and high torque load is applied in the carrier of the 1st transmission stage and the output with higher rotation velocity and lower torque is the pinion of the 3rd transmission stage. The detailed parameters of the transmission system are listed in Table 1. The system parameters were acquired from a specific type of real high-power wind turbine gearbox used in application. In Table 2, the bearing stiffnesses in corresponding directions were calculated by Romax software according to the detailed bearing designations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003375_j.triboint.2014.10.007-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003375_j.triboint.2014.10.007-Figure1-1.png",
        "caption": "Fig. 1. (A) The lateral lubricating interface in EGMs is highlighted (in yellow), and exists between the gears and lateral bushes. (B) High pressure (red) and low pressure (blue) balance areas separated by an elastomeric seal (yellow). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " The model is the first of the lateral lubricating interface in EGMs capable of considering heat transfer, thermal effects in the fluid film and solid components as well as thermo-elastic deformation of the solids enabling prediction of the film thickness in EGM lateral gaps considering thermoelastohydrodynamic lubrication. Model validation is performed using lateral gap leakage measurement which is dependent on absolute film thickness. A novel relative lubricant film thickness measurement method in gear machines using capacitive sensors is also presented, and used to validate the spatial film thickness predictions from the model. & 2014 Elsevier Ltd. All rights reserved. The lateral lubricating interface in external gear machines (EGMs) exists between the lateral bushes and gears shown in Fig. 1A. The lateral bushes are one of the most important components in high pressure EGMs. They are pressure loaded floating elements aimed at reducing losses due to fluid friction and leakage as well as undesirable wear at the interface. The necessary pressure loading is achieved by specially designed high pressure (HP) and low pressure (LP) balance areas as shown in Fig. 1B. The opposing aims of minimizing friction as well as leakage losses make the design of these balance elements a delicate and challenging proposition. Further complexity in this is added by the fact that the pressure loads acting on the lateral bushing from the lubricating gap also constitute of hydrodynamic loads due to squeeze micro-motion of the lateral bushing and solid deformation of the gears and the lateral bushes due to pressure and thermal loads. A few prior studies of the lateral lubricating interface in EGMs were present in existing literature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.4-1.png",
        "caption": "Fig. 1.4. Schematic representation of aerodynamic coordinate system",
        "texts": [
            " The three axes (XE , YE , ZE ) of this coordinate system are oriented respectively towards the north, the east and downward. The transformation matrix to go from the aircraft\u2019s to the earth\u2019s coordinate system - see Fig. 1.2 and 1.3 - is: MAC\u2192E = \u239b\u239dcos\u03a8 \u2212sin\u03a8 0 sin\u03a8 cos\u03a8 0 0 0 1 \u239e\u23a0\u239b\u239d cos\u03b8 0 sin\u03b8 0 1 0 \u2212sin\u03b8 0 cos\u03b8 \u239e\u23a0\u239b\u239d1 0 0 0 cos\u03d5 \u2212sin\u03d5 0 sin\u03d5 cos\u03d5 \u239e\u23a0 (1.1) The AIRBUS On-Ground Transport Aircraft Benchmark 5 The aerodynamic coordinate system is a mobile coordinate system (c.g.; Xaero, Yaero, Zaero) associated with the orientation of the aircraft velocity vector in relation to the air mass (Vair) - see Fig. 1.4 Its origin is the centre of gravity. The longitudinal axis Xaero is oriented in the direction of this \u201cair\u201d velocity vector. In relation to the aircraft coordinate system, the coordinate system associated with the aerodynamic coordinate system is obtained by a rotation of angle \u03b1 (angle of attack) around the YAC axis and of angle \u03b2aero (aerodynamic sideslip) around the ZAC-axis. The transformation matrix is: MAEROR\u2192AC = \u239b\u239d cos\u03b2aero sin\u03b2aero 0 \u2212sin\u03b2aero cos\u03b2aero 0 0 0 1 \u239e\u23a0\u239b\u239dcos\u03b1 0 \u2212sin\u03b1 0 1 0 sin\u03b1 0 cos\u03b1 \u239e\u23a0 = \u239b\u239d cos\u03b1 \u00b7 cos\u03b2aero sin \u03b2aero 0 \u2212sin\u03b2aero \u00b7 cos\u03b1 cos\u03b2aero sin \u03b1 \u00b7 sin\u03b2aero sin\u03b1 0 cos\u03b1 \u239e\u23a0 (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002260_iros.2009.5354557-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002260_iros.2009.5354557-Figure11-1.png",
        "caption": "Fig. 11. ZMP Trajectory of Humanoid Robot and Human",
        "texts": [
            "25 [s], respectively. On the other hand, Fig.10(b) shows the human motion shown in the 3rd sample of Table I. We can see from these figures that the sway of the humanoid robot\u2019s waist is much larger than the human\u2019s one. We consider two effects to reduce the sway of the humanoid robot\u2019s waist. One is to take \u2206yG in eq.(4) into account and the other is to make the robot\u2019s ZMP trajectory in the single support phase be close to the human\u2019s one. The ZMP trajectory in the single support phase is shown in Fig.11. As shown in this figure, the human\u2019s ZMP moves to the toe at the middle of the single support phase. We also make the robot\u2019s ZMP move during the single support phase. The motion of the ZMP in the x direction contributes to avoid the knee of the stance foot fall in the singular posture. On the other hand, the motion of the ZMP in the y direction contributes to reduce the waist\u2019s sway. Fig.12 shows the results of the reduction of the waist\u2019s sway where we set xzt = 0.04, xzh = \u22120.005, and yzh = 0",
            " This contributes to enlarge the step length. On the other hand, in our walking pattern generator, the heel always touch the ground during the single support phase. In this case, when the step length is large, we have to make the vertical position of the waist lower at the beginning of the double support phase. Hence, we modified eq.(9) as follows: \u03b6k+1 = 0.002 + 0.144L2 k (11) By using this equation, the magnitude of up/down of the waist becomes 0.015 [m] when the step length is Lk = 0.3[m]. Thirdly, as shown in Fig.11, the human\u2019s zmp trajectory during the single support phase moves close to the thumb finger. Learned from this characteristic, we set yzt = 0.01[m] in Fig. 12 and the sway of the waist could be reduced. However, the foot of our humanoid robot is connected to the ankle joint through the rubber bush. In this case, if we set yzt = 0.01[m], unexpected bend of the rubber is introduced and the swing leg touches the ground earlier than expected. Thus, in simulation and experiment shown in the next section, we set yzt = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001947_j.ijmecsci.2007.08.002-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001947_j.ijmecsci.2007.08.002-Figure2-1.png",
        "caption": "Fig. 2. Finite-element model of the shafts and the gear pair.",
        "texts": [
            " The beam section is constant in oz direction. These elements take into account the effects of torsion, bending and tensioncompression [12]. The generalized displacement of the jth node is given by fqjg T \u00bc fuj ; nj ;wj ;jj ;cj ; yjg, (6) ARTICLE IN PRESS M. Slim Abbes et al. / International Journal of Mechanical Sciences 50 (2008) 569\u2013577 571 where \u00f0uj ;cj\u00de and \u00f0vj ;jj\u00de are, respectively, the beam bending in the (x,y) plane and in the (y,z) plane, wj and yj are, respectively, the dof associated with the axial and torsional deformations (Fig. 2). The process of discretization of the shafts and gears leads to the following movement matrix equation: \u00bdMr f \u20acW rg \u00fe \u00bdK r\u00f0t\u00de fW rg \u00bc Ff g, (7) where [Kr(t)], [Mr] and {Wr} are, respectively, the stiffness matrix, the mass matrix and the nodal displacement vector of the transmission (shafts and gear pair). {F} represents the external forces applied to the shafts. It is assumed that the deformation and kinetic energies of the isotropic rectangular plate of thickness h and mass density r are, respectively, given by the classical equations: EU \u00bc 1 2 D Z S q2W q2x 2 \u00fe q2W q2y 2 \u00fe 2n q2W q2x q2W q2y \u00fe 2\u00f01 n\u00de q2W qxqy 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-5-1.png",
        "caption": "FIGURE 12-5 Internal-gear pump.",
        "texts": [
            " When hydraulic cylinders are arranged axially, as shown in figure 12-2, the rate of flow through the pump can be regulated by con trolling the angle between the piston block and the swash plate, a common method of control on a hydrostatic transmission. Radial piston pumps (fig. 12-3) can also be used as motors. The displace ment of a radial piston pump can be controlled by allowing the pressure to lift the pistons off the eccentric. By this method the pump unloads and does not do any work except when the pressure drops sufficiently to force the pistons back onto the eccentric. A spur-gear pump is shown in figure 12-4. It is normally used on tractor hydraulic systems of lower pressure. The spur-gear, the internal-gear pump (fig. 12-5), the gerotor-gear pump (fig. 12-6), and the vane-type pump (fig. 12-7) are all used on tractor hydraulic systems where lower pressures are used. Motor Performance* Because efficiencies are often high, very accurate instrumentation is required if the motor is externally loaded because a small error in measurement of *This section also applies to pumps. Equations I and 2 should be inverted when used for pumps. 316 MOTOR PERFORMANCE 317 input or output power may be larger than the losses involved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure3.5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure3.5-1.png",
        "caption": "Fig. 3.5. Definition of aerodynamic coefficients, SU -frame",
        "texts": [
            " In [10], data for mass and inertia depending on the amount of fuel are tabulated for three levels of fuel; 100%, 60% and 30%. In ADMIRE the mass and inertia are constant but could be modelled as functions of fuel consumption which is part of the engine model. The mass and inertia are chosen for a nominal case with a mass representing 60% of fuel loaded. The calculations of the resulting forces and moments with effects from gravity and aerodynamics transformation are done in different frames. The relative distance between the aerodynamic reference point, defined in the aerodynamic frame SU , (see figure 3.5) and the centre of gravity (c.g.), defined in the the body fixed frame, SB, (see figure 3.4) are used to transfer the moments and forces from one frame to another. The FCS is scheduled in altitude and Mach number and designed for the nominal model described in Table 3.1. A change in the centre of gravity will change the control performance. The flight envelope for the GAM-data extends to Mach 2.5 and an altitude of 20 km. The envelope for the engine model is valid up to Mach 2. With the bundled FCS the ADMIRE flight envelope is restricted to Mach numbers less than 1",
            " These limitations will be removed in future versions. The equations are described in more detail in [219]. The aircraft aerodata modelling consists of aerodata tables, interpolation routines and aerodata algorithms. This is a standard way of performing aerodynamic modelling. In these aerodata tables an interpolation is made and the six resulting aerodynamic coefficients, (CT , CN , CC, Cl , Cm, Cn), are calculated. These coefficients are calculated with respect to a reference point as depicted in figure 3.5. The aerodynamic reference point coincides with the nominal c.g. of the aircraft. The figures 3.4 and 3.5 are reproduced with the kind permission of Saab AB. ADMIRE is implemented in the MATLAB/SIMULINK environment as S-functions based on C-code. As mentioned earlier the original aerodata model, GAM, is valid for Mach numbers up to 2.5, altitudes up to 20 km, angles of attack up to 30\u25e6 and sideslip angles up to 20\u25e6.The model has been extended on two occasions. First the envelope was extended for angles of attack up to 90\u25e6 at Mach numbers less than 0",
            " There is no real effect of separation modelled. For instance, the aircraft is assumed to suffer from yaw instabilities at high \u03b1, when the airflow around the fin is strongly turbulent and disturbed. Further, the control efficiency of the surfaces is assumed to deteriorate. 42 M. Hagstro\u0308m However large the flight envelope of GAM, ADMIRE\u2019s is smaller since it is constrained by the bundled FCS. It is scheduled for altitudes up to 6 km and Mach numbers up to 1.2. With a different FCS the data is valid up to 20 km and Mach 2.0. In Figure 3.5, the definition of the direction of the forces and moments from the aerodata is shown. The aerodynamic forces are given in the form of body fixed normal, tangential and side forces. The aerodynamic reference point (OU ) and the centre of gravity (OB) are given in Figure 3.6. The reference point is fixed but the location of the c.g. can change. In the nominal case these two points coincide. Deviation in c.g. from the aerodynamic reference point will give additional effects in the moment equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002783_j.compstruct.2011.04.011-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002783_j.compstruct.2011.04.011-Figure9-1.png",
        "caption": "Fig. 9. The numerically generated folded core.",
        "texts": [
            " The resulting stress or strain states were ignored, which constitutes a simple model of the curing of the core. This section presents two main results. The first result is a comparison between the numerically generated defects and the observed defects. The second result is a comparison between the numerical and experimental results for an out-of-plane compression test. Following the strategy described previously, an imperfect CELPACT Pattern 31 folded core [28] (density 113 kg/m3) was gener- for the folding simulation. ated. Fig. 9 shows the resulting geometry. Only the inner row of cells (the dark gray row of cells in Fig. 8) was taken into account for the defects. One can first note that the configuration of the top edges is very similar to the top view of a core of Fig. 5. Buckling of the cell walls at the free edges and similar deviations from the nominal pattern can be observed. A core sample was also scanned at IFB Stuttgart using a laser probe, which enabled us to compare the out-of-straightness defect of the folded edges generated by our numerical process with the core\u2019s scan"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003792_icuas.2017.7991321-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003792_icuas.2017.7991321-Figure2-1.png",
        "caption": "Fig. 2. Side view for a standard hexacopter motor distribution, with tilted motors",
        "texts": [
            " In this work we assume that failures are identically likely to appear in any motor, then this configuration can not be considered fault tolerant. To overcome the lack of fault tolerance of the standard hexagon shaped hexarotor, in [6], instead of the standard design with rotors pointing in the vertical direction, an alternative is proposed, which turns out to be completely controllable even in case of failure in one rotor. It is shown that by tilting the rotors with respect to the horizontal plane that contains the motors, towards the vehicle\u2019s vertical axis (see Fig. 2), fault tolerant control can be achieved without losing control neither in attitude nor in altitude, even with a faulty motor. An aspect that must be pointed out about this design, is that tilting the motors (the multi-rotor\u2019s arms) is an already established practice, as it allows for a more stable vehicle given it lowers the center of mass. With the addition of a retractable landing skid, this also provides a clearer line of sight for camera-type payloads placed under the vehicle. There is plenty of research on actuators and sensors failure detection",
            " In practice, each motor is commanded through a Pulse Width Modulated (PWM) signal u i , which goes from 0 to 100%. Near the nominal operating point, a linear relation between the PWM percentage and the exerted force is assumed, with f i = k f u i . It is also considered that each motor exerts a torque on its spinning axis, m i = ( 1)ik t u i . The k f and k t , constants are usually established experimentally. The constant \u02dck t := k t k f is defined as it will used in what follows, for the sake of clarity. As it was mentioned above, by tilting the rotors an angle (as seen in Fig. 2), fault tolerant control can be achieved without losing control neither in attitude nor in the vertical direction (thrust), even with a faulty motor. Here we assume that the hexarotor has this fault tolerant configuration (see Fig. 2). We will define l as the length of the arm measured from the center of the vehicle to the motor axis along the arm, i.e. l = kd i k2, with i = 1, ..., 6. The angle will be the tilting angle of the motor, measured as depicted in Fig. 2. To simplify the notation, a parameter \u21b5 is defined in the following way: \u21b5 = \u21b5( ) = \u02dck tp 3 l tan( ) (1) In [6, Theorem 3], it was shown that this parameter should be chosen such that 0 < |\u21b5| < 1 so that fault tolerance can be achieved. In what follows, it is assumed that \u21b5 satisfies this condition. Let M x , M y and M z , be the control torques exerted by the motors on the vehicle. Also let F z be the resultant force exerted by the motors along the vehicle\u2019s z axis. When all motors are working properly, the relation between the (M x ,M y ,M z , F z ) 4-tuple, and the f forces vector is given by the following equation: 2 664 M x M y M z F z 3 775 = A( ,\u21b5) \u00b7 f, with f = 2 64 f1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure10-1.png",
        "caption": "Figure 10. The basic 4P linkage that has M= I .",
        "texts": [
            " Thus the chain can be closed by a fourth P-pair, PAt, directed in any fourth randomly chosen direction. A 4P single loop spatial linkage therefore has M = 1, corresponding to b = 3 in equation (1); single loops with 5, 6 and 7 prismatic pairs will have M equal to 2, 3 and 4 respectively. The rules relating numbers of joints and numbers of members in multiple-loop M = I spatial P-pair linkages comply exactly with those for planar linkages as described, for instance, by Davies and Crossley [9]. A single-loop 4P linkage is shown in Fig. 10. 5.2. Some other ways of closing a single M = 1 loop containing three P-pairs are given in Table 3(e). If, however, the loop were closed to form a 3P-1S-1G (or 3P-1R-1G) linkage (taking the pairs in any order), the mobility would still be I, but two of the three rotational freedoms possessed by the spherical joint (G-pair) would be inactive, the relative movement in the G-pair always being a rotation about an axis parallel to the S-pair (Fig. 11). In general, however, a 3P-..4S (or 3P--4R) linkage (taking the pairs in any order) will have a mobility of 1 provided that the axes of all the S-pairs, and of course of the P-pairs, are randomly orientated; it is only when there are as many as four randomly orientated S-pairs (or R-pairs) that the vector sum of four relative angular velocities about their four axes can always (uniquely) be made equal to zero, and this is a necessary condition for M = 1 in this context, as would indeed be expected from equation (1) taking b =6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001107_1.1564064-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001107_1.1564064-Figure7-1.png",
        "caption": "Fig. 7 Quasi-static multi-tooth contact analysis results of \u201ea\u2026 load sharing characteristic within one mesh cycle at 509 Nm pinion input torque; and \u201eb\u2026 load distributions for two different mesh positions",
        "texts": [
            " On the other hand, the natural frequencies of modes 7 and 9 with stronger gear mesh dependency vary slightly more with load due to change in effective mesh position and line-ofaction. 4.3 Nonlinear Time-Varying \u201eNLTV\u2026. The time-varying behavior of the hypoid gear pair is determined by the mesh characteristic vectors lu (l) and nu (l) related to the normal force, and tu (l) and nu (l) associated with the friction force. The variations in these mesh characteristic vectors partly caused by the change in the number of tooth pairs in mesh as the gears rotate through one mesh cycle are greater for lighter torque and consequently lower for higher torque as shown in Fig. 6. Figure 7 shows the number of tooth pairs in contact varying periodically between 1 and 2. Note that the equivalent normal and friction force vectors vary more rapidly in the vicinity of the angular positions where the number of tooth pairs in contact changes. For the present hypoid rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/20 gear example, the largest degree of variations occurs around 2100 and 80 of pinion roll angles shown in Fig. 7. It is this time-varying mesh characteristic that makes hypoid gear engagement unique, since it affects the instantaneous dynamic forces and moments acting on the pinion and gear. To understand the implications on the hypoid geared rotor system, the nonlinear time-varying ~NLTV! model given by Eq. ~8! is studied numerically as described earlier by applying the 5/6th order Runge-Kutta integration routine. In the analysis, the mesh force and bearing forces under steady state condition are predicted and compared to calculations for the time-invariant mesh cases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003722_tpel.2015.2506640-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003722_tpel.2015.2506640-Figure1-1.png",
        "caption": "Fig. 1 shows a cross-sectional view of a six-pole nine-slot IPMSM with concentric windings. Here, a1, a2, a3, b1, b2, b3, c1, c2, and c3 are the winding numbers of each phase. Fig. 2 shows the winding configuration of (a) series and (b) parallel connections. ia , ib , and ic denote the phase currents; and va , vb , and vc denote the voltages of the a-, b-, and c-phase windings, respectively. Because an insulation failure does not provide a zero resistance path [1], [2], the fault location can be described as a fault resistance Rf with an ITF current if . In this study, the a-phase a1 winding is assumed to have an ITF. The ITF windings shown in Fig. 2 have another fault circuit loop composed of the fault resistance Rf , a fault winding inductance, and a fault winding flux linkage.",
        "texts": [],
        "surrounding_texts": [
            "Index Terms\u2014Fault parameter estimation, inter-turn fault (ITF), motor fault detection, motor fault-tolerant control.\nI. INTRODUCTION\nMOTOR fault detection is a primary issue because faults can lead to reduced safety and increased repair time costs [1], [2]. As stated in part I, the most common motor fault is a winding interturn fault (ITF) due to coil insulation failure. The detection of stator ITFs in different types of electric machines, such as on induction motors [3]\u2013[13], brushless DC motors [14]\u2013[16], claw-pole generators [17], and synchronous motors [18]\u2013[23] has been performed in many studies.\nDetection methods can be categorized into three types, based on the selected fault signatures.\n1) Unbalanced signals resulting from unbalanced impedance and backelectromotive force (EMF): An ITF causes an unbalanced motor impedance and back-EMF that eventually induce unbalanced motor currents and voltages. In many previous studies, the unbalanced impedance, back-EMF, current, and voltage of motors have been the most commonly used fault detection signals.\nManuscript received May 24, 2015; revised August 9, 2015 and September 30, 2015; accepted November 23, 2015. Date of publication December 17, 2015; date of current version May 20, 2016. This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (2015R1C1A1A01052647). Recommended for publication by Associate Editor F. H. Khan.\nThe author is with the School of Energy Engineering, Kyungpook National University, Daegu 702-701, Korea (e-mail: bggu@knu.ac.kr).\nColor versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.\nDigital Object Identifier 10.1109/TPEL.2015.2506640\na) Unbalanced current [4]\u2013[6] [10], [13], [17], [19], [21]. The unbalanced current is a useful signal for ITF detection because it is easy to calculate from the phase current. In a conventional ITF detection scheme, the unbalanced current is calculated after the phase current has been sensed. Then, the ITF decision rule is used to compare the unbalanced current with the predefined fault limit value from a lookup table; lookup tables are created for various drive conditions using a rich pretest dataset. By monitoring the Park\u2019s vector of the motor current, the unbalanced current due to an ITF can be observed. Cardoso et al. [4] proposed an online diagnosis method that uses an ellipticity check for operating three-phase induction machines. The unbalanced current can also be observed in the abc frame in the ellipse form, which is similar to Park\u2019s vector [13]. Hadef et al. [21] used the direct torque control approach to apply a pattern recognition technique based on image composition to interior permanent magnet synchronous motors (IPMSMs). The unbalanced current can be observed in the form of a negative-sequence current or second harmonic current in the positive synchronous reference frame (SRF). Arkan et al. [5] and Kim et al. [19] used the negative-sequence current and the second harmonic current as the main signals for fault diagnosis. Briz et al. [6] utilized the negative-sequence current resulting from high-frequency carrier-signal injection to detect ITFs. The unbalanced current can be observed in the third current harmonic at the dc-link side. This method has also been utilized for fault detection in claw-pole generators [17]. b) Negative-sequence/transfer impedance or unbalanced back-EMF [7], [8], [11], [12], [16], [23]. The fault detection methods proposed in [7], [8], and [11] can be explained in terms of the negativesequence impedance and transfer impedance by including the effects of nonidealities. The estimated impedance is utilized as a fault detection signal. Tallam et al. [7] proposed a neural-network (NN)-based detection scheme to reduce the amounts of data memory usage and computation. Ostojic et al. [12] utilized the normalized cross-coupled impedance (ratio of cross-coupled impedance and positivesequence impedance) as the key signal for fault detection. Park et al. [16] used the phase impedance of\n0885-8993 \u00a9 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.",
            "brushless DC motors as the key signal for ITF detection. Sarikhani and Mohammed [23] compared the normalized back-EMF difference between values estimated in real time and reference values from finite element analysis for fault detection. c) Line-neutral voltages [3], [10], [14]. Cash et al. [3] and Awadallah et al. [14] used the sum of the three instantaneous line-neutral voltages to detect an ITF. Yun et al. [10] proposed an online monitoring technique for detecting and classifying ITFs and high-resistance connections in an induction motor, based on the neutral point voltage and negative-sequence current measurements.\n2) High-order harmonic current [18], [20]: Neti and Nandi [18] and Ebrahimi and Faiz [20] introduced frequency patterns for a synchronous motor with field windings and a permanent magnet synchronous motor (PMSM) with ITFs. Frequency pattern analysis is commonly used for the grid-connected induction motor ITF detection. However, for inverter-driven motors, the high frequency of the inverter PWM voltage interferes with the fault detection frequency. Therefore, frequency pattern analysis is not commonly used for inverter-driven motors. 3) Induced voltage in additional coil [15]: Kim et al. [15] proposed a detection coil for sensing the flux variation caused by the ITF. This method is simple, but it requires an additional detection coil installed within the motor.\nThe detection tools of previous works can generally be classified into lookup table schemes and NN-based schemes [9], [22]. Because the lookup-table-based detection schemes are easy to implement, they have been utilized in many studies. However, they require a fault threshold level table to be built based on rich pretest data because of the absence of accurate IPMSM models that include ITFs. To overcome this disadvantage, NNbased schemes have been proposed. NN-based schemes do not need any tables, but they do require a training phase. If an accurate ITF model of an IPMSM is derived, the pretest to define the threshold level or training phase for the NN will be much simpler. Hence, to implement an ITF detection method for a specific motor, an adequate IPMSM model including ITFs must be derived.\nThis paper proposes an online ITF parameter estimation method for IPMSMs using the ITF models proposed in part I. Because the ITF fault decision rule should be based on the threshold limit set for the fault parameter based on the motor heat radiation structure and operation environment, we focus on the fault parameter estimation method. First, it is proven that the two ITF parameters, namely, the healthy turn ratio and the fault contact resistance, cannot be separately estimated based on drive information because they have multiple solutions. Nevertheless, these multiple solutions theoretically have the same ITF Ohmic power loss, which is the key index used to define the additional internal heat generation and fault severity for the motor. Both parameters do not need to be estimated to obtain the Ohmic power loss. Thus, the proposed method estimates only one fault parameter by allowing the other to be set arbitrarily. Here, we\nset the fault resistance to zero in the simpler model, and the healthy turn ratio will be an estimation parameter. The estimation method implements a searching algorithm that finds one fault parameter that satisfies the minimum negative-sequence voltage difference between the drive voltage information and the ITF model. An experiment was performed to verify the proposed fault parameter estimation method.\nII. ITF ANALYSIS OF ONE WINDING",
            "proposed in part I are derived under the assumption of a balanced three-phase current, all of the unbalanced phase impedances and phase back-EMFs affect only the motor voltage, which is modeled by the negative-sequence voltage equations in the negative SRF. The assumed balanced three-phase currents are expressed as\nia = \u2212Iq sin \u03b8 + Id cos \u03b8 (1) ib = \u2212Iq sin ( \u03b8 \u2212 2\u03c0\n3\n) + Id cos ( \u03b8 \u2212 2\u03c0\n3\n) (2)\nic = \u2212Iq sin ( \u03b8 + 2\u03c0\n3\n) + Id cos ( \u03b8 + 2\u03c0\n3\n) (3)\nwhere \u03b8 denotes the electrical rotor angle, and Id and Iq are the dq-axis currents in the SRF. The negative-sequence voltage equations of IPMSMs employing series and parallel winding connections were derived in part I and are presented here: (4), (5) shown at bottom of the page. Rsij , ksij , Rpij , and kpij are defined with motor and fault parameters in part I. Here, i, j = 1, 2, 3, 4. The healthy turn ratio is x. The fault resistance is Rf . \u03c9(= d\u03b8/dt) and \u03c8m denote the electrical angular velocity and back-EMF constant, respectively. \u03b1s1,2 , \u03b2p1,2 , and \u03b1p1,2 represent the sine and cosine magnitudes of the fault current if for both the series and parallel winding IPMSMs and the a1 winding current ip1 of the parallel winding IPMSM. if and ip1 can be expressed as follows:\nif = \u03b1s1 sin \u03b8 + \u03b1s2 cos \u03b8 : series winding IPMSM (6)\nip1 = \u03b1p1 sin \u03b8 + \u03b1p2 cos \u03b8 if = \u03b2p1 sin \u03b8 + \u03b2p2 cos \u03b8\n} : parallel winding IPMSM.\n(7)\nThe healthy turn ratio of a1 is defined as x = Nhealthy/N , where Nhealthy and N denote the a1 winding\u2019s healthy turn number and total turn number, respectively.\nThe ITF is resolved into two fault parameters: the healthy turn ratio x and the fault resistance Rf . Because these two parameters define the fault severity, they should be estimated for better fault detection accuracy and the creation of a more fault-tolerant drive.\nFig. 3 shows the negative-sequence voltage plots of (a) series and (b) parallel winding IPMSMs with (4) and (5) when the ITF exists in the a-, b-, or c-phase windings. The negative-sequence voltages for a-, b-, and c-phase winding faults have phase differences of 2\u03c0/3 relative to each other. Table I presents the motor parameters, which are the same as those of the motors described in part I. L1 , L2 , and \u03b3 were obtained from FEM simulations [2]. As shown in Fig. 3, for a given motor speed and phase current, the absolute value of the negative-sequence voltage increases along a curve as x increases or Rf decreases. In other words, for a given point on the negative-sequence voltage plot, there are multiple solutions x and Rf that satisfy both (4) and (5). Thus, the two fault parameters x and Rf cannot be individually calculated or estimated using the model proposed in part I; however, an equation relating them can be obtained. In this section, we develop unbalanced voltage equations for a single winding with an ITF to show that the two fault parameters x and Rf cannot be individually estimated based on the unbalanced voltage. Then, we present the equation relating x and Rf and derive the additional Ohmic power loss.\nFig. 4 shows an a1 winding with an ITF and its equivalent circuit, where va1 , ia1 , and \u039ba1 denote the a1-winding voltage, a1-winding current, and total cross-flux linkage of both the other windings and the rotor flux in the complex domain, respectively. Ra1 and La1 denote the a1 winding resistance and inductance, respectively. The faulty windings and the remaining healthy windings have turn numbers of N(1 \u2212 x) and Nx, respectively. Because of the ITF\u2019s resistance Rf , the faulty and healthy windings have different current magnitudes and phases. Because the two windings are placed in the same\n[ V \u2212\nde V \u2212 qe\n] =\n1 3 \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 ( (Rs11 \u2212 Rs22)Id + Rs14\u03b1s2 + \u03c9L1(ks14 \u2212 ks24)\u03b1s1 + \u03c9L1(\u2212ks11 + 2ks12 + ks22 \u2212 2ks23)Iq ) ( \u2212 (Rs11 + 2Rs22)Iq + Rs14\u03b1s1 \u2212 \u03c9L1(ks14 \u2212 ks24)\u03b1s2\n+ \u03c9L1(\u2212ks11 + 2ks12 + ks22 \u2212 2ks23)Id + 2 P (1 \u2212 x)\u03c9\u03c8m\n) \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6\n+ \u03c9L2\n6\n[ (\u2212 ks11 + 2ks12 + ks22 \u2212 2ks23)Iq + (ks14 + 2ks24)\u03b1s1\n(ks11 \u2212 2ks21 \u2212 ks22 + 2ks23)Id + (ks14 + 4ks24)\u03b1s2\n] (4)\n[ V \u2212\nde V \u2212 qe\n] =\n1 3 \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 ( (Rp22 \u2212 Rp33)Id + \u03c9L1(\u2212kp22 + 2kp23 \u2212 2kp34 + kp33)Iq + \u03c9L1(kp21 \u2212 kp22 \u2212 kp31 + kp32)\u03b1p1 \u2212 Rp22\u03b1p2 + \u03c9L1(kp25 \u2212 kp35)\u03b2p1 ) ( (\u2212 Rp22 + Rp33)Iq + \u03c9L1(\u2212kp22 + 2kp23 + kp33 \u2212 kp 3 4 2 )Id\n+ \u03c9L1(\u2212kp21 + kp22 + kp31 \u2212 kp32)\u03b1p2 \u2212 Rp22\u03b1p1 + \u03c9L1(\u2212kp25 + kp35)\u03b2p2\n) \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6\n+ \u03c9L2\n6\n[ (kp21 \u2212 kp22 + 2kp31 \u2212 2kp32)\u03b1p1 \u2212 (kp22 + 2kp32)Iq + (2kp35 + kp25)\u03b2p1\n(kp21 \u2212 kp22 + 2kp31 \u2212 2kp32)\u03b1p2 + (kp22 + 2kp32)Id + (2kp35 + kp25)\u03b2p2\n] (5)"
        ]
    },
    {
        "image_filename": "designv10_10_0000916_s0003-2670(99)00308-6-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000916_s0003-2670(99)00308-6-Figure1-1.png",
        "caption": "Fig. 1. Schematic drawing and cross-section view of the thick-film electrode (A) and the creatinine sensor (B): (1) working electrode; (2) reference electrode; (3) epoxy film; (4) glass film; (5) immobilized enzymes; (6) adhesive; arrows indicate the flow direction.",
        "texts": [
            " The polymeric solution was \u00aerst prepared by dissolving polyvinylbutyral and polyvinylchloride in cyclohexanon at the mass ratio of 1 (PVB):2 (PVC):45 (cyclohexanon) and then 0.32 mg of Pt\u00b1CB was added per mg of polymeric solution and thoroughly mixed. Thick-\u00aelm carbon electrodes were fabricated on an epoxy \u00aelm using the conventional metal mask printing process. Conventional metal masks (140 mm 180 mm, 200 mm thick) and a polyurethane squeegee were used for constructed planar arrays of six electrodes. Finally, we constructed an electrode format as shown in Fig. 1. Electrodes of this type were printed as follows; each electrode was constructed in a two-electrode con\u00aeguration, consisting of working and Ag/AgCl pseudoreference electrodes. The printing paste for the working electrode was applied to an epoxy \u00aelm. The reference electrodes were then printed parallel to the working electrodes using the silver ink and an Ag/AgCl pseudo-reference electrode ink was applied to the end of remaining silver path. The layers were dried at 608C for 1 h at the end of each printing step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001183_robot.1995.525354-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001183_robot.1995.525354-Figure2-1.png",
        "caption": "Figure 2: Geometric properties of leg i and MP",
        "texts": [
            " 1 is a parallel manipulator composed of three legs OiOi+30i+~, for i = 1 , 2 , 3 , a rigid moving triangular platform 0 7 0 8 0 9 , henceforth abbreviated as MP, and a fixed platform 0 1 0 2 0 3 , assumed rigid as well. Each leg contains two flexible links that are coupled by a revolute joint. The legs are connected to the MP by spherical joints and coupled to the base by revolute joints. This manipulator has three rigid DOF and three motors, located on the fixed platform, that drive the actuated joints. 2 Modeling of an Individual Link Figure 2 shows the manipulator of Fig. 1 with its legs in their deformed configuration, leg i consisting 627 - of the flexible links i and i + 3. Before modeling the dynamics of link i , some definitions are given. The n: (= 7 + ni)-dimensional vector of generalized coordinates of link i is defined as and the mi(= 6 + ni)-dimensional vector of flexzble twist of the same link is vi = [ wT i-T liT(t) 1\u2019 (2) where, with reference to Fig. 3 , & is the 4-dimensional vector of Euler parameters representing the orientation of the frame X i x Z i ( F ; ) with origin at O;, attached to link i , r; is the position vector of joint Oi in the inertial frame XoYoZO (Fo), and u;(t) is the n;dimensional vector of independent nodal coordinates associated with the link flexibility of link i , ni denoting the number of nodal coordinates of the same link",
            " 3 Modeling of the Manipulator The twist-constraint equations of the holonomic system at hand can be expressed as AV = 0, (20) where v is the m'(= mi + 6)-dimensional vector of generalized flexible twist, which is composed of the vectors of flexible twist of all moving links plus the twist of the MP, namely, with r defined as the number of all moving links in the system, i.e., six, and wc and c denoting the angular velocity of the M P and the position vector of point C , the center of mass of the MP, with respect to the inertial frame, respectively, as depicted in Fig. 2, that can be obtained as explained in [5]. Matrix A is the p x m' twist-constraint matrix, and 0, is the p-dimensional zero vector, with p defined as the number of twist-constraint equations. Moreover, w ; and i-i can be expressed, in light of eq.(lO), as where i = 1 ,2 ,3 and ai is the vector shown in Fig. 2, while zj is the unit vector parallel to the joint axis Z j , depicted in Fig. 4. Here, U k =: U k ( t ) is as defined in eq.(l), and L k is the shape function matrix evaluated at point Ok+3 in link k . Moreover, w;,;+3 is the angular velocity of Fi+3 with respect to Fi, resulting from the elastic deformation of link i , that can be written for small displacements as - 629 - with IjaOiII being the Euclidean norm of the position vector of point Oi+3, depicted in Fig. 2 , in the undeformed configuration of link i, ( . ) j being the j t h component of vector (.I, while L; and ui are defined in eqs. (22). Vector v can be expressed as a linear transformation of ti , which is defined for a q-degree-of-freedom system as a q-dimensional vector of independent generalized speeds, rmmely, v = Nt; (24) and N is an m\u2019 x q matrix. Upon substitution of v from eq.(24) into eq.(20), we obtain ANti = 0, (25) Since all the components of ti are independent, the above equation holds if and only if AN = 0,, (26) where 0,, is the p x q zero matrix",
            " They are obtained by equating to zero the time-derivatives of the magnitudes of vectors a78, a 7 9 and a 8 9 , which are nothing but the lengths of the sides of the rigid triangle 0 7 0 8 0 9 , i.e., a&&78 = o aT92 i79 = o i28b) a&&89 = o (28c) Here, a 7 8 , a 7 9 and a89 are obtained by writing three loop equations, using Fig. 4, namely, 01 + a1 + a4 + a78 - a5 - a 2 - 0 2 = 0 2 (29a) 01 + a1 + a4 + a 7 9 - a6 - a3 - 03 = 0 2 (29b) 02 + a2 + a5 + a 8 9 - a 6 - a3 - 03 = 0 2 (29c) where oi is the position vector of the origin Oi, as depicted in Fig. 2. Therefore, upon eliminating the dependent joint rates, v can be expressed as a linear transformation o f t ; , which leads to N. Upon assembling of the dynamics models of all links together, we obtain the dynamics model of the overall manipulator as Mi. = bs + bE + bo + b K + b~ (30) where M is the m\u2019 x m\u2019 generalized extended mass matrix of the system, given by M = d i a g ( MI Ma . . . M6 Me ) (31) Here, Mi is the ma x m.: mass matrix of link i and Me is the 6 x 6 mass matrix of the MP, while bs, bE, bD, b K and b G are mi-dimensional vectors which result from a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001288_j.optlastec.2004.04.009-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001288_j.optlastec.2004.04.009-Figure3-1.png",
        "caption": "Fig. 3. Schematic of coaxial nozzle.",
        "texts": [
            " The focus length of the lens in the working head of the laser processing tool is 127 mm \u00f05 in\u00de: The minimum diameter of focused laser beam is about 0:1 mm: The metal powder delivery system consisted of a screw feeder, a powder splitter, soft tubes and a coaxial nozzle. The powder feed rate was decided by the feed screw rate. The powder was carried through the soft tubes by N2 gas flow and then divided into four flows by the powder splitter. After being focused by the coaxial nozzle, the four gas-powder flows touched on the substrate or the clad layer. The coaxial nozzle was shown in Fig. 3. In this presented experiment, the flow rates of shield gas and carriage gas were constant, and the distance from the tip of the nozzle to the substrate was prearranged as a constant at the beginning of laser cladding. The shield gas was N2; too. The carriage gas flow rate and the shield gas flow rate are 0:5 m3=h and 500 l=h; respectively. Therefore, the radius of the powder flow stream was regarded as a constant. The substrate material and clad material utilized in the experiments were Steel 20 (at 0:20 wt% C) and Steel 24 (at 0:24 wt% C)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002065_s0022-0728(81)80314-2-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002065_s0022-0728(81)80314-2-Figure1-1.png",
        "caption": "Fig. 1 . E q u i l i b r i u m cyc l i c v o l t a m m o g r a m s fo r IrCl~ - /2 - a n d Fe(CN)~ - /4 - p a r t i t i o n e d i n t o p o l y c a t i o n i c M P S - V P y H \u00f7 f i lms f r o m p H 2.8, 2 M LiC1 s o l u t i o n s o f I r C l ~ - a n d Fe(CN)~--. Curves A - - E : 0 .15 X 10 -~, 0 . 3 2 \u00d7 1 0 4 , 0 .71 X 10 -s, 1 .05 X 1 0 4 a n d 2.3 X 10 -8 m o l c m - : o f I rCl~- /3- ; S = 16 u A c m - : , 5 m V s ~ . Curves F - - I : 0 .61 x 10 -s, 1 .3 x 10 -~, 2.2 x 10 4 a n d 3.6 \u00d7 10 -~ c m ~ o f Fe (CN)~- /4 - ; S = 32 u A c m -2 . 10 m V s -1 .",
        "texts": [
            "8) 2 M LiC1, from which they scavenge IrCl~- and Fe(CN)~- with partition coefficients of ca. 700 and 850 [22], respectively, when the electrode potential is cyclically swept through the IrCl~-/3 - and Fe(CN)~ -/4 - waves for an equilibrating period. Coverage, CIr and F F e , and concentration, CIr and CFe (/mol cm -3 ), of the redox ions can be 0022-0728/81/0000--0000/$02.50, \u00a9 1981, Elsevier Sequoia S.A. systematically increased in a given film by incrementally increasing the concentrations of IrCl~- or Fe(CN)~- in the scavenging bath, as illustrated by the cyclic voltammograms in Fig. 1 [22] . At each coverage level, transferring the electrode to redox ion-free electrolyte and measuring the charge required in a potential step experiment to quantitatively oxidize or reduce the IrCl~- or Fe(CN)~-, respectively, gives coverage values agreeing (+ 5%) with those measured at slow potential scan rates from voltammograms like Fig. 1. Potential step chronoamperometric Dctl/~c measurements were made by our established technique [4] at each level of Clr or CFe in the film. Measurements were made in duplicate or triplicate (precision <_+ 5%), by exposing the electrode again to the scavenging bath, before incrementing to the next level of concentration. Linear Cottrell behavior was observed as shown in Fig. 2. For IrCl~-,the (oxidative) potential step was +0.5 to +1.02 V vs. SCE, and F i r w a s varied from 7.8 X 10 -1\u00b0 to 7.2 X 10 -s mol cm -2 or CIr = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003585_b978-0-12-803766-9.00007-5-Figure5.1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003585_b978-0-12-803766-9.00007-5-Figure5.1-1.png",
        "caption": "FIGURE 5.1 A schematic diagram of a one degree-of-freedom, cable-driven, robotic legged locomotion system with a series elastic actuator. This diagram uses an ankle device as an example. \u03b8m and \u03b8p are motor position and pulley position after gearing, respectively. \u03b8e is the device joint angle. R is the effective aspect ratio between motor output pulley radius rp and device joint velocity lever arm ra defined as R = ra rp .",
        "texts": [
            " A single exoskeleton system was used, experimentally controlling for hardware capabilities. Tests were conducted while a human wore the exoskeleton and walked on a treadmill, making results relevant to conditions with complex interactions between the robot, a human user, and the environment. We anticipate these results to help guide the selection and tuning of torque control elements in various robotic legged locomotion systems. A diagram of a typical one degree-of-freedom lower-limb robot driven by a series elastic actuator through a cable with a geared motor is shown in Fig. 5.1. Based on this structure, we used the following simplified models of system components to aid in our understanding of the system, make reasonable choices for model-free control elements, and design model-based control elements. \u2022 Motor Dynamics Assuming armature inductance dynamics occur at a substantially higher frequency than rotor dynamics, and therefore have negligible effects, the dynamics of the motor can be written as\u23a7\u23a8 \u23a9 Ka \u00b7 ia(t) = Ie \u00b7 N \u00b7 \u03b8\u0308p(t) + fe \u00b7 N \u00b7 \u03b8\u0307p(t) + 1 N \u00b7 \u03c4o(t), Va(t) = Ra \u00b7 ia(t) + Kb \u00b7 N \u00b7 \u03b8\u0307p(t), (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001682_cdc.2006.377137-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001682_cdc.2006.377137-Figure3-1.png",
        "caption": "Fig. 3. 3D Hover Quanser System",
        "texts": [
            " In Figures 1-2 the solid line represents the proposed controller (23), the dotted line is for the PD-controller (24) and the dashed line is for the saturated PD-controller in (25). In this section, the experimental results when the proposed controller is applied to a 3D Quanser helicopter and a 3D free quad-rotor helicopter are reported. A. 3D Quanser helicopter The 3D Hover system consists of a frame with four propellers mounted on a 3-DOF pivot joint such that the body can freely roll, pitch and yaw, (see Figure 3). The propellers generate a lift force that can be used to control the pitch and roll angles. The total torque generated by the propeller motors causes a yaw to the body as well. Two propellers in the system are counter-rotating propellers such that the total torque in the system is balanced when the thrusts of the four propellers are approximately equal. The platform used in these experiments is built by [11]. Three DC motors are mounted at the vertices of a planar round frame and drive four propellers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000967_20.877808-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000967_20.877808-Figure8-1.png",
        "caption": "Fig. 8. Position of permanent magnet and teeth.",
        "texts": [
            " In the conventional method, there are flat elements in order to insulate the slit in the permanent magnet. However, using the double nodes technique, there is no flat element for the slit. Fig. 4 shows the rotation angle-eddy current density characteristics. Fig. 5 shows the position of the element of the permanent magnet. It is found that the eddy current of these motors has the cycle of 30 degrees. Figs. 6 and 7 show the distributions of eddy current density vectors in the permanent magnet. Fig. 8 shows the positions of the permanent magnet and the teeth of the motor that correspond to Fig. 7. Fig. 6 shows the results of the divided model using the conventional method and that using our - method with double nodes technique. It is clarified that the results using our - method with double nodes technique agrees with the results using the method. Furthermore, it is clarified that the divided model has large advantage to decrease the eddy current in comparison with the standard model. Figs. 9 and Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002166_s11071-009-9504-1-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002166_s11071-009-9504-1-Figure5-1.png",
        "caption": "Fig. 5 Infinitesimal screws",
        "texts": [
            " Joint velocity vector, \u0307q , is an 8 \u00d7 1 vector: \u0307q = [\u03b8\u03071 \u03b8\u03072 \u03b8\u03073 \u03b8\u03074 d\u03071 d\u03072 d\u03073 d\u03074]T . (15) We define the linear and angular velocities of coordinate frame {B} to be vB and \u03c9B , respectively. Thus \u0307xB is a 6 \u00d7 1 Cartesian velocity vector: \u0307xB = [ vT B \u03c9T B ]. (16) To relate \u0307q and \u0307xB , we define Jacobian matrices: where Jx and Jq are the forward and inverse Jacobian matrices, respectively. Also, the overall Jacobian matrix J will be J = J\u22121 q Jx, (18) which relates \u0307q and \u0307xB as follows: \u0307q = J \u0307xB. (19) To determine Jx and Jq , we apply the concept of reciprocal screws. Figure 5 depicts the equivalent kinematic chain of a limb, where the universal joint is replaced by two intersecting unit screws, $\u03021 and $\u03022, and the spherical joint is replaced by three intersecting unit screws, $\u03024, $\u03025, and $\u03026. The prismatic joint in denoted by $\u03023. We now consider each limb as an open-loop chain and express the instantaneous twist of the moving platform in terms of the joint screws: $\u0302P = \u03c8\u0307i $\u03021,i + \u03b8\u0307i $\u03022,i + d\u0307i $\u03023,i + \u03c6\u03071,i $\u03024,i + \u03c6\u03072,i $\u03025,i + \u03c6\u03073,i $\u03026,i . (20) Taking the orthogonal product of both sides of (20) with reciprocal screw $\u0302r3,i = [ $\u03023,i bi \u00d7 $\u03023,i ] , one can obtain: [ l T i ( bi \u00d7 li )T ] \u0307xP = d\u0307i , for i = 1,2,3,4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001127_rob.4620120903-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001127_rob.4620120903-Figure10-1.png",
        "caption": "Figure 10. gait. Body trajectory for a discontinuous circling",
        "texts": [
            " In this section we will consider that the body trajectory consists of segments whose two end points lie on the ideal circular trajectory of radius R. Each one of these segments will be followed by the c.g. of the body at the end of every phase. These straight motions will be combined with body turnings about the z-axis to maintain the longitudinal body axis tangent to the circular trajectory. This way of describing trajectories is good enough for many applications such as those in agriculture, forestry, or nuclear inspection, where the accurate following of a trajectory is not very important. Figure 10 shows the ideal circular trajectory and the real segmented trajectory. If the coordinate frame given in Figure 10 is the body reference frame, the coordinates ( x i , yi) represent the location point of the body c.g. at the end of the current phase. This point is determined by the 608 Journal of Robotic Systems-2995 intersection of the ideal trajectory of radius, R, defined by: and the circumference of radius L, centered at the origin of the body frame and defined by: x 2 + y2 = L 2 where L is the body displacement in every phase. The simultaneous solution of both equations is: L 2 yi = g When the c.g. is placed on the point ( x , , y,), the body should rotate about an angle a. In doing that, the longitudinal axis of the body will be tangent to the circular trajectory and the previous procedure can be repeated. Referring to Figure 10, the following equations can be written: Therefore the angle rotated by the body is given by: a = 2p where angle p is given by There parameters define the motion of the machine. For discontinuous circling gaits, the same phasing leg as in discontinuous crab gaits will be considered. This circling gait should satisfy two conditions. First, leg locations have to be placed close to the position for the two-phase gait to maintain stability. Second, leg positions at the beginning and the end of one locomotion cycle have to be the same with respect to the body reference frame. The first requirement could be fulfilled by choosing L close to RJ2 , which is the displacement of the body in one phase for the discontinuous zero crab gait. To fulfil the second requirement, initial leg positions in the body reference frame (XB, Ys) must be transformed into the initial reference frame (Xl, Y,). This frame coincides with the body reference frame at the beginning of the body motion (see Fig. 10). In each phase, the body translates L = ( x i , yi) and rotates about an angle a. Hence the homogeneous transformation matrix is given by: RotTran(a, x i , y;) = (24) Legs 4 and 2 should be placed at the initial points of the gait in the body reference frame, (XM, y ~ ) and ( ~ 0 2 , y 0 2 ) , after the body has finished a locomotion cycle. Therefore, to compute these positions in the first reference frame, two homogeneous transformations must be performed. Thus, the leg positions become: p 4 = RotTran(a, x ; , y;)",
            " Stability Margin Figure 11 shows the LSM of a machine, with the same parameters as in previous examples, walking with a discontinuous circling gait. Leg 3 determines the LSM of the locomotion cycle, and the machine becomes unstable for circling radii of less than approximately 140 cm. In this circling gait, a distinction should be made between positive and negative circling, shown by the sign of the rotation vector. The phasing leg is similar for both cases, but the coordinates depend on the sign of the turning angle. For example, Figure 10 shows positive circling, and x , and y, are positive; but for negative circling, yl is negative while x, remains positive. Leg position on the right and left sides is not symmetrical; therefore the LSM depends on the circling sign. Nevertheless, the influence of the sign of the circling angle is evident in circling with a small radius, where the difference between leg positions is relatively significant. For large circling radii, the relative difference between leg position is insignificant. LSM curves are similar for both positive and negative circling with small differences for small radii"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000737_s0022-0728(97)00547-0-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000737_s0022-0728(97)00547-0-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of 1 mM NADH on various carbon paste electrodes (A\u2013C) in phosphate buffer of pH 7.3. Scan rate 20 mV s\u22121. (A) acetylene black; (B) Fluka graphite; (C) Aldrich graphite, (D) and (E) correspond to glassy carbon electrode and CCE (Bay Carbon graphite), respectively. The scan was carried out from 0 to 1 V.",
        "texts": [
            " The electrodes were moulded in capillaries of diameter 2 to 4 mm and were dried at room temperature for 3 days. 2.3.2. CCEs modified with Meldola\u2019s blue The graphite powder was impregnated with an aqueous solution of the mediator to yield 5 wt% with respect to carbon. The dried, mediator impregnated graphite powder was used instead of pure graphite and the electrodes were prepared using the same protocol as for blank CCEs. First, various carbon powders were tested for their electrochemical activity towards the oxidation of NADH. Carbon paste electrodes were used for the initial screening. Fig. 1 shows the comparative cyclic voltammograms for carbon paste electrodes made by mixing appropriate carbon powder and paraffin oil. The oxidation process occurred in a single step and was apparently irreversible. Cyclic voltammetry revealed that the electrodes made of graphite powders were better than the ones made of acetylene black and Ketjenblack (data not shown) based on the onset potential of the oxidation process. Among the graphite powders tested, electrodes made of Bay Carbon graphite were marginally better than the ones made of Aldrich and Fluka graphite. The onset potential, for the NADH oxidation, with the CCEs made of Bay Carbon graphite was slightly more negative than the others and was very similar to the carbon paste electrodes made of the same graphite (therefore the Bay Carbon paste electrode response was not included in Fig. 1). Hence, further studies were carried out with the CCEs made of Bay Carbon graphite. The electrochemical oxidation of NADH with the blank CCE, in phosphate buffer solutions of pH 7.3 is shown in Fig. 2. The anodic peak potential for a concentration of 1 mM, at a scan rate of 10 mV s\u22121, is $0.45 V vs. Ag AgCl KCl(satd.) reference electrode. The peak potentials were shifted in the positive direction with increase in the scan rate. A second peak at potentials more negative than the first peak is found to develop when the scan rate exceeded 60 mV s\u22121"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003250_s10846-015-0301-4-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003250_s10846-015-0301-4-Figure5-1.png",
        "caption": "Fig. 5 Free body diagram of Tilt-Roll rotor quadrotor. North-East-Down (NED) geographical coordinate system representation is used",
        "texts": [
            " Bias may exist by the accompanying reasons: Insufficiencies in actuators, noisy output due to internal and external disturbances, the geometrical flaws of the body frame concerning the perfect framework model, imbalanced propellers and their gyroscopic effects, windy conditions if the flight takes place in outdoor conditions. In this study these negative effects are displayed as one aggravation component called \u201cpenalty gain factor\u201d. Table 1 (continued) Symbols Definitions UT Throttle Input Fi Force Vector y\u03b8 Control output for pitch angle y\u03c6 Control output for roll angle y\u03d5 Control output for yaw angle \u03c4x Total torque along x axis \u03c4y Total torque along y axis \u03c4z Total torque along z axis dT Sampling Time Free body diagram of the proposed quadrotor is displayed in Fig. 5. Body fixed frame is thought to be at the focal point of gravity of the quadrotor, where z pivot is indicating downwards concurring N, E, D (North, East, Down) geographical coordinate system. As per the Euler edge representation, edges of revolution about the aircraft\u2019s center of mass in x, y and z axes are characterized individually as roll (\u03c6), pitch (\u03b8) and yaw (\u03d5) angles respectively. The earth\u2019s gravitational force mg is assumed to be constant and in downwards direction with respect to earth frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure3-3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure3-3-1.png",
        "caption": "FIGURE 3-3 Actual P-V diagram showing the deviation from the ideal cycle and the loss from pumping for a four-stroke-cycle engine.",
        "texts": [
            " l\\Iost engines are generally operated at part throttle, which changes the exhaust gas dilution and the pressure and temperature of the mixture in the cylinder. Heat is transmitted to the cylinder walls during the cycle, and leakage past the rings and valves contributes to the loss. The combustion process is not an instantaneous process as assumed for the ideal Otto cycle but takes place over a finite amount of time, during which the piston is moving and heat is being lost to the cylinder walls. Combustion will usually not be complete because of poor mixing or an insufficient supply of oxygen. An actual engine cycle is shown in figure 3-3. PROBLEMS 1. An ideal gas can undergo any of the processes shown in figure 3-4. Process 1-2 and process 3-a-b-4 are adiabatic. All processes are ideal. Four possible cycles beginning and ending at stage 1 can be devised. Describe these cycles and determine which cycle has the highest and which cycle has the lowest thermal efficiency. Draw the corre sponding T-S diagram. 2. An ideal Otto cycle operates with a compression ratio of 8 and a heat input of 2000 kJ/kg. If state 1 is 100 kPa and 300 K, find the conditions at points 2, 3, and 4 as well as the work and heat transfer for all four processes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-2-1.png",
        "caption": "FIGURE 11-2 Kinematics associated with planar motion of the chassis and drive wheels. The dashed outline shows the position of the chassis and drive wheels after an angular displacement 9.",
        "texts": [
            " The suggested readings at the end of the chapter provide additional information on methods of three as well as two-dimensional analysis. Simplifying Assumptions The following simplifying assumptions apply to the rear-wheel-driven tractor shown in figures 11-1 and 11-2: 272 EQUATIONS OF MOTION 273 1. The ground surface is planar and nondeformable. 2. The motion of the tractor can be analyzed as two dimensional. 3. Rotational motion of the front wheels is neglected. 4. Aerodynamic forces are neglected. The kinematics used to describe the rear wheel and chassis motions are illustrated in figure 11-2. The translational motions of the rear wheels and chassis are referenced to the fixed or inertial XZ coordinate system. Such a coordinate system, in which the positive Z axis points downward, is consistent with the terminology widely used in other areas of vehicle dynamics. The angle of rotation of the drive wheels, <p\"., is measured relative to the tractor 274 MECHANICS OF THE TRACTOR CHASSIS chassis so that the absolute angular motion of the drive wheels is given by the angle <l>w - e, where e is the pitch angle of the chassis",
            " - 8) + etl (7) Equation 7 may be simplified, since the traction mechanics of the unpowered front wheels assumes that er = (TFtIRtlrf. Equations 1, 2, and 4 are the differential equations of motion governing the three degrees of freedom that the rear wheels possess for general planar motion. Equations 5, 6, and 7 are the corresponding equations for the chassis. However, the constraint that the rear wheels arc attached to the chassis implies that the corresponding 6 degrees of freedom (xv., Zv., <Pw, Xc> Z\" 8) are not independent. Referring to figure 11-2, the following two equations express the con straint relation: Z, Xu + hIe cos (8 1e + 8) Zv\u00b7 - hI, sin (8 1, + 8) (8) (9) The two constraint equations reduce the number of degrees of freedom of the system from 6 to 4 and thus imply that the rear wheel-chassis system (the total tractor) can also be described by four independent differential equa tions. These four equations can be derived from equations 1, 2, 3, 5, 6, and 7 by eliminating the internal reactions H\" V\" and T\" using constraint equa tions 8 and 9, and considering the relations between the locations of the centers of gravity of the rear wheels, chassis, and tractor",
            " If the rear wheels are braked instead of driven, F, changes direction and acts to decrease the forward speed of the tractor. As discussed in the section Traction Performance Equations in chapter 10, F, may be considered to be equal to the product of the coefficient of gross traction J-lg and the soil reaction R,. The coefficient of gross traction is, in turn, a function of the slippage S of the rear wheels as well as of tire and soil surface parameters. V sing equation 7 in chapter 10 and the kinematics illus trated in figure 11-2, (13) Equations 11 and 12 govern the vertical translation and rotation of the tractor. These equations are particularly important for describing tractor rear ward overturning and vibration. Equation 12 may be simplified by using the relations er = (TF,IR,)rr and ef = (TFflRf)rf\u00b7 If we consider that the power delivered to the rear axle is equal to the power output of the engine multiplied by an overall efficiency 11, we can write where Tp is the engine torque produced at engin.e speed <!:>r. Letting N be the ratio of engine speed to axle speed (N = 4>,/<",
            " As a result, the moment arm hg cos (<1>0 - a) of the parallel component may be small or even negative, while the perpendicular component P sin a is increased. As equation 30 indicates, such a situation makes the development of a positive angular acceleration e more probable, and thus the chances for a rearward overturn are increased. Even though sufficient traction and power are available to develop a drawbar force in excess of PH the drawbar force required to cause the front wheels to just lose contact with the ground, the tractor may not be in danger of overturning if the drawbar load is properly hitched to the tractor. Equation 30 and figure 11-2 indicate that the moment arm, h3 cos (<1>0 - e), of the parallel drawbar force component, P cos a, tends to increase as the tractor rotates counterclockwise through a positive angle e. Simultaneously, the mo ment arm, hg sin (<1>0 - a), of the perpendicular component, P sin a, tends to decrease as e increases. Thus, for a properly hitched load, rotation of the tractor chassis may tend to stabilize the tractor, thus providing an explanation for situations in which a tractor may be in equilibrium with the front wheels of the tractor off the ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001682_cdc.2006.377137-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001682_cdc.2006.377137-Figure7-1.png",
        "caption": "Fig. 7. Quad-rotor helicopter",
        "texts": [],
        "surrounding_texts": [
            "In this paper a simple attitude stabilization of a quadrotor aircraft has been presented. The control strategy was obtained using the backstepping technique and adding saturation functions to bound the control input and in the same way the angular acceleration. The proposed controller was been tested in simulation and in real-time experiences in two prototypes of quad-rotors helicopters. The experimental results show that the controllers performs well even in presence of aggressive perturbations. It has been observed that the only attitude stabilization of a quad-rotor or VTOL aircraft is not enough to make hover in real conditions, but the study of this problem in testbed prototypes gives an idea of aerodynamics problems to solve in the take-off of the VTOLs vehicles."
        ]
    },
    {
        "image_filename": "designv10_10_0003934_msec2014-4151-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003934_msec2014-4151-Figure5-1.png",
        "caption": "FIGURE 5: TROCHOIDAL TOOL PATH",
        "texts": [
            " For trochoidal milling to become a viable process in industry, the benefits must outweigh the potential reductions in productivity and efficiency. The reduction in the material removal rate (MRR) is due to the fact that a smaller toolworkpiece contact area is utilized to reduce cutting forces in trochoidal milling, and the MRR changes between the on-time and the off-time of the trochoidal milling duty cycle. Therefore, two MRR values can be calculated. The cycle MRR (MRRcyc_troch), which is only concerned with contact duration, is calculated using the stepover distance w (Figure 5, Eq. 1), instead of the radial depth of cut, RDoC, that is utilized for conventional milling techniques (Eq. 2), where N is the rotational speed of the spindle and ap is the depth of cut. In Equation 1, ap is the depth of cut, f is the feed per revolution, Vc is the cutting speed, and Dt is the tool diameter. However, MRRcyc_Troch does not include the off-time duty cycle, where the tool travels to the beginning of its next cycle without cutting. To better compare MRR values between end milling and trochoidal milling, the total material removal rate of trochoidal milling (MRRtot) should be calculated (Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003575_j.ymssp.2017.11.011-FigureA.14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003575_j.ymssp.2017.11.011-FigureA.14-1.png",
        "caption": "Fig. A.14. Outer ring as a one degree-of-freedom system during the rolling element free flight.",
        "texts": [
            " We gratefully acknowledge the invaluable support of the Pearlstone Foundation. We would also like to thank Prof. Michael Lipsett for his constructive comments. The time needed for the outer ring to settle after the disconnection of the rolling element from the leading edge defines the range of the spall width for which the presented algorithms are valid. This appendix describes the derivation of this time. It is assumed that after the rolling element disconnects, the outer ring is loaded by only two rolling elements (marked by arrows in Fig. A.14). The horizontal acceleration of the outer ring is given by, Fig. A.1 magent to the w \u20acxo \u00fe co mo _xo \u00fe ko mo xo \u00bc g 2Fp cos 2p NRE \u00fe Fce mo \u00f0A:1\u00de where xois the location of the centre of the outer ring, co is the damping coefficient of the outer ring, ko is the outer ringfoundation stiffness, Fce is the force applied to the rolling element that enters the spall, Fp is the force applied to the rolling element that is within the loading zone but does not interact with the spall, NRE is the number of the rolling elements in the bearing and mo is the mass of the outer ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000591_978-1-4612-2104-3_13-Figure13.7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000591_978-1-4612-2104-3_13-Figure13.7-1.png",
        "caption": "FIGURE 13.7. At higher speeds, the an gle swept by the leg spring during the stance phase increases, and as a result, the vertical displacement of the cen ter ofrnass (Ily) decreases. In both ex amples, the displacement of the leg spring (Ill) is the same.",
        "texts": [
            " Crab Studies have shown that the stiffness of the leg spring remains nearly the same at all forward speeds in a variety of running, hopping, and trot ting mammals including humans (Figure 13.6A) (He et al. 1991; Farley et al. 1993). As animals run faster, the body's spring system is adjusted to bounce off the ground more quickly by increas ing the angle swept by the leg spring during the ground contact phase rather than by increasing the stiffness of the leg spring (Figure 13.6B). By in creasing the angle swept by the leg spring at higher speeds, the vertical excursion of the center of mass (Lly) is reduced without changing the leg stiffness (Figure 13.7). This method of adjusting the spring-mass system for different speeds is the same in all of the mammals studied to date (He et Quail Human Dog 0 Jl .l o ct DO Hare Kangaroo 1~~~~~~~~~~~~~~~~~~ 0.001 0.01 0.1 FIGURE 13.5. Relative individual leg stiffness as a func tion of body mass. Relative leg stiffness was determined by normalizing peak vertical ground reaction force by body weight and virtual leg spring compression by hip 10 100 Mass (kg) height. To determine relative individual leg stiffness, rel ative leg stiffness was simply divided by the number of legs used in a step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003478_9781118700280.ch1-Figure1.7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003478_9781118700280.ch1-Figure1.7-1.png",
        "caption": "Figure 1.7 Representative plastic composite bushings and thrust washers. Source: Courtesy of SKF.",
        "texts": [
            " This feed rate is proportional to the bearing length, width, clearance, and surface velocity and ranges up to 4m3/min (1000 gal/min) for the oil-film bearings in a steam turbine generator at an electric power station. Specially designed fluid-film bearings are unique in being able to operate with gas or ambient liquids such as water or gasoline as their hydrodynamic fluid. Dry and semilubricated bearings require a minimum of space. A porous metal, plastic, or plastic-lined bearing is commonly a bushing or thrust washer, such as that illustrated in Figure 1.7. These bearings have just enough wall thickness to provide the needed strength for insertion in a supporting housing. The bearing can even consist of no more than a formed or machined hole in a suitable plastic housing of an appliance or instrument. In the case of ball and roller bearings, the outside diameter commonly ranges from about one and a half to three times that of the bore, and the axial dimension ranges from one-fifth to Tribology \u2013 Friction, Wear, and Lubrication 17 one-half of the shaft diameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-5-1.png",
        "caption": "FIGURE 11-5 Free-body diagram illustrating the calculation of force Rj .",
        "texts": [
            " Then, summing moments about point C, taking counterclockwise moments as positive, and assuming e o when the tractor is in static equilibrium, Rf (hit cos elt + h2t cos e2t + ef - er) + Wt sin ~ (rr + hIt sin elt) - Wt cos ~ (hit cos elt - er) + P cos a (rr - h3 cos <1\u00bb + P sin a (h3 sin <I> + er) = 0 (16) Solving equation 16 for Rf , Rf = {W, [(hIt cos elt - er) cos ~ - (rr + hit sin elt) sin ~] - P [(rr - h3 cos <1\u00bb cos a + (h3 sin <I> + er) sin an I{h lt cos elt + h2t cos e2t + ef - eJ (17) Although equation 17 is useful for computation, its complexity tends to STATIC EQCILIBRICM ANALYSIS-FORCE ANALYSIS 279 obscure its physical meaning. Csing the notation of figure 11-5, equation 17 mav be written (18) With Rt now known, equation 15 may be solved for H, R, W, cos ~ + P sin 0: Rt W,L 2 Py W, cos ~ + P sin 0: + -' Ll L[ lV, cos ~ W,L 2 + P(y, + Ll sin 0:) Ll Ll W, cos ~ - W,L 2 + PYt (19) L[ LI The terms Py,lL[ and PYtlL1 express changes in the soil reactions R j and R, as a result of the drawbar force P. Although there is no actual shift of weight, the changes in the forces R, and R f are commonly known as weight transfer (see the section Traction Performance Equations in chapter 10)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000968_3516.868924-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000968_3516.868924-Figure2-1.png",
        "caption": "Fig. 2. Example of a single-input single-output nonlinearity N , which can be decomposed as a constant gain K and nonlinearity of bounded output.",
        "texts": [
            " L1e is a SISO linear or nonlinear controller that at least achieves the bounded-input bounded-output (BIBO) stability of S(N; P ). Remarks: 1) The nonlinearity N and the linear plant P form an integral part of the system S(N; P ). Thus, the output of N , denoted by in Fig. 1, cannot be measured. 2) The outputs of several nonlinearities of interest can be written as (3). For instance, let N be a SISO time-varying nonlinearity whose graph lies between or on two curves G+ and G for all instances of time (see Fig. 2). Furthermore, suppose that there exists a line of nonzero and finite slope K , passing through the origin and lying in the region between the curves G+ and G , 1083\u20134435/00$10.00 \u00a9 2000 IEEE such thatG+(u) Ku andKu G (u) are finite for all u 2 . Thus, the linear part ofN is the constant gain K and its output is (t) = (Nu)(t) = Ku(t) + d(t) (4) for all t 0 and u 2 L1e, where kdk1 = sup t 0 jd(t)j maxfsup u2 (G+(u) Ku); sup u2 (Ku G (u))g: (5) Typical examples of nonlinearities, whose graphs lie between two curves such as G+ and G , are dead-zone nonlinear amplifiers (see, e",
            " This dc motor is represented by P (s) = Kt Js+B (7) where Kt =0:809N m/A J =0:006 kg m2 B =0:005N m s (8) are, respectively, the torque constant, the inertia of the motor, and the friction coefficient. Let the nonlinearity N be the dead zone shown in Fig. 6. Clearly, the graph of N lies in the region between or on two parallel lines G+(u) = u+ 0:5 and G (u) = u 0:5 for all u 2 . Hence, N can be decomposed as (1), where the transfer function of the linear part is H(s) = 1 and is a nonlinearity whose output d y , respectively, in the presence of measurement noise . is bounded by 0.5. Therefore, the nonlinear system S(N; P ) can be represented byS(H; P ) in Fig. 2. Having the representationS(H; P ), it can be easily verified (for example, by the Routh\u2013Hurwitz test) that for the proportional and integral (PI) controller C(s) = Kp + Ki s (9) where Kp = 2:0159 and Ki = 1:6799, the system S(H; P ) is the BIBO stable, and so is S(N; P ). The response of the system S(N; P ) to the input r(t) = 1:5; 0:1 t 0:6 0:1; 0:6 < t (10) in the absence of measurement disturbance is plotted in Fig. 7(a) and is designated by yN . If there were no dead-zone nonlinearity in S(N; P ), i",
            " Therefore, the nonlinear system S(N; P ) can be represented S(H; P ), and S(N; P ; DOB), denoted by y , y , and y , respectively, in the absence of measurement noise . It is evident that y and y overlap and converge to zero. That is, the disturbance observer has suppressed the limit cycles caused by the backlash. (b) Responses of the systems S(N; P ), the disturbance-free S(H; P ), and S(N; P ; DOB), denoted by y , y , and y , respectively, in the presence of measurement noise . by S(H; P ) in Fig. 2. Having the representation S(H; P ), it can be easily verified that for the controller C(s) = Kc(s+ 2) s+ 3 (13) where Kc = 10, the system S(H; P ) is the BIBO stable, and so is S(N; P ). (By the Routh\u2013Hurwitz test, it can be shown that S(H; P ) is the BIBO stable for any Kc > 1:5.) The response of the system S(N; P ) to the input r(t) = 0:1; 0:1 t 0:2 0; 0:2 < t (14) in the absence of measurement disturbance is plotted in Fig. 9(a) and is designated by yN . This response is a periodic function of time, which implies that the system has the limit-cycle behavior"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002026_tmag.2009.2012785-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002026_tmag.2009.2012785-Figure3-1.png",
        "caption": "Fig. 3. 3-D finite element mesh.",
        "texts": [],
        "surrounding_texts": [
            "Here, the distribution of flux density vectors and the losses of the SCIM with the 4/3 slot pitch skewed rotor and that with rotor without skew are calculated. The calculated losses are compared with measured ones to clarify the validity of the 3-D analysis. Further more, the bar-current and the torque are calculated. Fig. 4 shows the distributions of flux density vectors of SCIM with the 4/3 slot pitch skewed rotor. The flux density vectors of the upper section are larger than those of the lower section. The imbalance of the magnetic flux distributions makes the loss distributions imbalanced in the SCIM with skewed rotor. Fig. 5 shows the contours of eddy current loss. The eddy current loss in the tip of teeth and the surface of the rotor is especially large. From Fig. 5(b), the eddy current loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 6 shows the contours of hysteresis loss. The hysteresis loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 7 shows the loss of the SCIM. The iron loss of the SCIM is decreased by the skewed rotor. The calculated total losses agree well with the measured ones. Fig. 8 shows the waveforms of bar-current. The ripple of the bar-current of the motor with the 4/3 slot pitch skewed rotor is smaller than that of the motor with the rotor without skew. Fig. 9 shows the torque waveforms. The average torque of the motor with the 4/3 slot pitch skewed rotor is larger than that of the motor with the rotor without skew, and the torque ripple of the SCIM is decreased by the skewed rotor. B. Effects of Skew Angle of Rotor on Motor\u2019s Characteristics Here, it is numerically clarified that the effects of the skew angle of the rotor of the SCIM on the secondary current, torque, loss and efficiency characteristics. Fig. 10 shows the waveforms of bar-current. The ripple of the bar-current becomes small as the rotor skew angle increases. rotor skew angle increases. The average torque once increases and then decreases as the rotor skew angle increases. Fig. 13 shows the loss characteristics. The iron loss becomes small as the rotor skew angle increases. Fig. 14 shows the efficiency characteristics. In this calculation, the efficiency approaches to the maximum value when the skew angle is 4/3 slot pitch. Table II shows the discretization data and CPU time. V. CONCLUSION In this paper, the influence that the skew angle of the squirrelcage induction motor exerted on the secondary current, torque, loss and efficiency characteristics was clarified by using a threedimensional finite element method. As a result, it has been understood that torque ripple and iron loss decreases as the rotor skew angle increases in this model. Moreover, it has been understood that the average torque once increases, then decreases as the rotor skew angle increases. The efficiency is the best when the rotor is skewed 4/3 slot pitch rotor angle. REFERENCES [1] T. Yamaguchi, Y. Kawase, and S. Sano, \u201c3-D finite-element analysis of skewed squirrel-cage induction motor,\u201d IEEE Trans. Magn., vol. 40, no. 2/2, pp. 969\u2013972, Mar. 2004. [2] S. Ito and Y. Kawase, Computer Aided Engineering of Electric and Electronic Apparatus Using Finite Element Method. Japan: Morikita, 2000. [3] K. Yamazaki, \u201cLoss calculation of induction motors considering harmonic electromagnetic field in stator and rotor,\u201d IEEJ Trans. IA, vol. 123, no. 4, pp. 392\u2013400, 2003. [4] Y. Kawase, T. Yamaguchi, M. Watanabe, and H. Shiota, \u201cNovel mesh modification method using Lapace equation for 3-D dynamic finite element analysis,\u201d in Conf. Record 16th Conf. Comput. Electromagn. Fields, 2007, vol. PB7-15. [5] Y. Kawase, T. Yamaguchi, M. Watanabe, N. Toida, Z. Tu, and N. Minoshima, \u201c3-D finite element analysis of skewed squirrel-cage induction motor using novel mesh modification method,\u201d in Int. Symp. Electromagn. Fields in Mechatron., Elect. Electron. Eng., 2007, pp. 269\u2013270."
        ]
    },
    {
        "image_filename": "designv10_10_0002986_10_2013_224-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002986_10_2013_224-Figure6-1.png",
        "caption": "Fig. 6 Distribution of transducers used to construct biosensors based on enzyme inhibition (period 2006\u20132012)",
        "texts": [
            " In addition, in the case of irreversible inhibition, the enzyme can\u2019t recover its original activity and thus only few experiments are carried out with the enzyme. The addition of activator can allow 60\u201390 % of the initial activity [50\u201352], but after a few generations the enzyme is totally inhibited. That is why it is recommended to adopt a procedure for the single use of an enzymatic biosensor using, for example, a disposable biosensor [22, 29, 31]. The choice of transducer is also important in order to have a sensitive, robust, and cost-effective system. As reported in Fig. 6, the most used type of transducer is the electrochemical one (81 % of the biosensors based on enzyme inhibition reported in the literature are electrochemical biosensors) for several reasons, because it is robust, cost-effective, fast, miniaturizable, and used also in the case of colored solutions. In addition, the possibility of using screen-printed electrodes renders this kind of sensor suitable for an easy, fast, and cost-effective measurement for each type of inhibitor both reversible and irreversible, avoiding reactivation in the latter case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002205_robot.2008.4543520-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002205_robot.2008.4543520-Figure4-1.png",
        "caption": "Fig. 4: SCARA robot : frames and joint variables",
        "texts": [
            " WS is obtained as a sampling of the ID model ( )SSS q,q,qIDS , \u2022 \u03c7k+1 is the LS solution of (18), \u2022 The algorithm stops when the relative error decreases under a chosen small number tol: tol k k1k \u2264 \u2212+ \u03b5 \u03b5\u03b5 . In the following, this identification process is applied to a 2 DOF robot. A. Presentation of the SCARA robot The identification method is carried out on a 2 joint planar direct drive prototype robot without gravity effect. The description of the geometry of the robot uses the modified Denavit and Hartenberg notation [29] and the notations are illustrated in Fig. 4. The robot is direct driven by 2 DC permanent magnet motors supplied by PWM amplifiers. The dynamic model depends on 8 minimal dynamic parameters, considering 4 friction parameters: \u03c7 = [ZZ1R fv1 fc1 ZZ2 MX2 MY2 fv2 fc2]T. Where: ZZ1R = ZZ1 + Ia1. More details about the modeling and ID identification can be found in [11]. The closed loop is a simple PD control law. The sample control rate is 200Hz. Torque data are obtained from the current reference vir assuming a large bandwidth (1 kHz) of the current closed loop such as: \u03c4j = gtj virj (16) gtj being the transmission gain of the joint j"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001310_tmag.2004.832157-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001310_tmag.2004.832157-Figure5-1.png",
        "caption": "Fig. 5. Photograph of the moving-magnet linear actuator with cylindrical Halbach array: (a) single-phase stator winding and Halbach array mover and (b) testing apparatus.",
        "texts": [
            " 3(a) and (b) show the comparison between analytical and FE results of radial and axial flux density distributions due to PM\u2019s for the moving-magnet linear actuator with cylindrical Halbach array respectively. Fig. 4(a) and (b) show the comparison between analytical and FE results of flux linkage and back EMF for the moving-magnet linear actuator with cylindrical Halbach array respectively. In particular, the analytical results of back EMF are compared with FE results in case of mover velocity . The results are shown in good agreement with those obtained from finite-element analysis (FEA). Fig. 5(a) shows the photograph of cylindrical Halbach array mover and single-phase stator windings. Fig. 5(b) shows the experimental system that consists of load cell, indicator, dc power supply, and moving-magnet linear actuator with cylindrical Halbach array to measure static thrust. Specifications of manufactured moving-magnet linear actuator are presented in Table I. Fig. 6(a) shows the cylindrical Halbach array composed of ideal radial and axial magnetized ring. In case of a ring magnet, a geometry-specific impulse magnetizing fixture is required to impart the magnetization, whereas arc segments can be magnetized with a parallel magnetization such as in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002395_asjc.211-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002395_asjc.211-Figure1-1.png",
        "caption": "Fig. 1. The principal forces and moments of the small-scale helicopter with respect to its body frame.",
        "texts": [
            " HELICOPTER DYNAMICS This section is intended to briefly review the nonlinear dynamic model of a small-scale helicopter with single main rotor and tail rotor. The four independent inputs to a helicopter system consist of one control thrust ubT =\u2212Tmre\u0302b3 and three control moments, ubM =[Lmr Mmr Ntr], where the sub-indices mr and tr denote the control generated from the main rotor and tail rotor, respectively. Both ubT and ubM with the upper-index b are applied along the body-axes and illustrated in Fig. 1. e\u0302bj and e\u0302ij , j =1,2,3, denote the unit vectors of the body frame and the inertial frame respectively. In addition to the three control moments, the net torques acting on the robotic helicopters should include the restraint torque in the blade attachment to the rotor head and the anti-torques on the main and the tail rotors. Hence, the net torques are computed as: b=\u2212Qtre\u0302 b 2\u2212Qmre\u0302 b 3+ JubM (1) where Qmr and Qtr respectively represent the antitorques on the main rotor and tail rotor. J is related to the helicopter mechanical characteristics and is expressed by: J = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 1+ k Tmrhmr 0 0 0 1+ k Tmrhmr 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (2) q 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society where hmr denotes the height of rotor head above the helicopter center of gravity (c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002545_1350650111433243-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002545_1350650111433243-Figure1-1.png",
        "caption": "Figure 1. Drawing of the FZG test machine.",
        "texts": [
            " In order to validate this model, comparisons with experimental measurements are presented for a variety of operating conditions: cooling or heating of the machine with free or forced convection. The pinion bulk temperature and its variations with the oil bath level are analysed and compared with the evidence of Ho\u0308hn et al.4 Then, maximum surface pinion temperatures are determined and compared with the results deduced from the AGMA9 and ISO10 standard formulas. Depending on the immersion depth, very different conclusions can be drawn with regard to the risk of scuffing which underlies the interest of the proposed methodology. The back-to-back test rig (FZG) is shown in Figure 1, it comprises a pair of test and slave gears connected in such a way that a power loop is created by elastic deformation of the shafts.11 The torque is externally applied by a lever and a series of weights, whereas rotational speeds are imposed by the electric motor which compensates for the losses in the mechanical chain. Using a torque sensor on the motor shaft and measuring the rotational speed, the total power losses can be derived. In this article, the results will refer to experiments based on types A and C gears (as defined in Table 1) lubricated by five different mineral oils whose properties are listed in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001758_robot.2008.4543731-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001758_robot.2008.4543731-Figure1-1.png",
        "caption": "Fig 1: Schematic of the experimental setup",
        "texts": [
            " This results in continuous adjustment of the actuating input by the human in the loop. The objective of this research is to model such a system and characterize the load and motion transmission from the actuator to the load. Ultimately, these models can be used to improve the control strategy of the system. S Cable 978-1-4244-1647-9/08/$25.00 \u00a92008 IEEE. 3407 A typical load actuation system of a surgical robot has been emulated in the present experimental setup using a two cable pull-pull transmission actuated with two brushed DC motors mounted on linear slides, as shown in Fig. 1. The first motor is controlled as the input or the drive motor, while the second motor emulates a passive load or environment. Each cable passes through a flexible conduit and is wrapped around pulleys attached to each of the DC motors. The tightly wound spring wire conduits are fixed at each end using two plates attached to the same platforms on which the linear slides are mounted. In this way, the platforms holding the plates are free to move in space, and applying a tension in the cable is counteracted by a compression in the conduit with no forces being transmitted through ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003263_tmag.2014.2320446-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003263_tmag.2014.2320446-Figure5-1.png",
        "caption": "Fig. 5. Schematics for the three three-phase concentrated winding configuration with 18 coils. (a) Winding arrangement. (b) MMF vectors for the working harmonic. (c) MMF vectors for unwanted harmonics.",
        "texts": [
            " The MMF harmonic amplitudes of a three-phase winding are 1.5 times those of a single-phase winding. If one phase contains a minimum of two coils, it is possible to devise multiple three-phase configurations if the total number of slots is no less than 12. By way of example, for an 18-slot 14-pole combination, three three-phase windings can be developed. The three threephase windings are uniformly arranged in space but with a specific spatial phase angle with respect to each other, as shown in Fig. 5(a). In addition, the phase shift in time for the currents in each three-phase set can also be selected in order to eliminate unwanted harmonics. The condition to cancel out a given order MMF harmonic is to select appropriate space and time phase shifts so that the MMF vectors produced by the three three-phase windings form a balanced three-phase system, as shown in Fig. 5(c), while their working harmonic vectors overlap with each other, as shown in Fig. 5(b). Based on the foregoing discussion, \u2212260\u00b0 phase shift in space and 20\u00b0 phase shift in time are selected for the 18-slot 14-pole nine-phase (three three-phase) configuration. The MMF spectra of the single three-phase and three threephase windings are shown in Fig. 6. It can be seen that the first-, fifth-, 13th-, 17th-, 19th-, 23rd- \u00b7 \u00b7 \u00b7 order harmonics are canceled out whereas the seventh- (working harmonics for 14-pole), 11th-, 25th-, 29th- \u00b7\u00b7\u00b7 order harmonics are combined. Quantitative determination of the space and time phase shifts will be described in the following section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-10-1.png",
        "caption": "FIGURE 11-10 Lateral force-slip angle functional relationship.",
        "texts": [
            " A pneumatic tire can be considered to develop a lateral force whenever the direction in which the tire is headed differs from the direction of the plane of the wheel itself. This difference in directions, called the tire slip angle, is expressed in terms of the velocities of the wheel in the vehicle co ordinate system. Figure 11-9 illustrates the slip angles of the front, asf, and rear, asn wheels. From that figure, asf = tan- 1 ((v + xfwr)/u) - of a sr = tan- 1 ((v - Xcgr)/u) The lateral force developed by a tire at a given vertical load takes the form shown in figure 11-10. The lateral force varies nearly linearly with slip angle at small slip angles and reaches a maximum value asymptotically. The slope of the curve at the origin is termed the cornering stiffness, Ca. Thus, for small slip angles, L = - Caas; i.e., a positive slip angle produces a negative lateral force. If the lateral force versus slip angle relation is nondimension alized by dividing the lateral force by the normal force on the tire, the resulting ratio, JoLl, is termed the cornering coefficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002939_1077546313483790-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002939_1077546313483790-Figure1-1.png",
        "caption": "Figure 1. (a) Schematic diagram of bearing with defect location; (b) representation of additional deflection due to outer race defect.",
        "texts": [
            " The \u00fe sign as subscript in these equations signifies that if the expression inside the bracket is greater than zero, then the rolling element at angular location i is loaded giving rise to a restoring force and if the expression inside the bracket is negative or zero, then the rolling element is not in the load zone, and the restoring force is set to zero. In this section, mathematical simulation of local defects in the model is described. Localized defects on races have been shown schematically in Figure 1. 2.2.1. Defect on the outer race. The local defects on the outer race are normally found in the loaded region of the bearing. Outer race defect is considered, as shown in Figure 1(b), which is located at an angle out from the X-axis. Moreover, for the stationary outer race the position of defect does not change with respect to the shaft rotation. The deflection of the ith ball varies when it reaches the defective zone of the outer race. Mathematically, the angular position i of the ith ball in the defect zone is defined by the following relation: out 2S R i out \u00fe 2S R \u00f02\u00de Additional deflection j at the jth defect of the ball when it passes through the jth defect is defined by the width of the defect as follows and added to ball deflection: j \u00bc rb rb cos\u00f0 b\u00de\u00bd \u00f03\u00de where S is the span of the defect, R is the radius of the outer race, rb is the radius of the ball and b defined as: b \u00bc S 2rb 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-25-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-25-1.png",
        "caption": "FIGURE 12-25 Tractor steering geometry. (From Wittren 1975.)",
        "texts": [
            " System efficiency 14. Front-end type (tricycle, single wheel, standard) 15. Tractive and braking forces 16. Chassis type Many references are available on the mechanics of steering geometry and the analysis of linkage forces. Most of this literature deals with highway ve hicles; however, the design techniques for the determination of steering forces with a stationary vehicle are valid for agricultural tractors using similar linkage geometry. Since the heaviest steering loads with Ackerman-type steering (fig. 12-25) usually occur with a stationary tractor on dry, clean concrete, this condition provides a convenient standard for calculating maximum power requirements. On Ackerman-steer-type tractors, tire loading is the most significant vari- 338 HYDRAULIC SYSTEMS AND CONTROLS able affecting power requirements. Tire loads range from the minimum needed for longitudinal stability to a maximum usually dictated by tire load rating. Rated tire capacities are often exceeded by the customer who expects some degree of controllability even under these extreme and sometimes abusive conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000772_s0094-114x(99)00068-3-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000772_s0094-114x(99)00068-3-Figure4-1.png",
        "caption": "Fig. 4. Balancing elastic system with cam and rotating follower II.",
        "texts": [
            " The co-ordinates of the contact point D between the cam 2 and the roll 3, in the mobile axes system x2Cy2, result from the envelope parametrical equations of the circle family that I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b11311 1303 represents the relative positions of the roll 3 with respect to the cam 2: x2D x2E2 RQ P2 Q2 p ; y2D y2E3 RP P2 Q2 p , where R represents the radius of the roll; P y2E dc dj x1Esin c\u00ff j \u00ff y1Ecos c\u00ff j ; Q x2E dc dj \u00ff x1Ecos c\u00ff j \u00ff y1Esin c\u00ff j : The reaction force that occurs in the higher pair D is given by: R31 m1OG1cos j m4AXA g Fs YAcos y\u00ff XAsin y y1Ecos c\u00ff F\u00ff j \u00ff x1Esin c\u00ff F\u00ff j Fig. 4 shows another constructional variant for the static balancing of the industrial robot arm. The helical spring 4 is joined with its B end to the follower 2, which is driven by a cam, rigidly connected with the arm 1. From the equilibrium condition for the forces system, the following di erential equation results: I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b113111304 Fs YB \u00ff YC cos y\u00ff XB \u00ff XC sin y \u00ff \u00ffm2XG2 m4BBC cos c g y2Ecos c F \u00ff j \u00ff x2Esin c F\u00ff j m1OG1cos j m4AXA g Fs YAcos y\u00ff XAsin y x1Esin F\u00ff y1Ecos F 0, 4 where: F arctan T Udc=dj V Wdc=dj ; T XCsin j YCcos j\u00ffU; U x2Esin c\u00ff j y2Ecos c\u00ff j ; V XCcos j\u00ff YCsin j\u00ffW; W x2Ecos c\u00ff j \u00ff y2Esin c\u00ff j ; x1E x2Ecos c\u00ff j \u00ff y2Esin c\u00ff j XCcos j YCsin j; y1E x2Esin c\u00ff j y2Ecos c\u00ff j \u00ff XCsin j YCcos j: As in the previous case, the directrix curves parametrical equations of the cylindrical active surfaces of the cam result as the envelope of a circle family: x1D x1E2 RP P2 Q2 p ; y1D y1E3 RQ P2 Q2 p , where: P x1E \u00ff x2Ecos c\u00ff j \u00ff y2Esin c\u00ff j dc dj ; Q y1E \u00ff x2Esin c\u00ff j y2Ecos c\u00ff j dc dj : The static balancing of the weight forces of the industrial robot arms is made in order to decrease the acting power"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000766_robot.2000.844099-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000766_robot.2000.844099-Figure1-1.png",
        "caption": "Figure 1: Cooperation by multiple branching robots",
        "texts": [
            " Various cooperation strategies have been proposed [14, 4, 10, 11, 1, 51. Our earlier work on cooperative manipulation by multiple fixed-base serialchain manipulators established the augmented object model describing the dynamics at the level of the manipulated object [7], and the virtual linkage model [13] characterizing internal forces. This paper presents the extension and integration of these two basic models in order to accommodate the closed-chain dynamics of systems involving branching mechanisms (Figure 1) while preserving overall performance. The discussion in this paper focuses on the augmented object model as dynamic modeling of cooperative manipulation among multiple robotic platforms involving multiple branches and parallel mechanisms. This model, in conjunction with the virtual linkage model, naturally renders a cooperative control * n-artment of Mechanical Engineering structure consistent with the operational space formulation. This control structure provides the effective object-level control of the closed-chain dynamics and the object internal forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000768_cdc.1996.572714-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000768_cdc.1996.572714-Figure1-1.png",
        "caption": "Figure 1: 3 link planar manipulator",
        "texts": [
            " We can also discuss the case of two revolute actuated joints in place of the two prismatic joints in the himilar way. Suppose that q = [ r x r y elT denote the displacement of the third joint, namely, r, and r y are the position, and 0 is the orientation of the third link. Let fi(z = 1,2) be the control input of the two prismatic actuated joints, m,(i = 1,2,3) be the mass of the link i and I, is the inertia of the third link, and 1 be the distance between the center of the mass of the third link and the third joint. Then the motion equation of the system shown in Fig.1 is given by m,?, - m 3 Z ~ ~ ~ f ? 8 2 - m31sin8e = f l my!y - m3~sine82 + m31coSe8 = f2 { I8 + mal COS e?', - m31 sin e?, = 0 where m,, my , andI express m, = ml + m2 + m3, my = m2 + m3, and I = I3 + m3Z2, respectively. (Theorem 1) Suppose that the desired point qd = [ r , d Tyd edIT , and q d = o is given. Assume that e belongs to the set (01 I 8 - e d /< 5 } . Then the system given by (1) is feedback equivalent to the chained system give by (1) For this system, we get the main result. $? = U1 $2 = U2 (21 { E3 = E2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000694_0094-114x(96)84593-9-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000694_0094-114x(96)84593-9-Figure5-1.png",
        "caption": "Fig. 5. 3-RPS mechanism with fixed branches.",
        "texts": [
            " They can only be determined using the method mentioned in previous sections. It is worth mentioning that the X and Y axes in the fixed coordinate system cannot be the rotating axes. The above analysis is on the tangential distributed mechanism. However, the method can also apply to the mechanism with three axes distributed arbitrarily, but not intersecting at a common point. There will be no difficulty in analysing the more complicated mechanism which has mixed RPS and SPR branches as shown in Fig. 5. The three force line vectors pass through the spherical centres. Like the case shown in Fig. 3, at the initial position there is a translation along the Z axis, and since $~ and $~ are in a same base plane and the intersecting point is E, any lines in the base plane that are parallel with $~ and all the connecting lines between point E and any point on $~ can be the rotational axes. This mechanism is different from those discussed in the previous sections. The axes of three revolute joints intersect at the same point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-28-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-28-1.png",
        "caption": "FIGURE 12-28 Actuator types. (From Wittren 1975.)",
        "texts": [
            " The location of the actuator in the linkage will determine the mechanical efficiency between the output member and the tire print. Overall efficiencies of manual steering gears and their associated linkage are generally in the 40 to 70 percent range, depending on the types of antifriction means employed. Typical efficiencies for actuators usually fall between 80 percent and 95 percent, with the cylinder types being somewhat higher, on the average, than the rotary rack and pinion or vane types (fig. 12-28). Actuator output travel (stroke or angular rotation) is governed to some extent by steering geometry limitations; however, it has been recommended that a stroke-to-bore ratio for cylinders between 5 and 8 be selected, if possible, to maintain adequate column strength and a favorable servo-valve amplifi cation to linkage deflection relationship. Linkage backlash, especially after significant wear, is equally important to elastic deflection in the selection of stroke-to-bore ratios. These recom mended ratios can be extrapolated to rotary-type actuators, although in their case, externally applied column loads do not occur"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-23-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-23-1.png",
        "caption": "FIGURE 5-23 Schematic diagram of a Lanchester bal ancer used on four-cylinder diesel engines to counter-balance the secondary shaking forces. (Courtesy Fiat Tratlori.) Key: I. Crankshaft 2. Two counter-rotating masses ;). Frame holding balancer is bolted to bottom of crankcase. Masses are located midway between the second and third cylinders. 4. Reversing gear so that the masses rotate opposite to each ot her.",
        "texts": [
            " It is quite satisfactory to balance a major part of the force only, using slightly smaller balance weights. 108 ENGINE DESIGN SOCRCE: Condensed from L. C. Lichty, Combustion Engine Processes, 7th ed. McGraw-Hill Book Co., New York, 1967. aHalf of this force can be eliminated by counterbalancing. b(V) indicates that the force or couple is in a vertical plane. Key: M = reciprocating mass, kg (piston plus part of rod) r = radius of crank, m I = length of connecting rod, m a = distance between cylinders, m k = ~ (;~r where n = rpm The secondary balancer (fig. 5-23) in its basic form was invented by F. W. Lanchester and is often called by that name. It has been used on most four-cylinder diesel and some gasoline engines for many years. Rocking vibrations in the plane formed by the cylinders of an in-line engine can exist in two- and three-cylinder engines. This type of unbalance is not a problem in one-, four-, and six-cylinder engines of the types shown in table 5-3. Inertia forces perpendicular to the crankshaft cause the engine to shake. From table 5-3 it can be seen that primary inertia forces do not exist in the usual three-, and four-, and six-cylinder engines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000764_s0094-114x(97)00022-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000764_s0094-114x(97)00022-0-Figure2-1.png",
        "caption": "Fig. 2. Applied coordinate systems.",
        "texts": [
            " 3) a~--parabola coefficient of the parabolic function Si--coordinate system u~0k~--surface parameters of the shaper 0o~--angular width of the space of the shaper on the base circle (Fig. 5) r ,~posi t ion vector in system S,(i = s, 1, 2) rh~--radius of the base circle of the shaper (Fig. 5) ~o--pressure angle [Fig. 6 (b)] ~--proflle angle for determination of pointing (Fig. 7) n,, N~--unit normal and normal (Fig. 5) to the shaper surface Mj~--matrix of coordinate transformation from system S~ to system S, E,--shaper (i = s), pinion (i = 1) or gear (i --- 2) tooth surface ~,--angle of rotation of the shaper (i = s) or face gear (i = 2) (Fig. 2) v,m~--~relative velocity vector ~c~-'~--relative angular velocity vector E--shortes t center distance between the shaper and the face gear (Fig. 2) X,, Y,, Z,---coordinates of the axis of meshing m.,,--gear ratio R,--inner (i = 1) and outer (i = 2) radii of face gear free of undercutting and pointing (Fig. 8) Pj---diametral pitch A/, Aq--segments for the determination of pointing [Fig. 6 (a)] vd~---velocity of contact point that moves over the tooth surface of the shaper L,----limiting line on the shaper tooth surface (i = s) (Fig. 9), or face-gear tooth surface (i = g) L--fillet line (Fig. 10) 87 88 F.L. Litvin et al. 0k,.--shaper parameter at the addendum cylinder r~,~--radius of the addendum cylinder of the shaper L,--limiting length of the shaper for avoidance of undercutting (Fig",
            " The developed theory was tested by computerized simulation of meshing and contact of pinion and face-gear tooth surfaces. Numerical examples are provided. 2. GENERATION OF FACE-GEAR DRIVES WITH LOCALIZED BEARING CONTACT The pinion is a conventional involute spur one (Fig. 1). A face gear may be generated by an involute spur shaper. The process of generation is based on the simulation of shaping as meshing Meshing of orthogonal offset face-gear drive 89 of the pinion and the face gear of the drive represented in Fig. 2. The shaper and the face gear form an offset drive that is similar to the face-gear drive to be designed, and perform rotational motions about the same axes as in the face-gear drive (Fig. 2). Misalignment of the face gear may cause separation of the pinion-gear tooth surfaces and edge contact. To avoid these defects, it is necessary to localize the bearing contact by substituting the instantaneous line contact of tooth surfaces by point contact. The localization of the bearing contact can be achieved: (i) by choosing a shaper whose tooth number N~ is slightly larger than the pinion tooth number N,, (Ns- N, = 1-3) [4]; (ii) by crowning of the pinion tooth surface as proposed in this paper",
            " The location and orientation of the axes of meshing in this particular case is as shown in Fig. 4. Axis of meshing I-I lies in plane x~ ~) = 0, and its orientation is determined as Z \") N2 y~l) Ns (2) Meshing of orthogonal offset face-gear drive 91 Axis of meshing II-II is parallel to Zh but lies in a plane x~ \") that approaches infinity along the negative direction of Xh. 4. EQUATION OF TOOTH SURFACES 4.1. Applied coordinate systems Movable coordinate systems Ss and $2 are rigidly connected to the shaper and the face gear, respectively (Fig. 2). Coordinate systems Sh and S~ are the fixed ones. This surface is represented in coordinate system Ss (Fig. 5) by the equation I+rbs[sin(Oks+OoO--Okscos(O~-~+Oo,)]l r~(u, 0~..,) = --rbs[COS(0~-,~ + 0os) + 0k.~ sin(0k, + 0o0] \" (3) ffs Here, (0ks, us) are the surface parameters; rbs is the radius of the base circle, and 0o~ determines the width of the space of the shaper on the base circle (Fig. 5). In the case of a standard shaper, 92 F.L. Litvin et al. parameter 0o~ is represented by the equation 7~ 0o~ = 2N---~ - inv~o (4) where ~0 is the pressure angle",
            " The first one requires simultaneous consideration of the equations of the surfaces of both sides of the face-gear tooth and the determination of the area where both surfaces have a common point. The other one is based on the consideration of cross-sections of tooth profiles of the shaper and the face gear. Both approaches have been applied by the authors; the results are compared but only the second one, the simpler one, is presented in this paper. This approach is based on the following considerations: (1) Drawings of Fig. 5 show that xs = 0 is the plane of symmetry of the shaper space. At a position of the shaper when \u00a2~ = 0, coordinate system & coincides with Sh (Fig. 2) and the axis of meshing I-I belongs to the plane x~ = 0. (2) It is evident that cross-sections of the shaper tooth surface, produced by planes that are parallel to xs axis, represent the same involute curves. Two such planes, H~ and I-I_,, are shown in Fig. 6(a). Plane Hi which is perpendicular to zs (it is parallel to x0 intersects the axis of meshing I-I at a point P~ that belongs to the axis of symmetry of the cross-section of the space of the shaper. Figures 6(b) and 7 show points P~ and P2 of the intersection of the axis of meshing I-I planes HI and I-I2, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001908_jes.0b013e31803ec43e-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001908_jes.0b013e31803ec43e-Figure1-1.png",
        "caption": "Figure 1. Positioning of predefined points of the tennis racket in a static backhand position into the laser beam. The ball machine trajectory was adjusted to hit the laser beam at the racket head level.",
        "texts": [
            " Because the dimension of the integrated rectified acceleration (mIsj1) can easily be confused with the quantity \u2018\u2018velocity,\u2019\u2019 the dimension of the acceleration integrals in this manuscript is given in arbitrary units or is normalized to a reference condition. The ball contacted the racket head at center and off-center locations, which influences the mechanical behavior of the ball-racket-arm system. A ball machine was placed at a distance of 1 m in front of the racket face to achieve a high accuracy in the location of the impact. A helium-neon laser, which produces a visible red light beam, was positioned at a location opposite the ball machine. The laser beam was used to guide the subject in positioning the racket at the desired location (Fig. 1). The point of impact was determined in a plane perpendicular to the floor, where the center of the impacting ball (velocity, 14 mIsj1) and the laser beam coincided. Volume 35 \u25cf Number 2 \u25cf April 2007 Interaction Between Arm, Tennis Racket, and Ball 63 Copyright @ 2007 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited. Off-center ball impacts resulted in approximately threefold greater vibration magnitudes compared with center impacts. There were large differences in acceleration values between different racket constructions",
            " Three of the rackets had the same carbon fiber construction material, and the only difference between these rackets was the distribution of material across the frame. For one racket, a carbon fiber material with a higher modulus of elasticity was used. The rackets were strung with an identical nylon material at the same string tensions (280 N/270 N). Racket stiffness was estimated from the resonance frequency of the rackets using a Fourier analysis of the free vibrating rackets; a higher resonance frequency corresponds to a stiffer racket. The experimental setup was almost identical to the one described in Figure 1. Rectified acceleration integrals were determined at the wrist for ball impacts at center and an offcenter location on the racket head. Especially for the off- center location, there was a frequency-dependent transfer of vibration to the body. The vibration load at the wrist was reduced with an increase in racket stiffness (higher resonance frequency) (Fig. 2). Stiffer rackets absorb less energy during tennis strokes, resulting in higher ball rebound velocities. Less energy absorption by the racket likely results in lower racket vibration amplitudes and thus less vibration transfer to the human body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003587_j.jfranklin.2018.01.032-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003587_j.jfranklin.2018.01.032-Figure1-1.png",
        "caption": "Fig. 1. Stewart manipulator (SM) and fixed coordinate system for task space generalized states.",
        "texts": [
            " Published by Elsevier Ltd. All rights reserved. Please cite this article as: H. Navvabi, A.H.D. Markazi, Position control of Stewart manipulator using a new extended adaptive fuzzy sliding mode controller and observer (E-AFSMCO), Journal of the Franklin Institute (2018), https://doi.org/10.1016/j.jfranklin.2018.01.032 2 H. Navvabi, A.H.D. Markazi / Journal of the Franklin Institute 000 (2018) 1\u201327 1. Introduction Stewart Manipulator (SM) is a parallel robot with 6 degrees of freedom (DOF), as shown in Fig. 1 . It consists of two plates named Moving Platform (MP) and Bottom Platform (BP) that are connected to each other with six arms. The remaining six links appear differently in the, so-called, 6-UPS 1 and 6-SPS 2 manipulator types. In the 6-UPS types, the arms are connected to MP by spherical joints and to the BP by universal joints or vice versa. However, in the more common 6-SPS types, the arms are connected to the MP and BP by spherical joints. The actuators are located on prismatic joints, i.e",
            " ( P ) \u0308P + V ( P, \u02d9 P ) \u02d9 P + Q ( P ) = J T ( P ) u (1) here, M(P) \u2208 R 6 \u00d76 is the mass matrix, V ( P, \u02d9 P ) \u2208 R 6 \u00d76 is the Coriolis and centrifugal orce matrix, Q (P) \u2208 R 6 \u00d71 is the gravity effect, J(P) \u2208 R 6 \u00d76 is the Jacobian matrix of he SM, u \u2208 R 6 \u00d71 is the control input vector, i.e., the force vector of the actuators, and = [ x y z \u03b1 \u03b2 \u03b3 ] T is a position and orientation vector of the MP in the fixed oordinate system. Fixed coordinate system, XYZ, is defined at the center of BP, as shown n Fig. 1 . The matrices M, V and the vector Q involve the effects of the MP, as well as, the egs. By algebraic operations, the effects of the MP and the legs can be separated to distinct erms [6] , as shown in Eq. (2 ). M up + M legs ) P\u0308 + ( V up + V legs ) \u02d9 P + ( Q up + Q legs ) = J T u (2) Matrices associated with MP, i.e., M up , V up and Q up , are simple and straight-forward to btain, as derived in the Appendix. The leg-dependent matrices, i.e., M legs , V legs and Q legs , owever, are much more complicated, and cannot be obtained in an explicit form, as shown in he Appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002696_e2013-02067-x-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002696_e2013-02067-x-Figure6-1.png",
        "caption": "Fig. 6. Creation of a single barrier inside the micro-channel: a) Modification of the molding form with focused ion beam lithography leads to small slits in the surface of the mold. b) In the PDMS-cast, these slits result in U-shaped, step-like barriers inside the channel. c) Atomic force microscope image of the barrier. The dimensions of the structure are 3\u03bcm in width and 500 nm in height. In the center of the U-shape, the height of the barrier is about 250 nm. This ensures that the particle transport through the center of the structure is favored. Also, the edges of the barrier are smoothed out through the casting process, leading to a parabolic-like cross section of the barrier. This justifies the choice of the parabolic potential used in the numerical simulation.",
        "texts": [
            " For the experiments presented in this section, we use the same setup as described in section 1.2. To alter the particle transport, small barriers are placed inside the channel. This is achieved by processing the molding form with a focused ion beam which leads to tiny slits in the surface of the mold, resulting in a perpendicular, Ushaped barrier inside the PDMS-cast. Due to the U-shape, the barrier is higher at the edges of the structure which results in a higher transmission probability of particles through the center of the barrier (see Fig. 6). The unconventional shape of the barrier is chosen for two reasons. In experiment and simulation, the particles are ordered in three lanes along the channel walls (one line close to each channel wall, one in the middle of the channel). To ensure that transport occurs only through the middle of the barrier, the outer lanes are blocked with the higher parts of the barrier. This also reduces the effect of sticking particles, which tend to be found more often at the walls than in the center of the channel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000691_1.2826900-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000691_1.2826900-Figure3-1.png",
        "caption": "Fig. 3 (a) Canonical graph representation of an epicyclic gear mecha nism, {b) linl(-to-link adjacency matrix of (a)",
        "texts": [
            " Theoretically a gear pair between two planets can be either external or internal. However, for all the EGMs studied, only external gear meshes between planets have been found. Therefore to keep the sketching algo rithm simple, we shall assume that a heavy edge connecting two vertices at the second level represents an external gear pair. In the adjacency matrix, an internal gear pair will be represented by a upper case G, an external gear pair will be represented by a lower case g, and a revolute joint will be represented by its edge label. Figure 3(b) shows the adjacency matrix for the canonical graph representation shown in Fig. 3(a) . If we remove the first row and the first column corresponding to the root, we can divide the remaining matrix into four sub-matrices marked I, II, III, and IV in Fig. 3(b) according to the vertex level distribu tions. Since the adjacency matrix is symmetrical, the submatrices III and IV are transposes of each other. All elements in the submatrix I are zero, since there can be no connections among the first level vertices. The submatrix II gives the interac- Journal of Mechanical Design SEPTEMBER 1996, Vol. 118 / 405 Copyright \u00a9 1996 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 06/08/2015 Terms of Use: http://asme.org/terms T5 6T (c) (d) tion among the second level vertices"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002600_1.4004962-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002600_1.4004962-Figure3-1.png",
        "caption": "Fig. 3 Geometry of contacting bodies",
        "texts": [
            " The contact force (Q) is Q \u00bc E 1 1 M 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3rhi 1:5 2K pl 3P q vuut rhi \u00f0N\u00de (11) Hence the nonlinear stiffness associated with point contact is k \u00bc E 1 1 M 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3rhi 1:5 2K pl 3P q vuut (12) Here P q is the sum of curvatures. This sum obtained from Harris [17] is as following: X q \u00bc qI1 \u00fe qI2 \u00fe qII1 \u00fe qII2 \u00bc 1 rI1 \u00fe 1 rI2 \u00fe 1 rII1 \u00fe 1 rII2 (13) Two bodies of revolution having different radii of curvature in a pair of principle planes passing through the contact between the bodies may contact each other at a single point under the condition of no applied load. Such a condition is called point contact. Figure 3 demonstrates this condition. The parameters rI1, rI2, rII1, rII2, qI1, qI2, qII1, qII2 are dependent upon calculations referring to the inner and outer races. If the inner race is considered, rI1 \u00bc D=2; rI2 \u00bc D=2; rII1 \u00bc r; rII2 \u00bc r and qI1 \u00bc 2=D; qI2 \u00bc 2=D; qII1 \u00bc 1=r;qII2 \u00bc 1=r (14) If the outer race is considered, the parameters are rI1 \u00bc D=2; rI2 \u00bc D=2; rII1 \u00bc R; rII2 \u00bc R and qI1 \u00bc 2=D;qI2 \u00bc 2=D; qII1 \u00bc 1=R;qII2 \u00bc 1=R (15) The parameters are calculated from the Harris [17] as For inner race qI1 \u00bc qI2 \u00bc 0:25220 qII1 \u00bc 0:06437; qII2 \u00bc 0:06451 mm\u00f0 \u00de 1 For outer race qI1 \u00bc qI2 \u00bc 0:25220 qII1 \u00bc 0:04261; qII2 \u00bc 0:04255 mm\u00f0 \u00de 1 (16) The value of (2K=pl) is needed to find the stiffness at point contact from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002120_j.proeng.2010.03.202-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002120_j.proeng.2010.03.202-Figure6-1.png",
        "caption": "Fig. 6. Finite element model (a), contact pressure distribution (b) and simulation of a rolling pass (c)",
        "texts": [
            " In the first one\u2014analytic calculation\u2014 subsurface stresses were calculated by means of Hertzian contact theory, hence only elastic material properties were taken into account. Fatigue life was calculated by using equation (9). This was also done by the program SDAL. In the second approach subsurface stresses were calculated by means of finite element analysis and fatigue life was also calculated by means of stress-life theory\u2014equation (9). In third approach finite element analysis was used for calculation of subsurface strains and fatigue life was calculated by means of strain-life theory\u2014equation (14). The finite element model, shown in Fig. 6a, represents a segment of an inner ring. Fixed boundary conditions were applied to the bottom surface and contact pressure was applied to the raceway by means of a function describing pressure distribution according to the Hertzian contact pressure as shown in Fig 6b. Rolling (loading and unloading) was simulated by displacing pressure distribution as shown in Fig 6c. The function is defined as: , (15) where is maximum contact pressure and and are major and minor semi axes of a contact ellipse defined by Hertzian contact pressure. Values of , and were calculated with a program SDAL as a part of calculation of maximum contact force acting on the raceway. Inner ring was chosen to be critical because of its convex shape, which means that the same contact force results in higher contact pressure on inner raceway than on the outer raceway. Distribution of contact forces along the perimeter of the raceway for non-deformed and deformed bearing ring geometry is shown in Fig 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002676_1.4006791-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002676_1.4006791-Figure1-1.png",
        "caption": "Fig. 1 The three toroid geometries: SHTV (a), SFTV (b), and DFTV (c)",
        "texts": [
            " As a basic distinction among the toroid geometries, we consider the possibility to arrange one single roller or a pair of counter-rotating Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 12, 2011; final manuscript received May 2, 2012; published online June 7, 2012. Assoc. Editor: Prof. Philippe Velex. Journal of Mechanical Design JULY 2012, Vol. 134 / 071005-1Copyright VC 2012 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use rollers inside the toroidal cavity (see Fig. 1). We then refer, respectively, to the single-roller or to the double-roller geometry. The former class includes the half- and full-toroidal variators, which differ for the value of the cone angle h. h ranges from 50 deg to 70 deg in the case of the SHTV (Fig. 1(a)) with an optimal value close to 60 deg [13]. The angle h is equal to 90 deg for the SFTV and DFTV variators (see Figs. 1(b) and 1(c)). Figure 1(c) shows the working principle of the DFTV variator: A pair of counter-rotating conical rollers in contact with each other is placed inside a full-toroidal cavity, combining the main advantages of the SHTV and SFTV. Indeed, as shown below, the DFTV leads to a strong reduction of the spin losses (as in the case of the SHTV) and does not need the presence of thrust bearings (as in the case of the SFTV). This in principle should allow to get much better efficiency. We observe that the toroidal variators can be provided with a number m of cavities and n rollers (or pair of rollers in the case of the DFTV)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000899_156855304773822464-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000899_156855304773822464-Figure2-1.png",
        "caption": "Figure 2. Model de nition.",
        "texts": [
            " Then, a new control law to ensure the above conditions, named the non-dissipative touchdown controller, is derived in Section 4. Simulation results and a discussion are also given. In addition, a new controller for asymptotic orbital stabilization to a desired period is proposed and two kinds of adaptation laws for input minimization are presented in Section 5. Section 6 gives a conclusion of the paper. We consider exactly the same model of passive running robot as in Ref. [13] in this paper. In this section, the mathematical model is reviewed. Figure 2 shows the model of a planar one-legged running robot considered here. The robot is tted not only with a leg spring, but also a hip spring. We impose the following assumptions on this model as seen in much of the related literature. D ow nl oa de d by [ U ni ve rs ity o f B or as ] at 2 3: 48 0 4 O ct ob er 2 01 4 360 S.-H. Hyon and T. Emura (i) The center of mass (CM) of the body is just on the hip joint and the CM of the leg lies on the leg. (ii) The mass of the foot (unsprung mass) is negligible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003441_2.099309jes-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003441_2.099309jes-Figure2-1.png",
        "caption": "Figure 2. Exploded view of the flow-through biofuel cell showing each component. The arrow shows the direction of fluid flow. Fluid ports (in blue) are shown inserted into the middle and top PMMA layers.",
        "texts": [
            " The ELAT electrode was heatpressed to the Nafion membrane using a Carver hydraulic press with an electric resistance heater (Specac) attached to it. The carbon cloth and Nafion were pressed together at 10,000 lbs-force and 140\u25e6C for 3 minutes. The Nafion side of the cathode was soaked in concentrated sulfuric acid (H2SO4) overnight before experiments. Figure 1 is a schematic showing the layout of the anode and cathode within the biofuel cell and the reactions that occur at the electrodes. The flow-through biofuel cell (Figure 2) consists of layers of PMMA and two different types of soft silicone gaskets. The device footprint measures 70 mm \u00d7 45 mm. The top and bottom PMMA sheets are 9 mm thick (Acrylic FF Clear, Regional Supply, Salt Lake City, Utah) and the middle PMMA sheet is 6 mm thick (Optix Acrylic Clear, Plaskolite, Columbus, Ohio). The middle silicone sheet (Bisco HT-6135, Stockwell Elastomerics, Inc., Philadelphia, Pennsylvania), is 0.38 mm thick and is used to retain and seal around the platinum foil current collector",
            " All layers and necessary fluid channels were designed in Solidworks and then cut using a CO2 laser cutter (Versa Laser, Universal Laser Systems). Bolt holes, outside profiles, cathode air openings, and fluid channels were cut in the same operation by specifying different laser speeds and intensities for each feature. After the sheets were cut, threaded holes were tapped by hand. This two-step fabrication process was rapid enough to quickly fabricate 6 design revisions before making the final design. As shown by the arrow in Figure 2, the fluid inlet port (part number K10-1, Value Plastics, Inc., Fort Collins, Colorado) is on the right and the outlet port is on the left. In order to prevent bubbles from becoming trapped under the anode, it is necessary to first assemble ) unless CC License in place (see abstract).\u00a0 ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 138.251.14.35Downloaded on 2014-12-04 to IP the lower portion of the biofuel cell, from the bottom PMMA sheet up to the thinner silicone gasket, and then fill the lower portion with fuel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000770_s0005-1098(01)00066-8-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000770_s0005-1098(01)00066-8-Figure1-1.png",
        "caption": "Fig. 1. Two-layer NN. Fig. 2. Backlash nonlinearity.",
        "texts": [
            " We use a backstepping approach (Krstic, Kanellakopoulos, & Kokotovic, 1995) with a \"ltered derivative to derive a compensator that has a neural network in the feedforward loop. We show detailed analysis using a real \"lter needed to calculate the derivative of the signals used in inverse dynamics design. The NN is used for compensating the dynamic inversion error. A modi\"ed Hebbian tuning algorithm for the NN is designed in order to simplify the computational burden in multi-axes mechanical systems with backlash. It o!ers computational advantages over gradient descent based algorithms. The two-layer NN in Fig. 1 consists of two layers of tunable weights and has a hidden layer and an output layer. The hidden layer has M neurons, and the output layer has m neurons. By collecting all the NN weights vl , w l into matrices < , = , the NN equation with linear output activation function, may be written in terms of vectors as y\"= (< x). (2.1) The thresholds are included as the \"rst column of the weight matrix < ; to accommodate this, the vector x needs to be augmented by placing a &1' as their \"rst element (e.g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002396_robot.2010.5509412-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002396_robot.2010.5509412-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor helicopter configuration frame system",
        "texts": [
            " To the authors\u2019 best knowledge this is the first time that a CFTO\u2013control scheme is designed and experimentally applied for attitude control of a UqH under the effect of atmospheric turbulence. This paper is structured as follows. In Section II, the modeling approach for the UqH is presented while in Section III the design and the development of the CFTO\u2013control scheme is analyzed. In Section IV, the experimental results that prove the efficacy of the proposed scheme are presented, followed by conclusions. The modeling of the Unmanned quadrotor Helicopter shown in Figure 1, assumes that the structure is rigid and symmetrical, the center of gravity and the body fixed frame origin coincide, the propellers are rigid and the thrust and drag forces are proportional to the square of propeller\u2019s speed. The UqH\u2019s nonlinear dynamics [11] is characterized by a set of twelve high non\u2013linear state equations in the form: X\u0307 = f (X,U)+W (1) with f a non\u2013linear function, W corresponds to the additive effects of the environmental (wind) disturbances, X the state vector, and U the input vector, where: X = [\u03c6 \u03c6\u0307 \u03b8 \u03b8\u0307 \u03c8 \u03c8\u0307 z z\u0307 x x\u0307 y y\u0307] (2) U = [U1 U2 U3 U4 \u03a9r] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001861_s11721-008-0012-6-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001861_s11721-008-0012-6-Figure2-1.png",
        "caption": "Fig. 2 S-bot: An autonomous, mobile robot capable of forming physical connections with other s-bots",
        "texts": [
            " We have written the rules by hand for the morphologies in this study. A compiler that automatically generates the rules for a desired morphology would, however, be trivial to implement for the type of structures that can be assembled with our robots. For our experiments, we use the innovative SWARM-BOT robotic platform (Mondada et al. 2004) created by Francesco Mondada\u2019s group at the Laboratoire de Syst\u00e8mes Robotiques of the \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne. The platform consists of a number of mobile autonomous robots called s-bots (see Fig. 2) that are capable of forming physical connections with each other. Thanks to its traction system that combines tracks and wheels, the s-bot has good mobility on moderately uneven terrain while still retaining the ability to rotate on the spot efficiently. The SWARM-BOT platform has been used for several studies, mainly in swarm intelligence and collective robotics (see, for instance, Dorigo et al. 2004, 2006; Trianni and Dorigo 2006). Overcoming steep hills and transport of heavy objects are notable examples of tasks which a single robot could not complete individually, but which have been solved successfully by teams of collaborating robots (Gro\u00df et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002125_tia.2009.2036534-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002125_tia.2009.2036534-Figure2-1.png",
        "caption": "Fig. 2. BEGA steady-state vector diagram at unity power factor. (a) Motoring mode. (b) Generating mode.",
        "texts": [
            " To avoid these During the unity power factor operation (with zero id and zero \u03c8q), from (1)\u2013(5), the steady-state d\u2013q equations of BEGA become vs =RsIqk + \u03c9rLmF iF , is = Iqk = const (6) te = 3 2 p1LmF iF Iqk (7) where Iqk = \u03a8q/Lq . Implicit unity power factor operation is obtained. The machine operation can be switched from motoring to generating in two ways: 1) by changing the sign of current, but in this case, the machine does not operate at unity power factor, and 2) by changing the sign dc excitation current. The vector diagram at steady state and unity power factor operation is shown in Fig. 2. For the prototype data in Table I, the saturation effect of d-axis flux, considering id = 0, is shown in Fig. 3. III. EXPERIMENTAL PLATFORM A set of experiments was carried out to prove the validity of the proposed solution (zero id and zero \u03a8q). The structure of experimental platform is shown in Fig. 4. The IM was driven by an ABB ACS600 bidirectional converter. The rated power of IM was 5.5 kW at n = 2945 r/min, enough to fully load BEGA. A four-quadrant dc\u2013dc converter with Idc_rated = 5 A and Vdc_rated = 48 V was built for current control in the dc field winding",
            " The total copper losses versus electromagnetic torque at id = 0 and different i\u2217q values, taking into account the saturation effect in the d-axis, are shown in Fig. 7 and are expressed as follows: Pcopper = 3i2qRs + i2F RF = 3i2qRs + ( te LmF (iF )iq )2 RF . (12) Fig. 7 shows that the proposed simplified current referencer reduces the total copper losses at minimum. The dotted red line in Fig. 7 represents the minimum losses that can be achieved using the proposed current referencer (Fig. 6). A theoretical analysis of the effect of the current referencer on the BEGA power factor during operation is done in what follows. As shown in Fig. 2 for peak torque values (iq = Iqk and id = 0), during BEGA operation, unity power factor is achieved. In addition, for low and very low torque levels, the unity power factor operation is possible, but with efficiency penalty. By using the current referencer (Fig. 6), for lower torque levels, the unity power factor cannot be maintained anymore, so we are interested to see how much the power factor degradation is. The BEGA power factor angle (\u03d5), at id = 0, can be expressed as \u03c6 = a sin \u239b \u239d \u03c9r(Lqiq\u2212\u03c8PMq)\u221a [\u03c9r(Lqiq\u2212\u03c8PMq)] 2+[(Rsiq+\u03c9rLmF iF )]2 \u239e \u23a0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure2-1.png",
        "caption": "Fig. 2. Elastic plastic stress distributions from (a) von Mises and (b) Tresca for a hollow disc rotating at similar speeds",
        "texts": [
            " The numerical procedure was initiated by dividing the wall into N 40 equal step lengths of h 5 mm, and allowing an error of ER 0:05 in the unity value of eq. (13). An iterative procedure was followed in which N was doubled (while h and ER were halved) until the difference in the interface radius between successive iterations was less than 1 mm. For example at the speed quoted four iterations gave rep 95:3125 mm for N 640 (h 0:3125 mm) and rep 95:156 mm for N 1280 (h 0:15 625 mm). This ensured the required match in both sr and sq at the interface. Fig. 2a shows the distribution in each normalised stress in which sr=Y 0 to match the stress free boundaries and sq=Y 1 for r ri. It is seen that by von Mises sq=Y increases along with sr=Y within the plastic zone. Whilst sq=Y reaches a maximum at rep, sr=Y reaches its maximum within the elastic zone where stresses conform to the Lam e distribution. In contrast, the Tresca distributions (Fig. 2b) show that within the plastic zone sq Y is constant and sr attains its maximum value. Tresca also predicts a greater spread of plasticity (rep 136:875 mm, rep=ri 2:738) than von Mises at similar speeds. These differences influence the normalised distributions of residual stress sRq =Y and sRr =Y for each criteria in the manner shown. We shall see later how residual stress are put to advantage when a disc rotates at its normal elastic speed. Figs. 3a, b present further comparisons between the two criteria for a fully plastic disc of similar dimensions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure4-1.png",
        "caption": "Figure 4. (a) A ladder of $~3's with a linear dependence of h-value with x resulting from the combination of a screw with an oblique prismatic pair. (b) The order of placing the pairs does not matter.",
        "texts": [
            " 3(b), one of them may have h =0) may be combined in the same cylindroid as a third ISA with h=oo and inclined at some angle e, not necessarily 90 \u00b0, to the plane containing the other two. In this section the reverse operation will briefly be demonstrated, namely that the combination of a prismatic pair P23 (placed anywhere in a member) with a screw pair $12 results in a comparable tapered ladder perpendicular to the plane defined by $12 and P23. $~3 must then lie along some rung of this ladder. Figure 4(a) should speak for itself, since nothing more is involved than the resolution of vectors along and transverse to $~2, leading to Only with St2 inactive (i.e. with o~t2 =0) wiU $t3 lie parallel to $23. Provided that ~#90 \u00b0 there will only be one rung for which ht3 =0, namely where x = - h i 2 tan :~. (9) A comparable ladder results when a revolute pair Rt , , with hi2 =0, (instead of the screw pair S~2) is combined with a prismatic pair. Finally one notes that the order of the pairs could have been reversed, as in Fig. 4(b), without any change in the form of the ladder for the instant considered, though the gross motion e ra mechanism containing these pairs would, of course, be affected if they were interchanged. 2.6. This combination of a P- and S-pair is now examined a little further before applying it. (a) If ~=0 (or 180\u00b0), the combination becomes a C-pair, The whole ladder is effectively condensed to negligible length, all rungs being available at the same axis, that of the C-pair. Effectively this combination is at the end of a degenerate cylindroid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.7-1.png",
        "caption": "Figure A.7 Vector A and its direction with respect to the coordinate axes.",
        "texts": [
            " 14) where A,, A,, A, are the scalar components of A in the 2 , y, 2 directions, respectively, and A,?, Ay$, Az2 are the vector components of A in the three directions 2 , $, 2, with 2 2 112 + I O P ~ = Irl = T = ( x2 + y + z ) . - -+ + (A. 15) 2 112 /A] = A = [Ax2 + AY2 + A , ] . Observe from Figure A.6 that - - + PP\u2019= 0 P \u2019 - OP = de element of vector displacement. Thus 12 = r\u2018 - r = dx it + dy y + dz S (A. 16) with ldel = d t = [ ( d ~ ) ~ + (dy)\u2019 + ( d ~ ) ~ ] \u201d ~ , as before. Consider a vector A defined at 0 (i.e. O P = A) as shown in Figure A.7. The algebraic expression in terms of its components is given by (A.14). It is convenient to identify the vector by its orientation with respect to three orthogonal axes, namely by the angles a,, ay, and aZ (shown in Figure A.7). + VECTOR ALGEBRA 41 9 The direction cosines of the vector A are defined by A, cosa, = - A A, coscry = A A, A \u2019 COSQZ = - and thus 2 2 2 cos Q, + cos ay + cos az = 1. (A.17) (A. 18) and vector components of PI P2; (2) the unit vector in the direction of PI P2; ( 3 ) the direction cosines of the unit vector in (2) that are the same as those of PI P2; (4) the angles between PI P2 (or the unit vector PI P2) and the coordinate axes x, y, and z . + + + + + - 420 VECTORS AND VECTOR ANALYSIS For an arbitrary origin the geometry of PI and P2 and other parameters are as shown in Figure A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003227_s11071-014-1701-x-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003227_s11071-014-1701-x-Figure6-1.png",
        "caption": "Fig. 6 Simulation results of phase diagrams, Poincar\u00e9 maps, Lyapunov exponent and fractal dimension obtained for gear center at s = 2.00 (l\u2217 = 0.3) in the horizontal direction (xg). a Phase diagram, b Poincar\u00e9 map, c Lyapunov exponent, d fractal dimension",
        "texts": [],
        "surrounding_texts": [
            "3.1 Analytical tools for observing nonlinear dynamics The analytical tools used for observing nonlinear dynamics of the gear-rotor\u2013bearing system with rubimpact effect in this study are dynamic trajectories, Poincar\u00e9 maps, bifurcation diagram, Lyapunov exponent and fractal dimension. We can check the dynamic trajectories and Poincar\u00e9 maps for each bifurcation parameters to clarify the more detailed dynamic behaviors. Then, a bifurcation diagram summarizes the essential dynamics of the system and is therefore a useful means of observing its nonlinear dynamic response at this step. Finally, maximum Lyapunov exponent and fractal dimension are used as the most useful tools to detect chaotic motions for nonlinear dynamical systems. The basic principles of each analytical tool are reviewed in the following subsections."
        ]
    },
    {
        "image_filename": "designv10_10_0000970_60.815064-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000970_60.815064-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of a synchronous machine during an internal single phase to ground fault.",
        "texts": [
            " The method for calculating the self and mutual inductances of the faulted winding of the synchronous machine is based on the analysis presented in [I], [Z], [5], [6], [7]. In this paper single phase to ground faults and two phase to ground faults will only be covered. However, the analysis can be easily extended to cover all kinds of internal faults. 11. INTERNAL SINGLE PHASE To GROUND FAULTS A schematic representation of a synchronous machine with two damper coils during an internal single phase to ground fault in phase a is shown in Fig. 1. It is assumed that the armature winding of a synchronous machine consisting of 2 parallel paths per phase is tapped at a certain point of one of the parallel paths of phase a. The tapped parallel path is divided in two parts, one part is adjacent to the neutral, which will be referred to as the rn winding, and the second part adjacent to the machine terminal, which will be referred to as the n winding. The remaining, I - 1, parallel paths of phase a are lumped into one equivalent winding that will be referred to as the p winding. In direct phase quantities, the performance of a synchronous generator, during an internal single phase to ground fault, connected to an infinite busbar through a short transmission line, Fig. 2, can be described by equations given below. A . Voltage Relationships The position of the rotor at any instant is specified with reference to the axis of phase a by the angle 0, Fig. 1. In terms of flux linkages, $1, voltage relationships for the stator and rotor circuits, e l , are linked with the winding resistances, RI , and instantaneous currents, ~ l , as follows: 0885-8969/99/$10,00 0 1998 IEEE 1307 - Lp Mpm Mpn M p b Mpc Mpf M p k d M p k q - Mmp Lm Mmn Mmb Mmc Mmf M m k d M m k g Mnp Mnm Ln Mnb M m Mnf M n k d hfnkq M b p Mbm Mbn L b Mbc Mbf M b k d Mbkq Mep Mcm Mcn Mcb Lc Mcf M e k d M c k q Mfp M f m M f n M f b Mfe Lf M f k d 0 MkdpMkdmMkdnMkdbMkdeMkdf L k d 0 L1 = ~ ~ k q p ~ k l m M k l n M k q b M k g c 0 0 L k q - P m n b c f kd kq The LI matrix can be viewed as having two parts, a healthy part and a faulty part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002382_jmor.10748-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002382_jmor.10748-Figure2-1.png",
        "caption": "Fig. 2. A mechanical model of the elbow joint and the effect of lever arm of m. triceps brachii. (A) A forelimb during the stance phase, and (B\u2013D) the lengths of lever arms (l) varying with the elbow joint angles (y). The lever arm increases from B to C, but decreases from C to D, while the elbow joint angle increases from B to D. Abbreviations: Fa, forearm skeletons; GRF, ground reaction force; Hm, humerus; Sc, scapula; O, pivot of elbow joint; P, the most distant point of the olecranon; S, shoulder joint; W, wrist joint; F, force vector obtained by triceps muscle; l, lever arm of triceps muscle; s, torque on the elbow joint obtained by F. OP, OS, and OW represents the shaft of olecranon, humerus, and forearm, respectively. Angles y, q, and /, represents elbow joint angle (angle SOW), olecranon orientation (angle POW; constant), and orientation of olecranon to humeral shaft (angle SOP), respectively. The distance OW shows the minimum lever of the forelimb, neglecting the functional lengths of the carpus and metacarpus.",
        "texts": [
            "10748 2009 WILEY-LISS, INC. but very few examples have been reported (Knussmann, 1967; Van Valkenburgh, 1987; Drapeau, 2004; Shockey and Flynn, 2007). These studies suggested that mammals having an upright posture (extended elbow joint) should have a caudally oriented olecranon, whereas mammals having a crouched posture (flexed elbow joint) should have a proximally oriented olecranon, because the lever arm of the extensor muscle, such as the m. triceps brachii, at these elbow angles is maximized (Fig. 2B\u2013D). This assumption was applied for reconstructing the forelimb posture of extinct taxa such as Thomashuxleya and Amsotemnus (Notoungulata, Mammalia; Shockey and Flynn, 2007). However, the assumption lacked quantification and rigorous testing based on known elbow joint angles of extant animals. Also, a comparative analysis of its consistency among extant taxa is required, before it can be applied as a reliable model to reconstruct specific elbow joint angles of extinct animals during their terrestrial locomotion",
            " Quadruped mammals tend to keep their forelimb joint within a limited range of angles during the stance phase of terrestrial locomotion (Goslow et al., 1981; Inuzuka, 1996; Fischer et al., 2002). Triceps muscles play an important role in maintaining the elbow joint angle during propulsion (Cohen and Gans, 1975; Jenkins and Weijs, 1979; Tuttle and Basmajian, 1983; Gregersen et al., 1998; Wickler et al., 2005). During the stance phase, the ground reaction force induces gravitational collapse of standing joints (Fig. 2A), and the triceps muscles contract against the ground reaction force, thereby applying joint torque against the collapse. In most extant quadruped mammals, such as the Virginia opossum (Didelphis virginiana, Didelphiomorphia), the dog (Canis familiaris, Carnivora), the brown rat (Rattus norvegicus, Rodentia), the gorilla (Gorilla gorilla), and the horse (Equus caballus, Perissodactyla), regardless of their gait, the triceps muscles contract starting from the end of the swing phase or from the beginning of the stance phase ending in approximately two-thirds of the stance phase or at the end of the stance phase (Cohen and Gans, 1975; Jenkins and Weijs, 1979; Tuttle and Basmajian, 1983; Gregersen et al",
            ", 1998; Wickler et al., 2005). The extending torques in the elbow joints of both small and large therian mammals, such as cavy (Galea musteloides, Rodentia), pika (Ochotona rufescens, Lagomorpha), common treeshrew (Tupaia glis, Scandentia), and horse (E. caballus, Perissodactyla) are the greatest at about one-third of the stance phase (Witte et al., 2002; Dutto et al., 2006). The triceps muscle originates from the caudal margin of the scapula or humeral shaft, and runs approximately parallel to the humeral shaft (Fig. 2A). The force vectors obtained by each muscle head are applied to the olecranon. The resultant force vector of all extensors at the elbow joint acts together along a line nearly parallel to the shaft of the humerus. Forces at the elbow joint may be determined by a simple model. In a forelimb of a typical terrestrial animal, the extending torque (s) of the elbow joint is s \u00bc l F where F is the resultant force of the extensors acting on the most distant point on the olecranon process (P), which represents the lever of the extensors, and l is a perpendicular line from the center of elbow joint rotation (O) to the line of F (Fig. 2A). The elbow joint angle (y) is the angle between OS and OW, where S is the pivot of the shoulder joint, and W is the distal end of the forearm (Fig. 2A). The line OW is a minimum measure for the length of the lever arm of the external force that can act against the autopodium, thereby flexing the elbow joint. The value of the angle between OP and OW (angle q), which is defined by the morphology of the ulna, is constant and determined by the individual, and partly by the taxon and the growth stage. The angle between OS and OP (angle /) depend on the elbow joint angle (y) and the olecranon angle (q) as given by the following formula. u\u00fe q\u00fe / \u00bc 360 If the value of F is constant, vector F is perpendicular to OP, and l 5 OP, the extending torque (s) is maximized (Fig. 2C). In other words, the energy necessary for elbow joint extensor contraction during the stance phase is minimized when the vector F is perpendicular to OP (Fig. 2C). If the vector F is assumed to run nearly parallel to the humeral shaft, the elbow extensor is set in the most effective position, when the humeral shaft (OS) and olecranon process (OP) are perpendicular to each other (/ 5 908; Fig. 2C; Drapeau, 2004). The effect of the lever arm (l) decreases when / deviates from 908 (Fig. 2B\u2013D). The value of l can be calculated as follows: l \u00bc OP sin/ For example, the effect of the lever arm is reduced by half in length from its maximum value when sin/ 5 1/2 (/ 5 308 or 1508) (Fig. 2B,D). Orientation of the olecranon to the long axis of forearm (angle q) varies among tetrapods. This study focuses on the relationship between q and angle y (see Fig. 2), and is based on two assumptions; (1) the orientation of the triceps muscle contraction force is parallel to the humeral shaft; and (2) the triceps muscles of quadrupeds contract during the stance phase to stabilize the elbow joint Journal of Morphology against the inverse torque generated by the ground reaction force. The effect of the olecranon lever is maximized when the resultant force of the contracting triceps muscle (F) and the olecranon OP are perpendicular to each other. To determine the elbow joint angle (y) in the stance phase of quadrupedal animals, it is hypothesized that the humeral shaft (OS) is maintained nearly perpendicular to that of the olecranon process (OP) (when angle / is 908; Fig. 2C; Van Valkenburgh, 1987; Drapeau, 2004; Shockey and Flynn, 2007). The model described above was tested in three steps. In Step 1, the modal classes of the observed elbow joint angles (OEJ; y1) during the stance phase were collected from a variety of taxa with various body sizes. In Step 2, the olecranon orientations (q) were measured in forelimb skeletons of various taxa, and the estimated elbow joint angles (EEJ; y2) were calculated when olecranon and humeral shaft (angle /) became perpendicular to each other",
            " The individuals videotaped at Ueno Zoo were selected randomly for every measurement of a step cycle (see Supporting Information 1 for the number of individuals and species available for the study at Ueno Zoo). In addition to measurements obtained from the video clips, the elbow joint angles from 76 step cycles were collected from the literature (Table 1). To verify the data among a broad range of quadruped taxa, mammals of various taxonomic position and locomotor guilds were chosen (Table 1). The ideal period selected for measuring the elbow joint angles (y1) was the moment when the torque generated by the ground reaction force (Fig. 2A), flexes the elbow joint, and when the triceps muscle contracts against that flexing torque. These periods are mostly synchronous with the stance phase in both small and large mammals (Witte et al., 2002; Dutto et al., 2006). In this study, the entire stance phase was included in the measurements of OEJ (y1). In the literature, three different methods were used to measure the elbow joint angles (Table 1). Miller and Van der Meche\u0301 (1975) took measurements from cineradiographic images. Clayton et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001516_acs.940-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001516_acs.940-Figure5-1.png",
        "caption": "Figure 5. Data fusion for pitch and roll estimation.",
        "texts": [
            " The gyro signal \u2019yg is passed through a low-pass filter F1\u00f0s\u00de while the accelerometer measurement ya is passed through a low-pass filter F2\u00f0s\u00de: The estimate #y is given as #y \u00bc F1\u00f0s\u00de\u2019yg \u00fe F2\u00f0s\u00deya: The filters are such that sF1\u00f0s\u00de \u00fe F2\u00f0s\u00de \u00bc 1 where F1\u00f0s\u00de \u00bc 1 k\u00fe s and F2\u00f0s\u00de \u00bc k k\u00fe s For k \u00bc 0; F2\u00f0s\u00de \u00bc 0; and F1\u00f0s\u00de becomes a pure integration and #y diverges due to gyro drift. On the other hand, for k \u00bc 1; F2\u00f0s\u00de \u00bc 1; and F1\u00f0s\u00de \u00bc 0; and the data from the gyro are completely suppressed. The filter scheme is given in Figure 5. The filter parameter k has been selected in practice to obtain an estimate #y that is as close as possible to the actual value of y: Figure 6 Copyright # 2007 John Wiley & Sons, Ltd. Int. J. Adapt. Control Signal Process. 2007; 21:189\u2013204 DOI: 10.1002/acs shows the behaviour of the estimate #y compared with respect to the filtered accelerometer measurement ya when the angular displacement is slow. Figure 7 shows the behaviour of the estimate #y compared with respect to the filtered accelerometer measurement ya when the angular displacement is fast"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001589_ip-cta:20050362-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001589_ip-cta:20050362-Figure4-1.png",
        "caption": "Fig. 4 Diagram of the inverted pendulum",
        "texts": [
            " 153, No. 6, November 2006652 To illustrate the performance of the proposed modified AFCMAC, three applications shall be discussed. The first one is on the tracking of an inverted pendulum with friction. The second is on the one-link robotic manipulator [5, 18]. For the third example, the tracking problem for a thirdorder highly nonlinear system is attacked. The inverted pendulum consists of a thin homogeneous rod of mass m and length l, with a load of point mass mL attached to the end, as depicted in Fig. 4. Assume that friction torque exists in the joint that can be modelled [22] as bv\u00f0_q\u00de \u00bc tc sgn\u00f0_q\u00de \u00fe cv _q; _q= 0 te; _q \u00bc 0; jtej , ts ts sgn\u00f0te\u00de; _q \u00bc 0; jtej ts 8< : \u00f064\u00de where te denotes the external torque, tc is the Coulomb friction, ts is the breakaway torque and cv is the coefficient of viscous friction. Let q denote the joint angle. Euler\u2019s law can be applied to find the equations of 0 10 20 30 40 50 60 -50 0 50 e time, sec 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 0 50 -5 0 5 time, sec 0 10 20 30 40 50 60 0 5 10 15 20 time, sec 0 10 20 30 40 50 60 0 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-16-1.png",
        "caption": "FIGURE 11-16 Determination of the vertical location of the center of gravity using the weighing method,",
        "texts": [
            " Then (78) As a check, the reaction Rr may be found and the distance L \u20ac determined, Since most tractors are approximately symmetrical about the vertical plane perpendicular to the axles and passing midway between the wheels, the lateral location of the center of gravity will normally be quite close to this plane. Given the wheel tread setting, the lateral location may be found by weighing one of the sides of the tractor. Again weighing the other side can serve as a check. The measurements required for finding the longitudinal and lateral lo cations of the center of gravity are straightforward. However, the determi nation of the height, h = hit sin elt , is considerably more difficult. Again the weighing method can be used with either the front or rear axle elevated. Figure 11-16 illustrates the geometry involved in the following derivation, Summing moments about the rear axle, \u20ac' = RiL'/Wt MOMEKT OF IKERTIA DETERMINATION 305 But from the geometry of figure 11-16, e' = e cos A - h sin A Thus e cos A - h sin A (79) But L' = (L + ~r tan A) cos A (80) Substituting equation 80 into equation 79, diyiding by cos A, and solving for h, h = W/ - RiL ) _ R;~r WI tan A WI (81 ) The angle A is the only quantity in equation 81 that cannot be directly measured. However, A = Al + A2, where tan Al (n - r,)IL' ~rlL To eliminate the need for measuring L' for use in calculating tan AI, L' = VU + (~r)2 - (n - 1',)2 Two assumptions implicitly made in the preceding analysis should be pointed out: (1) the tires are assumed rigid, and (2) fluid shifts occurring in the fuel, coolant, and oil compartments when the tractor is tilted are ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002491_1350650111405111-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002491_1350650111405111-Figure1-1.png",
        "caption": "Fig. 1 Mini-traction machine",
        "texts": [
            " Oil E2 has the peculiarity that one of its additives is a very high-viscosity ester oil (1000 cSt at Table 1 displays some of the properties of the lubricants that can be extracted from the manufacturers\u2019 data sheets. The piezoviscosity coefficient according to Gold et al. [14] is also included. It is interesting to note that, while no particular relation between the viscosities and the base oil types can be discerned, large differences in the piezoviscosity coefficient roughly correspond to changes in base oil types. The traction tests were performed on the minitraction machine (MTM) schematically represented in Fig. 1. Simplifying the description, the machine Proc. IMechE Vol. 225 Part J: J. Engineering Tribology at CARLETON UNIV on June 23, 2015pij.sagepub.comDownloaded from presses a rotating steel ball onto a rotating steel disc while the contact is lubricated and it measures the resulting coefficient of friction. The roughness of the disc and ball test specimens was measured: the measured roughness was isotropic and the combined root mean square (RMS) roughness varied between 9 nm and 13 nm. The parameters independently controlled by the machine are the disc rotating speed, the ball rotating speed, the contact force between ball and disc, and the temperature of the oil bath"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003589_s12206-017-1210-1-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003589_s12206-017-1210-1-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of the experimental modal analysis setup for rolling element bearing [23].",
        "texts": [
            " The impulse signal was measured using a force transducer built into the impact hammer. The corresponding response was measured using a vibration sensor (Piezoelectric uniaxial accelerometer) attached by wax to the outer ring of the bearing [27]. The accelerometer measures from 0.01 to 10000 m/s2. The following procedures were performed to determine the dynamic characteristics of each rolling bearing separately: 1. The tested bearing was hung in a rigid support using an elastic rubber band as shown in Fig. 3. 2. Four repeated light impacts were implied to the outer ring of the bearing using an impact hammer. 3. The vibration response to each hammer blow was meas- ured using an attached accelerometer. 4. Both impulse and response signals were recorded and processed using a signal analyzer equipped with acquisition front-end. The analyzer arithmetically averaged the results of the four impacts to obtain the Frequency response function (FRF) plots. 5. The FRF plots were used to determine the dynamic characteristics of each bearing using the analysis explained in the forthcoming sections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002036_iecon.2009.5414696-Figure21-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002036_iecon.2009.5414696-Figure21-1.png",
        "caption": "Fig. 21. Thermographic picture of the coupling with two-degree misalignment.",
        "texts": [
            " The amplitude evolution of the 2x component in the horizontal velocity spectrum, as a function of the misalignment degree, can be observed in Fig. 19. The same figure also shows the increase of the 2x component depending on the motor load for different misalignment degrees. VI. THERMOGRAPHIC ANALYSIS To quantify the severity of the angular misalignment, their effects over the flexible coupling were analyzed by infra-red thermography. In Fig. 20 shows the temperature distribution on the coupling rubber for the aligned shafts. The thermographic picture for the two-degree misalignment case is shown in Fig. 21, where the great increase in the rubber temperature can be appreciated. 978-1-4244-4649-0/09/$25.00 \u00a92009 IEEE 1037 VII. CONCLUSIONS Effects of misalignment on an induction motor input currents were analyzed in the present effort. The results obtained from simulation show that misalignment produces sidebands in the stator currents at frequencies f + 2fr, and f \u2212 2fr. It was demonstrated through experimental results that the rotor curvature or deformation produces f \u00b1 fr components. This is mainly due to a combination of the air-gap static and dynamic eccentricity produced by misalignment but also due to the residual eccentricity of the motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000901_irds.2002.1041594-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000901_irds.2002.1041594-Figure3-1.png",
        "caption": "Figure 3: The geometric view of dynamic parameters.",
        "texts": [
            " k(t) = r,w,(t){cosO(t) - 112 tana(t)sine(t)} (4) P(t) = r,w,(t){sinO(t) + 1/2 tana(t)cosO(t)} ( 5 ) B(t) = (r,/L)w,(t)tano(t) (6) We also derive the actual radii of point masses ml and mz as follows. = Q, - h l s in+( t ) sgn (4 t ) ) (7) Q,* = R - (hzsind(t) +d(t)cosd(t))sgn(a(t)) (8) In this paper, we can easily derive the simplified dynamic equation by considering centrifugal forces and gravitational forces. The centrifugal forces occur due to the curvature of the trajectory path of the bicycle and load mass. The geometric view of the dynamic parameter +(t) which denotes the tilt angle of the bicycle is shown in Fig. 3. We simplify the model of the bicycle system for the purpose of analyzing and predicting its motion easily and it can be modeled as two point mass system. Let denote T,, and T,, as torques occurred by the centrifugal forces from the curvature of the path of mass point ml and mz. Then we can obtain following equations. Tm, = -Frn,ms+(t)hl (9) Tm, - - F m 2 m s + 1 ( t ) d m (10) where Fm, = mlR,wi , , , sgn (a ( t ) ) Fm9 = mzRm,wi,,,sgn(a(t)) +l(t) = +(t) + sin-'(d(t)/d-) Let denote T,, and T,, as torques occurred from the gravitational forces of mass points ml and mz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-34-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-34-1.png",
        "caption": "FIGURE 5-34 Automatic advance mechanism for distributor-type fuel-injection pump. (Courtesy Roosa Master.)",
        "texts": [
            " 118 ENGINE DESIGN The quantity of fuel delivered by each stroke of the pump is controlled by rotation of the piston. Rotation of the piston is controlled by a rack, which in turn is attached directly or indirectly to the governor. Spring-loaded de livery valves are incorporated in the nozzles to prevent dribbling of excess fuel into the cylinder after the injection stroke of the piston has been com pleted. Figure 5-33 illustrates a distributor system that incorporates pump, metering device, distributor, and governor in one unit. The timing principle is shown in the phantom views in figure 5-34. In function the distributor system and the in-line or individual pump system are the same. The difference is that the distributor system replaces the in dividual pumps with a single pump plus a distributor rotor. Also, the distrib utor system incorporates a governor in the housing. Because of the compact nature of a distributor-type pump, its principle of operation is more difficult to understand. The distributor pump, however, is like the individual pump system in that it performs the following function: 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure13.16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure13.16-1.png",
        "caption": "Fig. 13.16. Computation of two-dimensional cross section of region of attraction (RA)",
        "texts": [
            " For evaluation of multidimensional regions of attraction a method automating the computation and visualization of its two-dimensional cross-sections is implemented [83, 84]. Every locally 312 M.G. Goman, A.V. Khramtsovsky, and E.N. Kolesnikov stable equilibrium x\u03b5 in the open- or closed-loop system may have a bounded region of attraction. A number of two-dimensional RA cross-sections are generated by direct integration of the dynamical system (13.3). Initial conditions are taken from a grid of points on the two-dimensional cross-section plane P2 (see Fig. 13.16). Final destinations of the integrated trajectories are identified by checking whether they enter into a close proximity of one of the available attractors stored in the database or leave the state space region of validity of the mathematical model [83,88]. Grid points on the plane P2 are marked in accordance with the attractor which has been approached by the trajectory initiated in this point. The computed two-dimensional cross-sections allow one to determine critical disturbances leading to departure from the normal flight conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000600_02783640122067543-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000600_02783640122067543-Figure3-1.png",
        "caption": "Fig. 3. A prototype cell made up of a motorized pair of roller wheels mounted orthogonally.",
        "texts": [],
        "surrounding_texts": [
            "We built a prototype MDMS in which each cell consists of a pair of orthogonally mounted motorized roller wheels (Figs. 2 and 3). These wheels are capable of producing a force perpendicular to their axes while allowing free motion parallel to their axes. The combined action of the two roller wheels effects force in any planar direction to an object resting on top of the array. Each of these cells is connected to a large breadboard-style base (Fig. 4) to create a regular array of manipulators. Currently, we have 18 cells that can be arranged at UCSF LIBRARY & CKM on April 19, 2015ijr.sagepub.comDownloaded from arbitrarily in a two-dimensional grid. A photograph of the prototype MDMS is shown in Figure 5 (see Extension 11). Each cell is controlled by an inexpensive single-board computer based on the MC68HC11 microcontroller. We are exploring the use of distributed control on the MDMS because we believe that it would become impractical or impossible for a single centralized controller to control hundreds or possibly thousands of cells. Each cell communicates with its four neighboring cells, allowing messages to be passed along the array. In addition, each cell contains one (or more) binary sensors to detect the presence of an object. Figure 6 shows this control architecture. 1. Please see the Index to Multimedia Extensions at the end of this article. at UCSF LIBRARY & CKM on April 19, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-14-1.png",
        "caption": "FIGURE 11-14 The friction ellipse concept. (a) Tractive coefficient-slip relation, (b) the friction ellipse, (c) cornering coefficient-slip angle relation, and (d) tractive and lateral forces on wheel.",
        "texts": [
            "rI, Then <t>wrr 24>11'([ + (1 Sri) (1 - Sn) Determining the required cornering coefficient fL' = L\"IR\" = L,JR\" and knowing the relationship for fL' as a function of slip angle, the slip angle, 0:.\", of the rear wheels can be determined. Since a.n \u00b7 = tan-1 (v/u), v can now be determined to complete the velocity analysis. A driven or braked wheel, operating near its tractive limit, becomes lim ited in the amount of lateral force it can develop. One often used method of expressing this limitation is termed the friction ellipse concept, which is il lustrated in figure 11-14. Suppose the wheel is operating at point A on its tractive coefficient, fLIP versus slip relation (fig. 11-14[a]). This operating point corresponds to the points Band C on the ellipse of figure 11-14( b). In turn, the cornering coef- 302 MECHANICS OF THE TRACTOR CHASSIS ficient, !-Lt, is limited, as shown by the arrows of figure 11-14( c). Thus, the wheel can operate at any point inside the ellipse (fig. 11-14[d]). When on the ellipse itself, the wheel is using all the available force-generating capacity of the surface upon which it is operating. If the force analysis indicates operation at a point outside the ellipse, the wheel will have exceeded the capacity of the surface to generate the required forces and a spinout (u = 0), locked wheel (<l> = 0), or sliding condition will exist. Returning to the analysis and assuming the lateral force capacity of the rear tires has not been exceeded, the cornering coefficient required of the front wheel is "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001636_s0263574704000347-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001636_s0263574704000347-Figure12-1.png",
        "caption": "Fig. 12. Cross-section of the workspace (px =py ; r = \u221a p2 x + p2 y).",
        "texts": [
            " In particular, the intersection point of the first octant bisector is located at the distance 1/ \u221a 6 \u2248 0.41 from the origin for the singularity surface and at the distance 1/ \u221a 3 \u2248 0.58 for the sphere SL (assuming that L =1). For the \u201cbar\u201d singularity, it is obvious that the corresponding points are located on the sphere SL. For design purposes, it is also useful to evaluate workspace properties along specific directions or within specific cutting planes. Such plots are presented in Figs. 12 and 13. The first of them (Fig. 12) illustrates the location of characteristic points along the bisector line px =py =pz, p1 =\u22121/ \u221a 3e \u2248 \u22120.58e; p2 = 1/ \u221a 6e \u2248 0.41e; p3 = 1/ \u221a 3e \u2248 0.58e; p4 = 1/ \u221a 2e \u2248 0.71e. (36) which are expressed via the unit vector e = (1, 1, 1). The second illustration (Fig. 13) shows the evolution of the Jacobian determinant det(J) while the manipulator is moving along this line. As follows from the analysis, it is prudent to limit the workspace by the parallel singularity surface (see Fig. 11) that extracts a fraction (of about 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001824_0169-8141(86)90012-0-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001824_0169-8141(86)90012-0-Figure3-1.png",
        "caption": "Fig. 3. Schultz and Anderson's (1980) Internal trunk model.",
        "texts": [
            " An imaginary plane was assumed to cut the trunk at the lumbosacral level. According to the model, the net forces and moments are balanced by the three mutually perpendicular components of the reaction forces and the three components of net reaction moments. The reaction forces and moments are provided by muscle contractions, 87 connective tissue tensions, intra-abdominal pressure and the resistance of the spinal segment. Schultz and Anderson's trunk model takes into consideration muscular contractions developed in five different muscle groups (Fig. 3). These muscle groups are: the rectus abdominis, the internal and external oblique abdominal muscles, the erector spinae muscles, and part of the latissimus dorsi muscles\u2022 These muscle contractions, along with abdominal pressure and compression and shear forces on the spine, make up the net reaction forces and moments at the lumbosacral level of the trunk. Equations (24) through (29) show the equations of equilibrium (between the net forces and moments and the net reaction forces and moments): F(x) = ( L , - L,) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure3.8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure3.8-1.png",
        "caption": "Fig. 3.8. Definition of the control surface deflections",
        "texts": [
            " The available control actuators in the ADMIRE model are: - left canard (\u03b4lc) - right canard (\u03b4rc) - left outer elevon (\u03b4loe) The ADMIRE Benchmark Aircraft Model 45 - left inner elevon (\u03b4lie) - right inner elevon (\u03b4rie) - right outer elevon (\u03b4roe) - leading edge flap (\u03b4le) - rudder (\u03b4r) - landing gear (\u03b4ldg) - air brake (\u03b4ab) - horizontal thrust vectoring (\u03b4th) - vertical thrust vectoring (\u03b4tv) The leading edge flap, landing gear and thrust vectoring are not used in the FCS. The sign of the actuator deflections follows the \u201cright-hand-rule\u201d, except for the leading edge flap that has a positive deflection down. The \u201cright-hand-rule\u201d means that a positive deflection corresponds to a positive rotation assuming that the hinge line is parallel to the respective axis in the body-fixed reference frame SB, see [10] and Figure 3.8. There are four different elevons. Only the outer two are drawn in the Figure 3.8. The inner and outer elevons on each side always move together in the bundled version of the FCS. The maximal allowed deflections and suggestions for the angular rate of the control surfaces are given in Table 3.2. The deflection limits are defined in the original GAM model and should not be violated. The maximum allowed deflections of the actuators depend on the Mach number, see Figure 3.3. 46 M. Hagstro\u0308m The modelling of the sensors is identical to the models of sensors in the HIRM model [3]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002840_s0074-7742(08)60139-7-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002840_s0074-7742(08)60139-7-Figure4-1.png",
        "caption": "FIG. 4. Van\u2019t Hoff plot of P efflux ( O ) , ATPase activity ( O ) , and P, incorporation into ATP ( A ) . The activity (log K ) is plotted against the reciprocal of the absolute temperature ( T ) ; and, from the Van\u2019t Hoff equation - E / R = ( A In K / A T - \u2019 ) the energy of activation E can be determined. Each point of each curve represents an average of 3 separate experiments and the variation from the mean was less than 8%.",
        "texts": [
            ", 1941) : c ~ e - ~ ~ 8 1 R ~ I = 1 f e-AHIRTeASIR (4) where Z = rate of reaction at equilibrium; T = absolute temperature; AH* = heat of activation of the activated complex (EX); AH = heat of activation of the denaturation reaction (i.e., heat of de- naturation); R = gas constant; S = entropy of denaturation (heat); and c = a constant. Actually c = Cs(X) (&)eAS*\u2019R where s, a proportionality constant to compensate for the units used in measurement, and all the other parameters are also constants. By plotting the relative rate of reaction (optimum = 100, at 37\u00b0C) of Ps2 incorporation into ATP against 1/T, it is possible to calculate the constants in Eq. (4) (Fig. 4). The quantity A H o is taken as equivalent to AE, the energy of activation (1-13,500 cal); AH is obtained by adding to AHO the value obtained from multiplying the decreasing slope by 4.6 cal (i.e., 2 .3R) . From the slope of the top curve in Fig. 4, AH = 76,500 cal. Then AS can be calculated from insofar as at the optimum temperature of 37\u00b0C ( I = 100) (see Koffler et al., 1947), AH* + RI\u2019 k\u2018,,,,, = A H - AH* - R 2\u2019 ( 6) By substituting in Eq. (6) and solving Eq. (5) , S is found to be 246 cal/degree/mole. The solid curve at the top in Fig. 4 (corresponding to A ) is the theoretical curve for the phosphorylation reaction derived from substituting the values for the thermodynamic constant in Eq. ( 4 ) and assuming I = 100. A good agreement is obtained with the experimental data for the reaction in normal Ringer\u2018s solution represented by the A in Fig. 4; therefore, the applicability of Eq. (4) to a kinetic analysis of the phosphorylative reaction under consideration appears justified. In a similar manner, the thermodynamic constants for the processes involving ATPase activity and P efflux can be calculated from Fig. 5. It is recognized that none of the above reactions are simply onestep, particularly that involving the esterification of adenosine diphosphate (ADP) to ATP. At best it can only be assumed that one step in a complex reaction scheme (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure6-15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure6-15-1.png",
        "caption": "FIGURE 6-15' Breakerless ignition system components. (Courtesy Deere & Com pany.)",
        "texts": [
            " Increasing the imep either by supercharging, as in figure 6-12, or by increasing the compression ratio, as in figure 6-11, will increase the voltage required to jump a given spark-plug gap. ... '-'\" S w it c h A m m e te r B a tt e ry .J- 1:- to \"0 C o (J OJ (J l F ir in g o rd e r 1, 2 ,4 , 3 B re a ke r p o in ts F IG U R E 6 -1 0 S ch em at ic d ia g ra m o f b at te n ' ig n it io n s ys te m . 4 144 In. of Hg boost (supercharge) A magneto in general use on small farm engines, as well as on outboard motor boat engines, is the flywheel type (fig. 6-15). The rotor of the magneto serves as the flywheel of the engine and also as a fan in air-cooled engines. Breakerless ignition systems exist for both magneto ignition systems (fig. 6- 15) and battery-powered ignition systems (not shown). Ignition Timing The optimum spark timing depends on the throttle position and the engine speed as well as on the plug location in the cylinder, compression ratio, mixture ratio, fuel distribution, valve timing, and octane number of the fuel used. The proper timing can be determined by making a full-load dynamometer test on the engine in question, and the setting that operates without objectionable ping or detonation can be determined for each speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003762_iet-smt.2016.0252-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003762_iet-smt.2016.0252-Figure1-1.png",
        "caption": "Fig. 1 Chaotic strange attractor of PMSMs",
        "texts": [],
        "surrounding_texts": [
            "The dynamics of PMSMs can be written [24\u201326], based on the d \u2212 q axis, as d dt\u0304 \u03c9\u0304 = np J (Ld\u2010\u2010Lq)i\u0304di\u0304q + np J \u03c8ri\u0304q \u2212 B J \u03c9\u0304 \u2212 T\u0304L J d dt\u0304 i\u0304q = \u2212 R Lq i\u0304q + Ld Lq \u03c9\u0304i\u0304d \u2212 \u03c8r Lq \u03c9\u0304 + 1 Lq u\u0304q d dt\u0304 i\u0304d = \u2212 R Ld i\u0304d + Lq Ld \u03c9\u0304i\u0304q + 1 Ld u\u0304d (1) where \u03c9\u0304, i\u0304d and i\u0304q are the speed of the motor (rad/s), d-axis currents (A), q-axis currents (A), respectively, u\u0304d and u\u0304q are the dand q-axis voltages (V), respectively, t\u0304 is the time (s), T\u0304L is the load torque (Nm), Ld and Lq are the d- and q-axis winding inductances (H), respectively, R is the motor winding resistance (\u03a9), \u03c8r is the permanent magnet flux (Wb) of the motor, B is the viscous damping coefficient (N/rad/s), J is the polar moment of inertia (kg\u00b7m2), and np is the number of pole pairs of the motor. In this paper, for the sake of simplicity, only the smooth-air-gap PMSMs are studied. In its dynamics, the d- and q-axis winding inductances have the relationship as Lq = Ld = L. So (1) can be rewritten as (2) d dt\u0304 \u03c9\u0304 = np J \u03c8ri\u0304q \u2212 B J \u03c9\u0304 \u2212 T\u0304L J d dt\u0304 i\u0304q = \u2212 R L i\u0304q + \u03c9\u0304i\u0304d \u2212 \u03c8r L \u03c9\u0304 + 1 Lu\u0304q d dt\u0304 i\u0304d = \u2212 R L i\u0304d + \u03c9\u0304i\u0304q + 1 Lu\u0304d (2) For clarity, we define the scalar variables \u03c4 = (L/R), \u03ba = (B/np\u03c4\u03c8r), and the nominal time t = (t\u0304 /\u03c4) and the state variables \u03c9, id, iq are defined as \u03c9 = \u03c9\u0304\u03c4, id = i\u0304d \u03ba , iq = i\u0304q \u03ba (3) where \u03c9, id, and iq are the nominal speed of the motor rotor, the daxis current and the q-axis current, respectively. When position is considered, the dynamics of PMSMs based on synchronous rotating coordinate can be rewritten as d\u03b8 dt = \u03c9 d\u03c9 dt = \u03c3(iq \u2212 \u03c9) \u2212 TL diq dt = \u2212 iq + id\u03c9 \u2212 \u03b3\u03c9 + uq did dt = \u2212 id + iq\u03c9 + ud (4) where the system parameters are defined as \u03b3 = \u2212 (\u03c8r/\u03baL) and \u03c3 = (B\u03c4/J), the nominal load torque is TL = (\u03c42T\u0304L/J), the nominal d-axis voltage is uq = (u\u0304q/\u03baR), and the q-axis voltage is ud = (u\u0304d /\u03baR). To analyse the chaotic behaviour of PMSMs, when its parameters fall into a certain area, Figs. 1 and 2 are depicted, based on (4), to exhibit the its aperiodic, random and intermittent morbid oscillation phenomenon of PMSMs under the condition that \u03c3 = 5, \u03b3 = 18, ud = uq = 0, TL = 0, \u03b8(0) = 0, \u03c9(0) = 0, iq(0) = 0.01, id(0) = 20. To simplify the model, the new state variables of PMSMs are defined as x1 = \u03b8, x2 = \u03c9, x3 = iq, x4 = id (5) The following parameters are defined as a1 = \u2212 B J , a2 = np J \u03c8r b1 = \u2212 R L , b2 = \u2212 \u03c8r L , b3 = 1 L c1 = \u2212 R L , c2 = 1 L (6) Then, the dynamics of PMSMs can be transformed as IET Sci. Meas. Technol., 2017, Vol. 11 Iss. 5, pp. 590-599 \u00a9 The Institution of Engineering and Technology 2017 591 x\u03071 = x2 x\u03072 = a1x2 + a2x3 \u2212 TL J + d2 x\u03073 = b1x3 + x2x4 + b2x2 + b3uq + d3 x\u03074 = c1x4 + x2x3 + c2ud + d4 (7) where di, i = 2, 3, 4 represents uncertainties and unmodelled dynamics of PMSMs, the state variables xi, i = 1, 3, 4 are measurable and the state variable x2 is unmeasurable."
        ]
    },
    {
        "image_filename": "designv10_10_0001130_j.jmatprotec.2005.05.020-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001130_j.jmatprotec.2005.05.020-Figure2-1.png",
        "caption": "Fig. 2. Cycloidal curv in meshing process.",
        "texts": [
            " 1, \u2220B2O2H2 = \u2220H2O2F2 = \u2220D1O1C1 = \u2220C1O1B1 = 30\u25e6, and F2H2 = rr = 2r sin 15\u25e6 and ra = r + rr The concave arc A1B1C1 can be given as,{ x1ca = r sin 30\u25e6 \u2212 rr sin(\u03b2 + 30\u25e6) ytca = r cos 30\u25e6 \u2212 rr cos(\u03b2 + 30\u25e6)( \u2212arc cos rr 2r \u2264 \u03b2 \u2264 arc cos rr 2r ) (1) where \u03b2 is the parameter of concave arc. The convex arc of H1D1J1 can be expressed{ x1ce = r + rr cos\u03d5 y1ce = rr sin \u03d5 ( \u2212arc cos rr 2r \u2264 \u03d5 \u2264 arc cos rr 2r ) (2) e C1H1 where \u03d5 is the parameter of the convex arc. The cycloidal C1H1 is a relative track of end point H2 of the circular arc H2D2J2 of rotor 2 rolling on rotor 1. To determine the equation of the cycloidal curve C1H1, a reverse method is used. Fig. 2 illustrates the relationship of rotor 2 rolling on rotor 1 in the reversed direction. The equation of cycloidal curve C1H1 can then be obtained as,{ x1cy = 2r cos\u03b1+ r cos(2\u03b1+ 150\u25e6) y1cy = 2r sin \u03b1+ r sin(2\u03b1+ 150\u25e6) 0\u25e6 \u2264 \u03b1 \u2264 30\u25e6 (3) where \u03b1 represents the parameter of cycloidal C1H1. 3. The arc\u2013cycloidal helical tooth profile The arc\u2013cycloidal helical rotor with three-lobes is illustrated in Fig. 3, where S1(x1, y1, z1) represents the rotor 1 coordinate system, r1 is the position vector of the helical rotor profile",
            " If the point is in the trajectory, both oordinate point and the normal vector will satisfy Eq. (15). inally, collect those coordinate points, which satisfy Eq. 15), the assemblage of those points form the cutter trajectory. .2. Cutter mounting angle and center distance in tooth achining Following the cutter trajectory, the tooth profile of the elical rotor can be manufactured. Since the abovementioned elical tooth profile consists of three sections of concave and onvex arcs connected by the cycloidal curve at the points C1 nd H1 in Fig. 2, whose arcs and cycloidal curve are presented n Fig. 6a, the connecting points C1 and H1 might not connect moothly due to the over-cut and undercut occurring in a anufacturing process. To solve this problem, the cutter distance a0 and the cutter ounting angle \u00b5 must be selected properly and match to ach other to enable the contact curve b1c1 of the concave elical tooth profile to coincide with contact curve c1h1 of he cycloidal helical tooth profile at the connecting point c1 n Fig. 6b. This needs to produce the correct cutter mounting angle \u00b5 and centre distance a0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002120_j.proeng.2010.03.202-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002120_j.proeng.2010.03.202-Figure3-1.png",
        "caption": "Fig. 3: Geometry of a double row four contact-point rolling bearing and contact forces acting on a ball",
        "texts": [
            " The calculation is based on the following assumptions: i) external loads acting on the bearing are in static equilibrium with the contact forces acting on the raceway; ii) the bearing rings are ideally stiff, thus taking into account only elastic contact deformations; iii) the procedure for calculation of contact forces is based on the Hertzian theory of contact, and iv) the internal ring is fixed, while external ring can move in , and directions, and rotate about and axes. The system is in static equilibrium when the outer ring is in such position that the external bearing loads are in the equilibrium with the contact forces acting on the outer ring raceways. Fig 3 shows the contact forces between the ball and the raceways. After applying external loads to a bearing an outer ring moves, hence its position can be defined by multiplying vectors by transformation matrix : . (1) By taking into consideration small rotations, such that and , the transformation matrix can be written as: , (2) where , and designate translations in , and directions, and and designate rotations about and axes, respectively. The magnitudes of the contact forces depend on the contact deformations between the balls and the bearing raceways",
            " This equation, therefore, better represents the beneficial effect of compressive mean stresses, which are suppose to cause crack closuring, thus slower crack propagation. According to strain-life theory fatigue life is calculated by solving the following equation: , (14) where are alternating principal strains, is Young\u2019s modulus of elasticity and and are fatigue ductility coefficient and fatigue ductility exponent, respectively. The calculation procedure is demonstrated by calculation of fatigue life of a four contact-point double row ball bearing (as schematically shown in Fig 3) with the following dimensions: pitch diameter , ball diameter , raceway curvature radius and nominal contact angle . Additionally, deformation of the bearing ring was taken into account as well. It was determined experimentally on the basis of the measured displacements of few points on the bearing ring, which was loaded by tilting moment 8140 kNm and radial force 300 kN. The deformed geometry of the outer ring was approximated with sine curves describing radial and axial deformations, which were fit to the measured displacements as shown in Fig 4a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000918_s0003-2670(99)00612-1-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000918_s0003-2670(99)00612-1-Figure14-1.png",
        "caption": "Fig. 14. Spectrum of S. cerevisiae: aerobic condition (a), anaerobic condition (b) and subtraction spectrum (anaerobic\u2013aerobic condition) (c).",
        "texts": [
            " The concentration of the reduced forms (NADH, FADH2) increases, whereas the oxidized forms (NAD+, FAD/FMN) decrease. The spectra under aerobic and under anaerobic conditions seem to be similar. However, when the aerobic spectrum is subtracted from the anaerobic one, differences become obvious. A fluorescence increase can be observed in the NAD(P)H fluorescence region (Ex370/Em450 nm), since NADH accumulates, while a fluorescence decrease is obvious in the FMN/FAD region (Ex450/Em530 nm), since these metabolites do not fluoresce in their reduced form. These results are presented in Fig. 14 indicating the potential of this method to monitor even the metabolic state of the cells without disturbing the bioprocess. The 2-d-fluorescence spectroscopy was also applied for the monitoring of oscillating yeasts as shown in Fig. 15. Here the overall dynamic behaviour of the synchronized cells becomes obvious. These studies are currently under investigation. The ratio of the flavin culture fluorescence (Ex450/Em530 nm) to the NADH fluorescence (Ex370/Em450 nm) shows the relation of the reduced coenzyme (NADH, FADH2) to the oxidized coenzyme (NAD+, FAD/FMN) in the oxidative phosphorylation during oscillatory behavior"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001292_1.342739-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001292_1.342739-Figure3-1.png",
        "caption": "FIG. 3. Surface temperature distribution alongy* = 0.5 at t\" = 0.5 for laser beam of power 600 Wand moving in the x direction at a constant velocity 0.25 cm/s J'elative to the substrate.",
        "texts": [],
        "surrounding_texts": [
            "ar' __ s = X T\" at x* = 0, ax\" ()\" (Sa) aTn __ s = X T\" at x* = 1, ax\" Y.\u00b7 s (Bb) BT\" __ S = :r: T If at y* = 0, a '\" 0 s y ( Be) aT\" Oy; = Yw T ;' at y* = 1, (Sd) aT\" __ $ = Z T\" at z* = 0, az* 0 s (8e) aT\" -_$ = P*e- r*' + Z Tn at z* = 1, az* H s ( 8f) where p* = 2PAH I[ 11'L 2r?;2k( Td ) Td ], r*2 = -~-z[ (x* - rg - t .. ) 1 + (1/ a2 )(y* - D \" f] , I~ r't; = foiL, and D * = D I W. The initial condition (1 b) simplifies to T;' = r; at t * = 0, where and T~ = TJTd \u2022 (8g) The governing equation (la) can be simplified by using the above non dimensional variables and the transformations de fined by Eqs. (4) and (7) to obtain a2 T\"* a21'''* ~ a 2T\"* 1 aT\"* --+a2 __ +s- __ =___ (8h) Bx*2 ayll<2 az*2 Fo at II< ' where the aspect ratio, a = L /w, the slenderness ratio, s = L IH, and the Fourier number, Fo = a( T)r/L 2. a( T) varies slowly with temperature for many materials. In this A. Kar and J. Mazumder 2925 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 study, a( n is considered constant, which is taken to be the temperature-averaged value of the thermal diffusivity over the temperature ranging from the ambient temperature to the melting point of the substrate. The above problem defined by Eqs. (8a)- (8h) is solved by successively applying Fourier transforms in thex,y, and z directions. The Fourier double-integral transform in the x and y directions is T\" (A1x,Amy,Z*,t *) = til dx* dy* T\"(x*,y*, z*, t*) Jo 0 X k lx (x* )Kmy (y*), (9a) and the inversion formula is ',0 '\" T\"(A A z* t*) Til (x*,y*,z*,t *) = L I Ix. my' , {=o m~O IV/x N\",y XK,x (x* )K\",y (y*), (9b) where the kernels [K/x (x*), Krny (y*)]. the characteristic equations for the eigenvalues (A[x,A my ), and the normaliza tion constants (Nix ,N my ) for the above integral transform in each of x andy directions are, respectively. defined as K1x(x*) =Xosin(AI.,x'\") + A/x COS(A/xX\"'), tan}./\" = [A/x (XO -XL )]I(A7x +XoXL), N,x = HXo + (A Z. + X~) [1 - X L /(A7x + XU n, and Kmy (y*) = Yo sin(AmyY*) + Amy eOS(AmyY*), tan Amy = [Amy(YO- Yw)JI[A~,y + YoYw], N my =Hyo+ (A~y + Y~)[1- ywl(A~y + Y;)]}. Here the kernels and the eigenvalues are so chosen that boundary conditions (8a)-(8d) are satisfied. The applica tion of the integra] transform (9a) to Eq, (8h) and the boundary and initial conditions (8e )-( 8g) yields the follow ing: Equation (8h) becomes _ (A. 2 + a2 A 2 ) T fI + 32 a iT fI = _1_ aT If , Ix my az*2 Fo at. ( lOa) The boundary conditions (8e) and (8f) become aT\" -Z-T\" --- 0 az\u00b7 at z* = 0 ( lOb) and aT\" = Z Til + t' (t*) at z* = 1, (lOc) az* II Jim where ftmU*) = t t dx* dy* K)x(x*) )0 )() XKmy(y'\")p*e- \"\"(x*,y\u00b7.,\"). ( We) This integral is evaluated in Appendix B. The initial condi tion (8g) becomes 1'''=T;, (lOd) where 2926 J, Appl. Phys,. Vol. 65. No, 8, 15 April 1989 Equation (lOa) will be solved by applying the Fourier inte gral tansform in the z direction after homogenizing bound ary condition (lOc) by the foHowing substitution: T\" (A/x,Amy,Z* ,t *) = T\"'(A1x,Amy,Z*,t *) (11) where Ti\"(A[x,Amy,Z*,t*) =ftm \u00ab*)(ZoZ* + 1)/.:lz and b-z = ZoO- ZH) - ZH' Substituting expression (11) into Eq. (lOa), the boundary and initial conditions (lOb)-(lOd), and then applying the following integral transform: Tiff (Alx,Amy,)'\"z,t \"') = f dz'\" T\"'(A/x,Amy,z*,t *)Knz (z*), where the inversion formula is 00 T\"\" A A ). t *)K (z*) -T\"'( ~ , * *) = \"\" ~ lx' my' 'nz' nz ,r'[x'/!,my'Z ,f \u00a3.., , n=O Nnz (12) and the kernel (Knz ), the characteristic equation for the eigenvalues (A. nz ), and the normalization constant (N\"z) are Knz (z*) = Zo sin(Anzz*) + Anz COS(AnzZ*), tan Anz = Anz (Zo - ZH )/(..1. ~z + ZoZu), N\", = !{Z() + (A~z +Z~)[1-ZII/(A~z +Z~)]}, we obtain the following results: Equation (lOa) becomes - (A;, + a2A ~y )[1'''' + l,b(t *)] - A ~zs2T'\" = _l_~[T'\" + l,b(t*)], (13) Fo dt* where l,b(t *) = f dz*Knz (z*) TiV(A[x,Amz,z*,t *) Itm (t '\") (Zo 1 1 .,) = -( -COSAr,z)+SlnA\"z ,6,z .A nz , Anz + . -'- (COS Anz - 1 sin Anz)] . A!z All\" To obtain Eq. (B), the kernel K\"z (z*) and the eigenvalues (A\"z) are chosen in such a way that boundary conditions (1 Ob) and (lOc) are satisfied. By adding and subtracting ? A ;'2 f/!( t *) on the left-hand side of Eq. (13), and letting ).7mn = FO(A 7x + a2A ;',y + S2A ~z), we obtain the following ordinary differential equation: A. Kar and J, Mazumder 2926 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 where tI!! = T\"'(A 1x ' Amy ,A liZ , t *) + !/J(t *). The solution of Eq. (14) is given by \u00a2I(t*) =\u00a2,(O)e Ain,,\" +e-AYm.,t\u00b7 (14) (15) X r' Fos2/';'c/.i\",,;i\u00b7\u00a2(i*)dt*. (16) Jo IP, (0) is determined from Eg. (15) by utilizing the results obtained after taking the Fourier transform in the z direction of expressions (1 Od) and (11). This yields \u00a2 I (0) = T a sin .,t \"z (ZoI.,t \"z ) (1 - cos .,t nz )] , By using Eq. (16) in expression (15), we obtain =T\"'( j 1 1 t*) .i (CJ)e . Ai\",,,\" + .. 1\u00b7 2 (t*), . A/x' Amy' A nz ' = 'if I 'I-' where \u00a22(t*) = \u00a2!Ct*) - \u00a2(t*) and (17) if! (t *) = e .J. t~nt' f' Fo S2.,t ;'z\u00a2(i *)i' 7m;;'dt '* -\u00a2(t\"). An explicit expression for 'iA (t .. ) is given in Appendix Co By applying inversion formula (12) to Eq. (17), and then using expression (11), inversi.on formula (9b), and expression (7), we obtain 00 K (x*) [ 00 K (y* ) T'*(x*,y*, z*, t*) = I . Ix L. _m..oY __ 1=0 IVlx m~O Nmy X (TilJ(A/x, Amy' z*, t *) + \"to X [\u00a5!! (O)e -At\"\",!\u00b7 + tP2(t *)] Knz (Z*))] X - Te\u00b7 N nz (18) From the transformed temperature (T'*) given by Eq. ( 18). the nondimensional temperature I'* is determined by using Eq. (6). m. RESULTS AND DISCUSSiON Equation (18) can be used to carry out parametric stud ies oflaser heating of finite slabs. Various parameters such as the wavelength of the laser beam, laser power, shape of the laser beam, diameter of the laser beam, speed of the laser beam relati.ve to the substrate, dimension of the substrate, the thermophysical and optical properties of the substrate, and the conditions of the medium surrounding the substrate can affect the temperature distribution in the substrate. Some typical results are presented in Figs. 2-13. Also, two simple expressions for the variation of the peak temperature with the laser power and with the substrate velocity are ob tained, For all these results, the value of ro is taken to be 2 mm. The laser beam is located at y* = 0.5 and moves in the posi- 2927 J. Appl. Phys., Vol. 65, No.8. 15 April 1989 1.0.' 0,4 1.0 io v f, 1,4 T' 1.2 1.0 1. 0,8 O.G \u00b70.4 FIGA. Surface temperature distribution alongy* = 0.5 at t\" = 0.8 forlaser beam of power 600 Wand moving in the x direction at a constant velocity 0.25 cmls relative to the substrate. A. Kar and J. Mazumder 2927 .\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022.\u2022.\u2022\u2022\u2022 -\u2022\u2022\u2022 \" \u2022\u2022\u2022\u2022\u2022 \" \u2022\u2022 -\u2022\u2022\u2022 -.-\u2022\u2022\u2022\u2022\u2022 -.... \" , \u2022\u2022 -, \u2022\u2022\u2022 --. .-.-............. ~ \u2022\u2022\u2022. o; \u2022\u2022\u2022\u2022\u2022\u2022\u2022 :.-;o_ ....... -\u2022\u2022 -.. .. \" ......................................................................................................... ; \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 ~ \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 , \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 y~ \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 -._-_ \u2022\u2022\u2022 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 2928 J. Appl. Phys., Vol. 65, No.8, 15 April 1989 A. Kar and J. Mazumder 2928 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 2,5~----,------,----.-----, - 2,0 .\" f- OJ '5 ;:; 1.5 Qj '\" E '\" f-1.O -\" \" A U \"0.,1 cm/s B U =0.,3 C!!l/s C U \"0.5 cm/s x\"\"\";;:0'3 8'. A , B 1~ o 250 ----~500~-~7~5~O--lO~,OO Laser Power (W) FIG. ! 1. Variation of the peak temperature with laser power for various scanning speeds relative to the substrate at x~ = 0.3 on the top surface of the substrate, 2929 J. Appl. Phys., Vol. 65, No.8, 15 April 1989 tive x direction with respect to the substrate. The values of the heat transfer coefficients in boundary conditions (lc) (lh) are determined from the following considerations: The slab considered in this study is very thin in the z direction. Its length, width, and height are 1, 1, and 0.1587 cm, respective ly. Since the slab is exposed to the laser beam at the z = H plane, the surfaces at z = 0 and H are expected to heat up more than the other four surfaces for the same ambient con ditions on an six sides of the slab. So the convective activities will be more at the planes z = 0 and H than at the other surfaces. In this study, the convective heat loss frem the sur faces at x = 0, x = L, Y = 0, and y = W is considered to be due to free convection and the heat transfer coefficients are taken to be 5 W 1m2 K (see ReI, 20) at these four surfaces. The heat transfer coefficients at z = 0 and H planes are de termined by assuming that the Biot (Bi) numbers are equal at all the surfaces, where the characteristic lengths in the Bi numbers are taken to be the length, width, and height of the slab for the surfaces perpendicular to the x, y, and z axes, respectively. Figures 2-4 represent the temperature distribution on the top surface of the substrate. Although the computation for the surface temperature distribution is carried out ac cording to the coordinate system of Fig. 1 (a), the three dimensional Figs. 2-4 are plotted by letting x*, y*, and the temperature (T*) increase along Ox\"', Oy\", and 01'* direc tions, respectively, as indicated in these three figures. Here point 0 represents one of the corners of the square contain ing the lines 0 ' V and 0 \" V as two of its sides on the plane of O'VO \". For improved clarity in representing the surface temperature field in three-dimensional plots, views from the two planes, one from the plane T' 0 ' V' located at x* = 1 and the other from T\" 0 \" V located at y* = 1 are shown. Figures 2-4 show the temperature fields for laser power, p = 600 W, laser scanning speed relative to the substrate, u = 0.25 em/s, and for the nondimensional time, t * = 0.2, 0.5, and 0.8, re spectively. It can be seen from these figures that the shape of the surface temperature field has Gaussian-like structure be cause of the consideration of Gaussian laser beam as the source of heat in this study. The temperature and length of the heated zone ahead of the laser beam in the x* direction are found to increase as t * increases. This is so because at a low scanning speed the Fourier number (Fo) is large, that is, the conduction rate is higher than the heat storage rate. Con sequently, the substrate material which is in front of the laser beam is heated up due to the heat conducted away from the laser heated spot. Hence, the laser energy is progressively imparted to points on the substrate which are at higher tem peratures than the preceding points. For the very same rea son, the laser heated zone in the y* direction increases as t * increases for low scanning speed, The knowledge of the width of the laser heated zone is very important in LCVD. The chemical reaction that gener ates the film forming material win take place wherever the temperature is more than or equal to the chemical reaction temperature. As explained above, the width of the heated zone will increase as the laser beam scans the substrate at a low scanning speed. This means that the width of the zone, to A. Kar and J. Mazumder 2929 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 be referred to as the chemically reactive zone, over which the temperature can be larger than or equal to the film forming chemical reaction temperature will increase progressively along the scanning direction for low scanning speed of the laser beam. Thus, the film width will not be uniform for low scanning speed of the laser beam as deposition progresses. On the other hand, if the scanning speed is high the Fourier number will be small, that is, the conduction rate will be lower than the heat storage rate. This reduces the area of the chemically reactive zone due to less conduction of heat from the laser heated spot. Because of this, a narrow film or con stant width can be deposited on the substrate by increasing the scanning speed of the laser beam. This concept is reflect ed in the results presented in Figs. 5-7. These figures show the width of the chemically reactive zone and its variation in the scanning direction for various scanning speeds and laser powers. The chemically reactive zones are symmetrical around the line, y* = 0.5 because the laser beam is located at y* = 0.5 in this study. In each of Figs. 5-7, the chemically reactive zones are bound by the curves, A, B, C, and D for the scanning speeds 0.35, 0.25, 0.167, and 0.125 em/s, re~ spectively. For a given laser power, it can be seen from each of these figures that the chemically reactive zone becomes wider and less uniform in width as the scanning speed de creases. The same can be found for a given scanning speed and different powers of the laser beam by comparing the results of Figs. 5-7. It is established from Figs. 5-7 that the chemically reac tive zone becomes narrower as the laser scanning speed in creases. However, there will be a critical scanning speed at which the two boundary curves of the chemically reactive zone will collapse into one, giving rise to the narrowest possi ble film deposition region. With any other scanning speed higher than the critical speed, the width of the chemically reactive zone cannot be reduced any further. So the film deposition process has to be operated at a scanning speed lower than the critical speed. The critical scanning speed is defined as the one at which the nondimensional peak tem perature T; is unity, where the peak temperature refers to the temperature at the center of the laser beam on the top surface of the substrate. The line T; = 1 is referred to as the line of the narrowest chemical reaction zone in Figs. 8-10. These figures are plotted on logarithmic scales which show the linear variation of the peak temperature (T;) with the laser scanning speed (U) for different powers of the laser beam at various locations on the top surface of the substrate. The points of intersections of the line of the narrowest chem ical reaction zone with the curves of Figs. 8-10 give the criti cal scanning speed of the laser beam. The region which is to the right of the critical speed is referred to as the chemically inert regime because the operating conditions of this region do not raise the surface temperature of the substrate to the film-forming chemical reaction temperature. The region to the left of the critical speed is referred to as the chemically reactive regime where the operating conditions are such that films of finite width can be deposited. However, the surface temperature of the substrate can reach its melting tempera ture at a low scanning speed for a given operating condition, as can be seen from Figs. 11-13. Since melting the substrate 2930 J. Appl. Phys., Vol. 65, No.8, 15 April i 989 is not desirable in LCVD processes, the scanning speed has to be higher than the upper limit of the speed at which melt ing occurs. The line T; = Tm/Td' where Tm is the melting temperature of the substrate, is referred to as the line of melt ing point in Figs. 8-10. The points of intersections of the line of melting point with the curves of Figs. 8-10 give the scan ning speed above which the process has to be operated to avoid melting the substrate. So, from the thermal consider ations, the operating regime for an LCVD process is bound by the line of melting point, the line of narrowest chemical reaction zone, and their points of intersections with the curves of Figs. 8-10. The values of r, 0, 7J, and /3 are given in Tables I and II for various operating conditions. It should be noted that the expression T; = rU'5 is applicable in the chemically reac tive regime. Since the substrate temperature decreases as the scanning speed increases, there will be a critical scanning speed, say U\", at and above which the substrate temperature will remain at its initial temperature. So the slopes of the curves of Figs. 8-10 will be zero for scanning speeds higher than U >1<. This physical aspect is not reffected by the equation T; = r[;>{; because this expression is obtained from the re sults of the chemically reactive regime. It should be noted that when P = 0, the peak temperature must be equal to the initial temperature of the substrate. This is indeed the case as TABLE 1. Values of rand b for the expression T; = rUb. Power (W) x\" r 6 600 0.3 0.985 - 0.141 0.6 UlO6 - 0.163 0.9 1.006 -0.244 700 0.3 1.101 -0.146 0.6 1.125 - 0.169 0.9 1.127 -0.253 800 0.3 1.217 - 0.150 0.6 1,244 -0.174 0.9 1.247 - 0.259 A. Kar and J. Mazumder 2930 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 evident by the values of /3 in Table II because the initial temperature (T;) of the substrate and the thermal decompo sition temperature (Td ) of the film-forming chemical reac tion are taken to be 343 and 1173 K, respectively, in this study for which the nondimensional initial temperature of the substrate is 0.2925. IV. CONCLUSIONS The three-dimensi.onal and transient heat conduction equation is solved in Cartesian coordinates for slabs having finite dimensions and moving at a constant velocity. The temperature-dependent thermophysical properties of the material of the slab are considered, and both convective and radiative losses of energy from the slab to the surrounding medium are taken into account. The laser beam is considered to be Gaussian in shape. Based on these considerations, an analytic expression for the three-dimensional and transient temperature field is obtained. The surface temperature field has a Gaussian-like struc ture for the problem considered in this study. The width of the chemically reactive zone is found to depend on the scan ning speed of the laser beam, becomes more uniform, and decreases as the scanning speed increases. The critical scan ning speed for the narrowest film deposition is determined. Also, the lower and the upper limits of the scanning speeds for LCVD processes are obtained. The peak temperature is found to vary linearly with the laser power for given scan ning speeds and the logarithm of the peak temperature is shown to vary linearly with the logarithm of the scanning speed in the chemically active regime for given laser power. ACKNOWLEDGMENT This work was made possible by a grant from National Science Foundation (Grant No. NSF MSM 84-12118). APPENDIX A: DETERMINATION OF OPTICAL PROPERTIES AT HIGH TEMPERATURES From among various optical properties of materials, the most important one is the optical absorptivity of materials. Such data for many materials can be found in Ref. 21. Some- 2931 J. AppL Phys., Vol. 65, No.8, i5 April 1989 times the complex refractive indices are reported in the liter ature, which can be used to determine the absorptivity under suitable conditions by using Fresnel's relation. Optical con stants (refractive indices) for various noble and transition metals at room temperature can be found in Refs. 22-24 as a function of wavelength of the incident electromagnetic radi ation. However, the optical constants of materials depend not only on the wavelength of the incident radiation but also on the temperature of the materials. Reference 21 provides the temperature variation of optical constants of some mate rials. In LCVD processes, the temperature of the laser irra diated spot is very high, and hence the absorptivity data of the substrate materials at high temperature are important. Since optical constants of materials are usually reported for room-temperature condition, we will show how high-tem perature data can be determined from the available room temperature data. The absorptivity data needed for the present mathemat ical model (that is, the study of LCVD of pure titanium on stainless-steel 304 from titanium tetrabromide) are that of a composite medium which is made up of S.S. 304, titanium film on the surface ofS.S. 304, the vapor phase of TiBr4 , and the chemical reaction products. Since the pressure of the system under consideration is very low, we will consider the optical properties of the vapor phase to be the same as those of vacuum. From the room-temperature data we will first determine the optical constants (n, k; the real and imaginary parts of the refractive index, respectivelY) ofTi and S.S. 304 at 1173 K since the decomposition temperature of the chemi cal reaction 25 4TiBr-.3Ti + TiBr4 is greater than 1173 K. Using the high-temperature values of nand k, the reflectivity of the composite material (made up of S.S. 304 and Ti film) is determined by using Fresnel's relation for composite medium. 26 The nand k values ofTi and S.S. 304 at room tempera ture are obtained from the experimental data of Ref. 24 where 2nk / A and k 2 - n2 values of various transition metals have been reported. Here A is the wavelength of the incident electromagnetIc radiation in micrometers (pm). To com pute the nand k values of 3.S. 304, we consider that the composition ofS.S. 304 is 71.5% Fe, 19% Cr, and 9.5% Ni by weight and that nss = 0.715 nFc + 0.095 flNi + 0.19 nCr and k\" = 0.715 KFe + 0.095 k Ni + 0.19 keT \u2022 Here, ni and k; are the real and the imaginary parts of the refractive indices of the ith material where i stands for S.S. 304 (ss), iron (Fe), nickel (Wi), and chromium (Cr). From this consideration and the data of Ref. 24, Table III can be prepared. For the CO2 laser, the wavelength A = 10.6 f.-im. Also, we have the following data from Ref. 27: PTum = 44 po' cm, P\u00b7!\"l.tI73 = 160 pO em, Pss,300 = 74,5 pO em, Pss,l173 = 122.5 pfl em, where Pi. j is the direct current (de) resistivity of the ith material at the fih temperature. It should be noted that Ref. A. Kar and J. Mazumder 2931 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 TABLE HI. Optical properties of various materials. Materials 2nk IA. Ti 25 Fe 50 Ni 60 Cr 54 S.S.304 Values at room temperature 300K k 2,n2 n 83 9.8665 833 1333 583 9.1417 k 13.4293 30.1586 27 provides the resistivity data for S.S. 303 which we are using for S.S. 304, To obtain the nand k values at higher temperature, we use the following empirical relation from Ref. 28: R = 1-112.2X 10-4 G, (Al) where R is the refiectivity andp is the dc resistivity inpfi em. Taking the derivative of Eq. (AI) with respect to tem perature T, we obtain dR 112.2x 10-4 dp dT 2.jp dT' (A2) Equation (A2) will be used to determine dR IdTatany tem perature by assuming that the resistivities ofTi and S.S. 304 vary linearly with T. From Fresnel's relation, we have for normally incident beams R= [en-I) +k 2 11[(n+ 1)2+k21. Taking the derivative of this equation with respect to tem perature T, we get the following equation for dnl dTand dk I dT: dn dk -+Ao -=A 3 \u2022 dT - dT . (A3) Here A2=A;IA~ and A3=A~/A~, (A6) Substituting Eqs. (AS) and (A6) into Eq. (A4), we obtain ( dn )2 ( dk)2 dn dk - + - +A4 -+As -=A6 \u2022 dT dT dT\" dT (A7) Here A4=A~/A3' A5=A;/A;, and A6=A;;/A;, where A 3 = 112.2 X lO-4( T - TO)2 ,jp, A ~ = 224.4 X 1O--4(no - 1)( T - To) [ji, A; = 224.4X 1O- 4 ko(T - To) ..[p, A~ = (l-1l2.2X 10-4[ji)[(no + 1)2+k6J - (no - 1) 2 - k ~ . Equations (A3) and (A7) are solved by substituting the value of the temperature T at which nand k values are re quired. Knowing dnldT and dk IdT from the solutions of Eqs. (A3) and (A 7), nand k are determined from Eqs. (AS) and (A6) for S.S. 304 and Ti, and then the reflectivity of the composite material which is made up of S.S. 304 and Ti is obtained by using Frensel's relation for composite me dium2 (, for a wide range of the Ti film thickness, The reflec tivity of the composite medium is found to be 0.86351 for O.4-.um-thick Ti film and 0.863 50 for Ti film of thickness 0.8, 1, 10, 100, 200, 500, 700, 900, and 1000 .urn. So, Ti film of thickness up to lOOO.um does not affect the refiectivity of the composite medium of S.S. 304 and Ti at 1173 K. Also, by using the nand k values determined at the high temperature ( 1173 K) by the above procedure in Fresnel's relation, the reflectivity ofS.S. 304 is found to be 0.8758. The absorptivity ofS.S. 304 obtained from this value ofrefiectivity agrees very well with the experimental data of Duley et al. 29 where APPENDIX B A ~ = (no - 1) [ (no + 1) 2 + k ~ ] - (110 + 1)[(no-1)2+k~], A; = 4noko\u2022 A ' 1 [ 2 k 2] 2(dR) 2 = - (no + 1) + (I -. 2 dT 0 The SUbscript 0 is used to refer to the values of the variables n, k, and dR IdTat room temperature. Also, Eq. (Al) can be written as (n--l)2+ k : =1-1l2.2XlO 4/p, (A4) (n+0 2 +k- which is applicable at any temperature. We assume that n and k vary linearly with temperature and therefore ( T 'f-) dn n =110+ - 10 - dT (AS) and 2932 J. App:' Phys., Vol. 65. No.8, 15 April i 989 Here we will evaluate the integrals that appear in the expression for fzm (t \"') : It should be noted that due to the exponential terms,the inte grands of the above two integrals will be very small at a radial distance larger than rif from the center of the laser beam on the top surface of the substrate. Therefore, if the center of the laser beam is away from any of the four edges of the top surface of the substrate by rif, the limits 0 and 1 of both integrations can be replaced by - 00 and 00, respec tively. Because of this, the first integration of the above equa tion can be approximated by A. Kar and J. Mazumder 2932 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 y = foooo dy* e 2( y' x (Yo sin(Amy y*) + Amy COS(A my y*) 1 x [Y;)sin(D*A my ) + Amy cos(D*Amy )]. Similarly, the second integration in the expression for Jim (t >1<) can be approximated by ( 1ir'fS2) 1/2 -A' ,.;l'2/s X= -- e ixO 2 X [Xo sin(r(J' + t *) + A/x cos A/x (r(J' + t *)]. Finally,lIm (t *) can be approximately written as lim (t \"') = p >I< YX. APPENDIXC The expression for If I (t >1<) will be simplified in this sec tion: where Using the expression for iIm (t *) from Appendix E, the above equation can be rewritten as where K2 = K j FOS2A ;'zP * Y(m1\\'2/2) 1/2. Carrying out the above integration, we obtain ::i. ( *) K( Xo -;'7,1,'2/8 ['2 . '( >I< .... ) 1 1 C'o!< ..... )]. )'/x ['2 '1'1 t = 2 --4- e A 1m\" SIn Alx t + rrj - AlxCOS A/x i +\"6 T. 4 2 /. Imll A Imn A., 1m\" + A Ix A./x e A7mnt *--A7.xr(f2/8 A. fmn + A Ix IJ. Mazumder, in Proceedings of Interdisciplinary Issues in Materials Pro cessing and Manufacturing, edited by S. K. Samanta, R. Komanduri, R. McMeeking, M. M. Chen, and A. Tseng (American Society of Mechani cal Engineers, New York, 1(87), pp. 559-630. 2E< M. Breinan and B. H. Kear, in Proceedings 0/ Laser Materials Process ing, edited by M. Bass (North-Holland, Amsterdam, 1983), pp. 235-296. 3J. Singh and J. Mazumder, Acta Metall. 35,1995 (1987). 4A. Kar and J. Mazumder, J. App!. Phys. 61, 2645 (1987). 'A. 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F Ready (Society of Photo-Optical Instrumentation Engineers, Wash ington, DC, 1980), Vol. 198, pp. 31-34. I4A. E. BeH, RCA Rev. 40, 295 (1979). 15y.1. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, J. AppL Phys. 51, 274 (1980). 168< A. Kokorowski, G. L. Olson, and L. D. Hess, in Proceedings of Laser and Electmn\"Beam Solid Interactions and Materials Processing, edited by J. F. Gibons, L D. Hess, and T. W. Sigmon (Elsevier-North\"Holland, New York, 1955, pp. 139-146. I7J. E. Moody and R. H. Hendel, J. App!. Phys. 53,4364 (1982). 18K Kant, J. App!. Mech. 55, 93 (1988). 19H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. ( Clarendon, Oxford, 1986), pp. 10-11. 2!)F. P. Incropera and D. P. Dewitt, Fundamentals of Heat and Mass Trans fe/', 2nd. ed. (Wiley, New York, 1985), p. 8. 21W. L. Wolfe and G. J. Zissis, Eds., The Infrared Handbook (Infrared Information and Analysis Center, Environmental Research Institute of Michigan, MI, 1978), pp. 7.1-7.76. 22p. B. Johnson and R. W. Christy, AppL Opt. 11, 643 (l9i2). 23p. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (! 974). 24A. P. Lenham and D. M. Treherne, J. Opt. Soc. Am< 56, 1137 (1966). A. Kar and J. Mazumder 2933 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 25K. Funaki, K. Uchimura, and Y. Kllniya, Kogyo Kagakll Zasshi 64, 1914- (1961). 260. S. Heavens, Optical Properties of Thin Solid Films (Academic, New York, 1955), pp. 76-77. 27 A. Goldsmith, T. E. Waterman, and H. J. Hirschhorn, Handbook afThe,.- 2934 J. Appl. Phys., Vol. 65, NO.8, j 5 April 19139 mophysical Properties of Solid Materials, revised edition, Vol. II: Alloys (MacMillan, New York, 1961), pp. 171 and 671. '\"Y. Arata and l. Miyamoto, Technocrat 11, 33 (1978). 19W. W. Duley, D. 1. Simple, 1. P. Morency, and M. Gravel, Opt. Laser Techno!., 313 (December 1979). A. Kar and J. Mazumder 2934 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47"
        ]
    },
    {
        "image_filename": "designv10_10_0001081_s0022-460x(03)00072-5-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001081_s0022-460x(03)00072-5-Figure6-1.png",
        "caption": "Fig. 6. Active control applied directly at the bearings (concept 3).",
        "texts": [
            " Note that this scheme may also provide some level of passive torsional vibration isolation in the lower frequency range due to the semi-active nature of the structural design. Since most gear whine problems are the result of structure-borne vibration transmission from the geared rotor system through the bearings and into the housing, a natural path control scheme inside the gearbox is to set-up \u2018choke\u2019 points at the support bearings. One way to accomplish this is to use two pairs of piezoelectric stack actuators placed in two orthogonal radial directions between the bearing raceway and the housing support structure, as shown in Fig. 6. One pair of opposing actuators is oriented parallel to the gear mesh line-of-action, while the second pair is oriented perpendicular to the line-of-action. Note that although only one pair of actuators oriented parallel to tooth load line-of-action is needed theoretically, this double set configuration is recommended in practice to achieve a more robust ability to control general transverse plane motions of the shaft-bearing structure. This is especially useful when non-negligible transverse vibration orthogonal to the load line-of-action caused by misalignment and friction force excitation exists"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.20-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.20-1.png",
        "caption": "Figure A.20 including their basic unit vectors. Rectangular (or Cartesian), cylindrical, and spherical coordinate systems,",
        "texts": [
            " A x (B x C ) = (A x B) + A x C . Choice of a specific coordinate system depends on the geometry of the problem under consideration. Various systems are in use. Most common are the righthanded, rectangular, circular cylindrical, and spherical systems. Detailed discussion of the coordinate systems are available in various references cited. Here we discuss the basic outlines. 434 VECTORS AND VECTOR ANALYSIS; The representation of a point F\u2019 in space in the three coordinate systems is given in the compact diagram Figure A.20. The location of any point P in space is specified by a combination of three basic space variables measured in the three orthogonal directions. Any vector can be expressed in terms of its three basic vector components in the three orthogonal directions (or base vector directions). Note that in each system the three unit vectors are orthog- COORDINATE SYSTEMS 435 onal to each other and they form a positive triad. Space Variables The basic space variables and base vectors for the three systems of interest are as given in Table A. 1. Vectors Three Coordinate Systems and Their Associated Coordinates and Base Coordinate System Space Variables Base Vectors Rectangular 2, Y, z 2 , y, 2 Circular cylindrical P, 4 , z b, 4, 2 Spherical T , 074 i , e ,4 Note with reference to Figure A.20, any point P in space is identified by the intersection of the three coordinate surfaces passing through the point P. Thus the coordinates of P are (z, y, z ) , (p, 4, z ) , and (T , 0 , 4 ) in the three systems. The coordinate surfaces in the three systems are: y = constant x = constant z = constant rectangular plane surfaces. z = constant, plane surface. p = constant, cylindrical surface, 4 = constant, plane surface, 8 = constant, conical surface 4 = constant, plane surface. I The ranges of the space variables are --oo<x,y,z<m (A",
            "39) The following expressions give the relationships between the space variables in the three systems: 436 VECTORS AND VECTOR ANALYSIS Rectangular to cylindrical systems, and vice versa, z = p c o s 4 y = psin4 4 = tan-l (A.40) p = (2 + y 2 y 2 2 0 z z = z z = z . Rectangular to spherical systems, and vice versa, J: = rsiri6cos6, r\u2019 == (x2 + y2 + z 2 ) & 2 0 z = rcos6 4 = tan-1 x. Cylindrical to spherical systetns, and vice versa, 1c p = r s in6 4 = 4 T = ( p 2 + z2) : 2 0 4 = 4 = tan -1 g X (A.41) (A.42) Base Vectors In each system the base vectors consist of three unit vectors along the three orthogonal coordinate directions (Figure A.20), and in each system they form a positive triad of unit vectors. In other words, the three unit vectors of each set are orthogonal to each other, so they form a positive triad. In the rectangular, cylindrical, and spherical system of coordinates they are as follows: Base vectors Interrelations 2, i j , 2 2 x i j = 2 , i j x 2 = 2 , 2 x 2 = ij 2 . 6 = 9 . 2 = 2 . :j 0 (A.43a) p , $ , 2 p >( 4 = i , 4 x 2 = p , 2 x p = 4 p . $ = 4 . ? = 2 . $ = 0 (A.43 b) i >: 6 = 4,O x 4 = i , 4 x i = 8 - A i , 6 , J A * , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure14-12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure14-12-1.png",
        "caption": "FIGURE 14-12 Transducers for measuring pressure inside of a combustion chamber. (Cour tesy Beckman Instrument Co.)",
        "texts": [
            " The mass of dry air flowing through the orifice is computed from where M A C du ' d\" M = d\"AC 2gh(~:J mass of dry air per second, kg area of orifice, m 2 orifice coefficient density of water, kg/m:1 density of air (air and vapor), kg/m:{ at the observed pressure It = pressure drop across orifice, mm H 20 If dw = 997.9 kg/m3, equation 6 can be simplified to M = 1.63 AC v'hd\" (6) (7) 418 TRACTOR TESTS AND PERFORMANCE Engine Pressure Indicators The high rotational speeds of internal combustion engines require the use of electronic measuring devices. One method of measuring the engine cylinder pressure is by means of a pressure transducer (fig. 14-12) of the unbonded strain gage or piezoelectric type. A transducer such as that in figure 14-12(a) is normally installed in a special hole drilled in the cylinder head. Pressure ENGINE PRESSURE INDICATORS 419 transducers using piezoelectric crystals can also be installed In modified spark plugs [fig. 14-12(b)]. The use of electrical resistance strain gages, radio transmission of signals (telemetry), plus the real-time processing of the data (computers) has opened up opportunities for engineers to learn much more when testing tractors and machines. Some techniques are described by Deere & Co. engineers in SAE SP-410 (Society of Automotive Engineers 1976). When engines were slow, a simple mechanical device called a pressure indicator would make a P-V (pressure-volume) diagram. Figure 14-13 shows the method of obtaining a P-V diagram from a high-speed engine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003424_tie.2015.2426671-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003424_tie.2015.2426671-Figure8-1.png",
        "caption": "Fig. 8. 12/10 stator/rotor pole all poles wound SFPM prototype machine.",
        "texts": [
            " After the stability of compensator at steady state, the speed correction \u03c9cor will converge to zero and the same to the phase difference \u0394\u03b8. Consequently, the average rotor speed with the speed error can 0278-0046 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. also be compensated. Thus, a higher accuracy of rotor position estimation can be achieved by the integrator under both steady and dynamic states. A 12-slot 10-pole prototype SFPM brushless machine as shown in Fig. 8 is used for the validation of proposed control strategy. The proposed rotor position error compensation based on asymmetric back-EMF with the aid of back-EMF harmonics elimination method is described in Fig. 9. The testing machine is introduced in Section II, and the parameters are listed in Table I. Only one PM machine with double-layer windings/all poles wound is prototyped. It is used for the investigation of sensorless control performance of such a machine with either single-layer or double-layer windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003318_access.2017.2779940-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003318_access.2017.2779940-Figure1-1.png",
        "caption": "FIGURE 1. Two-link robot manipulator\u2019s architecture.",
        "texts": [
            " The Lyapunov function candidate is given by L2 = L1 + 1 2\u03b71 tr ( P\u0303T0\u22121P\u0303 ) + 1 2\u03b72 m\u0303T m\u0303+ 1 2\u03b73 v\u0303T v\u0303 (26) Taking the derivative of the Lyapunov function (26) and using (9) yields L\u03072 = L\u03071 + 1 \u03b71 tr ( P\u0303T0\u22121 \u02d9\u0303P ) + 1 \u03b72 m\u0303T \u02d9\u0303m+ 1 \u03b73 v\u0303T \u02d9\u0303v = \u03b1TM \u03b1\u0307 + 1 2 \u03b1T M\u0307\u03b1 + 1 \u03b71 tr ( P\u0303T0\u22121 \u02d9\u0303P ) + 1 \u03b72 m\u0303T \u02d9\u0303m+ 1 \u03b73 v\u0303T \u02d9\u0303v = \u03b1T [\u2212(Kv + V )\u03b1 + f\u0303 + \u03c4d ]+ 1 2 \u03b1T M\u0307\u03b1 + 1 \u03b71 tr ( P\u0303T0\u22121 \u02d9\u0303P ) + 1 \u03b72 m\u0303T \u02d9\u0303m+ 1 \u03b73 v\u0303T \u02d9\u0303v = \u2212\u03b1TKv\u03b1 + 1 2 \u03b1T (M\u0307 \u2212 2V )\u03b1 + \u03b1T (f\u0303 + \u03c4d ) + 1 \u03b71 tr ( P\u0303T0\u22121 \u02d9\u0303P ) + 1 \u03b72 m\u0303T \u02d9\u0303m+ 1 \u03b73 v\u0303T \u02d9\u0303v = \u2212\u03b1TKv\u03b1 + \u03b1T (XT P\u0303T r\u2217 + XT P\u0302T r\u0303 + \u03b5 + uR + \u03c4d ) + 1 \u03b71 tr ( P\u0303T0\u22121 \u02d9\u0303P ) + 1 \u03b72 m\u0303T \u02d9\u0303m+ 1 \u03b73 v\u0303T \u02d9\u0303v = \u2212\u03b1TKv\u03b1 + \u03b1T (XT P\u0303T r\u0302 + XT P\u0302T ( rTm m\u0303+ r T v v\u0303 ) +\u03be (t) + uR + \u03c4d )+ 1 \u03b71 tr ( P\u0303T0\u22121 \u02d9\u0303P ) + 1 \u03b72 m\u0303T \u02d9\u0303m+ 1 \u03b73 v\u0303T \u02d9\u0303v = \u2212\u03b1TKv\u03b1 + tr [ P\u0303T ( r\u0302XT\u03b1 \u2212 1 \u03b71 0\u22121 \u02d9\u0302P )] + m\u0303T [ rmP\u0302X\u03b1 \u2212 1 \u03b72 \u02d9\u0302m ] + v\u0303T [ rvP\u0302X\u03b1 \u2212 1 \u03b73 \u02d9\u0302v ] +\u03b1T (\u03b5 + uR + \u03c4d ) = \u2212\u03b1TKv\u03b1 + \u03b1T (\u03b5 + uR + \u03c4d ) (27) In the expression above, the relationships \u03b1TXT P\u0302T rTm m\u0303 = m\u0303T rmP\u0302X\u03b1 and \u03b1TXT P\u0302T rTv v\u0303 = v\u0303T rvP\u0302X\u03b1 are used as scaling terms. Thus, the expression can also be defined as \u03b1XT P\u0302T r\u0302 = tr ( P\u0303T\u03b1r\u0302XT ) . Then, via (25), (27) can be rewritten as L\u03072 = \u2212\u03b1TA\u03b1 + \u03b1T (\u03b5 + uR + \u03c4d ) = \u2212\u03b1TA\u03b1 + \u03b1T (\u03b5 + uR + \u03c4d ) = \u2212\u03b1TA\u03b1 + \u03b1T (\u03b5 + \u03c4d )+ \u03b1T uR = \u2212\u03b1TA\u03b1 + \u03b1T (\u03b5 + \u03c4d )\u2212 \u2016\u03b1\u2016\u00b5 \u2264 0 (28) V. SIMULATION RESULTS The two-link robot manipulator shown in Fig. 1 is used to examine the effectiveness of the proposed control scheme. The adopted robot system\u2019s dynamic model can be expressed in the form of Eq. (1) as in [19]. The specific system parameters for robot manipulators are as follows in (29) shown at the bottom of this page. 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, and g is the gravity acceleration. Additionally, the following nonlinear viscous and dynamic friction terms of F(q\u0307) and unknown disturbances \u03c4d have been covered in the manipulator dynamics",
            "2 sin(t) ] (31) M (q) = [ l22m2 + l21 (m1 + m2)+ 2l1l2m2 cos (q2) l22m2 + l1l2m2 cos (q2) l22m2 + l1l2m2 cos(q2) l2m2 ] V (q, q\u0307) = [ \u2212l1l2m2q\u03072 sin(q2) \u2212l1l2m2(q\u03071 + q\u03072) sin(q2) m2l1l2 sin(q2) 0 ] G(q) = [ (m1 + m2)l1g cos(q1)+ l2m2 cos(q1 + q2) m2l2g cos(q1 + q2) ] (29) 1674 VOLUME 6, 2018 VOLUME 6, 2018 1675 1676 VOLUME 6, 2018 The initial state of the system is [q1d , q\u03071d , q2d , q\u03072d ]T = [0.09 0 \u2212 0.09 0]T , and the desired trajectory is expressed as q1d (t) = 0.1 sin t (32) q2d (t) = 0.1 sin t (33) and Kv = diag{20, 20}, \u00b5 = 0.3, 3 = diag{40, 40}. The performance of the proposed adaptive TFCMAC control system is evaluated after it is applied on a two-linkmanipulator, as shown in Fig. 1. To confirm the superiority and the robustness of the TFCMAC control scheme, three other neural network control methods (radial basis function (RBF) neural network [18], CMAC [29] and recurrent CMAC [30]) are used to simulate and compare the position tracking and the speed tracking of the joints. Based on Fig. 4, Fig. 5 and Fig. 6, under the same coordinate presented Fig. 8, the error tracking of four intelligent control schemes were compared. Obviously, the robust adaptive TFCMAC is superior to the other three control strategies in the error convergence rate of the two joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003941_1.4029273-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003941_1.4029273-Figure1-1.png",
        "caption": "Fig. 1 Quanser 2DOF helicopter",
        "texts": [
            " It is an educational control experiment made by Quanser Consulting Inc. [1] for testing control strategies on a nonlinear multiple-input multipleoutput (MIMO) system with coupled dynamics. Similar experimental testbeds have been successfully used to demonstrate and validate control techniques [2\u20134] on real world systems. Augmented techniques are of special interest for experimental control testbeds which are explored in Ref. [4] in the form of robust compensators. The experimental setup shown in Fig. 1 consists of a helicopter model mounted on a fixed base and free to rotate in both pitch and yaw directions. Pitch angle is controlled using a propeller driven by a direct current (DC) motor, and is restricted to a range of 40 deg 40 deg. Yaw angle is controlled using a propeller driven by a smaller DC motor, and is free to rotate without any restrictions. DC voltages of pitch and yaw motors serve as control inputs. Due to disparity in sizes of motors, the helicopter rests at a pitch angle of 40 deg in its unactuated initial state",
            " Low-Pass Filter. D(s) is a low-pass filter with a certain cutoff frequency. The cutoff frequency and subsequently D(s) are chosen to satisfy the L1 norm condition in Eq. (13). The adaptation gain C is set to 10,000 D\u00f0s\u00de \u00bc 1 s s 1000 \u00fe 1 1 0 0 1 (23) A lower bandwidth design was also implemented which successfully stabilized the model in simulation. However, this lower bandwidth design failed to stabilize the actual physical system. All experiments are carried out on Quanser 2DOF helicopter in Fig. 1 and the presented results are from encoder readings of the setup. A comparison of three controllers is presented. Adaptive augmentation of LQR\u00fe I is compared with controllers based only on LQR\u00fe I and L1 adaptive state feedback control. It is to be noted that all experiments start from the helicopter\u2019s resting or unactuated position of h\u00bc 40 deg. Three cases are presented in which tracking performance as well as robustness of each control technique is evaluated. L2 norms for tracking error calculated by key\u00f0t\u00dekL2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi\u00d0 T 0 \u00f0y\u00f0t\u00de yref\u00f0t\u00de\u00de2dt q are tabulated and time histories of states are plotted for three cases represented by (A), (B), and (C) are discussed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure7-1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure7-1-1.png",
        "caption": "FIGURE 7-1 Diagram of centrifugal governor.",
        "texts": [
            " 156 PRII\\'CIPLES OF CENTRIFUGAL GOVERNOR ACTION Principles of Centrifugal Governor Action 157 Although mechanical governors come in many shapes, they still operate on the same principle as the original governor designed by Watt for steam en gines. The regulation of a centrifugal governor results from a change in centrifugal force when the speed of rotation changes. For equilibrium to be attained, the masses must assume a new position in response to any change in speed, and this movement controls the device that varies the flow of fuel to the engine, thus restoring its speed to the normal value. Figure 7-1 is a schematic drawing of a simple spring-loaded, centrifugal force governor. The centrifugal force F is exerted by a m.ass M rotating about the center line at a radius r with an angular velocity of e rad/s. (1) The performance of a governor depends on the design, and certain definitions relating to design will now be discussed. Stability A governor is said to be stable when it occupies a definite position of equilib rium and does not oscillate for each speed within its working limits. 158 ENGINE ACCESSORIES Regulation The speed of an engine at no load will be higher than the speed at full-load",
            " Recirculation of hot radiator exhaust air to the cold side of the radiator should be prevented by baffling, which seals leaks between the radiator and the engine compartment hood. Engine Cooling Summary Specific heat rejection by a diesel engine ranges trom about 0.6 to 0.94 kW/kW of engine output, and water flow will range from 0.7 to l.4 lIkW of engine output. Fan power is nominally 5 percent of gross engine power, with a range of 2.5 to 10 percent. Radiator frontal areas of 19 to 29 cm2/k W per gross engine output are rules of thumb. PROBLEMS 1. Using automatic control analysis, make a block diagram of the governor shown in figure 7-1. 2. Using the dimensions shown in figure 7-1, fill in the boxes of the block diagram you have prepared of figure 7-1. A four-cylinder tractor diesel engine designed to run at 2000 rpm will develop 75 kW at rated load. The problem is to equip the engine with a proper radiator. Show computations, assumptions, and reasons for your procedure. (a) What is the necessary rate of heat dissipation to the air? (b) What rate of cooling-water circulation do you recommend? (c) What rate of airflow do you recommend? (d) How much power will the fan require? If the fan is the only accessory, what percentage is the fan power of the total power that the engine would develop without accessories"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.21-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.21-1.png",
        "caption": "Figure 6.21 Two-element X/Zdipole array: Dipole oriented along the z axis (array plane XY).",
        "texts": [],
        "surrounding_texts": [
            "Length dl with constant current of peak value /I01"
        ]
    },
    {
        "image_filename": "designv10_10_0000956_0890-6955(95)00073-9-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000956_0890-6955(95)00073-9-Figure1-1.png",
        "caption": "Fig. 1. Impact dampers.",
        "texts": [
            " In a previous report [9], in order to improve the damping capability of these cutting tools, an impact damper with the following features was developed: (1) small and simple in construction; (2) easy to mount on the main vibratory systems; and (3) no need to adjust parameters of an impact damper to the vibratory characteristics of the main vibratory systems. The damping mechanism of the impact damper and its vibratory characteristics were i nves t i ga t ed in a p r e v i o u s r e p o r t [9]. H o w e v e r , the c o n s t r u c t i o n of the i m p a c t d a m p e r u sed was a r r a n g e d so tha t the free mass cou ld m o v e o n l y in the d i r ec t i on of g rav i ty , Corresponding author: Dr. S. Ema tFaculty of Education, Gifu University, 1-1 Yanagido, Gifu-shi 501-11, Japan. ~tFaculty of Engineering. 293 as shown on the left in Fig. 1. Thus, the impact damper effective functioning was limited only when the main vibratory systems (cutting tools) vibrated in this direction. Therefore, in order to apply the impact damper to actual cutting tools, some problems had to be resolved. In the present study, the impact damper construction was improved so as to allow free mass motion in any direction, as shown on the right in Fig. 1. Using the impact damper of this form, the characteristics of the impact damper were investigated in detail when the main vibratory system was vibrated in the direction of gravity and perpendicular to it. Furthermore, improvement of the damping capability of drills using the impact damper was tried. In addition, the impact damper used in this study allows a free mass to be equipped on the main vibratory system, but in the vibratory system presented in Fig. 1, the free mass exists inside the main mass. In this experiment, leaf springs with a width of 30 mm and an overhang of 165 mm were used as the main vibratory system. The leaf springs were vibrated in the direction of gravity and perpendicular to it. The case in which the leaf springs vibrate in the direction of gravity is called vertical vibration, while the case in which the leaf springs vibrate in the direction perpendicular to gravity is called horizontal vibration. In vertical vibration, a leaf spring was fixed on the table by two bolts as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002486_1.4004225-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002486_1.4004225-Figure5-1.png",
        "caption": "Fig. 5 A 6R spherical mechanism",
        "texts": [
            " The second mechanism needs the axial link parameter constraint d3\u00bc 0. Substituting these constraints to Eqs. (5) and (6) yields d6 \u00fe d5cd5 d2ch1 \u00bc 0 a5sh6 d5sd5ch6 \u00bc 0 (25) 031004-4 / Vol. 3, AUGUST 2011 Transactions of the ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use For equations to satisfy simultaneously any given value of angle h1 and h6, it needs that d2 \u00bc d5 \u00bc a5 \u00bc d6 \u00bc 0 (26) This gives rise to a 6R spherical mechanism as in Fig. 5, and the mechanism has three degrees of freedom. The properties of the first two categories are to be further investigated. The third category of the 6R double-centered overconstrained mechanisms stems from the third solution in Eq. (24). It is more general than the first and second categories and covers some of the existing mechanisms. It gives rise to two sets of double-spherical mechanisms evolved from the double-centered mechanisms. Hence, it is treated separately from the other two categories"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001505_bf01320814-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001505_bf01320814-Figure2-1.png",
        "caption": "Fig. 2. Planar flagellar pattern, a The planar flagellum propagates approximately sinusoidal waves at velocity Vw; individual elements of the flagellum move first to one side and then to the other, the transverse velocity varying cyclically, b The water flow produced by an element of the flagellum is also directed alternately to one side and then the other, with periods of no lateral movement at the wave crests; the result is a series of local circulations that link to generate an axial flow in the direction of the wave along a smooth flagellum. c When mastigonemes are present on a flagellum, the form of the circulation created by the planar flagellar undulat ions is modified because CT > CN, and the dominant water flow around the flagetlum is in the opposite direction to the propagation o f waves along the flagellum",
        "texts": [
            " The reaction on the flagellum propels it in the opposite direction to the waves, but also induces a torque which will be considered later. Normal and tangential forces (dependent on CN and CT and the velocities in normal and tangential directions) both contribute to both the forward propulsion and torque (Fig. 1 c). By contrast, when a planar wave is propagated along the flagellum, the motion of each element of the flagellum is constantly changing, and so, consequently, is the motion of the surrounding water which is being moved by that element of the flagellum (Fig. 2 a). This wave appears approximately sinusoidal, and this form tends to be assumed in calculations, but waves formed head, b L C , ~V L F N ~r L Fig. I. Helical flagellar pattern, a A flagellum frothed into a left-handed helix turns with constant angular velocity and propagates waves at velocity Vw. b and e An element L of the flagellum moves with a velocity VL at a tangent to the helix and transverse to the axis of progression, as seen from the flagellar tip in b and from the side in c. The force on the water F N is given by CNVNL and the force FT is given by CTVT L, depending on the velocities V~ and V T at which the element L moves in the normal and tangential directions, respectively. FN will have a component Fe propelling water in the direction of the wave and FT has a component FD, the drag force, d The motion of water produced by each element of the flagellum wilt be obliquely to the right and in the direction of rotation, resulting in the generation of a spiral flow water propulsion is in the direction of the waves, and the local circulations of water induced as the flagellar waves are propagated towards the flagellar tip are as shown in Fig. 2b (Higdon 1979a). The longitudinal forces exerted by each wave produce a forward reaction on the flagellum, whereas the transverse forces of each half wave are in opposite directions and will tend to cancel each other out, although they generate lateral oscillations of the leading end (Holwill 1966). When waves of either configuration are propagated along a flagellum from base to tip they will tend to shear water towards and then shed it from the flagellar tip. If the flagellated cell is free to move, the flagellum will undulate its way through the viscous water as well as propelling some water backwards in real space. Flagella often carry external appendages that can affect water propulsion. The anterior flagellum of heterokont flagellates carries stiffmastigonemes, about 20 nm thick and about 1 gm long, in two rows. These flagella have a planar beat, and if the mastigonemes project rigidly from the flagellar surface they will increase CT to greater than CN, thereby causing the water movement to be reversed so that the resultant flow is in a direction opposite to the propagation of the flagellar waves (Fig. 2c). If the mastigonemes project all round the flagellum CT/CN = 1.2, whilst if the mastigonemes are from arcs and straight lines (Brokaw 1965) or from meanders (Silvester and Holwill 1972) may more correctly represent their shape. The water movement around the flagellum can be portrayed in the plane of beat by normal and tangential forces with components in longitudinal and transverse directions (as in Fig. 1 c). Because CN is about twice CT, the lengths of flagellum between wave crests exert substantial forces in the direction of the waves, but near the wave crests, where there is no normal motion but only axial motion, drag forces opposing the flow will dominate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002924_1.4023208-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002924_1.4023208-Figure4-1.png",
        "caption": "Fig. 4 (a) Measurement setup and the main transmission paths of the vibro-acoustic signal measured; (b) the measurement points used for signal strength analysis",
        "texts": [
            " The level of wear can be determined by comparing the characteristic frequencies in accordance to the following criteria [1\u20133,10,11]: \u2022 the ratio of the maximal value of the amplitude, which is the subject of investigation, to its root-mean-square (RMS) value \u2022 the ratio of total energy (or power spectral density) of mesh frequency harmonics to energy (or power spectral density) of fundamental mesh frequency \u2022 the ratio of total energy (or power spectral density) of mesh frequency components (or sidebands) to the energy (or power spectral density) of fundamental mesh frequency \u2022 absolute increment of total power spectral density of tooth mesh harmonics and their sidebands with respect to their reference values \u2022 absolute increment of total power spectral density of the chosen tooth mesh harmonics and their sidebands with respect to their reference values. The frequency spectrum of vibration was measured at a point in the gearbox by an accelerometer. The data was recorded and preprocessed in a data acquisition unit and postprocessed using MATLAB software. 4.1 Apparatus. The apparatus used in the experiment is listed in Table 1 and a measurement chain is shown in Fig. 4(a). The signal was picked up by a uniaxial piezoelectric accelerometer (either B&K 4391 used with B&K 2515 or B&K 4514-001 used with B&K PULSE) and processed by a data acquisition unit. For older measurements (set 1) B&K 2515 was used, newer measurements were analyzed by B&K PULSE 3560. Data processed were recorded and analyzed using a laptop with B&K LabShop and MATLAB software. The accelerometer was fixed into the gearbox\u2019s body by a stud in order to ensure a firm fixation and the same measurement position throughout the experiment (Fig",
            " To eliminate noise and unwanted random sources, the frequency spectra were averaged using 1000 exponential averages. 4.3 Optimal Measurement Point. In order to ensure that the strongest signal carrying the information of interest is to be recorded, a study on the optimal measurement point was done prior to measurements [12]. In general, the vibro-acoustic signal is transferred from the source (gear meshing) to the receiver (accelerometer) by two main transfer paths: (a) structure-borne (path 1 in Fig. 4(a)); (b) fluid-borne path (path 2 in Fig. 4(a)). To map the signal\u2019s strength in all directions (both axial and radial), 32 measurement points (shown in Fig. 4(b)) were chosen. To get a sufficient statistical sample, eight frequency spectra were measured for each point and power (RMS) values from the frequency bandwidth around the tooth mesh harmonics were averaged. The bandwidth was set to 107 Hz, also taking the four sidebands around the mesh harmonics into account. Comparing the average local RMS levels within the frequency bandwidth around the harmonics (Fig. 5), it can be concluded, that the information value of the signal is highly dependent on the measurement location"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003227_s11071-014-1701-x-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003227_s11071-014-1701-x-Figure5-1.png",
        "caption": "Fig. 5 Simulation results of phase diagrams, Poincar\u00e9 maps, Lyapunov exponent and fractal dimension obtained for bearing center at s = 2.00 (l\u2217 = 0.3) in the horizontal direction (x1). a Phase diagram, b Poincar\u00e9 map, c Lyapunov exponent, d fractal dimension",
        "texts": [],
        "surrounding_texts": [
            "3.1 Analytical tools for observing nonlinear dynamics The analytical tools used for observing nonlinear dynamics of the gear-rotor\u2013bearing system with rubimpact effect in this study are dynamic trajectories, Poincar\u00e9 maps, bifurcation diagram, Lyapunov exponent and fractal dimension. We can check the dynamic trajectories and Poincar\u00e9 maps for each bifurcation parameters to clarify the more detailed dynamic behaviors. Then, a bifurcation diagram summarizes the essential dynamics of the system and is therefore a useful means of observing its nonlinear dynamic response at this step. Finally, maximum Lyapunov exponent and fractal dimension are used as the most useful tools to detect chaotic motions for nonlinear dynamical systems. The basic principles of each analytical tool are reviewed in the following subsections."
        ]
    },
    {
        "image_filename": "designv10_10_0003458_j.tust.2015.11.022-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003458_j.tust.2015.11.022-Figure1-1.png",
        "caption": "Fig. 1. Structure diagram of the driving system in TBM.",
        "texts": [
            " Taking a TBM working in a water project as an example, both the modal characteristics and vibration response of the driving system, as well as their sensitivity to the dynamic parameters such as coupling stiffness and damping coefficients are investigated. It provides the data support in the dynamic design of TBM driving system, and the modeling method can be generalized to other complex driving system. The TBM cutter head driving system provides steady rotary power for cutter head to cut rock continuously. It is a driving system with multiple pinions, and the ring gear is driven by six, or eight, or ten or more driving motors via planetary gears. Fig. 1 shows the structure diagram of the cutter head driving system in TBM. 2.1. Hierarchical principle Obviously, the TBM cutter head driving system can be seen as an integrated system which is assembled by several basic subsystems and components with couplings such as gear mesh, bolt connection and spline connection. It is suited to use hierarchical principle to establish the FE model of TBM cutter head driving system. The main idea of this theory is to define the unit matrix of different basic elements and load vector firstly, and then assemble them via the coupling elements to obtain the overall mass, stiffness, damping matrix and load vector, which forms the dynamic equation of the whole system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure2-1.png",
        "caption": "Fig. 2. Solution region of 3-D transient electromagnetic field.",
        "texts": [
            " The pressure values at the end outlet and the velocity value at the fan inlet were determined and are shown in Table II. B. Influence of press plate permeability on eddy current losses of the end parts Based on electromagnetic field theory, the mathematical equations of the 3-D transient eddy current field in the turbogenerator end region are calculated with ANSOFT commercial FEA (finite element analysis) software [11], [12]. This turbogenerator provides reactive power under the rated load condition. The loading conditions (real power is 330 MW and reactive power is 58 MVar) are given. Fig. 2 shows the solution region of the 3-D transient electromagnetic field. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 3 The eddy current losses of end parts can be determined using 2 -1 =1t 1 = k e e e r e P J dt T  (1) where r is the conductivity (in S/m), e is the element volume (in m 3 ), eJ is the element eddy current density (in A/m 2 ), k is the total number of elements in the different end parts, tT is the period of time (in s), and eP is the eddy current loss (in W)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003172_s12206-013-0218-4-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003172_s12206-013-0218-4-Figure4-1.png",
        "caption": "Fig. 4. Schematic of the melting mechanism of formed droplet.",
        "texts": [
            " At the time of T3, the stretched liquid droplet turns to spatters because of exposure to the laser beam of high energy. Based on this observation from the high speed images, it can be analyzed that when the distance Wx is at 1.45 mm and VF is at 3 m min-1, the filler wire and laser beam have no direct interaction between each other and therefore, the melting dynamics under this case is mainly influenced by the laserinduced metal vapor/plasma radiation heat PM and molten pool radiation heat PW as shown in Fig. 4. Based on the observation from these high speed images, it is also found that the formed droplet always sticks to the end of the filler wire during the whole process of melting transition. The free fall of the droplet which is the typical phenomenon observed in arc welding is not observed in the process of WFLW. Therefore, it indicates that the mechanisms of the formation and transition of the droplet in filler wire laser welding and arc welding are different. In order to further understand the reason in terms of force that why and how this big droplet forms in filler wire laser welding and study the differences between filler wire laser welding and arc welding, different forces that act on the droplet are schematically analyzed and compared as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002234_j.triboint.2010.06.014-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002234_j.triboint.2010.06.014-Figure1-1.png",
        "caption": "Fig. 1. Proposed 2D numeri",
        "texts": [
            " Moreover, all the elements perform planar movements, in the plane normal to the bearing axis (the so-called movement plane). Finally, the forces between components, as well as the external one, also lie in planes that are parallel to the movement plane, which is a plane stress problem. For all these reasons, the dynamic and elastic behavior of a radial roller bearing can be adequately described by a 2D numerical model, consisting of the section of the assembly by the movement plane. The model (see Fig. 1) is composed of the shaft, the inner ring, 13 rolling elements (rollers), the outer ring, the cage, and a system of radial elements that gives the prescribed speed to the shaft. We call this system \u2018\u2018motor torque\u2019\u2019. The shaft, the rings and the rollers are meshed into 2D elements with material properties of common steel (see Table 1), whereas the cage is composed of 13 beam elements articulated at each roller centre. The elements composing the motor torque are beam rigid elements. The software employed for modeling preprocessing running and post-processing mechanical event simulations was AlgorTM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002098_j.mechatronics.2008.11.013-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002098_j.mechatronics.2008.11.013-Figure2-1.png",
        "caption": "Fig. 2. Vector diagram of a PSS kinematic chain.",
        "texts": [
            " So how to implement the actuator redundancy and improve the performance for the parallel manipulator, especially used for the application of the large load requirement, is a very interesting problem. It is also one of motivation for us to write this paper. This paper presents the development of 6-dof parallel seismic simulator with novel redundant actuation used for the application of large load requirement. The structure is presented firstly. Then, the kinematics analysis is carried out. In the following, the consideration for the prototype building is illustrated. Finally, the paper is finished with conclusions. The schematic of the 6-dof seismic simulator is shown in Fig. 1 and Fig. 2. As shown in Fig. 1. The parallel seismic simulator is composed of a moving platform and six sliders. In each kinematic chain, the platform and the slider are connected via spherical ball bearing joints by a strut of fixed length. Each slider is driven by Dc motor via linear ball screw. The detail of the implementation of the actuation is presented in the Section 4. The lead screw of B1, B2 and B3 are vertical to the ground. The lead screw of B4, B5 and B6 are parallel with the ground and are orthogonal to lead screw of B1, B2 and B3",
            " Let the rotation matrix be defined by the roll, pitch, and yaw angles, namely, a rotation of Eq. (1) about the fixed x axis, followed by a rotation of Eq. (1) about the fixed y axis, and a rotation of Eq. (1) about the fixed z axis. Thus, the rotation matrix is oRo0 \u00bc Rot\u00f0z;/z\u00deRot\u00f0y;/y\u00deRot\u00f0x;/x\u00de \u00bc c/zc/y c/zs/ys/x s/zc/x c/zs/yc/x \u00fe s/zs/x s/zc/y s/zs/ys/x \u00fe c/zc/x s/zs/yc/x c/zs/x s/y c/ys/x c/yc/x 2 64 3 75 \u00f01\u00de where c/ \u00bc cos /; s/ \u00bc sin /. The angular velocity of the moving platform is given by [21] x \u00bc \u00bd _/x _/y _/z T \u00f02\u00de As shown in Fig. 2, the closed-loop position equation associated with the ith kinematic chain can be written as r\u00fe ai \u00bc liwi \u00fe bi \u00fe di \u00fe qiei \u00f03\u00de where r; qi; ei; wi; ai; bi and di denote the vector OO0, the joint variable, the unit vector along the lead screw, the unit vector along strut CiAi, the vector O0Ai, the vector OBi and the vector from the lead screw to the center point of the joint Ci respectively. Taking 2-norm on both sides of the Eq. (3) and considering the assembly model, gives the inverse position solution q1 \u00bc A1z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l21 \u00f0A1x a\u00de2 \u00f0A1y \u00fe a d1\u00de2 q \u00f04a\u00de q2 \u00bc A2z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l22 \u00f0A2x\u00de2 \u00f0A2y a d2\u00de2 q \u00f04b\u00de q3 \u00bc A3z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l23 \u00f0A3x \u00fe a\u00de2 \u00f0A3y \u00fe a d3\u00de2 q \u00f04c\u00de q4 \u00bc A4y \u00fe h1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2 4 \u00f0A4x c\u00de2 \u00f0A4z h2 d4\u00de2 q \u00f04d\u00de q5 \u00bc A5y \u00fe h1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2 5 \u00f0A5x \u00fe c\u00de2 \u00f0A5z h2 d5\u00de2 q \u00f04e\u00de q6 \u00bc A6x \u00fe h1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l26 \u00f0A6y\u00de2 \u00f0A6z h2 d6\u00de2 q \u00f04f\u00de Taking the derivative of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure4.9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure4.9-1.png",
        "caption": "Figure 4.9 Periodic trapezoidal pulse train representing a clock signal.",
        "texts": [
            " Using (4.23) and (4.24), we find that I U , ~ ~ = f2Alnl7r /sin I , n = 1 , 2 , . . A a0 = - 2 \u2019 (4.29) (4.30) 7r 7r and etc. al = ~~ u.3 = -- 2 \u2019 2 \u2019 Thus, (4.22) reduces to (4.3 1) We conclude from here that a periodic rectangular pulse having a 50% duty cycle will have only odd harmonics, although there is a constant term present. 128 SIGNAL WAVEFORM AND SPECTRAL ANALYSIS POWER SIGNALS 129 Generally, clock signals in digital circuits are periodic pulses of trapezoidal waveforms sketched in Figure 4.9 where the key parameters of the waveform are also indicated. The pulse width r is defined as the time interval between the 50% points of the waveform amplitude A. rr, rf are the pulse rise time and fall time from level 0 to level A, and vice versa. T is the time period of the repeating signal. In [7] the required Fourier coefficients for the signal f ( t ) are derived by decomposing the given function into linear combinations of simpler functions. We will represent f ( t ) as a Fourier series in a standard manner described earlier. Since the integrations required for the determination of the Fourier coefficients a, are rather lengthy, we will present here the key steps involved. From Figure 4.9 the complete representation of f ( t ) in the time interval 0 5 t 5 T is At f ( t ) = fi( t) = - 70 I t I r r r r r r 7 f = f2(t) = A, T~ 5 t 5 T + - - - 2 2 At A Tf 7-f 2 2 (4.32) = f3(t) = -- + - (T + 2 + 2) , <fIT+-+- Tr rf 2 2 7r Tf = O , T + - + - < t 5 T. 2 2 - 130 SIGNAL WAVEFORM AND SPECTRAL ANALYSIS From the preceding representation off ( t ) , we can now express the required an as where an 1 I1 + 12 f 13, (4.33) (4.34a) 1 r + r r / 2 - r i / 2 I , = - f 2 ( t ) e-jnwot (4.34b) T .I, r+rr /2+ri /2 f 3 @ ) e- jnwot (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003296_j.ymssp.2017.05.041-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003296_j.ymssp.2017.05.041-Figure5-1.png",
        "caption": "Fig. 5. Gear tooth with 0.5 mm root crack.",
        "texts": [
            " Based on the above-mentioned expression, the total effective TVMS K\u00f0t\u00de of a single tooth pair which includes a cracked tooth can be written as: Table 2 Values of the coefficients of Eq. (18). Ai \u00f0 10 5\u00de Bi \u00f0 10 3\u00de Ci \u00f0 10 4\u00de Di \u00f0 10 3\u00de Ei Fi L \u00f0hfi; hf \u00de 5.574 1.9986 2.3015 4.7702 0.0271 6.8045 M \u00f0hfi; hf \u00de 60.111 28.100 83.431 9.9256 0.1624 0.9086 P \u00f0hfi; hf \u00de 50.952 185.50 0.0538 53.300 0.2895 0.9236 Q \u00f0hfi; hf \u00de 6.2042 9.0889 4.0964 7.8297 0.1472 0.6904 where Kn is the stiffness of the healthy pinion and Kc is the stiffness of the cracked gear. According to the faulty gear model of the experimental table shown in Fig. 5. The main parameters of gear and pinion are shown in Table 3. The TVMS K\u00f0t\u00de of the healthy and cracked gear pair are shown in Fig. 6, with the crack depths and inclination angle q \u00bc 0:1;0:2; . . . ;1:9;2:0 (mm) and ac \u00bc 90 , respectively. Above-mentioned AM of the TVMS is convenient and effective. But in the process of calculation of the tooth crack stiffness, the gear tooth is considered as a non-uniform cantilever beam, which can not accurately calculate the local small deformation of the tooth",
            " 14, rRMS, rKurtosis, rNA4 and rRMSF all increase monotonically along with the growth of the crack depth, and all the new feature indicators of the dynamic response have obvious sensitivity to the gear crack fault. The one-stage spur gear with crack defect of rotating machinery experimental device is shown in Fig. 10, and the parameters of spur gear system and experimental table of gear system are listed in Tables 3 and 6, respectively. In order to simulate the fault of gear crack, we manufacture cracks near the tooth root of the pinion, and the crack depths of 0.5 mm, 1.0 mm, 1.5 mm, 2.0 mm are acquired by wire-electrode cutting (Fig. 5). In the whole vibration signal sampling process, the rotation speed of input is 1000 rpm and the load is 50 N m. The sampling frequency is 8192 Hz. Therefore, the rotation frequency of the gear is 16.7 Hz, and the meshing frequency of the gear is 666.7 Hz. Then the health status, 0.5 mm, 1.0 mm, 1.5 mm, 2.0 mm tooth root crack fault status vibration signals are acquired through the experimental rig. Vibration signals waveforms of gear system with four kinds of crack condition are given in Fig. 15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure10-17-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure10-17-1.png",
        "caption": "FIGURE 10-17 Common North American types of trac tor tire treads. (a) R-I or general-purpose tread; (b) R-2 or deep lug cane and rice tread; (c) R-3 or flotation; and (d) R4 or industrial lug. (Courtesy Goodyear Tire and Rubber Co.)",
        "texts": [],
        "surrounding_texts": [
            "Some traction conditions that affect performance are:\n1. Soil parameters (physical properties) 2. Presence of crop residues and cover crops 3. Direction of loading of tire (e.g., hillside use) 4. Load carried by tire 5. Tire pressure (deflection ratio*)\n*Deflection ratio (deflectionltire section height)",
            "TREAD DESIGN\n261\nThe decision as to which tire tread performs best is also dependent on the criteria being used. Some of the criteria are;\n1. Tractive efficiency 2. Net tractive coefficient 3. Tire life 4. Soil compaction",
            "262"
        ]
    },
    {
        "image_filename": "designv10_10_0003781_j.ymssp.2017.05.036-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003781_j.ymssp.2017.05.036-Figure3-1.png",
        "caption": "Fig. 3. Motor-gear transmission mechanism.",
        "texts": [
            " One can control id \u00bc 0 such that stator current only has the q-axis component. Therefore, with the implementation of the field-oriented control, the PMSM driving system can be simplified into the DC motor model. In this case, Eqs. (13) and (15) can be rewritten as ud \u00bc xrwq uq \u00bc Rsiq \u00fe Lqpiq \u00fexrwf \u00f016\u00de Tem \u00bc 3 2 npwf iq \u00bc Ktiq \u00f017\u00de where Kt \u00bc 3 2npwf is the torque coefficient. Equation of motion of the rotor is Tem \u00bc TL \u00fe Bmxr \u00fe Jm _xr \u00f018\u00de where TL, Bm and Jm are the load torque, the damping coefficient and the inertia of rotor, respectively. Fig. 3 shows a motor-gear transmission mechanism including a geared speed reducer with a gear ratio n \u00bc n1 n2 \u00bc T TL \u00bc xr x \u00f019\u00de Substituting Eqs. (17) and (19) into Eq. (18), the output torque can be obtained T \u00bc n\u00f0Ktiq nBmx nJm _x\u00de \u00bc n\u00f0Ktiq nBm _a nJm\u20aca\u00de \u00f020\u00de where x is the angular velocity of mechanism. For the elevation and azimuth servomotors, the output torque vector can be written as T \u00bc n\u00f0K tiq nBm _q nJm\u20acq\u00de \u00f021\u00de where n, K t , Bm and Jm represent the diagonal matrices composed of the elevation and azimuth servomotor parameters n \u00bc n1 0 0 n2 ; K t \u00bc Kt1 0 0 Kt2 ; Bm \u00bc Bm1 0 0 Bm2 ; Jm \u00bc Jm1 0 0 Jm2 \" # In this subsection, the PMSM model is built based on the field-oriented control theory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure9-3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure9-3-1.png",
        "caption": "FIGURE 9-3 A sinusoidal vibration with peak and the R~lS value of the signal.",
        "texts": [
            " 208 HUMAN FACTORS IN TRACTOR DESIGN NOTE: Exposure to impulsive or impact noise should not exceed 140-dB peak sound pres sure level. aSound level meter using A-scale, slow re sponse. Acoustic noise is sound, and sound is, physically speaking, mechanical vibrations in gaseous, fluid, or solid media. Sound is characterized by fre quency, amplitude, and phase. The frequency range of the human ear extends from as low as 16 Hz to as high as 20,000 Hz. From a practical standpoint, however, few adults can perceive sound above 11,000 Hz. The simplest vibration is a pure tone that consists of a sinusoid (fig. 9-3) with the frequency: f= T (2) where T = period in seconds The magnitude is most commonly expressed as the RMS (root mean square) value because of its direct relation with the energy content of the signal in linear systems. For a simple, pure tone (3) Airborne sound is a variation in the normal atmospheric pressure. Most sound-measuring instruments are calibrated to read RMS airborne sound pressures on a logarithmic scale in decibels. Sound pressure can be expressed OPERATOR EXPOSURE TO l\\;OISE 209 as a sound pressure level (SPL) relative to a reference sound pressure",
            " In our present discussion, vibration will be confined to the mechanical context of a solid medium. Many important mechanical vibrations in tractors lie in the frequency range of 1 to 100 Hz (corresponding to rotational speeds of 60 to 6000 rpm). The oscillatory motion can be simple harmonic or extremely complex. Like sound, mechanical vibration is characterized by frequency, amplitude, and phase. In the simplest case, mechanical vibration can be derived from a simple harmonic wave form as shown in figure 9-3 and mathematically described by the displacement function: x = A sin wt (6) where X displacement, m A peak amplitude, m w frequency of vibration, radls time, s X wA cos wt (7) where X= velocity, mls X -w2 A sin wt (8) 214 HUMAN FACTORS IN TRACTOR DESIGN where X = acceleration, m/s2 One readily notes that the acceleration is proportional to the displacement and to the square of the frequency. Vibration is usually measured with an accelerometer, which senses X in equation 8. An accelerometer is an electromechanical transducer that pro duces an output voltage signal proportional to the acceleration to which it is subjected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001938_0020-7403(76)90006-0-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001938_0020-7403(76)90006-0-Figure1-1.png",
        "caption": "FIG. 1. The shape of the water surface around a sphere at various stages of oblique impact, after Richardson. ~",
        "texts": [
            " 8 Although Rayleigh's result was derived for a plane lamina, and is only strictly true for steady-state laminar flow, it will be assumed in the following sections that the pressure on any element of a curved surface in contact with the water is given by this equation. This is clearly only an approximation to the complex pressure distribution acting on a partially submerged projectile, but it will be argued below that equation (2) gives a better representation of the true forces than Birkhoff's equation. Figure 1 shows the wetted area of a sphere at various depths of immersion during oblique impact on water; these diagrams were taken from those of Richardson. 4 From Fig. 1 it appears that the water pressure must act over a considerably greater area than that assumed by Birkhoff et al.; 3 in this work it is proposed that ~b~, the angular extent of the wetted area, over which the pressure acts, is equal to 2~b0 for 0~<~b0~<Tr/2 and ~bw = ~r for 4)o > 7r/2, as showh in Fig. 2. 3. SPHERICAL PROJECTILE WITH NO SPIN The ricochet of a projectile is caused by the vertical component of the pressure distribution resulting from its *Morpurgo 2 shows a photograph of an oblate spherical bomb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002924_1.4023208-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002924_1.4023208-Figure2-1.png",
        "caption": "Fig. 2 The FZG device\u2014Niemann\u2019s gearbox\u2014(a) [6]\u2014used installed in the laboratory before measurements; with open gearboxes\u2014(b)",
        "texts": [
            "asme.org/pdfaccess.ashx?url=/data/journals/jvacek/926645/ on 04/22/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use To determine the state of wear of HCR gear sets, an FZG backto-back gear test-rig has been used. This standardized device (DIN 51 354 [6]) serves to investigate the load carrying capacity, which is limited by pitting, micropitting, thermal scuffing, slow speed wear or tooth breakage. A schematic drawing as well as a picture of the device used in experiments is shown in Fig. 2. The test rig consists of two gearboxes, the first one equipped with test gears and the second one with so-called power return gears. Gearboxes are connected with two shafts to close the power flow between them. The loading of the system is ensured by a prestress of the shaft using a load coupling. Input power is delivered by an electromotor [6]. Both gearboxes are equipped with high contact ratio (HCR) spur gearwheels (with the number of teeth z1\u00bc 21 and z2\u00bc 51, respectively, Fig. 3(a)). The HCR gear wheels differ from commonly used spur gears by a higher value of contact ratio, ea\u00bc 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001952_cdc.2009.5400277-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001952_cdc.2009.5400277-Figure4-1.png",
        "caption": "Fig. 4: 4th-order homogeneous differentiation",
        "texts": [],
        "surrounding_texts": [
            "The differentiator based on high-order sliding modes [19] is modified to allow faster convergence. As previously differentiation of signals up to the order k with a known upper bound L of the (k+1)th-order derivative is obtained. Linear terms are added to the differentiator in order to provide for the faster convergence, when the initial errors are large. The modified differentiator preserves the robustness and exactness of the standard differentiator, as well as its asymptotic accuracies. Theoretically the new non-homogeneous differentiator may feature a peaking effect, as a result of linear dynamics with large errors. In practice it is not observed. The next step will be further improvement of the differentiator convergence by introduction of higher order terms. Differentiator convergence with variable function L(t) is to be studied. The differentiator can be used for feedback control, since the separation principle is trivially fulfilled in the absence of noises."
        ]
    },
    {
        "image_filename": "designv10_10_0002260_iros.2009.5354557-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002260_iros.2009.5354557-Figure4-1.png",
        "caption": "Fig. 4. Definition of Parameters used to Analyze the Motion Capture Data",
        "texts": [
            " Although, in [24], we propose the real-time gait generation method, we use the same method for the off-line walking pattern generation in this research. In most of the cases, although \u2206x (j) G is much smaller than x\u0304G, we show later of this paper that \u2206x (j) G is important in realizing the human-like motion. \u2206x (j) G is calculated by using the dynamics filter based on the preview control [16]. In this section, we consider analyzing the human-motion captured data and obtaining the parameters used for the walking pattern generator. Fig.4 shows the definition of the physical quantities obtained by using the motion capture data. In this research, we focus on the motion of the lower body of the human. Assuming that each leg of the robot has 6 + 1 (toe) joints, the motion of the humanoid robot\u2019s lower body can be completely specified if we can specify the 6 dimensional motion of the waist and the both feet and the joint motion of the toe. First, we analyze the motion capture data. If the vertical velocity of both feet is smaller than the predefined threshold, we define the double support phase around this period of time",
            " With regard to the motion of the foot, since we consider the human motion walking straight ahead, the roll and the yaw rotation of the foot is much smaller than the pitch rotation. Thus, we focus on the x \u2212 z motion and the pitch rotation of the foot. B. Vertical Motion of Waist We first consider the vertical motion of the waist. Vertical position of the waist becomes maximum at the single support phase and becomes minimum at the double support phase. Let us consider the k-th step. As shown in Fig. 4, let the difference between the maximum and the minimum vertical position of the waist be \u03b6k. Fig.5 show the result of the human motion capture. As far as we tried, there is no remarkable relationship between the cycle time and \u03b6k. On the other hand, although it is not remarkable too, we can recognize that \u03b6k increases as the step length increases. The line shown in the right figure expresses the 2nd order curve fitted by using the least squares method. This curve is calculated as \u03b6k = 0.0019\u2212 0",
            "157L2 k (10) When the humanoid robot walks with large step length, the leg often falls in the singular posture. The yaw rotation of the waist is effective in avoiding the leg to be in the singular posture. On the other hand, when the robot walks with small step length, the yaw rotation is not needed. By using our method, since the yaw rotation can be obtained as a function of the step length, it is effective in avoiding the leg to be in singular posture when the step length is large. The left of the Fig.4 shows the motion of the swing foot. As shown in this figure, the pitch rotation becomes maximum after the foot lifts off. Then, the foot touches the ground after the pitch angle becomes minimum. Fig.7 shows the plot of the ankle height. The top left of Fig.7 shows rak = (tamax \u2212 tf,k\u22121)/Tk as a function of the cycle time where tamax denotes the time when the ankle height becomes maximum. As shown in this figure, the height of the ankle becomes maximum almost at the middle of the single support phase while this time slightly increases as the cycle time increases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002109_j.rcim.2009.10.002-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002109_j.rcim.2009.10.002-Figure6-1.png",
        "caption": "Fig. 6. Manufacturing process of HPDM.",
        "texts": [
            " Then the path including depositing path, the milling path and the hybrid path are scheduled. The scheduled path can be simulated at the HPDM\u2013CAM software to examine whether the path is fit for the part forming. If unsatisfactory, it will be re-scheduled till it fully fits the part structure. Then the NC instructions are generated and exported automatically by the HPDM\u2013CAM software. The NC instructions can be simulated with special numerical control simulation software to avoid overrunning or interference accidents [13]. Along the HPDM manufacture processes shown in Fig. 6, a superalloy (GH163) double helix integral impeller was trialmanufactured using the pre-scheduled path as well as the corresponding NC instructions (described above). The current processing scene of PDM shown in Fig. 7(a) is different from that of traditional NC milling in terms of contour milling shown in Fig. 7(b) and planar milling shown in Fig. 7(c and d) shows the photograph of the finish-machined superalloy double helix integral impeller. The whole manufacture process needs about 10 h. According to Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001892_iros.2008.4650991-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001892_iros.2008.4650991-Figure1-1.png",
        "caption": "Fig. 1: Body-referenced velocities, rates and axes",
        "texts": [],
        "surrounding_texts": [
            "An Autonomous Surface Vehicle (ASV) (also called an Unmanned Surface Vehicle (USV)) is a robot capable of carrying out a mission on the water surface without human assistance (or very limited human assistance). Such vehicles have varying capabilities, ranging from the simplest vehicles which have rudimentary guidance and navigation relying completely on pre-defined mission waypoints to more advanced versions which have the ability to avoid obstacles and reactively perform path planning. ASVs are very useful in automating tasks that would either be too expensive, dangerous or mundane for human operators to perform. Noteworthy examples are the Delfim ASV [15], the Autocat [11] and the ROSS [2], all designed for oceanographic and marine sensing. Almost every ASV that is designed to perform dynamic positioning has redundant sets of thrusters and actuators. Station keeping is achieved by applying the necessary thrust in opposition to any measured external disturbance. For systems that operate in the ocean, care has to be taken to ensure that the ship is filtering out high-frequency wave disturbances [6]. [10] describes the use of acceleration feedback in dynamic positioning. In many applications vehicles that do not have control in their sway axis will be required to keep station in the vicinity of a particular location. Such, underactuated dynamic positioning is discussed in [8] which describes a feedback control law that keeps a model of a small boat in station in an asymptotic manner using accurate visual position feedback. [1] addresses dynamic positioning 978-1-4244-2058-2/08/$25.00 \u00a92008 IEEE. 3164 of underactuated AUVs in the presence of constant unknown ocean currents. Our work follows the nonlinear control approach [7] designed for weather optimal positioning control. The system relies upon estimating a disturbance force and then using it for weather-vaning the vehicle into position. The control law proposed in [7] is designed for vehicles with multiple thrusters and the capability of simultaneously generating thrusts in the sway direction."
        ]
    },
    {
        "image_filename": "designv10_10_0001390_j.mechmachtheory.2005.09.004-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001390_j.mechmachtheory.2005.09.004-Figure2-1.png",
        "caption": "Fig. 2. Gear teeth processing by hob.",
        "texts": [
            " 1 it follows ~n \u00f0gw\u00de gw \u00bc cos u sin u zp cotga0 0 2 66664 3 77775; \u00f03\u00de ~v\u00f0gw\u00de gw \u00bc x\u00f0w\u00de zgw sin sgw ygw cos sgw \u00f0xgw \u00fe agw\u00de cos sgw \u00fe kw sin sgw \u00f0xgw \u00fe agw\u00de sin sgw \u00fe kw cos sgw 2 64 3 75. \u00f04\u00de The axial profile of the ground worm is defined by xwa \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 w \u00fe y2 w q ; zwa \u00bc zw kw tghwg; \u00f05\u00de where tghwg \u00bc yw xw . For the corresponding worm surface it follows ~r \u00f0w\u00de w \u00f0u; hw\u00de \u00bc xwa cos hw xwa sin hw zwa \u00fe kw hw 1 2 6664 3 7775; \u00f06\u00de where kw = r0w \u00c6 tgx0w. The gear teeth are generated by a hob (Fig. 2). As it was mentioned before, in order to provide tool life, the new hob has a slightly larger diameter than the worm. Therefore, the generator surface of the hob for gear teeth processing slightly differs from the worm surface, and it is defined by the equation ~r \u00f0h\u00de h \u00f0u; hh\u00de \u00bc xha cos hh xha sin hh zha \u00fe kh hh 1 2 66664 3 77775; \u00f07\u00de where kh = r0h \u00c6 tgx0h. The coordinate systems for gear teeth generation are shown in Fig. 2: coordinate system Kh is attached to the hob, K0 is the stationary coordinate system and Kg is attached to the gear. The machine tool setting angle Dc is due to the difference in lead angles of the worm and the hob (because of different diameters) Dc \u00bc x0w x0h. \u00f08\u00de The gear tooth surface is defined by the following equations ~r \u00f0g\u00de g \u00bcMhg ~r\u00f0h\u00deh ; ~n \u00f0h\u00de h ~v \u00f0h;g\u00de h \u00bc 0; \u00f09\u00de where matrix Mhg transforms the coordinates from system Kh into system Kg; on the basis of Fig. 2 it follows Mhg \u00bc m11 m12 m13 m14 m21 m22 m23 0 m31 m32 m33 m34 0 0 0 1 2 6664 3 7775; \u00f010\u00de where m11 \u00bc cos wh cos wg \u00fe sin wh sin wg sin Dc; m12 \u00bc sin wh cos wg cos wh sin wg sin Dc; m13 \u00bc sin wg cos Dc; m14 \u00bc ah cos wg; m21 \u00bc sin wh cos Dc; m22 \u00bc cos wh cos Dc; m23 \u00bc sin Dc; m31 \u00bc cos wh sin wg sin wh cos wg sin Dc; m32 \u00bc sin wh sin wg \u00fe cos wh cos wg sin Dc; m33 \u00bc cos wg cos Dc; m34 \u00bc ah sin wg; where wg \u00bc wh ig ; ig \u00bc Ng Nw . The normal vector of the hob generator surface is given by the equation ~n \u00f0h\u00de h \u00bc xha dzha du cos h\u00fe kh dxha du sin h xha dzha du sin h kh dxha du cos h xha dxha du 2 6666664 3 7777775 . \u00f011\u00de For the relative velocity of the hob to the gear, based on Fig. 2, it follows ~v \u00f0h;g\u00de h \u00bc x\u00f0g\u00de zh cos wh cos Dc ig yh \u00fe sin Dc \u00f0yh ah sin wh\u00de zh sin wh cos Dc\u00fe ig xh sin Dc \u00f0xh ah cos wh\u00de cos Dc \u00f0 xh cos wh yh sin wh \u00fe ah\u00de 2 64 3 75. \u00f012\u00de In fully conjugated worm gears line contact exists between the worm thread and gear teeth. The instantaneous contact line on the gear tooth surface, for a prescribed value of the rotational angle of the worm, ww, is defined by ~r \u00f0g\u00de g \u00bcMg M0 Mw r\u00f0w\u00dew \u00bcMwg ~r\u00f0w\u00dew ; ~n \u00f0w\u00de w ~v \u00f0w;g\u00de w \u00bc 0; \u00f013\u00de where matrix Mwg transforms the coordinates from system Kw (attached to the worm) into the system Kg (attached to the gear),~n\u00f0w\u00dew is the normal vector of the worm surface, and~v\u00f0w;g\u00dew is the relative velocity vector of the worm to the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001662_s00422-006-0117-1-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001662_s00422-006-0117-1-Figure2-1.png",
        "caption": "Fig. 2 A schematic drawing of a leg of a stick insect. It consists of four functional segments: coxa (cx), femur (fe), tibia (ti) and tarsus (ta). As a simplification the leg can be modeled as a manipulator of three segments connected through hinge joints: the thorax-coxa joint (TC, in the figure the axis of the joint is shown; the joint angle is labelled \u03b1.), coxa-trochanter joint (CT = \u03b2) and femur-tibia joint (FT = \u03b3 ) (from D\u00fcrr et al. 2004)",
        "texts": [
            " Its function is inspired by data conceived from experiments with stick insects. In this paper only aspects that are relevant in our context will be addressed (for further details see (D\u00fcrr et al. 2004), the model is formally defined in the appendix). The Walknet represents an autonomous agent in a virtual environment. It controls the legs of the agent to obtain a walking behaviour. The agent is therefore embodied\u2014it has a body and six legs, each consisting of three main parts (coxa, femur and tibia in Fig. 2) which are coupled through three hinge joints. The morphology of the body and its segments as well as the orientation of the axes of the joints are comparable to those found in the stick insect. Furthermore, the virtual animal is able to act on its environment by controlling the joints and to sense its surrounding through sensors. A main aspect of the Walknet is its decentralized modular architecture. Each leg has its own controller. The controller can be in one of two states: \u2022 The leg is in protraction (\u2018swing\u2019): the leg is lifted off the ground and swings from its posterior extreme position (PEP) to the front",
            " The two modules controlling the leg, the swing-net and the stance-net, are both implemented as neural networks. The swing-net is a simple, one layered neural network generating the trajectories to a target point by exploiting the loop through the world. Control of retraction is more difficult: all standing legs are mechanically coupled through their contact to the ground forming closed kinematic loops. Moving one joint has an effect on all the other joints. To cope with this problem, the different joints are treated differently in the retraction phase: the coxa-trochanter joint (CT, see Fig. 2), which is mainly responsible for holding the body in a specific distance over the ground (Cruse et al. 1989, 1993; Cruse 1976b), is driven through a simple negative feedback controller (as can be found in Diederich et al. 2002): depending on the current angles of the CT and femur-tibia joint (FT) of the leg the feedback controller steers the joint to an angle which results in the specific body height. To control the thorax-coxa joint (TC) and the FT we use a different approach, termed local positive feedback control (Kindermann 2002)",
            " The simulation provides the controller with the sensory signals\u2014they result from the movements of the joints (controlled by the controller) in interaction with the body, with each other and with the environment. Each leg has a position: we define the position in a local frame of reference with respect to the body oriented to the front. The position is one-dimensional and describes the position of the tarsus in the direction of the body long axis. The anterior extreme position defines the origin while the normal posterior extreme position is located at \u221210. posi(t), t \u2208 N0 (1) The joint angles (orientation of joint axes as in Fig. 2): \u03b1i(t), \u03b2i(t), \u03b3i(t), t \u2208 N0 (2) The load acting on the leg is determined through a simulated sensor which mimics the function of the campaniform sensilla in the insect. The sensor is mainly influenced by the torque in the beta-joint. Its values are linearly connected to the torque. The scale of the load is arbitrarily chosen (usually the load of a standing leg has a value of 12\u201324): loadi(t), t \u2208 N0 (3) The coordination rules influence the current posterior extreme position. The current PEP is used by the selector to decide if the leg shall switch from stance to swing mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000676_robot.1997.620040-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000676_robot.1997.620040-Figure3-1.png",
        "caption": "Fig. 3 Representation of Joint Angle",
        "texts": [
            " When the ZMP exists within the domain of the support surface, the contact between the ground and the support leg is stable. where pzmp denotes a position of ZMP. S denotes a domain of the support surface. This condition indicates that, no rotation around the edges of the foot occurs. 0 Boundary Condition for Continuous Walk- For continuous Walking, the hoiindary condiing tions of reference trajectory are given where T is the period of one step. This condition represents the continuity of joint angles. The places of joint angles are shown in Fig.3. 0 Free Leg Condition The free leg should not be contact to the ground during it moves. where ( p z , p y , p 2 ) denotes a foot position of the free leg, and F(p, ,p , ) represents the ground shape. 21 2 0 Other Conditions The foot plate is parallel against t.he ground to avoid collision between free leg and ground. The waist plate is parallel against the ground during the double support, period. (5) 4 Dynamic Equation of Biped Locomotion Robot We calculate the torque of each actuator to generate natural motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002497_j.conengprac.2010.02.014-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002497_j.conengprac.2010.02.014-Figure7-1.png",
        "caption": "Fig. 7. Notations in the body frame.",
        "texts": [],
        "surrounding_texts": [
            "In this section, the fundamentals of small-scaled helicopter modeling as used in the data fusion algorithm are recalled. Further details can be found in Mettler (2003)."
        ]
    },
    {
        "image_filename": "designv10_10_0002563_inista.2011.5946069-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002563_inista.2011.5946069-Figure3-1.png",
        "caption": "Figure 3. Definition of forces, moments and velocity components in a body fixed frame [1].",
        "texts": [
            " Roll control is a lateral problem and this work is developed to control the roll angle of an aircraft for roll control in order to stabilize the system when an aircraft performs the rolling motion. The roll control system is shown in Fig. 2. In this figure, Yb and Zb represent the aerodynamics force components, \u03c6 and a\u03b4 represent the orientation of aircraft (roll angle) in the earth-axis system and aileron deflection angle respectively. The forces, moments and velocity components in the body fixed frame of an aircraft system are shown in Fig. 3 where L, M and N represent the aerodynamic moment components, the term p, q and r represent the angular rates components of roll, pitch and yaw axis and the term u, v and w represent the velocity components of roll, pitch and yaw axis. Referring to Fig. 2 and Fig. 3, the rigid body equations of motion are obtained from Newton\u2019s second law, see [1]. But, a few assumption and approximation need to be considered before obtaining the equations of motion. Assume that the aircraft is in steady-cruise at constant altitude and velocity, thus, the thrust and drag cancel out and the lift and weight balance out each other. Also, assume that change in pitch angle does not change the speed of an aircraft under any circumstance [5]. Under these assumptions, the lateral directional motion of an aircraft is well described by the following kinematic and dynamic differential equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002109_j.rcim.2009.10.002-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002109_j.rcim.2009.10.002-Figure4-1.png",
        "caption": "Fig. 4. Double helix integral impeller CAD model.",
        "texts": [
            " The service life of the augmentor made of double helix integral impellers is longer than that of the others, and the operating cost is low. Besides, the impeller can meet the demand of clockwise air-in and anticlockwise air-out to ensure uniform air flowing. The double helix integral impeller is selected as the subject investigated in this paper, because it is difficult to manufacture it using traditional machining technologies. The STL format CAD model of a double helix integral impeller used in this study and proportionally minified from that used in a certain type aeroengine is shown in Fig. 4. The material is nickel-based superalloy. 3.2. Path planning The part with free surfaces will bring machining shadows and interferences. So the cutter path is difficult to obtain if using traditional machining processes. Moreover, since the material is nickel-based superalloy, the part is difficult to manufacture with the five-axis milling machine. This problem will be readily solved if we adopt the HPDM lamination hybrid process. The HPDM\u2013 CAM software interface and the parameter attribute setting page shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001851_978-1-4020-8600-7_24-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001851_978-1-4020-8600-7_24-Figure1-1.png",
        "caption": "Fig. 1 SCARA systems test trajectory.",
        "texts": [
            " Moreover, the motivation of this work being the optimization of the McGill Sch\u00f6nflies Motion Generator (SMG) [3], the focus is on four-dof (degree-of-freedom) Cartesian trajectory optimization. Typically, SMG, or SCARA systems, are used for PPO in industry. A trajectory for this type of operation has been adopted by the industry in order to provide a basis for comparison among the different systems on the market. This trajectory involves a vertical upward translation of 25 mm, a horizontal translation of 300 mm and a final vertical downward translation of 25 mm as shown in Figure 1. The moving platform (MP) of the SCARA system has to move through this trajectory back and forth with a rotation of 180\u25e6, along the horizontal segment, in a given cycle time. Adept Technology1 boasts cycle times of 500 ms, while EPSON2 claims cycle times of 409 ms. As specified, the test trajectory includes square corners between its vertical and horizontal segments, which are obvious sources of acceleration discontinuities. These corners have to be smoothed in order to remove these discontinuities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003801_j.matdes.2017.10.020-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003801_j.matdes.2017.10.020-Figure5-1.png",
        "caption": "Fig. 5. Bonding fixture assem",
        "texts": [
            " The clad layer/HAZ interface was made at the structural transition, as shown in Fig. 4b. In order to obtain the interfacial bond strength, a circular-arc notch was machined exactly at the interface using a profile cutter. Several notched T-shaped samples constructed of substrate material were prepared as control samples. The bonding test experimentwas performed on aWDW-100/E testing machine with a \u00b1100 kN maximum loading capacity. The bonding fixture system was developed to constrain the testing samples, as shown in Fig. 5. Tensile tests were conducted at room temperature at a displacement rate of 0.05 mm/s. The fracture morphology of the samples was investigated with the scanning electron microscope (SEM). Fig. 6 shows the magnified dilatometric curves of FV520B steel corresponding to the continuous heating process. Thematerial experiences three stages during the heating process, as shown in Fig. 6b. As the temperature of thematerial increases from the austenitizing initiation temperature (Ac1) to the complete austenitizing temperature (Ac3), the material transforms from martensite (\u03b1-Fe) to austenite (\u03b3-Fe)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001081_s0022-460x(03)00072-5-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001081_s0022-460x(03)00072-5-Figure3-1.png",
        "caption": "Fig. 3. An infinitesimal spring\u2013damper gear mesh model.",
        "texts": [
            " These matrices correspond to the coordinate vector fuz1; yx1; yy1; uz2; yx2; yy2g T; where the numeric subscript represents the corresponding node in Fig. 2. The gear mesh kinematics is modelled using a concept originally proposed by Tuplin [12], which has been widely used by many gear researchers [13\u201315]. The linear time-invariant model consists of an infinitesimal spring\u2013damper element positioned in series with the loaded static transmission error excitation e(t) at the mesh point as shown in Fig. 3. The mesh model couples the translational co-ordinates of the gear and pinion centroids along the tooth load line-of-action. Additionally, the bending rotation and torsion co-ordinates of the gears are considered, which match exactly to the corresponding shaft degrees of freedom. However, the direct coupling between the gear bending rotation and the other two gear co-ordinates is assumed negligible when formulating the mesh model because of the horizontally straight spur gear tooth arrangement and the fact that the shaft geometries are nearly symmetric with respect to the gear and pinion positions",
            " In the case of actuation concept 2 on semi-active gear\u2013shaft torsional coupling, the gear\u2013shaft connection (that is rigid in the baseline FE model) is replaced by a lumped spring\u2013damper element along the rotational co-ordinate, while all other parameters remain the same. The geared rotor system is assumed to be excited only by the gear transmission error under loaded conditions, which is typically on the order of 1\u2013100mm depending on manufacturing errors, tooth profiles, elastic deformations and transferred loads [20]. In this study, it is assumed that the magnitude of the transmission error at the mesh frequency of excitation is nominally 10mm. As depicted in Fig. 3, the transmission error excitation yields a pair of translational dynamic force and torque fluctuations acting on the gear and pinion. Hence, the excitation force vector F in Eq. (6) can be expressed as F \u00bc \u00bd0?0 Km 0 KmRg 0?0 Km 0 KmRp 0?0 T e; m m m m uzg yyg uzp yyp \u00f09\u00de where e is loaded transmission error represented mathematically as 10eiomt mm that considers only the fundamental mesh harmonic, and uzg; uzp; yyg and yyp are the gear and pinion translation and rotation co-ordinates, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001833_1.2806163-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001833_1.2806163-Figure5-1.png",
        "caption": "Fig. 5 The rolling contact cycle and the RVE",
        "texts": [
            " In the numerical model, these weak planes orrespond to the interelement joints along which fatigue cracking an occur. Since these joints are randomly oriented in space, the agnitude of the critical stress quantity and its corresponding epth both vary with the microstructure. imulation of Rolling Contact Cycle The actual loading history experienced by points in the subsur- ace region of a bearing contact during a single pass of the rolling lement can be simulated to a good degree of accuracy by moving he appropriate contact pressure distribution along the surface of he semi-infinite domain. Figure 5 shows the domain used in the urrent analysis. In theory, a semi-infinite domain is infinite in xtent. However, for computational purposes, the domain created s restricted to 10b in the x rolling direction and 6b in the z 11011-4 / Vol. 130, JANUARY 2008 om: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/d depth direction. The limits are selected in consideration of the fact that in Hertzian contacts, stresses at points sufficiently remote from the contact region are practically unaffected by the contact loading",
            " It is to be noted that this variation is only possible by using a randomly generated Voronoi domain such as the one considered in this analysis. Since, in the current analysis, only the depth coordinate of the joints is of significance, the analysis is restricted to joints located within a representative volume element RVE . It is assumed that this RVE is periodic in space and is repeated along the circumference of the bearing inner race. The selected RVE extends to a depth of b in the z direction, is 2b wide in the rolling x direction, and is aligned with the x-z coordinate frame, as illustrated in Fig. 5. The depth dimension of the RVE is selected large enough so that the critical stress occurs within the RVE. This is based on experimental observations that indicate that subsurface cracks initiate within this depth 11,12 . During the rolling contact cycle, the surface pressure distribution is moved with respect to the x-z coordinate frame from \u22123b to 3b. Table 1 shows the simulation parameters used for the current analyses. Figure 7 illustrates the variation of the orthogonal shear stress xz along the depth direction for four different material domains generated using the Voronoi tessellation process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-10-1.png",
        "caption": "FIGURE 5-10 Zero-lash hy draulic valve lifter. (Courtesy Wil cox Rich Division, Eaton Manufac turing Co.)",
        "texts": [
            " The stem material is welded to the head section of the valve and heat-treated to provide better scuff resistance. 6. Valve Rotators-These are mechanical devices [see fig. 5-9] which cause the valve to turn in the opening portion of the cycle. Rotation tends to ensure good heat transfer from the valve face to the seat. Several types are in use. Valve rotators have been responsible for durability improvements of from two to ten times of the same material without rotation. 7. Hydraulic Valve Lifters-Hydraulic valve lifters [see fig. 5-10] compensate for wear and for thermal changes in the valve train. Their use tends to avoid excessive stresses resulting from too large a clearance, as well as excessive valve temperatures resulting from too small a clearance. Valves are subjected to high acceleration forces. For example, in an en gine operating at 2400 rpm, an exhaust valve must open, permit the burned mixture to escape, and then close, all within about 0.01 s. During this cycle the exhaust valves and seats are exposed to temperatures that may be as high as 2500\u00b0C during the combustion and may be about 650\u00b0C during the exhaust"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001753_41.31494-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001753_41.31494-Figure5-1.png",
        "caption": "Fig. 5 . Two-linkage robotic arm: /, length between joint i and center of mass link i; m, mass of link i.",
        "texts": [
            " (14 The nonlinear compensation term is of the form ti=6 [ ( E + $ ) e+ (m,+f iL)g sin e +ed-2he-h2e 1 (20) where 1 . -\\ 1 The saturating function term is composed of a saturatin:. function and control gain A 9 R = k(8) - k(8d) + - P e = b I-([+:) e - (ml+ML) g s i n 8 +bu 3 324 The boundary layer thickness a varies in accordance with the folowing law: Xk P k(8d) 2 - * 6 + ha =Pk(8d) The flowchart of this algorithm is shown in Fig. B. Control Implementation of Two-link Arm (23) 4. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 36, NO. 3, AUGUST 1989 Consider the two-linkage arm of Fig. 5 . All of its physical parameters are given in Table I. The physical model of the robotic arm has the form M ( e ) e + h ( e , e ) = ~ (24) where M(8) E R 2 x 2 is the inertia matrix h(8, e ) , and eR2 represents nonlinear terms such as Coriolis, centrifugal forces, gravity, and viscous damping forces. As stated previously, the available model is in fact the estimated form n;r(e)e + &(e, e ) = 7. (25) The discrepancies between (24) and (25) may arise from wellknown factors: imprecisions on the robot arm geometry or inertias, uncertainties on friction terms or the loads, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001730_j.cirp.2007.05.092-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001730_j.cirp.2007.05.092-Figure1-1.png",
        "caption": "Figure 1: Milling motor spindle with rolling bearings.",
        "texts": [
            " The rough machining of steel, for example, is characterised by high cutting forces and moments and moderate rotational speeds. In those cases, bigger spindle and bearing diameters are essential to bear these loads. The following basic approaches for the design of main spindles can be derived from the diverging demands presented above. To fulfil those demands, the characteristic speed coefficient n x dm has to be increased up to 3.5 \u2013 4.0x106 mm/min, ensuring a sufficient stiffness and robustness of the spindle body and the spindle bearings. Figure 1 presents a typical motor spindle with a power output of 80 kW and a maximum rotational speed of 30,000 rpm. The stator of the drive is water-cooled. The spindle body has a hollow shaft taper and is rotationally supported by an elastically preloaded back-to-back spindle bearing arrangement. In order to develop an improved spindle and bearing design the optimisation of the fixed bearing unit (varied inner bearing geometry), of the movable bearing unit(elastic cylindrical roller bearings) as well as of the tribological properties (surface coatings, lubrication) shall be analysed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000955_bf00045108-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000955_bf00045108-Figure1-1.png",
        "caption": "Figure 1. Definition of some kinematical quantities associated with a disk in motion on a horizontal plane.",
        "texts": [
            " The Dynamics of Rolling Disks and Sliding Disks 289 In this paper we consider a disk of radius R and mass M which moves with one point in contact with a horizontal surface. A vertical gravitational force acts on the disk. Various equivalent developments of the equations of motion for this system are contained in standard dynamics texts (e.g. [6, 7, 9, 10, 13, 14]). Their complete development is presented in this section in the interests of future comprehension. Several of the kinematical results presented here differ from these texts and may be found in Casey [23], and Casey and Lain [24, 25]. Referring to Figure 1, let {E~, E2, E3} define a fixed Cartesian coordinate system. The vector E3 is chosen to be perpendicular to the horizontal surface. A second orthonormal basis {el, e2,e3} is defined such that e3 is always parallel to the relative position vector of the instantaneous point of contact P to the center of mass G of the disk, while el and e2 are parallel to the other principal axes of the disk. The basis vectors ei and Ei are related by ei = 0E i , where 0 = 0 ( t ) is a proper orthogonal (rotation) tensor (cf. [25]). The rotation tensor () may be parameterized using 2 angles, 0 and a, which are shown in Figure 1. It should be noted that when a = -t-7r/2 the disk is horizontal and when a = 0 the disk is vertical. We recall, from [14, 25], that 6i = ~ x ei, where the superposed dot denotes time derivative, and = &el + 0(sin(o~)e2 + cos(o0e3 ). (1) The kinematics of the disk are specified by the position vector of G, ~, and the three Euler angles O, o~, and ~, where ~p represents the spin of the disk about the e2 axis. The angular velocity vector of the disk is w = if) + ~e2 = ~1el + w2e2 + 0:3e3. (2) For future reference, the total energy of the disk (modulo an additive constant) is recorded: 1 1 E = M y "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001081_s0022-460x(03)00072-5-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001081_s0022-460x(03)00072-5-Figure5-1.png",
        "caption": "Fig. 5. Active control of gear\u2013shaft torsional coupling (concept 2).",
        "texts": [
            " This is especially critical when a piezoelectric type actuator is selected since its resonant frequency is inherently high. In the latter problem, suitable slip rings with proper power ratings must be used to ensure sufficient supply of power to the rotating actuators. Of course, the slip rings are also needed for the accelerometer signals. The second proposed concept is aimed at modifying the torsional vibration transmission path between the gear and shaft. In this set-up, the gear body and corresponding shaft are connected via several piezoelectric actuators, as shown in Fig. 5 for one set of gear\u2013shaft coupling set-up. The piezoelectric actuators serve two purposes. They transmit the mean torque in the gear\u2013shaft load path and simultaneously generate reactive dynamic forces to minimize transmitted perturbations. Like the first concept, slip rings are needed to provide input power to the actuators. Note that the translation force of the gear is transmitted via a rolling element bearing between the gear body and shaft. This particular actuation concept is similar to the application of an active dynamic force directly on the shaft (the receiver) with a reaction against a gear body (the mass), as described in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003145_j.mechmachtheory.2013.09.013-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003145_j.mechmachtheory.2013.09.013-Figure2-1.png",
        "caption": "Fig. 2. Coordinate frames assigned to A0,\u2026,A6 at the initial configuration.",
        "texts": [
            " moving base for themobilemanipulator that is shown in Fig. 1. Themulti-body systemMS(6) = {(Bi,Ai)|i = 0,\u2026, 6, Bi \u2282 Ai} consists of two branches and six joints. The first branch consists of B0 to B5. The secondbranch contains B6 and joint six is its last joint. Joint one is a free joint, the second joint is a nonholonomic three-d.o.f. planar joint, the next joint is a three-d.o.f. spherical joint and the rest of the joints are one-d.o.f. revolute joints. The coordinate frames assigned to A0,\u2026,A6 at the initial configuration are shown in Fig. 2. In the sequel, the joint parameters are specified, and Forward and Differential Kinematics maps of MS(6) are determined. Note that, in the following, a basis for Vj at the initial configuration is denoted by X\u0302 j; Y\u0302 j; Z\u0302 j n o , and the linear operator 0\u03c4jj \u2212 1 in the chosen coordinates is represented by the matrix 0Tj j \u2212 1. 6.1. Forward kinematics The first joint is a six-d.o.f. holonomic joint between B0 and B1. The classic joint parameters are q1 = [x1,y1,z1,\u03b81,x,\u03b81,y,\u03b81,z]T, where [x1,y1,z1]T is the position of H1 0(t)(O1) with respect to H1 0(0)(O1) and expressed in V0, and [\u03b81,x,\u03b81,y,\u03b81,z]T is the rotation angles of V1 with respect to the axes of V1 at the initial configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001620_iros.1992.587401-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001620_iros.1992.587401-Figure2-1.png",
        "caption": "Fig. 2. The Ambler",
        "texts": [
            " Furthermore, dead reckoning navigation is less expensive, typically by several orders of magnitude, than other navigational devices. Although in certain special instances dead reckoning navigation alone may provide sufficient navigational accuracy, in general, it should be combined with other navigational techniques to provide greater accuracy. See Section VI for further details. For the reasons elucidated above, dead reckoning navigation was implemented on the Ambler, an autonomous, six-legged walking robot for planetary exploration. Fig. 2 is a diagram of the Ambler. References [2] and [12] provide a description of the machine, its capabilities and dynamics. Since wheeled vehicles maintain continuous contact with the ground, the distance the vehicle travels can be calculated from the number of wheel revolutions. (This assumes benign terrain. In rough terrain, the body displacement can be estimated by averaging the rotations of all wheels, however this is typically not 111. Problem Statement The problem is to determine the position and orientation of a walking robot at any given time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003748_s11071-016-3218-y-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003748_s11071-016-3218-y-Figure1-1.png",
        "caption": "Fig. 1 Geometry of rack [2]",
        "texts": [
            " 2 F Total tooth contact force F0, F1 External excitations due to static load Tj and tooth profile deviations ei Hi Contact function at Mi M Moment about Y -axis due to total contact force F M, C, K Overall system mass, viscous damping ,and stiffness matrices Kg, Kb Stiffness matrices regarding to bearing and gear pair Rb, R f Radii of the gear base circle and reference circle, respectively T Transform matrix between the U\u2013V coordinate and R\u2013 S coordinate system Tj ( j = 1, 2) Torques appliedon thedriving ( j = 1) and driven ( j = 2) gear, respectively V i Structure vector at Mi W , Wc Length of the tooth width and the crack along tooth width a, b, c, f , \u03b1 Geometries of the rack in Fig. 1 ci Distance of Mi to the tooth center along Z -axis e ji Tooth profile deviation error at Mi for j th gear ew(E) Distance between points E \u2032 and E \u2032\u2032, i.e., plastic deformation at point E fi Contact force at Mi ki , kci Cell stiffness and local contact stiffness at Mi kg Global stiffness l0, l2, lw Crack location at the two ends of tooth and variation of crack location along tooth width in Figs. 3 and 7 m Gear module m j , I j , Ipj Mass, transverse moment of inertia, and polar moment of inertia of the j th gear kBx , kB\u03b8y , kB\u03b8 z Radial stiffness and rotational stiffness along Y - and Z - axes of the bearing support q DOF vector of the gear pair q0, q2, qw Crack depth at the two ends of tooth andvariationof crack depth along tooth width as shown in Figs",
            " This will cause uneven plastic inclination deformation along the tooth width. Therefore, it is necessary to build a gear tooth plastic inclination model for the spatially cracked tooth. 2.1 Determination of gear tooth geometry An accurate description of the gear tooth geometry is the prerequisite to analytically investigate the gear tooth plastic inclination deformation. For a standard spur gear tooth whose profile is generated by the standard rack (i.e., f = 1, c = 0.25, \u03b1 = 20\u25e6) with double tooth tip at each side as shown in Fig. 1, the straight line AB of the rack generates the gear tooth involute profile, whereas the rounded corner at tip BC generates the tooth fillet curve, i.e., trochoid curve. The involute and fillet region of the spur gear tooth profile can be expressed by two separate parametric equations, whichmeans that the coordinate of any point on the tooth profile can be exclusively determined [2, 17]. Suppose a general coordinate systemU\u2013V with its origin at the gear center O and the V -axis at the center line of the tooth being cut (as shown in Fig",
            " \u03b10 indicates the angle between the tooth center line and the line OQ, where point Q is the intersection point of involute curve and the base circle. Fig. 2 Generation of the tooth profile [2]: a involute region, b fillet region aP V O a Rb a0 up vp GEAR \u03c9 RACK U Q T P a' \u03c6 Rp up U O GEAR \u03c9 V RACK (a) (b) For the fillet region, the coordinate of any specific point P at the fillet region is given as [2,17]:{ u p = Rp sin \u03d5 \u2212 ( a sin \u03b1\u2032 + r ) cos(\u03b1\u2032 \u2212 \u03d5) vp = Rp cos\u03d5 \u2212 ( a sin \u03b1\u2032 + r ) sin ( \u03b1\u2032 \u2212 \u03d5 ) (2) where \u03d5 is computed as [2,17]: \u03d5 = a cot \u03b1\u2032 + b Rp (3) where a, b, and r are the dimensions of the rack as shown in Fig. 1, Rp is the radius of the pitch circle, \u03d5 and \u03b1\u2032 are illustrated in Fig. 2b. Detailed discussion about this can be found in Yu et al. [2]. Therefore, the standard spur gear tooth shape is completely defined by the 2 parametric equations. 2.2 Gear tooth plastic inclination model The gear tooth plastic inclination model due to the planar crack with uniform crack depth along the tooth width direction has already been investigated in Shao and Chen [1]. For this type of crack, a two-dimensional (2D)model is capable of defining the crack dimensions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure3-1.png",
        "caption": "Fig. 3. Blade profiles of a pair of fixed-setting face-milling cutters: (a) inner blade; (b) outer blade.",
        "texts": [],
        "surrounding_texts": [
            "positioning settings, while the last four motions, represented by E m , X B , X D and \u03b3 m , let positioning the work head. Additionally, \u03c9 t , \u03c9 w and \u03c9 c represent the tool (face-milling cutter), work and cradle rotation velocities, respectively. In this work both tilt angle i and swivel angle j will not be taken into account, since their effect will be compensated with the search for the pressure angles corresponding to the inner and outer cutter blade profiles.\nThe head-cutter is mounted on the cradle of the gear generator and it performs a planetary motion when considering the following two rotations: (b) rotation in transfer motion together with cradle around its own axis and (b) rotation in relative motion respect to the cradle around head-cutter axis. The rotation motion of the cradle and the work are related to each other. Rotation of the face-milling head-cutter about its own axis is not related to the generation process and is chosen to provide the desired cutting or grinding velocity.\n2.1. Geometry of generating profiles of tool cutting blades\nThe geometry of the profiles of both inside and outside blades are depicted in Figs. 2 and 3 for spread-blade and fixedsetting face-milling cutters, respectively. The main settings and parameters to define a face-milling head-cutter are presented in Table 2 . In case of grinding operations, both inside and outside profiles represent the cross section corresponding to the grinder applied instead of a head-cutter.\nAuxiliary coordinate systems have been defined as follows:\n\u2022 S s ( x s , y s , z s ). This coordinate system is fixed to the face-milling cutter. Its axis x s is directed along the cutter radius, while\nz s is directed along the head-cutter axis. As well, its origin O s is contained in the head-cutter bottom axial plane.\n\u2022 S i ( x i , y i , z i ). This coordinate system is fixed to the inside cutting profile. Its axis x i is oriented along the cutting profile\ntowards the dedendum of it, while its origin O i is contained in the head-cutter bottom axial plane.\n\u2022 S o ( x o , y o , z o ). This coordinate system is fixed to the outside cutting profile. Its axis x o is oriented along the cutting profile\ntowards the dedendum of it, while its origin O o is contained in the head-cutter bottom axial plane.\nAs shown in Figs. 2 and 3 , the geometry of cutting profiles is basically comprised of two sections: (i) the main generating profile, which generates the working part of gear tooth surfaces, and (ii) the blade edge profile, which generates the root fillet of the gear tooth surfaces.",
            "As shown in Figs. 2 and 3 , straight lines have only been considered as main generating profiles. Although settings might be different for inside and outside cutting profiles, according to Table 2 , henceforth general geometric parameters \u03b1, \u03c1 and R will be used for the sake of clarity. The appropriate standards will be adopted later on in order to distinguish between the inside and the outside cutting profiles.\nThe profile parameter s , strictly positive, constitutes the first surface parametric coordinate for the face-milling cutter\nmain generating surface, and its lower limit is obtained as follows\ns \u2265 \u03c1\n( 1 \u2212 sin \u03b1\ncos \u03b1\n) (1)\nThe position vector of a point P belonging to the main generating profile is represented in coordinate systems S i and S o for the inside and outside profiles, respectively, by\nr (P) p (s ) = r (P) i (s ) = r (P) o (s ) =\n\u23a1 \u23a2 \u23a3 s 0\n0 1\n\u23a4 \u23a5 \u23a6\n(2)\nMatrix M sp represents the coordinate transformation from coordinate systems S i and S o , fixed to the inside and outside cutting profiles, respectively, to reference coordinate system S s . The upper sign in Eq. (3) represents a point belonging to the inside profile ( x \u2261 i ), while the lower sign represents a point belonging to the outside profile ( x \u2261 o ). The aforementioned sign convention will be adopted from now on, unless another different one is mentioned.\nM sp = M s,x =\n\u23a1 \u23a2 \u23a3 \u2213 sin \u03b1 0 cos \u03b1 R 0 1 0 0\n\u2212 cos \u03b1 0 \u2213 sin \u03b1 0\n0 0 0 1\n\u23a4 \u23a5 \u23a6\n(3)",
            "Finally, if we denote point P as a point on the main generating profile, independently of whether it belongs to the inside\nor outside blade, P is represented in coordinate system S s by\nr (P) s (s ) = M sp r (P) p (s ) =\n\u23a1 \u23a2 \u23a3 R \u2213 s sin \u03b1 0\n\u2212s cos \u03b1 1\n\u23a4 \u23a5 \u23a6\n(4)\n2.1.2. Blade edge generating profile r f ( \u03bb)\nThe blade edge generating profile is a circular arc of radius \u03c1 (see Figs. 2 and 3 ). The center of the blade edge generating profile will be represented as O f i for the inside cutting profile and O f o for the outside cutting profile. The angular parameter \u03bb characterizes a point on the blade edge generating profile, and constitutes the first surface parametric coordinate for the face-milling cutter blade edge generating surface. Its variation range is given by\n\u03b1 < \u03bb <\n\u03c0\n2\n(5)\nThe derivation of the position vectors of the centers of the circular arcs corresponding to the edge profiles in coordinate system S s is required to represent a point of the blade edge generating profiles in the same coordinate system. The position vectors of point P in coordinate systems S i and S o , corresponding to the inside and outside profiles, respectively, are given by\nr ( O f p ) p = r ( O f i ) i = r ( O f o ) o =\n\u23a1 \u23a2 \u23a3 \u03c1 ( 1 \u2212sin \u03b1 cos \u03b1 ) 0\n\u00b1\u03c1\n1\n\u23a4 \u23a5 \u23a6\n(6)\nTaking into account matrix M sp , given by Eq. (3) , the centers of the circular arcs O f i and O f o are represented in coordinate\nsystem S s , as\nr ( O f p ) s = M sp r ( O f p ) p =\n\u23a1 \u23a2 \u23a3 R \u00b1 \u03c1 ( 1 \u2212sin \u03b1 cos \u03b1 ) 0\n\u2212\u03c1\n1\n\u23a4 \u23a5 \u23a6\n(7)\nFinally, the position vector of a point P on the blade edge generating profiles is determined in coordinate system S s by\nr (P) s (\u03bb) =\n\u23a1 \u23a2 \u23a3 R \u00b1 \u03c1 [( 1 \u2212sin \u03b1 cos \u03b1 ) \u2212 cos \u03bb ] 0\n\u03c1( sin \u03bb \u2212 1 )\n1\n\u23a4 \u23a5 \u23a6\n(8)\n2.2. Geometry of head-cutter generating surfaces\nThe geometry of the face-milling cutter generating surfaces is obtained as the locus of the cutting blades in their rotation motion about the cutter-head axis. They are derived by coordinate transformation from coordinate system S s ( x s , y s , z s ), fixed to the face-milling cutter, to coordinate system S t ( x t , y t , z t ), fixed to the cradle. Fig. 4 shows the previously mentioned coordinate transformation from S s to S t .\nThe angular parameter \u03b8 represents the angular position of the head-cutter blades in their rotation motion around the cutter axis of rotation, z t , and constitutes the second surface parametric coordinate of the head-cutter generating surfaces. Transformation matrix M ts , given by Eq. (9) , represents the coordinate transformation from S s to S t .\nM ts (\u03b8 ) =\n\u23a1 \u23a2 \u23a3 cos \u03b8 \u2212 sin \u03b8 0 0 sin \u03b8 cos \u03b8 0 0\n0 0 1 0 0 0 0 1\n\u23a4 \u23a5 \u23a6\n(9)\nThe inside and outside cutter generating surfaces constitute a pair of conical surfaces represented by Eq. (10) as a function of generalized surface parameters s and \u03b8 . Along the same lines, inside and outside blade edge generating surfaces constitute a pair of torus surfaces represented by Eq. (11) as a function of generalized surface parameters \u03bb and \u03b8 .\nr (P) t (s, \u03b8 ) = M ts (\u03b8 ) r (P) s (s ) (10)\nr (P) (\u03bb, \u03b8 ) = M ts (\u03b8 ) r (P) s (\u03bb) (11)\nt"
        ]
    },
    {
        "image_filename": "designv10_10_0003022_j.matdes.2012.10.010-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003022_j.matdes.2012.10.010-Figure5-1.png",
        "caption": "Fig. 5. Illustration of the laser clad layer cross section, left as-clad and right",
        "texts": [
            " However, only a few data points are available and two of the three laser-clad fractures were induced by surface pore defects, as described in detail in another study [37]. In contrast, for 42CrMo4-steel the Inconel 625 cladding has significantly enhanced the fatigue life, see Fig. 4b. Hence, the material combinations, despite having rather similar properties, have significant influence on the fatigue life. The macro field generated by the fatigue load situation can experience local stress raisers through a variety of defects from laser cladding, as illustrated in Fig. 5. Micrographs of some of the defects are shown in Fig. 6. We have distinguished three categories of defect, long wavy geometries (one-dimensional, 1D), local defects (0D) and planar (2D) defects. Long wavy geometries, see Fig. 6a, are the wavy surface (A in Fig. 5) generated by overlapping laser clads, and the wavy interface between the clad layers and the substrate (B in Fig. 5). Postmachining would eliminate the notches from the wavy surface (A) to a flat surface. Local defects comprise pores, see Fig. 6b\u2013f, and inclusions, Fig. 6d\u2013g. As described in another study [37], for example an oxide inclusion such as in Fig. 6d will act as a stress raiser similar to a spherical cavity while the inclusion substance itself is of minor importance. So the inclusion in Fig. 6d mainly acts like a spherical pore to the stress field while the inclusion in Fig. 6g acts as a cavity with an irregular, sharp shape [38]. Spherical pores can appear at the surface (F in Fig. 5) see Fig. 6c, and can be detected by the dye penetration test, see Fig. 6b for a cylindrical bar. Alternatively, the pores can be located inside the clad layer (I in Fig. 5) see Fig. 6f. Moreover, semi-spherical pores J were found at the clad-substrate interface, see Fig. 6e. As illustrated in Fig. 5, pores and inclusions can have a variety of critical locations, particularly just below the surface, G, H, and at the side edges of rectangular bars, K, L, M, as will be analyzed below. Another category is plane-like defects, namely hot cracks, D, see Fig. 6h and LOF, C, E, see Fig. 6i. Notches from as-clad surfaces are extended in one direction, but in the case of defects that have plane-like non-bonded interfaces their vertical inclination is of importance as well as their lateral orientation",
            " As mentioned above, inclusions within a spherical pore have very little effect on the stress raising property of that pore but non-spherical cavities or inclusions with sharp corners, see Fig. 6f, can be critical stress raisers. Due to their large variety these were not simulated here [38]. While for the cylindrical bar the azimuthal position of a pore can be important, for a square bar any pores close to the side edges experience an additional stress raiser. The stress concentration fac- after machining, with the variety of possible defects and their positions. tor of a pore semi-spherically open to the side edge, L in Fig. 5, is shown in Fig. 10 as a function of the depth below the surface. As in the case without the edge, a peak is achieved when the pore is just below the surface, as shown in Fig. 7h. If located in the clad layer, the edge pore L and the in-clad pore I have almost the same stress concentration factors. Close to the clad layer surface the edge pore achieves significantly higher values, due to the combined impact from two surfaces. Another special case is the semi-spherical interface pore J, see Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003250_s10846-015-0301-4-Figure29-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003250_s10846-015-0301-4-Figure29-1.png",
        "caption": "Fig. 29 Conceptual design of tilt-roll rotor quadrotor with prototype parts",
        "texts": [
            " The rotation of the axes and horizontal-vertical control inputs are given according to this diagram. In the tilt-roll system on the quadrotor, X1 and X2 are used for tilt motion of the rotors and Y1 and Y2 are used for roll motion of the rotors. The ground connection is fixed the same with the main Li-Po batteries and control board of the quadrotor. 4.3 Conceptual Design of Tilt-Roll Rotor Quadrotor In the automation systems laboratory, a representative conceptual design of tilt-roll rotor quadrotor was built with prototype level parts. Please see Fig. 29 for the initial photo of the quadrotor. In this design, MCI\u2019s car wing mirror tilting mechanism is successfully transferred to the quadrotor system. By using this tilting mechanism, it is possible to change four of the rotors surface planes along x and y axes with tilt and roll motions. In the Figure it is already clear that the front motors (#1 and #4) are both tilted and rolled different angles with respect to the quadrotor frame of reference. In this paper control, modeling and system design of a novel quadrotor that can tilt and/or roll its rotors is introduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001105_robot.2001.933160-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001105_robot.2001.933160-Figure7-1.png",
        "caption": "Figure 7: Top view of two Conro configurations and the module representation used to distinguish them",
        "texts": [
            ", each possible connection in each port needs to be labeled. In the case of the Conro module, a given port of a module can be connected to a given port of another module in one of two relative orientations: belly-down or belly-up. Hence, each port has only two associated connections d l and d2 as shown in Fig. 3.a. The corresponding labeled graph of this module representation is that of Fig. 3.d. As before, the labeled graph of the module is replaced by a digraph to make the label itself a part of the graph. This multiconnection digraph is shown in Fig. 7.c. Using this representation of the module, the configurations in Figs. 7.a-b are represented by the graphs shown in Figs. 8.a-b. which have nonisomorphic unlabeled graphs. The module representations described in this section are quite general and can be used to represent other homogeneous modular robots. The extension to heterogeneous modular robots is straightforward as different types of modules can be labeled by attaching to a given vertex of each digraph a tag that identifies the type of the module (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003159_j.jpowsour.2012.05.101-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003159_j.jpowsour.2012.05.101-Figure1-1.png",
        "caption": "Fig. 1. Microfluidic component used in this study, a) Y-shape microchannel and electrodes, b) operation with two separated laminar flows and c) operation with a single combined flow.",
        "texts": [
            " Bimetallic materials formation is evidenced from these techniques. Microfluidic fuel cell setup used in this work has been described previously [5]. The device is composed of PMMA component in which a Y-shape microchannel has been defined by hot embossing at 140 C and pressed to 24,000 lbs in 2. The dimensions are 2 mm width, 1 mm high and 45 mm long. Anode and cathode current collectors were fabricated using XC72-Vulcan. Anode and cathode electrocatalysts have been incorporated on the microchannel walls using spray coating technique. Fig. 1 shows a schematic illustration of the device and the two operationmodes used. Threemicrofluidic fuel cells were constructed, in which the catalyst materials for anode and cathode were varied as shown in Table 1. Two solutions of D (\u00fe) glucose (Aldrich) at concentrations of 10 mM and 100 mM in 0.3 M KOH (J.T. Baker) were used as fuel, feeding the anode at a flow rate of 100 mL min 1 using a SingleSyringe Infusion Pump (Cole-Palmer 78-0100C). Oxygen was passed through a saturation tower to be dissolved 60 (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003365_j.snb.2013.11.110-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003365_j.snb.2013.11.110-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the LIFT process.",
        "texts": [
            " The liquid film to be deposited s coated to the donor substrate using a microblade and forms a niform liquid film of 10 m in thickness. This method relies on the displacement of the material to e deposited from a donor substrate to an acceptor substrate. rradiation of the donor substrate results in the rapid heating f the Ti film and the explosive boiling of the adjacent liqid, thus producing a high vapor cavity, which expands and rives through the remaining film. The acceptor substrate is laced parallel to the donor substrate at 300 m, so that folowing irradiation, the biomaterial is printed onto the former Fig. 1). .2. Enzyme preparation Laccase solutions were prepared by dissolving a suitable amount f lyophilized enzyme with known enzymatic activity (40 U), in hosphate buffered saline (PBS) solution pH 4.5. Graphite SPEs RP110 were used for these experiments, purchased by DropSens, hich consist of a counter, a reference, and a working electrode 4 mm diameter). The working electrode was printed with the nzyme (86 mU) in PBS via LIFT technique and afterwards, 50 L BS were added for amperometric measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure4-1.png",
        "caption": "Fig. 4. Schematic diagram of shaft element.",
        "texts": [
            " According to the shaft structure, power input/output positions and bearing mounting positions, the wide-faced geared rotor system which is given in Fig. 1 is divided into a series of shaft elements and nonlinear contact elements, as shown in Fig. 3 . B g is the gear width, B b is the bearing width. The shaft element is modeled using Timoshenko beam element with 2 nodes and 12 degrees of freedom. The two shafts are coupled using a series of nonlinear contact elements that consist of sliced mesh stiffness and clearance. The model of a Timoshenko beam element with 2 nodes and 12 degrees of freedom is shown in Fig. 4 (a). The generalized coordinate vector of the i th Timoshenko beam element is given as q i s = { x i s , y i s , z i s , \u03b8 i xs , \u03b8 i ys , \u03b8 i zs , x i +1 s , y i +1 s , z i +1 s , \u03b8 i +1 xs , \u03b8 i +1 ys , \u03b8 i +1 zs } T (6) where x i s , y i s , z i s , x i +1 s , y i +1 s , z i +1 s are translational displacements of the i th shaft element along coordinate axis, and \u03b8 i xs , \u03b8 i ys , \u03b8 i zs , \u03b8 i +1 xs , \u03b8 i +1 ys , \u03b8 i +1 zs are rotational angles of the i th shaft element around coordinate axis. The matrix form of static balance equations for the i th shaft element can be written as K i s q i s (t) = 0 (7) where K i s is the stiffness matrix for the i th shaft element. The model of nonlinear contact element i with 12 degrees of freedom is shown in Fig. 4 (b). r p and r g are the base circle radii of driving and driven gear respectively. \u03c8 is phase angle of installation, \u03b1 is mesh angle of the gear pair. k i m is the stiffness of the i th sliced helical gear pair, e i m is mesh clearance that is caused by shaft deflection, gear modification, manufacturing and assembly errors. When the relative displacement of the i th sliced gear pair is larger than e i m , the stiffness of the sliced contact point pair works. If not, the stiffness of the sliced contact point pair is equal to zero",
            " Introducing composite mesh stiffness, composite mesh error and gear mesh damping, the lumped gear mesh element model with 2 nodes and 12 degrees of freedom is established, as shown in Fig. 7 . k m and e m are the composite mesh stiffness and composite mesh error considering mesh misalignment caused by shaft deflection, respectively. x j , y j , z j ( j = p, g ) are the translational degree of freedom along coordinate axis of gear mesh element. \u03b8 xp , \u03b8 yp , \u03b8 zp ( j = p, g ) are the rotational degree of freedom around coordinate axis of gear mesh element. The meanings of other symbols are the same as that in Fig. 4 (b). The generalized coordinate vector of gear mesh element is defined as q m = { x p , y p , z p , \u03b8xp , \u03b8yp , \u03b8zp , x g , y g , z g , \u03b8xg , \u03b8yg , \u03b8zg } T (14) The relative displacement of driving and driven gear along normal line of action can be given as \u03b4m = V q m (15) where V is the projective vector from generalized coordinate to normal line of action, as given in Eq. (9) . Introducing the composite mesh stiffness and the composite mesh error, the motion equation of gear mesh element considering shaft deflection can be written as \u23a7 \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 \u23a9 m p \u0308x p + [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] cos \u03b2b sin \u03c6 = 0 m p \u0308y p \u00b1 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] cos \u03b2b cos \u03c6 = 0 m p \u0308z p \u2213 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] sin \u03b2b = 0 I xp \u0308\u03b8xp + [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] r p sin \u03b2b sin \u03c6 = 0 I yp \u0308\u03b8yp \u00b1 c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] r p sin \u03b2b cos \u03c6 = 0 I zp \u0308\u03b8zp \u00b1 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] r p cos \u03b2b = 0 m g \u0308x g \u2212 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] cos \u03b2b sin \u03c6 = 0 m g \u0308y g \u2213 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] cos \u03b2b cos \u03c6 = 0 m g \u0308z g \u00b1 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] sin \u03b2b = 0 I xg \u0308\u03b8xg + [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] r p sin \u03b2b sin \u03c6 = 0 I yg \u0308\u03b8yg \u00b1 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] r p sin \u03b2b cos \u03c6 = 0 I zg \u0308\u03b8zg \u00b1 [ c m \u0307 \u03b4m + k m ( \u03b4m \u2212 e m )] r p cos \u03b2b = 0 (16) where m j ( j = p, g ) is the mass of driving and driven gear, I xj , I yj , I zj ( j = p, g ) are the moment of inertia of driving and driven gear around the corresponding coordinate axis respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure8-1.png",
        "caption": "Fig. 8 Interference between the planer tool and the shaper tooth profile",
        "texts": [
            " After the manufacturing of one Basic cutter location group is finished, the workpiece and the basic cutter location group will rotate through an angle around the respective axis according to the design parameters and, then, undergo the planing of the next group of points. This process will go on until the manufacturing of a single tooth is finished. During the processing, the planer tool with a long tool shank cannot rotate, and it will interfere with the shaper tooth profile at a moment, as shown in Fig. 8. However, it is proved that such interference cannot cause overcutting through derivation and verification of simulation machining (see section 5.1). Observed along the vertical direction of the X-Y plane in the moving coordinate system of the shaper Ss, there are different position relations between the face-gear tooth profile and the shaper tooth profile, as shown in Fig. 9. With the shaper rotating from a negative angle to a positive angle, the face-gear tooth profile L2 contacts the shaper tooth profile LS in different areas at each angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002040_978-3-540-36119-0_18-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002040_978-3-540-36119-0_18-Figure6-1.png",
        "caption": "Fig. 6. Spring-Mass Walking. (A) For certain combinations of leg stiffness k and angle of attack \u03b10 a cyclic movement of the center of mass can be found. (B) The single leg force patterns (upper line: vertical force, lower line: horizontal force) resemble that found in human and animal walking [9]",
        "texts": [
            " What happens to the system dynamics if more than one leg is in contact with the ground at the same time? In a previous simulation study we investigated the behavior of a bipedal spring-mass model [9]. This model consists of two massless springs (leg stiffness k) and a point mass representing the center of mass (COM). During the single support phase one leg spring remains in contact with the ground while the other is positioned at a constant angle of attack. If the COM reaches the corresponding landing height of the second leg before the first leg leaves the ground a double support phase occurs (Fig. 6A). Although slightly more complex than the previous running model, stable solutions can again be found using different combinations of leg stiffness k and angle of attack \u03b10. In contrast to the single leg model, stable solutions with double support phases can only be found for low system energies (forward speed lower than about 1.4 m/s). The single leg forces predicted by the bipedal spring-mass model are very close to the observed patterns in human and animal walking (Fig. 6B). The corresponding maximum walking speed is only slightly above the preferred walking speed observed in humans. This suggests higher control efforts at higher walking speeds. Hence, mechanical stability and therefore a relaxed control (rather than metabolic considerations) could be important criteria to explain the preferred walking speed. At high energies (forward speed larger than about 3 m/s) the previously observed running pattern is found if the leg is allowed to contact the ground after take-off of the opposite leg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003645_j.wear.2013.12.025-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003645_j.wear.2013.12.025-Figure1-1.png",
        "caption": "Fig. 1. Coordinates on the surface of the pinion tooth flank. Fig. 2. Diagram of the numerical wear model.",
        "texts": [
            " Archard [2] published in 1953 his famous wear law, which describes the wear volume loss due to the sliding contact between flat surfaces: \u0394V S \u00bc K H FN \u00f01\u00de where \u0394V is the volume loss, S the sliding distance, K the dimensionless wear coefficient, H the softer surface0s hardness and FN the normal contact load. To use Archard0s wear law in the more complex case of contact between gear teeth, it must be written in a differential form: dh\u00f0x; t\u00de dt \u00bc \u03bap\u00f0x; t\u00de U2\u00f0t\u00de U1\u00f0t\u00dej \u00f02\u00de where h is the wear depth, p the contact pressure and \u03ba the wear coefficient (with units of Pa 1), which is presumed to be constant in time and position. The coordinate x is the position on the surface of the tooth as shown in Fig. 1 and t is the time coordinate. U2 and U1 retain the meaning of tangential velocity respectively of pinion and wheel tooth. During one full revolution of the pinion, a point situated at coordinate x on its tooth will then have its height diminished by \u0394h\u00f0x\u00de \u00bc Z tE tA \u03bap\u00f0x; t\u00dejU2\u00f0t\u00de U1\u00f0t\u00dej dt \u00f03\u00de where tA is the instant when the tooth first comes in contact with its counterpart on the wheel and tE is the instant when the tooth ceases contact. Consequently, the depth worn during Nturns turns of the pinion will be h\u00f0x\u00de \u00bcNturns\u0394h\u00f0x\u00de \u00f04\u00de Hence, the volume lost by wear \u0394V on all pinion teeth during Nturns turns of the pinion is \u0394V \u00bc Z1b Z xA xE h\u00f0x\u00de dx \u00f05\u00de where b is the tooth width and Z1 the number of pinion teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003897_icuas.2015.7152383-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003897_icuas.2015.7152383-Figure1-1.png",
        "caption": "Fig. 1. External moments and forces applied to tiltrotor aircraft.",
        "texts": [
            " Moreover, X , Z are the forces along the longitudinal and vertical axes and M is the moment around the lateral axis of the aircraft with the following structure X = FTxb \u2212mgs\u03b8 + Ls\u03b1 \u2212Dc\u03b1 Z = \u2212FTzb +mgc\u03b8 \u2212 Lc\u03b1 \u2212Ds\u03b1 (2) M = \u2212zHs\u03b7FTxb \u2212 (xR \u2212 zHc\u03b7)FTzb +Mac where \u03b1 = arctan ( w u ) represents the angle of attack. FTxb and FTzb are the thrust rotor components expressed in x and z axis body frame respectively. L and D are the lift and drag aerodynamic forces respectively. Mac represents the aerodynamic moment. xR is the distance between the GC and the pivot point of nacelle over the x body frame. zH is the distance between the pivot point of nacelle and the rotor hub center. From Figure 1, it is easy to verify that FTxb = Tc(\u03b7\u2212a1s) FTzb = \u2212Ts(\u03b7\u2212a1s) (3) with T the thrust generated by the rotors, \u03b7 the tilt angle of the nacelles of the rotors and a1s the longitudinal cyclic pitch angle. It is assumed that the aerodynamic forces and moments appearing in (2) have the following structure L = 1 2 \u03c1(V + vi) 2SCL(\u03b1, q, \u03b4e) D = 1 2 \u03c1(V + vi) 2SCD(\u03b1, q, \u03b4e) (4) Mac = 1 2 \u03c1(V + vi) 2Sc\u0304CM (\u03b1, q, \u03b4e) where V = \u221a u2 + w2 is the aircraft velocity, \u03c1 is the air density, c\u0304 is the wing aerodynamic mean chord, S is the wing area, \u03b4e is the elevator control input, vi is the induced velocity by the rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure14-2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure14-2-1.png",
        "caption": "FIGURE 14-2 Prony brake.",
        "texts": [
            " Dynamometer An instrument for determining power, usually by the in dependent measure of force, time, and the distance through which the force is moved. Dynamometers may be classified as brake, drawbar, or torsion, according to the manner in which the work is being applied. Also, they may be classed as absorption or transmission, depending on the disposition of the energy. Absorption Dynamometers Prony Brake An absorption dynamometer measures the power applied and at the same time converts it to some other form of energy, usually heat. A Prony brake, the most elementary form of absorption dynamometer, is sketched in figure 14-2. The brake is essentially an arrangement whereby wooden blocks a can be clamped more or less tightly around the engine pulley b by means of the handwheel c. When the engine turns in the direction shown by the arrow, the lever arm d presses upon the scale e, causing a reading, F, on the scale. *Standard conditions listed previously are those formerly used by the Nebraska tractor tests. SAE J816 standard conditions are slightly different. ABSORPTION DYl\\AMOMETERS 407 A clear conception of the principle of operation of the Prony brake is essential for an understanding of nearlv all dynamometers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-7-1.png",
        "caption": "FIGURE 5-7 Typi cal valve-lifting mechanism. (Cour tesy Aluminum In dustries, Inc.)",
        "texts": [
            " Valve Clearance Adjustment A certain amount of clearance between the tappets and the valve stems is usually necessary to make certain that the valves are able to seat properly. If clearance is insufficient, the valves will be held off the seats, the engine will not have proper compression, and the valves and seats will be damaged by burning because the hot gases will be forced between the valve and the seat. Also, the transfer of heat from the valve to the engine block will be interfered with when the valve is in the closed position. A typical valve-opening mechanism is shown in figure 5-7. To ensure complete closing of the valve, clearance of 0.15 to 0.41 mm must be provided at the end of the valve stem. This clearance provides for expansion of the valve stem and valve-lifting mechanism when it becomes hot. If the clearance is insufficient, the valve will be held open and the leaking valve will soon be burned. If the clearance is too large, the valve range will be decreased and the operation of the valve will be noisy. VALVE-OPENING AREA Valve Seats 91 The valve and valve seat are the most critical parts, for it is the seal here that must prevent leakage of gases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000929_0954406991522509-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000929_0954406991522509-Figure1-1.png",
        "caption": "Fig. 1 FE model of two meshing gears and the necessary boundary conditions",
        "texts": [
            "71 and includes contact between engaging teeth the material properties required for the analysis are Young\u2019s modulus of elasticity and Poisson\u2019s ratio.through the use of gap elements. 7. The effect of the lubricating oil film pressure on the gear mesh stiffness is neglected. In applying the FE method to model gear tooth defor- 3 FINITE ELEMENT MODELLING mation, several assumptions are made to simplify the simulation process. A list of the assumptions adopted in The developed finite element model of two meshing gears the present work is given below: is shown in Fig. 1. The rim thickness is taken to be 2.5 times the tooth height (i.e. a back-up ratio of 2.5) in1. Sliding friction between the mating gear teeth is neg- lected, since its effect on deflection is small [13, 14 ]. order to obtain tooth deflections that are independent of the rim effects. The lower gear has its bore rigidly2. The load distribution along the tooth face width is assumed to be uniform and hence a two-dimensional fixed, while the upper one is allowed to rotate about its centre. The latter condition is effected by connectingfinite element analysis, based on plane stress con- ditions, is adopted. each node lying on the upper gear bore to a node lying at the gear centre with truss elements of considerable3. Root fillet curves are assumed to be circular. 4. The presence of surface asperities and waviness or stiffness (approximately 13 MN/mm), as shown in Fig. 1 by the straight lines emerging radially from the centreundulation, and hence the corresponding non-uni- form pressure distribution at the micro- and macro- of the upper gear. Constraining the centre of the upper gear in the x and y directions will therefore constrainlevels respectively, is neglected. 5. Geometrical errors, such as radial runout, as well as the gear bore radially, allowing only free rotation of the gear. A counterclockwise torque is applied on the upperdimensional errors, such as tooth-to-tooth spacing errors, are neglected, since the deflection under load gear, causing contact between the gear teeth. This is done by loading the gear with two equal and opposite tangen-of the teeth of heavily loaded, high-speed precision gears is large in comparison with manufacturing tial forces acting at two diametrally opposed nodes located on the gear bore to form a couple, as shown inerrors [9, 15 ]. C08797 \u00a9 IMechE 1999 Proc Instn Mech Engrs Vol 213 Part C at Glasgow University Library on June 30, 2015pic.sagepub.comDownloaded from Fig. 1. According to Saint-Venant\u2019s principle, these two the \u2018contactor\u2019 tooth approaches a \u2018target\u2019 entity, the program internally determines the point of contact andconcentrated forces have practically no effect on the stress distribution within the gear teeth. applies the necessary contact force. This force, which is known as the gap force, is applied normal to the con-The analysis presented in this work involves quasistatic meshing conditions in which the mesh compliance tacting surfaces such that the node lying on the \u2018contactor\u2019 entity is prevented from penetrating the \u2018target\u2019 andis evaluated at discrete meshing positions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure12-1.png",
        "caption": "Fig. 12 Some 3-DOF PPR-PMs of family 3.",
        "texts": [
            "org/ on 01/15/2018 Term (d) substitute one or more P joints each with a planar parallelogram [18, 27]; (e) substitute two of three successive P joints with a spatial parallelogram [42]; (f) substitute one or more R joints in the leg with a ci-\u03b6\u221esystem each with a coaxial H joint. For example, PPR-PMs proposed in [33] are in fact the variations of the PPR-PMs shown in Fig. 14, which are obtained by (a) substituting a combination of two successive R joints with non-parallel axes with a U joint and (b) replacing the unactuated P joints each with a planar parallelogram. Figure 15 shows a 2- RPU-UPU PPR-PM under our current investigation. It is in fact obtained from the 2-(RPR)ERC-RA(RPR)Y RA PPR-PMs shown in Fig. 12(b) by substituting a combination of two successive R joints with non-parallel axes with a U joint. Virtual chains have been introduced to represent the motion patterns of 3-DOF motions. A procedure for the type synthesis of Copyright  2004 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Dow 3-DOF PPR-PMs has also been proposed. Using the proposed procedure, 3-DOF PPR-PMs are synthesized in three steps: (a) Type synthesis of legs, (b) Type synthesis of 3-DOF PKCs and (c) Selection of actuated joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000711_s0094-114x(02)00066-6-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000711_s0094-114x(02)00066-6-Figure3-1.png",
        "caption": "Fig. 3. 3-UPU mechanism.",
        "texts": [
            " Recently, Karouia and Herv e [13] have sought after the three dof SPMs with three equal legs in which the platform can perform an elementary spherical motion. The capacity of performing an infinitesimal spherical motion is requested, but it is not a sufficient condition to guarantee that the platform performs a finite spherical motion, i.e., the manipulator is a parallel wrist. Hence their research is only useful to select the architecture that might be parallel wrist. The result of their investigation is that a mechanism architecture, called 3-UPU (Fig. 3) and used already for translational manipulators [4], under some mounting and manufacturing conditions, can be used to obtain manipulators able to make the platform perform infinitesimal spherical motions. In the 3-UPU manipulators, the platform and the base are connected to each other by three legs of type UPU in which the prismatic pair is the actuated joint (Fig. 3). The mounting and manufacturing conditions enunciated by Karouia and Herv e [13] are as follows (see Fig. 4): (i) the three revolute pair axes fixed in the platform (base) must converge at a point fixed in the platform (base), (manufacturing condition); (ii) in each leg, the intermediate revolute pair axes must be parallel to each other and perpendicular to the leg axis which is the line through the universal joints centers (manufacturing condition); (iii) the platform s point located in the intersection of the platform s revolute pair axes must coincide with the base s point located in the intersection of the base s revolute pair axes (mounting condition)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.2-1.png",
        "caption": "Fig. 1.2. Aircraft \u03b8 and \u03a8 rotations",
        "texts": [
            " In general, this point is taken as being equal to the initial position of the centre of gravity. It would also be possible to choose a reference point as an airport or the intersection of the Greenwich meridian and the equator. Such modifications only impact the initial value of the centre of gravity coordinates. The three axes (XE , YE , ZE ) of this coordinate system are oriented respectively towards the north, the east and downward. The transformation matrix to go from the aircraft\u2019s to the earth\u2019s coordinate system - see Fig. 1.2 and 1.3 - is: MAC\u2192E = \u239b\u239dcos\u03a8 \u2212sin\u03a8 0 sin\u03a8 cos\u03a8 0 0 0 1 \u239e\u23a0\u239b\u239d cos\u03b8 0 sin\u03b8 0 1 0 \u2212sin\u03b8 0 cos\u03b8 \u239e\u23a0\u239b\u239d1 0 0 0 cos\u03d5 \u2212sin\u03d5 0 sin\u03d5 cos\u03d5 \u239e\u23a0 (1.1) The AIRBUS On-Ground Transport Aircraft Benchmark 5 The aerodynamic coordinate system is a mobile coordinate system (c.g.; Xaero, Yaero, Zaero) associated with the orientation of the aircraft velocity vector in relation to the air mass (Vair) - see Fig. 1.4 Its origin is the centre of gravity. The longitudinal axis Xaero is oriented in the direction of this \u201cair\u201d velocity vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002745_pime_proc_1966_181_036_02-Figure30-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002745_pime_proc_1966_181_036_02-Figure30-1.png",
        "caption": "Fig. 30. The platinum-silver assembly in the bearing housing",
        "texts": [
            " has to be kept low so that no oil film of significant thickness should break down as a result of a high field intensity, and that the passage of current has to be limited to a minimum when contact takes place at the minute points of the asperities: this is the reason for the series resistance shown in Fig. 29. The requirements call for particular attention to the construction of a 'low-noise' slip ring. Space limitation excluded the use of conventional mercury-type slip rings on the top shaft. The contacts and the slip rings used in the experiments are made of silver and platinum respectively and were found initially to give good results when the rig was tested with unlubricated rollers. Fig. 30 shows a bearing housing assembly fitted with a slip ring. Specimen and test procedures The dimensions of the toroid or 'ball' and the cylinder were chosen to give a circular contact area. The dimensions and heat treatment of the specimens are given in Table 4. Proc Imtn Mech Engrs 1966-67 Except for the preliminary tests the surface finish of the toroids and rollers was of two kinds, either as ground to 12-15 pin c.1.a. or polished to 2.0-2.5 pin c.1.a. Care has been taken to ensure a homogeneous, non-directional surface topography; it was particularly difficult to achieve this with the large cylinders",
            " It is interesting to observe that with spin the peaks of the curve corresponding to different velocities tend to move towards the right with increasing velocity. From the point of view of stability, particularly in an angular-contact ball bearing, an ascending frictional characteristic is a desirable feature. However, at this stage it was felt that rolling with sliding was more promising as a tool for fundamental study and in what follows only the latter will be described. The results, such as shown in Figs 32b and 35, refer to the region between points A and B in Fig. 30, and can be correlated by the equation where 10 < U < 500 ft/min and tan ,5l < and where U--, the sliding velocity, equals U tan is. In this region of \u2018primary transition\u2019 the constant k is largely dependent on the value of sliding friction at the boundary lubrication condition: k = 0-885 for the present case. Fig. 36 is a graph off obtained from equation (85) plotted against the experimental results. The measure of agreement obtained with equation (85) is quite evident from this graph. f = k + U n "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002886_1.4007809-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002886_1.4007809-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the meshing of a pair of involute spur gears (taken from Johnson [11] with permission)",
        "texts": [
            " This paper aims to develop such a first-principle based model focusing on meshing efficiency of involute spur gears. The model is fundamentally simple with a few clearly defined physical parameters so that the cause-and-effect results produced by the model can be easily traced and evaluated. The accuracy of the model is evaluated against well documented experimental data of Petry-Johnson et al. [7]. Subsequently, it is used to study the trends and relative magnitudes of the meshing losses with respect to the variations of a few key parameters that describe gear design and lubricant property. Figure 1, taken from Johnson [11], shows a schematic of the meshing of a pair of involute spur gears. It suggests that the meshing is instantaneously equivalent to the contact of two cylinders. The two cylinders rotate at constant angular velocities equal to the angular velocities of the underline gears but their radii vary as the meshing proceeds along the line of action. Furthermore, the contact force between the two cylinders may vary, primarily due to the change of the number of meshing pairs in the process",
            " Thereafter, the solution process advances to the next grid column until it reaches Hertz outlet. Upon completion, the friction in the gear contact is calculated: f \u00bc b \u00f0a a s\u00f0x\u00dedx (23) In addition, an average temperature rise in the lubricant film is also calculated: DT \u00bc 1 2aho \u00f0a a \u00f0ho 0 T\u00f0x; z\u00dedzdx To (24) It provides a single-variable measure on the level of temperature in the contact similar to the Hertz pressure on the level of pressure. The pressure, film thickness, temperature and friction force may be calculated at any meshing position. Referring to Fig. 1, a meshing-position variable, s, may be defined along the line of action from left to right. It is negative before the meshing position reaches the pitch point and positive thereafter. The meshing initiates and terminates, respectively, at si \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 a2 r2 b2 q r2 sin w (25) and st \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 a1 r2 b1 q r1 sin w (26) For a pair of spur gears, the contact ratio, mc, is usually between one and two. There are two meshing pairs when the meshing position is in the range of si s s1 or s2 s st. There is a single meshing pair when s1 < s < s2. It can be shown with gear fundamentals that s1 \u00bc si \u00fe \u00f0mc 1\u00dest mc (27) and s2 \u00bc \u00f0mc 1\u00desi \u00fe st mc (28) The radii of the two equivalent cylinders at a given meshing position, referring to Fig. 1, are given by R1 \u00bc r1 sin w\u00fe s (29) and R2 \u00bc r2 sin w s (30) Thus, the equivalent radius of the EHL contact is R\u00f0s\u00de \u00bc R1R2 R1 \u00fe R2 \u00bc \u00f0r1 sin w\u00fe s\u00de\u00f0r2 sin w s\u00de c sin w (31) The surface velocities of the two cylinders are given by u1\u00f0s\u00de \u00bc x1R1 (32) and u2\u00f0s\u00de \u00bc x2R2 (33) Thus, the entraining velocity of the EHL contact is u\u00f0s\u00de \u00bc u1 \u00fe u2 2 \u00bc x1r1 sin w\u00fe 0:5\u00f0x1 x2\u00des (34) and the sliding velocity is us\u00f0s\u00de \u00bc u1 u2 \u00bc \u00f0x1 \u00fe x2\u00des (35) In the equations, the angular velocities of the gear pair, x1 and x2, are taken to be positive valued with their directions defined in Fig. 1. The tooth contact force generally varies as the meshing proceeds along the line of action. The variation is primarily due to the switch between one meshing pair and two meshing pairs. Other secondary effects may be neglected, which should not result in meshing-loss calculation error greater than the errors associated with other model uncertainties and imperfections. Therefore, the contact force per unit gear face width is given by w\u00f0s\u00de \u00bc kTp br1 cos w (36) where k \u00bc 0:5 si s s1 or s2 s st 1 s1 < s < s2 (37) With R\u00f0s\u00de, w\u00f0s\u00de, u\u00f0s\u00de and us\u00f0s\u00de determined, the pressure, film thickness, temperature, and friction in the gear contact can now be calculated as the meshing progresses along the line of action. The energy loss in the contact, DEm, in a time period, tm, as one tooth pair go through their meshing can also be calculated. Referring to Fig. 1, the line of action may be wrapped on the base circle of the pinion and thus the meshing point progresses from s \u00bc si to s \u00bc st with a constant velocity, which is given by vm \u00bc ds dt \u00bc x1rb1 (38) Therefore, DEm \u00bc \u00f0tm 0 fusdt \u00bc 1 x1rb1 \u00f0st si fusds (39) Because N1x1=2p numbers of tooth pairs go through the meshing in unit time, the meshing power loss is equal to DP \u00bc N1x1 2p DEm \u00bc 1 pm cos w \u00f0st si fusds (40) The integration in Eq. (40) can be evaluated using a simple numerical summation with a sufficiently small Ds to progress the meshing position and calculate the corresponding friction force and sliding velocity in the tooth contact",
            "org/terms h \u00bc lubricant film thickness ho \u00bc central film thickness kf \u00bc lubricant thermal conductivity k1,2 \u00bc pinion, gear thermal conductivity m \u00bc 1/Pd, gear module mc \u00bc \u00bd\u00f0r2 a1 r2 b1\u00de 1=2 \u00fe \u00f0r2 a2 r2 b2\u00de 1=2 c sin w =\u00f02pm cos w\u00de, gear contact ratio N1,2 \u00bc pinion, gear numbers of teeth p \u00bc lubricant pressure ph \u00bc 2w/(pa), Hertz peak pressure P \u00bc Tpx1, pinion input power DP \u00bc meshing power loss DP% \u00bc 100(DP/P), percentage meshing loss Pd \u00bc N1/(2r1), gear diametral pitch r1,2 \u00bc pinion, gear pitch-circle radius ra1,2 \u00bc pinion, gear addendum-circle radius rb1,2 \u00bc r1,2, cos w, pinion, gear base-circle radius R1,2 \u00bc pinion, gear tooth radius of curvature at contact R \u00bc R1R2/(R1\u00feR2), contact equivalent radius s \u00bc meshing position along the line of action s1,2 \u00bc meshing positions across which the numbers of meshing pairs change si \u00bc initial meshing position st \u00bc ending meshing position t \u00bc time T \u00bc lubricant temperature T1,2 \u00bc pinion, gear surface temperature in the tooth contact To \u00bc lubricant ambient temperature DT \u00bc average temperature rise in the tooth contact [Eq. (24)] Tp \u00bc pinion input torque u \u00bc (u1\u00fe u2)/2, entraining velocity in the tooth contact u1,2 \u00bc pinion, gear surface velocity in the tooth contact uf \u00bc lubricant velocity us \u00bc u1 \u2013 u2, sliding velocity in the tooth contact U \u00bc gou/(E0R), EHL speed parameter w \u00bc contact force per unit width of gear flank W \u00bc w/(E0R), EHL load parameter x \u00bc coordinate along tooth contact (Fig. 1) Dx \u00bc grid spacing of finite difference along x direction z \u00bc coordinate along film thickness Dz \u00bc grid spacing of finite difference along z direction a \u00bc lubricant pressure-viscosity coefficient b \u00bc lubricant temperature-viscosity coefficient _c \u00bc shear strain rate g \u00bc lubricant viscosity ge \u00bc effective viscosity go \u00bc ambient viscosity 1,2 \u00bc pinion, gear Poisson\u2019s ratio q1,2 \u00bc pinion, gear density qf \u00bc lubricant density s \u00bc shear stress so \u00bc Erying stress, so 5.0 MPa x1,2 \u00bc pinion, gear angular velocity w \u00bc gear pressure angle [1] Britton, R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002623_1.3580271-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002623_1.3580271-Figure4-1.png",
        "caption": "FIG. 4. Schematic representations of the modal structure for a suspension of random tumblers for differing values of . Note that the hatched region, which denotes the neutral continuous spectrum modes r=0, i =iUk \u00b7p0 for straight swimmers, is absent for finite .",
        "texts": [
            " 23, except for the inclusion of random tumbling leading to the factor 1 / in the present analysis. A nondimensional form of the dispersion relation can be obtained by defining the nondimensional wavenumber k\u0303=k / C\u0302nL2 and a shifted nondimensional growth rate \u0302= kU \u22121 + \u22121 , whence Eq. 35 takes the form 0 1 dt \u0302t2 1 \u2212 t2 \u03022 + t2 = 2 3 k\u0303 . 36 Equation 36 implies that the eigenspectrum for a suspension of randomly tumbling bacteria can be obtained from that for straight swimmers = by simply shifting the real part of the growth rate by \u22121 / . This is illustrated in Fig. 4, which provides a qualitative sketch of the spectrum for straight swimmers as well as that for tumbling bacteria with successively smaller . Quantitative results for the real and imaginary parts of the growth rate, as a function of wavenumber, are obtained using a combination of bisection and Muller\u2019s method to solve Eq. 36 with numerical integration using Simpson\u2019s method. The results are plotted in Fig. 5, which is equivalent to the plot of the growth rate for straight swimmers presented in Fig",
            " 4 and 5 can be elucidated by analyzing Eq. 36 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.33.16.124 On: Wed, 26 Nov 2014 09:12:16 in appropriate limits. For small k\u0303, the solutions for the growth rate are real. In the limit k\u0303\u21920, the integral in Eq. 36 must be asymptotically small and this may be achieved in either of the limits \u0302 1 or \u0302 1, yielding a pair of stationary modes labeled 1 and 2, respectively, in Fig. 4. The solution for mode 1 is \u0302 = 1 5k\u0303 . 37 The corresponding dimensional growth rate remains finite even in the limit of zero wavenumber and is given by = 1 5 C\u0302nUL2 \u2212 1 . 38 The orientation perturbation in this case arises from a local balance of the shearing motion and relaxation due to tumbling see Fig. 1 , so the bacterial stress takes a Newtonian form with a negative bacterial viscosity, B=\u2212 1 5 C\u0302nUL2 . The suspension is unstable when this negative viscosity exceeds the suspending fluid viscosity",
            " The decay is only in the velocity field which may be regarded as an integral norm for the vorticity field via the Biot\u2013Savart law ; the vorticity field itself does not converge pointwise. This lack of pointwise convergence in physical space is mirrored in orientation space for the bacterial suspension examined here. Hohenegger and Shelley33 demonstrated the temporal decay of an appropriate integral norm over orientation space. The nature of the eigenspectrum for a suspension of random tumbling bacteria depends on the tumbling frequency, 1 / , as illustrated in Fig. 4. For straight swimmers 1 / =0 , two unstable stationary modes modes 1 and 2 exist for k km=0.17C\u0302nL2, where they merge and then bifurcate into two oscillatory modes in the range km k km =0.09C\u0302nL2. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.33.16.124 On: Wed, 26 Nov 2014 09:12:16 Beyond this wavenumber, one has the continuous spectrum alone. For tumbling bacteria with 0 \u22121 0",
            " A similar analysis for the mode 2 branch yields an enhancement of the growth rate at O and a wave speed in a direction opposite to that of the averaged swimming in the base state. Owing to the smallness of the leading-order growth rate along this branch, the regular perturbation formulation may only be valid in the interval 2 1; we do not delve into this issue any further since these modes are stable. Nevertheless, the appearance of a wave speed at O for arbitrarily small implies that the perfect bifurcation, in the absence of the chemoattractant, from a pair of real growth rates to complex conjugate ones at m =0.17 nUL2 see Fig. 4 , is now broken. Figure 6 shows the spectrum for a suspension of random tumblers for =0. The structure in this case is, of course, known from the analysis in Sec. IV A and is shown in Fig. 5. However, Fig. 6 uses the scalings 64 and 65 for the growth rate and the wavenumber, respectively, which facilitates comparison with results incorporating the attractant gradient. The new scalings imply that the threshold concentration now appears explicitly in the eigenrelation, and Fig. 6 shows the spectrum for =4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003696_1.4032078-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003696_1.4032078-Figure2-1.png",
        "caption": "Fig. 2 Surface boundary conditions for the DMLS problem, which include convection, laser flux, and fixed temperature boundary conditions",
        "texts": [
            " The threedimensional counterpart of the governing equation is generalized as follows: @T r; t\u00f0 \u00de @t \u00bc 1 cq k$\u00f0 \u00de $T r; t\u00f0 \u00de\u00f0 \u00de \u00fe Q r; t\u00f0 \u00de (1) where T\u00f0r; t\u00de is the temperature at a position vector r in threedimensional space and time t, k is the three-dimensional material conductivity tensor of order 2 and rank 3 at a position vector r, c is the three-dimensional specific heat of the material at a position vector r, q is the density of the powder bed at a position vector r, and Q\u00f0r; t\u00de is the inner heat generation at point x and time t. Similarly, the three-dimensional counterpart of flux is modified as q\u00f0r; t\u00de \u00bc k\u00f0$T\u00f0r; t\u00de\u00de (2) where q\u00f0r; t\u00de is the flux at a position vector r and time t. The spatiotemporal periodicity of the flux boundary condition in three dimensions is modified as q\u00f0r\u00fe v\u00f0dt\u00de; t\u00fe dt\u00de \u00bc q\u00f0r; t\u00de (3) The Dirichlet boundary condition considered here is a constant temperature at the bottom surface of the base plate as shown in Fig. 2 T\u00f00; t\u00de \u00bc T0 \u00bc 353 K The time-periodic Neumann boundary condition considered here is the laser flux distribution in two dimensions 061003-2 / Vol. 138, JUNE 2016 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 02/01/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use q rjr:ez\u00bczmax; t \u00bc 2P pr2 laser exp 2j r vt r0\u00f0 \u00dejr:ez\u00bczmaxj r2 laser ! \u00fe h Tjr:ez\u00bczmax Tambient (4) where P is the laser beam power (\u00bc180 W), rlaser is the laser beam spot size incident perpendicular to the length (l\u00bc 100 mm)\u00bc 100 lm, vt is the displacement by the laser beam from the left end of the bar with a speed \u00f0v \u00bc 1200 mm=s\u00de at time instant t, r0 is the initial position vector of the laser spot on the exposed powder surface, jr:ez\u00bczmax is the condition for the laser flux to always hit the top surface of the powder bed, jj is the second norm of the included vector, and Tambient is the ambient temperature also assumed to be 353 K"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002283_1.4001813-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002283_1.4001813-Figure7-1.png",
        "caption": "Fig. 7 von Mises stress results from PEHL solutions in comparison with those from corresponding EHL Solutions \u201ecross section views at Y=0\u2026",
        "texts": [
            " The largest deformation occurs at the center of contact, where the surface is plastically depressed most. The negative deformation in the vicinity of contact zone indicates that the surface is slightly raised there, which is often referred to as a residual pile-up, resulting in a small pressure increase at the edge of the contact. Note that the plastic deformation displayed here is from a different solution with an enlarged solution domain in order to show the deformation distribution more clearly. Figure 7 gives two sets of subsurface von Mises stress distributions, caused by PEHL solutions at dimensionless loads of W /Wy =9.9 and 19.6, respectively, in comparison with those obtained from the corresponding EHL solutions under the same operating conditions. The material properties and other input data are the same as those in the cases given in Fig. 4. It is found that, as the load increases, the maximum von Mises stress caused by the EHL pressure increases significantly, sometimes to an unrealistic level, but that resulted from the PEHL solution appears to have a relatively small increase, capped by the yielding property of material. For example, at W /Wy =19.6 the plastic deformation causes a remarkable reduction of maximum subsurface von Mises elastic-plastic indentation by Hardy et al. \u202021\u2021. e as W /Wy elsewhere. ig. 5 Comparison of PEHL results with those of elastic- stress, from 1.4 GPa to about 0.5 GPa, as shown in Fig. 7. JULY 2010, Vol. 132 / 031501-5 of Use: http://asme.org/terms 0 Downloaded Fr 31501-6 / Vol. 132, JULY 2010 Transactions of the ASME om: http://tribology.asmedigitalcollection.asme.org/ on 05/21/2015 Terms of Use: http://asme.org/terms 5 e h i t T t J Downloaded Fr Two sets of PEHL solutions are obtained under an increasing xternal load, one set with the presence of material workardening, ET /E=0.4, and the other without, ET /E=0, in order to nvestigate the effect of load increase on the PEHL behavior",
            " For the comparison purpose, corresponding EHL solutions uner the same operating conditions are provided on the left hand ide of Fig. 8. Clearly, both pressure and lubricant film are sigificantly altered if taking into account the surface plastic deforation. In these cases, the dimensionless maximum pressure hanges from 2.69 to 1.44, a 46% reduction, at W /Wy =19.6, hile the film thickness drops about 37%, from 0.00033 to .00021. The plastic deformation also causes a remarkably large ecrease in subsurface von Mises stress, from 1.4 GPa to about 00 MPa, as demonstrated in Fig. 7. 31501-8 / Vol. 132, JULY 2010 om: http://tribology.asmedigitalcollection.asme.org/ on 05/21/2015 Terms Variations of pressure and lubricant film with increasing load for the material with work-hardening, ET /E=0.4, are illustrated in Fig. 9, in comparison with those from the material without workhardening, ET /E=0.0. Generally, the PEHL behavior with workhardening shows similar trends to those without work-hardening, but the pressure distribution is less flattened under heavy loads, and the maximum pressure remains at the center of the contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure9-12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure9-12-1.png",
        "caption": "FIGURE 9-12 Tvpical vibration isola tion mount for an operator enclosure. (From R.F. Zitko, \"Control Center Design Con cepts Series 86 Tractors,\" ASAE Paper 77-",
        "texts": [
            " This design approach includes isolation mounts for the cab and suitable insulating materials for ceiling, walls, and floors. Sellon (1976) and Zitko (1977) report design practice for proper sound control. Sound reaching the operator is structure-borne, airborne, or a combi nation of both. Structure-borne sound results from vibrations transmitted from the vehicle through the cab attaching points. Airborne sound is trans- 1049, 1977.) mitted through air and enters the operator area through holes or through the enclosure walls. One type of cab isolation mount currently in use is shown in figure 9-12. Vibration isolation is achieved by a rubber interfacing between the mounting bracket and the control platform. The magnitude of isolation is dependent on the transmissibility of the rubber being used (curves similar to those in fig. 9-9) and the input frequency of the vibration. The floor of the cab is treated with a barrier material. A rubber material then overlies the barrier. Surface areas above the floor are treated with noise absorption materials that are effective in the 125- to 2000-Hz range"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002766_s11044-011-9281-8-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002766_s11044-011-9281-8-Figure2-1.png",
        "caption": "Fig. 2 Kinematical scheme of first leg A of the mechanism",
        "texts": [
            " One of three active legs (for example leg A) consists of a prismatic joint as well as a piston linked at the xA 1 yA 1 zA 1 moving frame, having a translation with the displacement \u03bbA 10, the velocity vA 10 = \u03bb\u0307A 10 and the acceleration \u03b3 A 10 = \u03bb\u0308A 10. It has the length l1 and the mass m1. An intermediate link of length l2, mass m2 and tensor of inertia J\u03022 has a relative rotation about zA 2 axis with the angle \u03d5A 21, the angular velocity \u03c9A 21 = \u03d5\u0307A 21 and the angular acceleration \u03b5A 21 = \u03d5\u0308A 21. Finally, a spherical joint is introduced at a planar moving platform, which is schematized as an equilateral triangle with edge l, mass mp and tensor of inertia J\u0302p (Fig. 2). At the central configuration, we also consider that all legs are initially extended at equal length \u03bb0 + l1 = [h \u2212 l2 sin(\u03b8 \u2212 \u03b2)]/ cos \u03b8 and that the angles of orientation of the legs are given by sin \u03b8 = \u221a 2 3 , cos \u03b8 = 1\u221a 3 , \u03b1A = 0, \u03b1B = 2\u03c0 3 , \u03b1C = \u22122\u03c0 3 , \u03b2 = \u03b8 \u2212 tg\u22121 h \u2212 (\u03bb0 + l1) cos \u03b8 (\u03bb0 + l1) sin \u03b8 \u2212 r . (3) In the following, we apply the method of successive displacements to geometric analysis of closed-loop chains and we note that a joint variable is the displacement required to move a link from the initial location to the actual position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003084_tsmc.2013.2266896-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003084_tsmc.2013.2266896-Figure4-1.png",
        "caption": "Fig. 4. Attachment points for the accelerometer and gyro sensors.",
        "texts": [
            " To solve (4), the initial posture matrix N (0) is required, which is determined by the 3-D acceleration at t = 0, the \u201ctime during addressing and motion starting time\u201d as defined in Section III-A. The algorithm for calculating N (0) is described in the following section. Here, we describe how to determine the initial posture matrix N (0) from ax(t), ay (t), az (t) and \u03c9x(t), \u03c9y (t), \u03c9z (t) measured by the local motion sensors set at the grip end of the club. This is an important algorithm because N (0) is required to solve (4) as the initial posture matrix. Fig. 4 shows how the sensing device is set and how the local coordinates are defined. First, we must obtain the following initial posture matrix N (0): N(0) = [Px(0) Py (0) Pz (0)] = \u23a1 \u23a2\u23a3 Xx(0) Xy (0) Xz (0) Yx(0) Yy (0) Yz (0) Zx(0) Zy (0) Zz (0) \u23a4 \u23a5\u23a6 . (5) At t = 0 during addressing, motion is at rest and accelerations ax (0), ay (0), and az (0) include only the gravity component; thus \u221a ax(0)2 + ay (0)2 + az (0)2 = 9.8065 m/s2 (magnitude of gravity acceleration) and the addressing angles from the gravity direction are calculated as follows: \u03b8address x = cos\u22121 ( ax(0)\u221a ax(0)2 + ay (0)2 + az (0)2 ) \u03b8address y = cos\u22121 ( ay (0)\u221a ax(0)2 + ay (0)2 + az (0)2 ) \u03b8address z = cos\u22121 ( az (0)\u221a ax(0)2 + ay (0)2 + az (0)2 ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002676_1.4006791-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002676_1.4006791-Figure7-1.png",
        "caption": "Fig. 7 The reference frames",
        "texts": [
            " As a consequence, in heavy loaded EHL contacts, the interfacial pressure distribution resembles the Hertzian distribution except for the appearance of a peak close to the exit and a certain asymmetry which slightly moves the pressure center toward the leading edge of the contact [21]. Hence, in most heavy loaded EHL contact, the assumption of Hertzian distribution leads to quite accurate results. Therefore, we assume that the real pressure distribution is Hertzian and only depends on the applied load and the contact geometry. To analyze, the contact between the roller and the disks let us consider the reference frames shown in Fig. 7. The equivalent radii of curvature along the x and y directions are [15] Journal of Mechanical Design JULY 2012, Vol. 134 / 071005-5 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 1 qeqx \u00bc 1 rax \u00fe 1 rbx (36) 1 qeqy \u00bc 1 ray 1 rby (37) where the subscript a refers to the roller and b to the disk, and rax \u00bc \u00f0r0 \u00fe e\u00de tan a=2 \u00bc r2= cos a=2\u00f0 \u00de, rbx \u00bc r11, ray \u00bc r22, and rby \u00bc r0 (in the case of half- and full-toroidal, rax \u00bc r0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002330_b978-0-08-022010-9.50056-6-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002330_b978-0-08-022010-9.50056-6-Figure1-1.png",
        "caption": "Fig. 1: Basic system",
        "texts": [
            " This was shown in [5J by a digital simulation of various control methods together with linear decoupling for a robot with three-degrees of freedom of the arm. The working speed considered in this con text was not unrealistically high but in the range of human speed of motion. In order to improve the control behaviour of these highly nonlinear systems for high performance, a new approach is presented here by employing non linear system theory [6J, [7J. This concept is an applied to the model of a redundant manipulator with four degrees of freedom of the arm which is shown in fig. 1. (The hand of the robot is designed to have in addition three degrees of freedom.) For the exact modelling of this system, a direct approach is used inste~d of t~e Denavit-Har tenberg-matrices ([ 1J, La], [9J). This direct approach takes advantage of a very simple kinematic representation of the system in connection with a basic physical treatment of the problem, contrary to the more mechanized and very general ap~roach based on Denavi t-Har tenberg-matrices [9J. The model gained for the manipulator in fig. 1 in the paper, represen tents a complete dynamical description of the system with a minimal number of parameters. Application of the nonlinear control concept leads to explicit nonlinear control laws for the sUbsystems connected with the different variables of motion. These control laws pro vide an overall System behaviour where all outputs of the system are complete de coupled and are governed by second order characteri stic equations that can be arbitrarily chosen. 395 396 E. Freund The control laws derived can be realized with relatively small computational effort and do not need readjustment for different working conditions in comparison to linear control and decoupling concepts. 2. BASIC SYSTEM AND KINEMATIC EQUATIONS The manipulator which is considered in the paper is shown in the (x,y) plane in fig. 1. The main arm has a rotational joint with the angle of rotation ~1(t) corresponding to the torque M (t) and as translational joint the variable 11ength of the arm r 1(t) driven by the force K (t). This arm is connected with an additiorlal arm of constant length r2 by another rotary joint (the \"elbow\") that is characterized by the angle of rotation ~?(t) and the torque M2(t). Both arms can be Ilfted along the z-axis (vertical on the (x,y)-plane) for z(t) by the force K (t) which is the fourth degree of freedom",
            " For the development of a control concept for an advanced redundant manipulator with high performance, the exact kinematic and ki netic equations of the basic system are needed. For the derivation of the kinematic equations, ~h~ concept of the Denavit-Hartenberg-matrices LSJ can be used. This method was systematized in [1J and employed for control purposes for the Stanford Arm [2J, [3J and related problems. If the concept based on the Denavit-Hartenberg matrices is applied to the basic system in fig. 1 (without the hand), it means that the four degrees of freedom are characterized by four 4 x 4 matrices related to each degree of free dom separately. Each link (or degree of free dom) is joint by a set of three cartesian co ordinates describing its position and related to each other by transformation matrices which are the Denavit-Hartenberg-matrices. Based on these in most cases nonlinear kinematic rela tions is the derivation of the kinetic equa tions [9J. The generalized coordinates in Lagrange's equations which is employed for this purpose are therefore these relatively complicated sets of cartesian coordinates as sociated witb ~ach joint. Due to this fact, the concept L9J based on Denavit-Hartenberg matrices does not lead in all cases to the kinetic description with a minimal number of parameters. This is especially true for more complicated systems. In order to achieve a model with a minimal number of parameters for the basic system in fig. 1, a more direct approach is used in the paper. So instead of using cartesian coordina tes for each joint, the four variables of mo tion for the manipulator in fig. 1 are used directly: r 1 = r 1(t); ~1 = ~1(t); ~2 = ~2(t); z = z(t~1) This means that the entire derivation of the dynamic representation of the system in fig. will be based simply on (1) instead of nonli near kinematic relations. However, if the cartesian coordinates are needed this can easily be achieved by a trans formation which is directly related to (1) and unconcerned with the dynamical system repre sentation. If the cartesian coordinates of the \"elbow\" (the joint between main arm and addi tional arm) are denoted xE(t), YE(t) and zE(t), then it is from fig. 1: xE(t) r 1 (t) cos ~ 1 (t) (2a) YE(t) r 1 (t) sin ~ 1 (t) (2b) zE(t) z (t) (2c) For the coordinates of the hand called x~t), Yf\"f t), z~t) follows from fig. 1 : xE(t) + r 2 cos(~1(t)+~2(t\u00bb YE(t) + r 2sin (~1(t)+~2(t\u00bb z (t) Oa) Ob) Oc) The inverse transformation, i. e. determination or r , ~ , ~2 and z from the cartesian coordi nate 1system, is given by: r 1 (t) 1 2 2 1 xE(t) + YE(t) (4a) ~1 (t) arc tg YE(t) (4b) xE(t) ~2(t) xH(t) xE(t) YE(t) arc cos (-- --) - arc tg x;m r 2 r 2 YH(t) YE(t) - arc tg YE(t) arc sin (-- --) x;m r 2 r 2 (4c) z(t) = zE(t) = zH(t) (4d) where r? is in this case a constant. (The equa tions would change very little in case r 2 is a variable, i. e. for a fifth degree of freedom.) Equations (2), (3) and (4) can be easily and fast calculated by computers so that the varia bles of the motions are available in every form. So the basic approach is here to keep the non linear kinematic equations (2), (3) and (4) se parate and to use for the treatment of the dyna mics (i. e. the kinetic model and the control) simply relation (1). This simplification is of course not restricted to the basic system (fig. 1) considered here but applies also to other configurations; it is especially of advantage for rotary joints due to the nonlinear repre sentation in a cartesian coordinate system. A nonlinear control concept 397 3. DYNAMIC MODEL For the derivation of the dynamic model for the basic system in fig. 1 Lagrange's equations can be used which have the form (5) i = 1,2,3,4 where T is the kinetic energy of the system, V denotes the potential energy; qi and q. are the generalized coordinate and velocity,lre spectively, and Q. is the generalized external force corresponding to q .\u2022 If Lagrange's equa tions (5) are evaluated an the basis of Dena vit-Hartenberg concept [9J, [2J, [3J (as pointed out in section 3), then the q. correspond to the cartesian coordinates assaciated with each of the four joints of the basic system",
            " of a rigid body is employed: (the index j r~feres to the body j, here j = 1,2) 1 2 1 E J . 2\" mJ.VA . + m.~ (w.xr )+ 2\" w. 9 A w. (9) J J j -J -Sj -J j-J where mj is the mass of the rigid body, ~ .is the velocity vector and ~j the angular J velocity, both at the reference point; Es. is the displacement vector from the reference J point to the center of mass and 9Aj is the moment of inertia related to the reference point. Before equation (10) is applied, the fol lowing notations are introduced for the basic system in fig. 1: m1 = mass of main arm m* mass of additional arm mass of upright column (rotating with ~1(t), as shown in fig. 1) mL mass of hand and applied load overall length of main arm overall length of additional arm r* radius of upright column With the index j = 1 refering to the main arm in fig. 1 and the origin as point of referen ce, the moment of inertia is by Steiner's law 2 m*r*2 m111 11 2 ---2-- + --1-2-- + m1 (r 1- ~) With (10) follows from (9) for the kinetic energy of the main arm (10) 2 1(m*r*2 m111 2) \u00b72 + 2\" -r-+---3-- -m1l1r1+m1r1 ctl1 ( 11 ) because it is IVAjl = r 1 and 1~11 = ~1 and the second term in 19) vanishes due to (~1XEs ) being vertical to ~ \u2022 1 1 The additional arm in fig. 1 which is characterized by the index j = 2 has as refe rence point the joint between main arm and additional arm (the \"elbow\"). The displacement vector ES2 between the reference point and the center of mass is from fig. 1 r ~2 + mL \u2022 r 2 \u2022 [:~o~ :~] -s2 m2 + mL y and the moment of inertia related to the refe rence point is With these terms and the velocity vectors given by ~2 = [ ~~ .j ~2 = [ ~, .J + follows from (9) for the kinetic energy of the additional arm (im2+mL)\u00b7 r 2\u00b7 {-r 1\u00b7 (q, 1+tp2 ) sinctl2+r 1\u00b7q, 1 (tp1+~2) cosC!'Z} (12) For abreviation, the following constants are introduced which are (exept for the load) fixed for the individual type of robot con sidered 398 E. Freund m1 11 1 c 2 ('2m2+ mL)r2 m*r*2 1 2 --2-+3\"m 11 (13) m2 2 c3 = (3+mL)r2 Then, the total energy of the system moving in the (x,y)-plane is due to (9) from (11) and (12): 1 21{ 2l'2 E='2c 1t 1(t) +'2 cS-c4r1(t)+c1r1(t) J~1 (t) -c2'r1(t)[~1(t)+~2(t)J sin ~2(t) +c2\u00b7r1(t)\u00b7~1(t)L~1(t)~2(t)J cos ~2(t) (14) If Lagrange's equations (6) are written down for the variables (7), then they have the form with the external force and torques K1 , M1 and M",
            " \u2022 2 +c2r1(t)'~1(t)cOSql2(t)+c2r1(t)'ql1 (t) .sinql2(t) (20 ) The motion along the z-axis is decoupled so that the equation for this motion can be ob tained directly without employing Lagrange's equation (S): (21) where K is the force driving z(t) and g is the graOity coefficient. In (21) it is assumed that K is acting in direction of the positive z-axis~ while the gravity works in opposite direction. Equations (18), (19), (20) and (21) re present the complete dynamical model of the basic system in fig. 1. The problem is to de sign a controller for this system that pro vides the values of K 1 (t), M 1 (t), M2 (t) and K (t) such that the variables r (t), ql1(t), ~~(t) and z(t) reach the desired values with a suitable dynamic behaviour. In previous wor~ e. g [2J, [3J, this problem is treated for a different type of manipulator (with three de~ grees of freedom of the arm) by linearization of the model with respect to a new set of de pendent variables. These new variables repre sent the deviation from the desired final po sition; the sines and cosines are replaced by the first order terms of the series expansionr Then the design of the controller and the de coupling can be based on this linearized equa tions. In this paper, the nonlinear equations (18) to (21) will be used directly; due to their derivation they have a minimal number of parameters. 4. STATE SPACE DESCRIPTION For the application of modern control con cepts to the basic system in fig. 1, the equa tions (18) to (21) have to be formulated in the state space. In this context it is useful to consider the total system as four subsy stems related to the four variables of motion of the basic system which are r 1 (t), ~1(t), l\"P 2 (t) and z(t). So the state variables x 1 to x 8 ' the input variables u 1 to u4 and the out put variables Yj to y~ are defined according to equations (1e) to (21) as follows: 1. Subsystem: x 1 (t) = r 1 (t) x!i:(t) = r 1(t) 2. Subsystem: x 3 (t) = tt'1(t) x 4 (t) = cD 1 (t) 3",
            " This would result into the usual state space representation. For the practical appli cation of the control concept, however, this formal way is not apropriate which will be described in section 7. From this reason, the accelerations in these coupling terms will be included in the state matrix and denoted bV special variables: (26) These variables do not represent of course the accelerations of the uncoupled dynamics. Then from (18), (19), (20) and (21),the state space description of the redundant manipula tor in fig. 1 has the form ><1 x 2 0 0 0 0 )(2 f 1 (~) L 0 0 0 c 1 -------------------- )(3 x 4 0 0 0 0 u 1 )(4 f2(~) + 0 f 4 (x 1 ) -f 4 (x 1 ) 0 u2 -------------------- u3 ><5 x6 0 0 0 0 u 4 lt6 f3(~) 0 0 1 c 3 0 -------------------- (27a) )(7 x8 0 0 0 0 )(8 0 0 0 0 L c 1 V1 =x 1 ; Y2=x 3 ; Y3 where f1(~(t)) = ( c 4 ) 2 c 2 2 c 2 .. . x1-~ x 4 +C-x6 cos(x5-x3)+C-Y3s1n(x5-x3) 1 1 1 (28) 1 {(c -2c x )x .x c5+c1x12-c4x1 4 1 1 2 4 (29) +c2x1\u00b7x62.sin(x5-x3) -c2\u00b7x1\u00b7Y3\u00b7cos(x5-X31 (29) -:~{(2X2\u00b7X4+X1\u00b7Y2\")COSCX5-X3) +(x1\u00b7X42_Y1\")sin(x5-x3)} 5. GENERAL NONLINEAR CONTROL CONCEPT To develop a control system for high ac curacy and rapid motion for the redundant ma nipulator in fig. 1, nonlinear decoupling and control will be applied to the state space description (27) of the system. For this purpose the non linear control concept is briefly in troduced here in general form without proof. For a morE detailed representation it is re fered to 6 J and [7J. The following general nonlinear time variable system is considered: ~(t) .y. (t) ~(~,t) + ~(~,t) ~(t) f(~,t) + Q(~,t) ~(t) (32a) (32b) where x(t) is the n-dimensional state vector, ~(t) and .)L(t) are the m-dimensional input and output vector, respectively, and ~(~,t), 8(x,t), C(x,t) and D(x,t) are of compatible order",
            " Subsystem: r; (t) r 1 (t) + Q 01 r 1(t) ), 1 w (t) 2 2 * u2 (t)=uM (t)=(-c4+2c1x1)x2,x4+c2(x1x4-x1,x6-Y1) 1 + Q 11 r 1 CD 1 (t) + Q 12 ~1 et) + Q 02 qJ1(t) A2 wqJ (t) * * +c 2 (x 1Y3 +2x 2x4+x 1Y2 ) cos(xS-x 3 ) 2 ~(c3+cS+c1x1-c4x1)\u00b7(Q02x3+Q12x4) +c3Q03(x3-XS)+C3Q13(x4-X6) 2 + e c 3 + c S + c 1 x 1- c 4 x 1 \u00bb), 2 wqJ 1 + c 3 ), 3 WqJ2 (S7) 1 e 60) CP2 (t) + Q13 cP2 (t) + Q 03 qJ2 et ) A3 wqJ (t) 2 Y( t) + Q 14 Ht) + Q 04 z(t) ), 4 wzet) In these equations, the state variables were replaced according to (22), (23), (24) and (25). The Qk i and A. (k = 1,2; i = 1,2,3,4) of the equations (60' can be chosen arbitrarily in the control laws (S6) to (59). 7. SUMMARY 3. Subsystem: Fig. 2 shows schematically the block structure of the redundant manipulator as pre sented in fig. 1 in connection with the non linear control concept that was given as a new approach for the control of computer~controlled manipulators in the paper. It can be seen in fig. 2 that the whole consideration of the dy namics inclusive the control are based on the four variables r 1 (t), qJ~(t), qJ?(t) and z(t). The complicated Kinematic relations for the * u3 (t)=uM (t)=c2(2x2'x4+x1'Y2)cos(xS-x3) 2 2 * . +c 2 ex 1 , x 4 -Y 1 )sl.n(xS-x 3 ) -(c3Q02-c3Q03)x3-(c3Q12-C3Q13)x4 -C3Q03XS-C3Q13x6+c3A2W +c3 A 3W qJ1 qJ2 (S8) A nonlinear control concept 403 cartesian coordinates xE(t), YE(t), and zE(t) of the \"elbow\" (joint between main arm and additional arm) and of the hand xH(t), YH(t) and zH(t) are shown as two blocks(for trans formation and inverse transformation) outside the dynamical part of the manipulator system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure14-3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure14-3-1.png",
        "caption": "FIGURE 14-3 Hydraulic dynamometer. (Courtesy Taylor Dynamometer and Ma chine Co.)",
        "texts": [
            " Now if the wheel is rotated n times in one minute, the work accomplished will be 27TeFn, or where e = meters F = newtons Power 27TeFn k -- W 60,000' n = revolutions per minute (3) Torque is measured by the Prony brake and similar dynamometers. In the preceding equation, torque is equal to Fl. Power 27TnT k -- W 60,000' (4) 408 TRACTOR TESTS AND PERFORMANCE where T = torque in newton meters The Prony brake is not entirely suitable for power versus speed deter minations of an internal combustion engine since the torque versus speed curves of the brake and engine are approximately the same. Therefore, speed control may be difficult. Hydraulic The hydraulic dynamometer (fig. 14-3) also operates on the principle of con verting work into heat. The working medium, usually water, is circulated within the housing and because of friction comes out at a higher temperature than when it entered. The outer case, which is free to rotate about the shaft, is connected to and restrained by the torque arm. With the exception of bearing friction, the torque produced is equal to that supplied to the dyna mometer. The power-absorbing capacity for any given type of design varies approximately as the cube of the speed of rotation and the fifth power of the ELECTRIC DIRECT-CURRENT DYNAMOMETERS 409 diameter (Culver 1937)",
            " The accuracy is independent of the electrical efficiency of the machine. Accuracy within 0.25 percent is possible. This type of electric dynamometer can usually be arranged to operate as a motor. In either arrangement, the power put into or developed by the unit is 410 TRACTOR TESTS AND PERFORMANCE 2-rrCFn Power = 60,000' kW which is the same as for the Prony brake (equation 3). Shop-Type Dynamometers (5) It is often desirable to measure the pto power of a tractor in the field or in an implement dealer's repair shop. Since dynamometers, such as are shown in figure 14-3 or 14-4, are much too expensive and difficult to use except in laboratories, there have been developed several inexpensive and portable devices generally classified as shop-type or agricultural dynamometers. An example is shown in figure 14-5. This type of dynamometer is used primarily as an indicator of the condition of the engine. It is also used in the process of adjusting or tuning an engine and in indicating to customers the improve ment in a tractor engine as a result of an overhaul, maintenance, or adjust ment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-15-1.png",
        "caption": "FIGURE 13-15 Gear-tooth terminology.",
        "texts": [],
        "surrounding_texts": [
            "GEAR DESIGN\n379\ntangential rolling diameters called the pitch diameters and the number of teeth can be determined. The pitch diameter of the pinion, or smaller gear, for spur and helical gears is\nwhere D CD\nD = 2(CD)/(1 + R)\nthe pitch diameter of the smaller gear the shaft center distance\nR the gear ratio greater than 1\n(8)\nIt follows that the pitch diameter of the larger gear can be calculated by",
            "380 TRANSMISSIONS AND DRIVE TRAINS\nsubtracting D from 2( CD) or setting R = llR. The relationship between the gear module, gear pitch diameter, and number of teeth is\nwhere m D N\nm = DIN\ntooth size, module nominal pitch diameter number of teeth\n(9)\nFor helical gears, m is the module in the transverse plane and is related to the normal or cutter module mn by\nm = mnlcos IjJ (10)\nwhere IjJ = the helix angle\nThe general range of tooth modules for various gears in the drive train is as follows:\n1. Transmission gears-4 to 5 2. Power shift planetary gears-2.5 to 3.5",
            "GEAR DESIGN 381\n3. Spiral bevel gears-8 to 12 4. Final drive gears-5 to 7\nUsually cutters of nominal size and pressure angle are used, but often center distances and tooth numbers are chosen so that the nominal pitch diameters will not touch, as shown in figure 13-13. This only means that the operating or working pitch diameter is different from the nominal pitch diameter shown in equation 9. There is a corresponding working pressure angle, which is given by\nwhere <1>\",\nm N1,N2\nCD\n<1>1\n<1>\"\n_ [ m (N1 + N2) cos <1>1 <1>\" = cos 2 CD (11)\nthe working pressure angle the gear module in the transverse plane from equation 10 the number of teeth in gear 1 and gear 2 shaft center distance the transverse pressure angle = tan -[ (tan <l>n1cos tV) the nominal or cutter pressure angle\nGear geometry and stress calculations are too complex to be done man ually now that computers are readily available. Even with computers doing the mathematical work, gear design is complex and involved and is often done by a specialist. For, in addition to gear geometry and stresses being calculated,"
        ]
    },
    {
        "image_filename": "designv10_10_0002664_s10999-012-9181-y-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002664_s10999-012-9181-y-Figure1-1.png",
        "caption": "Fig. 1 Model of 6-SPS parallel mechanism",
        "texts": [
            " Based on the principle of Kane, the dynamics formulations of a multibody system with n bodies could be written as follows. Kc \u00fe K c \u00bc 0 c \u00bc 1; 2; . . .; f\u00f0 \u00de \u00f01\u00de In Eq. 1, Kc is generalized active force of the generalized velocity c; K c is generalized inertial force of the generalized velocities c. According to principle of Kane, the calculation of acceleration and partial acceleration, the partial velocities of mass centers, and partial angular velocities of all links are required. The mechanism studied in this paper is a 6-DOF parallel mechanism, which is shown in Fig. 1, herein referred to as a 6-SPS (spherical-prismatic-spherical) parallel mechanism. This parallel mechanism consists of a moving platform which is manipulated by six actuated links. Each link is connected with fixed platform and moving platform through spherical hinge. Since six links are identical, one link is choosed to derive dynamic equation. As shown in Fig. 2, it illustrates a link of parallel mechanism. Coordinate frames Cum-XumYumZum and Cbm-XbmYbmZbm are two moving coordinate frames that are located in up link and bottom link respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001952_cdc.2009.5400277-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001952_cdc.2009.5400277-Figure2-1.png",
        "caption": "Fig. 2: 2nd-order homogeneous differentiation",
        "texts": [],
        "surrounding_texts": [
            "The differentiator based on high-order sliding modes [19] is modified to allow faster convergence. As previously differentiation of signals up to the order k with a known upper bound L of the (k+1)th-order derivative is obtained. Linear terms are added to the differentiator in order to provide for the faster convergence, when the initial errors are large. The modified differentiator preserves the robustness and exactness of the standard differentiator, as well as its asymptotic accuracies. Theoretically the new non-homogeneous differentiator may feature a peaking effect, as a result of linear dynamics with large errors. In practice it is not observed. The next step will be further improvement of the differentiator convergence by introduction of higher order terms. Differentiator convergence with variable function L(t) is to be studied. The differentiator can be used for feedback control, since the separation principle is trivially fulfilled in the absence of noises."
        ]
    },
    {
        "image_filename": "designv10_10_0003458_j.tust.2015.11.022-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003458_j.tust.2015.11.022-Figure5-1.png",
        "caption": "Fig. 5. Equivalent dynamic model of (a) a typical two-stage planetary gear system and (b) planetary stage j.",
        "texts": [
            " According to the Newton\u2019s second law, the equation of motion for gear and pinion is written in matrix form as Mm\u20acq\u00fe Cm _q\u00fe Kmq \u00bc Fm \u00f04\u00de where Mm, Cm, Km are the mass matrix, damping matrix and stiffness matrix respectively, Fm is the vector of force and torques caused by meshing errors. Refer to meshing stiffness km, meshing damping cm, and the projection vector V, Cm, Km, Fm are obtained by the formulas: Km \u00bc kmV TV ; Cm \u00bc cmV TV ; Fm \u00bc \u00bdkme\u00f0t\u00de \u00fe cm _e\u00f0t\u00de VT \u00f05\u00de 2.2.3. Dynamic model of multi-stage planetary gears Fig. 5(a) shows the equivalent dynamic model of a two-stage planetary gear system with equally spaced planets. Each carrier, ring, sun and planet has three degrees of freedom: two translations and one rotation. Fig. 5(b) shows the equivalent dynamic model of a single-stage planetary gear system. The gear mesh interactions are represented by linear springs and dampers acting along the line of action. The dampers which are parallel to the springs are not depicted in Fig. 5. As an example, the deflection of the n-th sun-planet mesh and ring-planet mesh in the j-th stage is d j sn \u00bc r jbsh j s\u00fe r jbph j n xj s sinw j sn\u00feyj s cosw j sn f jn sina j s g j n cosa j s\u00feej sn\u00f0t\u00de \u00f06\u00de where a j s is the pressure angle of the sun-planet mesh, and w j sn \u00bc u j n a j s . e j sn\u00f0t\u00de is the time-varying, unloaded static transmission error. The coupling interaction between sun j and carrier i in two connected planet stages is Dij s \u00bc kijcs;u\u00f0uj s ui c\u00de \u00fe cijcs;u\u00f0 _u j s _ui c\u00de; u \u00bc x; y; h \u00f07\u00de where kijcs;u, c ij cs;u are the coupling stiffness and damping of the connecting shaft",
            " 7, where the FE model of cutterheadbearing subsystem and FE model of driveshaft subsystem are included. In Fig. 7, the node number of each beam element is determined based on its own structure features and the connection relations. The gear mesh between ring gear and pinions are equivalent to the spring-damper elements plus meshing error effects. The bearing/bolt/spline connections are equivalent to the spring-damper element for supporting or connection. The planetary gearbox is equivalent to the dynamic model of multi-stage planetary gears shown in Fig. 5(a), which is not repeated in Fig. 7. In the FE model of cutter head driving system, there are (13 + 5n) nodes for the beam element, and each node has 6 degrees of freedom, where n is the number of driveshaft subsystems. In the dynamic model of two-stage planetary gearbox, there are 13 components, and each component has 3 degrees of freedom. Therefore, the total degrees of the cutter head driving system are (72 + 69n). Table 1 shows the number of nodes and the degrees of freedom in both the whole system and subsystems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001825_3.55753-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001825_3.55753-Figure1-1.png",
        "caption": "Fig. 1 Canted ring configuration, showing the cant angle y and the orientation angle Oy. .",
        "texts": [
            " For larger motion, the location of e3 can be computed.6 We now consider the projectile to consist of its external symmetric body with mass mb and an internal symmetric component of mass mct which is free to move perpendicular to the body's axis of symmetry. The axis of symmetry of the internal mass is assumed to cant at constant angle 7 with respect to the body's axis of symmetry, and the plane of this cant angle is assumed to maintain a constant phase angle </>y with the angle-of-attack plane (Fig. 1). If 0 and 0T are the orientation angles of the angle-of-attack plane and the cant plane, respectively, then fHodapp5 has derived general equations for this motion, but applied them to the very simple case of longitudinal motion of a mass on the shell's axis of symmetry. D ow nl oa de d by U N IV E R SI T Y O F O K L A H O M A o n Ja nu ar y 29 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .5 57 53 MARCH-APRIL 1978 INFLUENCE OF MOVING PARTS ON PROJECTILE ANGULAR MOTION 119 The motion of the c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002745_pime_proc_1966_181_036_02-Figure24-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002745_pime_proc_1966_181_036_02-Figure24-1.png",
        "caption": "Fig. 24. The schematic diagram of the apparatus",
        "texts": [],
        "surrounding_texts": [
            "Apparatus The rig, shown schematically in Fig. 26, consists of a circular base A, supporting a roller By and a semicircular vertical ring C to which the toroid is attached. The semicircular ring is perpendicular to the plane of the base and is constrained by an extended strain-gauge ring D which allows movement in the plane of the ring. It can be shown (38) that the kinematic relation between general types of ball motion can be specified by two \u2018angle\u2019 parameters, as shown in Fig. 27. The spin ratio is given by tan a and the slide/sweep ratio by tan ,8. By adjusting the vertical and the base rings any orientation of the ball axis with respect to the track can be achieved. Both angles can be read directly from the vernier scales to within one-tenth of a degree. It was found necessary, however, to subdivide the vernier scale by means of a micrometer screw to 0.001 of a degree in order to have the degree of accuracy required. The rig when used for sliding experiments is not dissimilar to that used by Smith (33) and Misharin The extended octagonal ring D with eight strain gauges is mounted on the adjustable platform by means of two flexible cross-springs. Fig. 28 shows the different combinations of gauges with which the two force components, F, and F,, and the moment, M y can be measured. The selector and the monitor were designed to allow each output circuit to be balanced individually through potentiometers. The high gain of the bridge circuit with four active gauges permitted the use of a relatively stiff dynamometer ring. For example, at a total bridge current of 6 mA, ( 4 0 Vol18I Pr 1 No 16 at PENNSYLVANIA STATE UNIV on June 4, 2016pme.sagepub.comDownloaded from FRICTIONAL BEHAVIOUR OF LUBRICATED ROLLING-CONTACT ELEMENTS 365 Proc Instn Mech Emgrs 1966-67 Val 181 Pt 1 No 16 at PENNSYLVANIA STATE UNIV on June 4, 2016pme.sagepub.comDownloaded from 366 S . Y. POON AND D. J. HAINES the accuracy when used in connection with a high-gain d.c. recorder was better than 0.02 lb and F, maintained its linearity over the range of 0-24 lb. The four-gauge circuit together with the good thermal conductivity of the duralumin dynamometer ring may also have accounted for the extremely stable output without which it would not have been possible to carry out some of the experiments described in later sections. The moment associated with rolling with spin is, however, too small to be measured accurately by the circuit as described and further thought is being given to this problem. The normal load was applied to the bearing housing through cords attached to it and the pulley assembly F is designed to equalize the load on the bearings. Whenever there is a friction force at the contact surface (and even the presence of ball spin generates a small sideways-acting friction force) the line of the resulting load will not remain normal to the plane of the contact surface and the \u2018load line\u2019 will not remain in the centre of the contact area. The strain gauging on the dynamometer ring D has been deliberately designed and wired to eliminate these load-line effects from the results. The lubricant was applied to the roller for low-speed running by means of a continuously replenished felt pad, placed about 3 in from the contact on the inlet side. Later, when the speeds were raised, it became the source of frictional heat, and was replaced by a jet of oil-air mixture. Proc Instn Mech Engrs 1966-67 The contact area of point contact, unlike that of line contact, was comparatively minute, and provided the slide/ sweep ratio was low a steady surface temperature, for a given inlet oil temperature, could easily be established under controlled ambient conditions. The surface temperature on which the initial viscosity qo depended was recorded after the fashion of Crook (32) by a trailing thermocouple. The roller was driven from a variable-speed motor. The speed of the roller was recorded by a frequency meter which picked up signals from a 60-teeth gear mounted on the shaft of the roller. No attempt was made to monitor the speed of the upper shaft. The friction at the upper bearings did not present any difficulty with carefully selected and properly installed bearings, For instance, the force transmitted across the contact to overcome the overall friction at the contact and the bearings was less than 0.17 lb at 27-3 lb normal load and 1200 ft/min (or about 0.4 per cent of the normal load) and much less at lower speeds. Measurement of electrical conductivity The technique used has been favoured by a number of authors. The circuit arrangement is described in Fig. 29 and is essentially that used by Furey (42). The electrical-conductivity tester is basically a \u2018go no-go\u2019 device, indicating the presence or absence of any direct metallic contact between the surface asperities. When good electrical contact is maintained no potential difference (p.d.) across the contact area is observed, but when the surface asperities are submerged by an interposing lubricant film, the difference in potential surges to the full applied value. At a moderate rate of interruption the phenomenon can be exhibited on a cathode-ray oscillograph (c.r.0.); and the average voltage recorded on a d.c. voltmeter with a long-time constant indicates the fraction of the time in which contact between the rolling elements has been interrupted. Let Y be the ratio of the recorded voltage to the applied p.d. and 7 be the time ratio. Vol idi Pt i KO 16 at PENNSYLVANIA STATE UNIV on June 4, 2016pme.sagepub.comDownloaded from FRICTIONAL BEHAVIOUR OF LUBRICATED ROLLING-CONTACT ELEMENTS 367 It has been shown (35) that, if the law of a resistancecapacitor circuit at interruption is assumed, the following relation exists : V = T2,/(CRC+T). , . . (81) where c is the rate of contact interruption, R the series resistance of the circuit, and C the inter-specimen capacity. In the present case the value of C over the range of applied load is about 1 pF. Thus at a moderate interruption rate the above relation can be simplified to that is the ratio of contact interruption is equivalent to the ratio of the recorded average voltage to the applied p.d. Let T,, be the fraction of the time during which electrical contact is maintained. Clearly r = v . . . . * (82) T ~ = 1--7 . . . . (83) In the implementation of the circuit two points have to be borne in mind: that the applied p.d. has to be kept low so that no oil film of significant thickness should break down as a result of a high field intensity, and that the passage of current has to be limited to a minimum when contact takes place at the minute points of the asperities: this is the reason for the series resistance shown in Fig. 29. The requirements call for particular attention to the construction of a 'low-noise' slip ring. Space limitation excluded the use of conventional mercury-type slip rings on the top shaft. The contacts and the slip rings used in the experiments are made of silver and platinum respectively and were found initially to give good results when the rig was tested with unlubricated rollers. Fig. 30 shows a bearing housing assembly fitted with a slip ring. Specimen and test procedures The dimensions of the toroid or 'ball' and the cylinder were chosen to give a circular contact area. The dimensions and heat treatment of the specimens are given in Table 4. Proc Imtn Mech Engrs 1966-67 Except for the preliminary tests the surface finish of the toroids and rollers was of two kinds, either as ground to 12-15 pin c.1.a. or polished to 2.0-2.5 pin c.1.a. Care has been taken to ensure a homogeneous, non-directional surface topography; it was particularly difficult to achieve this with the large cylinders. The test procedures adopted were as follows. A new testpiece was given a good running-in at loads increasing in steps to the final value at which it was going to be tested (see Fig. 31). The specimens were run under these conditions until the average voltage across the contact settled down to a steady value. The null point of the skew angle was adjusted and the bridge circuit balanced. At a later stage it was found necessary to swing the base ring about its null point in order to locate its true position by interpolating the readings from the tangential-force measurements. The ultimate accuracy which could be so achieved was better than 2.5 x For each series of tests one ball specimen was used as far as possible. However, with a frequency depending on the severity of the running condition, it had to be replaced from time to time and the test repeated. Any slight damage to the surfaces (or the presence of wear debris) shows on the conductivity test as an irregular movement of the recorder pen. In contrast the tangential force records tend to be insensitive to the early signs of damage and cannot be used as an indication that material has become detached from the metal surfaces. degrees. 1 lo4 in t b Vol181 Pt I No 16 at PENNSYLVANIA STATE UNIV on June 4, 2016pme.sagepub.comDownloaded from 368 S. Y. POON AND D. J. HAINES the direction of rolling and this is unlikely in view of the magnitude of the driving force required. The lubricants used in group A and group B were Shell Tellus oil 15 (0.20 P at 20\u00b0C) and a mineral oil to OM-100 specification respectively. The mineral oil is of particular interest. It is one of the lubricants which has been extensively used by earlier investigators and a great deal is known about its physical properties (32) (43). Its viscosity varies from 3.30 to 0.66 P between 18 and 40\u00b0C. The corresponding variation of the pressure viscosity coefficient y is estimated to be from 2-98 to 2.5 x cm2/dyn."
        ]
    },
    {
        "image_filename": "designv10_10_0000816_tcst.2003.813374-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000816_tcst.2003.813374-Figure1-1.png",
        "caption": "Fig. 1. General n-trailer and the Frenet frames.",
        "texts": [
            " Even in presence of realistic problems like saturation and of limited measurement information, it is shown how the \u201creduced off-tracking\u201d notion is implementable in practice. 1063-6536/03$17.00 \u00a9 2003 IEEE We would like to stress the fact that the whole analysis is local and to point out that, due to the singularities of the Frenet frame representation, there is no way to formally prove a well-behaved transient even for admissible (wrong) initial conditions that are too close to the limits of the region of attraction. Notation, modeling assumptions and equations are the same as [3] and are briefly recapitulated here. The legenda for the symbols used is (see also Fig. 1): Number of trailers. Number of off-hitching ( ). Indexes of the axles having off-hitching ( ). Midpoint of the th axis Distance between and the hitching point in front of it . Distance between and the hitching point behind it . Longitudinal velocity of . Absolute orientation angle. . Reference path. Curvature of the path. Orthogonal projection of on Arclength coordinate of the th curvilinear frame. Orientation angle of the th frame with respect to the Cartesian axes Distance between and . . It was shown in [18] and [19] that a frame moving on the path can be useful to locally describe a point moving on the plane, instead of a fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003375_j.triboint.2014.10.007-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003375_j.triboint.2014.10.007-Figure4-1.png",
        "caption": "Fig. 4. The lubricating gap (in yellow) between the lateral bushing (transparent view) and the gears is shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " The FSI\u2013Thermal coupled model was created as an independent application using C\u00fe\u00fe , and was linked with some open-source libraries to leverage their capabilities: GMSH [25] for meshing, GSL [26] for multidimensional root-finding and spline interpolation, and OpenFOAM [27] for FV discretization of PDEs and linear system solving. The geometry of the lubricating interface between gears and lateral is a plane when solid deformations are not considered, and therefore can be fully determined considering the 3 points that are shown in Fig. 4. Using the gap height information stored at the points T0, T1 and T2 the gap height for an arbitrary point in the lateral lubricating film for an undeformed but arbitrarily tilted bushing can be calculated using the following, hUD x; y\u00f0 \u00de \u00bc x 2hT2 hT1 hT0 2\u00f0d\u00feR\u00de \u00fey hT1 hT0 2R \u00fehT0 hT1 2 \u00f01\u00de The solid deformation due to pressure and thermal loading were added to this film thickness as described in following sections. The information about the axial motion of the lateral bushing are stored in the form of the axial \u201cnormal squeeze\u201d velocities at the three points shown in Fig. 4 and the resultant squeeze velocity at an arbitrary point is given by \u2202h x; y\u00f0 \u00de \u2202t \u00bc x 2\u00f0\u2202hT2=\u2202t\u00de \u00f0\u2202hT1=\u2202t\u00de \u00f0\u2202hT0=\u2202t\u00de 2\u00f0d\u00feR\u00de \u00fey \u00f0\u2202hT1=\u2202t\u00de \u00f0\u2202hT0=\u2202t\u00de 2R \u00fe\u00f0\u2202hT0=\u2202t\u00de \u00f0 \u2202hT1=\u2202t\u00de 2 \u00f02\u00de The fluid flow and the structural deformation solvers were developed to enable isothermal simulation of the lateral lubricating interface, and have been presented in great detail in [7,8,10]. Therefore, in the present work, a brief overview is provided. Reynolds equation [28] was used to model the fluid in the micron level lubricating gap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003109_978-0-8176-4893-0_6-Figure6.6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003109_978-0-8176-4893-0_6-Figure6.6-1.png",
        "caption": "Fig. 6.6 3-sliding nested car control (a) Car trajectory tracking (b) 3-sliding tracking deviations (c) Steering angle derivative (control) (d) Steering angle",
        "texts": [
            " 6.5a\u2013d respectively. It is seen from Fig. 6.5c that the control u remains continuous until the 3-sliding mode is obtained. The steering angle remains smooth and is quite practical. In the presence of output noise of magnitude 0:01 m, tracking accuracy levels of j j 0:02; j P j 0:14; j R j 1:3 were obtained. With measurement noise of magnitude 0:1 m, the accuracy changes to j j 0:20; j P j 0:62; j R j 2:8. The performance of the controller with a measurement error magnitude of 0:1 m is shown in Fig. 6.6. It is seen from Fig. 6.6c that the control u is a continuous function of t. The steering angle vibrations have a magnitude of about 7 degrees and a frequency of 1 rad/s, which is also quite feasible. The performance does not significantly change, when the frequency of the noise varies in the range 100\u2013 100,000 rad/s. The normal blood glucose concentration level in a human lies in a narrow range, 70\u2013 110 mg/dl. Different factors including food intake, rate of digestion, and exercise can affect this concentration. Two pancreatic endocrine hormones, glucagon and insulin, are responsible for regulating the blood glucose level"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000709_s1350-6307(01)00002-4-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000709_s1350-6307(01)00002-4-Figure11-1.png",
        "caption": "Fig. 11. Coordinate system used for the computation of KI and KII.",
        "texts": [
            " Thus the computation took this mechanism into account, with variations during the meshing cycle, as in [8]. The analysis allowed one to compute the value of the stress intensity factor K, specifically modes I and II and to determine the real K (variation of the stress intensity factor in a load cycle), caused by the applied loads and by the state of residual stress, by varying the shot-peening conditions. Computation was based on the values of nodal displacements on the opposite faces of the crack ( \u00bc 180 , see Fig. 11). By considering displacements of nodes, located on the opposite faces of the crack, both parallel (ux) and perpendicular (uy) to the direction of propagation we obtain: KI \u00bc limr ! 0 2E \u00f01\u00fe \u00de ffiffiffiffiffi 2 r r uy KII \u00bc limr ! 0 2E \u00f01\u00fe \u00de ffiffiffiffiffi 2 r r ux \u00f01\u00de These equations allow one to find an \u2018\u2018equivalent stress intensity factor\u2019\u2019, which considers both kinds of propagation, defined as: Keq \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K2 I \u00fe K2 II q \u00f02\u00de The equations above consider cases with no residual stress and with residual stress caused by shotpeening with 8 A, 12 A and 14 A intensities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-17-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-17-1.png",
        "caption": "FIGURE 11-17 Determination of the pitch moment of inertia using the pendulum method.",
        "texts": [
            " As was the case for the center of gravity location, the many, often irregularly shaped parts composing a tractor make it difficult to analytically calculate the moments of inertia of a tractor about the longitudinal, transverse, or vertical axes passing through its center of gravity. 306 MECHANICS OF THE TRACTOR CHASSIS The moments of inertia about the transverse (pitch) and longitudinal (roll) axes passing through the center of gravity of the tractor may be measured using the setup illustrated in figure 11-17. The tractor and the supporting sling form a compound pendulum that will oscillate with a period T given by where ~o T = 2'lT -- WRo 10 = moment of inertia of tractor plus sling about pivot 0 W = weight of tractor plus sling Ro = distance between pivot 0 and the center of gravity of the tractor plus sling (82) Measurements of the distance Ro and the period of oscillation allow the cal culation of 10 , Often the weight and moment of inertia of the sling can be neglected with respect to the corresponding quantities for the tractor",
            "1') mm) (b) \"'ith the center of the front wheels raised to n = 1600 mm above the level surface used in (a), the weight supported by the rear axle, R;, is measured as 38.307 kK. Values of 483.1 and 875,0 mm are determined for the radii of the front (rj) and rear (r,) wheels respectively. Find the height h of the center of gravity of the tractor above the rear axle center. (h = 194.5 mm) 2. To determine the pitch moment of inertia of the tractor about its center of gravity, the tractor is supported as shown in figure 11-17. The lengths of the supporting cables connecting the axles to the pivot are adjusted so that the tractor is level in the equi librium position. Because the distance Ro between the piyot and the tractor center of grayity is difficult to measure directly, the vertical distance between the pivot and the rear axle center is measured and found to be 2200 mm. The tractor is set into oscillation and the elapsed time for several O'cles recorded. The average period is determined as 3.247 s. Assuming the weight and moment of inertia of the supporting cables are negligible, find the pitch moment of inertia I,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure7-1.png",
        "caption": "Fig. 7. Schematic representation of objective and rough-cut surfaces for a spiral bevel pinion for determination of deviations between surfaces.",
        "texts": [
            " Minimization of deviations The main purpose of the applied numerical procedure is minimizing deviations n between the objective, o , and rough-cut, rc , surfaces at every point of a regular grid on the spiral bevel pinion objective active tooth surfaces ( Eq. 33 ), satisfying that all deviations are positive (no damage of the objective tooth surface) and the machine-tool settings and other geometric restrictions are met. From the mathematical point of view, a nonlinear constrained optimization problem must be set up. Surface o, CC represents the objective concave surface of the pinion whereas surface rc, CC represents the corresponding rough-cut concave surface ( Fig. 7 ). Point P o, CC will be considered on a regular grid on the pinion objective surface, and point P rc, CC will be obtained as the intersection of the normal vector traced from point P o, CC with the rough-cut surface. Similar procedure will be followed for both convex surfaces, the objective and the rough-cut surface. ( n CC ) i, j = ( P o,CC ) i, j ( P rc,CC ) i, j \u2265 0 (33a) ( n CV ) i, j = ( P o,CV ) i, j ( P rc,CV ) i, j \u2265 0 (33b) An objective function f ( x ) subjected to M \u00b7 N constraint functions c ij ( x ) ( \u2200 i = 1 , 2 , ",
            " Accordingly, the objective function can be expressed by f ( x ) = M \u2211 i =1 N \u2211 j=1 ([ n i, j ( x ) ] CC )2 + M \u2211 i =1 N \u2211 j=1 ([ n i, j ( x ) ] CV )2 = M \u2211 i =1 N \u2211 j=1 (( r \u2217w, CC ( s i, j , \u03b8i, j ) \u2212 r w, CC ( s i, j , \u03b8i, j , x )) \u00b7 n w, CC ( s i, j , \u03b8i, j , x ))2 (36) + M \u2211 i =1 N \u2211 j=1 (( r \u2217w, CV ( s i, j , \u03b8i, j ) \u2212 r w, CV ( s i, j , \u03b8i, j , x )) \u00b7 n w, CV ( s i, j , \u03b8i, j , x ))2 Subscript CC refers to the concave active tooth surface, while subscript CV refers to the convex active tooth surface. \u2022 The condition that the rough-cut surfaces do not damage the objective surface must be taken into account as follows: (i) The deviation between objective and rough-cut surfaces n at every point of the spiral bevel pinion both concave and convex active surfaces must be positive, so that rough-cut surfaces are always outside the objective surfaces, as shown in Fig. 7 . Additionally, an offset distance \u03b4s might be introduced if a certain quantity of stock material has to remain on the spiral bevel pinion objective surfaces before starting the finishing operations. This condition of non-damaging the objective surfaces is considered as c ( j\u22121) \u00b7M+ i (x ) \u2261 [ n i, j (x ) ] CC \u2265 \u03b4s > 0 \u2200 { i = 1 , 2 , . . . , M j = 1 , 2 , . . . , N (37a) A. Fuentes-Aznar et al. / Mechanism and Machine Theory 112 (2017) 22\u201342 33 { c M \u00b7N+( j\u22121) \u00b7M + i (x ) \u2261 [ n i, j (x ) ] CV \u2265 \u03b4s > 0 \u2200 i = 1 , 2 , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001051_s00170-005-0032-y-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001051_s00170-005-0032-y-Figure12-1.png",
        "caption": "Fig. 12 The geometric parameters and the free-body diagram of the steel-ball",
        "texts": [
            " In practice, the centrifugal force of the ball at high speed will add another force on the final draw force. Therefore, it is necessary to predict and control the additional centrifugal force. A balltype pull-in mechanism is shown in Fig. 11(a). At the pullin status, the spring force is amplified through the contact geometry of the steel ball. A simplified model is shown in Fig. 11(b). The input force is the spring force and the output is the draw force. Geometrical parameters of the contacted ball of the pullin mechanism are defined in Fig. 12(a). Free body diagram of the steel ball is depicted in Fig. 12(b). Friction of the ball contact interface is assigned as \u03bck. At static state, the force and moment equivalent conditions must be satisfied as:X Fx \u00bc 0 ) F3 sin \u00fe \u00f0 \u00de \u00fe ukF3 cos \u00fe \u00f0 \u00de \u00feukF1 sin \u00f0 \u00de F1 cos \u00f0 \u00de \u00fe f2 \u00bc 0 (11) X Fy \u00bc 0 ) F2 \u00bc F3 cos \u00fe \u00f0 \u00de ukF3 sin \u00fe \u00f0 \u00de F1 sin \u00f0 \u00de ukF cos \u00f0 \u00de (12) X M0 \u00bc 0 ) f2 \u00bc uk F3 F1\u00f0 \u00de (13) Pin \u00bc F1 sin \u00fe uk cos \u00bd (14) Pout \u00bc F3 cos uk sin \u00bd (15) Solving the Eqs. (11\u201315) simultaneously, we can obtain the following results: Pout Pin \u00bc cos \u00fe \u00f0 \u00de sin \u00fe \u00f0 \u00de cos \u00fe \u00f0 \u00de \u00fe uk=r sin \u00fe \u00fe \u00f0 \u00de \u00fe uk=r (16) r sin \u00fe \u00f0 \u00de (17) where \u00bc tan 1uk r \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe u2k q : The \u03bb in Eq",
            " (16) is defined as the mechanical efficiency of the ball-type pull-in mechanism. The mechanical efficiency can be determined by selecting a set of proper geometric parameters in Eq. (16). Figure 13 shows an example of the mechanical efficiency, spring force, and draw force as a function of the displacement of the pull-in process at static case. A draw force triple that of the spring force is gained from the designed mechanical efficiency. At the dynamic state, if the centrifugal force of the steel ball must be taken into account (as shown in the Fig. 12 (b)), the dynamic draw force can be formulated through the same procedures and becomes: PT out \u00bc PT in \u00fe cos cos \u00fe \u00f0 \u00de sin \u00fe \u00fe \u00f0 \u00de \u00fe uk=r I : (21) where I=mR\u03c92 is the centrifugal force of the steel ball. Notice that the centrifugal force will be a plus to the draw force in this case. However, depending on the geometric parameters, the centrifugal force is possible to be a minus to the draw force. Figure 14 shows the simulation result of the centrifugal force effect at different friction coefficient values"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002544_j.optlastec.2011.08.026-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002544_j.optlastec.2011.08.026-Figure9-1.png",
        "caption": "Fig. 9. (a) Schematic arrangement of temperature measurement setup and (b) typical temperature\u2013time pattern, obtained by experiments and modeling.",
        "texts": [
            "5 kW CO2 laser system [30], a co-axial powder-feeding nozzle with a volume controlled powder feeder [31] and a five axis CNC laser workstation. Fig. 8 presents a schematic arrangement of LRM setup. A laser beam of spot diameter 1.2 mm was used to deposit single tracks of Inconel 625 on sand-blasted SS316L substrate (size: 10 mm 10 mm 5 mm) at various processing parameters. Table 2 presents the processing parameters used for model validation. For temperature measurements, two mineral insulated type K thermocouples were mounted below the substrate, as shown in Fig. 9a. The measured temperature signals were captured through National instrument\u2019s data acquisition card PCI-6281. The acquired data were time stamped and stored in standard MS-excel format using Labview code. For the evaluation of track geometry, the deposited single tracks were cut normal to the track traverse direction and prepared by epoxy potting and polishing. The track geometry was measured using optical microscopy. Thus obtained experimental results were compiled and compared with simulated results. In order to verify the accuracy of the numerical modeling, the temperature distribution patterns along the fabrication path in the work piece were measured. In experiments, the laser beam was scanned on the substrate and passed from point A to point C via point B (refer Fig. 9(a)). The temperature was measured at point D using a K-type thermocouple and recorded in MS-excel sheet using Labview code. The temperature at point D was simulated in time steps by thermal numerical computations for average laser energy deposited on the surface area with unit width and length corresponding to time-step. Thermal numerical computations were based on time-integrated effect of laser heating, conduction, convection and radiation. Thus simulated temperatures at various time steps were compared with that of experiments and presented in Fig. 9(b). In the simulation, the effect of moving laser beam normal to x\u2013z plane at any time was incorporated by considering instantaneous width of laser beam equal to the chord length of the circle at reference x\u2013z plane (where, circle diameter\u00bc laser beam diameter) for that time. In this way, the local effect of laser beam at any point on y-axis in the substrate can be represented by cumulative effect of energy balance at that time. This condition holds true for the time period less than the interaction time of laser beam for any point in the y\u2013z plane. Thus, the effect of processing in y-axis and time-axis will be identical for the above condition. The whole phenomenon was simulated in 2-D at the time step of 0.01 s to get overall 3-D picture for a time period less than the interaction time. In the experiments, this condition was achieved by starting the laser experiments at the point A (refer Fig. 9(a)) and moving the laser beam towards point C. For instance, at the simulation time t\u00bc0.01 s, front end of laser beam was located at point A on the substrate. At this point, there was no significant effect of laser heating on point D. The corresponding measured and simulated temperatures at point D are shown at line segment E\u2013E in Fig. 9(b). As front end of laser beam moved towards point B, the temperature at point D also increased. It reached the maximum value and decreased due to dominance of other physical processes, e.g. conduction and convection. At point D, the maximum temperature was achieved when the center of laser beam (line segment F\u2013F) was at the least distance from the point D. The time period for sustaining the maximum temperature depended upon on laser processing parameters, (e.g. laser power, interaction time, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure4-1.png",
        "caption": "Fig. 4. The air flow and pressure distribution around ball surface (without additional oil\u2013air input).",
        "texts": [
            " In addition, due to the clearance variation of cylindrical pocket, another vortex forms at upper of cage pocket, which is also adverse for bearing lubrication and heat dissipation. Compared to the inlet of B side, air flow of the A side is much clear and ordered. It suggests that for a higher rotation speed, it\u2019s better to mount the lubrication device (oil\u2013air nozzle) at the A side, in order to diminish the barricading effect from the air vortex, and increase the lubrication efficiency. In the prior analysis in Refs. [16\u201318], the effect of ball spinning on air flow characteristic was ignored. In Fig. 4 the air flow around ball surface was compared at rotation speed 2.0 104 r/min, with and without considering ball spinning motion. Before considering ball spinning effect, the average air pressure around spherical surface is 17.43 Pa, with maximum pressure 275.30 Pa and minimum 303.12 Pa. After considering the spinning effect, the average pressure is 23.22 Pa, with extreme value 309.47 Pa and 1011.50 Pa. It can be derived that, the average air pressure inside bearing cavity increases with ball spinning motion, especially the negative pressure",
            " It should be particularly noted that, at high rotation speed, a small new vortex appears near the entrance of inner ring contact area, which directly blocks oil\u2013air flowing into the contact area, and leads to the decline of lubrication performance. Based on the streamline monitoring technology, vortexes near the ball and inner ring were analyzed in three dimensional streamline view, seen in Fig. 7. Influenced by the ball\u2019s motion, chaotic streamline appears in front and behind the contact area, where the high pressure areas form (seen in Fig. 4). Due to the combined effect of ball and inner ring\u2019s interaction, the streamline of the contact area is sparse. As mentioned above, at high rotation speed, the air flow in the A side cavity is regular and intense while in B side it is weak, which are consistent with the streamline distribution. Near the entrance of the contact area, the streamline is curved, which indicates the existence of the secondary vortex. The fluid flow in bearing contact area is vital important to its lubrication and heat dissipation performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002037_978-3-540-77657-4-Figure4.4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002037_978-3-540-77657-4-Figure4.4-1.png",
        "caption": "Fig. 4.4. Monolithic and structured productive systems, which can be defined by changing the system configuration SC.",
        "texts": [
            " This system might be active in its role as a productive system (e.g. transforming sensory inputs into control outputs according to a built-in algorithm) but it is passive under the aspect of changing its own structure and behavior. In order for a system to be (re-)organized, it must be adaptable, i.e. it must allow for changes of its structure and/or behavior. In technical systems this means that certain control parameters must be visible and changeable at the outside of the system. Let us call the set of these parameters system configuration SC (figure 4.4). SC is a bit string and might be as short as one bit (to change the working mode) or as long as a full system description (a program or a VHDL file). Each (legal) value of SC defines a point in the system\u2019s configuration space. The configuration space comprises all possible configurations of the system. Further, we can define the size of the configuration space, its variability, as the number of bits of SC. Systems with only a few possible configurations (\u201cmodes\u201d) are called monolithic because they do not display structure to the outside world"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001332_ja056866s-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001332_ja056866s-Figure4-1.png",
        "caption": "Figure 4. Thermal and UV shape shifting in azo-LCE disks.",
        "texts": [
            " The shape of the surface features can be reversibly switched between cigar-like and circular column by cycling the material through a disordered-isotropic and ordered-nematic phase. This can be achieved using temperature as well as UV light. When heated at 120 \u00b0C (well above the clearing temperature TNI), the LCE loses its nematic order and forms circular columns to minimize the surface tension of the network, analogous to our earlier work on nanoparticles.10 This morphology was fixed for imaging by rapidly quenching the sample in liquid nitrogen (Figure 3c). The general principle behind the molecular reorganization processes is illustrated in Figure 4. This result indicates that the constraints of spontaneous elongation of small monodomain disks, randomly oriented in the plane and distorting the elastic substrate, thus leading to the loss of grid order, are removed above TNI. After subsequent annealing at 55 \u00b0C for 10 min, the mesogenic components reorient and relax to the equilibrium cigar shape again (Figure 3d). This cycle can be repeated many times without obvious fatigue. This behavior is also observed on LCE stamps which did not contain azo moieties (see Supporting Information)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003952_c4an00975d-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003952_c4an00975d-Figure3-1.png",
        "caption": "Fig. 3 Schematic diagram of a working electrode in this study.",
        "texts": [
            " D ow nl oa de d by U ni ve rs ity o f N ew ca st le o n 28 /0 9/ 20 14 1 3: 01 :3 4. adsorbed AChE seemed to reach saturation and was around 0.38 mg per 100 mg of F127-MST. Then, TG-DTA measurements were done for AChE\u2013(F127-MST). As seen in Fig. 2b, the degree of weight loss increased with an increase in the amount of AChE adsorbed, which was consistent with previously reported data.27,28 Therefore, the composite membrane was conrmed to effectively immobilize AChE. Electrochemical experiments were conducted with the AChE\u2013 (F127-MST)-based electrode as described in Fig. 3. The details of electrochemical set-up are described in Experimental section. Amperometric measurements for sensing acetylthiocholine were performed in phosphate buffer (pH 7.4) solution containing 0.5 mM TCNQ as a mediator. Fig. 4 shows the amperometric responses of AChE\u2013(F127-MST) and the native AChE, which is not immobilized and dissolved in the electrolyte solution, aer the injections of different concentrations of 4656 | Analyst, 2014, 139, 4654\u20134660 acetylthiocholine, ranging from 18 mM to 72 mM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001283_02640410500520401-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001283_02640410500520401-Figure9-1.png",
        "caption": "Figure 9. (a) Top and (b) side views of the ball \u2013 rim \u2013 board interactions without the bridge. Neglecting the bridge allows the ball to assume unrealistic configurations such as shown in (b).",
        "texts": [
            " This leads to the question: \u2018\u2018Is the increased model complexity including the bridge warranted by substantially different predictions?\u2019\u2019 To answer this question we developed a dynamic model similar to that of Silverberg et al. (2003) that neglected the bridge and allowed simultaneous ball contact with the rim and backboard. Because the results of this model show that it is inadequate, we here omit the details of its derivation, except to say that we used techniques similar to those described above (Kane & Levinson, 1985). Figure 9 shows top and side views of the coordinate system with the ball centre in the YZ plane. Without a bridge, the ball can have simultaneous contact with the rim and board at variable points on the ball, B\u0302 and B\u0302z, respectively, and can assume unrealistic configurations such as shown in Figure 9. Figure 10 shows capture conditions for the model without the bridge, for backspin angular velocities of 0, 2p, and 4p rad s 1 with no lateral deviation and the standard high release point. Obviously predictions of this model differ from those of the model including the bridge only for shots that result in some contact with the bridge. On the dashed line in Figures 10(a) \u2013 (c), the ball first contacts the back rim and board simultaneously, which unrealistically requires the lower surface of the ball to penetrate the bridge upper surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-3-1.png",
        "caption": "FIGURE 12-3 Radial piston pump, with variable displacement. (Courtesy Deere & Company.)",
        "texts": [
            " Controls (manual or automatic) 9. Fluid 10. Actuators 11. Filters 315 Pumps and motors are often quite similar and can sometimes be inter changed in their purpose. The simplest type of pump or motor is a hydraulic cylinder (fig. 12-1). When hydraulic cylinders are arranged axially, as shown in figure 12-2, the rate of flow through the pump can be regulated by con trolling the angle between the piston block and the swash plate, a common method of control on a hydrostatic transmission. Radial piston pumps (fig. 12-3) can also be used as motors. The displace ment of a radial piston pump can be controlled by allowing the pressure to lift the pistons off the eccentric. By this method the pump unloads and does not do any work except when the pressure drops sufficiently to force the pistons back onto the eccentric. A spur-gear pump is shown in figure 12-4. It is normally used on tractor hydraulic systems of lower pressure. The spur-gear, the internal-gear pump (fig. 12-5), the gerotor-gear pump (fig. 12-6), and the vane-type pump (fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001989_s11012-009-9251-x-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001989_s11012-009-9251-x-Figure7-1.png",
        "caption": "Fig. 7 Simplification to a one-mass-oscillator",
        "texts": [
            " Along with the proper setting of the degrees of freedom for each part of the vibration an adequate sub model needs to be chosen. For this kind of analysis multi-body simulation software is used, cosimulation with other external software, e.g. analytic model, FEsolver, is necessary to introduce accurate sub models into the simulation. A single gear stage can be simplified to a model with two degrees of freedom\u2014one for the pinion and one for the wheel [4]. With a further simplification it can be modified to the one-mass-oscillator with the system coordinate x\u2014the deflection of the teeth (see Fig. 7). The one-mass-oscillator shows the characteristic properties of a parameter-excited oscillation system with the consideration of the variable mesh stiffness (see Fig. 2) and the damping. Other properties of the oscillation system are not taken into consideration, e.g. backlash or multi-body model of the shafts. The attenuation constant DZE for the tooth contact can be calculated depending on the viscosity of the injected oil (\u03b7 in mPas), the centre distance (a in mm) and the running speed (vt in m s ) with (1) according to [4] DZE = 0",
            " for a gearing with centre distance a = 140 mm at an oil viscosity of 55 mPas and a running speed of vt = 22 m s both graphs deliver an attenuation constant DZE of 0.05. According to [4] equation (1) is validated for 15 m s < vt < 50 m s and 50 mm < a < 250 mm by measurement results. For higher centre distances Gerber suggests to use the attenuation constant DZE for a = 250 mm. The oscillation behaviour is decisively determined by the ratio between the excitation frequency and the natural frequency. The excitation frequency corresponds to the mesh frequency fz. The natural frequency of the one-mass-oscillator shown in Fig. 7 can be determined according to ISO 6336 [6] with the fol- lowing equation: fE = 1 2 \u00b7 \u03c0 \u221a C\u03b3 mred (2) It should be mentioned that the shown one-massoscillator is only a basic vibration model, which might not be applicable on a real multi-stage gearing. Nevertheless this simplified model shows basic phenomena. For validation of a vibration model measurement results of the natural frequencies are helpful. The ratio fz fE is called resonance ratio N (ratio between excitation frequency and natural frequency)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure6-1.png",
        "caption": "Fig. 6. Transformation scheme of involute coordinate of worn profile into Cartesian coordinates.",
        "texts": [
            " This apparatus records the wear in the function of curvilinear coordinate L (length of involute), which is defined for an arbitrary point as follows: Li \u00bc LE\u2212\u0394L nz\u2212i\u00f0 \u00de\u2212\u03b4L \u00bc Rb 2 tan\u03b1E\u00f0 \u00de2\u22122\u03c0 zs Rk nz\u2212i\u00f0 \u00de\u2212\u03b4L \u00f024\u00de where LE is the length of the involute from the base circle of radius Rb to the top of the tooth, \u03b1E is the involute angle at the top of the tooth, \u0394L is the movement step of the probe along the profile of the tooth and zs is the total number of teeth of the ratchet sector. According to values of the involute length, the angles of involute expansion \u03c6i and involute angles \u03b1i are defined as: \u03c6i \u00bc ffiffiffiffiffiffi 2Li Rb s \u03b1i\u00bc arctan\u03c6i 9>= >;: \u00f025\u00de The transformation scheme of an involute coordinate of theworn tooth profile into Cartesian coordinates is shown in Fig. 6, which implies obvious relationships for the calculation of Cartesian coordinates of the tooth worn profile according to the wear Ii (Eq. (24)). xi \u00bc Rie cos\u03b3i\u2212x0\u2212Ii sin \u03c6i\u2212\u03b30\u00f0 \u00de yi \u00bc Rie sin\u03b3i\u2212Ii cos \u03c6i\u2212\u03b30\u00f0 \u00de \u00f026\u00de where Rie \u00bc Rb cos arctan\u03c6i\u00f0 \u00de is the radius-vector of a point on the involute profile, \u03b30 \u00bc \u03c0 2z \u00fe 2xtg\u03b1b z \u00fe tg\u03b1b\u2212\u03b1b\u00f0 \u00de is the angular coordinate of the start of the involute (point), \u03b3i= arctan\u03c6i\u2212 (\u03c6i\u2212 \u03b30) is the angular position vector, x0= Rb cos \u03b30 is the abscissa of the involute starting point (Fig. 6), and \u03b1b = 20\u00b0 is the standard angle of the initial contour. The main factors influencing the accuracy of the measurement of tooth wear are: \u2013 Deviation of probe 7 from the normal to the involute at the measurement points; \u2013 Error of basing because of multiple installations in the same tooth cavity. As a result of the analysis, the effect of the deviation of themeasuring probe from the perpendicular to the involute profile (n0\u2212 n0 in Fig. 6) on the accuracy of the wearmeasurement is relatively small. Themeasurement error in this case depends mainly on the average curvature of the involute tooth profile defined by the number of gear teeth z, and may be determined from: \u03b4no \u00bc 30 z3 100%: \u00f027\u00de Thus, at an error of wear measurement \u03b4no \u00bc 3%, the apparatus in this construction can measure teeth gear wear for z \u2265 10. The error of the apparatus basingwas estimated from the results of numerousmeasurements of one profile (m=12mm, z=31) with the number of settings being equal to 50"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003605_j.aej.2018.07.010-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003605_j.aej.2018.07.010-Figure9-1.png",
        "caption": "Fig. 9 Generated CAD model of the spur gear.",
        "texts": [
            " The output data of this program will be sent to the SolidWorks software by the developed system to generate the corresponding CAD model as per the calculated geometrical dimensions. Thus, design and modeling work is automated. Fig. 8 illustrates the flowchart of the design of the spur gear that has been developed, followed and implemented in this work. In this section, sample results that are generated by the developed CAD modeling system are presented. Table 1 provides the sample inputs for the design of spur gear. Using this input data, the developed spur gear design system generated a CAD model as shown in Fig. 9. The dimensions with which the model has been generated are shown in the Fig. 10. These dimensions are recommended by the proposed modeling system. It is observed that these dimensions are very close to the AGMA results and are compared in Table 2. Normally, the complete design calculation and CAD modeling process take 150\u2013200 man-hours if it is done manually. But, by using the proposed method, the time taken for the whole process came down to not more than 54 s when it has executed on a computer with minimum hardware requirements of SolidWorks 2015"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000711_s0094-114x(02)00066-6-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000711_s0094-114x(02)00066-6-Figure5-1.png",
        "caption": "Fig. 5. ith leg of the 3-UPU wrist.",
        "texts": [
            " 4 shows a 3-UPU wrist. With reference to Fig. 4, the points Ai, i \u00bc 1; 2; 3, are the centers of the universal joints which connect the legs to the base; the points Bi, i \u00bc 1; 2; 3, are the centers of the universal joints which connect the legs to the platform and the point P is the common intersection of the revolute pair axes fixed in the platform. The 3-UPU wrist is mounted so as to make the platform s point P coincide with the base s point located by the intersection of the revolute pair axes fixed in the base. Fig. 5 shows the ith leg, i \u00bc 1; 2; 3, of the 3-UPU wrist. With reference to Fig. 5, wji, j \u00bc 1; . . . ; 4, is the unit vector of the jth revolute pair axis with the j index increasing from the base to the platform; hji, j \u00bc 1; . . . ; 4, is the joint coordinate of the jth revolute pair; ai and bi are constant lengths of the segments AiP and BiP respectively; di is the variable length of the segment AiBi and it is the joint coordinate of the actuated prismatic pair; ui is the unit vector of the leg axis. The point P is fixed in the platform and can be chosen as the origin of a reference system embedded in the platform",
            " With these notations, by taking into consideration separately the three legs, the platform angular velocity, x, and the velocity, _P, of the point P , measured in the base, can be written in the following three different ways: x \u00bc _h1iw1i \u00fe _h4iw4i \u00fe \u00f0 _h2i \u00fe _h3i\u00dew2i i \u00bc 1; 2; 3 \u00f01:1\u00de _P \u00bc _Bi \u00fe x \u00f0P Bi\u00de i \u00bc 1; 2; 3 \u00f01:2\u00de where _hji, j \u00bc 1; . . . ; 4, are the time derivatives of the joint coordinates hji, j \u00bc 1; . . . ; 4, respectively, and _Bi is the velocity of the platform s point Bi. Moreover the following vector relationships hold (Fig. 5): Bi Ai \u00bc diui i \u00bc 1; 2; 3 \u00f02:1\u00de P Bi \u00bc biw4i i \u00bc 1; 2; 3 \u00f02:2\u00de Differentiating relationship (2.1) yields _Bi \u00bc _diui \u00fe di _ui i \u00bc 1; 2; 3 \u00f03\u00de where _di and _ui are the time derivatives of di and ui respectively. By using the time differentiation rule for constant intensity vectors, the following expression for _ui is obtained (Fig. 5): _ui \u00bc \u00f0 _h1iw1i \u00fe _h2iw2i\u00de ui i \u00bc 1; 2; 3 \u00f04\u00de By taking into account the relationships (1.1), (2.2), (3), (4), the relationship (1.2) becomes _P \u00bc _diui \u00fe bi\u00f0 _h2i \u00fe _h3i\u00dew2i w4i \u00fe di _h2iw2i ui \u00fe _h1ivi i \u00bc 1; 2; 3 \u00f05\u00de where vi \u00bc w1i \u00f0P Ai\u00de i \u00bc 1; 2; 3 \u00f06\u00de Finally, the dot product of the ith vector Eq. (5) by w2i yields (Fig. 5) _P w2i \u00bc _h1ivi w2i i \u00bc 1; 2; 3 \u00f07\u00de If the 3-UPU mechanism starts moving from rest in a configuration (Figs. 4 and 5) in which the platform s point P coincides with the base s point located at the intersection of the base s revolute pair axes, i.e., the 3-UPU wrist s geometric conditions are matched, then the following additional vector relationships will hold in the initial configuration: w1i \u00bc P Ai ai i \u00bc 1; 2; 3 \u00f08\u00de By taking into account the relationships (8), the relationships (6) become vi \u00bc 0 i \u00bc 1; 2; 3 \u00f09\u00de Thus, the relationships (7) become _P w2i \u00bc 0 i \u00bc 1; 2; 3 \u00f010\u00de System (10) is a linear, homogeneous system of three scalar equations in three unknowns: the three components of _P",
            " Thus, the next elementary motion also must keep the point P at rest and the 3-UPU wrist s geometric conditions. As a consequence, the platform is bound to perform a sequence of elementary motions keeping the point P at rest, i.e., the platform is constrained to perform finite spherical motions with center P , until the mechanism reaches a singular configuration. The ith equation of system (10) is the analytic expression of the constraint that the ith leg of type UPU imposes to the platform. With reference to Fig. 5, it can be interpreted as follows: a leg of type UPU, with the intermediate revolute pair axes parallel to each other and perpendicular to the leg axis (Fig. 5), forbids the displacement along the w2i s direction of the platform point (point P in Fig. 5) instantaneously coinciding with the intersection of the revolute pair axes at the leg endings. When this point (point P in Fig. 5) goes to infinity, i.e., w1i and w4i (Fig. 5) are parallel to each other, the forbidden displacement becomes a forbidden platform rotation around the direction of the free vector w2i w4i [18]. The position analysis of the 3-UPU wrist focused on the mechanism configurations that keep the platform s point P (Fig. 4) at rest is identical with the one of the Innocenti and ParentiCastelli s parallel wrist (Fig. 1) [11]. Thus, with reference to the demonstration reported in [11], it can be stated that the platform orientations compatible with a given set of values of the three parameters di, i \u00bc 1; 2; 3, are at most eight, whereas only one triplet of di values is compatible with a given platform orientation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003386_10402004.2014.968699-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003386_10402004.2014.968699-Figure3-1.png",
        "caption": "Fig. 3\u2014Contact reference frame (Xc, Yc) of a contact ellipse between two contacting bodies. An example of a contact ellipse is seen in Fig. 2. The Xc axis is along the major axis and the Yc axis is along the minor axis of the contact ellipse.",
        "texts": [
            " This tangential force is determined using the relative tangential velocity and the normal force within a contact ellipse. An example of a contact ellipse can be seen in Fig. 2. In DBM, translational and rotational velocities of each bearing component are monitored in inertial and body-fixed reference frames, respectively. To reduce the calculation of relative tangential velocities within the contact, the relative translational and rotational velocities are transformed to a contact reference frame whose origin is located at the center of the contact ellipse, as shown in Fig. 3. The relative slip varies according to location within the contact area. In this study, the length of the minor axis is considered sufficiently narrow such that the variation in relative velocity along the minor axis is negligible as described by Gupta (31), (32). However, the variation in slip along the major axis is considered. The velocity at the center of the contact, which consists of both translational and rotational motion of the body, is calculated for D ow nl oa de d by [ FU B er lin ] at 2 3: 04 0 2 M ay 2 01 5 each of the two contacting bodies and is defined by ub = vb + (\u03c9b \u00d7 rb) , [13] where ub is the total velocity vector at the point of contact for the body, vb is the translational velocity vector of the body, \u03c9b is the angular velocity vector of the body, and rb is the vector locating the point of contact relative to the center of the body",
            " The ball passes through the loaded region and, outside of that, it only maintains contact with the OR due to centrifugal forces. The ball had abrupt motions as the cage and IR engaged the ball into the loaded region. The ball motion also oscillated as it was pressed out of the loaded region. Fig. 27\u2014Bearing 2 with a +5 \u03bcm interference for the case of an overhung load: (a) orientation of the body-fixed reference frame (Xbf, red, Ybf, green, Zbf, blue axes) from a view normal to the outer race (OR) surface; (b) view perpendicular to (a); (c) ball spin about the axis normal to contact plane defined as \u03c9relc in Fig. 3; and (d) slip magnitude at the point of contact between the ball and OR. D ow nl oa de d by [ FU B er lin ] at 2 3: 04 0 2 M ay 2 01 5 Figure 25 illustrates the orientation of the ball body-fixed reference frame. Presented is the ball motion in a radial loaded bearing operating under the planar assumption for the inner race. Figure 25a illustrates the view normal to the OR from the perspective at the center of the bearing. The angle of the view rotates with the cage such that the view remains normal to the OR surface",
            " This is an unrealistic condition for any loading configuration of the rotor\u2013bearing system. For bearing 2 with interference, Fig. 27 depicts the orientation of the body-fixed reference frame of the ball, spin of the ball, and also the magnitude of slip between the ball and OR when considering all 6 degrees of reedom of the bearing components. Fig. 27a and 27b represent the same views as those presented in Fig. 25a and 25b. Figure 27c illustrates the spin of the ball at the point of contact with the OR about the axis normal to the point of contact, Zc, as defined in Fig. 3 as \u03c9relc. Figure 27d depicts the magnitude of slip in the Xc\u2013Yc plane at the point of contact. Figure 27a illustrates the orientation of the body-fixed reference frame of the ball as it rolls down the path through the groove of the OR. The ball spins about the point of contact such that the Xbf axis remains perpendicular to the path of motion. At approximately 0.25 and 0.75 revolutions, the ball traveled in a constant direction, which resulted in no spin. At every half revolution, the ball changed direction, resulting in the maximum amount of spin",
            " Figure 29 depicts the normal reaction force between the ball and IR in polar form as the ball rotates around the bearing. Bearing 1 was loaded in the positive Z direction (90\u25e6), whereas Fig. 28\u2014Bearing 2 with a \u221220 \u03bcm clearance for the case of an overhung load: (a) orientation of the body-fixed reference frame (Xbf, red, Ybf, green, Zbf, blue axes) from a view normal to the outer race (OR) surface; (b) view perpendicular to (a); (c) ball spin about the axis normal to contact plane defined as \u03c9relc in Fig. 3; and (d) slip magnitude at the point of contact between the ball and OR. D ow nl oa de d by [ FU B er lin ] at 2 3: 04 0 2 M ay 2 01 5 Fig. 29\u2014Polar plot of the normal reaction force between an individual ball and the inner race (IR) for bearing 1 (blue) and bearing 2 (red) for the overhung shaft: (a) \u221220 \u03bcm clearance and (b) +5 \u03bcm interference. bearing 2 was loaded in the negative Z direction. For the interference case, Table 5 indicates a displacement magnitude greater than 10 \u03bcm for both bearings 1 and 2 in the Z direction, which would overcome the interference, but the axial motion of the shaft and the tilt of the IR allowed the ball to remain loaded throughout the rotation of the cage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001989_s11012-009-9251-x-Figure21-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001989_s11012-009-9251-x-Figure21-1.png",
        "caption": "Fig. 21 Experimental results of Low Loss Gears",
        "texts": [
            " It is necessary to follow an iterative process including all steps several times to get an optimised specification. \u2013 Corrections for load reduction in contact areas with high sliding speed \u2013 Reduction of module down to tooth root fracture limit \u2013 Reduction of transverse contact ratio down to pitting capacity limit \u2013 Tooth root fillet radius as large as possible \u2013 Increase of pressure angle \u2013 Increase of face width \u2013 Helix angle for adequate overlap contact ratios 3.4 Power loss reduction with optimised gearings Figure 21 shows experimental results of the power losses of type C gear which is a frequently used test gear geometry for many kinds of gear and lubrication tests and corresponding Low Loss Gears. In Fig. 20 the main geometry parameters of type C gears are given as well as those of the corresponding Low Loss Gears. Additionally, the calculated safety factors are shown. Those of Low Loss Gears are at least equal to or even higher than those of type C gears. For the shown example, enormous power loss reduction up to two third can be achieved with Low Loss Gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002098_j.mechatronics.2008.11.013-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002098_j.mechatronics.2008.11.013-Figure7-1.png",
        "caption": "Fig. 7. Hooke and rotation joint combination. (a) Left view, (b) top view and (c) sectional view.",
        "texts": [
            " And the load of each motor has been reduced greatly by virtue of the actuated interface. So the life length of the lead screw can be increased by a long way. The contribution of the novel redundantly actuated interface is that it makes possible for the motors to drive a much large load by the novel redundantly actuated interface and expand the age of the lead screw. It is recognized that the stiffness of the spherical joint is not very high. So the spherical joint is replaced by the combination of Hooke joint and rotation joint shown in Fig. 7. This project is suitable for the case that the large load is required. The 6-dof parallel seismic simulator with novel redundant actuation developed by Shanghai Jiao Tong University is presented in this paper. The contribution of the novel redundantly actuated interface is that it makes possible for the motors to drive a much large load by the novel redundantly actuated interface and expand the age of the lead screw. Since the stiffness of the spherical joint is not high enough for the 6-dof parallel seismic simulator, the spherical joint is also replaced by the combination of Hooke joint and rotation joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure3-1.png",
        "caption": "Fig. 3. Standard involute helical surface of diamond dressing gear.",
        "texts": [
            " The coordinate systems S 1 ( O 1 \u2212 x 1 , y 1 , z 1 ) and S 2 ( O 2 \u2212 x 2 , y 2 , z 2 ) are the auxiliary coordinate systems for the dressing process. On a CNC internal gear honing machine, there are two dressing movements: a rotation of the dressing tool \u03c6 (the C2-axis movement in Fig. 1 ) and a rotary motion of the honing stone \u03c6 (the C1 axis motion in Fig. 1 ). d h The tooth flank of the dressing tool used to generate the honing stone that will generate the standard involute work gear is the standard involute helical surface. According to Fig. 3 , the position vector and normal vector of the dressing tool\u2019s surface can be expressed in the coordinate system S d ( O d \u2212 x d , y d , z d ) as follows: r d ( u d , \u03b8d ) = \u23a1 \u23a2 \u23a2 \u23a3 x d ( u d , \u03b8d ) y d ( u d , \u03b8d ) z d ( u d , \u03b8d ) 1 \u23a4 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a3 r bd cos ( \u03c30 d + u d + \u03b8d ) + r bd u d sin ( \u03c30 d + u d + \u03b8d ) r bd sin ( \u03c30 d + u d + \u03b8d ) \u2212 r bd u d cos ( \u03c30 d + u d + \u03b8d ) \u03b8d p d 1 \u23a4 \u23a5 \u23a5 \u23a6 (1) n d ( u d , \u03b8d ) = \u23a1 \u23a3 n dx ( u d , \u03b8d ) n dy ( u d , \u03b8d ) n dz ( u d , \u03b8d ) \u23a4 \u23a6 = \u2202 r d ( u d , \u03b8d ) \u2202 u d \u00d7 \u2202 r d ( u d , \u03b8d ) \u2202 \u03b8d = \u23a1 \u23a3 p d r bd u d sin ( \u03c30 d + u d + \u03b8d ) \u2212p d r bd u d cos ( \u03c30 d + u d + \u03b8d ) r 2 bd u d \u23a4 \u23a6 (2) where u d and \u03b8d are the surface parameters, r bd is the radius of the base cylinder, \u03c3 0 d is the starting angle of involute, and p d is the helix parameter whose meaning is the distance that the generatrix moves in the direction along the axis z d when the unit angle is turned"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002773_tpas.1966.291548-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002773_tpas.1966.291548-Figure14-1.png",
        "caption": "Fig. 14. Form taken by current loci.",
        "texts": [
            " + 2 (1 -e+j) and, therefore, V81 1 2 Z. + Zr Cos) asq -p 0, IS, - V/2Z,, i.e., magnetizing current as 5 -- 180, Is - V/2(Z, + Z',), i.e., normal behavior. From (2), the torque may be shown to be given by F= 2_r |Ir | 2 S (40) CIZI2 03M2 Z. + Zr (1 - cost) 2 S (1 - cos4) (v) which may be compared with (18). (41) Because |Z + Z/4 [(1 cos \u00a2)/2J 1 |Z + Z/J then the torque given by (44) is < the torque given from (18) for any particular value of 0 and S. The form taken by the current loci is shown in Fig. 14 where the (42) diameters of the semicircles are given by Diameter = 1-o D (45) 2/(1 cos -0) Pc where k, the coefficient of coupling, is M/VL7L., and D, the normal diameter of the current locus, is obtained when .& = 180\u00b0. The loci of Vs1 and Vs2 may be obtained from (40)-(42), but as (43) their geometrical form is not particularly straightforward, they will not be discussed here. (44) 1966 131"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003748_s11071-016-3218-y-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003748_s11071-016-3218-y-Figure9-1.png",
        "caption": "Fig. 9 Mesh stiffness model: a discretization of the contact line, b network of springs to model the gear mesh",
        "texts": [
            " A linear crack growth path leads to a linear decreasing trend, whereas a parabolic growth path leads to a parabolic decreasing trend. These demonstrate that aside from the crack depth and plastic inclination angle, the crack position in the fillet region will also affect the plastic deformation distributions. 2.4 Tooth mesh stiffness model The tooth mesh stiffness model proposed in this study is based on thework by Eritenel and Parker [21]. In correspondence with the slicing method introduced in the previous section, the nominal contact line is discretized into a series of segments (as shown in Fig. 9a), and each contact line segment is assigned a linear stiffness kiat its center Mi , which is calculated as: ki = kgkci Hi kg + \u2211n i=1 kci Hi (20) where kg is the global stiffness accounting for all stiffness except the local contact stiffness (i.e., k1g and k2g as shown in Fig. 9a), and is assumed to be the same for all contact segments; kci is the local contact stiffness of the i th segment, and is probably nonlinear depending on the contact function Hi : Hi = { 1, \u03b4i \u2212 ei > 0 0, \u03b4i \u2212 ei \u2264 0 (21) where ei is the profile deviation error of the i th segment (i.e., e1i and e2i as shown in Fig. 9a) which includes the tooth profile manufacturing errors, profile modifications, and the plastic inclination deformations discussed above, \u03b4i is the normal approach at the i th segment. For spur gear pair, \u03b4i is the same for each segment. Hi represents the contact condition at the i th segment. When Hi is 0, it means that there is a contact loss at the i th segment, and the local contact stiffness kci will not contribute to the effective mesh stiffness ki at the i th segment. kg and kci can be obtained from finite element analysis of gears [21,22]. They can also be estimated using analytical approaches [3\u201310]. The effect of the tooth fillet crack does not affect the local contact stiffness kci . However, it will directly influence the global stiffness kg as it can weaken the cracked tooth bending and shearing strength. Detailed discussion about this can be found in [2,7]. 3 Dynamic analysis 3.1 Dynamic model The research objective is a spur gear pair system as shown in Fig. 9a. A Cartesian coordinate system (X\u2013 Y\u2013Z ) is established. The X -axis is in the direction of LOA, and the Y -axis is in the off-line of action (OLOA) direction. The Z -axis is along the axial direction and can be determined by following the right-hand rule. The frictional forces developed between the contact tooth pair are neglected. Therefore, the only translational degree of freedom (DOF) considered is along the X -axis, i.e., x1 and x2. Since the plastic deformations resulting from the spatial crack are non-uniformly distributed on the cracked tooth flank, there will be a tilting moment about the Y -axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001545_0921-8890(91)90045-m-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001545_0921-8890(91)90045-m-Figure1-1.png",
        "caption": "Fig. 1. CEBOT operation inside a tank.",
        "texts": [
            " This corresponds to concepts found in biological organisms, where surprisingly simple cells are conglomerated to organs to perform complicated tasks. The flexible task and environment adaptable concept guarantees universal applicability of CEBOT in many fields, e.g. advanced flexible manufacturing systems, outer space (CEBOTtransport cell by cell), maintenance systems for hostile and restricted environments. An application example for maintenance in restricted environments like the inside of a tank is shown in Fig. 1. CEBOT cells can be fed in the tank with narrow inlet one by one, build up a large manipulator structure inside, and maintain the tank very efficiently. To perform given tasks flexibly, CEBOT has to be organized as an intelligent planning system with flexibility in hardware and software. The top 0921-8830/91/$03.50 \u00a9 1991 - Elsevier Science Publishers B.V. (North-Holland) \u2022 Waseda Toshio Fulmda University,(M '83) Tokyo,graduated Japan fr0min 1971 and received the Master of Engineering degree and the Doctor of Engineering degree both from the University of Tokyo, in 1973 and 1977, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001505_bf01320814-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001505_bf01320814-Figure4-1.png",
        "caption": "Fig, 4. Cells propelled by helical waves, a When the flagellum turns helically with angular velocity co, the cell body turns in the opposite direction at an angular velocity g~, so that the flagellum must also rotate around its own internal axis at an angular velocity ~ ; the effective angular velocity of the flagellum is co- ft. b The flagellum of Euglena turns back through 180~ the effective angular velocity of the flagellum is here co + f~. e The body of a dinoflagellate turns at velocity Vb in the direction of propagation of the waves on the transverse flagellum at velocity Vw; this enhances the propulsive effect of the transverse flagellum",
        "texts": [
            " The optimum flagellar length is therefore shorter for helical waves than for planar waves; this is because all elements of the helical flagellum contribute to forward propulsion whereas some elements of the planar flagellum produce only drag (Higdon 1979 c). Helical waves are also almost twice as efficient as planar waves, especially with a larger cell body (Holwill 1966, 1974). However, the propulsion of a cell by a helically beating flagellum is more complex because the flagellar waves produce a turning moment about the axis of propulsion which causes the cell body itself to rotate with a couple such that its motion opposes the turning due to the flagellum (Holwill 1966, Chwang and Wu 1971) (Fig. 4a). In equilibrium swimming the turning moments of the cell body and the flagellum must balance, so a large body will turn slowly and a small body must turn quickly to balance the flagellar torque. Clearly, when the cell body rotates the flagellar axoneme must rotate around its internal axis in the same direction as the cell body turns, since there is no rotary joint at the flagellar base comparable to that of the prokaryote flagellum. The rotation of the cell body (at an angular velocity f~) in the opposite direction to the helical motion of the flagellum (at an angular velocity co) reduces the speed at which waves move relative to the water (to co - f~), and will reduce propulsive efficiency; the slower the body turns, the less the loss, but with a larger body more work must be done to propel the body forwards against the resistance of the water",
            " Thicker flagella tend to have an increased power consumption, but flagellar thickness has little influence on swimming speed. Where larger cells are propelled, special mechanisms may be invoked, e.g., the flagellum of Euglena is turned back from the anterior end of the cell and propagates helical base-to-tip waves; because the flexible flagellum bends through 180 ~ near its base, the rotation of the cell body is communicated to the flagellum so as to increase its helical motion and increase the speed with which waves move in relation to the water (Holwill 1966, Lighthill 1976) (Fig. 4 b). In dinoflagellates such as Heterocapsa the transverse flagellum clearly has a left-handed helix (Taylor 1987) (Fig. 4 c), and this helix must therefore turn anticlockwise (as seen from the flagellar tip) as waves are propagated towards the tip; the cell body rotates clockwise (seen from the posterior end) (Gaines and Taylor 1985), presumably because of flagellar torque, thereby increasing the effective rate of propagation of the flagellar helix. Since a helical wave can be more efficient in propulsion than a planar wave, it is not surprising to find that many fagellates and sperm whose flagellar undulations are basically planar show a tendency towards a three dimensional beat near the tip (Holwill 1966); this causes a slow rotation and aids directed locomotion by reducing effects of pitching and yawing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure14-1.png",
        "caption": "Fig. 14 Feed range of the planer tool",
        "texts": [
            " (6): rt \u21c0 \u03b8s\u00f0 \u00de \u00bc x y z 2 4 3 5 \u00bc rbs sin f 2\u00f0 \u00de\u2212\u03b8scos f 2\u00f0 \u00de\u00bd f 1cos f 2\u00f0 \u00de H=2 \u2212rbs cos f 2\u00f0 \u00de \u00fe \u03b8ssin f 2\u00f0 \u00de\u00bd \u2212 f 1sin f 2\u00f0 \u00de us 2 4 3 5 f 1 \u00bc Rt \u00fe\u0394Z f 2 \u00bc \u03b8os\u00fe \u03b8s 8>>< >>: \u00f015\u00de Where rbs represents the base circle radius of the shaper, \u03b8S and uS represent, respectively, the angle parameter and the axial parameter in the shaper, and \u03b8OS represents the angle between the starting point of the involute and the symmetrical line of the gullet. In order to cut the whole tooth surface of the spur face-gear in the process of planing, the planer tool needs to make translational motion lt in the radial direction of the facegear every time when the coordinate system of the planer tool swings at a small angle, as shown in Fig. 14. Besides, the translational range should be greater than the radial width of the face-gear tooth surface. The translational range can be given as ZL1\u2264\u0394lt\u2264ZL2 \u00f016\u00de The axis y2 relative to the central axis of the planer tool is assumed to be ytool, then, ZL1 \u00bc min ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R12\u2212 ytool\u00fe H 2 2 s ; ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R12\u2212 ytool\u2212 H 2 2 s8< : 9= ; \u00f017\u00de ZL2 \u00bc max ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R22\u2212 ytool\u00fe H 2 2 s ; ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R22\u2212 ytool\u2212 H 2 2 s8< : 9= ; \u00f018\u00de Where R1 and R2 represent the inner radius and the outer radius of the face-gear, respectively, and H represents the width of the planer tool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000831_1.533552-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000831_1.533552-Figure4-1.png",
        "caption": "Fig. 4 Coordinate systems of the proposed mathematical model",
        "texts": [
            " The cutting edges of bevel-worm-shaped hob perform an involute curve on the imaginary generating plane. In this paper, the mathematical models of the above-mentioned cutters are assumed to be given and the position and unit normal vectors of the cutter are denoted as rt and nt , respectively. rt~a ,b!5@xt ,yt ,zt,1#T (1) nt~a ,b!5@ntx ,nty ,ntz# T5 ]rt ]a 3 ]rt ]b U]rt ]a 3 ]rt ]bU Based on the mathematical model developed by Litvin @6#, a modified mathematical model for universal hypoid generator with supplemental flank correction motions is proposed. As shown in Fig. 4, the coordinate system St is rigidly attached to the cutting tool. The rotation angle of the cutter is denoted as cutter rotation angle mg . The tilt of cutter spindle denoted as tilt angle i. The orientation of cutter tilt is denoted as swivel angle j. The distance between the center of cutter to the center of cradle is denoted as radial setting SR . The rotation of cradle is denoted as q and q 5uc1fc , where uc is the initial cradle angle setting and fc is the cradle generating roll angle during generating cutting of workpiece"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001368_icar.2005.1507466-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001368_icar.2005.1507466-Figure5-1.png",
        "caption": "Fig. 5. A frame and a wheel in a force-transfer-mechanism",
        "texts": [
            " But it is too difficult to reduce ones of electronics, in general. Electronics is defined by objects, which robots need. Therefore, to reduce costs of electronics isn\u2019t a realistic way. If we selected the way, our robot\u2019s cost would be very high price. And we hope that design and structure of devices are simple. Therefore, we selected a basketball. III. A MECHANISM OF FORCE TRANSMISSION In this section, we describe a mechanism of transmitting force to a basketball as a spherical tire. We show a force-transfer-mechanism, which we developed, in Fig.5 and 6. However, forces are friction forces between wheels and a basketball. In Fig.5, a drive axis and a free rotation axis are shown. A drive axis is to transmit force on a basketball, and a free rotation axis isn\u2019t to transmit force on it. Two axes are orthogonal. And a wheel is sliced on both sides. In Fig.6, two wheels are shown. A DC-motor drives two frames, which have a drive axis, respectively. Then, a chain synchronizes two frames and a DC-motor. And wheels, which frames have, contact on a basketball, either-or or both. It\u2019s no problem that wheels contact both. Since, wheels are synchronized, and they transmit the same forces and velocities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001930_j.nonrwa.2008.02.014-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001930_j.nonrwa.2008.02.014-Figure1-1.png",
        "caption": "Fig. 1. The 3-UPU parallel manipulator [9].",
        "texts": [
            "  xn+1 \u2212 xn yn+1 \u2212 yn ...  = \u2212H1(xn,yn, . . .) \u2212H2(xn,yn, . . .) ...  . (6) To avoid divergence, Wu [2] provided some useful choices about the auxiliary homotopy function. They are polynomial, harmonic, exponential or any combinations of them. By appropriately choosing/adjusting the auxiliary homotopy function, we can obtain the solutions of Eq. (1) [3]. Here we study an offset 3-UPU (Universal\u2013Prismatic\u2013 Universal) parallel manipulator with an equal offset in its six universal joints, as shown in Fig. 1 [9]. A special 3-UPU parallel manipulator with zero offsets in the six universal joints was proposed by Tsai in 1996 [10,11]. Tsai\u2019s 3-UPU manipulator has three extensible limbs (legs) that connect the base to the mobile platform through universal joints, and it can provide a 3-DOF pure translational motion [9]. Due to zero offsets in the universal joints, the kinematics of the manipulator is simple and straightforward [10]. Fig. 2 shows a schema of the i th limb (i = 1, 2, 3), which connects point B on the mobile platform and point A on the base by a passive universal (U) joint, an active prismatic (P) joint, and another passive universal (U) joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002839_s10514-013-9343-2-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002839_s10514-013-9343-2-Figure9-1.png",
        "caption": "Fig. 9 Simple model of an inverted pendulum falling under gravity. P is CoP, m is the humanoid mass, and \u03c6 is the lean angle between the CoP\u2013CoM line and the vertical. We use this model for the fast estimation of time duration and other parameters of the robot",
        "texts": [
            " An exit through the FTB is an indication of an unavoidable fall and this event can be used to activate the switch from the robot\u2019s balance controller to a fall controller. The parameters that characterize the feature space can include both sensor data such as joint angle and ground reaction force (GRF), and any number of computed variables such as CoM and CoP positions, robot lean angle, angular momentum, etc. 5.2 Fall mode detector (FMD) In order to choose the correct fall strategy, it helps for the falling robot to quickly estimate how it is going to fall. For this, we approximate the robot as an equivalent inverted pendulum as shown in Fig. 9. The pendulum connects the CoP and CoM of the robot and has a point mass equal to the robot mass. If the CoP is located on an edge of the support area, the pendulum is constrained to rotate on a plane perpendicular to the edge. In this case, we model the robot as a 2D inverted pendulum. If instead, the CoP is located at a corner, the estimation uses a 3D spherical inverted pendulum model. The 2D pendulum model has a closed-form solution. However, since the 3D pendulum does not have closed-form solutions, we simply simulate its dynamic equations for the period of control duration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure8.12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure8.12-1.png",
        "caption": "Fig. 8.12. Initial allocation of nose wheel steering and rudder as a function of airspeed",
        "texts": [
            " Other variants have been evaluated at low speeds using the inverted bicycle model for controller design, but applied to the full model in desktop simulations [174]. For turning the aircraft, the two most obvious controls are rudder \u03b4R and nose wheel steering \u03b8NW . The first is mostly effective at higher dynamic pressure, the second mostly at lower speeds. Other means, like differential braking have been left out for the moment. In order to invert the model, some rule must be provided for how to distribute the available control power between both effectors. As a first step, the distribution is based on calibrated airspeed, as shown in Fig. 8.12. If Vcas < Vlow = 30 m/s only nose wheel steering is used, if Vcas > Vhigh = 80 m/s only rudder is used for yaw control, and in between a linear blend based on generated yawing moments is applied. Of course, the values of Vlow and Vhigh can be optimised or a more advanced allocation structure may be selected in the detailed design phase. In order to implement the control architecture, a structure as depicted in Fig. 8.13 has been implemented. To the left, the control allocation can be recognised",
            " This is done by the model compiler by adding an in-line integration algorithm [57]. In this case, a simple explicit Euler integration method with the required 40 ms sampling period has been included. After automatic model inversion and coding, first simulation runs can already be performed. To this end, step inputs on the yaw rate command (ucmd) are given starting at four different trimmed airspeeds: well below Vlow (10 m/s), well over Vhigh (85 m/s), and two in between (40 m/s and 60 m/s), see Fig. 8.12. The yaw rate responses are of most interest of course. These are depicted in Fig. 8.14. They match the expected first order behaviour as in Fig. 8.6 quite well. At this point, only hand-picked values have been set for the linear control law and command filter parameters. In subsequent design steps, these values may be tuned to optimise robustness and performance, for example using multi objective optimisation [139, 174]). 168 G. Looye ya w ra te (d eg /s) Next, it is interesting to look at the moment distributions (Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003176_s11012-013-9803-y-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003176_s11012-013-9803-y-Figure1-1.png",
        "caption": "Fig. 1 One-stage gear system",
        "texts": [
            " The results showed that the dynamic behavior depends on the critical variance and the mean value of the backlash simultaneously. Therefore, a potential economic way to improve the dynamic response of the gear system can be available. For one-stage involute spur gear pair, it is assumed that the friction of the bearings and the deformation of the gear shafts can be omitted, and it is assumed the stiffness of the gear shafts and bearings are great. Only the torsional vibration of the gear pair is considered in this paper, as a result, the dynamic model of the system can be shown as Fig. 1. The differential equation of the system is given by mc \u00a8\u0304qg(\u03c4 ) + ch \u02d9\u0304sg(\u03c4 ) + k\u0304h(\u03c4 )f\u0304h(s\u0304g) = Fgm + Fga(\u03c4 ) (1) in which [22, 23], q\u0304g(\u03c4 ) = rg1\u03b8g1(\u03c4 ) \u2212 rg2\u03b8g2(\u03c4 ) mc = Ig1Ig2 Ig1r 2 g2 + Ig2r 2 g1 Fgm = Tgm1 rg1 = Tgm2 rg2 Fga(\u03c4 ) = mcTga1(\u03c4 )rg1/2Ig1 f\u0304h(s\u0304g) = \u23a7 \u23a8 \u23a9 s\u0304g \u2212 b\u0304h, s\u0304g > b\u0304h 0, \u2212b\u0304h \u2264 s\u0304g \u2264 b\u0304h s\u0304g + b\u0304h, s\u0304g < \u2212b\u0304h Since the fluctuation of the input torque applied on the driving gear is usually much less than that on the driven gear, it can be supposed that the torque applied on the driving gear is fixed, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002427_iros.2011.6095091-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002427_iros.2011.6095091-Figure7-1.png",
        "caption": "Fig. 7. Experiment environment.",
        "texts": [
            " 4) To reduce the impact of supplying and exhausting air and to keep a given elasticity of the exhausted muscle, soleus (\u266f1) in this case, we supply air to the muscle for a fixed period of time. Although the control process is the same in falling forward, we supply and exhaust air to the opposite muscles. The process of 1) \u223c 4) is repeated. C. Impact experiment We conducted an experiment to evaluate the performance of the control method in the previous section. We applied an impulse force to the head of the robot, and we evaluated whether the robot can keep standing or not. Fig. 7 shows an overview of the experimental environment. We attach a protractor and a rope to a pillar in the vertical direction from the robot and attach a ball to the other end of the rope. An experimenter releases the ball from different given angles toward the head of the robot gently. To vary impulse, we use two kinds of balls, a tennis ball (55.4 [g]) and a rubber ball (134.2 [g]), and release them from six different angles, 15, 30, 45, 60, 75, or 90 [deg]. We conducted five trials for each combination with feedback or without feedback, totaling 60 trials in all"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure3-1.png",
        "caption": "Figure 3. Bearing cut view at roller j position. (a) Bearing ring deflections and (b) roller j equilibrium.",
        "texts": [
            " Based on the rotation about z, the azimuth position of the cage, c, is determined by kinematic considerations as pure rolling of the rolling elements is assumed c \u00bc z ri 2 rp \u00f01\u00de In equation (1) the inner ring rotation, z, must account for angle wrapping and not be limited to z 2 \u00bd0, 2 . If cage clearances are neglected, the position of roller j is determined by j \u00bc c \u00fe \u00f0 j 1\u00de 2 Z \u00f02\u00de at Eindhoven Univ of Technology on June 17, 2014pik.sagepub.comDownloaded from To evaluate the contacts of roller j, Figure 3(a) shows a bearing cut view in the (xj,zj)-plane of Figure 2 where the coordinate system translations and rotations are transferred into the roller j coordinate system. Subscript ij designates the inner ring coordinate system rotated about its z-axis into the roller j position and oj designates the equivalent coordinate system of the outer ring. The grey outline indicates the initial position of the inner ring. The two local translations and the rotation are calculated as zj \u00bc z\u00fe ap sin\u00f0 j \u00de ri \u00f03\u00de xj \u00bc x cos\u00f0 j \u00de \u00fe y sin\u00f0 j \u00de \u00f01 cos\u00f0 j \u00de\u00de ri \u00f04\u00de j \u00bc yj \u00bc cos\u00f0 j \u00de y sin\u00f0 j \u00de x \u00f05\u00de where ap is the axial preload translation of the inner ring",
            " As it will be demonstrated in subsequent comparisons in Figure 13, an excellent agreement is obtained, and ignoring the three components allows for faster calculations and improved solution convergence since less factors impact the calculated contacts. Having established the radial and axial displacements as well as raceway tilt at the position of each interface node, the elastic deflection of the outer raceway can now be interpolated at the roller positions. For this purpose, a linear interpolation is used because it has been found to be sufficiently precise while providing high computational performance. The bearing ring deflections at roller j position shown in Figure 3(a) for the six-dof model are now slightly modified to include the deflections of the outer ring, as shown in Figure 5. Subscript ij designates the inner ring coordinate system rotated about its z-axis into the roller j position and oj designates the equivalent coordinate system of the outer ring relative to the reference node translated into the bearing centre along the x1 axis and rotated into the roller j position. Since the interface nodes are located at the centre of the outer raceway, the rotation oj only impacts the contact alignment and not the contact deflection",
            " The approach of the two raceways measured orthogonally on the roller axis at the roller j centre is thus j \u00bc \u00f0 zj zoj\u00de sin\u00f0 o\u00de \u00fe \u00f0 xj xoj\u00de cos\u00f0 o\u00de \u00f012\u00de The total relative misalignment between the raceways is j \u00bc cos\u00f0 j \u00de y sin\u00f0 j \u00de x oj \u00f013\u00de The raceway approach and misalignment of the flexible bearing at roller j position defined in equations (12) and (13) have identical physical interpretation as equations (5) and (6) for the six-dof model. The following section is thus valid for both models. at Eindhoven Univ of Technology on June 17, 2014pik.sagepub.comDownloaded from The roller equilibrium equations ensure that each roller is in quasi static equilibrium while respecting the calculated approach and misalignment of the raceways. For each roller, the loads shown in Figure 3(b) are considered, i.e. raceway contact forces, Fij and Foj, moments,Mij andMoj, flange forces, Ffj, and the roller centrifugal force Fc. The roller inertia can cause additional roller loads, which can be included if, for example, the outer ring is subjected to translational accelerations. In such cases, the inertia of the inner ring and shaft will generally be orders of magnitude higher than the rollers. Since this inertia is included in the multi-body formulation of the system, the exclusion of the additional roller loads is justified",
            " Assuming that the flange contact is parallel to the roller symmetry axis, the flange contact force is calculated by equilibrium considerations along the roller symmetry axis Ffj \u00bc sin\u00f0 m\u00de Fc \u00fe sin\u00f0 r=2\u00de \u00f0Fij\u00f0 ij, ij\u00de \u00fe Foj\u00f0 oj, oj\u00de\u00de \u00f014\u00de In the orthogonal direction of the roller symmetry axis, the equilibrium is cos\u00f0 r=2\u00de Foj\u00f0 oj, oj\u00de \u00bc cos\u00f0 r=2\u00de Fij\u00f0 ij, ij\u00de \u00fe cos\u00f0 m\u00de Fc \u00f015\u00de Finally, the moment equilibrium is Moj\u00f0 oj, oj\u00de \u00bcMij\u00f0 ij, ij\u00de \u00fe Ffj \u00f0rr \u00fe sin\u00f0 r=2\u00de l=2 hf \u00de \u00f016\u00de where Fc is the inertial force excerted on all the rollers, each having the mass mr Fc \u00bc mr rp _ 2z \u00f017\u00de By referring to Figure 3(a) or 5, the inner and outer raceway contact deflection must equal the total j \u00bc \u00f0 ij \u00fe oj\u00de cos\u00f0 r=2\u00de \u00f018\u00de Equivalently, the inner and outer raceway tilt equals the total j \u00bc ij \u00fe oj \u00f019\u00de Equations (14)\u2013(19) contain four unknowns, i.e. ij, oj, ij and oj. The roller equilibrium must be solved iteratively due to the non-linear contacts. In the iterations, equations (18) and (19) are considered as constraints and violations of equations (15) and (16) as residuals. In this new bearing model, these iterations consist of fast interpolations of the pre-processed contacts, a method further described in the section on Contact pre-processing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11\u00b71-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11\u00b71-1.png",
        "caption": "FIGURE 11\u00b71 Free-body diagrams of the chassis and drive wheels of a rear wheel-driven tractor.",
        "texts": [],
        "surrounding_texts": [
            "11 MECHANICS OF THE TRACTOR CHASSIS If the agricultural engineer who is specializing in farm power is to make his best contribution to the agricultural engineering profession, if as an agricultural engineer he is to earn and hold a recognized place among other engineers, he must have more than the garage mechanic's conception of the tractor. He must visualize the tractor as a unit and have a clear conception of all forces acting upon it. He must be informed concerning the fundamental laws of mathematics and physics which govern its kinematic and dynamic response to these forces. In no other way will he be able to make the tractor per form its maximum service.\nE. C. McKIBBEt\\ (1927)\nAn understanding of the statics and dynamics of farm tractors is important in the analysis of tractor performance, stability, ride, and handling. This chapter provides an introduction to these individual areas while attempting to emphasize their interrelationships. Because of the introductory nature of this chapter, the two-dimensional analysis of rear-wheel-driven tractors is emphasized. The suggested readings at the end of the chapter provide additional information on methods of three as well as two-dimensional analysis.\nSimplifying Assumptions\nThe following simplifying assumptions apply to the rear-wheel-driven tractor shown in figures 11-1 and 11-2:\n272",
            "EQUATIONS OF MOTION 273\n1. The ground surface is planar and nondeformable. 2. The motion of the tractor can be analyzed as two dimensional. 3. Rotational motion of the front wheels is neglected. 4. Aerodynamic forces are neglected.\nThe kinematics used to describe the rear wheel and chassis motions are illustrated in figure 11-2. The translational motions of the rear wheels and chassis are referenced to the fixed or inertial XZ coordinate system. Such a coordinate system, in which the positive Z axis points downward, is consistent with the terminology widely used in other areas of vehicle dynamics. The angle of rotation of the drive wheels, <p\"., is measured relative to the tractor",
            "274 MECHANICS OF THE TRACTOR CHASSIS\nchassis so that the absolute angular motion of the drive wheels is given by the angle <l>w - e, where e is the pitch angle of the chassis. Letting mw be the mass of the rear wheels and summing forces on the rear wheels in the X and Z directions,\n(1)\n(2)\nLetting Iyyw be the moment of inertia of the wheels about the y or lateral axis passing through their center of gravity and summing moments about the rear axle center (assumed to be coincident with the center of gravity of the rear wheels),\n(3)\nHowever, in the traction mechanics of Chapter 10, er is considered to be equal to (TF)Rr)r\" so that equation 3 may be written\n(4)\nLetting me be the mass of the chassis and summing forces on the chassis in the X and Z directions,"
        ]
    },
    {
        "image_filename": "designv10_10_0002705_acc.2011.5990793-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002705_acc.2011.5990793-Figure3-1.png",
        "caption": "Fig. 3. Condition of chattering elimination (per Popov\u2019s criterion)",
        "texts": [
            " Considering the constraints on the class of nonlinearities (8)-(10) we can see that for this class km is \u03a6= hkm for every nonlinearity, and, therefore, the stability analysis again arrives at checking the location of the point ( ) ( )0,0,1 jhjkm \u03a6\u2212=\u2212 relative to a certain frequencydomain characteristic in the complex plane. This frequencydomain characteristic is the Popov\u2019s curve (modified frequency response), which is formed from the frequency response )( \u03c9jWl by multiplying the imaginary part by frequency \u03c9: )(Im)(Re)( \u03c9\u03c9\u03c9\u03c9 jWjjWW llm += . The sufficient condition of absolute stability of the origin, and therefore, the condition of the elimination of chattering, is the possibility of drawing a straight line through the point ( mk1\u2212 ,j0) that would not intersect the plot )(\u03c9mW (Fig. 3). This is possible only if the value of km is sufficiently small, which in turn would reduce the system performance. Therefore, as it was noted earlier, there is a trade-off between the possibility of chattering suppression and the system performance. We now approach the problem being studied assuming that chattering exists and derive Poincare map for the system being analyzed. We find analytical solution for every part of the piece-wise linear control, and join the solutions. Consider solutions for the following controls:      \u2212\u2264\u2212 <<\u2212 \u2265 = b\u03c3h b\u03c3bK b\u03c3h u if if if \u03c3 , (17) Assume the existence of a symmetric limit cycle and find parameters of this limit cycle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure1-1.png",
        "caption": "Fig. 1. The structure and the definition of axis of an internal gearing power honing machine.",
        "texts": [
            " The sensitivity matrix is obtained by the normal deviation of the tooth surface caused by changing the polynomial coefficients one by one in a small amount. The tooth surface of work gear can be approximated to the target tooth surface by altering the coefficients of the polynomials through least squares estimation with the aim of minimization of the tooth surface errors based on sensitivity matrix. The validity of this crowning tooth flank modification method is corroborated numerically using a helical gear on the internal gearing power honing machine. 2. Mathematical model of the internal gear honing stone As shown in Fig. 1 , the representative machine used to generating hone involute helical gears requires seven CNC controlled axes with three linear and four rotational movements: the axial feed Z2 in dressing process and honing process which parallel to the rotation axis of work gear, the rapid feed Z1 of headstock carrying the work gear spindle, the radial feed X of the honing stone towards the work gear or dressing tool, the rotation axis C2 of work gear or dressing tool, the swivel rotation of honing stone A for axis crossing angle, the swivel rotation of honing stone head B for longitudinal crowning and tapering, and the rotation of honing stone C1, respectively. Most cylindrical gear honing processes are developed with these 7DOFs or their subset. In a normal generating honing process, the dressing tool profile is given, the profile of honing stone is shaped by a dressing tool using a generating dressing process, and the work gear profile is generated by the honing stone using a generating honing process. Fig. 1 shows that the honing stone is dressed by a standard involute diamond dressing gear mounted on the C2 axis. The dressing process is completed by A, X, C1, and C2 axis of the internal gear honing machine. CNC axes X, C1, and C2 are the simultaneously controlled axis for the dressing motion, while A is the machine setting, which is kept constant during the dressing process. The coordinate systems for the honing stone dressing process are shown in Fig. 2 , in which coordinate systems S d ( O d \u2212 x d , y d , z d ) and S h ( O h \u2212 x h , y h , z h ) are rigidly connected to the dressing tool and honing stone, respectively. The coordinate systems S 1 ( O 1 \u2212 x 1 , y 1 , z 1 ) and S 2 ( O 2 \u2212 x 2 , y 2 , z 2 ) are the auxiliary coordinate systems for the dressing process. On a CNC internal gear honing machine, there are two dressing movements: a rotation of the dressing tool \u03c6 (the C2-axis movement in Fig. 1 ) and a rotary motion of the honing stone \u03c6 (the C1 axis motion in Fig. 1 ). d h The tooth flank of the dressing tool used to generate the honing stone that will generate the standard involute work gear is the standard involute helical surface. According to Fig. 3 , the position vector and normal vector of the dressing tool\u2019s surface can be expressed in the coordinate system S d ( O d \u2212 x d , y d , z d ) as follows: r d ( u d , \u03b8d ) = \u23a1 \u23a2 \u23a2 \u23a3 x d ( u d , \u03b8d ) y d ( u d , \u03b8d ) z d ( u d , \u03b8d ) 1 \u23a4 \u23a5 \u23a5 \u23a6 = \u23a1 \u23a2 \u23a2 \u23a3 r bd cos ( \u03c30 d + u d + \u03b8d ) + r bd u d sin ( \u03c30 d + u d + \u03b8d ) r bd sin ( \u03c30 d + u d + \u03b8d ) \u2212 r bd u d cos ( \u03c30 d + u d + \u03b8d ) \u03b8d p d 1 \u23a4 \u23a5 \u23a5 \u23a6 (1) n d ( u d , \u03b8d ) = \u23a1 \u23a3 n dx ( u d , \u03b8d ) n dy ( u d , \u03b8d ) n dz ( u d , \u03b8d ) \u23a4 \u23a6 = \u2202 r d ( u d , \u03b8d ) \u2202 u d \u00d7 \u2202 r d ( u d , \u03b8d ) \u2202 \u03b8d = \u23a1 \u23a3 p d r bd u d sin ( \u03c30 d + u d + \u03b8d ) \u2212p d r bd u d cos ( \u03c30 d + u d + \u03b8d ) r 2 bd u d \u23a4 \u23a6 (2) where u d and \u03b8d are the surface parameters, r bd is the radius of the base cylinder, \u03c3 0 d is the starting angle of involute, and p d is the helix parameter whose meaning is the distance that the generatrix moves in the direction along the axis z d when the unit angle is turned",
            " 5 shows that the coordinate systems S h ( O h \u2212 x h , y h , z h ) and S g ( O g \u2212 x g , y g , z g ) are rigidly connected to the honing stone and work gear, respectively, while coordinate systems S 3 ( O 3 \u2212 x 3 , y 3 , z 3 ) , S 4 ( O 4 \u2212 x 4 , y 4 , z 4 ) , and S 5 ( O 5 \u2212 x 5 , y 5 , z 5 ) are auxiliary coordinate systems for simplicity of coordinate transformation during the gear honing process. The honing stone has three movements: axial feed F z1 along the axis of gear z g , the swivel rotation \u03c6A of honing stone head A for axis crossing angle, and the swivel rotation \u03c6B of honing stone head B for longitudinal crowning and tapering. It also has two rotary motions: that of the work gear and that of the honing stone (the C 2- and C 1-axis rotations in Fig. 1 ). By applying the homogeneous coordinate transformation matrix equation, transforming from the coordinate system S h ( O h \u2212 x h , y h , z h ) to S g ( O g \u2212 x g , y g , z g ) , the position and normal vector of the work gear can be represented in the coordinate system S g ( O g \u2212 x g , y g , z g ) as follows: r g ( u d , \u03b8d , \u03c6d , F Z1 , \u03c6C1 ) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 x g ( u d , \u03b8d , \u03c6d , F z1 , \u03c6C1 ) y g ( u d , \u03b8d , \u03c6d , F z1 , \u03c6C1 ) z g ( u d , \u03b8d , \u03c6d , F z1 , \u03c6C1 ) 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 = M gh ( F Z1 , \u03c6C1 ) \u00b7 r h ( u d , \u03b8d , \u03c6d ) (7) n g ( u d , \u03b8d , \u03c6d , F Z1 , \u03c6C1 ) = \u23a1 \u23a3 n gx ( u d , \u03b8d , \u03c6d , F z1 , \u03c6C1 ) n gy ( u d , \u03b8d , \u03c6d , F z1 , \u03c6C1 ) n gz ( u d , \u03b8d , \u03c6d , F z1 , \u03c6C1 ) \u23a4 \u23a6 = L gh ( F Z1 , \u03c6C1 ) \u00b7 n h ( u d , \u03b8d , \u03c6d ) M gh ( F Z1 , \u03c6C1 ) = M g5 M 54 M 43 M 3 h M 3 h ( \u03c6C1 ) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 cos \u03c6C1 \u2212 sin \u03c6C1 0 0 sin \u03c6C1 cos \u03c6C1 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 , M 43 ( \u03c6A ( F Z1 )) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 1 0 0 E B 1 0 cos \u03c6A ( F Z1 ) \u2212 sin \u03c6A ( F Z1 ) 0 0 sin \u03c6A ( F Z1 ) cos \u03c6A ( F Z1 ) 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 M 54 ( \u03c6B ( F Z1 )) = \u23a1 \u23a2 \u23a2 \u23a2 \u23a3 cos \u03c6B ( F Z1 ) 0 \u2212 sin \u03c6B ( F Z1 ) \u2212( E gh + E B ) 0 1 0 0 sin \u03c6B ( F Z1 ) 0 cos \u03c6B ( F Z1 ) 0 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a6 M g5 ( \u03c6C2 ( \u03c6C1 , F Z1 )) = \u23a1 \u23a2 \u23a2 \u23a3 cos \u03c6C2 ( \u03c6C1 , F Z1 ) sin \u03c6C2 ( \u03c6C1 , F Z1 ) 0 0 \u2212 sin \u03c6C2 ( \u03c6C1 , F Z1 ) cos \u03c6C2 ( \u03c6C1 , F Z1 ) 0 0 0 0 1 \u2212F Z1 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a6 (8) where M gh ( F z 1 , \u03c6C 1 ) is transformation matrix from coordinate system S h ( O h \u2212 x h , y h , z h ) to S g ( O g \u2212 x g , y g , z g ) , L gh ( F z 1 , \u03c6C 1 ) is the upper-left (3 \u00d7 3) submatrix of the matrix M gh ( F z 1 , \u03c6C 1 ), E gh is the operating center distance between the work gear and honing stone, and the center distance E B between the honing stone and B axis and is usually machine setting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002893_cdc.2012.6426131-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002893_cdc.2012.6426131-Figure1-1.png",
        "caption": "Fig. 1. Kinematic car model.",
        "texts": [
            " Details on real sliding mode and real HOSM can be found in Section 2 of [17]. Remark 4: For both choices of controllers from [22] or Proposition 1, it is not difficult to show that there exists C0,\u03b3 > 0 such that for sufficiently small \u03b5 > 0, we have m\u03b5 \u2264 C0\u03b5 \u03b3 with \u03b3 < \u03b1 . Then, both upper bounds for the gain value k\u03b5 and the upper bound on \u03d5\u0302\u03b5 tend to infinity as \u03b5 tends to zero. The performance of the control laws presented in the previous sections has been evaluated through simulation. Let us consider an academic kinematic model of a car [5] (see Fig.1), given by:  x\u03071 x\u03072 x\u03073 x\u03074 =  wcos(x3) wsin(x3) w/ L tan(x4) 0 +  0 0 0 1 u, (17) where x1 and x2 are the cartesian coordinates of the rear axle middle point, x3 is the orientation angle, x4 is the steering angle and u is the control input. w is the longitudinal velocity (w = 10ms\u22121), and L is the distance between the two axles (L = 5m). All the state variables are assumed to be measured and the velocity is assumed to have an uncertainty of \u03b4w = 5% . The goal is to steer the car from a given initial position to the trajectory x2re f = 10sin(0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure3.4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure3.4-1.png",
        "caption": "Fig. 3.4. Body fixed frame, SB-frame",
        "texts": [
            " In ADMIRE the mass and inertia are constant but could be modelled as functions of fuel consumption which is part of the engine model. The mass and inertia are chosen for a nominal case with a mass representing 60% of fuel loaded. The calculations of the resulting forces and moments with effects from gravity and aerodynamics transformation are done in different frames. The relative distance between the aerodynamic reference point, defined in the aerodynamic frame SU , (see figure 3.5) and the centre of gravity (c.g.), defined in the the body fixed frame, SB, (see figure 3.4) are used to transfer the moments and forces from one frame to another. The FCS is scheduled in altitude and Mach number and designed for the nominal model described in Table 3.1. A change in the centre of gravity will change the control performance. The flight envelope for the GAM-data extends to Mach 2.5 and an altitude of 20 km. The envelope for the engine model is valid up to Mach 2. With the bundled FCS the ADMIRE flight envelope is restricted to Mach numbers less than 1.2 and altitudes below 38 M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003172_s12206-013-0218-4-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003172_s12206-013-0218-4-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the position between filler wire and laser beam.",
        "texts": [
            " The active illuminating light source and the high speed camera are arranged on the two sides of the welding head. A fiber laser with a rated power of 4 kW is used for welding. The side shielding gas is Ar with purity higher than 99.99%. The filler wire SA1-Mg5 with a diameter of D is fed by a wire feeding system from Fronius corporation. The chemical compositions of 5A06 aluminum and the filler wire SA1-Mg5 and welding parameters for different experiments are shown in Tables 1 and 2. The distance between the filler wire and laser beam can be defined as the distance between their axes as shown in Fig. 2. In the direction that is perpendicular to the welding seam on the surface of the base metal, the distance Wy is always kept constant as 0 mm in order to guarantee the weld bead is right on the welding seam. In the direction that is the same as the welding direction, the distance between the filler wire and laser beam is denoted as Wx. According to the characteristic interaction between the filler wire and laser beam, this distance Wx can be classified into three different cases: (1) filler wire and laser beam fully detach; (2) filler wire and laser beam partially overlap; (3) filler wire and laser beam fully overlap or laser beam is fully blocked by filler wire. Based on the parameters in the experimental setup, in which the diameter of the laser beam is d, the diameter of the filler wire is D and the angle between the filler wire and surface of the base metal sheet is 70\u00b0, the corresponding Wx can be calculated for each case such as: (1) Wx > Wa = (d+2Dsin70\u00b0\uff0dDcsc70\u00b0) /2; (2) Wb =\uff0d(Dcsc70\u00b0\uff0dd)/2 \u2264 Wx \u2264 Wa = (d+2Dsin70\u00b0\uff0d Dcsc70\u00b0)/2 ; (3) Wx < Wb = \uff0d(D csc70\u00b0\uff0dd)/2. Fig. 2 shows the relative position between the filler wire and laser beam in three different cases. To study the characteristics of melting dynamics expediently, some values can be given. Both of diameter of feeding fiber and focal point diameter is 0.3 mm, and the diameter of the filler wire SA1-Mg5 is 1.2 mm. According to the above formulas, we can figure out that Wa is about 0.64 mm and Wb is about -0.49 mm. When the distance Wx is larger than Wa, the filler wire and laser beam is fully detached. So the distance Wx at 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003733_978-3-319-19740-1-Figure42-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003733_978-3-319-19740-1-Figure42-1.png",
        "caption": "Fig. 42 Positive feedback system for the development of gear failure, progressive failure to final failure",
        "texts": [
            " The abrasive wear of the crater mountain and the projecting part of the tooth flank, i.e., wear of surface roughness asperity, is very fine. On the bottom of the craters, very local melting of the tooth flank or melting of crushed wear debris is observed. Summing up much of the observation of tooth flanks of heavily operated gears, we feel the following impression becomes apparent: the progress of tooth flank wear as a function of operating time is described by the positive feedback system, as shown in Figs. 42 and 43. Figure 42 describes the positive feedback system of gear failure development using names of commonly specified failure. During the life time of gears, the situation of tooth flanks is one of being under \u201cprogressive failure\u201d or Cause of Failure Beyond Conjugate Theory of Gear Meshing 93 94 A. Kubo \u201cfailure-in-progress\u201d, and this situation becomes worse due to the feedbacked dynamic loading and deterioration of gear accuracy. The final state of this gear life is tooth breakage, heavy spalling or the wearing out of teeth",
            " The advantages of this technology are reflected primarily in the lower cost of production, while at the same time, the quality of parts meets all the requirements of operating conditions. After producing sintered parts, it is possible to carry out the final thermal treatment, which can affect the structure of the sintered steel, and thus develop a high resistance in relation to wear and pitting. The paper presents the performed experimental research relating to the characteristics of sintered steel depending on various after treatments: case-hardening, 226 A. Miltenovi\u0107 b Fig. 42 Equivalent stress (a), (b), (c), (d) and contact thermal flux (e), (f), (g), (h) over time in meshing of crossed helical gears for n1 = 1500 min\u22121 [16]. a Equivalent stress T2 = 12 Nm, time 0.0049 (1/8 of full revolution), b Equivalent stress T2 = 12 Nm, time 0.01 (1/4 of full revolution), c Equivalent stress T2 = 24 Nm, time 0.0049(1/8), d Equivalent stress T2 = 24 Nm, time 0.01 (1/4), e Thermal contact flux T2 = 12 Nm, time 0.0049 (1/8), f Thermal contact flux T2 = 12 Nm, time 0.01 (1/4), g Thermal contact flux T2 = 242 Nm, time 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure9-1.png",
        "caption": "Fig. 9 shows the fluid velocity distribution around the surface of the finger plate.",
        "texts": [
            " Due to the blocking effect of the shelter board located between the press plate and stator end core in the outer diameter of the long finger plate, the axial distance (50 mm) between the press plate and the stator end core suddenly reduces to the axial distance (3 mm) between the press plate and stator end core, as shown in Figs. 8(b) and 8(c). It results in a sharp fluid velocity increase. The fluid velocity around the D region of the press plate reaches 94.7 m/s. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 6 It can be seen from Fig. 9(a) that the cooling fluid around the surface of the long finger plate flows along the radial direction. The cooling fluid velocity distribution around the surface of the short finger plate is relatively uniform, and the fluid velocity is about 9 m/s. E. Influence of different relative magnetic permeability of press plate on the temperature of end parts Fig. 10 shows the highest temperature and average temperature of end parts with different relative magnetic permeability of press plate in the turbogenerator end region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003796_j.prostr.2017.07.166-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003796_j.prostr.2017.07.166-Figure2-1.png",
        "caption": "Fig. 2: Meshed geometry of bracket. Fig. 3: Load cases 1 (left), 2 (middle) and 3 (right).",
        "texts": [],
        "surrounding_texts": [
            "A preliminary characterization of material Ti-6Al-4V obtained by AM was provided by an external supplier by resorting to static tests, namely the tensile test and the fracture test. Two lots of tensile test specimens were produced along different deposition directions, by using both the DMLS and EBM techniques. Up to 16 specimens were tested. They were obtained through a machining operation from raw cylinders, by fitting requirements of the ASTM E8 [1]. Results communicated are reported in Table 1, although they are related to a limited number of specimens. For the DMLS specimens, some average values (standard deviation) were also provided. Set referred to as \u2018X\u2019 exhibited Yield = 1209 (7) MPa; UTS = 1329 (8) MPa; Elongation = 8.3 (1.0) %, while test referred to as \u2018Y\u2019 exhibited Yield = 1208 (6) MPa; UTS = 1323 (3) MPa; Elongation = 6.7 (0.9) %. In case of the EBM process, supplier did not provide average and standard deviation values. Results of the fracture toughness test were successfully determined according to ASTM E399 [2]; three specimens were obtained by Electrical Discharge Machining (EDM) from larger blocks produced by EBM. Critical stress intensity factor (KIC) was found equal to 60.3, 59.0 and 57.6 MPa\u221am, respectively for x, y and z samples. Those values were used to define a simplified model of the elastic-plastic behavior of material to be inputted into the numerical model of the analyzed bracket."
        ]
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure9-14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure9-14-1.png",
        "caption": "FIGURE 9-14 Optimum hand and foot control positions (top view of hg. 9-13). (From Purcell 19HO.)",
        "texts": [
            " Purcell (1980) and Stikeleather (1981) discuss in depth the functional and dimensional requirements for the design of seat cushions, back cushions, and armrests relative to a seated operator. Also addressed are functional and dimensional requirements for proper seat location relative to the controls. Purcell (1980) provides functional and dimensional visual requirements for instrumentation location and readout. Graphical layout and use of anthropometric data are the basic tools for seating placement and location of controls. Figure 9-13 shows a typical layout. Figure 9-14 is a top view of figure 9-13. The weight of the thighs and upper body should be supported by a seat cushion with a 5-degree seat angle from horizontal (front of cushion elevated). The angle between the backrest and seat should be approximately 95 degrees, with a minimum of 90 degrees. The backrest must support the lumbar back. Armrests are necessary to provide support and comfort to the shoulders. Also, they must be adjustable vertically to accommodate varying sizes of per sons for freedom of movement of the forearm and elbow when operating hand controls",
            " Electronic monitoring and digital readout of tractor performance func tions are replacing dials and gages. A digital instrument cluster used by one manufacturer is shown in figure 9-17. Details of the electronics are discussed in chapter 6. ROLLOVER PROTECTION 231 Primary hand controls that are used continuously such as hand throttle, shift levers, and rock shaft control lever should be placed within the cross hatched area shown in figure 9-13 and to the right of the operator as shown in the cross-hatched area of figure 9-14, leaving the left hand available for steering at all times. The less frequently used controls such as PTO clutch, parking brake, and differential lock can be allocated to left hand or foot operation outside of the cross-hatched areas indicated previously. Color cod ing of hand controls, as recommended in ASAE EP443, will aid the operator in control identification. Rollover Protection for Wheeled Agricultural Tractors The National Safety Council reported in the 1983 edition of Accident Facts that for 1982, overturns accounted for 49 percent of all on-farm tractor fatalities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002427_iros.2011.6095091-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002427_iros.2011.6095091-Figure4-1.png",
        "caption": "Fig. 4. Femur design of Pneumat-BS. Left: Femur of human. Center: Femur of Pneumat-BS (3D-CAD). Right: Pneumat-BS.",
        "texts": [
            " For this reason, we designed the system so that the location and points of origin of the muscles can be easily changed. Fig. 3 shows the joint drive system around the hip joint of the robot. The hip joint of the robot is driven by 9 muscles (\u266f8\u223c\u266f16). To drive a redundant system like this, we adopted a drive system to put PE braided lines through polyacetal bearings. This structure enables us to easily rearrange the pathway of the muscles and make it possible to generate appropriate joint torques. Fig. 4 shows standard human femur, and the femur part of Pneumat-BS (CAD, photograph). The angle of inclination of the human femur and the projection of the greater trochanter to the side increase the moment arm of the gluteus medius (\u266f10). Because of this, the pelvis is fixed in the frontal plane and stability of the pelvis is increased [11]. In the field of robotics, the cantilever type structure of the leg like in humans enables to have less collision between both inside upper-limbs and also enables to cross legs [12]",
            " In addition, the cantilever type structure is also important to reduce rolling motion of the gait. Since the cantilever type structure can make the width between hip joints shorter, this structure enables to make the length between landing points of pitch axis shorter too [12]. For these reasons, we designed the legs of the robot to include an angle of inclination. Imitating a normal human leg, we set the parameters 125 [deg] as angle of inclination and 170 [deg] as physiological valgus (please refer to Fig. 4 for illustration), so that the spherical center of hip ball joint is in range with the tibia. Fig. 5 shows the outline of the system configuration of Pneumat-BS. Each joint is driven by pneumatic artificial muscles arranged antagonistically. Compressed air driving the muscles is supplied by an outside air compressor. Supplying and exhausting compressed air is controlled by on-off electric valves (SYJ3320 produced by SMC Corp). We selected the on-off valves because of its light weight and small size to drive multiple muscles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure5-1.png",
        "caption": "Fig. 5. Construction of apparatus for measuring tooth wear (m = 12 mm, z = 11).",
        "texts": [
            " 3, the change in frequency of torque Ti is in the range of frequencies for the variation of resistance torque for mining machines. Thus, using gear parameters and manufacturing technology, the characteristics and level of loading and lubrication of the test bench correspond to the range of operating conditions of mining machine gears. The device shown schematically in Fig. 4 is overlaidwith a specialized apparatus formeasuring toothwear atfixed points along the involute profile of the irreversible gear [28]. In Fig. 5, a general view of the instrument for measuring the tooth wear of the pinion (reducer 1 in Fig. 2) is shown. The apparatus consists of two parts, namely a base I and a lever II. Lever II is set in slide conic bearings of base I, and can be rotated around the axisOk, the position ofwhich is chosen such that the circular arc of the radius Rk passes through the primaryH, secondary P (usually pitch point), and the ending E points of the active part of the involute tooth profile. Base I ismade in the formof a framewith thewidth equal to the facewidth of the ring, embracing the ends of the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000579_s0094-114x(98)00043-3-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000579_s0094-114x(98)00043-3-Figure2-1.png",
        "caption": "Fig. 2. Location and description of the variables and vectors used in the calculations.",
        "texts": [
            " Therefore, the linkage ARB can now be replaced by a single link OrR with a revolute joint at Or and a spherical joint at R. The revolute joint Or will be located on the intersection of the line AB and the line passing through R and perpendicular to the line AB. This implies that the revolute joint Or has the joint axis along the direction of AB. Similarly, the linkages ATC and BSC can now be replaced by the links OtT and OsS, with the revolute joints at Os and Ot and spherical joints at S and T, respectively. These replacements are shown in Fig. 2. Next, consider the mechanism shown in Fig. 2 with the top platform RST being placed. This con\u00aeguration leads to a three-arm, parallel mechanism as shown in Fig. 3. As compared with Fig. 2, Fig. 3 reveals that additional constraints on the movement of the joints R, S and T will be imposed. These additional constraints state that the distances between joints R and T, R and S, and S and T, should be \u00aexed. As compared with Fig. 1, Fig. 3 shows that the present three-arm parallel mechanism is kinematically equivalent to the octahedral Stewart platform mechanism of Fig. 1. As the determination of the locations of the revolute joints Or, Os and Ot of Fig. 3 is a ected by the displacements of the six links of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001369_0096-1523.19.1.3-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001369_0096-1523.19.1.3-Figure6-1.png",
        "caption": "Figure 6. Air flows smoothly around the ball until it gets to the separation points. There the air flow changes into a chaotic, swirling flow called the wake. If this were a top view, it would explain the curve of a ball. If it were a side view, it would explain the abrupt drop of the ball. Note. Reprinted from Engineering Modeling and Design (p. 33) by W. Chapman, A. Bahill, and W. Wymore, 1992, Boca Raton, FL: CRC Press. Copyright CRC Press. Reprinted by permission.",
        "texts": [
            " Inbaseball, most curveballs curve horizontally and drop ver-tically. The advantage of the drop is that the sweet spoton the bat is about 6 in. (15.24 cm) long but only !/2 in.(1.27 cm) high. Thus a vertical drop would be more effec-tive at taking the ball away from the bat's sweet spot than ahorizontal curve. We now present the principles of physicsthat explain why the curveball curves.The first part of our explanation invokes Bernoulli's prin-ciple. When a spinning ball is placed in moving air, asshown in Figure 6, the movement of the surface of the balland a thin layer of air that \"sticks\" to it slows down theair flowing over the top of the ball and speeds up the airflowing underneath the ball. Now, according to Bernoulli'sequation, the point with lower speed (the top) has higherpressure, and the point with higher speed (the bottom) haslower pressure. This difference in pressure pushes the balldownward.The second (and probably more important) part of ourexplanation involves the wake of chaotic air behind the ball",
            " In a boat, swinging the rudderto the right deflects water to the right, and to conservemomentum the back of the boat must be pushed to the left. 10 A. TERRY BAHILL AND WILLIAM J. KARNAVAS You can feel this force if you put your hand out the window of a moving car. (Make sure the driver knows you are doing this!) Tilt your hand so that the wind hits the palm of your hand at an angle. This deflects the air downward, which causes your hand to be pushed upward. Now let us relate this to the spinning baseball in Figure 6. Before the ball interacts with the air, all the momentum is horizontal. Afterward, the air in the wake has upward momentum. The principle of conservation of momentum therefore requires that the ball have downward momentum. Therefore, the ball will move downward. There are several ways to shift the wake behind a baseball. The wake is shifted by the spin on a curveball. The friction that slows the flow of air over the top of the ball causes the air to separate from the ball sooner on the top than on the bottom, as shown in Figure 6. This shifts the wake upward, thus pushing the ball downward. For nonspinning pitches such as the knuckleball and the scuff ball, when the seams or the scuff are near the bottom separation point they create turbulence, which delays the separation, as shown in the bottom of Figure 6, again shifting the wake upward and pushing the ball downward. So, when the pitcher puts spin on the ball, the wake of chaotic air behind the ball is moved to one side, causing the ball to curve and thereby confounding the poor batter who is trying to hit it. The Curveball Simulation Now let us return to the breaking curveball. The simplified 90-mph (40 m/s) pitch of Table 1 and Figure 1 falls 2Vi ft (0.76 m) because of gravity. A plot of this vertical distance as a function of time would be parabolic Q/iat2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002985_03321641311293731-Figure15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002985_03321641311293731-Figure15-1.png",
        "caption": "Figure 15. (a) Cross-section of a magnetic gear (Atallah and Howe, 2001); (b) schematic configuration of a magnetic-geared outer-rotor wind-turbine driven PMSG (Jian et al., 2009)",
        "texts": [
            " Sometimes, the use of reduced-stage (single- or two-stage) mechanical gears plus a relatively medium-speed generator may have the reduction of overall size and weight as compared with the low-speed direct-drive generator. Recently, the concept of magnetic gears was proposed and developed by Atallah and Howe (2001) and Rasmussen et al. (2005). In both papers, the torque was transmitted through a stationary segmented steel part having many poles with low magnetic reluctance. The idea with this part is to commutate the magnetic field from the low-speed side with many permanent magnetic poles (gear outer rotor) into the high-speed side with few poles (gear inner rotor), as shown in Figure 15(a). COMPEL 32,1 26 D ow nl oa de d by D ok uz E yl ul U ni ve rs ity A t 0 1: 59 0 5 N ov em be r 20 14 ( PT ) The magnetic gear seems to have the following advantages when compared with classical mechanical gears (Rasmussen et al., 2005), namely: . no mechanical fatigue; . no lubrication; . overload protected; . no mechanical contact losses; . no mechanical contact acoustic noise; Figure 14. Parallel connections of three-phase two-level low-voltage back-to-back voltage-sourced converters for a wind-turbine driven six-phase PMSG 6 phase Six phase half-bridge MSC GSC 1 C Ls Ls Lg Lg ig0 GSC 2 Transformer Ac grid ONE dc-link capacitor PMSG Six phase half-bridge MSC GSC 1 C C Ls Ls Lg Lg GSC 2 Transformer Ac grid TWO dc-link 6 phase PMSG (a) One dc-link for six-phase PMSG's machine-side converter and parallel-connected grid-side converter",
            " (b) Two dc links for six-phase PMSG's machine-side converter and parallel-connected grid-side converter High-power wind energy generation 27 D ow nl oa de d by D ok uz E yl ul U ni ve rs ity A t 0 1: 59 0 5 N ov em be r 20 14 ( PT ) . potential for very high efficiency (only a little core loss and bearing loss); and . high torque per volume ratio (ten times standard motors). More recently, the magnetic gear has been integrated into a PM motor to offer low-speed high-torque operation for electric vehicles (Chau et al., 2007). Further, by incorporating the attractive features of both the outer-rotor PMSG and the magnetic gear, a magnetic-geared outer-rotor PMSG for wind power generation, as shown in Figure 15(b), was proposed and implemented (Jian et al., 2009). A quantitative comparison illustrated that the magnetic-geared outer-rotor PMSG features smaller size and lighter weight than both the direct-drive PMSG and the planetary-geared PMSG, with lower material cost than the direct-drive one as well. Despite that the proposed generator and its prototype in Jian et al. (2009) were mainly used to illustrate the concept of magnetic gearing for wind power generation, this type of magnetic-geared outer-rotor PMSG with a full-capacity power converter may be highly competitive for wind power generation due to its other distinct merits as: "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000772_s0094-114x(99)00068-3-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000772_s0094-114x(99)00068-3-Figure1-1.png",
        "caption": "Fig. 1. Balancing elastic system with movable cam and translational follower.",
        "texts": [
            " This coe cient is equal to the ratio of the mechanical work consumed for acting the unbalanced arm and the mechanical work consumed for moving the balanced arm. The static balancing mechanism is useful if the e caciousness coe cient is greater than one. In the same manner as the discrete balancing [4], in order to realise a continuous balancing of the weight force of a industrial robot arm by the elastic force of a helical spring [2\u00b13,5], it is necessary that the spring be joined with one of its ends to a link which moves with respect to the frame or with respect to the arm (Figs. 1 and 2). In the kinematics scheme depicted in Fig. 1, the balancing spring 4 is joined with the B end to the follower 2 of a cam mechanism. The cam is \u00aexed to the arm 1. If the work \u00aeeld is de\u00aened by the limits jmin p=4, jmax 3p=4, then the follower 2 should slide along the OY co-ordinate axis for reasons of symmetry. The parametrical equations of the directrix curves of the cam active surfaces are: x1 YCsin j3 R dYC=dj cos j\u00ff YC sin j P ; y1 YCcos j2 R dYC=dj sin j YCcos j P , where R is the radius of the follower roll 3, I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b113111300 P dYC dj 2 Y 2 C s , and j represents the position angle of the arm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.2-1.png",
        "caption": "FIGURE 1.2 Combined side force and brake force characteristics.",
        "texts": [
            "1 shows the adopted system of axes (x, y, z) with associated positive directions of velocities and forces and moments. The exception is the vertical force Fz acting from road to tire. For practical reasons, this force is defined to be positive in the upward direction and thus equal to the normal load of the tire. Also, U (not provided with a y subscript) is defined positive with respect to the negative y-axis. Note that the axes system is in accordance with SAE standards (SAE J670e 1976). The sign of the slip angle, however, is chosen opposite with respect to the SAE definition, cf. Appendix 1. In Figure 1.2 typical pure lateral (k \u00bc 0) and longitudinal (a \u00bc 0) slip characteristics have been depicted together with a number of combined slip curves. The camber angle g was kept equal to zero. We define pure slip to be the situation when either longitudinal or lateral slip occurs in isolation. The figure indicates that a drop in force arises when the other slip component is added. The resulting situation is designated as combined slip. The decrease in force can be simply explained by realizing that the total horizontal frictional force F cannot exceed the maximum value (radius of \u2018friction circle\u2019) which is dictated by the current friction coefficient and normal load",
            " The track width has been neglected with respect to the radius of the cornering motion which allows the use of a two-wheel vehicle model. The steer and slip angles will be restricted to relatively small values. Then, the variation of the geometry may be regarded to remain linear, that is, cos az 1 and sin aza and similarly for the steer angle d. Moreover, the driving force required to keep the speed constant is assumed to remain small with respect to the lateral tire force. Considering combined slip curves like those shown in Figure 1.2 (right), we may draw the conclusion that the influence of Fx on Fy may be neglected in that case. In principle, a model as shown in Figure 1.9 lacks body roll and load transfer. Therefore, the theory is actually limited to cases where the roll moment remains small, that is, at low friction between tire and road or a low center of gravity relative to the trackwidth. This restrictionmay be overcome by using the effective axle characteristics in which the effects of body roll and load transfer have been included while still adhering to the simple (rigid) two-wheel vehicle model",
            " The resulting change in tire normal loads causes the cornering stiffnesses and the peak side forces of the front and rear axles to change. Since, as we assume here, the fore-and-aft position of the center of gravity is not affected (no relative car body motion), we may expect a change in handling behavior indicated by a rise or drop of the understeer gradient. In addition, the longitudinal driving or braking forces give rise to a state of combined slip, thereby affecting the side force in a way as shown in Figure 1.2. For moderate driving or braking forces, the influence of these forces on the side force Fy is relatively small and may be neglected for this occasion. This means that, for now, the cornering stiffness may be considered to be dependent on the normal load only. The upper-left diagram of Figure 1.3 depicts typical variations of the cornering stiffness with vertical load. The load transfer from the rear axle to the front axle that results from a forward longitudinal force FL acting at the center of gravity at a height h above the road surface (FL possibly corresponding to the inertial force at braking) becomes DFz \u00bc h l FL (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003993_1.4944659-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003993_1.4944659-Figure7-1.png",
        "caption": "FIG. 7. (a) The coordinates system for a buckled paper strip consisting of wet and dry domains whose interface moves with time. The points C1 and C2 move to C\u20321 and C\u20322, respectively, by deformation. The experimental image corresponding to the computational domain (half of an image of Fig. 1) is also shown. (b) Forces and moments acting on an arc starting from the origin.",
        "texts": [
            " Hence, during water impregnation, we can effectively assume that the wet portion instantaneously assumes the thickness \u03c4s and Young\u2019s modulus Es. These findings allow us to decouple the deformation process from the hygroexpansive swelling dynamics, so that the elastic response of the paper strip caused by hygroexpansive swelling is limited by the slow capillary imbibition process which provides wetted length with a constant cross-sectional area at each instant. To predict the temporal shape evolution of the paper strip using the rate of water imbibition, we now turn to a theoretical account of the process. Figure 7 shows the coordinate system to account for the observations in Fig. 1. We assume one-dimensional infiltration of water along the X-direction and use symmetry to consider the half-domain of length L from the pinned origin where the tube touches the paper to the clamped end. We note that the surface tension of the liquid holds the paper beam in contact with the capillary and prevents snapping from the nominally unstable second mode of buckling.16 The initially straight paper extends as the liquid begins to permeate into the paper from the tube and eventually buckles into the second mode that is stabilized by the capillary",
            " For each domain, we set up the geometrically nonlinear post-buckling equations of force and moment equilibrium and geometric compatibility.17 The center line of the paper strip expands on being wet and has a stretch defined by ri = dSi/dX , where S is the length of the strip measured from the origin and i = 1,2 correspond to the wet and dry regions, respectively. Denoting the horizontal and vertical deformations of the strip at X by U(X) and W (X), respectively, we have dUi/dX = ri cos \u03b8i \u2212 1 and dWi/dX = ri sin \u03b8i. Then, force equilibrium perpendicular to the sheet, as shown in Fig. 7(b), leads to N\u0302i + P\u0302 cos \u03b8i + V\u0302 sin \u03b8i = 0, (4) where N\u0302i is the internal tension given by N\u0302i = EiAi(ri \u2212 1 \u2212 \u03f5h, i), and P\u0302 and V\u0302 are the horizontal and the vertical reaction at the ends, respectively. The hygroexpansive strain, \u03f5h, in the wet domain is assumed to be \u03f5c at saturation thus \u03f5h,1 \u2248 0.0156 and \u03f5h,2 = 0. Similarly, moment equilibrium yields M\u0302i + P\u0302Wi \u2212 V\u0302 (Ui + X) = 0, (5) where M\u0302i = EiIid\u03b8i/dX is the moment at (X +Ui,Wi), and the area moment of inertia, Ii, in each domain is given by I1 = b\u03c43 s/12 and I2 = b\u03c43 d /12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000691_1.2826900-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000691_1.2826900-Figure4-1.png",
        "caption": "Fig. 4 Epicyclic gear mechanism of 8 links: (a) graph representation, (b) functional representation showing coaxial shafts and overhead con nection",
        "texts": [
            " The link chosen as the output link is to be permanently connected to the final reduction unit of a transmission. The other links are connected either to the input shaft through rotating clutches or to the casing through band clutches, depending on the clutching condition. Therefore, it is necessary that, in the functional schematic of an EGM, these links be arranged in such a way that they remain accessible and hence can be connected to other elements of the transmission as, and when, required. Few Coaxial Shafts - Link No. 1 of the functional schematic shown in Fig. 4{b) has a carrier and a ring gear connected^ to each other by a shaft. This shaft is coaxial with another shaft. ^ The difference between the words connections smd joints as used here is: two or more meinbers such as gears or carriers are said to be connected when they form a linlc with no relative motion between them, whereas two linlis are said to be joined when they can have specific relative motion with respect to each other. 406 / Vol. 118, SEPTEMBER 1996 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 06/08/2015 Terms of Use: http://asme.org/terms which connects the carrier and the ring gear of link 3. From a manufacturing point of view coaxial shafts are undesirable as tolerance limits on such shafts are too rigid. Therefore, their number should be kept as low as possible. Low Inertia - Link No. 3 of the functional schematic shown in Fig. 4(b) has two ring gears attached edge to edge. Such connection will be referred to as overhead connection, This way one can reduce the number of coaxial shafts. However, this results in a high moment of inertia of the link. It also requires more material in its manufacture. Thus one has to strike a bal ance between the two desirable features. A method of main taining a proper balance between coaxial shafts and overhead connection will be described in a later section. It should be noted that the accessibility of a link is a more desirable feature than the last two features"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure12-1.png",
        "caption": "Fig. 12 Copying coordinate system of the planer tool",
        "texts": [
            " Overcutting is unlikely to occur even though the planer tool interferes with the face-gear tooth profile, as shown in Fig. 10. The same is true of the right side. What should be noticed is that the case mentioned above is only suitable for the occasion when the planer tool shank is vertical or protruding, as shown in Fig. 11. With the consideration of planer tool performance, only vertical shank is adopted, and the blade should be arc or right angle. The copying coordinate system of the planer tool is established, as shown in Fig. 12.: the moving coordinate system of the shaper Ss (xs,ys,zs) is fixed to the shaper so that they can rotate together; St0 is the fixed coordinate system of the planer tool; the moving coordinate system of the planer St is a copy of Ss; and they completely coincide. Initially, St0 coincides with St. \u03b8t is the rotation angle of the basic cutter location group. As shown in Fig. 13, P is an arbitrary point on the tooth profiling curve, Ot is the corresponding point on the profiling curve after compensation, and Ot is also the original point of St, PQ with the length of the sum of the allowance and the radius of the tool corner is the normal of the tooth profile, and QOt is the horizontal segment with the length of H/2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000689_s0094-114x(02)00030-7-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000689_s0094-114x(02)00030-7-Figure1-1.png",
        "caption": "Fig. 1. Manipulator with two degrees of freedom.",
        "texts": [
            " In the second example, the motion of a PUMA robot is simulated by means of the integration of the mathematical model of the system, to which the necessary torques have been provided, so that the end effector of the manipulator makes a pre-established straight trajectory. We use the first example proposed by Ascher et al. [22]. These authors used this example to demonstrate that the ABA method is numerically more stable than the CRBA method. They proposed a system made up of two bodies with very different dimensions with the purpose of increasing the condition number of the generalized inertia matrix. Then, they solved the forward dynamics problem with single precision, for a set of positions obtained by rotation, through a complete turn of the second body. Fig. 1 shows a representation of the proposed manipulator. Body 1 is bound to a coordinate inertial system by means of a revolute joint in O1. Body 2 is joined to the previous one by means of a revolute joint (O2). The links are 0.02 m wide and their lengths are: l1 \u00bc 0:02 m, l2 \u00bc 2:0 m. Their masses are: m1 \u00bc 0:1 kg and m2 \u00bc 10:0 kg. The pro- cedure contemplates the rotation of body 2 around O2 at two degree intervals until completing a turn (180 steps). In this work the CRBA and ABA methods are compared with the method developed in Section 4.2 (GA). For each of the methods a FORTRAN program is written using single precision numbers. The Gauss\u2013Jordan elimination is used to solve the linear system for the CRBA and GA methods. The acceleration due to gravity (9.81 m/s2) acts orthogonal to the length of the links in Fig. 1 (y-axis), and the generalized forces are null. Fig. 2 shows, as a continuous line, the results obtained by using single precision for each of the methods. The dashed line shows the results calculated by using double precision. In the same figure is depicted the variation in the condition number of the generalized inertia matrix observed during the process. Additionally, Table 5 shows a comparison of the average and maximum differences between the solutions in single and double precision for each of the methods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure2-1.png",
        "caption": "Fig. 2. Blade profiles of a spread-blade face-milling cutter.",
        "texts": [],
        "surrounding_texts": [
            "Throughout the last two decades, several procedures for obtaining the machine-tool settings involved in the different stages of the Five-Cut Process have been developed. Prof. Faydor L. Litvin has probably been the pioneer in this field developing and applying the local synthesis method as part of an integrated computerized approach for design and stress analysis of low-noise high endurance face-milled spiral bevel gear drives with adjusted bearing contact. His methodology is based on the analytic determination of pinion machine tool settings which allow obtaining favorable conditions of meshing and contact at a chosen contact point on the gear tooth driven surface [3,4,7,8] . Later, some micro-geometry modification methodologies of both spiral bevel and hypoid gear drives based on ease-off topography were developed [9\u201311] . Lastly, in [12\u201315] , the employment of mathematical nonlinear optimization algorithms in the numerical derivation procedure was proposed for getting the finishing machine-tool settings corresponding to the pinion member of hypoid gear drives provided with improved mechanical properties: maximum average mechanical efficiency, optimal contact pattern and minimum loaded transmission errors; what is more, recently Han Ding has presented a similar approach which takes into account contact ratio as additional objective function in a multi-objective optimization framework [16] . In [17,18] , analytical procedures for the derivation of finishing machine-tool settings corresponding to face-milled or face-hobbed spiral and hypoid bevel gears from their blank geometries were proposed.\nNonetheless, despite the great number of published works related to the identification of finishing machine-tool settings in spiral bevel and hypoid gear drives, hardly any methodology of derivation of roughing machine-tool settings corresponding to face-milled fixed-setting spiral bevel pinions has been proposed. In this field, Claude Gosselin presented an optimization procedure of stock distribution between roughing and finishing operations in face-milled fixed-setting hypoid pinion machining [19] , whereas Jinliang Zhang proposed a methodology of derivation of roughing machine-tool settings corresponding hypoid pinions designed though Method 1 of American National Standard ANSI/AGMA ISO 23509-A08 [20,21] . Additionally, Standard AGMA 929-A06 [22] describes a calculation procedure of both roughing and finishing tool settings involved in the manufacturing process of bevel gear drives. Lastly, Szu-Hung Chen proposed a novel hypoid gear generator cutting plan, including both roughing and finishing operations, which let essentially reduce machining time [23] .\nIn this paper, a complete procedure for the numerical derivation of the roughing machine-tool settings involved in the machining process of face-milled fixed-setting spiral bevel pinions is presented. Specifically, and as described above, the aforementioned machining operation corresponds to the Stage (iii) of the Five-Cut Process . Finally, a numerical example will highlight the utility of the proposed approach.\n2. Mathematical model of computerized generation of face-milled spiral bevel gear drives\nIn this section, a mathematical model of derivation of gear tooth surfaces corresponding to face-milled spiral bevel gears is presented. Fundamentally, it is based on a matrix formulation [24] and follows the approach proposed in [3,4,7,8] , which in turn is based on the kinematic model corresponding to the traditional cradle-style generator employed in both spiral bevel and hypoid gear manufacturing, and is represented in Fig. 1 .\nAs depicted in Fig. 1 , the primitive generator requires eight motions in order to machine either spiral bevel or hypoid gears, which are described in Table 1 . The first four motions, represented by i, j, q and S r , constitutes the cutter head",
            "positioning settings, while the last four motions, represented by E m , X B , X D and \u03b3 m , let positioning the work head. Additionally, \u03c9 t , \u03c9 w and \u03c9 c represent the tool (face-milling cutter), work and cradle rotation velocities, respectively. In this work both tilt angle i and swivel angle j will not be taken into account, since their effect will be compensated with the search for the pressure angles corresponding to the inner and outer cutter blade profiles.\nThe head-cutter is mounted on the cradle of the gear generator and it performs a planetary motion when considering the following two rotations: (b) rotation in transfer motion together with cradle around its own axis and (b) rotation in relative motion respect to the cradle around head-cutter axis. The rotation motion of the cradle and the work are related to each other. Rotation of the face-milling head-cutter about its own axis is not related to the generation process and is chosen to provide the desired cutting or grinding velocity.\n2.1. Geometry of generating profiles of tool cutting blades\nThe geometry of the profiles of both inside and outside blades are depicted in Figs. 2 and 3 for spread-blade and fixedsetting face-milling cutters, respectively. The main settings and parameters to define a face-milling head-cutter are presented in Table 2 . In case of grinding operations, both inside and outside profiles represent the cross section corresponding to the grinder applied instead of a head-cutter.\nAuxiliary coordinate systems have been defined as follows:\n\u2022 S s ( x s , y s , z s ). This coordinate system is fixed to the face-milling cutter. Its axis x s is directed along the cutter radius, while\nz s is directed along the head-cutter axis. As well, its origin O s is contained in the head-cutter bottom axial plane.\n\u2022 S i ( x i , y i , z i ). This coordinate system is fixed to the inside cutting profile. Its axis x i is oriented along the cutting profile\ntowards the dedendum of it, while its origin O i is contained in the head-cutter bottom axial plane.\n\u2022 S o ( x o , y o , z o ). This coordinate system is fixed to the outside cutting profile. Its axis x o is oriented along the cutting profile\ntowards the dedendum of it, while its origin O o is contained in the head-cutter bottom axial plane.\nAs shown in Figs. 2 and 3 , the geometry of cutting profiles is basically comprised of two sections: (i) the main generating profile, which generates the working part of gear tooth surfaces, and (ii) the blade edge profile, which generates the root fillet of the gear tooth surfaces.",
            "As shown in Figs. 2 and 3 , straight lines have only been considered as main generating profiles. Although settings might be different for inside and outside cutting profiles, according to Table 2 , henceforth general geometric parameters \u03b1, \u03c1 and R will be used for the sake of clarity. The appropriate standards will be adopted later on in order to distinguish between the inside and the outside cutting profiles.\nThe profile parameter s , strictly positive, constitutes the first surface parametric coordinate for the face-milling cutter\nmain generating surface, and its lower limit is obtained as follows\ns \u2265 \u03c1\n( 1 \u2212 sin \u03b1\ncos \u03b1\n) (1)\nThe position vector of a point P belonging to the main generating profile is represented in coordinate systems S i and S o for the inside and outside profiles, respectively, by\nr (P) p (s ) = r (P) i (s ) = r (P) o (s ) =\n\u23a1 \u23a2 \u23a3 s 0\n0 1\n\u23a4 \u23a5 \u23a6\n(2)\nMatrix M sp represents the coordinate transformation from coordinate systems S i and S o , fixed to the inside and outside cutting profiles, respectively, to reference coordinate system S s . The upper sign in Eq. (3) represents a point belonging to the inside profile ( x \u2261 i ), while the lower sign represents a point belonging to the outside profile ( x \u2261 o ). The aforementioned sign convention will be adopted from now on, unless another different one is mentioned.\nM sp = M s,x =\n\u23a1 \u23a2 \u23a3 \u2213 sin \u03b1 0 cos \u03b1 R 0 1 0 0\n\u2212 cos \u03b1 0 \u2213 sin \u03b1 0\n0 0 0 1\n\u23a4 \u23a5 \u23a6\n(3)"
        ]
    },
    {
        "image_filename": "designv10_10_0002838_1.3559128-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002838_1.3559128-Figure2-1.png",
        "caption": "FIG. 2. The penny rolls upright while turning on an inclined plane of angle \u03b1. Directions of space-fixed axes are I\u0302 , J\u0302, and K\u0302 , as indicated. Disk rolls along the plane with angular velocity \u03c8\u0307 j\u0302 about symmetry axis j\u0302(t) which turns with constant angular velocity \u03c6\u0307k\u0302 about fixed figure axis k\u0302. The C M has velocity v(t) = [R\u03c8\u0307(t)]i\u0302(t) and the point of contact P is instantaneously at rest.",
        "texts": [
            "6). Both options can be exercised for only holonomic and linear-velocity constraints. Option 2 provides the only viable method for general nonholonomic constraints. Example 4: The two different approaches based on (2.14) and on (4.6) or (4.8) are now illustrated via a specific example of nonintegrable linear-velocity constraints. The familiar nonintegrable constraints for the nonholonomic upright penny of radius R, rolling with speed R\u03c8\u0307 and turning with angular speed \u03c6\u0307 on the inclined plane of Fig. 2, are, \u03b8\u03071 = G1 = x\u0307 \u2212 R\u03c8\u0307 cos \u03c6 = 0, (B1) \u03b8\u03072 = G2 = y\u0307 \u2212 R\u03c8\u0307 sin \u03c6 = 0, (B2) the Cartesian components of vP , where (x,y) are the Cartesian coordinates of the point of contact P with the plane, and where \u03c6 is the angle between the x axis and the penny\u2019s velocity along the tangent to the curve x(t),y(t). Let x\u0307,y\u0307 be the dependent velocities. The coordinate functions \u03b8k(q,t) Downloaded 24 Apr 2013 to 128.205.114.91. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://jmp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000760_1.1338118-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000760_1.1338118-Figure13-1.png",
        "caption": "Fig. 13 Comparison of OH-58 spiral-bevel pinion tooth crack propagation simulation to experiments",
        "texts": [
            " Figure 12 shows exploded views of the pinion crack simulation after seven steps. It should be noted that the loading was placed only at the HPSTC for the last three steps. This was due to modeling difficulties encountered using the multi-load analysis. It was felt that this simplification did not significantly affect the results due to the smoothing curve-fit used. In addition, the tangential stress near the crack tip was either largest, or near its largest value, when the load was placed at the HPSTC. Comparison to Experiments. Figure 13 shows the results of the analysis compared to experimental tests. The experimental tests were performed in an actual helicopter transmission test facility. As was done with the gear fatigue tests described before, notches were fabricated in the fillet of the OH-58 pinion to pro- Table 1 Results of multiple load case crack simulation analysis. Step Crack area ~mm2! Crack front point~s! Load case for largest suu 0 3.12 1 8 2-25 11 1 5.96 1 9 2,4-7,21,23-25 10 3,8-20,22 11 2 10.35 1 10 2-25 11 3 13.35 7,9,20 8 5-7,10-15,21,26,27 9 1-4,8,16-19,22-25 11 Transactions of the ASME shx?url=/data/journals/jmdedb/27689/ on 01/26/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F mote fatigue cracking. The pinion was run at full speed and a variety of increasing loads until failure occurred. Shown in the figure are three teeth that fractured from the pinion during the tests ~Fig. 13b!. Although the notches were slightly different in size, the fractured teeth had basically the same shape. A side view of the crack propagation simulation is shown in Fig. 13a for comparison to the photograph of the tested pinion in Fig. 13b. From the simulation, the crack immediately tapered up toward the tooth tip at the heel end. This trend matched that seen Journal of Mechanical Design rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.a from the tests. At the toe end, the simulation showed the crack progressing in a relatively straight path. This also matched the trend from the tests. Toward the latter stages of the simulation, however, the crack tended to taper toward the tooth tip at the toe end. This did not match the tests"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003306_tmag.2017.2665639-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003306_tmag.2017.2665639-Figure3-1.png",
        "caption": "Fig. 3. (a) Center taps in the phase \u201ca\u201d of the IM for the ITSC creation. (b) Phase \u201ca\u201d single layer stator winding diagram. In Fig. 5, 6, 7 and 8(a) the response of the IM for the 4 locations of the fault can be observed. Four IM\u2019s variables are investigated: mechanical speed (Fig. 5(a)), electromagnetic torque (Fig. 5(b)), faulty current (Fig. 6), the current in the winding (Fig. 7), the 2D distribution of the magnitude of the magnetic field density and flux lines (Fig. 8(a)). Notice that the electrical variables respond similarly respect to the location of the fault. However, a zoom view of each variable indicates that the fault location is affecting subtly each of them. In Fig. 5(a),",
        "texts": [
            " (4) where and are the leakage inductances of the healthy and faulty part of the phase \u201ca\u201d winding, is the total and healthy leakage inductance of one phase and and are defined as the leakage factors. From (1), and following the procedure on [2], the complex vector operational equivalent circuit of the asymmetric IM is shown in Fig. 2. The IM stator winding is single layered and each phase consists of two main coils ( and for the case of the phase \u201ca\u201d). Each of these coils is divided into 3 sub-coils as displayed in Fig 3(a), where , \u2026 are the slot numbers as in Fig. 3(b). Each sub-coil has 85 turns, therefore the total number of turns per phase is 510. For the purpose of creating the ITSC, the motor was dismantled and 8 center taps were performed in the IM phase \u201ca\u201d as depicted in Fig. 3(a). The winding profile of the phase \u201ca\u201d with one of the fault cases is shown in Fig. 3(b). Four cases of the fault were performed with a fault severity factor of 42/510 (8.2%). The 4 cases were conducted in the following positions of the phase winding \u201ca\u201d: : , : , : and : . indicates the position where 1, 2, 3, 4 . The fault resistance is imposed 0.67 \u03a9. The complete geometry of the IM is depicted in Fig. 4(a) and (b). The stator consist of an iron core M19 USS with 36 slots numbered as in Fig. 3(b). The rotor bars are made of Aluminum 3.8e7 Siemens/m and there are 44 of them. The air gap is 0.31 mm. The FE simulation is performed by strong coupling simulation between FE and circuit analysis. The FE is used to model the phase \u201ca\u201d as the combination of 7 coils (6 healthy and 1 faulty windings) all connected in series to form the phase. The faulty circuit part is connected as a step-down autotransformer configuration where is added as in Fig. 8(b). 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000831_1.533552-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000831_1.533552-Figure1-1.png",
        "caption": "Fig. 1 Face milling method",
        "texts": [
            " All above-mentioned cutting process and the supplemental flank correction motions are included in the proposed mathematical model. The majority of the existing cutting method can be simulated by the proposed mathematical model with simple machine setting conversion. Based on the derived mathematical model, an OOP object is developed to simplify the simulation of gear cutting and accelerate the tooth contact analysis of hypoid and spiral bevel gears. There are three cutting methods used by industry: circular face milling method, epicycloid face hobbing method, and the bevelworm-shaped hobbing method. As shown in Fig. 1, the face milling process and plunge cutting method uses a circular face milling cutter with all blades are mounted on the concentrical circles. Therefore, the cutting blades of the face-milling cutter perform a 2000 by ASME Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F circular motion on the imaginary generating plane. The facemilling process is an indexed cutting process with plunge cutting or generating roll cutting. The circular face-milling cutter is fed into the predetermined cutting depth to form one tooth slot and then withdraw to let workpiece index to the next tooth slot and so on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003022_j.matdes.2012.10.010-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003022_j.matdes.2012.10.010-Figure2-1.png",
        "caption": "Fig. 2. Four-point bend fatigue load of a cylindrical laser-clad bar; (a) rod after laser cladding, (b) four point bending geometry (force F, rod length L), (c) fatigue test rig, (d) cracked specimen, (e) clad layer cross section with seconday crack propagation, (f) 1st principle macro stress field (in MPa; longitudinal section of the bar, cut in half).",
        "texts": [
            " Thus, the vertical position of a clad layer defect can be very important (however, laser clad layers are often very thin) while the influence of the axial position is small over a wide range. In the lateral direction the stress field remains constant. Nevertheless, as will be shown later, the side edges of a square bar can have significance for defects located close to the surface. If the product has no significant clad defects the region of maximum macro stress will initiate cracking, as a benchmark for the stress raisers discussed below. The cylindrical laser-clad rod with its radial clad track pattern can be seen in Fig. 2a. The four loading points are shown in Fig. 2b and their corresponding fatigue test equipment can be seen in Fig. 2c. The corresponding stress field for a cylindrical laser-clad bar under four-point bend fatigue loading (note the force locations B and C) is shown in Fig. 2f, for a longitudinal section of half the bar length. While in the longitudinal section the stress field is similar to the square bar, the circular geometry induces a strong azimuthal decay of the surface stress field, as described in another study [39]. Again, in the central region the surface stress field varies only weakly in the axial direction, while in the outer axial regions it drops rapidly. The location of a defect can become important for the radial direction where the stress field strongly decays. A cylindrical laser-clad bar after fatigue testing is shown in Fig. 2d where, beside the main fracture, a secondary crack was detected, note also their positions, labelled D and E in Fig. 2d. The propagation of the secondary crack through the clad layer is shown in Fig. 2e where also the lateral orientation of the clad layers can be seen from the wavy interface. Here the clad layer surface is smooth due to post-machining (before fatigue testing). Fig. 3a shows the torsional fatigue test rig. In Fig. 3c the ISO 1352:2011 [34] standard test sample of a cylindrical laser-clad bar under torsional fatigue loading can be seen. Crossing crack patterns, which are typical for torsional loads, can be seen. The propagation of multiple cracks through the laser clad layer is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003109_978-0-8176-4893-0_6-Figure6.1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003109_978-0-8176-4893-0_6-Figure6.1-1.png",
        "caption": "Fig. 6.1 Convergence of various 2-sliding homogeneous controllers (a) Twisting controller (b) Prescribed convergence law (c) Quasi-continuous controller (d) Contractivity",
        "texts": [
            "\"1=2/, if the maximal errors arising from sampling and P are of the order of \" and \"1=2, respectively. Almost all known 2-sliding controllers are 2-sliding homogeneous. Let us check the homogeneity of the 2-sliding controllers studied in Chap. 4. In other words, condition (6.19) is to be checked: \u2022 The twisting controller (Sect. 4.2.2) satisfies Eq. (6.19); indeed u D .r1sign. / C r2sign. P // D .r1sign 2 C r2sign . P // has the convergence conditions .r1 C r2/ Km C > .r1 r2/ KM C C; .r1 r2/ Km > C Its typical trajectory in the plane , P is shown in Fig. 6.1. \u2022 The controller with the prescribed convergence law Eq. (4.21) satisfies u D \u02db sign P C \u02c7 j j1=2 sign. / D \u02db sign P C \u02c7 \u02c7\u030c 2 \u02c7\u030c1=2 sign 2 \u2022 The quasi-continuous controller Eq. (4.21) satisfies u D \u02db P C \u02c7j j1=2sign. / j P j C \u02c7j j1=2 D \u02db P C \u02c7j 2 j1=2sign. 2 / j P j C \u02c7j 2 j1=2 Next consider the super-twisting controller Eq. (4.36) applied to a system of relative degree 1, satisfying Eqs. (4.34) and (4.35) (see the end of the proof of Theorem 4.5). Starting from the moment when ju1j < UM is established, the closedloop system solutions satisfy the inclusion P 2 \u0152Km; KM j j1=2sign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002486_1.4004225-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002486_1.4004225-Figure1-1.png",
        "caption": "Fig. 1 A general 6R mechanism",
        "texts": [
            " Following the Denavit-Hartenberg\u2019s convention [39], a Cartesian coordinate system is attached to each link of the mechanism. The zi-axis is aligned with the ith revolute joint axis, and the xi-axis is defined along the common normal between the ith and the (i\u00fe1)th joint axes. The link and axis parameters are axis perpendicular-link parameters ai, axial link parameters di, and axis intersection-angles di. The motion parameters are hi. Thus, a general 6R closed-loop mechanism with arbitrary joint axis arrangement of the above link and axis parameters and motion parameters can be presented in Fig. 1. Applying the homogeneous transformation [40], a closed-loop equation can be obtained as H1 H2 H3 H4 H5 H6 \u00bc I (1) Equation (1) can be rearranged as follows: H1 H2 H3 \u00bc H 1 6 H 1 5 H 1 4 (2) Since the focus is on the 6R double-centered mechanism, it is assumed that axes z3, z4, and z5 intersect at a point to form one center and the axes z6, z1, and z2 intersect at another point to form the second center. This arrangement assigns zero to the axis perpendicular-link parameters a1, a3, a4, and a6 and the axial link parameters d1 and d4 as a6 \u00bc d1 \u00bc a1 \u00bc 0; a3 \u00bc d4 \u00bc a4 \u00bc 0 (3) and leads to forming the 6R double-centered overconstrained mechanisms in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001292_1.342739-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001292_1.342739-Figure2-1.png",
        "caption": "FIG. 2. Surface temperature distribution alongy* = 0.5 at t\" = 0.2 for laser beam of power 600 W and moving in the x direction at a constant velocity 0.25 cm/s relative to the substrate.",
        "texts": [],
        "surrounding_texts": [
            "ar' __ s = X T\" at x* = 0, ax\" ()\" (Sa) aTn __ s = X T\" at x* = 1, ax\" Y.\u00b7 s (Bb) BT\" __ S = :r: T If at y* = 0, a '\" 0 s y ( Be) aT\" Oy; = Yw T ;' at y* = 1, (Sd) aT\" __ $ = Z T\" at z* = 0, az* 0 s (8e) aT\" -_$ = P*e- r*' + Z Tn at z* = 1, az* H s ( 8f) where p* = 2PAH I[ 11'L 2r?;2k( Td ) Td ], r*2 = -~-z[ (x* - rg - t .. ) 1 + (1/ a2 )(y* - D \" f] , I~ r't; = foiL, and D * = D I W. The initial condition (1 b) simplifies to T;' = r; at t * = 0, where and T~ = TJTd \u2022 (8g) The governing equation (la) can be simplified by using the above non dimensional variables and the transformations de fined by Eqs. (4) and (7) to obtain a2 T\"* a21'''* ~ a 2T\"* 1 aT\"* --+a2 __ +s- __ =___ (8h) Bx*2 ayll<2 az*2 Fo at II< ' where the aspect ratio, a = L /w, the slenderness ratio, s = L IH, and the Fourier number, Fo = a( T)r/L 2. a( T) varies slowly with temperature for many materials. In this A. Kar and J. Mazumder 2925 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 study, a( n is considered constant, which is taken to be the temperature-averaged value of the thermal diffusivity over the temperature ranging from the ambient temperature to the melting point of the substrate. The above problem defined by Eqs. (8a)- (8h) is solved by successively applying Fourier transforms in thex,y, and z directions. The Fourier double-integral transform in the x and y directions is T\" (A1x,Amy,Z*,t *) = til dx* dy* T\"(x*,y*, z*, t*) Jo 0 X k lx (x* )Kmy (y*), (9a) and the inversion formula is ',0 '\" T\"(A A z* t*) Til (x*,y*,z*,t *) = L I Ix. my' , {=o m~O IV/x N\",y XK,x (x* )K\",y (y*), (9b) where the kernels [K/x (x*), Krny (y*)]. the characteristic equations for the eigenvalues (A[x,A my ), and the normaliza tion constants (Nix ,N my ) for the above integral transform in each of x andy directions are, respectively. defined as K1x(x*) =Xosin(AI.,x'\") + A/x COS(A/xX\"'), tan}./\" = [A/x (XO -XL )]I(A7x +XoXL), N,x = HXo + (A Z. + X~) [1 - X L /(A7x + XU n, and Kmy (y*) = Yo sin(AmyY*) + Amy eOS(AmyY*), tan Amy = [Amy(YO- Yw)JI[A~,y + YoYw], N my =Hyo+ (A~y + Y~)[1- ywl(A~y + Y;)]}. Here the kernels and the eigenvalues are so chosen that boundary conditions (8a)-(8d) are satisfied. The applica tion of the integra] transform (9a) to Eq, (8h) and the boundary and initial conditions (8e )-( 8g) yields the follow ing: Equation (8h) becomes _ (A. 2 + a2 A 2 ) T fI + 32 a iT fI = _1_ aT If , Ix my az*2 Fo at. ( lOa) The boundary conditions (8e) and (8f) become aT\" -Z-T\" --- 0 az\u00b7 at z* = 0 ( lOb) and aT\" = Z Til + t' (t*) at z* = 1, (lOc) az* II Jim where ftmU*) = t t dx* dy* K)x(x*) )0 )() XKmy(y'\")p*e- \"\"(x*,y\u00b7.,\"). ( We) This integral is evaluated in Appendix B. The initial condi tion (8g) becomes 1'''=T;, (lOd) where 2926 J, Appl. Phys,. Vol. 65. No, 8, 15 April 1989 Equation (lOa) will be solved by applying the Fourier inte gral tansform in the z direction after homogenizing bound ary condition (lOc) by the foHowing substitution: T\" (A/x,Amy,Z* ,t *) = T\"'(A1x,Amy,Z*,t *) (11) where Ti\"(A[x,Amy,Z*,t*) =ftm \u00ab*)(ZoZ* + 1)/.:lz and b-z = ZoO- ZH) - ZH' Substituting expression (11) into Eq. (lOa), the boundary and initial conditions (lOb)-(lOd), and then applying the following integral transform: Tiff (Alx,Amy,)'\"z,t \"') = f dz'\" T\"'(A/x,Amy,z*,t *)Knz (z*), where the inversion formula is 00 T\"\" A A ). t *)K (z*) -T\"'( ~ , * *) = \"\" ~ lx' my' 'nz' nz ,r'[x'/!,my'Z ,f \u00a3.., , n=O Nnz (12) and the kernel (Knz ), the characteristic equation for the eigenvalues (A. nz ), and the normalization constant (N\"z) are Knz (z*) = Zo sin(Anzz*) + Anz COS(AnzZ*), tan Anz = Anz (Zo - ZH )/(..1. ~z + ZoZu), N\", = !{Z() + (A~z +Z~)[1-ZII/(A~z +Z~)]}, we obtain the following results: Equation (lOa) becomes - (A;, + a2A ~y )[1'''' + l,b(t *)] - A ~zs2T'\" = _l_~[T'\" + l,b(t*)], (13) Fo dt* where l,b(t *) = f dz*Knz (z*) TiV(A[x,Amz,z*,t *) Itm (t '\") (Zo 1 1 .,) = -( -COSAr,z)+SlnA\"z ,6,z .A nz , Anz + . -'- (COS Anz - 1 sin Anz)] . A!z All\" To obtain Eq. (B), the kernel K\"z (z*) and the eigenvalues (A\"z) are chosen in such a way that boundary conditions (1 Ob) and (lOc) are satisfied. By adding and subtracting ? A ;'2 f/!( t *) on the left-hand side of Eq. (13), and letting ).7mn = FO(A 7x + a2A ;',y + S2A ~z), we obtain the following ordinary differential equation: A. Kar and J, Mazumder 2926 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 where tI!! = T\"'(A 1x ' Amy ,A liZ , t *) + !/J(t *). The solution of Eq. (14) is given by \u00a2I(t*) =\u00a2,(O)e Ain,,\" +e-AYm.,t\u00b7 (14) (15) X r' Fos2/';'c/.i\",,;i\u00b7\u00a2(i*)dt*. (16) Jo IP, (0) is determined from Eg. (15) by utilizing the results obtained after taking the Fourier transform in the z direction of expressions (1 Od) and (11). This yields \u00a2 I (0) = T a sin .,t \"z (ZoI.,t \"z ) (1 - cos .,t nz )] , By using Eq. (16) in expression (15), we obtain =T\"'( j 1 1 t*) .i (CJ)e . Ai\",,,\" + .. 1\u00b7 2 (t*), . A/x' Amy' A nz ' = 'if I 'I-' where \u00a22(t*) = \u00a2!Ct*) - \u00a2(t*) and (17) if! (t *) = e .J. t~nt' f' Fo S2.,t ;'z\u00a2(i *)i' 7m;;'dt '* -\u00a2(t\"). An explicit expression for 'iA (t .. ) is given in Appendix Co By applying inversion formula (12) to Eq. (17), and then using expression (11), inversi.on formula (9b), and expression (7), we obtain 00 K (x*) [ 00 K (y* ) T'*(x*,y*, z*, t*) = I . Ix L. _m..oY __ 1=0 IVlx m~O Nmy X (TilJ(A/x, Amy' z*, t *) + \"to X [\u00a5!! (O)e -At\"\",!\u00b7 + tP2(t *)] Knz (Z*))] X - Te\u00b7 N nz (18) From the transformed temperature (T'*) given by Eq. ( 18). the nondimensional temperature I'* is determined by using Eq. (6). m. RESULTS AND DISCUSSiON Equation (18) can be used to carry out parametric stud ies oflaser heating of finite slabs. Various parameters such as the wavelength of the laser beam, laser power, shape of the laser beam, diameter of the laser beam, speed of the laser beam relati.ve to the substrate, dimension of the substrate, the thermophysical and optical properties of the substrate, and the conditions of the medium surrounding the substrate can affect the temperature distribution in the substrate. Some typical results are presented in Figs. 2-13. Also, two simple expressions for the variation of the peak temperature with the laser power and with the substrate velocity are ob tained, For all these results, the value of ro is taken to be 2 mm. The laser beam is located at y* = 0.5 and moves in the posi- 2927 J. Appl. Phys., Vol. 65, No.8. 15 April 1989 1.0.' 0,4 1.0 io v f, 1,4 T' 1.2 1.0 1. 0,8 O.G \u00b70.4 FIGA. Surface temperature distribution alongy* = 0.5 at t\" = 0.8 forlaser beam of power 600 Wand moving in the x direction at a constant velocity 0.25 cmls relative to the substrate. A. Kar and J. Mazumder 2927 .\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022.\u2022.\u2022\u2022\u2022 -\u2022\u2022\u2022 \" \u2022\u2022\u2022\u2022\u2022 \" \u2022\u2022 -\u2022\u2022\u2022 -.-\u2022\u2022\u2022\u2022\u2022 -.... \" , \u2022\u2022 -, \u2022\u2022\u2022 --. .-.-............. ~ \u2022\u2022\u2022. o; \u2022\u2022\u2022\u2022\u2022\u2022\u2022 :.-;o_ ....... -\u2022\u2022 -.. .. \" ......................................................................................................... ; \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 ~ \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 , \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 y~ \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 -._-_ \u2022\u2022\u2022 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 2928 J. Appl. Phys., Vol. 65, No.8, 15 April 1989 A. Kar and J. Mazumder 2928 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 2,5~----,------,----.-----, - 2,0 .\" f- OJ '5 ;:; 1.5 Qj '\" E '\" f-1.O -\" \" A U \"0.,1 cm/s B U =0.,3 C!!l/s C U \"0.5 cm/s x\"\"\";;:0'3 8'. A , B 1~ o 250 ----~500~-~7~5~O--lO~,OO Laser Power (W) FIG. ! 1. Variation of the peak temperature with laser power for various scanning speeds relative to the substrate at x~ = 0.3 on the top surface of the substrate, 2929 J. Appl. Phys., Vol. 65, No.8, 15 April 1989 tive x direction with respect to the substrate. The values of the heat transfer coefficients in boundary conditions (lc) (lh) are determined from the following considerations: The slab considered in this study is very thin in the z direction. Its length, width, and height are 1, 1, and 0.1587 cm, respective ly. Since the slab is exposed to the laser beam at the z = H plane, the surfaces at z = 0 and H are expected to heat up more than the other four surfaces for the same ambient con ditions on an six sides of the slab. So the convective activities will be more at the planes z = 0 and H than at the other surfaces. In this study, the convective heat loss frem the sur faces at x = 0, x = L, Y = 0, and y = W is considered to be due to free convection and the heat transfer coefficients are taken to be 5 W 1m2 K (see ReI, 20) at these four surfaces. The heat transfer coefficients at z = 0 and H planes are de termined by assuming that the Biot (Bi) numbers are equal at all the surfaces, where the characteristic lengths in the Bi numbers are taken to be the length, width, and height of the slab for the surfaces perpendicular to the x, y, and z axes, respectively. Figures 2-4 represent the temperature distribution on the top surface of the substrate. Although the computation for the surface temperature distribution is carried out ac cording to the coordinate system of Fig. 1 (a), the three dimensional Figs. 2-4 are plotted by letting x*, y*, and the temperature (T*) increase along Ox\"', Oy\", and 01'* direc tions, respectively, as indicated in these three figures. Here point 0 represents one of the corners of the square contain ing the lines 0 ' V and 0 \" V as two of its sides on the plane of O'VO \". For improved clarity in representing the surface temperature field in three-dimensional plots, views from the two planes, one from the plane T' 0 ' V' located at x* = 1 and the other from T\" 0 \" V located at y* = 1 are shown. Figures 2-4 show the temperature fields for laser power, p = 600 W, laser scanning speed relative to the substrate, u = 0.25 em/s, and for the nondimensional time, t * = 0.2, 0.5, and 0.8, re spectively. It can be seen from these figures that the shape of the surface temperature field has Gaussian-like structure be cause of the consideration of Gaussian laser beam as the source of heat in this study. The temperature and length of the heated zone ahead of the laser beam in the x* direction are found to increase as t * increases. This is so because at a low scanning speed the Fourier number (Fo) is large, that is, the conduction rate is higher than the heat storage rate. Con sequently, the substrate material which is in front of the laser beam is heated up due to the heat conducted away from the laser heated spot. Hence, the laser energy is progressively imparted to points on the substrate which are at higher tem peratures than the preceding points. For the very same rea son, the laser heated zone in the y* direction increases as t * increases for low scanning speed, The knowledge of the width of the laser heated zone is very important in LCVD. The chemical reaction that gener ates the film forming material win take place wherever the temperature is more than or equal to the chemical reaction temperature. As explained above, the width of the heated zone will increase as the laser beam scans the substrate at a low scanning speed. This means that the width of the zone, to A. Kar and J. Mazumder 2929 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 be referred to as the chemically reactive zone, over which the temperature can be larger than or equal to the film forming chemical reaction temperature will increase progressively along the scanning direction for low scanning speed of the laser beam. Thus, the film width will not be uniform for low scanning speed of the laser beam as deposition progresses. On the other hand, if the scanning speed is high the Fourier number will be small, that is, the conduction rate will be lower than the heat storage rate. This reduces the area of the chemically reactive zone due to less conduction of heat from the laser heated spot. Because of this, a narrow film or con stant width can be deposited on the substrate by increasing the scanning speed of the laser beam. This concept is reflect ed in the results presented in Figs. 5-7. These figures show the width of the chemically reactive zone and its variation in the scanning direction for various scanning speeds and laser powers. The chemically reactive zones are symmetrical around the line, y* = 0.5 because the laser beam is located at y* = 0.5 in this study. In each of Figs. 5-7, the chemically reactive zones are bound by the curves, A, B, C, and D for the scanning speeds 0.35, 0.25, 0.167, and 0.125 em/s, re~ spectively. For a given laser power, it can be seen from each of these figures that the chemically reactive zone becomes wider and less uniform in width as the scanning speed de creases. The same can be found for a given scanning speed and different powers of the laser beam by comparing the results of Figs. 5-7. It is established from Figs. 5-7 that the chemically reac tive zone becomes narrower as the laser scanning speed in creases. However, there will be a critical scanning speed at which the two boundary curves of the chemically reactive zone will collapse into one, giving rise to the narrowest possi ble film deposition region. With any other scanning speed higher than the critical speed, the width of the chemically reactive zone cannot be reduced any further. So the film deposition process has to be operated at a scanning speed lower than the critical speed. The critical scanning speed is defined as the one at which the nondimensional peak tem perature T; is unity, where the peak temperature refers to the temperature at the center of the laser beam on the top surface of the substrate. The line T; = 1 is referred to as the line of the narrowest chemical reaction zone in Figs. 8-10. These figures are plotted on logarithmic scales which show the linear variation of the peak temperature (T;) with the laser scanning speed (U) for different powers of the laser beam at various locations on the top surface of the substrate. The points of intersections of the line of the narrowest chem ical reaction zone with the curves of Figs. 8-10 give the criti cal scanning speed of the laser beam. The region which is to the right of the critical speed is referred to as the chemically inert regime because the operating conditions of this region do not raise the surface temperature of the substrate to the film-forming chemical reaction temperature. The region to the left of the critical speed is referred to as the chemically reactive regime where the operating conditions are such that films of finite width can be deposited. However, the surface temperature of the substrate can reach its melting tempera ture at a low scanning speed for a given operating condition, as can be seen from Figs. 11-13. Since melting the substrate 2930 J. Appl. Phys., Vol. 65, No.8, 15 April i 989 is not desirable in LCVD processes, the scanning speed has to be higher than the upper limit of the speed at which melt ing occurs. The line T; = Tm/Td' where Tm is the melting temperature of the substrate, is referred to as the line of melt ing point in Figs. 8-10. The points of intersections of the line of melting point with the curves of Figs. 8-10 give the scan ning speed above which the process has to be operated to avoid melting the substrate. So, from the thermal consider ations, the operating regime for an LCVD process is bound by the line of melting point, the line of narrowest chemical reaction zone, and their points of intersections with the curves of Figs. 8-10. The values of r, 0, 7J, and /3 are given in Tables I and II for various operating conditions. It should be noted that the expression T; = rU'5 is applicable in the chemically reac tive regime. Since the substrate temperature decreases as the scanning speed increases, there will be a critical scanning speed, say U\", at and above which the substrate temperature will remain at its initial temperature. So the slopes of the curves of Figs. 8-10 will be zero for scanning speeds higher than U >1<. This physical aspect is not reffected by the equation T; = r[;>{; because this expression is obtained from the re sults of the chemically reactive regime. It should be noted that when P = 0, the peak temperature must be equal to the initial temperature of the substrate. This is indeed the case as TABLE 1. Values of rand b for the expression T; = rUb. Power (W) x\" r 6 600 0.3 0.985 - 0.141 0.6 UlO6 - 0.163 0.9 1.006 -0.244 700 0.3 1.101 -0.146 0.6 1.125 - 0.169 0.9 1.127 -0.253 800 0.3 1.217 - 0.150 0.6 1,244 -0.174 0.9 1.247 - 0.259 A. Kar and J. Mazumder 2930 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 evident by the values of /3 in Table II because the initial temperature (T;) of the substrate and the thermal decompo sition temperature (Td ) of the film-forming chemical reac tion are taken to be 343 and 1173 K, respectively, in this study for which the nondimensional initial temperature of the substrate is 0.2925. IV. CONCLUSIONS The three-dimensi.onal and transient heat conduction equation is solved in Cartesian coordinates for slabs having finite dimensions and moving at a constant velocity. The temperature-dependent thermophysical properties of the material of the slab are considered, and both convective and radiative losses of energy from the slab to the surrounding medium are taken into account. The laser beam is considered to be Gaussian in shape. Based on these considerations, an analytic expression for the three-dimensional and transient temperature field is obtained. The surface temperature field has a Gaussian-like struc ture for the problem considered in this study. The width of the chemically reactive zone is found to depend on the scan ning speed of the laser beam, becomes more uniform, and decreases as the scanning speed increases. The critical scan ning speed for the narrowest film deposition is determined. Also, the lower and the upper limits of the scanning speeds for LCVD processes are obtained. The peak temperature is found to vary linearly with the laser power for given scan ning speeds and the logarithm of the peak temperature is shown to vary linearly with the logarithm of the scanning speed in the chemically active regime for given laser power. ACKNOWLEDGMENT This work was made possible by a grant from National Science Foundation (Grant No. NSF MSM 84-12118). APPENDIX A: DETERMINATION OF OPTICAL PROPERTIES AT HIGH TEMPERATURES From among various optical properties of materials, the most important one is the optical absorptivity of materials. Such data for many materials can be found in Ref. 21. Some- 2931 J. AppL Phys., Vol. 65, No.8, i5 April 1989 times the complex refractive indices are reported in the liter ature, which can be used to determine the absorptivity under suitable conditions by using Fresnel's relation. Optical con stants (refractive indices) for various noble and transition metals at room temperature can be found in Refs. 22-24 as a function of wavelength of the incident electromagnetic radi ation. However, the optical constants of materials depend not only on the wavelength of the incident radiation but also on the temperature of the materials. Reference 21 provides the temperature variation of optical constants of some mate rials. In LCVD processes, the temperature of the laser irra diated spot is very high, and hence the absorptivity data of the substrate materials at high temperature are important. Since optical constants of materials are usually reported for room-temperature condition, we will show how high-tem perature data can be determined from the available room temperature data. The absorptivity data needed for the present mathemat ical model (that is, the study of LCVD of pure titanium on stainless-steel 304 from titanium tetrabromide) are that of a composite medium which is made up of S.S. 304, titanium film on the surface ofS.S. 304, the vapor phase of TiBr4 , and the chemical reaction products. Since the pressure of the system under consideration is very low, we will consider the optical properties of the vapor phase to be the same as those of vacuum. From the room-temperature data we will first determine the optical constants (n, k; the real and imaginary parts of the refractive index, respectivelY) ofTi and S.S. 304 at 1173 K since the decomposition temperature of the chemi cal reaction 25 4TiBr-.3Ti + TiBr4 is greater than 1173 K. Using the high-temperature values of nand k, the reflectivity of the composite material (made up of S.S. 304 and Ti film) is determined by using Fresnel's relation for composite medium. 26 The nand k values ofTi and S.S. 304 at room tempera ture are obtained from the experimental data of Ref. 24 where 2nk / A and k 2 - n2 values of various transition metals have been reported. Here A is the wavelength of the incident electromagnetIc radiation in micrometers (pm). To com pute the nand k values of 3.S. 304, we consider that the composition ofS.S. 304 is 71.5% Fe, 19% Cr, and 9.5% Ni by weight and that nss = 0.715 nFc + 0.095 flNi + 0.19 nCr and k\" = 0.715 KFe + 0.095 k Ni + 0.19 keT \u2022 Here, ni and k; are the real and the imaginary parts of the refractive indices of the ith material where i stands for S.S. 304 (ss), iron (Fe), nickel (Wi), and chromium (Cr). From this consideration and the data of Ref. 24, Table III can be prepared. For the CO2 laser, the wavelength A = 10.6 f.-im. Also, we have the following data from Ref. 27: PTum = 44 po' cm, P\u00b7!\"l.tI73 = 160 pO em, Pss,300 = 74,5 pO em, Pss,l173 = 122.5 pfl em, where Pi. j is the direct current (de) resistivity of the ith material at the fih temperature. It should be noted that Ref. A. Kar and J. Mazumder 2931 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 TABLE HI. Optical properties of various materials. Materials 2nk IA. Ti 25 Fe 50 Ni 60 Cr 54 S.S.304 Values at room temperature 300K k 2,n2 n 83 9.8665 833 1333 583 9.1417 k 13.4293 30.1586 27 provides the resistivity data for S.S. 303 which we are using for S.S. 304, To obtain the nand k values at higher temperature, we use the following empirical relation from Ref. 28: R = 1-112.2X 10-4 G, (Al) where R is the refiectivity andp is the dc resistivity inpfi em. Taking the derivative of Eq. (AI) with respect to tem perature T, we obtain dR 112.2x 10-4 dp dT 2.jp dT' (A2) Equation (A2) will be used to determine dR IdTatany tem perature by assuming that the resistivities ofTi and S.S. 304 vary linearly with T. From Fresnel's relation, we have for normally incident beams R= [en-I) +k 2 11[(n+ 1)2+k21. Taking the derivative of this equation with respect to tem perature T, we get the following equation for dnl dTand dk I dT: dn dk -+Ao -=A 3 \u2022 dT - dT . (A3) Here A2=A;IA~ and A3=A~/A~, (A6) Substituting Eqs. (AS) and (A6) into Eq. (A4), we obtain ( dn )2 ( dk)2 dn dk - + - +A4 -+As -=A6 \u2022 dT dT dT\" dT (A7) Here A4=A~/A3' A5=A;/A;, and A6=A;;/A;, where A 3 = 112.2 X lO-4( T - TO)2 ,jp, A ~ = 224.4 X 1O--4(no - 1)( T - To) [ji, A; = 224.4X 1O- 4 ko(T - To) ..[p, A~ = (l-1l2.2X 10-4[ji)[(no + 1)2+k6J - (no - 1) 2 - k ~ . Equations (A3) and (A7) are solved by substituting the value of the temperature T at which nand k values are re quired. Knowing dnldT and dk IdT from the solutions of Eqs. (A3) and (A 7), nand k are determined from Eqs. (AS) and (A6) for S.S. 304 and Ti, and then the reflectivity of the composite material which is made up of S.S. 304 and Ti is obtained by using Frensel's relation for composite me dium2 (, for a wide range of the Ti film thickness, The reflec tivity of the composite medium is found to be 0.86351 for O.4-.um-thick Ti film and 0.863 50 for Ti film of thickness 0.8, 1, 10, 100, 200, 500, 700, 900, and 1000 .urn. So, Ti film of thickness up to lOOO.um does not affect the refiectivity of the composite medium of S.S. 304 and Ti at 1173 K. Also, by using the nand k values determined at the high temperature ( 1173 K) by the above procedure in Fresnel's relation, the reflectivity ofS.S. 304 is found to be 0.8758. The absorptivity ofS.S. 304 obtained from this value ofrefiectivity agrees very well with the experimental data of Duley et al. 29 where APPENDIX B A ~ = (no - 1) [ (no + 1) 2 + k ~ ] - (110 + 1)[(no-1)2+k~], A; = 4noko\u2022 A ' 1 [ 2 k 2] 2(dR) 2 = - (no + 1) + (I -. 2 dT 0 The SUbscript 0 is used to refer to the values of the variables n, k, and dR IdTat room temperature. Also, Eq. (Al) can be written as (n--l)2+ k : =1-1l2.2XlO 4/p, (A4) (n+0 2 +k- which is applicable at any temperature. We assume that n and k vary linearly with temperature and therefore ( T 'f-) dn n =110+ - 10 - dT (AS) and 2932 J. App:' Phys., Vol. 65. No.8, 15 April i 989 Here we will evaluate the integrals that appear in the expression for fzm (t \"') : It should be noted that due to the exponential terms,the inte grands of the above two integrals will be very small at a radial distance larger than rif from the center of the laser beam on the top surface of the substrate. Therefore, if the center of the laser beam is away from any of the four edges of the top surface of the substrate by rif, the limits 0 and 1 of both integrations can be replaced by - 00 and 00, respec tively. Because of this, the first integration of the above equa tion can be approximated by A. Kar and J. Mazumder 2932 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 y = foooo dy* e 2( y' x (Yo sin(Amy y*) + Amy COS(A my y*) 1 x [Y;)sin(D*A my ) + Amy cos(D*Amy )]. Similarly, the second integration in the expression for Jim (t >1<) can be approximated by ( 1ir'fS2) 1/2 -A' ,.;l'2/s X= -- e ixO 2 X [Xo sin(r(J' + t *) + A/x cos A/x (r(J' + t *)]. Finally,lIm (t *) can be approximately written as lim (t \"') = p >I< YX. APPENDIXC The expression for If I (t >1<) will be simplified in this sec tion: where Using the expression for iIm (t *) from Appendix E, the above equation can be rewritten as where K2 = K j FOS2A ;'zP * Y(m1\\'2/2) 1/2. Carrying out the above integration, we obtain ::i. ( *) K( Xo -;'7,1,'2/8 ['2 . '( >I< .... ) 1 1 C'o!< ..... )]. )'/x ['2 '1'1 t = 2 --4- e A 1m\" SIn Alx t + rrj - AlxCOS A/x i +\"6 T. 4 2 /. Imll A Imn A., 1m\" + A Ix A./x e A7mnt *--A7.xr(f2/8 A. fmn + A Ix IJ. Mazumder, in Proceedings of Interdisciplinary Issues in Materials Pro cessing and Manufacturing, edited by S. K. Samanta, R. Komanduri, R. McMeeking, M. M. Chen, and A. Tseng (American Society of Mechani cal Engineers, New York, 1(87), pp. 559-630. 2E< M. Breinan and B. H. Kear, in Proceedings 0/ Laser Materials Process ing, edited by M. Bass (North-Holland, Amsterdam, 1983), pp. 235-296. 3J. Singh and J. Mazumder, Acta Metall. 35,1995 (1987). 4A. Kar and J. Mazumder, J. App!. Phys. 61, 2645 (1987). 'A. Kar and J. Mazumder, Acta Metall. 36, 702 (1988). \"5. D. Allen, J. App!. Phys. 52, 6501 (1981). 7W. B. Chou, M. Azer, and J. Mazumder (unpublished). 8J. Mazumder and S. D. Allen, in Proceedings a/the Society of Photo-Opti cal Instrumentation Engineers, edited by J. F. Ready (Society of Photo Optical Instrumentation Engineers, Washington, DC, 1980), Vol. 198, pp.73-80. \u00b0H. E. Cline and T. R. Anthony, J. App!. Phys. 48, 3895 (1977). HM. Lax, J. AppL Phys. 48, 3919 (1977). I'M. Lax, J. App\\. Phys< Lett. 33, 786 (1978). 12M. Lax, in Proceedings of Laser-Solid Interactions and Laser Processing- 1978, edited by S. D. Ferris, H. J. Leamy, and J. M. Poate (Americaa Institute of Physics, New York, 1979), pr. 149-154. \"L. D. Hess, R. A. Forber, S. A. Kokorowski, and G. L. Olson, in Proceed\" 2933 J. Appl. Phys<, Vol. 65, No.8, 15 April 1989 ings of the Society of Photo\" Optical Instrumentation Engineers, edited by J. F Ready (Society of Photo-Optical Instrumentation Engineers, Wash ington, DC, 1980), Vol. 198, pp. 31-34. I4A. E. BeH, RCA Rev. 40, 295 (1979). 15y.1. Nissim, A. Lietoila, R. B. Gold, and J. F. Gibbons, J. AppL Phys. 51, 274 (1980). 168< A. Kokorowski, G. L. Olson, and L. D. Hess, in Proceedings of Laser and Electmn\"Beam Solid Interactions and Materials Processing, edited by J. F. Gibons, L D. Hess, and T. W. Sigmon (Elsevier-North\"Holland, New York, 1955, pp. 139-146. I7J. E. Moody and R. H. Hendel, J. App!. Phys. 53,4364 (1982). 18K Kant, J. App!. Mech. 55, 93 (1988). 19H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed. ( Clarendon, Oxford, 1986), pp. 10-11. 2!)F. P. Incropera and D. P. Dewitt, Fundamentals of Heat and Mass Trans fe/', 2nd. ed. (Wiley, New York, 1985), p. 8. 21W. L. Wolfe and G. J. Zissis, Eds., The Infrared Handbook (Infrared Information and Analysis Center, Environmental Research Institute of Michigan, MI, 1978), pp. 7.1-7.76. 22p. B. Johnson and R. W. Christy, AppL Opt. 11, 643 (l9i2). 23p. B. Johnson and R. W. Christy, Phys. Rev. B 9, 5056 (! 974). 24A. P. Lenham and D. M. Treherne, J. Opt. Soc. Am< 56, 1137 (1966). A. Kar and J. Mazumder 2933 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47 25K. Funaki, K. Uchimura, and Y. Kllniya, Kogyo Kagakll Zasshi 64, 1914- (1961). 260. S. Heavens, Optical Properties of Thin Solid Films (Academic, New York, 1955), pp. 76-77. 27 A. Goldsmith, T. E. Waterman, and H. J. Hirschhorn, Handbook afThe,.- 2934 J. Appl. Phys., Vol. 65, NO.8, j 5 April 19139 mophysical Properties of Solid Materials, revised edition, Vol. II: Alloys (MacMillan, New York, 1961), pp. 171 and 671. '\"Y. Arata and l. Miyamoto, Technocrat 11, 33 (1978). 19W. W. Duley, D. 1. Simple, 1. P. Morency, and M. Gravel, Opt. Laser Techno!., 313 (December 1979). A. Kar and J. Mazumder 2934 [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: 150.135.239.97 On: Thu, 18 Dec 2014 20:20:47"
        ]
    },
    {
        "image_filename": "designv10_10_0001535_j.mechmachtheory.2006.11.002-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001535_j.mechmachtheory.2006.11.002-Figure1-1.png",
        "caption": "Fig. 1. A 3SPU + UPR parallel manipulator at initial pose and its simulation mechanism at general pose.",
        "texts": [
            " Therefore, this novel parallel manipulator possess some potential applications for the 4-dof PMK, such as high precision machine tools, high precision sensor, surgical manipulator, tunnel borer, barbette of warship, and satellite surveillance platform. 2. The displacement analysis 2.1. The 3SPU + UPR parallel manipulator and its dofs A 3SPU + UPR parallel manipulator is composed of a (moving) platform m, a (fixed) base B, and three SPU-type active legs ri (i = 1,2,3) with the linear actuators, and one UPR-type active constrained leg ro with a rotational actuator (motor), see Fig. 1a. Where m is an equilateral ternary link Da1a2a3 with 3 sides li = l, 3 vertices ai, and a center point o. B is an equilateral ternary link DA1A2A3 with 3 sides Li = L, 3 vertices Ai, and a central point O. Let {m} be a coordinate system o-xyz fixed on m at o, {B} be a coordinate system O-XYZ fixed on B at O. Each of ri connects m to B by a spherical joint S at ai, an active leg ri with a prismatic joint P, and a universal joint U at Ai. The UPR-type active constrained leg ro connects m to B by a revolute joint R3 attached to m at o, an active constrained leg ro with a prismatic joint P, and a universal joint U attached to B at O. U at O is composed of two cross revolute joints R1 and R2. The axis of R1 is coincident with Z. The axis of R2 is perpendicular to Z. The axis of R3 is coincident with y and perpendicular to the axis of R2. Since each of the SPU-type active legs ri only bears the active force along ri, obviously, it has relative larger capacity of load bearing and it is simple in structure. In order to verify analytic results and solve workspace, a 3SPU + UPR simulation mechanism is constructed (Fig. 1b). The construction processes are explained in Appendix A. In the 3SPU + UPR parallel manipulator, the number of links is q0 = 10 for 1 platform, 4 cylinders, 4 piston-rods, and 1 base; the number of joints is q = 12 for 4 prismatic joints P, and 4 universal joint U, 1 revolute joint R, and 3 spherical joints S; the dof (degree of freedom) mi of various joints are m1 = 1 for prismatic or revolute joint, m2 = 2 for universal joint, m3 = 3 for spherical joint. Using a Kutzbach Gru\u0308bler equation [1,2], the dof of the 3SPU + UPR parallel manipulator is calculated as M \u00bc 6\u00f0q0 q 1\u00de \u00fe Xq i\u00bc1 mi \u00bc 6 \u00f010 12 1\u00de \u00fe \u00f04 1\u00fe 4 2\u00fe 1\u00fe 3 3\u00de \u00bc 4 \u00f01\u00de 2",
            " (2a) and (3a), aB i (i = 1,2,3) are derived as aB 1 \u00bc 1 2 ffiffiffi 3 p exl eyl \u00fe 2X offiffiffi 3 p exm eym \u00fe 2Y offiffiffi 3 p exn eyn \u00fe 2Zo 2 64 3 75; aB 2 \u00bc eyl \u00fe X o eym \u00fe Y o eyn \u00fe Zo 2 64 3 75; aB 3 \u00bc 1 2 ffiffiffi 3 p exl eyl \u00fe 2X o ffiffiffi 3 p exm eym \u00fe 2Y o ffiffiffi 3 p exn eyn \u00fe 2Zo 2 64 3 75 \u00f03b\u00de Under the structure constraints of the UPR-type active leg, RB m is formed by 3 rotations of (Z,X1,Y2), namely, a rotation of a about Z-axis i.e. R1, followed by a rotation of b about X1-axis i.e. R2, and a rotation of k about Y2-axis i.e. R3. Where X1 is formed by X rotating about Z by a, and Y2 is formed by Y1 rotating about X1 by b, see Fig. 1b. Thus, RB m and oB are derived as RB m \u00bc ca ck sa sb sk sa cb ca sk\u00fe sa sb ck sa ck\u00fe ca sb sk ca cb sa sk ca sb ck cb sk sb cb ck 2 64 3 75 \u00bc xl yl zl xm ym zm xn yn zn 2 64 3 75; oB \u00bc ro sa sb ca sb cb 2 64 3 75 \u00f04a\u00de where ca = cosa, cb = cosb, ck = cosk, sa = sina, sb = sinb, sk = sink. Comparing items in Eq. (4a), we obtain xl \u00bc ca ck sa sb sk; yl \u00bc sa cb; zl \u00bc ca sk sa sb ck xm \u00bc sa ck\u00fe ca sb sk; ym \u00bc ca cb; zm \u00bc sa ck ca sb ck xn \u00bc cb ck; yn \u00bc sb; zn \u00bc cb ck X o \u00bc rosa sb; Y o \u00bc roca sb; Zo \u00bc rocb; ro \u00bc \u00f0X 2 o \u00fe Y 2 o \u00fe Z2 o\u00de 1=2 \u00f04b\u00de Each of ri (i=1,2,3) can be solved as [1,2] ri \u00bc aB i AB i \u00bc \u00bd\u00f0X Ai X ai\u00de 2 \u00fe \u00f0Y Ai Y ai\u00de 2 \u00fe \u00f0ZAi Zai\u00de2 1=2 \u00f05a\u00de From Eqs",
            " The 3SPU + UPR parallel manipulator has some potential applications for the 4-dof PMK, such as parallel machine tool, parallel sensor, surgical manipulator, tunnel borer, barbette of warship, and satellite surveillance platform. Acknowledgements The authors would like to acknowledge the financial support of the Natural Sciences Foundation Council of China (NSFC) with Grant No. 50575198. Appendix A. The creation processes of simulation mechanism In order to verify inverse/forward analytic solutions and construct workspace, a simulation mechanism of the 3SPU + UPR parallel manipulator is created by using CAD variation geometric approach in Solidworks [20], see Fig. 1b. The construction processes are explained as follows: 1. Construct B in 2 D sketch. The sub-procedures are: (a) Construct an equilateral triangle DA1A2A3 by the polygon command. (b) Coincide its center point O with origin of default coordinate, set its one side horizontally, and give its one side a fixed dimension Li = 120 cm in length. (c) Transform DA1A2A3 into a plane by the planar command. 2. Construct m in 3 D sketch. The sub-procedures are: (a) Create three lines li(i = 1,2,3), and connect them to form a closed triangle Da1a2a3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001183_robot.1995.525354-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001183_robot.1995.525354-Figure1-1.png",
        "caption": "Figure 1: 3-DOF parllel manipulator",
        "texts": [
            " First, the modeling of the dynamics of a flexible link is formulated as an IEEE lnternatlonal Conference on Robotlcs and Automatlon 0-7803-1965-6/95 $4.00 01995 IEEE uncoupled link. Then, using the natural orthogonal complement, the constraint forces are eliminated from the equations of motion to obtain the governing equations of the manipulator in minimum coordinates. Finally, to show the effect of link flexibility, we obtain some numerical results using the governing equations of motion in a simulation of the manipulator at hand for both rigid-link and flexible-link models. Shown in Fig. 1 is a parallel manipulator composed of three legs OiOi+30i+~, for i = 1 , 2 , 3 , a rigid moving triangular platform 0 7 0 8 0 9 , henceforth abbreviated as MP, and a fixed platform 0 1 0 2 0 3 , assumed rigid as well. Each leg contains two flexible links that are coupled by a revolute joint. The legs are connected to the MP by spherical joints and coupled to the base by revolute joints. This manipulator has three rigid DOF and three motors, located on the fixed platform, that drive the actuated joints. 2 Modeling of an Individual Link Figure 2 shows the manipulator of Fig. 1 with its legs in their deformed configuration, leg i consisting 627 - of the flexible links i and i + 3. Before modeling the dynamics of link i , some definitions are given. The n: (= 7 + ni)-dimensional vector of generalized coordinates of link i is defined as and the mi(= 6 + ni)-dimensional vector of flexzble twist of the same link is vi = [ wT i-T liT(t) 1\u2019 (2) where, with reference to Fig. 3 , & is the 4-dimensional vector of Euler parameters representing the orientation of the frame X i x Z i ( F ; ) with origin at O;, attached to link i , r; is the position vector of joint Oi in the inertial frame XoYoZO (Fo), and u;(t) is the n;dimensional vector of independent nodal coordinates associated with the link flexibility of link i , ni denoting the number of nodal coordinates of the same link"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001376_icca.2005.1528213-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001376_icca.2005.1528213-Figure8-1.png",
        "caption": "Fig. 8. Assembled UAV helicopter.",
        "texts": [
            "2 kbps within 20 miles light of sight. This is far beyond the range that the operating range of the UAV helicopter in the in- ight tests. IV. ASSEMBLING OF THE UAV HELICOPTER The assembling of the UAV helicopter will be introduced in this section in two stages. At rst, the original landing gear of the Raptor 90 helicopter will be revised, and then the designed avionic system will be packed appropriately and installed under the fuselage of the basic helicopter. The assembled UAV helicopter with the necessary components is shown in Figure 8. The original landing gear of the basic helicopter is plastic, which is too weak to undertake amount of bumping momentum when the UAV helicopter is landing on the ground in the automatic or manual mode. There is no enough room in the fuselage of the basic helicopter to install the designed avionic system (see Figure 1). Thus, we have designed and changed the material of the landing gear to aluminum alloy and make a larger room under the fuselage of the basic helicopter for the avionic system. The avionic system is packed in a carbon- ber box",
            " 3) The IMU is taken as the horizontal center of the gravity of the avionic system to locate the other components. Such a design will make the projected point of the center of gravity of the integrated UAV helicopter near to the location of the IMU on the horizontal bottom plane of the carbonber box. If necessary, extra considerations can be taken to balance the distribution of the weight of the components to ensure that the IMU is placed in the horizontal center of gravity of the avionic system. Because of the structure of the integrated UAV helicopter shown in Figure 8, the IMU cannot be placed perpendicularly close to the center of the gravity of the integrated UAV helicopter. This should be taken into account in data processing for the modeling and design of the ight control laws. All of the printed circuit boards and units are x ed on an aluminum alloy frame inside the carbon- ber box. We use pin-and-socket or locked for cable connections, which is robust to shock and vibration. The carbon- ber box is hanged to the fuselage of the basic helicopter with a supporting metal frame hooked on the landing gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002153_j.rcim.2010.05.007-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002153_j.rcim.2010.05.007-Figure2-1.png",
        "caption": "Fig. 2. Hexaglide parallel robot.",
        "texts": [
            " The Gauss\u2013Newton method is very fast, provided that there is a good initial estimate d0 of the geometric parameter vector. Nominal geometric parameter vector dn can be used as the initial estimate. As another approach for solving this nonlinear optimization problem, nonlinear least-square function (lsqnonlin) of MATLAB can be used. This method is not as fast as the Gauss\u2013Newton method but does not need obtaining jacobian matrix A. With the calibration method proposed above, we would like to calibrate a Hexaglide parallel robot. The first Hexaglide parallel robot has been developed at ETH Zurich [22]. As shown in Fig. 2, Hexaglide is composed of a moving platform that is connected to the six legs through universal joints and these legs are connected to six linear actuators or sliders through spherical joints. These sliders that are distributed on three parallel rails are actuated by ball screws and servo motors. Movements of the sliders or the spherical joints guide the platform in 6 DOF. As shown in Fig. 3, two coordinate systems are used for modeling of this robot. Global coordinate system is fixed to the base frame and local coordinate system is fixed to the moving platform whereas its origin is the end-effector center point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003330_b978-0-08-010973-2.50015-x-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003330_b978-0-08-010973-2.50015-x-Figure2-1.png",
        "caption": "FIG. 2",
        "texts": [
            " Demonstration of the vibrational moment M and of the stability of a pendulum with the oscillating suspension point due to this moment is not less effective than the phenomenon of gyroscopic stability of a top. Although experiments with a pendulum with the oscillatory suspension point are simple, they are nevertheless associated with greater difficulties than are those with a top, because a special device is needed to impart rapid oscillations to the suspension point of the pendulum. We carried this out by mean of a simple device presented schematically in Fig. 2. The ball-bearing 2 is set eccentrically at the axis of a small electromotor 1 with a high number of revolutions (we used the motor of a sewing-machine). The traction 3, which sets the lever 4 in oscillation, is connected to the ball race. One end of the lever 4 is moving in a fixed bearing, while the rod 5 of the pendulum is suspended on the other end of the lever in such a way that it may freely oscillate. As shown by expression (31), the following values of the constants provide the stability of the pendulum in the turned position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001672_j.robot.2007.06.001-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001672_j.robot.2007.06.001-Figure2-1.png",
        "caption": "Fig. 2. 2D robot model.",
        "texts": [
            " If the ZMP is within this region which is the convex hull of all contact points between the foot and the ground, the biped robot can walk without falling down [14,15]. However, it is difficult to calculate the ZMP of a 3D robot model as in Fig. 1 because of the coupling between the frontal plane (y\u2013z plane) and sagittal plane (x\u2013z plane) motions. In order to make the model simple, we do not consider the coupling and transform the 3D robot model into two 2D models. A walking motion was generated from two 2D models in [17] where the sagittal plane model has 8 segments and 7 DoFs as shown in Fig. 2(a), and the frontal plane model has 6 segments and 5 DoFs as shown in Fig. 2(b). The ZMP equations of the sagittal plane robot model (Fig. 2(a)) and the frontal plane robot model (Fig. 2(b)) are xZMP = 8\u2211 i=1 mi (z\u0308i + g)xi \u2212 8\u2211 i=1 mi x\u0308i zi 8\u2211 i=1 mi (z\u0308i + g) (1) yZMP = 8\u2211 i=1 mi (z\u0308i + g)yi \u2212 8\u2211 i=1 mi y\u0308i zi 8\u2211 i=1 mi (z\u0308i + g) , (2) where g is the gravity, (xi , yi , zi ) and mi are the position and mass of the i-th point mass (i = 1, . . . , 8), respectively [16,19]. It is noted that the robot with the parameters in Table 1 has a slightly different mass distribution from a human being. In a human body, the upper body, hips and legs constitute 50%, 20% and 30% of the total mass, respectively [32,36]",
            " Therefore, it is possible to assume that hips are kept parallel to the ground in walking robots and their height is kept constant. Because of the robot kinematics, the hip height limits the possible step length. In this paper, the hip height is fixed at 60 cm from the ground in order for the robot to walk with a step length of 40 cm. (v) The swing foot trajectory in the sagittal plane can be represented as follows: x f (t) = \u2212S cos (\u03c0 T t ) z f (t) = h 2 ( 1 \u2212 cos ( 2 \u03c0 T t )) , where (x f , z f ) is the center position of the swing foot in Fig. 2(a), T is the step period, S is the step length and h is the maximum height of the swing foot. This trajectory is different from the swing foot trajectory in human walking. However, this trajectory was used in GCIPM [24], and we also use it to compare the performance of the various trajectory generation methods. This trajectory can reduce the impact produced by the contact between the foot and the ground, but this trajectory may become sticky to the ground at the end of the swing stage. This motion is not as natural as the walking motion of humans, especially in the swing foot trajectory, but it is good enough to describe the walking motion of a robot with limited DoFs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003867_j.mechmachtheory.2018.10.018-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003867_j.mechmachtheory.2018.10.018-Figure1-1.png",
        "caption": "Fig. 1. Experimental test rig.",
        "texts": [
            " In this context, the objective of this Technical Brief is twofold: (a) introduce an original test rig aimed at measuring the windage losses of a pinion-gear pair while avoiding pocketing loss interferences; this imposes that the two members do not mesh and that their rotational speeds are externally controlled in order to reproduce the actual kinematics of the pair, (b) present preliminary results on WPL for several disk/gear arrangements and assess the classic approach based on the addition of individual losses. The experimental test rig shown in Fig. 1 consists of three parallel shafts (further denoted transmission, left and right shafts) connected by pulleys and timing belts at their rear ends, which control the rotational speeds and senses of rotation of all the shafts. A pinion and a gear are mounted at the front end of two of the shafts ( Fig. 1 (a)) which are driven by the timing belt so that the right and left wheels rotate in opposite directions with a speed ratio equal to that of the pinion-gear pair if it were in mesh ( Fig. 1 (b)). The technical specifications of the test rig are given in Table 1 . In what follows, the two gears are not in contact but can be positioned close enough so as to reproduce the actual windage conditions from a geometrical and kinematical viewpoint, i.e. generate similar air flows around the two gears while avoiding tooth friction and pocketing which, otherwise, would interfere with WPL measurements. The system is operated by a motor via a friction wheel which multiplies the rotational speed of the transmission shaft up to 10,0 0 0 rpm",
            " A typical WPL measurement sequence is as follows: \u2022 The friction wheel is pressed against the transmission shaft by the pneumatic jack. \u2022 The electric motor operates the whole system until the specified speed is reached. \u2022 The friction wheel is moved apart from the input shaft by the jack and the system comprising the shafts, gears, pulleys and belt carries on rotating but with decreasing rotational speed because of the overall power losses. During the deceleration phase, speed is continuously measured by a magnetic encoder (see Fig. 1 (a)) as illustrated in Fig. 2 representing a typical speed versus time recording. In order to minimise the measurement scatter possibly caused by thermal transients, the test rig was operated at con- stant speed for about one hour before power losses were actually measured. Speed is measured on the transmission shaft only and the other rotational speeds are deduced from the pulley diameters. The power loss can then be expressed using the Kinetic Energy Theorem as: P = d dt ( \u2211 i 1 2 I i \u03c9 2 i ) = d dt ( \u2211 i 1 2 I i ( n 1 n i )2 \u03c9 2 1 ) = \u03c9 1 d \u03c9 1 dt ( \u2211 i I i ( n 1 n i )2 ) where I i is the inertia of the i th shaft determined partly experimentally and partly numerically, \u03c9 i = n 1 n i \u03c9 1 is the rotational speed of shaft i (shaft 1 is the transmission shaft) and n i is the number of teeth for the i th pulley"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003380_bf02654739-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003380_bf02654739-Figure6-1.png",
        "caption": "FIG. 6. P o l a r o g r a p h i c m e a s u r e m e n t o f the a n t i o x i d a n t a c t i v - i t y o f a - t o c o p h e r o l . E m u l s i o n s w e r e 10 '% l a r d ( L ) a n d 1 0 % m e t h y l l i n o l e a t e ( M L ) . A l p h a - t o c o p h e r o l ( ~ - T ) w a s 1 X 10-*M.",
        "texts": [],
        "surrounding_texts": [
            "Appara tus similar to that described by Packer (7) was used. The complete apparatus with a 10 m amp recorder (Var iaa G-11A) is shown in Figure 1. De- 1 Supported in par t by Grant 1%G-5759 from the National Institutes of Health. s On sabl>atical leave from Universi ty of Wyoming, Laramie, Wyo. 52 scriptions of the silver and pla t inum electrodes and the bridge circuit will be given since the original source (7) is not readi ly available. For the plat inum electrode a piece of l-ram boTe soft glass tubing is heated and drawn. A 1 in. piece of #32 size plat inum wire is heated unti l red hot and then dropped into the drawn-out glass tube and the tube tapped gently. The tube is heated at the tip unti l the glass melts and surrounds the platinum. The plat inum tip and glass are t r immed so that the wire is sealed flush with t he end. The exposed tip is polished with a fine abrasive unti l microscopic examination reveals a smooth polished wire tip firmly sealed in the glass with no air bubbles in the seal. The glass tube is filled with mercury, and a soft iron wire is inserted into the mercury to carry the current generated to the center e r a shielded cable. A short length of sterling silver wire is used as the other electrode and is connected to the ground of the shielded cable and thus to the bridge circuit shown in Figure 2. For the reaction vessel a short tube, capacity approx 3 ml, is attached to a 60 revolution/rain synchronous rooter by a plastic bushing to provide a rotating cuvette. The suction device is used to empty and assist in cleaning the cuvette. The reaction system used for the determinations consisted of 10 or 30% (v:~/) lipid emulsified in a phosphate buffer with a minimal amount of solid emulsifier (Myrj 53), and hemoglobin catalyst. The phosphate buffer contained a concentration of 0.01M KC1 and sufficient K2HP04 and KH,~PO4 to yield a concentration of 0.1M and a pH of 7.2. The following lipids were used at various times: linoleie acid (Nutri t ional Bioehemicals Co.), s tr ipped lard (Distillation Products Co.), and methyl linoleate (Pacific Vegetable Oil Co~rp.). S t r ipped lard oxidized at a satisfactory rate, however, some difficulty was encountered in prepar ing and maintaining satisfactory emulsions. Linoleie acid and methyl linoleate were equally satisfactory and were used for nearly all determinations. The emulsion was stable for 30' rain or longer; since slow oxidation occurs without addition of catalyst fresh emulsions should be prepared at 30 rain intervals. The emulsions were prepared by use of either a hand piston homogenizer or a glass FEBRUARY~ 1963 I-IXMILTON AI~D TAPPEL: ~kNTIOXIDANTS BY A ]:~APID POLARO(~RAPtIIC METHOD 53 tissue homogenizer. The materials to be tested were either added in weighed quantit ies to the emulsion or added in a buffer solution, if soluble, replacing a like amount of buffer. I f they were soluble in organic solvents the desired amount was added to the emulsifying vessel and the solvent removed by evaporat ion prior to addit ion of the emulsion or emulsion components. The electrode t ip should be dipped into dilute hydrochloric acid and rinsed prior to use and should remain in a fixed location in the euvette dur ing the determinations. The emulsion at 26-30C is shaken in air to sa turate with air and 2 ml is pipet ted into the cuvette. The concentrat ion of oxygen of air sa turated water at 26C is 240 ~M. The solubility of oxygen in the lipid phase is much greater. Wate r comprises 90% of the emulsion system and the l ipid 10%. We mainta ined a relat ively constant temp, used only compara t ive measurements, and expressed the results in relative amounts of oxygen consumed dur ing lipid peroxidation. The polarizing voltage was adjusted to 0.7V. When the electrode is in position and the emulsion added the pen is adjusted to 100 on the recorder with the sensit ivity coarse and fine resistors. A 2 X 10-~!V[ hemoglobin solution was measured by micropipette, and amounts of 5-20 ~1 were t rans fe r red to a small loop glass rod and added to the emulsion with thorough stirring. Blank determinations, using same amount of hemoglobin were run at the beginning and near the end of the experimental period. Duplicate determinations were made and the average time values of two runs were used. The results are conveniently expressed as protective indices ( P I ) calculated for the t ime needed to utilize 90% of the dissolved oxygen. The protective indices are the ratios of the time required for reaction of 90% of the dissolved oxygen in the antioxidan t system divided by the t ime for the control. The t ime required for the reaction of oxygen varied somewhat f rom one day to another, however, i f the control and test reactions were run dur ing the same experimental period the protective indices for the same reaction were near ly identical f rom one experimental period to another. Several antioxidants or different concentrations of the same ant ioxidant can be evaluated within a short period of t ime with precision. Results and Discussion In this method any of a number of lipids might be used. We found l~roleie acid, methyl linoleate, and lard quite sa t i s fac~ry . These ]ipids peroxidize rap id ly enough to make ,pQssible rapid determinations but not so rap id ly th~t~:~.the ant ioxidant effects of relat ively weak antioxid:ants cannot be detected. Typical oxidation curves are shown in F igures 3, 4 to i l lustrate the variables of:. 1) kind and amount of lipid present in th~ emulsign , and 2) the amount of hemoglobin added. Since hemoglobin is a powerful l ipid peroxidation catalyst the amount added great ly affects the oxida- 2 0 - - Z t l J x 40 O w _ J o 60 , 0 0_i , , L , I0 0 I 2 $ 4 5 MIN FIG. 3. Ra te s of oxygen r eac t i ng in pe rox lda t ion of ] inoleate emuls ions wi th hemoglob in ca ta lys t . A. 10% linoleic acid, 2 \u2022 10-T1V[ hemoglobin . B. 10% linoleic acid, 1 \u2022 10-7M hemoglobin . C. 30% linoleic acid, 2 \u2022 10-~IV[ hemoglobin . D. 30% linoleic acid, 1 X 10-xM hemoglobin . t ion rate. We use 10% v / v of lipid in the emulsion since this emulsion appears to be more sensitive to ant ioxidant effects, oxidizes at a slightly fas ter rate, and the emulsion is more stable than is a 30% lipid emulsion. I f we are tes t ing strong antioxidants we use 1 oz' 2 X 10-7M hemoglobin, and i f a very weak ant ioxidant we use 0.5 \u2022 10=-7!V[ hemoglobin. Except in unusual situations 1~ \u2022 10-7M hemoglobin is used as this gives a fas t control reaction, usual ly less than 2 rain for 90% oxygen uptake, and a good degree of sensitivity. A s e a n b e seen from: F igure 4 the length of t ime required for 90% oxygen uptake varies f rom 96 see for :2 \u2022 10~7M hemoglobin to 211 see for 0.5 \u2022 10-7M hemoglobin w h e n the emulsion contains 10% methyl- linoleate. 9 :. : Da ta to indicate t h e ~reprodueibility of results for b lank determinat io~ run, at different intervals dur ing a single day are shown in Table I. These results indic a t e the excel lent : : reproducibi l i ty of results by this method when: the same ~ emulsion is used. In actual 0 2C 4C ~, ~r ~ y IOC 0 I 2 3 4 MIN F I G . 4 . -Effect o f incl 'e~sed hemoglob in on t h e ra te of oxygen reac t ing . The e m u l s i 0 f l . l s 1 0 % me thy l l inoleate and hemoglob in cbiic6ntratid~s are2, 1, ~nd 9 X 10-7M. 54 T H E J O U R N A L OF T H E A M E R I C A N 0 I L C H E M I S T S ' S O C I E T Y VoL. 40 0 / , , / /, / / / / N00 ,:/ ~40 /NO\"NNO ANTIOX S / / , P B H T 9 B/HB/HA~ . .s,,,~G - o w, IOC I I I 4. $ II IO MIN F r o . 5. P o l a r o g r a p h i c e v a l u a t i o n o f a n t i o x i d a n t s . T h e r e a c - t i o n s y s t e m i s 1 0 % m e t h y l l i n o l e a t e , t h e c a t a l y s t i s 1 \u2022 10-~IK h e m o g l o b i n . A n t i o x i d a n t s a t 1 \u2022 10-dM a r e : b u t y l a t e d h y d r o x y - t o l u e n e ( B H T ) , b u t y l a t e d h y d r o x y a n i s o l e ( B t t A ) , n o r d i h y d r o - g u a i a r e t l c a c i d ( N D G A ) , a n d p r o p y l g a l l a t e ( P G ) . practice over a 3 month period some var iabi l i ty in the times required to consume 90% of the dissolved oxygen was noted. These variat ions for different dates using the same sample and amounts of lipid, s imilar buffer, and hemoglobin catalyst varied f rom 90-141 sec with a mean value of 112 and a s tandard deviation of \u2022 This var ia t ion was largely the resul t of the technique used. We measured the buffer and lipid with graduated cylinders and some loss of mater ial occurred using the emulsification process. This var ia t ion is not serious when it is realized tha t the protect ive index values were calculated using exper imental and blank values obtained each period with the same emulsion. The values obtained for the same protect ive index determinat ion per formed on different occasions were near ly identical. I t should be emphasized tha t this method measures only the ant ioxidant act ivi ty exerted dur ing a br ief port ion of the total period of lipid pero~idation, however, i t is ve ry useful in determining the existence or absence of ant ioxidant act ivi ty or peroxidizabil i ty by certain var ia t ions in system components. We have found it useful as a means of indicat ing and measuring the ant ioxidant effects of low concentrations of known powerful ant ioxidants present in the reaction system. Data on some of the powerful ant ioxidants tha t are widely used in indus t ry are shown in F igure 5. The protect ive indices calculated f rom the polarographic measurements of some ant ioxidants are shown in Table I I . The antioxidants grea t ly extend the t ime required to utilize 90% of the dissolved oxygen and the reaction curves are slightly variable in shape. I t is interest ing to note tha t despite the addit ion of a powerful ant ioxidant the reaction proceeds, in most instances, unti l 90% of the oxygen is utilized. In the T A B L E I I Protect ive Indices Determined by Po la rograph ic :~fethod a Ant ioxidant a-Tocopherol .......................................... Butylated hydroxytoluene ..................... Butylated hydroxyanisole . . . . . . . . . . . . . . . . . Propyl gallate ........................................ Novdihydroguaiaret ic acid .................... N N'-Diphenyl p-phenylene diamine ..... 1 ,2 -n ihydro 6-ethoxy 2,2,4-tri- methyl quinoline ................................ ~Iydroquinone ....................................... Pyrogallol .............................................. Quercetin .......... : .................................... 1 X I O - K IXIO-4M ...... 3.7 4.2 5.7 5.2 ii:~ 2.5 7.2 3.4 2.0 1 X 10 \"-~M 1.2 3.8 2.8 1.8 4.2 1.9 a Methyl linoleate (10%) -]- antioxidant Jr- 1 X 10-7M homo lobin. interest of t ime conservation we often found it necessary to decrease the concentrat ion of these a n t i o x i - dants in the emulsion. I f for example we use 1 \u2022 10 -3 M NDGA the time required for 90% oxygen consumption would be an hour or more. Results obtained by use of the polarographic method can be supplemented by use of manometr ic techniques if i t seems advisable to follow the ant ioxidant effects dur ing several hours or days of the l ipid peroxidation. S t r ipped lard is a sat isfactory lipid for use in the emulsion since it is readl ly peroxidized. The shaPe of the reaction curves shown in F igure 6 indicates, certain differences between the rates and kinetics of the blank reactions using lard and methyl linoleate and 1 \u2022 I0-TM hemoglobin. The differences in the shapes of the curves with lard and methyl linoleate are evident even when a-tocopherol is added to the system. ~-Tocopherol has been shown by many investigators to be a weak ant ioxidant when tested by different methods. Manometr ic studies indicate that the protective indices of 1 \u2022 l@3M a-tocopherol (8), added to hemoglobin-catalyzed linoleic acid emulsion were 1.3 at the end of 0'.5 hr and 1.6 a f te r 1 hr. These values compare favorably with protective indices of 1.5 for 1 \u2022 10-3M a-tocopherol added to the methyl linoleate and lard emulsions as shown in F igure 5. These results indicate the close agreement between the protective indices for the same concentration of an antioxidant when included in different lipid sys tems and measured by the polarographic method. Fur ther , the protect ive indices obtained by the polarographic method compared closely with the values obtained by the manometr ic method (6,8) regardless of whether a weak or a s trong ant ioxidant is being tested. We found the polarographic method readily adaptable to a s tudy of the ant ioxidant propert ies of certain animal and plant fract ions that we re screened for ant ioxidant act ivi ty and synergism of certain amino acids, selenoamino acids, selenium compounds, and others. Many of these compounds are weak antioxidants and this method is readily applicable to dete rmining weak ant ioxidant activity. The simplicity, ease, and speed of ca r ry ing out this determination, and the accuracy and reproducibi l i ty of this method are factors tha t indicate its usefulness for screening substances for ant ioxidant act ivi ty and measur ing this activity. R E F E R E N C E S 1. Official and Tentative Methods of the AOCS, Active Oxygen Method Cd 12-57. 2. Pohle, W. D., R. L. Gregory, and J. R. Taylor, JAOCS 89, 226 (1962) . 3. Gearhar t , W. ~ . , B. N. Stuckey, and J. J . Austin, JAOCS 34, 427 (1957) . 4. Olcott, H . S., and E. Einsot, JAOOS 35, 161 (1958) . 5. Watts , B. ~ . , Adv. Food R es. 5, 1 (1954) . . Lew, Y. T., and A. L. Tappel, Food Tech. I0 , 285 (1956) . 9 Packer , L., Wal te r Reed A r m y Institute of Research, Report 1 4 3 - 57, 13 pp. (1957) . 8. Tappel, A. L., W. D. Brown, H. Zalkin, a n d V. P . Maier, JAOCS 88, 5 (1961) . [ R e c e i v e d M a y 28, 1 9 6 2 - - - A c c e p t e d O c t o b e r 23, 19 '62]"
        ]
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.3-1.png",
        "caption": "Fig. 1.3. Aircraft \u03d5-rotation",
        "texts": [],
        "surrounding_texts": [
            "The aerodynamic coordinate system is a mobile coordinate system (c.g.; Xaero, Yaero, Zaero) associated with the orientation of the aircraft velocity vector in relation to the air mass (Vair) - see Fig. 1.4 Its origin is the centre of gravity. The longitudinal axis Xaero is oriented in the direction of this \u201cair\u201d velocity vector. In relation to the aircraft coordinate system, the coordinate system associated with the aerodynamic coordinate system is obtained by a rotation of angle \u03b1 (angle of attack) around the YAC axis and of angle \u03b2aero (aerodynamic sideslip) around the ZAC-axis. The transformation matrix is: MAEROR\u2192AC = \u239b\u239d cos\u03b2aero sin\u03b2aero 0 \u2212sin\u03b2aero cos\u03b2aero 0 0 0 1 \u239e\u23a0\u239b\u239dcos\u03b1 0 \u2212sin\u03b1 0 1 0 sin\u03b1 0 cos\u03b1 \u239e\u23a0 = \u239b\u239d cos\u03b1 \u00b7 cos\u03b2aero sin \u03b2aero 0 \u2212sin\u03b2aero \u00b7 cos\u03b1 cos\u03b2aero sin \u03b1 \u00b7 sin\u03b2aero sin\u03b1 0 cos\u03b1 \u239e\u23a0 (1.2)"
        ]
    },
    {
        "image_filename": "designv10_10_0003073_j.ijfatigue.2012.09.008-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003073_j.ijfatigue.2012.09.008-Figure10-1.png",
        "caption": "Fig. 10. Compressive residual hoop stress state within raceway segment prior to ball impact.",
        "texts": [
            " The residual stresses within the FE model can be applied many different ways, but in this analysis an external elastic displacement was applied at either end of the raceway segment to induce the desired bulk compressive hoop stress of 400 MPa. This is similar to applying an increase in temperature and coefficient of thermal expansion to the raceway segment while it is constrained at either end. In that case the segment is allowed to expand a certain amount and then elastically compressed to the desired stress state. Fig. 10 shows the initial residual hoop stress state of the FE model prior to ball impact with the spall edge. All stresses are compressive and their values according to their color1 are indicated in Fig. 10. The gradient in residual stress is due to the spall edge geometry. Note the residual stress is a compressive 400 MPa throughout the raceway segment with the exception of the immediate spall edge. At the free surface of the spall edge, the residual stresses drop to 70 MPa at the location where initial ball contact occurs. Boundary conditions cannot be applied to the spall edge in order to induce more compressive stress because this is the same location as the ball impact. The compressive residual stress of 400 MPa is present just below the spall edge at a depth of 1 For interpretation of color in Fig. 10, the reader is referred to the web version of this article. 127 lm. This is likely to occur in the actual spalled bearing but cannot be verified directly by XRD because the spot size of 1 1 mm is too large to detect this lack of residual stress on the immediate spall edge where the actual cracks are forming. The fact that the residual compressive stresses are so low at the spall edge may not affect the formation of plastic strain within this region when compared to a spall edge with zero initial compressive stress",
            " As an example, Table 2 shows the maximum principal plastic strain, the plastic zone width and depth, and the residual-tensile hoop, hydrostatic, and maximum principal stresses for two separate ball impact analyses that used steel balls and included the gradient in flow curve. Due to the amount of data presented in the following tables the contour plots of the residual plastic strain and stresses will not be shown. The only variable here is the absence or presence of initial residual stress. It is shown that the maximum plastic strain increases by 2% and that the plastic zone depth can increase by 12% when there is no initial residual compressive stress present. Recall from Fig. 10 that the initial residual compressive stresses were relatively small within the spall edge where the most severe plastic strains are forming. This explains the relatively minimal change in maximum principal plastic strain observed in this region (2%). Beneath the spall (depth = 127 lm), however, where the compressive stresses are present, the plastic zone depth has been reduced by 12% in this test case. Reduction in plastic zone volume is beneficial to materials undergoing many stress cycles as this reduces the probability of crack initiation when compared to larger plastic zones and a similar number of stress cycles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002859_1.4810959-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002859_1.4810959-Figure1-1.png",
        "caption": "FIG. 1. Considered configurations and notation; (a) bubble or drop supported by a spherical bowl (constraint of SS), (b) bubble attached to a ring (constraint of BS).",
        "texts": [
            " Subsequent studies regarding free bubbles or drops have improved the theory by including higher-order terms,7, 13 have focused on nonlinear behavior,14\u201317 or have studied the effects of surface-active agents.4, 8, 18\u201320 A bubble or drop that is in contact with a solid support behaves differently from the free bubbles discussed above. Strani and Sabetta have analyzed both inviscid21 and viscous22 cases (the former of which will be referred to as SS hereafter). They assume a spherical drop, of which the bottom part is constrained (unable to move) (Figure 1(a)). In this case, unlike a free drop, a supplementary low-frequency mode of oscillations appears; this mode, for which the order k = 1, is degenerated (\u03c91 = 0) in the case of free bubbles or drops. Bostwick and Steen23 (referred to as BS hereafter) have analyzed eigenmode oscillations of a spherical drop that is pinned to a ring (Figure 1(b)). The same conditions have recently been studied by Ramalingam et al.24 and Prosperetti,25 who explicitly account for the discontinuity of the interface slope at the pinning. The dynamics of supported drops have been studied experimentally2, 26\u201332 and numerically.33, 34 Rodot et al.26, 27 have demonstrated the strong influence of the size of the support on the oscillation frequency of a drop. With tiny mercury droplets, Smithwick and Boulet28, 29 have observed agreement between experimentally measured eigenfrequencies and Strani and Sabetta\u2019s21 predictions",
            " The Appendix presents an alternative form of the analysis, in which the oscillatory shape is decomposed into an arbitrary series replacing Legendre polynomials; this latter approach should be considered by readers interested in changes in the interface slope at the point of contact with the support. The present paper is accompanied by the supplementary material,37 which presents some principal steps of the analysis in more detail. An axially symmetric deformation of the bubble (or drop) is characterized by the deformation \u03b7 = \u03b7(t, \u03bc) from the spherical shape with radius R (Figure 1(b)), where \u03bc is the cosine of polar angle, \u03bc = cos \u03b8 . The deformation is approximated by the series \u03b7(t, \u03bc) = N\u2211 j = 0 b j (t)Pj (\u03bc), (3) where Pj is the Legendre polynomial of order j and N is the order of approximation. Using this approximation, the actual deformation is described by a set of N + 1 coefficients b0, b1,. . . , bN, which are functions of time. The first objective of this analysis is to formulate equations of motion (differential equations for bj). The present analysis can also be carried out using series that are based on functions other than Legendre polynomials, as shown in the Appendix",
            " The non-zero 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: 129.100.58.76 On: Tue, 07 Oct 2014 06:49:34 V is also considered because volume variations can be imposed (e.g., by injecting a gas into the bubble). Another constraint is due to contact of the bubble/drop with a solid support. Its simplest implementation was studied by BS,23 who considered the situation where the bubble/drop\u2019s interface is pinned to one or more rings (Figure 1(b)). The present study considers pinning to M rings, which is characterized by positions \u03bck = cos \u03b8\u0303k and is discerned by index k = 1,. . . , M. The pinning constrains the motion of the interface as described by \u03b7(t, \u03bck) = \u03b7k(t), (6) where \u03b7k(t) is the prescribed motion of the interface at the kth pinning location in the radial direction. It is useful to express the kth constraint in the form gk(b1,b2,. . . ,bN, t) = 0. Using Eq. (6) with the decomposition (3) and keeping only the leading powers of bj, we obtain the following formula: gk(b1, b2, ..., bN , t) \u2261 N\u2211 j = 1 b j Pj (\u03bck) + V (t) 4\u03c0 R2 \u2212 \u03b7k(t) = 0 (7) for k = 1,. . . , M. For brevity, constraint(s) (7) is referred to as the BS constraint hereafter. A different type of constraint due to a solid support has been considered by SS.21, 22 In their analysis, a zero deformation was imposed on the entire supported portion of the interface (\u03b7 = 0 for \u22121 \u2264 \u03bc \u2264 \u03bca, where \u03bca = cos \u03b8\u0303a), as shown in Figure 1(a). This constraint has been generalized by imposing non-zero deformation ( \u03b7) on any portion of the interface. A \u201cmarking\u201d function f(\u03bc) determines which parts of the interface are constrained (f = 1 for constrained interface and f = 0 for freely movable interface). Thus, the constraint is given by \u03b7(t, \u03bc) = \u03b7(t, \u03bc) if f (\u03bc) = 1. (8) Hereafter, the deformation is prescribed only to the bottom part of the interface (f(\u03bc) = 1 for \u22121 \u2264 \u03bc \u2264 \u03bca). Other configurations can be studied by changing f(\u03bc) appropriately"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000786_1.1518501-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000786_1.1518501-Figure8-1.png",
        "caption": "Fig. 8 Relative displacements for pitch point p and of contact c",
        "texts": [
            " Dooner and Seireg use the axis of the twist $ along with the radius r to define a cylinder of osculation to a spatial curve.4 Associated with each geodesic curve at a point on a surface is a cylinder of osculation. A cylindroid is defined by the loci of central axes of these cylinders of osculation. 4The axis of the twist to parameterize the instantaneous displacement of a point on the striction curve ~of a ruled surface! is the well know Disteli axis. rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/20 Depicted in Fig. 8 are two twists $'i and $'o 5 perpendicular to the tooth contact normal $ l along with the two velocity components V'pi and V'po . The twist $'i is fixed in the input body and is used to parameterize the displacement of the pitch point p in the polar direction in terms of the displacement of the tooth surface normal $ l . Similarly, the twist $'o is embedded in the output body and parameterizes the displacement of the pitch point p in the polar direction in terms of the displacement of the tooth surface normal $ l ",
            "org/about-asme/terms-of-use Downloaded F termine gear tooth curvature in terms of cutter geometry. Principle or extreme curvatures for both the input and output gear along with the included angle between the principle directions associated with these extreme curvatures are necessary to determine the relative gear tooth curvature. The principle curvatures bk i and dk i for the input gear tooth are determined by introducing a curvature cylindroid. An input curvature cylindroid is defined by the two twists $'i and $ i i ~see Fig. 8! whereas an output cylindroid is defined by the two twists $'o and $ io . Corresponding to bk i and dk i are the pitches bhi5 dhi50. A similar procedure is repeated for the output gear element in order to obtain the extreme curvatures bko and dko . The two curvature cylindroids ($'i ;$ i i) and ($'o ;$ io) are different than the two cylindroids ($'i ;$'o) and ($ i i ;$ io). The two cylindroids ($'i ;$ i i) and ($'o ;$ io) interest along the twist $j that parameterizes the displacement of a point on the gear tooth surface ~either input or output",
            " In general two gear surfaces are in line-contact and that the relative curvature between two gear surfaces is a parabolic point as depicted in Fig. 10. Nominal pitch contact \u201eq\u00c40\u2026 . Expressions for relative curvature are simplified for the special case where the nominal contact is restricted to coincide with the reference pitch surface. This scenario occurs when the distance q between the point of contact c and the point p where the tooth contact normal $ l intersects the reference pitch surface is zero ~see Fig. 8!. Dk' and Dk i define the relative curvatures in the polar and spiral directions respectively. For the special case q50, h50 and A i reduces to A i5~a i i2b io! 1 q . l1;-3qIn the limit as q approaches zero, A i reduces to 0/0 and hence A i is indeterminate. Applying L\u2019Hospital\u2019s rule to determine A i for q50 produces limit q\u21920 A i5 r i i r i i 2 1h i i 2 2 r io r io 2 1h io 2 5k i i2k io . (26a) The normal curvatures k i i and k io for the tooth surface are evaluated in terms of the tooth spiral and projected onto the contact normal $ l "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001368_icar.2005.1507466-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001368_icar.2005.1507466-Figure3-1.png",
        "caption": "Fig. 3. A sideview diagram of \u201dB. B. Rider\u201d",
        "texts": [
            " For instance, they are used in medical, transport, amusement and remote control. Therefore, many researchers worked on their development. To develop available vehicles is very important. Our goal is to develop a small-size omni-directional vehicle for personal mobility. It would be useful for many people. II. SPECIFICATIONS OF \u201dB. B. RIDER\u201d In this section, we describe our robot that we named \u201dB. B. Rider\u201d (Basketball Rider). We named our robot after riding on a basketball. Fig.1 and Fig.2 show overview and downside-view of \u201dB. B. Rider\u201d. Fig.3 shows the robot\u2019s side view diagram. Fig.4 shows PC structure in the robot. TableI shows specifications of the robot. And tableII shows control PC\u2019s specifications. The seat, which is mounted on our robot, is made of tree. A human, who rides on the robot, can sit on it. There is a force torque sensor mounted under the seat. It is to sense forces and torques, when one riding on the robot shifts the center of mass. If he/she wants to go somewhere, he/she just shifts his/her weight to a direction desired"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002208_tie.2009.2031190-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002208_tie.2009.2031190-Figure3-1.png",
        "caption": "Fig. 3. 2-D finite-element analysis of demonstrator machine, showing no-load flux distribution.",
        "texts": [],
        "surrounding_texts": [
            "The choice of pole and tooth number is dependent upon a number of factors. The pole number is dictated by a compromise between increased mass and increased iron loss. The Heliplat motor is 16 pole and the Solar Impulse motor, 24 pole, but if iron loss is not significant, then higher pole numbers can be beneficial because the core-back depth can be reduced, thereby, reducing mass. At high pole numbers, the core-back depth eventually falls to the point where it cannot be reduced further without compromising mechanical integrity. For the Zephyr motor, this occurs at a depth of 2.5 mm, which can be achieved with a 36-pole motor."
        ]
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure8-2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure8-2-1.png",
        "caption": "FIGURE 8-2 Cannon-Fenske VIS cometer for transparent liquids. (From 1976 Supplement to Book of ASTM Stan danis, Test for Kinematic Viscosity D44S.)",
        "texts": [
            " Sir Isaac Newton deduced the following relationship for a fluid being shear-stressed between two plates (fig. 8-1): where F = force 11 absolute viscosity A area v = velocity v F=flA h h clearance between plates (1) A fluid is said to be Newtonian if the viscosity is constant, except for temperature changes, or FIA 11 = vlh shear stress ------ = constant rate of shear (2) The absolute value of 11 can be determined by several methods. The two most common methods are based on (1) laminar flow through some type of a capillary tube such as the Cannon-Fenske viscometer shown in figure 8-2 or (2) some type of rotational viscometer such as the MacMichael viscometer shown in figure 8-3. The latter instrument was designed for very viscous liquids, but variations of this type of instrument have been adapted to many kinds of fluids. If SI units are used in equation 2, the coefficient of viscosity, 11, will be VISCOSITY 185 in pascal-second (Pa . s = N . s/m2 ). If the English system of units is used in equation 2, the viscosity will be in reyns (lb\u00b7 s/in. 2 ). Conversion to SI units can be made as follows: 1 Pa "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure3.6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure3.6-1.png",
        "caption": "Fig. 3.6. Definition of reference frames",
        "texts": [
            " Hagstro\u0308m However large the flight envelope of GAM, ADMIRE\u2019s is smaller since it is constrained by the bundled FCS. It is scheduled for altitudes up to 6 km and Mach numbers up to 1.2. With a different FCS the data is valid up to 20 km and Mach 2.0. In Figure 3.5, the definition of the direction of the forces and moments from the aerodata is shown. The aerodynamic forces are given in the form of body fixed normal, tangential and side forces. The aerodynamic reference point (OU ) and the centre of gravity (OB) are given in Figure 3.6. The reference point is fixed but the location of the c.g. can change. In the nominal case these two points coincide. Deviation in c.g. from the aerodynamic reference point will give additional effects in the moment equations. The aerodynamic model is built up in a conventional way, by interpolating (unstructured) data tables to obtain the different contributions. Different aerodata tables are used at different Mach numbers. A transition is made between Mach numbers 0.4 and 0.5 and at Mach number 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002030_tro.2007.906250-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002030_tro.2007.906250-Figure2-1.png",
        "caption": "Fig. 2. Robot configuration.",
        "texts": [
            " 2) x(tk ) and x(tk\u22121 ) are the position at k and k \u2212 1 sample times, respectively. Then, the passivity of the sampled system can be defined as follows. Definition 2: The one-port network N with initial energy storage E(0) is sampled time passive if and only if E(tk ) = k\u2211 j=0 F (tj )(x(tj )\u2212 x(tj\u22121 )) + E(0) \u2265 0 (2) where j = 0, 1, 2, . . . , k = 0, 1, 2, . . . , for sampled force F (tj ) and position x(tj ). Note that, if E(tk ) \u2265 0 for every k, the system dissipates energy, and if E(tk ) < 0, the system generates energy at time tk . Fig. 2 illustrates the robot\u2019s model and coordinates, where \u03a3O is the global coordinates frame. We assume that the robot\u2019s center of gravity (COG) is at the midpoint of the hip joints, and define it as the origin of the body coordinate frame \u03a3B . The position and posture of the robot\u2019s foot can be described with respect to this coordinate frame. 3-D vectors pr and pl represent the position of robot\u2019s right and left foot, respectively, and 3 \u00d7 3 matrices Rr and Rl represent the posture of robot\u2019s right and left foot, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001016_s0921-8890(02)00351-2-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001016_s0921-8890(02)00351-2-Figure2-1.png",
        "caption": "Fig. 2. Five-link biped robot.",
        "texts": [
            " In the regularization network, the number of hidden neurons is the same with the training data. In the generalization RBFNN, the number of hidden neurons is smaller then the number of training samples. The hidden neurons are added one by one until the mean square error (mse) gets smaller than the desired one. The generalization RBFNN is used when the number of training data is large. During walking, the arms of the humanoid robot will be fixed on the chest. Therefore, it can be considered as a five-link biped robot in the saggital plane, as shown in Fig. 2. The motion of the biped robot is considered to be composed from a single support phase and an instantaneous double support phase. To satisfy repeatability conditions, the postures at the beginning and at the end of the step are considered to be the same. Also, the angular velocities of links 1 and 2 at the end of the step become equal to the angular velocities of links 5 and 4 at the beginning of the step, respectively. The friction force between the robot\u2019s feet and the ground is considered to be great enough to prevent sliding"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000775_iros.2000.894664-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000775_iros.2000.894664-Figure2-1.png",
        "caption": "Figure 2: The AESOP arm",
        "texts": [
            " Furthermore there is no scaling of the instrument\u2019s velocity depending on the position of the trocar point, which means that the velocity is independent of the actual working geometry (see Fig.1). For further control algorithms, like force-, impedance- or shared-control a Cartesian interface is also useful. 2 Kinematic In this section the kinematic of the AESOP robot is presented. After that we show how the pivot point is - 565 - 0-7803-6348-5/00/$10.00 02000 IEEE. 'instru= V. instrument j i __. . . . . . . . . .. . . . . . . . . .. -. . :j The robot consists of four active joints, the linear axis 6 1 and three rotational joints &,&,e7 and two passive joints 65 and $6 (see Fig. 2). These two passive joints are not motor driven and have no breaks. They guarantee that no forces are exerted to the entry point t = [t,, t,, tZIT (see Fig. 1). This entry point can be considered as a geometric constraint to the kinematic that binds two degrees of freedom (DOF). As a result, inside the abdomen only four DOFs are left (see Fig.3 ). Additionally the robot consists of another rotatory joint 04, that can be used to suit the geometry to the actual situation. The transformation from the tool-center point frame to the world frame is: with and A ( O i ) representing homogeneous transformations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000901_irds.2002.1041594-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000901_irds.2002.1041594-Figure2-1.png",
        "caption": "Figure 2: The geometric view of kinematic pammeters.",
        "texts": [
            "00 02002 IEEE 2200 2 Unmanned Elec t r i c Bicycle In this section, we consider the kinematic and dynamic model of electric bicycle which has the load mass balance mechanism which plays important role in controlling the direction of bicycle. 2.1 Kinematic and Dynamic Models A bicycle is depicted in Fig. 1. The main problem discussed in this paper is to find the control strategy for controlling the load mass, steering angle and driving wheel speed which makes bicycle go forward without falling down. The geometric view of the bicycle model is shown in Fig. 2. Let pf denote the center point of the steering front wheel and p, the center point of the driving rear wheel. Let L be the distance between pf and p,. We assume that the mass center of bicycle is located in the middle b e tween center points of the steering and the driving rear wheel. We denote by wr the angular velocity of the driving wheel, by OL the steering angle, by r$ the tilt angle of the center of mass of bicycle with respect to the normal axis of the ground, by hl the height of the center of mass of bicycle from the ground, by h2 the height of the load mass from the ground and by rr the radius of driving wheel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002839_s10514-013-9343-2-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002839_s10514-013-9343-2-Figure7-1.png",
        "caption": "Fig. 7 Comparing inertia shaping about CoM (left) and CoP (right). Shaded solid ellipsoids and ellipsoids with dashed outlines, in each case, denotes current and desired inertia matrices, respectively. Note that inertia shaping about the CoP allows a movement of the CoM (G to G \u2032), which the other does not",
        "texts": [
            " We have earlier performed inertia shaping about the CoM (Yun et al. 2009). However, since the desired angular velocity used to derive the desired inertia matrix is computed about the CoP, it is preferable to perform inertia shaping about CoP as well. Moreover, partial inertia shaping about CoP is more effective than that about CoM because the arm and the upper body configurations make more significant contributions to the CRB inertia about CoP. So, the desired inertia matrix Id derived here is about CoP i.e., I P d as shown in Fig. 7. In the previous section, we described the general nature of the two strategies that we use to change the fall direction of humanoid robots. However, there are additional details to pay attention to: a specific control needs to be selected along with the associated parameters and it is to be executed at a specific time and for a specific duration. Moreover, the implemented control may contain the two strategies executed either independently, sequentially or simultaneously. We need a plan to coordinate and supervise these strategies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003375_j.triboint.2014.10.007-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003375_j.triboint.2014.10.007-Figure13-1.png",
        "caption": "Fig. 13. (A)\u00f0hGap;Rlv=hRef \u00de from FSI\u2013thermal model simulation (left) and calculated from capacitive measurements (right) at n\u00bc2000 rpm and \u00f0p=pRef \u00de\u00bc0.8. (B)\u00f0hGap;Rlv=hRef \u00de from FSI\u2013thermal model simulation (left) and calculated from capacitive measurements (right) at n\u00bc2000 rpm and \u00f0p=pRef \u00de\u00bc0.64. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " The conditions point to the importance of considering TEHD, since at high speeds the thermal effects assume greater importance due to higher viscous dissipation, while pressure deformation are lower at low pressure operating conditions. Therefore, the effects of thermal deformation are more visible at these operating conditions. For the reference EGM used for relative film thickness comparison, measurements and simulations were performed for two pump speeds n\u00bc1000 and 2000 rpm and for a range of pressures up to \u00f0p=pRef \u00de\u00bc0.8. The result for n\u00bc2000 rpm and \u00f0p=pRef \u00de\u00bc0.8, a high pressure operating condition is shown in Fig. 13. The agreement between the result from the simulation and from the measurements was quite good, both in the qualitative sense as well as in the relative film thicknesses reported at the exact locations at which the measurements were conducted. Higher film thicknesses were seen on the HP port side of the bushing with generally lower film thicknesses on the LP port side. However, from both measurement and simulation the region of lowest film thickness was observed near the meshing zone of the gears",
            " The FSI\u2013thermal model also predicts a local region of relatively high film thickness between the two measurement locations on the LP side of the bushing which was not reflected by the measurements due to the lack of sensors in this specific region. While model results provide a lot of spatial detail, the relatively fewer measurement locations prevents the experimental results from having the same level of detail. However, the general relative film thickness trends show good agreement. The assumption of lubricating film thickness symmetry made earlier in the chapter can now be confirmed from the observation that the independent measurements taken at the two symmetric points (points 1 and 2, highlighted in red in Fig. 13) resulted in film thicknesses which differed by an extremely small margin. Similar observations were also be made from the results presented for other operating conditions later in this section. While the \u00f0hGap;Rlv=hRef \u00de fields from simulation and experiments generally show good agreement, an area near the high pressure relief groove (highlighted in blue) shows very low film thickness in the experimental results, which are not reflected at all in the simulation results. Due to space constraints in instrumenting the EGM only one capacitive sensor could be placed near the meshing zone of the gears, resulting in one measurement point in this location. While the measurement point accurately reflects the low film thickness in this region, the region of low film thickness is spread further due to the interpolation performed\u2014which could possibly explain the discrepancy in results observed in this area. Moving to a slightly lower pressure the comparison for n\u00bc2000 rpm and \u00f0p=pRef \u00de\u00bc0.64 is shown in Fig. 13. Again, the lowest film thickness was located near the meshing zone of the gears, with generally higher film thicknesses on HP side of the gap and lower film thicknesses on the LP side of the gap. The local low film thicknesses on the LP side have become less apparent with reduced pressure in both the measurements and in the simulation results. Moving to a relatively low pressure operating condition at n\u00bc2000 rpm and \u00f0p=pRef \u00de\u00bc0.4, the film thickness distribution undergoes a significant change While the general high and low film thickness areas remain on the HP and the LP side respectively and area of lowest film thickness was still near the meshing zone of the gears, a prominent area of low film thickness was now observed near the LP port of the EGM, in results from both experiment as well as simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003098_physreve.88.023012-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003098_physreve.88.023012-Figure1-1.png",
        "caption": "FIG. 1. (Color online) Model system [8]: Two beads move along fixed circular trajectories, each driven by a constant tangential force F .",
        "texts": [
            " As an extension, we take into account the time dependence of the hydrodynamic interactions. We demonstrate that the presence of the temporal acceleration term leads to synchronization of the rotor dynamics. Hence, our studies provide a counterexample to the paradigm that highly symmetric systems at low Reynolds number require additional measures to achieve a synchronized motion. II. MODEL We adopt the rotor model of Ref. [8]: Two beads of radius a move along circles of radius R, each driven by an active force Fi (cf. Fig. 1). The two circles are centered at r0 i = (\u22121)i(d/2)ex (i = 1,2), where ex is the unit vector along the x axis and d the center-to-center distance, and both beads are confined in the xy plane. The trajectories of the bead centers can be expressed as r i(t) = r0 i + [R cos \u03d5i(t),R sin \u03d5i(t),0]T , (1) in terms of the phase angles \u03d5i(t). The driving forces Fi(t) = F t i(t) (2) are of equal magnitude and point along the tangents t i(t) of the trajectories, where t i(t) = [\u2212 sin \u03d5i(t), cos \u03d5i(t),0]T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003340_978-3-319-06698-1_23-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003340_978-3-319-06698-1_23-Figure2-1.png",
        "caption": "Fig. 2 Top view of cable i extending from point Ai (or from A\u2032 i if the output pulley is considered) to the platform point Bi",
        "texts": [
            " The positions in the mobile frame RP of the cable attachment points Bi on the platform are denoted bi . In the fixed frame R, the vector \u2212\u2212\u2192 Bi Ai from the cable attachment point to the cable drawing point is defined as li = (li x , liy, li z) T = ai \u2212 Qbi \u2212 p. As detailed in several previous works, notably in [6], in order to account for cable mass and elasticity, the elastic catenary cable modeling [5] can be considered. Under static loading conditions, cable i lies in the vertical plane Pi containing both points Ai and Bi . As shown in Fig. 2, let us consider the local frame Ri = (Ai , Xi , Yi , Zi ) such that Zi \u2261 Z (directed vertically upward) and with Xi pointing toward the mobile platform point Bi . The angle \u03b1i between X and Xi is given by \u03b1i = atan2(\u2212liy,\u2212li x ). (1) Angle \u03b1i depends only on the pose (position and orientation) of the mobile platform and on the constant position vectors ai and bi . The rotation matrix Qi defining the orientation of (Xi , Yi , Zi ) with respect to (X, Y, Z) is Qi = (xi , yi , zi ) = \u239b \u239d cos \u03b1i \u2212 sin \u03b1i 0 sin \u03b1i cos \u03b1i 0 0 0 1 \u239e \u23a0 = 1\u221a l2 i x + l2 iy \u239b \u239c\u239d \u2212li x liy 0 \u2212liy \u2212li x 0 0 0 \u221a l2 i x + l2 iy \u239e \u239f\u23a0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure32-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure32-1.png",
        "caption": "Fig 32 Roeking bearing system (dual centres) applied to crosshead of GMT 1060 engine (Ciliberto and Mariani, 1977)",
        "texts": [
            " Booker et a119 gives many references where applications using similar concepts have been suggested previously. In Italy, Grandi Motori Trieste use a similar basic concept for many of their two-stroke engines. The operating prin- TRIBOLOGY international 161 ciples associated with their 1060 low speed 1urge diesel engine were well described at the 1977 CIMAC conference 47 . More recently, with co-operation between Grandi Motori Triesti; Glacier Metal Company and Cornelt University, Booker has carried out an analysis on the 1060 engine 4s'49 . Fig 32 shows an exaggerated view of the bearing arrangement with the bearings (rather than the journals) as the oscillating members 47 . The main squeezing action is taken on the inner bearings while the outer bearings are being pulled away from the journal (by rocking action) allowing more oit in. The rocking principle of aitemately squeezing and lifting on the inner and outer bearings is i~Austrated in Fig 33. The lower diagram shows the sequence of events during one cycle of operation and the upper drawing shows the relative position of the two journal centres (A and B) in their respective clearance spaces (note that the offsets of the centres are greater than the bearing clearance)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001636_s0263574704000347-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001636_s0263574704000347-Figure6-1.png",
        "caption": "Fig. 6. Geometrical solution of the direct kinematics.",
        "texts": [
            " To solve the system (1) for px, py, pz, first, let us derive linear relations between the unknowns. By subtracting three possible pairs of the equations (1), we leave 2\u03c1xpx \u2212 2\u03c1ypy = \u03c12 x \u2212 \u03c12 y 2\u03c1xpx \u2212 2\u03c1zpz = \u03c12 x \u2212 \u03c12 z 2\u03c1ypy \u2212 2\u03c1zpz = \u03c12 y \u2212 \u03c12 z (11) As follows from these expressions, the relation between px , py , pz may be presented as px = \u03c1x 2 + t \u03c1x ; py = \u03c1y 2 + t \u03c1y ; pz = \u03c1z 2 + t \u03c1z , (12) where t is an auxiliary scalar parameter. From a geometrical point of view, the expression (12) defines the set of equidistant points for the prismatic joint centres (Fig. 6). Also, it can be easily proved that the full set of equidistant points is the line perpendicular to and passing through (\u03c1x, \u03c1y, \u03c1z)/2, where = { p \u2223\u2223\u2223\u2223px \u03c1x + py \u03c1y + pz \u03c1z = 1 } (13) After substituting (12) into any of the equations (1), the direct kinematic problem is reduced to the solution of a quadratic equation in the auxiliary variable t , At2 + Bt + C = 0, (14) where A = (\u03c1x\u03c1y)2 + (\u03c1x\u03c1z)2 + (\u03c1y\u03c1z)2; B = (\u03c1x\u03c1y\u03c1z)2; C = (\u03c12 x/4 + \u03c12 y/4 + \u03c12 z /4 \u2212 L2)(\u03c1x\u03c1y\u03c1z)2. The quadratic formula yields two solutions t = \u2212B + m \u221a B2 \u2212 4AC 2A ; m = \u00b11 (15) that geometrically correspond to different locations of the target point P (see Fig. 6) with respect to the plane passing through the prismatic joint centres (it should be noted that the intersection point of the plane and the set of equidistant point corresponds to t0 = \u2212B/(2A)). Hence, the Orthoglide direct kinematics is solved analytically, via the quadratic formula (14) for the auxiliary variable t and its substitution into expressions (12). The direct kinematic solution exists if and only if the joint variables satisfy the inequality B2 \u2265 4AC, which defines a closed region in the joint variable space L = { |(\u03c12 x + \u03c12 y + \u03c12 z \u2212 4L2 )( \u03c1\u22122 x + \u03c1\u22122 y + \u03c1\u22122 z ) \u2264 1 } (16) Taking into account the joint limits (2), the feasible joint space may be presented as + L = { \u2208 L|\u03c1x, \u03c1y, \u03c1z > 0} (17) Therefore, for the considered positive joint limits (2), the existence of the direct kinematic solutions may be summarised as follows: \u2022 Inside the region + L , there exist exactly two direct kinematic solutions, which differ by the target point location relative to the plane (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002166_s11071-009-9504-1-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002166_s11071-009-9504-1-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the redundant mechanism",
        "texts": [
            " The upper part of linear actuators is connected to 4 corners of the upper platform Bi using spherical joints, see Fig. 3. Cartesian coordinates A(O,x, y, z) and B(P,u, v,w) represented by {A} and {B} are connected to the base and moving platforms, respectively. Coordinates Ci(Ai, xi, yi, zi ); i = 1, ..,4, are connected to the base platform with their xi axes aligned with the rotary actuators (see Fig. 2). Moreover, si represents the unit vector along the axes of the ith rotary actuator, li is the unit vector along \u2212\u2212\u2192 AiBi and ai is used to represent the vector \u2212\u2212\u2192 OAi (Fig. 1). Assuming that each limb is connected to the fixed base by a universal joint, the orientation of the ith limb with respect to the fixed base can be described by two Euler angles, rotation \u03b8i around the rotary axis si , followed by rotation \u03c8i around ni which is perpendicular to li and si (Fig. 4). Also, di is the length of \u2212\u2212\u2192 AiBi . It is to be noted that \u03b8i and di are active joints actuated by the rotary and linear actuators, respectively. However, \u03c8i is inactive. In the 6-leg Stewart-like UPS mechanisms, the workspace is constructed by intersection of 6 spheres"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.12-1.png",
        "caption": "Figure 6.12 two-wire line of length 6/2 fed by a generator. (a) Center-fed linear antenna of length 6 fed by a generator and (b) open-circuited",
        "texts": [
            " Finding the current distribution involves a difficult electromagnetic boundary value problem, which is described in advanced books on antenna theory [5-71. We will not attempt to do that here because the linear antennas we consider sustain current distributions that are sinusoidal in nature. Approximate justification for the assumption above is provided by the twowire transmission line problem applied to the dipole antennas. From this viewpoint, consider a segment of an open-circuited transmission line of length e l 2 excited by a generator similar to that of the dipole shown in Figure 6.12b. It can be seen that if the two lines are folded out in the manner shown, the configuration resembles the dipole under consideration. From transmission line theory (Chapter 5 ) we know that there will be a standing wave current on the line, and hence a sinusoidal distribution of current having zeros at the two ends of the antenna seems to be plausible. It is appropriate to remark here that under thin wire approximations, the rigorous theory predicts a sinusoidal distribution of current [ 3 ] . For an antenna with length e and the element wire radius a, the thin wire approximations are t > a , n < < X , a n d (6",
            "1 10) thickness parameter S2 = 2 In - > 12, where X is the wavelength in the medium. We now assume that the current distributions on the dipole of length under thin wire approximation is e U (6.1 11) LINEAR ANTENNAS 233 where 10 is the peak value of the current, = 27r/X, X being the wavelength in the medium, and z\u2019 refers to the coordinate on the antenna. The current distributions (6.1 1 1) or dipoles of length ! = X/4, X/2, A, 3X/2, and 2X are shown in Figure 6.13 with the currents noted at the feed point and the two end points. We assume that the far fields of the dipole Figure 6.12~1 are the same as those produced by a filamentary current I ( z ) given by (6.1 10). The geometry of 234 ANTENNAS AND RADIATION the equivalent problem and the coordinate system used are as shown in Figure 6.14 for far field approximations. We now follow the procedure given in Section 6.6.3 to determine the fields. We evaluate N given by (6.96) appropriate for the antenna. In the present case we have J(r\u2019) dv\u2019 = I ( z \u2019 ) dz\u2019 2. Therefore (12 d z\u2018 (6.1 12) I ( ~ / ) ejPz\u2019 cos 6 with I(z\u2019) given by (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001605_tro.2007.900639-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001605_tro.2007.900639-Figure1-1.png",
        "caption": "Fig. 1. Humanoid model: reference frames and forces. (a) Humanoid robot. (b) Contact forces at foot.",
        "texts": [
            " Moments and forces are also represented in combined form as the wrench (m, f) \u2208 se(3)\u2217, where se(3)\u2217 denotes the dual of se(3). Finally, we recall the adjoint matrix representation AdT of T \u2208 SE(3) as the 6 \u00d7 6 matrix AdT = [ R 0 [p]R R ] (1) where R \u2208 SO(3) and p \u2208 3, respectively, denote the rotation and position components of T \u2208 SE(3), with [p] as the 3 \u00d7 3 skew-symmetric matrix representation of p. The dual adjoint Ad\u2217 T is simply given by the transpose of AdT . Referring to the biped humanoid model of Fig. 1, we denote the fixed reference frame by {o}, and attach a frame {r} to the point at which the floor exerts a reaction force on the sole of the foot. The shape of each sole is assumed to be rectangular. The wrench F \u2208 se\u2217(3) denotes the reaction moment and force expressed in the {r} frame. Let Fo 1094-6977/$25.00 \u00a9 2007 IEEE denote the wrench F expressed in the fixed frame, i.e., Fo = Ad\u2217 T F . In anticipation of our later optimization formulation, we define the vector q\u0308 = (V\u03070, \u03b8\u0308), where V0 \u2208 se(3) is the twist velocity of the pelvis and \u03b8 \u2208 K is the vector of joint variables",
            ", minimizing joint torques or joint accelerations subject to equality or inequality ZMP and COM constraints, and tracking the desired acceleration profile to within some prescribed bound) also admit a straightforward formulation as an SOCP problem; due to space limitations, we do not provide details of these formulations here. To assess both the computational performance and the qualitative nature of the motions generated by our SOCP active balancing algorithms, several case studies with the biped humanoid robot of Fig. 1 are conducted. The robot has 31 DOFs and 25 actuated joints: six at each limb and one at the rotational DOF about the waist. Values for the kinematic and inertial parameters are set to approximate a typical full-size biped humanoid. All simulations are performed in Matlab v6.5 running on a Pentium 1.4-GHz laptop. Each simulation time interval is 0.025 s. For the SOCP optimization, we use the Matlab toolbox provided by MOSEK. For the input motions and environmental disturbances used in our case studies, we assume that the maximum joint torques are sufficient for the robot to maintain active balance and set the friction coefficient to be 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000915_jsvi.2000.3430-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000915_jsvi.2000.3430-Figure2-1.png",
        "caption": "Figure 2. Mechanical model of a geared rotor-bearing system.",
        "texts": [
            " As a consequence, in the special cases where the gear backlash and the bearing non-linearities are not essential, system (18) becomes linear, since the gear meshing force is expressed in the simple form f g (u 1 , w, wR )\"c g wR #k g w, (19) instead of equation (9), while the forces developed in each bearing are represented by the classical eight-coe$cient element [10, 12] with f b \"K b u b #C b u5 b , (20) instead of the non-linear form represented by equation (11). In such cases, the elements of the sti!ness and damping matrices in equation (20) are evaluated by applying standard procedures [10], after determining the corresponding equilibrium position by taking into account the weight, the torque and the tooth loads applied on the gears. In typical rotordynamic systems, gear pairs are only one of several components of the whole system. For instance, Figure 2 presents such a system, which includes a motor providing the power necessary for the function of the system, a gear-pair system as part of a gear box reducing the rotor spin speed and a load subsystem (fan, pump, propeller, generator, etc.). Here, the gear box is connected to the motor and the load subsystems through #exible shafts. The model shown in Figure 2 is more realistic than the gear-pair system of Figure 1. On the other hand, it is also more complicated and more di$cult to analyze. In fact, the order of the resulting dynamic model is so high that even the application of numerical analysis methodologies is impractical. However, there is an attractive feature of the system, which can be exploited in order to perform a systematic investigation of its dynamics; namely, the important non-linearities of the system appear in the gear mesh and the hydrodynamic bearing locations only. This localization of the non-linearities is quite common in practice and as a result, several appropriate methodologies have already appeared in the literature for such systems [15}17, 27}29]. The approach chosen in the present study for the e$cient analysis of the system shown in Figure 2 is based on such methodologies and especially on that presented in reference [27]. The basic steps of this methodology are explained brie#y in the remaining part of this section. First, the system shown in Figure 2 is divided into three main components, including the driving motor and shaft (component A), the gear pair and journal bearings subsystem (component B) and the driven subsystem with its shaft (component C). Components A and C are linear and their equations of motion are obtained by applying classical \"nite element methodologies in the general form M< A uK A #K< A u A \"f< A (t) and M< C uK C #K< C u C \"f< C (t) (21) respectively. The displacement vectors u A and u C include contributions from \"ve-degree-of-freedom per node (four for the bending and one for the torsional action)",
            " Here, the emphasis is placed on demonstrating the validity and e!ectiveness of the methodology described in section 4, rather than on obtaining another exhaustive set of numerical results. The system shown in TABLE 1 Natural frequencies of linearized model at X 1 \"0)207 Complete Reduced model model 0 0 0)084 0)084 0)151 0)151 0)161 0)161 0)175 0.175 0)422 0)422 0)426 0)426 0)459 0)459 0)557 0)556 0)911 0)911 0)941 0)941 0)995 0)995 1)076 1)076 1)260 1)261 3)017 3)031 3)027 3)116 3)158 4)174 3)892 5)122 Figure 2 is examined and its shafts are modelled by beam \"nite elements. In the reduction stage, component A was represented by three rigid-body modes, \"ve free interface #exible modes and \"ve boundary degrees of freedom, while component C was represented by an identical number of modes. As a result, the reduced system consisted of 26 degrees of freedom. The accuracy of the component mode synthesis method is \"rst veri\"ed by the results of Table 1, presenting the lower natural frequencies of the reduced and complete linearlized nominal system, at a speci\"c spin speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001757_tia.2007.908162-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001757_tia.2007.908162-Figure6-1.png",
        "caption": "Fig. 6. Voltage and current of proposed PFC drive. (a) Voltage and current in one period of source voltage. (b) Zoom in \u201c\u00a9a \u201d and \u201c\u00a9b \u201d of (a).",
        "texts": [
            " However, the state of discharge switch QF is controlled by (9). Therefore, the stored energy of the capacitor can be used to decrease the torque ripple that comes from the pulsating ac source. Additionally, if the voltage drop of the switches or diodes is ignored, when source charging mode happens, the phase voltage and capacitor voltage and source must be the same. Therefore, (7) and (9) are also suitable for mode 4. The waveforms for source voltage Vs, capacitor voltage Vc, phase voltage Vm and phase current im are shown in Fig. 6. The source voltage is ac supply and given by Vs = Vsm sin\u03c9t, \u03c9t \u2208 [0, \u03c0]. (11) Based on the proposed switching topology, the capacitor voltage supplies the main power for motor operation when Vs is lower than the capacitor voltage. The capacitor voltage fluctuates during charging and discharging of the capacitor as shown in Figs. 5 and 6. When the capacitor voltage is lower than the source voltage, the source will charge the capacitor and supply the power to the motor at the same time. To simplify the analysis of the proposed PFC drive, the capacitor voltage is simplified as twice the supply frequency with dc offset Vc = Vc\u2212av \u2212 Vcm sin 2\u03c9t (12) where Vc\u2212av is average voltage, and Vcm is magnitude of fluctuation. Assume that the motor operates at speed, \u03c9rm, dwell angle \u03b8dw, and advance angle \u03b8ad. In Fig. 6(a), based on the proposed switching topology, the source voltage is zero at point A. In this dwell region, the capacitor supplies the energy to drive the motor alone. Thus, the energy variation of point A can be described as follows: discharging the energy of the capacitor during current buildup, W1A, discharging the energy of the capacitor during torque development, W2A, and the changed and accumulated energy of the capacitor during energy feedback mode, W3A. At point A, the total energy variation of the capacitor can be given as \u2206WA = W3A \u2212 W1A \u2212 W2A. (13) On the contrary, only the ac source supplies all energy to the motor for the excitation energy at point B in Fig. 6(a). The changing energy of the capacitor is 0 when the motor operates in the excitation region and torque production region, so W1B and W2B are zero, and feedback energy is given by W3B . At point B, the total energy variation of the capacitor can be given by \u2206WB = W3B . (14) The \u03bdc\u2212av and \u03bdcm can be solved from (13) and (14). More detailed mathematical equations are shown in the Appendix. In the proposed PFC, three cases are possible for calculating peak current\u2014only the capacitor supplies current, only the source supplies current, or both the capacitor and source supply current. However, in the half source period, the capacitor voltage is higher than the peak value of the source voltage shown as Fig. 6(a). The maximum peak current can calculate from when maximum voltage of the capacitor supplies the current. Thus, maximum peak current ipeakmax is given by ipeakmax = 1 Lmin Vcmax \u00b7 \u03b8ad \u03c9rm . (15) The minimum peak current only appears in both the capacitor and source supplied current. Thus, minimum peak current ipeakmin is given by ipeakmin = 1 Lmin ( \u03bdc \u00b7 \u03b8c \u03c9rm +\u03bds \u00b7 \u03b8ad \u2212 \u03b8c \u03c9rm ) , \u03b8c < \u03b8ad. (16) Therefore, in the proposed drive system, maximum peak torque Tpeakmax and minimum peak torque Tpeakmin can be obtained from (15) and (16) T = 1 2 K \u00b7 i2lim (17) where K = dL(\u03b8, i)/d\u03b8, ilim is phase current limit, so K is the differential inductance, which varies with rotor position for a given current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000700_rsta.1997.0049-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000700_rsta.1997.0049-Figure1-1.png",
        "caption": "Figure 1. Cross-section of shallow strip with arbitrary edge displacements z\u2217 and slopes \u03c6 of the liquid surface.",
        "texts": [
            "1) where \u03ba1, \u03ba2 = principal curvatures of surface, \u03b3 = density of liquid, g = gravitational acceleration. For the one-dimensional case of a strip of liquid aligned to the y-axis, say, equation (2.1) is therefore given by S d2z dx2 { 1 + ( dz dx )2}\u22123/2 \u2212 \u03b3gz = 0. (2.2) (a ) General equilibrium conditions for shallow strip The equilibrium conditions for a shallow strip of rectangular cross-section are now expressed in terms of arbitrary slopes \u03c61, \u03c62 and deflexions z\u22171 , z\u22172 of the free surface of the liquid at its junction with the strip, as shown in figure 1. The strip is supported by surface tension and hydrostatic pressure, and hence vertical equilibrium yields S(sin\u03c61 + sin\u03c62) + \u03b3gb(z\u22171 + z\u22172) cos\u03b1 = W, (2.3) where W is the weight of the strip per unit length, 2b is the width of the strip and \u03b1 is the angle of tilt of the strip cross-section, so that sin\u03b1 = ( z\u22171 \u2212 z\u22172 2b ) . (2.4) Phil. Trans. R. Soc. Lond. A (1997) Likewise, horizontal equilibrium yields H12 = S(cos\u03c61 \u2212 cos\u03c62) + \u03b3gb(z\u22171 + z\u22172) sin\u03b1, (2.5) where the suffices for H indicate the direction of the horizontal force required for equilibrium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure1-1.png",
        "caption": "Figure 1. Basic nomenclature for bearing cross-section.",
        "texts": [
            " The main assumptions in the model presented are that friction is neglected, pure rolling without skewing is assumed, the material is assumed linearly elastic and the model is quasi-static with dry contacts not considering elastohydrodynamic effects from the lubrication film. Tapered roller bearing model In this section, the bearing model is described, starting from the six-dof bearing model and subsequently extended to include the flexibility of the outer ring supporting structure. The nomenclature used for the cross section is shown in Figure 1, where ri, rp and ro are the inner raceway, pitch circle and outer raceway radius, respectively, i, m, o and r are the inner raceway, roller centre, outer raceway and roller included angles, respectively, and l is the roller length. The six-dof tapered roller bearing model is based on coordinate systems attached to the inner bearing ring and the outer bearing ring, respectively. Based on the location and orientation of the two coordinate systems, the deflection at each roller position is calculated and roller contact forces and moments are subsequently calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure6-1.png",
        "caption": "Fig. 6 \u2013 Positioning of the vehicle on the platform [3].",
        "texts": [],
        "surrounding_texts": [
            "Rollover test on a complete vehicle is performed on a test bench. The test bench comprises a tilting platform, on which the tested vehicle is placed, and a concrete ground surface on which the vehicle is rolled over. The tilting platform, related to the ditch, should be placed as presented in Figs. 6 and 7. The vehicle to be tested should be prepared appropriately. In the case of a rollover test on a complete vehicle, it does not need to be in a fully finished condition. Any alteration from the fully finished condition is acceptable if the basic features and behaviour of the superstructure are not influenced by it. The basic requirement is the position of the centre of gravity of the test vehicle \u2013 it should be the same as in its fully finished version. Also the total value of vehicle mass and the distribution of masses should correspond to the fully finished version. All of those elements which contribute to the strength of the superstructure should also be installed in their original position. However, elements, which do not contribute to the strength of the superstructure can be replaced by additional elements equivalent in mass and size. Since the rollover test is for the worst case, the vehicle should include other masses and their distributions, such as fuel, battery acid, etc. which may be substituted with safer equivalents. In the case where occupant restraint devices (safety-belts\u2013 coaches) are part of the vehicle type, a mass should be attached to each seat fitted with an occupant restraint following one of these two methods, at the choice of the manufacturer: mass constitutes 50% of the individual occupant mass of 68 kg and should be fixed rigidly and securely, or mass constitutes an anthropomorphic ballast with a mass of 68 kg and should be restrained with a 2-point safety-belt (Fig. 8). The platform on which the vehicle is situated should be tilted with a constant velocity not exceeding 0.087 rad/s (58/s) until the bus or tested section loses stability. According to the Regulation, the impact area on which the bus is tilted should have a dry and smooth concrete surface. This is essential as the friction coefficient on dry concrete and steel may vary significantly depending on the humidity. According to PN-82/ B-02003 \u2018\u2018Actions on building structures \u2013 variable actions during exploitation and assembling\u2019\u2019 the value of the static friction coefficient for steel and concrete with smooth surface equals 0.45 0.7, whereas for steel and concrete with rough surface it is 0.3. The rollover test on a complete vehicle is the most objective and reliable but due to economic reasons these tests are performed using other equivalent methods. In the case of a rollover test using body sections the result may be subject to significant error, which is influenced by the choice of section to be tested. Most often the sections of a bus substantially differ in terms of stiffness. The section with front or back wheel arches is much stiffer, whereas a section with a door has lower stiffness. The complete structure is additionally stiffened by the front and back walls, which cannot be taken into consideration when analysing a single section. Analytical calculations assume the formation of plastic hinges and the absorption of energy only in wall pillars, which may lead to unnecessary overdimensioning of the structure resulting from the choice of larger sections of wall pillars. For safety reasons, the most accurate results come from tests on a complete vehicle. The cost of performing such tests may be reduced by implementing numerical methods to determine the method of deformation of the structure during dynamic deformation [5]. What is very functional in this respect is the finite element method [6]."
        ]
    },
    {
        "image_filename": "designv10_10_0000615_20.573842-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000615_20.573842-Figure5-1.png",
        "caption": "Fig. 5. FEM meshes of an 11 kW skewed motor after a rotation of 30 (four slices, each has 3232 nodes, 5304 elements). (a) At the first slice and (b) at the fourth slice.",
        "texts": [
            " Two upper layers belong to the stator, and a lower layer belongs to the rotor. For each part, the mesh is automatically generated fully using the deduction of points algorithm and the mesh refinement method [9]. The unknowns at the inner-most nodes of the stator and at the outer-most nodes of the rotor are connected by virtue of the \u201cperiodic boundary conditions.\u201d That is to say when the rotor is rotated, the shape of the rotor mesh will not be changed, but the coordinates and the periodic boundary conditions will (Fig. 5). Thus, the stator mesh and the rotor mesh are required to be generated once and once only. Because the meshes can be kept unchanged, the \u201cnoise\u201d caused by the changes in the meshes can be eliminated [10]. The geometrical difference between the basic slice and the other slice is that the rotor of the other slice has rotated by a small angle because of the skewing in the rotor bars. The meshes at the other slices can be easily obtained by rotating the basic rotor mesh marginally (Fig. 5). The nodes, elements, etc., in the FEM model are renumbered slice by slice continually. Therefore, the data structure is 2-D. The time-stepping FEM is very similar to the general method with the exception of the relationship between the adjacent slices that are introduced in this multislice technique. For time-stepping process in FEM, the Backward Euler\u2019s method is used. For steady-state problems, the complex FEM model is solved first to give an initial guess of (0) and (0) [11]. At each time step, the iterative solver is most suitable in solving the system of large equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000899_156855304773822464-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000899_156855304773822464-Figure1-1.png",
        "caption": "Figure 1. Passive one-legged hopper.",
        "texts": [
            " These studies contributed to biomechanics in investigating mechanisms of animal locomotion. On the other hand, it was found that in addition to \u00a4To whom correspondence should be addressed. E-mail: sangho@ieee.org D ow nl oa de d by [ U ni ve rs ity o f B or as ] at 2 3: 48 0 4 O ct ob er 2 01 4 358 S.-H. Hyon and T. Emura the leg spring, a hip spring also plays an important role in animal running because it enables the leg to be swung passively [9]. Tompson and Raibert showed that the spring-driven one-legged running robot depicted in Fig. 1 can hop without any inputs, provided the initial conditions are appropriately chosen [10]. Therefore, this is a good template model for the purpose of studying energy-ef cient running. However, a numerically determined solution was shown to be marginally stable and eventually fails without controls. Therefore, some suitable controller should be applied to ensure orbital stability. The rst successfull controller was found by Ahmadi and Buehler. They applied Raibert\u2019s celebrated Foot Placement Algorithm [2] to this passive running robot model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000915_jsvi.2000.3430-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000915_jsvi.2000.3430-Figure1-1.png",
        "caption": "Figure 1. Mechanical model of a gear-pair.",
        "texts": [
            " This method exploits the fact that the system non-linearities are related directly to relatively few degrees of freedom and reduces the order of the system without sacri\"cing much of the computational accuracy. Numerical results are then presented in sections 5 and 6, illustrating the in#uence of the system parameters on its dynamic response and stability. The \"nal section includes a synopsis and the main \"ndings of the study. The study focuses on geared rotordynamic systems, involving hydrodynamic bearings. Figure 1 shows a simple mechanical model, retaining the essential characteristics which arise from the interaction of the gear mesh and the bearing non-linearities. It consists of a spur gear pair, with equivalent mass m i , polar moment of inertia I i and base radius R i . The driving gear (i\"1) is subjected to a known torsional moment M 1 , while the driven gear (i\"2) develops a resistance moment M 2 , with known form. Both gears are supported on plain oil journal bearings through rigid shafts. As a consequence, the motion of the system is described adequately by the following set of generalized co-ordinates u (t)\"(u 1 v 1 u 1 u 2 v 2 u 2 )T",
            " In typical rotordynamic systems, gear pairs are only one of several components of the whole system. For instance, Figure 2 presents such a system, which includes a motor providing the power necessary for the function of the system, a gear-pair system as part of a gear box reducing the rotor spin speed and a load subsystem (fan, pump, propeller, generator, etc.). Here, the gear box is connected to the motor and the load subsystems through #exible shafts. The model shown in Figure 2 is more realistic than the gear-pair system of Figure 1. On the other hand, it is also more complicated and more di$cult to analyze. In fact, the order of the resulting dynamic model is so high that even the application of numerical analysis methodologies is impractical. However, there is an attractive feature of the system, which can be exploited in order to perform a systematic investigation of its dynamics; namely, the important non-linearities of the system appear in the gear mesh and the hydrodynamic bearing locations only. This localization of the non-linearities is quite common in practice and as a result, several appropriate methodologies have already appeared in the literature for such systems [15}17, 27}29]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003250_s10846-015-0301-4-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003250_s10846-015-0301-4-Figure2-1.png",
        "caption": "Fig. 2 Tiltable geometry with unmanned quadrotors. Cetinsoy et al. proposed design and construction of a quad tilt-wing UAV",
        "texts": [
            " In literature, tilting rotors of a quadrotor was mainly used to convert a quadrotor to an aircraft like vehicle. This combines the advantage of a VTOL vehicle with an aircraft. Quad Tilt Rotor (QTR) is one of the most popular variance of quadrotor airframe. QTR is able to shift between helicopter mode to aircraft mode. This feature enhances the QTR to have extra thrust along the desired axes (front direction) [17, 18]. Curtiss-Wright X-19 QTR aircraft [19] developed in 1963 (Fig. 1), and Bell X-22A [20] was developed 1966 (Fig. 2) are one of the first two prototypes of QTR system on a full-scale. In literature, another design, named Bell Boeing Quad TiltRotor (V-44) is proposed as a fourrotor derivative of the V-22 Osprey tiltrotor. It is reported to be under development jointly by Bell Helicopter and Boeing [21]. Cetinsoy et al. [22] and Ryll et al. [23] has come up with the idead of tiltable geometry in quadrotors. Quad tilt wing [22] that is illustrated in Fig. 2, is able to tilt their wings in order to adapt itself into either a quadrotor helicopter or a plane. This feature makes the aircraft to vertical take off and land while have relatively better cruising speed with respect to a regular quadrotor. On the other hand Ryll\u2019s study [23] is based on a \u201cquadrotor with tilting propellers\u201d. Jeong et al. [24, 25] study on omni-directional aircrafts with VTOL and CTOL (Conventional take off and landing) modes are also an enthusiasm for our study on the tilt-roll capable quadrotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003458_j.tust.2015.11.022-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003458_j.tust.2015.11.022-Figure4-1.png",
        "caption": "Fig. 4. Equivalent dynamic model of gear mesh in the dimensional coordinate.",
        "texts": [
            " The stiffness matrix Kb and mass matrix Mb of Timoshenko beam element can be deduced according to elasticity theory (Wang, 2003). Hutchinson calculated the shear coefficients in Timoshenko\u2019s beam theory for various cross sections (Hutchinson, 2001). The damping matrix Cb is defined as Rayleigh damping, Cb = aMb + bKb, where, a and b are the Rayleigh scaling factors. Therefore, neglecting the rotate effect, the dynamic equation of beam element is Mb\u20acqb \u00fe Cb _qb \u00fe Kbqb \u00bc 0 \u00f01\u00de where qb is the force vector of the beam element. 2.2.2. Gear mesh element Fig. 4 shows the equivalent dynamic model of gear mesh in the space coordinate. The displacement vector of both gear node and pinion node is qm = [xr, yr, zr, hxr, hyr, hzr, xp, yp, zp, hxp, hyp, hzp]T, where the subscript \u2018\u2018r\u201d represents the gear node, and \u2018\u2018p\u201d represents the pinion node. The deflection of tooth mesh along the line of action is drp \u00bc V qm \u00fe e\u00f0t\u00de \u00f02\u00de where e(t) is the time-varying, unloaded static transmission error; V is the projection vector, which can be defined as V \u00bc sinwrp cos bb; coswrp cosbb; sin bb; rbr sinwrp sinbb; rbr coswrp sinbb; rbr cos bb; sinwrp cosbb; coswrp cosbb; sinbb; rbp sinwrp sin bb; rbp coswrp sinbb; rbp cos bb \u00f03\u00de where bb is the helix angle, wrp = u a is defined as the angle between the normal vector of the contact surface and axis-y, where a is the pressure angle, u is the installation angle, and the middle symbol is taken the positive value when the gear rotate clockwise, while the negative value corresponds to the counterclockwise rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002122_s0263574708004256-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002122_s0263574708004256-Figure4-1.png",
        "caption": "Fig. 4. Example of geometrical interpretation of inverse kinematic singularities.",
        "texts": [
            " For each limb to be in inverse singularities, both of the following conditions must be satisfied: \u03c1i = 0 and \u03b1i = ( 2n+ 1 2 ) \u03c0 + \u03b8i n= 0, 1, 2, . . . (12) Inverse singularities thus take place when length AiDi is zero (i.e., \u03c1i = 0) and DiBi is perpendicular to the direction of the prismatic actuator. Therefore, by avoiding configurations where the \u03c1is approach zero values while \u03b1i relative to \u03b8i approaches a right angle, it is possible to avoid inverse singularities for the redundant 3-RPRR manipulator. Figure 4(a) illustrates a configuration where the third limb of the 3-RPRR manipulator is in an inverse kinematic singularity. According to Eq. (7), inverse singularities take place for the non-redundant 3-PRR manipulator, when any or all of the terms ui are zero. Hence, the 3-PRR is in an inverse kinematic singularity when DiBi is perpendicular to AiDi . Figure 4(b) illustrates a configuration where the first limb is in an inverse kinematic singularity. The combined singularities occur when both direct and inverse kinematic singularities take place. Workspace analysis in the present work is based upon the dexterous workspace of the manipulators. The dexterous workspace as defined in ref. [19] is a region that includes all points the reference point of the end-effector (i.e., P ) can reach in any orientation of the end-effector. Here, the dexterous workspace of the manipulators are obtained geometrically as shown in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.25-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.25-1.png",
        "caption": "FIGURE 1.25 Large disturbance in a curve. New initial state vector (Dv, Dr) after the action of a lateral impulse S. Once outside the domain of attraction, the motion becomes unstable and may get out of control.",
        "texts": [
            " As a result, all trajectories starting above the lower separatrix tend to leave the area. This can only be stopped by either quickly reducing the steer angle or enlarging d to around 0.2 rad or more. The latter situation appears to be stable again (focus) as has been stated before. For the understeered vehicle of Figure 1.24, stability is practically always ensured. For a further appreciation of the phase diagram, it is of interest to determine the new initial state (ro, vo) after the action of a lateral impulse to the vehicle (cf. Figure 1.25). For an impulse S acting at a distance x in front of the center of gravity, the increase in r and v becomes Dr \u00bc Sx l ; Dv \u00bc S m (1.98) which results in the direction aDr Dv \u00bc x b ab k2 (1.99) The figure shows the change in state vector for different points of application and direction of the impulse S (k2 \u00bc I/m \u00bc ab). Evidently, an impulse acting at the rear (in outward direction) constitutes the most dangerous disturbance. On the other hand, an impulse acting in front of the center of gravity about half way from the front axle does not appear to be able to get the new starting point outside of the domain of attraction irrespective of the intensity of the impulse"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000722_1.2794209-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000722_1.2794209-Figure3-1.png",
        "caption": "Fig. 3 Model for a quadruped (uniform bar represents the body)",
        "texts": [
            " The equations of motion with the appro priate initial conditions form a set of differential equations. These differential equations will be solved using a commercially available simulation package called Advanced Continuous Sim ulation Language (ACSL) on a VAX-8550. A time step of 1 ms was found to be sufficient for an accurate simulation. RungeKutta fourth order was used to solve these equations in ACSL. This section is being repeated from Nanua and Waldron (1992) for completeness. The two-dimensional model for the quadruped is shown in Fig. 3. The body is modeled as a rigid beam. Two legs are attached to the front end of the beam and the other two legs are attached to the rear end of the beam. Each leg is modeled as a massless spring (Pandy et al , 1988). Let the coordinates of the center of mass of the quadruped (the center of the main body) be {x, y) and the velocity of the center of mass denoted by the pair (\u00ab, w). The angular orientation of the body is given by the pitch angle 0 (positive in counterclockwise direction). Let the coordinates of the front end of the body be {xi, yO and the coordinates of the rear end of the body be {x2, ya)",
            " 117, NOVEMBER 1995 Transactions of the ASME Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use o \u00bb o o t o o o \u2022 o o o o \u2022 o o stance phase and the following aerial phase to reposition itself for the next stance phase. This scheme would lead to biped running. Note that a periodic solution for this system would be the same as the one developed for the single spring in Sec tion 2. Let use extend this concept further and consider four springs attached to a rigid beam (Fig. 3). The above solution translates into a fast trot for this system. This is explained in the following. In a fast trot, the diagonally opposite legs act together. After the stance phase of a pair of diagonally opposite legs is over, it is followed by an aerial phase, and then followed by the stance phase for the other pair of diagonally opposite legs. This can be represented by a support graph shown in Fig. 4. In this figure, the circles represent the legs. In each set of four, a shaded circle signify that the corresponding foot is in contact with the ground, and an empty circle signifies that the foot is in the air",
            " Then the various forms of energy were computed for this trajectory. These results are shown in Fig. 6. This figure shows that during the stride, there is an exchange of energy between all the forms of energy. It also shows that the potential energy and the kinetic energy are in phase with each other. This observation agrees with the experi mental results obtained by Cavagna et al. (1977) for a biped (it has been argued earlier that the trajectory for biped running and quadruped trot is the same). The simple quadruped model shown in Fig. 3, can be used to generate other forms of gaits for a quadruped. One of those is the bound. In this gait, the front two legs and the back two legs act together. The support graph for this gait is shown in Fig. 7. During a stance phase, the front two legs push the body off the ground. After the aerial phase, the quadruped lands on the rear two legs. Then the rear two legs push the body off the ground and the sequence is repeated. In this gait the body pitches back and forth. Unlike the case of trot, the moment about the center of mass is not zero (Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001231_1521-4109(200205)14:9<611::aid-elan611>3.0.co;2-7-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001231_1521-4109(200205)14:9<611::aid-elan611>3.0.co;2-7-Figure4-1.png",
        "caption": "Fig. 4. Cyclic voltammograms of a) PCV modified glassy carbon electrode in 0.1 M phosphate buffer (pH 7.0) solution and b) the same electrode in 1.0 mM NADH, pH 7.0 solution. c) as (a) and d) as (b) for an unmodified glassy carbon electrode. In all cases the sweep rate was 25 mV s 1.",
        "texts": [
            " The value obtained for ks is significantly lower than those previously reported for electrodes modified by chlorogenic acid [29], caffeic acid [30] and some other compounds with catechol ring [38]. This difference originates most probably from the nature of functionalities bound on ortho-hydroquinone ring. However, this value of ks is comparable or evenhigher than those reported for some other modified electrodes [4, 39]. The electrocatalytic oxidation of NADH at a glassy carbon electrode modified with an electrodeposited film of PCV is Electroanalysis 2002, 14, No. 9 shown in Figure 4, where cyclic voltammograms at 25 mV s 1 of the modified electrode in 0.1 M phosphate buffer (pH 7), in the absence (a) and in the presence (b) of 1.0 mM NADH are shown. Under the same experimental conditions, the direct oxidation ofNADHat an unmodified glassy carbon electrode shows an irreversible wave (Figure 4, curve d). The catalytic effect can be seendirectlywhen curve b is compared with curve d in Figure 4. At the modified electrode, the oxidation of NADH gives rise to a typical electrocatalytic response with an anodic peak current that is greatly enhanced over that observed for the modified electrode alone and with virtually no current on the reverse (cathodic) sweep. The catalytic peak potential is found to be about 243 mV, whereas that of the uncatalyzed peak is about 690 mV. Thus, a decrease in the overvoltage of approximately 447 mVand an enhancement of peak current is also achieved with the modified electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure2-5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure2-5-1.png",
        "caption": "FIGURE 2-5 Iso thermal and adiabatic compression lines on temperature-entropy plane.",
        "texts": [
            " For ideal or reversible processes, the compression of a gas in a cylinder approaches adi abatic when the process is extremely rapid, because then there is little time for heat to be lost by conduction and radiation. The line 1-3 in figures 2-4 and 2-5 represents an adiabatic compression from a pressure of PI to a pressure of P3 = P2 \u2022 The work on the gas is represented in figure 2-4 by the area 1-3-5-6. Since this is an adiabatic change, no heat is received from or rejected to an outside body. Therefore the line 1-3 in figure 2-5 covers no area. Equation 9 now becomes o C,,(T3 - T l ) + W W -c,,(T3 - T l ) for a unit mass -c (P 3V3 _ PIV 1 ) W = l' R R (21 ) Since R cp - C\" then W W k (22) for a unit mass of gas. For M mass units of gas, W which is a convenient expression for determining the work during an adiabatic change. The equation will give a negative arithmetical answer for compression of the gas (work on the gas) and a positive answer for expansion. An expression for the work under an adiabatic curve can be developed by integration in a manner similar to that used for the isothermal process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003231_s00332-013-9174-5-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003231_s00332-013-9174-5-Figure4-1.png",
        "caption": "Fig. 4 Periodic trajectory of a single dipole in doubly periodic domain. (a) According to Eq. (16), rational values of q/p give \u03b1(0) that produce periodic trajectories. (b) Periodic trajectory for p/q = \u22122 and parameter values = 1/2\u03c0 and \u03c9 = 5. The value of \u03b1(0) is obtained from plot (a). (c) Same trajectory depicted on a torus",
        "texts": [
            " That is, we look for solutions that satisfy the condition z(T ) = z(0) + 2p\u03c91 + 2q\u03c92, (15) where p and q are integers and T is the period of the motion. Using (14), the above equation amounts to \u0393 2\u03c0 i [ \u03b6 (\u2212i ei\u03b1) \u2212 ( \u03c0\u03c91 \u0394\u03c91 \u2212 \u03b71 \u03c91 ) i ei\u03b1 \u2212 \u03c0 \u0394 i e\u2212i\u03b1 ] T = 2p\u03c91 + 2q\u03c92, p, q \u2208 Z. (16) In a square domain, \u03c91 = \u2212i\u03c92 = \u03c9, (16) is satisfied only when the imaginary and real parts on the left-hand side of the equation are in a rational ratio of q to p. The corresponding value of \u03b1 can be evaluated numerically for different q-to-p ratios. See Fig. 4 for a depiction of a periodic trajectory for q/p = \u22122. We close this section by noting that in the limiting case of an infinitely large domain, \u03c91, \u03c92 \u2192 \u221e, \u03b6(z) reduces to 1/z and \u0394 \u2192 0 in (15). The left-hand side of (15) thus becomes lim \u03c91,\u03c92\u2192\u221e \u0393 2\u03c0 i [ \u03b6 (\u2212i ei\u03b1) \u2212 ( \u03c0\u03c91 \u0394\u03c91 \u2212 \u03b71 \u03c91 ) i ei\u03b1 \u2212 \u03c0 \u0394 i e\u2212i\u03b1 ] T = \u0393 e\u2212i\u03b1 2\u03c0 T . (17) The ratio of the imaginary and real parts of the above expression is -tan\u03b1, and the self-induced velocity reduces to the case of an unbound plane, represented by (11)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure6-1.png",
        "caption": "Fig. 6 Schematic diagram of the spur face-gear planing",
        "texts": [
            " The 4-axis CNC planer is needed, for the location of planing should be precise, and the positioning should be rapid in the process of planing. As the spur gear matched with the spur face-gear can be regarded as a stretched body, the stretched body can be obtained through enveloping by the straight line. Hence, the planing method proposed in this paper is based on the straight line motion of the planer tool, which simulates the generating motion of a single tooth of the shaper cutter (as shown in Fig. 6). Geometrically, the motor direction of the planer tool is parallel with the axis of the shaper cutter, and then the planer tool copies the section profile of the shaper cutter in the axial direction. According to the meshing principle, the spur face-gear gullet needs to be obtained through numerous continuous envelopes of the tool. However, with the consideration of the practical efficiency, the copying profile and the rotation of the tool are reasonably discretized to obtain the qualified tooth surface in the highest efficiency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure11-1.png",
        "caption": "Fig. 11 \u2013 Geometric model of bus frame \u2013 rear view.",
        "texts": [],
        "surrounding_texts": [
            "The object of study was a bus structure based on Volkswagen LT vans type: 2DX0AZ model LT produced by Automet in Sanok, Poland (Fig. 9). The basic technical specifications of the vehicle are presented in Table 2. The body of the bus was made of steel characterized by the following properties (Table 3): yield limit, Re_min = 198 MPa, tensile strength, Rm_min = 364 MPa, elongation, A5 = 22% Table 3 \u2013 Tensile characteristics for the material of the body. Strain [ ] Stress (MPa) 0.005 210.3 0.01 222.5 0.02 245.2 0.04 277.5 0.06 299.8 0.08 316.6 0.10 328.8 0.12 341.0 0.14 347.8 0.16 353.1 0.18 357.5 0.20 361.1 0.22 363.7 According to the manufacturer (VW) the frame of the vehicle was made of steel St 12.03 and St 37-2, whose strength properties are listed in table: St 12.03 yield limit, Re_min = 210 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% St 37-2 yield limit, Re_min = 235 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% Taking into account the quantitative changes in the material, i.e. the strain rate, the material model based on the assumed viscoplasticity of the material was obtained. A broad review of this characteristic is included in works [10,11]. The hardening velocity \u00c7 e equals elastic hardening velocity \u00c7 eel and viscoplastic hardening velocity, \u00c7 ev p \u00c7 e \u00bc\u00c7 eel \u00fe \u00c7 ev p; whereas the value of stress equals: s \u00bc E \u00c7 e \u00c7 ev p ; where E is the elasticity module. The finite element method uses the models of hardening at deformation velocity based on the abovementioned model, e. g. Cowper\u2013Symonds model [12]: s \u00bc\u00c5 s0 1 \u00fe \u00c7 e D 0 @ 1 A 1= p2 64 3 75; where \u00c5 s0 is the static yield limit, p, D are material constants, equalled to 5 and 40 s 1 respectively. The bodywork is supported by a frame on wheels (twin wheels in the rear). The bodywork was furnished with basic elements of bus interior, i.e. seats, seats frame, reinforcement of side wall, reinforcement of back wall, reinforcement of roof with a support structure for the emergency compartment, shelves and ventilation shaft and the air-conditioning system. It also includes glass panes which are glued to the reinforced body structure. All these elements constitute a load to the bodywork structure but do not alter its original shape. The first stage was to prepare the geometric model of the external shape of the structure. The strength calculations [13] were conducted using specialized software which implements an explicit algorithm for computing simultaneous differential equations [14]. The geometric model served as a basis for a discreet model of the bus bodywork, which was used for calculations using the finite element method. The body and frame were modelled using shell elements. These are rectangular four-node shell elements with 6 degrees of freedom in the node. The average size of the finite element is approximately 20 mm. Due to the fact that during a strength test the material may be subject to partial plastification (material nonlinearity) and large hinges may cause the configuration to change significantly (geometric nonlinearity), all finite elements are adapted to calculations with both types of nonlinearity [15]. The geometric model of the bus is shown in Figs. 10 and 11. The discrete model with division into finite elements is presented in Figs. 12 and 13. In total the discreet model comprises 105 151 finite elements on 102 879 nodes. The complete model has approximately 617 000 degrees of freedom. Since there are two rows of seats on the left side of the bus, the centre of gravity is somewhat moved leftwards relative to the axis of the vehicle. Its coordinates relative to the system, whose beginning is on the tilting edge above the rear wheel, are presented in Table 4. By tilting the bus on its right side the worst case was analysed (greater kinetic energy). From the law of conservation of energy: Ep \u00bc Ek; Table 4 \u2013 Moments of inertia relative to the edge of tilt (the Z axis along the tilting edge) (kg T m2). Ixx Iyy Izz 28130 28840 7226 Ixy Iyz Izx 2586 4036 6493 where Ep is the potential energy, Ek is the kinetic energy of rotational motion. Thus, in accordance with point the Regulations Ep \u00bc M g h1 \u00bc M g 0:8 \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 0 \u00fe B t\u00f0 \u00de2 q where M = Mk is the unladen kerb mass of the vehicle type if there are no occupant restraints, or Mt is the total effective vehicle mass when occupant restraints are fitted, and, Mt = Mk + k*Mm, where k = 0.5. h0 is the height (in metres) of the vehicle centre of gravity for the value of mass (M) chosen, t is the perpendicular distance (in metres) of the vehicle centre of gravity from its longitudinal vertical central plane, B is the perpendicular distance (in metres) of the vehicle's longitudinal vertical central plane to the axis of rotation in the rollover test, g is the gravitational constant, h1 is the height (in metres) of the vehicle centre of gravity in its starting, unstable position related to the horizontal lower plane of impact. Ek \u00bc I v2 2 where I is the moment of inertia relative to the temporary axis of rotation (Table 4), v is the angular velocity relative to the temporary axis of rotation. Therefore v \u00bc 2:558 rad=s Fig. 14 depicts main initial conditions of the analysis. An additional initial condition was the influence of gravity and the contact phenomena occurring on the contact points of the bus bodywork and the tilt plane as well as in the structural elements of the superstructure. Method of performing the strength test of the bus is shown in Fig. 14 while Fig. 15 presents the location of the seats inside the vehicle and the definition of residual space [16]."
        ]
    },
    {
        "image_filename": "designv10_10_0001620_iros.1992.587401-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001620_iros.1992.587401-Figure1-1.png",
        "caption": "Fig. 1. Dead reckoned course",
        "texts": [
            " This paper discusses the problem, a solution, preliminary test results and future goals for dead reckoning navigation. Experiments were done with the Ambler, an autonomous, six-legged walking robot, but the results are general and apply to any statically stable walking robot. Dead reckoning is defined as: The determination, without the aid of external observations, of the position and orientation of a vehicle from the record 01 the courses travelled, the distance made, and the known estirnaled drifi. A vehicle, starting from an initial position, P,, travels along a path segment defined by d, and O , , see Fig. 1. The new position, Y, , can be esririzated from the course and distance travelled. The accuracy of the location is dependent on the accuracy of the data, since diere is no way to verify the new location. Therefore, the proper representation of the new location is a position with an xssociated uncertainty, which is represented as a circle in Fig. 1. Furthermore, at each subsequent location, the positional uncertainty increases The implementation of dead reckoning for a vehicle such as ;I car (travelling over smooth terrain), boat or plane is straight 'Mwli tied from Wrbster's Dictionary, wlucli restrict? the definition to the position of sliips a ~ l planes. o-78o3-o737-2~92$03.00 19920IEEE 607 forward. The instrumentation required is a speedometer, a compass and a clock (or alternatively an odometer and a compass). The drift can be estimated by the known precision and accuracy of the devices and an estimation of non-measurable displacement, such as ocean currents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-18-1.png",
        "caption": "FIGURE 5-18 Piston and crank rela tion. TDC = top dead center, BDC = bot tom dead center.",
        "texts": [
            ", one not supercharged) the volumetric efficiency will be less than 100 percent. 5. Complete combustion does not occur. Nevertheless, there is a definite relationship between the compression ratio r, and the specific fuel consumption of an engine. For one LP gas engine the effect of the compression ratio upon efficiency is shown clearly in figure 5-17. Large changes in the compression ratio of diesel engines are not prac- PISTON CRANK KINEMATICS 95 tical. Most diesel engines have compression ratios that range from 16: 1 to 22: 1. Piston Crank Kinematics In figure 5-18 the piston displacement s after the crank has turned 8\u00b0 from top dead center is expressed as s = r + I - r cos 8 - I cos <!> (3) where r and I are the crank radius and the connecting rod length, respectively. Since then I cos <!> 96 ENGINE DESIGN Substituting the latter in equation 3 and simplifying, we obtain s = r[ (1 - cos 9) + ; (1 - VI - r2/l2 sin2 9) ] (4) Adding r 4sin4 9/4[4 to the terms under the radical to complete the square results in the approximate relation PISTON CRANK KINEMATICS 97 5 - r[ (l - COS 8) + ~-l sin2 8 J = r[ (1 - cos 8) + ~l (l - cos 28) J (5) The piston velocity (i at a given crank angle can be derived by differ entiating equation 5 ,,-ith respect to time t to obtain ds ds d8 ( r ) v = dt = d8 dt = rw sin 8 + 21 sin 28 (6) ,,-here w is the angular velocity of the crank",
            " The components in the x and y directions are X\"~ = me w 2r cos 8 } Y\" = me w2r sin 8 (12) Then the inertia force components XII and YII due to the rotating part can be obtained from equations 11 and 12 as 2 } Xe + X, = m/iw r cos 8 Y(, + Y( = m/iw2r sin 8 (13) where mil = me + m,2' These inertia forces vary with crankshaft rotation and thus become one source of engine vibration. Crank Effort The gas pressure and the inertia forces may be combined to determine the net force P acting along the cylinder axis (fig. 5-18). The angularity of the connecting rod causes the net force to be divided into components, one pro ducing piston thrust against the cylinder wall, the other acting along the axis of the connecting rod. As shown in figure 5-18, the tangential force Q; acting at the crankpin is obtained by resolving the force Q acting along the rod into two components, one acting tangentially on the crank circle at the crankpin, the other acting radially at the crankpin. Since Q = P/cos <\\> and Q, = Q sin (8 + <\\\u00bb, the torque T acting on the crankshaft is expressed in the form T = Q,I = PI sin(8 + <\\\u00bb/cos <\\> (14) A Iso, cos <\\> VI - (lIlf sin 2 8 and { sin <\\> = r sin 8. Thus 102 ENGINE DESIGN sin (8 + <!\u00bb sin 8 cos <!> + cos 8 sin <"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.6-1.png",
        "caption": "Fig. 1.6. Wheel coordinate systems",
        "texts": [],
        "surrounding_texts": [
            "The core of the model is based on differential equations derived from the fundamental principle of dynamics and the Euler angle formalism."
        ]
    },
    {
        "image_filename": "designv10_10_0002658_j.jsv.2012.12.025-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002658_j.jsv.2012.12.025-Figure2-1.png",
        "caption": "Fig. 2. A rotor-bearing model with three disks.",
        "texts": [
            " DE algorithm uses a greedy algorithm to select the better vector which replaces the target vector in the next generation zi,g\u00fe1 \u00bc ui,g if f \u00f0ui,g\u00der f \u00f0xi,g\u00de zi,g otherwise ( (28) After completed some generations of mutation, crossover and selection operations, the optimal solution is obtained to rebuild the Kriging surrogate model. The Kriging surrogate model is updated by this point-adding process until it is sufficiently accurate according to SMC or SDF criterion. To demonstrate the accuracy and reliability of the present method, a numerical study of a rotor-bearing system with three disks is carried out [31] and Fig. 2 shows the FE model with thirteen grids. An unbalance mass is added on disk 2 with magnitude of 200 g mm. The unbalance responses at the 2nd node are selected as simulation measured responses. Details of the rotor-bearing model are given in Table 1. x\u00bc[kxx,kyy,cxx,cyy,u] are chosen as identification parameters, where kxx and kyy are the horizontal and vertical stiffness coefficients, cxx and cyy are the horizontal and vertical damping coefficients, respectively. u is the magnitude of mass unbalance of disk"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003748_s11071-016-3218-y-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003748_s11071-016-3218-y-Figure5-1.png",
        "caption": "Fig. 5 Crack model at gear tooth fillet region: a Case A b Case B",
        "texts": [
            "3 Gear tooth plastic inclination deformation In this section, we will simulate the gear tooth plastic inclination deformation when a spatial crack exists on one of the driven gear teeth. The main parameters of the spur gear set are shown in Table 1. All the gear teeth except the cracked tooth are ideal without any profile errors. Firstly, we assume that the crack is initiated at the position (i.e., l0) determined by the 30\u25e6 tangential method defined in BS ISO 6336-3:2006 [20], and propagates only in tooth width and tooth depth directions, i.e., Also, suppose the crack depth is distributed as a parabolic function along tooth width as shown in Fig. 5. If the crack extends only a part of the tooth width (i.e., crack length Wc < W ), as shown in Fig. 5a:{ qw = \u2212 q0 W 2 c \u2217 w2 + q0, w \u2208 [0,Wc] qw = 0, w \u2208 [Wc,W ] (15) If the crack extends through the whole tooth (i.e.,Wc = W ), as shown in Fig. 5b: qw = q2 \u2212 q0 W 2 c \u2217 w2 + q0, w \u2208 [0,W ] (16) where q2 is the crack depth at the other end surface of the cracked tooth. All the crack parameters are shown in Table 2. Two groups of tooth damage are considered where the crack inclination angle \u03b1c is kept at a constant 60\u25e6. Group A represents the case where the crack extends through only a part of the tooth width, whereas group B represents the case where the crack extends through the whole tooth. Suppose the plastic inclination angle \u03b8p along the tooth width direction is proportional to the crack depth, and the initial plastic angle \u03b8p0 is increasing from 0 to 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002166_s11071-009-9504-1-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002166_s11071-009-9504-1-Figure2-1.png",
        "caption": "Fig. 2 Fixed platform",
        "texts": [
            " Rotary actuators are situated on the 4 corners Ai (for i = 1,2,3,4) of the base platform and their shafts are connected to the lower part of linear actuators through a universal joint (Figs. 1 and 2). The upper part of linear actuators is connected to 4 corners of the upper platform Bi using spherical joints, see Fig. 3. Cartesian coordinates A(O,x, y, z) and B(P,u, v,w) represented by {A} and {B} are connected to the base and moving platforms, respectively. Coordinates Ci(Ai, xi, yi, zi ); i = 1, ..,4, are connected to the base platform with their xi axes aligned with the rotary actuators (see Fig. 2). Moreover, si represents the unit vector along the axes of the ith rotary actuator, li is the unit vector along \u2212\u2212\u2192 AiBi and ai is used to represent the vector \u2212\u2212\u2192 OAi (Fig. 1). Assuming that each limb is connected to the fixed base by a universal joint, the orientation of the ith limb with respect to the fixed base can be described by two Euler angles, rotation \u03b8i around the rotary axis si , followed by rotation \u03c8i around ni which is perpendicular to li and si (Fig. 4). Also, di is the length of \u2212\u2212\u2192 AiBi "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003844_tia.2018.2859310-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003844_tia.2018.2859310-Figure8-1.png",
        "caption": "Fig. 8. No load flux distributions, DC current is 13.44A. (a) Model 1. (b) Model 2. (c) Model 3. (d) Model 4. (e) Model 5. (f) Model 6.",
        "texts": [
            " Then the total flux linkage of Phase A in Model 3-6 are: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) a a a a a a a b a c dc a a a b a c dc a a a a b a c dc a a a b a c dc t t t t L M M I M M M I t M M M I L M M I                                                (9) where the subscripts + and \u2013 imply the DC current direction in the armature windings. Then the fundamental back-EMF is: 1 ( ) ( ) sin( )a a r r aa dc r r d t e t N L I N t dt     (10) When only DC current is injected to the windings as the specified direction in Fig. 2, an exciting field will be produced in the air gap. The no load flux distributions with a DC current of 13.44 A are compared in Fig. 8, and the radial air gap flux densities are shown in Fig. 9. The asymmetric flux of Models 5 and 6 is mainly due to an odd number of rotor slots while the number of stator slots is even. Assuming that on one side, the stator tooth aligns with the rotor tooth and the magnetic flux is maximal. Then in the opposite position, the stator tooth must align with the rotor slot and the magnetic flux is minimal. The waveforms are irregular. In fact, as listed in Table III, the main harmonic can be divided into three categories: the stationary components, which are created by the interaction between stationary MMF and constant air gap permeance; the working field harmonics, which are the modulated results of fundamental rotating permeance on stationary MMF; the rotating harmonic fields, which are caused by the rotating permeance harmonics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003736_j.ifacol.2016.07.092-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003736_j.ifacol.2016.07.092-Figure1-1.png",
        "caption": "Fig. 1. Four rotors quadcopter",
        "texts": [
            " Keywords: quadcopter control, evolving fuzzy control An unmanned aerial vehicle (UAV) is an aircraft that does not need a human pilot aboard. Many types of UAVs have been developed since 1900, and their study continued during the first World War. Later, between 1920 and 1930, quadcopters with four rotors as propellants were introduced to eliminate the need of aerodynamic fuselages of UAVs. Quadcopters use four rotors to produce thrust. Two of the motors rotate counterclockwise and the other two rotate clockwise (Huang et al., 2009). See Fig. 1. Quadcopters are complex nonstationary nonlinear systems, and tuning the controllers gains usually is an art. Yet, load and parameter changes like inertia, and lateral and up-down wind disturbances can significantly affect the performance of the control system. Contrary to classic control systems, fuzzy controllers depend mostly on expert knowledge (Pedrycz and Gomide, 2007). But similarly to classic control systems, they require a proper choice of the universes, membership functions, control rules, scale factors, and gains",
            " Sections 4 shows how SPARC is used for stabilization and navigation control of quadcopters. Simulation results and performance evaluation of the fuzzy and autonomous fuzzy controllers in a complex operational scenario are reported in section 5. Section 6 concludes the paper summarizing its findings and suggesting issues for further development. The quadcopter model considered in this paper is based on Gibiansky (2012, accessed June 8, 2015), whose dynamics has been studied by Luukkonen (2011). The quadcopter frame has four orthogonal flat rigid bars, as shown in Fig. 1. A rotor is placed at the extremity of each bar to generate thrusts orthogonal to the frame plane. The coordinate system is also shown in Fig. 1. As Fig. 1 emphasizes, rotors 1 and 3 rotate counterclockwise, whereas rotors 2 and 4 rotate clockwise. This setup allows the three basic rotations of the quadcopter frame: yaw around Z axis, pitch around X axis, and roll around Y axis. Let \u03be be the vector of the absolute coordinates and \u03b7 the Euler angles: 4th IFAC International Conference on Intelligent Control and Automation Sciences June 1-3, 2016. Reims, France Copy ight \u00a9 2016 IFAC Autonomous Fuzzy Control and Navigation of Quadcopters Diego Domingos \u2217, Guilherme Camargo \u2217, Fernando Gomide \u2217 \u2217 School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil",
            " Keywords: quadcopter control, evolving fuzzy control An unmanned aerial vehicle (UAV) is an aircraft that does not eed a human pilot aboard. M y types of UAV have been developed since 1900, and their study c ntinued during the first World War. Later, between 1920 an 1930, quadcopters with fou rotors as propellants were introduced t eliminate the need of aerodynamic fu elages of UAVs. Quadcopters use four rotors to produce thrust. Two of the motors rotate counterclockwise an the other two rotat cl ckwise (Huang e al., 2009). See Fig. 1. Quadcopters are complex nonstationary nonlinear systems, and tuning the controllers gai s usually is n art. Yet, load and parameter changes like inertia, and late al and up- ow wind distu bances can significantly affec the performance of the cont ol system. Contrary to classic control systems, fuzzy controllers depend mos ly on expert knowledge (Pedrycz a d Gomi , 2007). Bu similarly to classic control systems, they require a proper choice of he universes, memb rship functions, control ules, scale factors, and gains",
            " Sections 4 shows how SPARC is used for stabilization and navigation control of quadcopters. Simulation results and performance evaluation of the fuzzy and autonomous fuzzy controllers in a complex operation l scenario are reported in section 5. Se tion 6 concludes the paper summarizing its findings and suggesting issues for further development. The quadcopter model considered in this paper is based on Gibiansky (2012, acc ssed June 8, 2015), whose dynamics has been studied by Luukko n ( 1 . T e quadcopter fr me has four orthogonal flat rigid bars, as shown in Fig. 1. A r tor is placed at the extremity of each bar to generate th usts orthogonal to the frame plane. The c ordinate system is also shown in Fig. 1. As Fig. 1 emphasizes, rotors 1 and 3 rotate counterclockwise, whereas rotors 2 and 4 rotate clockwise. This setup allows the three ba ic rotations of the quadcopter frame: yaw around Z axis, pitch r und X axis, nd roll a ound Y axis. Let \u03be be the vector of the absolute coordinates and \u03b7 the Euler angles: 4th IFAC International Conference on Intelligent Control and Automation Sciences June 1-3, 2016. Reims, France Copyright \u00a9 2016 IFAC utono ous Fuzzy ontrol and avigation of uadcopters Diego Domingos \u2217, Guilherme Camargo \u2217, Fernando Gomide \u2217 \u2217 School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil",
            " Keywords: quadcopter control, evolving fuzzy control An unmanned aerial vehicle (UAV) is an aircraft that does not need a human pilot aboard. Many types of UAVs have been developed since 1900, and their study continued during the first World War. Later, between 1920 and 1930, quadcopters with four rotors as propellants were introduced to eliminate the need of aerodynamic fuselages of UAVs. Quadcopters use four rotors to produce thrust. Two of the motors rotate counterclockwise and the other two rotate clockwise (Huang et al., 2009). See Fig. 1. Quadcopters are complex nonstationary nonlinear systems, and tuning the controllers gains usually is an art. Yet, load and parameter changes like inertia, and lateral and up-down wind disturbances can significantly affect the performance of the control system. Contrary to classic control systems, fuzzy controllers depend mostly on expert knowledge (Pedrycz and Gomide, 2007). But similarly to classic control systems, they require a proper choice of the universes, membership functions, control rules, scale factors, and gains",
            " Sections 4 shows how SPARC is used for stabilization and navigation control of quadcopters. Simulation results and performance evaluation of the fuzzy and autonomous fuzzy controllers in a complex operational scenario are reported in section 5. Section 6 concludes the paper summarizing its findings and suggesting issues for further development. The quadcopter model considered in this paper is based on Gibiansky (2012, accessed June 8, 2015), whose dynamics has been studied by Luukkonen (2011). The quadcopter frame has four orthogonal flat rigid bars, as shown in Fig. 1. A rotor is placed at the extremity of each bar to generate thrusts orthogonal to the frame plane. The coordinate system is also shown in Fig. 1. As Fig. 1 emphasizes, rotors 1 and 3 rotate counterclockwise, whereas rotors 2 and 4 rotate clockwise. This setup allows the three basic rotations of the quadcopter frame: yaw around Z axis, pitch around X axis, and roll around Y axis. Let \u03be be the vector of the absolute coordinates and \u03b7 the Euler angles: 4th IFAC International Conference on Intelligent Control and Automation Sciences June 1-3, 2016. Reims, France Copyright I AC Autono ous Fuzzy Control and Navigation of Quadcopters Diego Domingos \u2217, Guilherme Camargo \u2217, Fernando Gomide \u2217 \u2217 School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil",
            " Keywords: quadcopter control, evolving fuzzy control An unmanned aerial vehicle (UAV) is an aircraft that does not need a human pilot aboard. Many types of UAVs have been developed since 1900, and their study continued during the first World War. Later, between 1920 and 1930, quadcopters with four rotors as propellants were introduced to eliminate the need of aerodynamic fuselages of UAVs. Quadcopters use four rotors to produce thrust. Two of the motors rotate counterclockwise and the other two rotate clockwise (Huang et al., 2009). See Fig. 1. Quadcopters are complex nonstationary nonlinear systems, and tuning the controllers gains usually is an art. Yet, load and parameter changes like inertia, and lateral and up-down wind disturbances can significantly affect the performance of the control system. Contrary to classic control systems, fuzzy controllers depend mostly on expert knowledge (Pedrycz and Gomide, 2007). But similarly to classic control systems, they require a proper choice of the universes, membership functions, control rules, scale factors, and gains",
            " Sections 4 shows how SPARC is used for stabilization and navigation control of quadcopters. Simulation results and performance evaluation of the fuzzy and autonomous fuzzy controllers in a complex operational scenario are reported in section 5. Section 6 concludes the paper summarizing its findings and suggesting issues for further development. The quadcopter model considered in this paper is based on Gibiansky (2012, accessed June 8, 2015), whose dynamics has been studied by Luukkonen (2011). The quadcopter frame has four orthogonal flat rigid bars, as shown in Fig. 1. A rotor is placed at the extremity of each bar to generate thrusts orthogonal to the frame plane. The coordinate system is also shown in Fig. 1. As Fig. 1 emphasizes, rotors 1 and 3 rotate counterclockwise, whereas rotors 2 and 4 rotate clockwise. This setup allows the three basic rotations of the quadcopter frame: yaw around Z axis, pitch around X axis, and roll around Y axis. Let \u03be be the vector of the absolute coordinates and \u03b7 the Euler angles: 4th IFAC International Conference on Intelligent Control and Automation Sciences June 1-3, 2016. Reims, France Copyright \u00a9 2016 IFAC utono ous Fuzzy ontrol and avigation of uadcopters Diego Domingos \u2217, Guilherme Camargo \u2217, Fernando Gomide \u2217 \u2217 School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil",
            " Keywords: quadcopter control, evolving fuzzy control An u manned aerial vehicle (UAV) is aircraft that doe not need a human pilot aboard. Many types f UAVs have been developed since 1900, and their study continue during the first World Wa . Later, between 1920 and 1930, quadc pters with four rotors as propellant were introduced to eliminate the need of aerodynamic fuselages of UAVs. Quadcopters use four rotors to pro uce thrust. Two of th m tors rotate coun erclockwise and the other two rotate clockwise (Huang et al., 2009). See Fig. 1. Quadcopters are complex nonstatio ary nonline r systems, and tuning the controllers gains usually is an a t. Yet, loa a d paramete changes like inertia, and la eral and up-down wind distu bances can significantly affect the performance of the control syste . Contrary o classic control systems, fuzzy co trollers - pend mos ly on expert knowledge (Pedrycz and Gomide, 2007). But similarly o classic control syst ms, they require a prope choice of the universes, membership functions, control rules, scale factors, and gains",
            " Sections 4 shows how SPARC is used for stabilization and navigation control of quadcopters. Simulation results and performance evaluation of the fuzzy nd autonomous fuzzy controllers in a omplex operational scenario are reported in section 5. Section 6 concludes the paper summarizing its findings and suggesting issues for further development. The quadcopter mod l considered in this paper is based on Gibiansky (2012, accessed Ju 8, 5 , w ose dynamics h s been studied by Luukkonen (2011). The quadcopter frame has f ur orthogonal flat rigid bars, as shown in Fig. 1. A roto is placed at the extremity of each bar t generate thrusts orthogonal to the frame plane. The coordinate system is also shown in Fig. 1. As Fig. 1 emphasizes, rotors 1 and 3 rotate counterclockwise, whereas rotor 2 and 4 rotate clockwise. This setup allows the three basic rot ti ns of the qu dcopter f ame: yaw around Z axis, pitch around X axis, and roll around Y axis. Let \u03be be the vector of the absolute coordinates and \u03b7 the Euler angles: 4th IFAC International Conference on Intelligent Control and Automation Sciences June 1-3, 2016. Reims, France Copyright \u00a9 2016 IFAC 74 Diego Domingos et al. / IFAC-PapersOnLine 49-5 (2016) 073\u2013078 \u03be = [ x y z ] (1) \u03b7 = [ \u03a6 \u03b8 \u03c8 ] (2) The rotation around the inertial system is defined by the orthogonal matrix R",
            " \u2022 one suction-based device located at the center of the quadcopter to catch and hold objects and payloads. \u2022 four uniform and rigid cylinders with dm = 2.7cm, height Am = 2.8cm and mass Mm = 80g as rotors, and propellers with null mass. Using the values above, the moment of inertia about the motor z axis is IM = 7.6g\u00b7m2, and from (4), assuming total quadcopter mass Mquad = 1.513kg, the inertial matrix of quadcopter model becomes: IFAC ICONS 2016 June 1-3, 2016. Reims, France Diego Domingos et al. / IFAC-PapersOnLine 49-5 (2016) 073\u2013078 75 \u03be = [ x y z ] (1) \u03b7 = [ \u03a6 \u03b8 \u03c8 ] (2) Fig. 1. Four rotors quadcopter The rotation around the inertial system is defined by the orthogonal matrix R. Assume Sx = sin(x) and Cx = cos(x). Thus R = [ C\u03c8C\u03b8 C\u03c8S\u03b8S\u03a6 \u2212 SpsiC\u03a6 C\u03c8S\u03b8C\u03a6 + S\u03c8S\u03a6 S\u03c8C\u03b8 S\u03c8S\u03b8S\u03a6 + C\u03c8C\u03a6 S\u03c8S\u03b8C\u03a6 \u2212 C\u03c8S\u03a6 \u2212S\u03b8 C\u03b8S\u03a6 C\u03b8C\u03a6 ] (3) The quadcopter frame has four orthogonal bars aligned with the x and y axis, which results in an inertial matrix I of the form I = [ Ixx 0 0 0 Iyy 0 0 0 Izz ] (4) Because the bars are equal, and their weight are uniformly distributed along the respective lengths, we may assume Ixx = Iyy",
            " The reference signals, determined by the mission to be performed by the quadcopter, are refpitch,k, refroll,k, refyaw,k, refalt,k. The outputs of the evolving fuzzy controllers upitch,k, uroll,k, uyaw,k and ualt,k are input to SAM to produce drive signals uri,k as follows: ur1,k = ualt,k \u2212 upitch,k + uroll,k \u2212 uyaw,k ur2,k = ualt,k + upitch,k + uroll,k + uyaw,k ur3,k = ualt,k + upitch,k \u2212 uroll,k \u2212 uyaw,k ur4,k = ualt,k \u2212 upitch,k \u2212 uroll,k + uyaw,k (28) where the index ri refers to the rotors r1, r2, r3, and r4 as numbered in Fig. 1. The navigation control performs trajectory tracking using evolving latitude and longitude controllers. The inputs of these controllers are the actual latitude and longitude values ylat,k, ylon,k, and their corresponding references reflat,k, reflon,k. The output of the navigation controllers are pitch and roll refpitch,k and refroll,k reference values which are forwarded to the picth and roll controllers shown in Fig. 4. The first step for safe autonomous navigation and control of quadcopters evolving is training",
            " The reference signals, determined by the mission to be performed by the quadcopter, are refpitch,k, refroll,k, refyaw,k, refalt,k. The outputs of the evolving fuzzy controllers upitch,k, uroll,k, uyaw,k and ualt,k are input to SAM to produce drive signals uri,k as follows: ur1,k = ualt,k \u2212 upitch,k + uroll,k \u2212 uyaw,k ur2,k = ualt,k + upitch,k + uroll,k + uyaw,k ur3,k = ualt,k + upitch,k \u2212 uroll,k \u2212 uyaw,k ur4,k = ualt,k \u2212 upitch,k \u2212 uroll,k + uyaw,k (28) where the index ri refers to the rotors r1, r2, r3, and r4 as numbered in Fig. 1. 4.2 Navigation control The navigation control performs trajectory tracking using evolving latitude and longitude controllers. The inputs of these controllers are the actual latitude and longitude values ylat,k, ylon,k, and their corresponding references reflat,k, reflon,k. The output of the navigation controllers are pitch and roll refpitch,k and refroll,k reference values which are forwarded to the picth and roll controllers shown in Fig. 4. 5. SIMULATION RESULTS 5.1 Training The first step for safe autonomous navigation and control of quadcopters evolving is training"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000722_1.2794209-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000722_1.2794209-Figure13-1.png",
        "caption": "Fig. 13 Initial conditions for a periodic solution for quadruped gallop",
        "texts": [
            " In that case, the energy exchange was between all of the three types of energy. Other investigators (Alexander, 1988) have speculated about this result but they have not been able to quantitatively verify it. The primary difference between gallop (Fig. 12) and bound is that the rear legs and the front legs do not act together in gallop. This adds another variable to the simulation (in the case of a two-dimensional model). Fortunately, this can be accom modated easily in the simulation by choosing appropriate initial conditions. Now the starting position is that shown in Fig. 13. The legs are separated by a phase angle a in the initial posi tion. The feet are placed symmetrically on the ground with respect to the rear end of the body and the simulation is started by setting initial height y, and speed \u00ab,-. As each foot leaves the Journal of Biomechanical Engineering ground the angle made by that leg with the vertical is stored. When the body starts descending, the legs are again placed at the same angle at which they left the ground. If the setting for the body angle is correct, then a periodic solution can be ob tained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002070_j.mechmachtheory.2008.05.009-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002070_j.mechmachtheory.2008.05.009-Figure2-1.png",
        "caption": "Fig. 2. Kinematical scheme of first leg A of the mechanism.",
        "texts": [
            " Thus, all actuators can be installed on the fixed base. In the second configuration (RPR) each prismatic joint is an actively controlled prismatic cylinder. For the purpose of analysis, we attach a Cartesian frame x0y0z0(T0) to the fixed base with its origin located at triangle centre O, the z0 axis perpendicular to the base and the x0 axis pointing along the direction C1A1. Another mobile reference frame xGyGzG is attached to the moving platform. The origin of this coordinate central system is located just at the centre G of the moving triangle (Fig. 2). To simplify the graphical image of the kinematical scheme of the mechanism, in the follows we will represent the intermediate reference systems by only two axes, so as it is used in most of robotics papers [1,3,9]. The zk axis is represented for each component element Tk. It is noted that the relative rotation with uk,k 1 angle or relative translation of Tk body with kk,k 1 displacement must be always pointing about or along the direction of zk axis. In what follows we consider that the moving platform is initially located at a central configuration, where the platform is not rotated with respect to the fixed base and the mass centre G is at the origin O of fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002042_9780470753842.ch2-Figure2.5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002042_9780470753842.ch2-Figure2.5-1.png",
        "caption": "Figure 2.5 Proposed electron transfer pathway for a QH\u2013ADH/PPy electrode from PQQ via the enzyme-integrated heme groups to the conducting PPy chains and finally to the electrode. The membrane-bound enzyme consists of three subunits. Subunit I (83 kDa) is considered to be the dehydrogenase unit containing one PQQ and one heme moiety; subunit II (52.1 kDa) contains three heme moieties; and subunit III (16.6 kDa), essential for the expression of the active enzyme, does not contain any electrochemically active groups [85]. (Anal. Chem., Polypyrrole-entrapped quinohemoprotein alcohol dehydrogenase. Evidence for direct electron transfer via conductingpolymer chains, 71, 3581\u20133586, A. Ramanavicius, K. Habermuller, E. Csoregi, V. Laurinavicius, W. Schuhmann. Copyright 1999 American Chemical Society.",
        "texts": [
            " About 90% of HRP was wired to the electrode in SPAN/(HRP/PSS)3 films with a 4 nm SPAN underlayer, confirming efficient wiring of enzyme through the conductive polymer. Enzyme wiring is probably facilitated because of extensive intermixing [52] of the individually deposited layers of SPAN, HRP and PSS. Schuhman et al. reported electron transfer from the multicofactor quinone-hemoprotein alcohol dehydrogenase (QH\u2013ADH) wired to a platinum electrode via Ppy [85]. They proposed that electrons first transfer from the pyrroloquinoline-quinone (PQQ) cofactor to a heme group located near the outer protein shell, and then to the PPy chains (Figure 2.5). The cooperative action of the PQQ and heme group was suggested to allow stepwise electron transfer from the active site to the conductive polymer backbone. Thus, a multicofactor enzyme can be viewed as a combination of a primary redox site accompanied by proteinintegrated electron transfer relays. Such an electron transfer pathway leads to an increase of the apparent Michaelis dissociation constant (Kapp M ) and a significantly increased linear response range for ethanol. Other multicofactor enzymes such as PQQ and heme-containing D-fructose dehydrogenase [86] and FAD and heme-containing D-gluconate dehydrogenase [87] were found to follow a similar mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001636_s0263574704000347-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001636_s0263574704000347-Figure2-1.png",
        "caption": "Fig. 2. Orthoglide geometrical model.",
        "texts": [
            " Inside each chain, one parallelogram is used and oriented in a manner that the output body is restricted to translational movements only. The arrangement of the joints in the PRPaR chains has http://journals.cambridge.org Downloaded: 15 May 2014 IP address: 186.233.152.15 been defined to eliminate any constraint singularity12 in the Cartesian workspace. To obtain the Orthoglide kinematic equations, let us locate the reference frame at the intersection of the prismatic joint axes and align the coordinate axis with them (Fig. 2), following the \u201cright-hand\u201d rule. Let us also denote the input vector of the prismatic joints variables as = (\u03c1x, \u03c1y, \u03c1z) and the output position vector of the tool centre point as p = (px, py, pz). Taking into account obvious properties of the parallelograms, the Orthoglide geometrical model can be presented in a simplified form, which consists of three bar links connected by spherical joints to the tool centre point at one side and to the corresponding prismatic joints at another side. Using this notation, the kinematic equations of the Orthoglide can be written as follows (px \u2212 \u03c1x)2 + p2 y + p2 z = L2 p2 x + (py \u2212 \u03c1y)2 + p2 z = L2 p2 x + p2 y + (pz \u2212 \u03c1z)2 = L2 (1) where L is the length of the parallelogram principal links and the \u201czero\u201d position p0 = (0, 0, 0) corresponds to the joints variables 0 = (L, L, L), see Fig",
            " From the Orthoglide geometrical model (1), the inverse kinematic equations can be derived in a straightforward way as: \u03c1x = px + sx \u221a L2 \u2212 p2 y \u2212 p2 z \u03c1y = py + sy \u221a L2 \u2212 p2 x \u2212 p2 z (3) \u03c1z = pz + sz \u221a L2 \u2212 p2 x \u2212 p2 y where sx, sy, sz are the branch (or configuration) indices that are equal to \u00b11. It is obvious that (3) yields eight different branches of the inverse kinematic algorithm, which will be further referred to as PPP, MPP . . . MMM, following the sign of the corresponding index (i.e. the notation MPP corresponds to the indices sx =\u22121; sy = +1; sz = +1). The geometrical meaning of these indices is illustrated by Fig. 2, where \u03b8x , \u03b8y , \u03b8z are the angles between the bar links and the corresponding prismatic joint axes. It can be proved that s = 1 if \u03b8 \u2208 (90\u25e6, 180\u25e6) and s = \u22121 if \u03b8 \u2208 (0\u25e6, 90\u25e6). Hence the branch transition (\u03b8 = 90\u25e6) corresponds to the serial singularity (where the leg is orthogonal to the relevant translational axis and the input joint motion does not produce the end-point displacement). It is obvious that if the inverse kinematic solution exists, then the target point (px, py, pz) belongs to a volume bounded by the intersection of three cylinders CL = { p \u2223\u2223p2 x + p2 y \u2264 L2; p2 x + p2 z \u2264 L2; p2 y + p2 z \u2264 L2 } (4) that guarantees non-negative values under the square roots in (3)",
            " Configuration indices As follows from the previous sub-sections, both the inverse and direct kinematics of the Orthoglide may produce several solutions. The problem is how to define numerically the configuration indices, which allow one to choose among the corresponding algorithm branches. For the inverse kinematics, when the configuration is defined by the angle between the leg and the corresponding prismatic joint axis, the decision equations for the configuration indices are trivial: sx = sgn(\u03c1x \u2212 px); sy = sgn(\u03c1y \u2212 py); sz = sgn(\u03c1z \u2212 pz); (18) Geometrically, s > 0 means that \u03b8x, \u03b8y, \u03b8z \u2208 ]\u03c0 2 3\u03c0 2 [ (see Fig. 2). For the direct kinematics, the configuration is defined by the end-point location relative to the plane that passes through the prismatic joint centres (see Figs. 6\u20137). Hence, the decision equation may be derived by analysing the dot-product of the plane normal vector (\u03c1\u22121 x , \u03c1\u22121 y , \u03c1\u22121 z ) and the vector directed along any of the bar links (for instance, (px \u2212 \u03c1x, py, pz) for the first link): m = sgn ( px \u03c1x + py \u03c1y + pz \u03c1z \u2212 1 ) (19) which for the positive joint limits is equivalent to m = sgn(px\u03c1y\u03c1z + \u03c1xpy\u03c1z + \u03c1x\u03c1ypz \u2212 \u03c1x\u03c1y\u03c1z) (20) It should be stressed that the feasible solutions for the inverse/direct kinematics, located in the neighbourhood of the \u201czero\u201d point, have the following configuration indices: sx = sy = sz =+1 and m =\u22121",
            " If det(J) = 0 (serial, or inverse kinematic singularity), the mapping from the joint velocity space to the tool velocity space is ill-conditioned. It means that certain directions of motion are unattainable and the manipulator loses at least one degree of freedom. The corresponding relations between the manipulator variables are: (px = \u03c1x) or (py = \u03c1y) or (pz = \u03c1z) (29) px\u03c1y\u03c1z + \u03c1xpy\u03c1z + \u03c1x\u03c1ypz \u2212 \u03c1x\u03c1y\u03c1z = 0 (30) Geometrically, this type of singularity corresponds to the orthogonal orientation of the parallelogram links relative to the relevant prismatic joint axes (i.e. px = \u03c1x , \u03b8x =\u03c0/2, etc.; see Fig. 2) and the work point P is located on the corresponding surface of the cylinder CL. As follows from the workspace analysis, such points belong to the external border of the thin non-convex solid GL (Fig. 10, singularity \u201ca\u201d). If det(J\u22121) = 0 (parallel, i.e. direct kinematic singularity), the mapping from the tool velocity space to the joint velocity space is ill-conditioned. It means that the manipulator loses instantaneously its stiffness and certain output motion may exist while the actuators are locked"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001730_j.cirp.2007.05.092-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001730_j.cirp.2007.05.092-Figure2-1.png",
        "caption": "Figure 2: Different alternatives of multipoint(3P,4P)spindle bearings.",
        "texts": [
            " presented in [1] spindle bearings with varied inner geometries in order to reduce the negative effects of the centrifugal forces acting on the balls. In addition, the robustness of the bearings should be improved. Weck et al. provided additional contact points on the raceways of the inner and outer ring of conventional spindle bearings. Due to this, the axial and radial movement of the balls is prevented and constant contact angles and a reduced axial displacement of the inner ring can be ensured over a wide speed range. The bearing concepts introduced in [1] are shown in Figure 2 (a), (b). Figure 2 (c) presents a third, novel concept introduced in this paper. The contents of [1] focus on the operating behaviour of multipoint(3P)-bearings, both theoretic and experimental investigation. The test bearings were manufactured at the Laboratory for Machine Tools and Production Engineering (WZL) based on conventional spindle bearings. Also some characteristics of multipoint(4P)-Bearings were analysed by means of numerical calculations. Subsequently, further results regarding the development of new bearing kinematics with four contact points per ball under consideration of thermal effects will be presented",
            " At a maximum rotational speed of 30,000 rpm the Hertzian pressures on the inner ring rise above the limiting value of 2,000 N/mm\u00b2. In addition to these theoretical results, one has to take into consideration that the increase of internal stresses on the one hand and the thermal overloading on the other are coupled selfenergising effects. Therefore, one can expect jamming of a multipoint(4P)-bearing with a pronounced excess temperature of the inner ring in case of higher rotational speeds. This assumption will be investigated in experimental tests in section 2.3. Figure 2 (c) shows a third concept of a new bearing geometry. It was developed in order to prevent the internal overloading of the multipoint(4P)-bearing. The concept is characterised by a divided inner ring. One half of the ring which is oriented towards the tool side of the spindle is fixed to the spindle body. By that, it can bear the forces resulting from the machining process. The second half of the ring is axially movable and pressed against the balls by a disc spring, creating an internal preloading of the bearing",
            " The test bearings can be loaded axially by a hydraulic piston. A tempering of the outer ring is realised by a water circulation in the flange. Thereby, the heating of the outer ring caused by the additional rolling contact can be reduced. The inner bearing temperature is measured by a non-contacting sensor positioned closely to the rotating inner ring. The diagram in Figure 7 presents experimental results for both a rigid and an elastic multipoint(4P)-bearing. At first, the rigid bearing (concept (b), Figure 2) was tested. The tests were performed with and without tempering of the outer ring. Subsequently, the flexible bearing (concept (c), Figure 2) was tested with tempering of the outer ring. The measured temperatures are shown related to ambient temperature. The torque values are derived from the motor current during the tests. The abbreviations used in Figure 7 are explained in Table 2. The curves [it1] and [ot1] illustrate the inner and outer temperatures of first test bearing, concept (b). The axial load amounts to 1,000 N. The bearing is greaselubricated with 5 g of Kl\u00fcberSpeed BF72-22. Up to 19,000 rpm the rotational speed is increased by 2,000 rpm every 2 hours, then by 1,000 rpm every 2 hours"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure4-1.png",
        "caption": "Fig. 4. Elastic-plastic stress distributions from (a) von Mises and (b) Tresca for a solid disc rotating at similar speeds",
        "texts": [
            "2 Solid disc Next consider a thin, solid steel disc with outer radius 250 mm of similar material properties rotating at a speed of 13000 rev/min. This lies between the initial yield speed of 11930 rev/min and a fully plastic (Tresca) speed of 13232 rev/min from eqs. (20b) and (21b), respectively. In this case a von Mises numerical solution to the interior elastic-plastic stress distribution was initialised for N 50 (h 5 mm). Iterating as for the hollow disc provided rep 110 mm with the required accuracy ER < 0:05 when N 200 h 1:25 mm). Fig. 4a shows the normalised radial and hoop stress distributions and their residuals for a stationary disc. By this criterion both stresses remain close to the yield stress throughout the plastic zone. In contrast Tresca (see Fig. 4b) predicts that sq Y constant, while sr falls within this region. Again, a greater spread of plasticity appears from Tresca at the given speed. The contrasting behaviour is reflected in both the magnitude and the sense of the residual stresses. It appears that Tresca magnitudes are greater but nowhere do they exceed 25% of the yield stress. Also, the sense of both sRr and sRq oppose those of von Mises within the prior elastic zone. We should only need to measure the residual hoop strain at the outer diameter to establish which criteria is more realistic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001635_cdc.2006.377165-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001635_cdc.2006.377165-Figure3-1.png",
        "caption": "Fig. 3. Convergence of the differentiator in the normalized coordinates",
        "texts": [
            " The measured output is y(t), the parametric function L(t) =3(y2 2+y 2y +y2 + 36)12 is taken. The differentiator takes the form zo Vo , vo -3 L(t) zo - y(t)0 sign(zo - y(t)) +z,\u00b1 1/3 2/3 z1 = v1, v1 = -2 L(t) z1 - v0 sign(z1 - v0) + Z2 = vk4 , vk 1 = -1.5 L(t) Zkl 2 sign(zk -vk-2) + Zk, Z3 = -ii. vL(t) sign(Zk-fVk1)The initial values of the differentiator are zo(O) = 10, zl(\u00b0) The normalized coordinates cGo(t) = (zo(t) - y(t))/L(t), cyl(t) =Z()-y (t)Lt,C72(t) = (Z2(t) - y t)Lt,c73(t)= (z3(t) - y (t))/L(t) are shown in Fig. 3. The accuracies laol < 6.9-10-,y16T < 1.2-10-1, IG21 < 1.0-10- , 1GU31 < 4.6 10 were obtained withX = 10 . With X = 10 the accuracies change to lcToI < 2.0 10 , Icy,J < 5.0.109, GC21 < 5.2 10 , 1U31 < 2.4 103. The convergence of the normalized coordinates to zero during the first 2 time units is shown in Fig. 3. 1 -6 .1 -4 ICThe accuracies change to Icyol < 7.8.10, Ic < 2.0 10 21 < 2.5.103, 1y31 < 0.017 when a measurement noise is introduced with the normalized magnitude E = 10 . Note that FrBl 0.6 45th IEEE CDC, San Diego, USA, Dec. 13-15, 2006 L(10) = 9.42 106, and respectively the real noise magnitude is 9.42 10 at t = 10. Taking E = 10 obtain Icyol < 5.5 10 , 1-3 .1 -2 laosGCTJ < 4.9 10, 21 < 2.110, y31 < 0.047 with the real noise magnitude 9.42. 10 at t= 10. The differentiator based on high-order sliding modes [19] is modified to allow differentiation of signals up to the order k with a known functional bound L(t) of the (k+l)th-order derivative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-4-1.png",
        "caption": "FIGURE 12-4 Spur-gear pump.",
        "texts": [
            " When hydraulic cylinders are arranged axially, as shown in figure 12-2, the rate of flow through the pump can be regulated by con trolling the angle between the piston block and the swash plate, a common method of control on a hydrostatic transmission. Radial piston pumps (fig. 12-3) can also be used as motors. The displace ment of a radial piston pump can be controlled by allowing the pressure to lift the pistons off the eccentric. By this method the pump unloads and does not do any work except when the pressure drops sufficiently to force the pistons back onto the eccentric. A spur-gear pump is shown in figure 12-4. It is normally used on tractor hydraulic systems of lower pressure. The spur-gear, the internal-gear pump (fig. 12-5), the gerotor-gear pump (fig. 12-6), and the vane-type pump (fig. 12-7) are all used on tractor hydraulic systems where lower pressures are used. Motor Performance* Because efficiencies are often high, very accurate instrumentation is required if the motor is externally loaded because a small error in measurement of *This section also applies to pumps. Equations I and 2 should be inverted when used for pumps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002855_bio.2337-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002855_bio.2337-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of flow-injection CL detection system; Pa, pump A; Pb, pu cell; S, power supply; R, recorder.",
        "texts": [
            "8%), cadmium chloride (CdCl2, 99%) and sodium borohydride (NaBH4, 99%) from Aldrich Chemical Co. The blood was provided by a local hospital. All solutions were prepared with deionized water with resistivity higher than 18 M\u03a9/cm. The UV\u2013vis absorption spectrum was obtained using a Varian GBC Cintra10e UV-visible spectrometer. In both experiments, a 1 cm pathlength quartz cuvette was used. CL analysis was conducted on a flow-injection (FI) analysis processor (FIA-3110, (Beijing Titan Instruments Co., Ltd, China); a schematic diagram of the system is shown in Fig. 1. The FI analysis system consisted of two peristaltic pumps (Pa and Pb), a 16 hole, eight-way valve (V) for delivery of reagents and samples, a digital system for flow time control, an ultra-weak luminescence analyser (type BPCL, manufactured by the Beijing Institute of Biophysics, Chinese Academy of Science); a photomultiplier tube (PMT) operating at 1080V and 30 C serves for amplification of the CL signal. The temperature in the CL reaction chamber is automatically readjusted by a temperature control system",
            "com/journal/luminescence All received blood samples contained EDTA as anti-coagulant, and tests showed that this does not influence CL intensity. A 10 mL blood sample was diluted to 10mL with 1 10\u20133mol/L phosphate-buffered saline (PBS) solution, then 1.5mL diluted blood sample was taken into a test tube with 5 mL HCl (0.1mol/L). After 10min of ultrasonication, 2 mL NaOH (0.1mol/L) was added to adjust the pH, then the solution was centrifuged for 10min at 6000 rpm and the supernatant collected for analysis. Fig. 1 illustrates the FI\u2013CL detection system employed in the study. The sample was injected into the K4Fe(CN)6 stream, both being pumped by peristaltic pump A at a flow rate of 1.2mL/min, so that the mixture filled the 150 mL loop. The H2O2, CdTe QDs and fluorescein were delivered by peristaltic pump B, at a flow rate of 4.5mL/min; the mixture from pump B and the sample solution from pump A were mixed in the loop and then were carried to the CL detection chamber. The CL generated in the colourless glass coil was captured by the detector and then amplified by the PMT"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000764_s0094-114x(97)00022-0-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000764_s0094-114x(97)00022-0-Figure3-1.png",
        "caption": "Fig. 3. Crowning of the pinion tooth surface.",
        "texts": [
            " Numerical results for the test of the developed theory and its illustration are provided. The authors limit the discussions to the case of an orthogonal face-gear drive with a crossing angle of 90 . However, the proposed approach is easy to extend for non-orthogonal face-gear drives. \u00a9 1998 Elsevier Science Ltd. NOMENCLATURE N~-number of teeth of the sharper (i = s), pinion (i = 1), and face-gear (i = 2) Eo--nominal value of the shortest center distance between the pinion and the grinding disk (Fig. 3) Er-- instantaneous value of the shortest center distance between the pinion and the grinding disk (Fig. 3) l~d i sp l acemen t of the grinding disk in the direction of the pinion axis (Fig. 3) a~--parabola coefficient of the parabolic function Si--coordinate system u~0k~--surface parameters of the shaper 0o~--angular width of the space of the shaper on the base circle (Fig. 5) r ,~posi t ion vector in system S,(i = s, 1, 2) rh~--radius of the base circle of the shaper (Fig. 5) ~o--pressure angle [Fig. 6 (b)] ~--proflle angle for determination of pointing (Fig. 7) n,, N~--unit normal and normal (Fig. 5) to the shaper surface Mj~--matrix of coordinate transformation from system S~ to system S, E,--shaper (i = s), pinion (i = 1) or gear (i --- 2) tooth surface ~,--angle of rotation of the shaper (i = s) or face gear (i = 2) (Fig",
            " Misalignment of the face gear may cause separation of the pinion-gear tooth surfaces and edge contact. To avoid these defects, it is necessary to localize the bearing contact by substituting the instantaneous line contact of tooth surfaces by point contact. The localization of the bearing contact can be achieved: (i) by choosing a shaper whose tooth number N~ is slightly larger than the pinion tooth number N,, (Ns- N, = 1-3) [4]; (ii) by crowning of the pinion tooth surface as proposed in this paper. The number of teeth of the shaper, in the second case, is the same as that of the pinion. Figure 3 shows an example of crowning of the pinion tooth surface when this surface is generated by form-grinding. The axial profile of the grinding disk is the theoretical involute profile of the 90 F.L. Litvin et al. pinion. During generation, the grinding disk is plunged and the shortest distance is varied in accordance to the equation (Fig. 3) Ep ~ - Eo - a,l~ (1) Here, Eo and Ep are the nominal and instantaneous values of the shortest center distance, ld is the displacement of the grinding disk in the direction of the pinion axis, (Ep - Eo) is the plunge of the grinding disk, ad is the parabola coefficient of the parabolic function (aal~). 3. AXES OF M E S H I N G Litvin [2] has proven the following theorem: tooth surfaces are in line contact at every instant and one of the interacting surfaces is a helicoid. Then, there are two straight lines I-I and II-II that lie in parallel planes, have constant location and orientation during the process of meshing, and the normal to the interacting surfaces at any regular point of surface tangency passes through I-I and II-II"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000593_jsvi.2000.3412-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000593_jsvi.2000.3412-Figure2-1.png",
        "caption": "Figure 2. Rotor-gear coupling system and Co-ordinate systems.",
        "texts": [
            "m je )2#(g ji !g je )2 (mQ ji !mQ je )# (g ji !g je ) J(m ji !m je )2#(g ji !g je )2 (gR ji !gR je ). (17) Integrating the above equation, \"nally we can obtain r2 b (h ji !h je )2\"(m ji !m je )2#(g ji !g je )2. (18) Equation (18) is a constraint condition that should be satis\"ed in normal meshing between the lateral displacements in the centers and torsional angles of the hub and the sleeve of gear couplings, and the constraint is holonomic on analytical mechanics. 3. MODELLING OF THE GEAR COUPLING HALVES Figure 2(a) shows a rotor-gear coupling system that may be separated by n-station, n-section breakup. There are \"ve d.o.f. per station (m, g, d, e, h shown in Figure 2(b), neglecting the displacement in the z direction). Oxyz is the \"xed co-ordinate system, where x- and y-axis are vertical and horizontal directions respectively. For the rotor stations the vibration equations can be derived by the lumped parameters method or the \"nite element method (FEM); which is simple, hence neglected here. Now, we pay more attention to the modelling of the subsystem of gear coupling half, which includes a hub, a sleeve, and two sections j and j#1. 3.1. THE KINETIC ENERGY OF THE SUBSYSTEM Let e, d denote the angles of a disc around axes m and g respectively. Hence, in the rotating co-ordinate system shown in Figure 2(b), the kinetic energy of the hub or sleeve can be written as \u00b9 jk \"1 2 mV c )V c #1 2 G )x, k\"e, i, (19) where V c )V c \"xR 2#yR 2\"mQ 2#gR 2#X2(m2#g2)#2X (gR m!mQ g), G )x\"Jd (!eR cos d!X cos e sin d)2#Jd(dQ !X sin e)2 #Jz[!eR sin d#(X#hQ ) cos e cos d]2. The kinetic energy \u00b9 of the subsystem is given by \u00b9\"\u00b9 je #\u00b9 ji , (20) where the subscripts je and ji denote the hub and sleeve of the gear coupling at station j. 3.2. THE POTENTIAL ENERGY OF THE SUBSYSTEM The potential energy function ; of the subsystem consists of two parts, one part is from the elastic deformation of the rotor sections beside the coupling, another part from the teeth deformation of the coupling that was modelled by Marmol [3] with the lateral and angular sti",
            " Traditionally, the vibration models of the rotor system with a gear coupling we onsidered were divided into two uncoupled directions [3, 5, 7}9], or their generalized o-ordinates (or generalized displacements) are uncoupled both in the lateral and orsional directions; therefore, their dynamic characteristics are not a!ected by each other. owever, from equation (24) we can see clearly that the inertia terms and elastic terms re coupled both in the lateral direction and torsional directions, respectively, and annot be divided again. Meanwhile the system becomes non-linear at the station of gear oupling. Assembling all the equations of motion of the stations, we can obtain the dynamic quations of the system [Figure 2(a)]. If some journal bearings existed in the rotors, the linearized sti!ness and damping coe$cients of oil \"lm may be introduced as follows: G DF x DF y H\"C k xx k xy k yx k yy D G x yH#C d xx d xy d yx d yy D G xR yR H . (25) After transforming expression (25) into the rotating co-ordinate system, it becomes G DFm DFgH \"C cosXt sinXt !sinXt cosXtDG DF x DF y H . (26) Therefore equations of motion of the rotor-bearing-gear coupling system can be expressed as [M]MfG N#[C]MfQ N#[K]MfN\"0, (27) where the elements of the matrices [M], [C], and [K] are not constant, they are functions of the generalized co-ordinates"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000579_s0094-114x(98)00043-3-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000579_s0094-114x(98)00043-3-Figure3-1.png",
        "caption": "Fig. 3. Kinematically equivalent mechanism with respect to the octahedral Stewart platform mechanism of Fig. 1.",
        "texts": [
            " The revolute joint Or will be located on the intersection of the line AB and the line passing through R and perpendicular to the line AB. This implies that the revolute joint Or has the joint axis along the direction of AB. Similarly, the linkages ATC and BSC can now be replaced by the links OtT and OsS, with the revolute joints at Os and Ot and spherical joints at S and T, respectively. These replacements are shown in Fig. 2. Next, consider the mechanism shown in Fig. 2 with the top platform RST being placed. This con\u00aeguration leads to a three-arm, parallel mechanism as shown in Fig. 3. As compared with Fig. 2, Fig. 3 reveals that additional constraints on the movement of the joints R, S and T will be imposed. These additional constraints state that the distances between joints R and T, R and S, and S and T, should be \u00aexed. As compared with Fig. 1, Fig. 3 shows that the present three-arm parallel mechanism is kinematically equivalent to the octahedral Stewart platform mechanism of Fig. 1. As the determination of the locations of the revolute joints Or, Os and Ot of Fig. 3 is a ected by the displacements of the six links of Fig. 1, thus in Fig. 3 we use the lengths r1, s1 and t1 to locate the positions of the revolute joints of Or, Os and Ot, and, also, the lengths of OrR, OsS and OtT are denoted as mr, ms and mt, respectively. It is also noted that r1, s1 and t1 can be regarded as another three variables, these three variables contribute to additional degrees of freedom. The relationships between the variables of r1, s1, t1, mr, ms, and mt in Fig. 3, and the link lengths L1, L2, . . . ,L6 in Fig. 1, are derived \u00aerst. As shown in Fig. 4, in the triangle ARB, because the line OrR is perpendicular to the line AB, according to the Pythagorean theorem, one can derive the following expressions: r1 L2 A L2 1 \u00ff L2 2 =2LA; r2 LA \u00ff r1; mr L2 1 \u00ff r21 1=2: 1a Similar procedures could also be applied in the triangles BSC and CTA, and one can lead to the expressions: s1 L2 B L2 6 \u00ff L2 5 =2LB; s2 LB \u00ff s1; ms L2 6 \u00ff s21 1=2; 1b t1 L2 C L2 4 \u00ff L2 3 =2LC; t2 LC \u00ff t1; mt L2 4 \u00ff t21 1=2: 1c Next, it is necessary for us to de\u00aene the position vectors of the revolute joints of Or, Os and Ot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001051_s00170-005-0032-y-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001051_s00170-005-0032-y-Figure1-1.png",
        "caption": "Fig. 1 Bearing/shaft layout of the developed high-speed spindle",
        "texts": [
            " This paper reports the analysis and test results of a motorized high-speed spindle for machining centers, developed in the National Chung Cheng University. As reported in our previous work [20], thermally-induced bearing load of this developed spindle is managed by an active bearing load control mechanism and other design measures. The emphases of this paper are put on the centrifugal-force-induced characteristic variations of the shaft/ bearing and draw bar mechanism performance at dynamic state. Figure 1 is the layout of a high-speed spindle with 20 000 rpm/14 kw developed in the National Chung Cheng University. The dmN value of the spindle is approximated to 1.65 million (in the case of steel ball bearing) or 2 million (in case of ceramic ball bearing). The preload is initially set by a spring preload mechanism. An optional active bearing load monitoring and control mechanism [20] consisting of the piezoelectric actuators and strain-gauge load sensors is used to on-line adjust the bearing loading according the cutting conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure8-1.png",
        "caption": "Figure 8. (a) The conventional Sarrus Linkage. (b) the general screw-version of Sarrus's Linkage that allows no rotational motion of 4 relative to 1,",
        "texts": [
            " Also when one or two of the P-pairs have ~ = 9 0 \u00b0, one then notes that the c o m m o n planar four-bar slider-crank mechanism (P-R-R-R) , Rapson ' s slide (P -R-P-R) and the elliptic t rammel ( P - R - R - P ) all emerge as special eases, and in all of them one S-pair in the loop has become inactive. Even the c o m m o n three-prism (three-wedge) planar loop derives f rom a degenerate fo rm o f the P - P - P - S - S (or equally f rom the P - P - S - P - S ) linkage when one o f the P-pairs lies in a plane parallel to that defined by the other two, both o f the S-pairs then becoming inactive. , A Six-Screw Linkage and Derived Linkages with Prismatic Pairs 4.1. Sarrus's Linkage, for constraining two members [1 and 4 in Fig. 8(a)] in pure relative translation, has been known for a long time. Usually the two sets of three parallel hinges are arranged at rightangles to one another. Figure 8(b) shows a more general screw version of the linkage that, as proved in 4.2. below, has a mobility of 1. The three parallel screws in each set are quite randomly arranged with respect to one another and are assigned randomly chosen finite h-values. There can be no relative rotation between members 1 and 4, but there is, in general, relative translation with components in two directions, not just 'up and down' as in the purely-hinged Sarrus version. Such relative translation in which points in one member trace out curved paths relative to another member can be described as curvilinear translation. Both the linkages in Fig. 8 have n=g =6 and f = 6 . Thus for M = 1 the coefficient b in equation (1) must take the value 5. 4.2. The screw version of Sarrus's linkage may in fact be derived from one of the linkages in Table 3(c), namely the P - P - S - S - S linkage illustrated in Fig. 7(b). Member 4 in Fig. 7(b) is constrained by the P-pairs P51 and P4 ~ to move in curvilinear translation relative to member 1, this curvilinear translation having two components only, namely those directed along the axes of Psi and P4s. It therefore follows that, at any instant, to12+to23+t~34=0",
            " This same conclusion can also be reached by mapping out all possible locations for S ~ from an examination of the series of available ladders arising from S~2, $23 and $3,~. Then one finds that the resultant movement must at any instant be a translation in some direction parallel to a uniquely defined plane. So, if the two P-pairs t}st and P45 were removed and replaced by another set of three parallel screws aligned differently from the first set, the same mobility and the same general form of relative curvilinear translation would result. The linkage in Fig. 8(b) depicts such an arrangement. 4.3. Table 4 gives the possible combinations of S-, P-, R- and C-pairs derived from one set of three parallel screw pairs constituting one half of the joints in a six-screw linkage. Two linkages obtained from Table 4 containing two C-pairs and two R-pairs are illustrated in Fig. 9(a) and (b). In Fig. 9(c) is shown a somewhat more generalised form of an often-quoted R-C-C-R linkage that allows the transmission of uniform rotational motion from one shaft to another one placed skew to it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003385_12.2010577-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003385_12.2010577-Figure9-1.png",
        "caption": "Figure 9. Comparison between CAD model data and measurement points on the airfoil.",
        "texts": [
            " It has been pointed out that the number and distribution of measurement points greatly impact on the measurement accuracy and efficiency; therefore, the layout of sampling points should be adequate to the geometric characteristics of the workpiece under test12. Points have been sampled with 1 mm gap between one another; the actual profile has then been compared with the original CAD one in order to assess shape tolerance. Shape mismatch of 0.623 and 0.767 mm result for upper and lower camber side respectively due to unexpected bulging, as shown in Figure 9. This seems to suggest that a further improvement of support definition is required in order to avoid shape distortion on the airfoil. Furthermore, the airfoil could be thickened to obtain good accuracy via finishing operations. Proc. of SPIE Vol. 8677 86771H-7 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/07/2013 Terms of Use: http://spiedl.org/terms Additional checks have been carried out on the side hole and platform rails on specific items which are critical for mechanical assembly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000600_02783640122067543-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000600_02783640122067543-Figure7-1.png",
        "caption": "Fig. 7. Interaction between wheel and object. The rotating wheel supports the object and provides a traction force.",
        "texts": [
            " For example, V is a matrix made up of velocity (column) vectors Vi for each cell, with components Vxi and Vyi . V can also be said to be made up of component (row) vectors Vx and Vy listing the velocity components for all the cells. A model of the contact between the wheels and object riding on the array is essential for modeling the dynamics of object manipulation on the MDMS. In the model, each wheel applies a force in the plane to the object through friction between the wheel and the object (see Fig. 7). There are several possible models of this friction force. Viscous Friction. The wheel slides on the object. The friction force is proportional to the normal force between the wheel and the object and to the difference between the wheel\u2019s speed and the speed (in the direction of the wheel) of the surface of the object at the wheel. The roller wheels used in the prototype system ensure that the friction will only occur in the direction perpendicular to the wheel\u2019s axis. The assumption is that the motor is strong enough to maintain its speed regardless of the traction force",
            " Because the object cannot actually \u201cpull\u201d on the springs in the support model, the object lifts off these cells, and the other normal forces must be recalculated with the negative supports removed from the set of supports. This occurs, however, only in exceptional cases, and we will ignore this effect from now on (its only effect is to change the set of supports). We will now represent the planar dynamics of an object resting on the array as a net planar force and torque acting on the object as a function of the object\u2019s position, linear velocity, and rotational velocity. We will first apply the viscous friction model to derive the planar forces from the supporting forces (see Fig. 7). Under the viscous friction assumption, the horizontal force from each cell fi is proportional to a coefficient of friction \u00b5, the normal force Ni exerted by the cell, and the vector difference between the velocity of the wheel and the velocity of the object at the point of the cell. This velocity difference is a function of the translational velocity of the object, \u0307Xcm, the velocity of the wheel, Vi , the rotation speed of the object about its center of mass, \u03c9, and the position difference between the cell and the center of mass, Xi \u2212 Xcm: fi = \u00b5 ( Vi \u2212 \u0307Xcm + \u03c9 [ 0 1 \u22121 0 ] ( Xi \u2212 Xcm )) Ni"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002238_iros.2010.5653006-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002238_iros.2010.5653006-Figure13-1.png",
        "caption": "Fig. 13 Internal structure of the unit",
        "texts": [
            " Each unit of this pump can be contracted toward the center annularly as in the intestinal tract. The peristaltic action of the pump can be carried out by contracting each unit according to a pattern of regular motion. It is possible to transport the inclusion by this peristaltic action. In addition, the number of units can be easily changed in case of three or more units. In this study, we produced a peristaltic pump with six units B. Internal Structure of a Unit The internal structure of a unit is shown in Fig. 13, and its specifications are shown in Table 3. When the units are connected, the chamber contains an air tube supplying air to each unit. The air tube is arranged so as to save space; Moreover, it is arranged in a circle to prevent it from breaking when the unit contracts. This structure prevents the air channel becoming cut. In this unit, flanges A and B form a pair. The cylindrical tube is fixed in place by interleaving one end of each unit between flanges A and B. Adopting this fixation method eliminates conveyance loss due to the influence of the thickness of the flanges"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001661_nme.1620220315-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001661_nme.1620220315-Figure5-1.png",
        "caption": "Figure 5. (a) Strip footing on elastic-plastic subsoil; (b) stress-strain behaviour",
        "texts": [
            " For simplicity the same integration rule ( 3 x 3 Gauss points) was adopted for the evaluation of the out-of-balance forces and the iteration matrix. Convergence in the Newton-type iteration procedure after N iterations is checked by comparing the errors emax and eeuc with the tolerance 6,, i.e. where 1 1 . 1 1 may be the maximum norm (e = emax) or the normalized Euclidean norm ( e = eeuc). Elastic response is denoted uE. Rigid strip footing on cohesive soil A rigid strip footing (plane strain) of width 2 B resting on cohesive sub-soil (which obeys von Mises' yield criterion) was analysed for both hardening and softening behaviour, Figure 5. The load settlement curves due to drawdown of the footing in 20 equal steps are shown in Figure 6, where W denotes the average contact stress beneath the footing. From the solution by Prandtl,34 lower and upper bounds of the collapse load W, for von Mises' yield criterion are easily obtained as W,,/a, = 2.57 and W,,/a, = (2/J3)2.57 N 2.97. Although the overshoot of the Prandtl-load is expected, considering the coarse mesh adopted, the 'spurious' hardening inherent in the element approximation may be noted",
            " This behaviour, which is considerably more pronounced for the four-node quadrilateral, is due to the inability of the finite element model to produce a singular Hessian (and tangent stiffness) matrix. As we predicted above the overall response does not seem to be considerably affected by the choice of c(, although it has been observed that fewer time increments will increase the difference (which is demonstrated in Table I). 782 K. RUNESSON, A. SAMUELSSON AND L. BERNSPANG NUMERICAL TECHNIQUE IN PLASTICITY W is also converging faster than the local response represented by the effective plastic strain ti (in a Gauss point marked in Figure 5). Furthermore the response for CY = 0.5 seems to oscillate with respect to the converged result for a = 1. Finally, it may be noted that a < 1 does not make any sense for n = 1. The necessary number of iterations to achieve convergence within each time step is shown in Table I1 for the choice CY = 1, n = 5 and 6, = l op3 while different iteration matrices were adopted. Letting the CPU-time involved be a measure of the efficiency, we may conclude that N is slightly better than BFGS(H) for hardening, at least for this simple problem of monotonic proportional loading",
            " The modified Newton schemes failed to handle the abrupt change in behaviour after the displacement amplitudes were reached (indicated by N > 100). It is believed, however, that the behaviour of any BFGS scheme should be considerably improved if the Hessian is updated in an automatic 784 K . RUNESSON, A. SAMUELSSON AND L. BERNSPANG fashion (as to form a new K O ) when the convergence rate becomes too slow. In Figure 8 is shown the number of iterations ( N ) after which true Newton converged in the various time steps. Nonproportional loading and displacement control The perfectly plastic cohesive subsoil of Figure 5 is now loaded by two flexible strips with different loading histories, (Figure 9). NUMERICAL TECHNIQUE IN PLASTICITY 785 Settlements w1 and w 2 of the loads are calculated for two load programs (A and B) according to three methods; direct and indirect arc-length with pure displacement control (b = 1) and constant time steps A t = 0.1. The settlements versus time are displayed in Figure 10. The calculated time steps and number of iterations for a selection of steps are given in Table 111. Both the indirect and the direct method yield, of course, the same size of the time steps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003154_s11071-013-1125-z-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003154_s11071-013-1125-z-Figure13-1.png",
        "caption": "Fig. 13 Deformed shape of the single sector for the mode shape nd = 2, first family",
        "texts": [
            " The mesh of the contact surface comprises Nc = 126 contact pairs uniformly distributed along the circumferential direction over the contact interface, all coupled by contact elements. As already described in the introduction, the motion that occurs on the contact plane is projected along two perpendicular onedimensional in-plane tangential components (hoop and axial direction) associated to two perpendicular contact elements [22, 23], assuming independent tangential components of the contact force. In fact, a predominant direction during slip cannot be determined a priori as it is suggested by the deformed shape (Fig. 13) of the single sector for the first mode at nd = 2 without ring damper (undamped). In this case, the motion close to the groove is characterized by an amount of axial and hoop components on the contact plane of the same order of magnitude, and a planar relative motion between mating nodes may not consist in a simple trajectory along one direction only. A number of p.e.s equal to 21 are equally distributed both on the front and on the rear side of the ring damper in order to avoid the undetermined static offset of the ring damper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000588_s0022-5096(98)00100-8-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000588_s0022-5096(98)00100-8-Figure2-1.png",
        "caption": "Fig[ 2[ Spontaneous and imposed deformations plus rotations of a solid in its isotropic and nematic phases[ \"a# The initial\\ isotropic reference state with a material point X[ The dashed arrow indicates the direction of future symmetry breaking n9[ \"b# The same system after a spontaneous deformation l m\\ along a director n9\\ which transforms material points X to positions R9\"X# l mX[ \"c# The isotropic reference state X is rotated by f about an axis f perpendicular to n9] X : X? U fX[ \"d# A spontaneous distortion l m of the isotropic solid along n9 transporting points X? in \"c# to R\"X?#] X? : R\"X?# l m\"X?# l mU fX[ The director n9 in \"d# is disposed di}erently \"by angle f# with respect to the matrix from how it is in the state \"b#[ \"e# Further uniform rotation by u of the matrix and director together gives material positions R? U uR[ A third perpendicular axis m f g n9 is also de_ned[ The axis system for strains\\ both spontaneous and imposed and the rotation axis f \"along the negative y!axis# is also shown[",
        "texts": [],
        "surrounding_texts": [
            "Golubovic and Lubensky \"0878# \"GL# _rst demonstrated that some solids must\\ on symmetry grounds\\ possess soft modes[ We expand the arguments of GL which were given in a compressed form by the original authors[ It is particularly important to examine the reference states chosen[ We shall later _nd that it is in the reference states that the conditions for the theorem to hold can be invalidated[ Semi!softness results[ An argument of Olmsted is extended in order to display within continuum elasticity the mechanism by which the GL energy is attained and also violated[ 3[0[ The ar`uments of GL Consider just the _rst three terms of the continuum free energy \"5#\\ that is we take a uniaxial body but do not follow the evolution of an internal degrees!of!freedom it might possess] fGL 0 1 m9\"n = o = n#1\u00a60 1 m0\"n g o g n#1\u00a60 1 m1\"n = o g n#1[ \"8# On suppressing the internal degrees!of!freedom\\ we cannot assume the m9\u00d0m1 are as in \"5#*indeed we shall _nd they are renormalised by the evolution of these modes[ Take Fig[ 2\\ an initially isotropic body \"a# with material points X[ On cooling from the isotropic into a uniaxial nematic state\\ there is a spontaneous distortion l m[ The elongation shown is for a transition from state \"a# to the prolate state \"b#[ The material points are transformed] X:R9\"X# where R9\"X# l mX[ However\\ the truly isotropic body \"a# must be invariant under rotations U f^ X:X ? U fX to give \"c#[ If now\\ after rotation\\ the distortion to the uniaxial state occurs\\ we instead have for the material points R of the body] R l mX ?0 l mU fX\\ that is the state \"d# of Fig[ 2[ When the distorted system is then further bodily rotated \"with its director# by U u\\ then the _nal position R? of a material point is R? U uR U ul mU fX\\ the state \"e#[ The states \"b# and \"d# or \"e# are entirely equivalent for two reasons] \"0# the distorted bodies \"b# and \"d# \u00f0or \"e#\u0141 di}er only by a body rotation between the nematic states \"b# and \"d#^ \"1# the reference states \"a# and \"c# are equivalent since we have rotated an isotropic body \"Olmsted\\ 0883#[ However\\ non!trivial strains connect these states\\ the equivalence of which then demands the vanishing of the elastic modulus corresponding to the strains connecting them[ The direction chosen by n9 is insensitive to rotations of a truly isotropic body\\ that is it is independent of the orientation of matrix[ We examine the consequences of condition \"1# being violated in elastomers[ To sense the nematic possibilities we have restricted U f to be rotations about an axis perpendicular to n9\\ see Olmsted \"0883# eqn \"5[4# and the following\\ for a discussion of the e}ect of U f on the strain tensor[ Note that there are two symmetries U f and U u associated with body rotations of the isotropic initial \"reference# and the nematic _nal states[ The additional\\ independent symmetry \"under U f# is the basis of the GL prediction of the soft response of nematic solids[ Its absence will lead to the partial loss of softness[ Following Olmsted\\ we demonstrate explicitly how the additional symmetry renor! malises a mi to zero[ Write R l mU fX in order to replace the isotropic reference state X by R9\\ a nematic reference state\\ \"b# of Fig[ 2[ This is experimentally natural^ one imposes deformations on a relaxed\\ equilibrium nematic solid[ The nematic reference state R9 derives from the isotropic reference state by the spontaneous deformation \"see \"6# for the explicit form#\\ that is R9 l mX\\ which on inversion X l \u22120 m R9 yields for the points in Fig[ 2\"d# R l mU fl \u22120 m R9[ The deformation tensor connecting \"b# and \"d# is then l 1R:1R9 l mU fl \u22120 m and the symmetric strain is thus] o 0 1 \u00f0l mU fl \u22120 m \u00a6\"l mU fl \u22120 m #T\u0141\u2212d [ \"09# The strain connecting states \"b# and \"d#\\ stemming from rotations about an axis f perpendicular to n\\ clearly is neither an extension along n \"i[e[ not onn and hence n = o = n 9#\\ nor a shear in the plane \"f\\m# perpendicular to n which would leave n unchanged \"i[e[ not ofm and hence n g o g n 9#[ It must involve components both along n and m0f g n\\ that is n = o g n 9[ It follows that the in_nitesimal strain o from \"b#\u00d0\"d# will be o \u00bd \"nm\u00a6mn#[ This can be con_rmed by putting l m into the relevant 1\u00d71 part of the deformation connecting R\"X?# of \"d# with X of \"a#\\ that is into l mU fl \u22120 m : 0 0 \u2212fl\u22122:1 m fl2:1 m 0 1 at small angles f[ Constructing the symmetric strain o from this distortion\\ we obtain] o f 1 \"l2:1 m \u2212l\u22122:1 m # 0 9 0 0 91 f 1 \"l2:1 m \u2212l\u22122:1 m #\"nm\u00a6mn#[ \"00# In the 0 1 m1\"n = o g n#1 term of \"5# we obtain] fel m1 7 f1\"l2:1 m \u2212l\u22122:1 m #1 m1 7 f1\"l2 m\u00a6l\u22122 m \u22121# \u00bdm1f 1Q1 \"01# where Q is the nematic order[ We have used lm 0\u00a6const[Q\u00a6O\"Q1# for small Q to estimate the energy cost in \"01#[ This energy must be zero\\ hence the GL symmetry under U f demands that m1 9[ Since this modulus has been eliminated\\ the response of the system to any onm related to m1 \"with n = o g n 9 but onn omm omf 9# is soft[ Such deformations are shears in a plane encompassing the director\\ see Olmsted \"0883# for further discussion[ Explicit examples of softness\\ even at very large ampli! tude\\ are given in Sections 4[0 and 4[1[ A deeper underlying symmetry associated with Gaussians is also discussed at the end of Section 3[3[ 3[1[ Olmsted|s demonstration of soft elasticity^ relation with the de Gennes coef_cients Olmsted has shown that by keeping track of n one can explicitly _nd cancellations that\\ by the symmetry argument\\ must be exact in order to give no overall energy cost[ He thereby _nds exact relations between the de Gennes coupling constants\\ D0 and D1 and the elastic modulus m1[ Conversely\\ when the GL theorem is violated\\ we shall show how this explicit relation de_nes the degree of hardening\\ that is of semi! softness[ If the relative rotation \"u\u2212v# of the director with respect to the matrix \"see Fig[ 1# is coaxial with f\\ Olmsted|s argument is simple[ Considering the director and body rotations of Fig[ 2\"b# strained to \" f#\\ the de Gennes part of the energy \"5# becomes] fdeG 0 1 D0\"u\u2212v#1\u00a6D1f\"l2:1 m \u2212l\u22122:1 m #\"u\u2212v# \"02# on putting the relative rotations and the symmetric strain o from \"00# into the last two terms of \"5#[ For a given f\\ on minimising over \"u\u2212v# there must be a spontaneous relative rotation u\u2212v \u22120 1 \"D1:D0#\"l2:1 m \u2212l\u22122:1 m #f and thus fdeG \u22120 7 \"D1 1:D0#\"l2 m\u00a6l\u22122 m \u22121#f1[ If fdeG is returned to the free energy \"5# and o of \"00# inserted into the m9\u00d0m1 terms\\ then the total free energy associated with this particular distortion becomes] f 0 7 \"m1\u2212D1 1:D0#\"l2 m\u00a6l\u22122 m \u22121#f1 0 0 7 mR 1 \"l2 m\u00a6l\u22122 m \u22121#f1[ \"03# The bare m1 has been renormalised to mR 1 m1\u2212D1 1:D0 as a result of the de Gennes relaxations due to the terms quadratic \"D0# and linear \"D1# in the anti!symmetric shear[ The GL symmetry argument still stands and dictates the free energy not dependent on the rotation U f of the isotropic reference state\\ that is mR 1 9 implies m1 D1 1:D0[ Olmsted \"0883# _rst proposed this continuum mechanism behind the GL theorem] shape depends on the orientation of an internal \"nematic# degree!of! freedom\\ the rotation of which causes a natural shape change at zero cost for suitable solids[ He thereby found the relation between the uniaxial rubber moduli and the de Gennes moduli for systems that meet the GL criteria[ The picture is similar to that already drawn in the statistical description \"Warner et al[\\ 0883#\\ see Section 1[0 and Fig[ 0\"c# where a distribution of anisotropic polymers is rotated at constant entropy[ 3[2[ Semi!soft elasticity For systems which cannot attain the isotropic GL reference state\\ the rotations U f of the reference state generate physical strains with real energies^ thus mR 1 \u00d7 9 and m1 \u00d7D1 1:D0[ There exist several mechanisms for retaining anisotropy in all reference states and hence for losing ideal softness[ One can show experimentally \"Ku pfer and Finkelmann\\ 0880# and theoretically \"Verwey and Warner\\ 0886b#\\ that if crosslinks are rod!like\\ then crosslinking in the nematic state pins their orientation even at high temperatures and the network is always at least weakly nematic[ Similarly\\ random _elds of like origin dictate a residual nematic order at high temperatures and polydomains at lower temperatures \"Fridrikh and Terentjev\\ 0886#[ These and other mechanisms give quadratic \"l 1# additions to \"4# each of similar form[ We can\\ as an illustration\\ concentrate on one \u00d0 ~uctuation in chemical composition and hence strand anisotropy\\ that are found in the copolymers commonly used for nematic elastomers[ Other mechanisms\\ for instance _nite chain extensibility \"Mao et al[\\ 0887^ Semenov\\ 0887#\\ give softness!breaking additions of O\"l 3# and higher\\ but the message is similar[ It has been pointed out \"Verwey and Warner\\ 0884a^ Verwey et al[\\ 0885^ Verwey and Warner\\ 0886a# that if each chain a has a slightly di}erent shape tensor l a then an average deformation tensor l \u00f0l 0:1 a V l \u22120:1 9a \u0141a cannot be simultaneously soft for every individual strand a and the result is a l trajectory that is not quite soft[ It does however\\ provide only a minimal energy rise and has been termed {semi!soft|[ The averaging of \"3# over strands with di}ering intrinsic anisotropies \" for instance as a result of compositional ~uctuations or rigid rod crosslinks# yields a free energy with small but _nite moduli along semi!soft trajectories and _nite thresholds to a nearly soft stripe response[ We are now in a position to see how semi!softness can arise in the continuum picture[ Olmsted has given molecular expressions for D0\\ D1\\ m9\u00d0m1 derived from \"3# in the limit of small strains[ Let m be the characteristic rubber energy scale m0 nskBT[ ns is the number of network strands per unit volume and is thus the conversion factor between F\\ a free energy per strand \"3#\\ and free energy densities f and fGL in equations \"5# and \"8#[ The moduli are D0 m\"r\u00a60:r\u22121#\\ D1 m\"r\u22120:r#\\ m9 m0 1m\\ m1 m\"r\u00a60:r\u00a61#[ One can see explicitly that mR 1 9[ If now chains ~uctuate for instance in composition\\ and therefore in anisotropy\\ we replace r:\u00f0r\u0141 and 0:r: \u00f00:r\u0141 in the above\\ the averaging \u00f0[ [ [\u0141 being over strands[ There is no longer a cancellation in the renormalised mR 1 to give zero\\ but instead] mR 1 m1\u2212D1 1:D0 3m\u00f0\u00f0r\u0141\u00f00:r\u0141\u22120\u0141:\u00f0\u00f0r\u0141\u00a6\u00f00:r\u0141\u22121\u0141[ \"04# Convexity arguments on the distribution of r and 0:r show that the renormalised modulus \"04# of the statistical mechanical model does indeed satisfy m1 \u2212D1 1:D0 and hence mR 1 \u2212 9 which is a necessary condition for stability] the arguments leading to \"01# and \"03# involve deformations unrelated to m9 and m0 which thus\\ do not enter the above inequality for stability[ The extent to which mR 1 is positive is the continuum measure of how semi!soft an elastomer becomes in response to ~uctuations in its structure or other sources of non!ideality[ We shall below in Section 4[1 use such semi!soft continuum elasticity theory to describe the threshold to the striped semi! soft deformation observed by Ku pfer and Finkelmann \"0883# and by Disch et al[ \"0883# in a series of mechanical experiments[ 3[3[ The effect of formation history on elastic softness The e}ect of formation history is of vital important since monodomain elastomers are produced by using magnetic or stress _elds during crosslinking[ The essential part of the argument for softness is that an isotropic reference state be able to be found[ Depending on non!ideality in the network and the _elds applied during formation\\ such a state may not exist[ In general\\ if the formation state was ordered\\ then non! ideality permanently imprints the order in the network[ Then all states\\ even at high temperature\\ are at least paranematic[ Semi!softness is the result of the residual order and failure to _nd an isotropic reference state[ However\\ if the formation state is isotropic\\ then the order associated with the non!ideality can be relaxed away* we shall show explicitly that an elastomer formed in the isotropic state but with compositional ~uctuations\\ can be soft*in accord with the Golubovic and Lubensky \"0878# theorem[ This is despite relaxation into the nematic state where the current shape tensor\\ l a\\ varies between strands a\\ apparently suggesting a semi!soft defor! mation analogous to that derived in Section 3[2 for a rubber actually formed in an anisotropic state[ When the formation condition is isotropic\\ the free energy F \"in terms of kBT:1# is F \u00f0Tr \"ad l T t l \u22120 a l t#\u0141 where a is the step length in the isotropic state \"with shape tensor l ad # and l t is the total deformation from that state[ \u00f0[ [ [\u0141 denotes averaging over strands a[ Consider a relaxation l m on cooling to a nematic state with l a for the ath strand[ The average strand energy is then F \u00f0l1 m\"a:l>a#\u00a6\"1:lm#\"a:l_a#\u0141 where! upon the relaxation of the elastomer as a whole is lm\\ with l2 m \u00f00:l_a\u0141:\u00f00:l>a\u0141[ Now consider distortions l with respect to the relaxed state\\ so that l t l l m is the total distortion from the formation state[ Then F \u00f0Tr \"al ml T ml Tl \u22120 a l #\u01410 \u00f0Tr \"l 9l Tl \u22120 a l #\u0141 where we denote al ml T m l 9[ The {average| soft trajectory2 would be l \u00f0l 0:1 a V l \u22120:1 9 \u0141 \u00f0l 0:1 a \u0141V l \u22120:1 9 [ Returning this deformation tensor l to F yields F \u00f0Tr \"\u00f0l 0:1 a \u0141l \u22120 a \u00f0l 0:1 a \u0141#\u01410Tr \"\u00f0l 0:1 a \u0141\u00f0l \u22120 a \u0141\u00f0l 0:1 a \u0141# const[3 The free energy is inde! pendent of the relative orientation of the frames of l 9 and l [ Its constancy implies softness[ Despite the apparent complexity of F\\ the GL theorem is obeyed and no stress is required for deformation[ When there is anisotropy in the formation state\\ then l 9a varies from chain to chain[ If the formation state has l fa as the shape of the ath chain\\ then l 9a l ml fal T m where now lm in l m is l2 m \u00f0l_fa:l_a\u0141:\u00f0l>fa:l>a\u0141[ The analogous elastic energy F is \u00f0Tr \"l 9a\u00f0l \u22120:1 9a V l 0:1 a \u0141l \u22120 a \u00f0l0:1 a V l \u22120:1 9a \u0141#\u0141\\ that is of the form \u00f0Tr \"l 9aM Tl \u22120 a M #\u0141[ Clearly F depends on the relative orientations of l 9 and l [ Thus\\ as l develops\\ n rotates and the energy rises[ The GL theorem has thus been practically illustrated*an initially isotropic state is necessary for softness[ Conversely\\ ~uctuating\\ non!ideal systems with an anisotropic formation state cannot attain the isotropic state even at high temperatures[ E}ectively a permanent paranematic state survives at elevated temperatures and transitions are smeared out\\ subjects explored at some length experimentally \"Ku pfer and Fink! elmann\\ 0883^ Disch et al[\\ 0883# and theoretically \"Verwey and Warner\\ 0886a\\ b#[ Can ideal Gaussian networks formed in the nematic state ever obey GL< The formation\\ reference state is anisotropic\\ thereby apparently violating GL[ But the deformation l l 0:1V l \u22120:1 9 is soft\\ even when l 9 is anisotropic[ Ideal Gaussian systems have an additional symmetry allowing elastomers formed in the anisotropic state to be soft[ Shape relaxation l m \"6#\\ from formation to current conditions\\ l 9 to l \\ is uniaxial and need not rotate the director \"l 9 and l remaining coaxial#[ The value lm minimising \"3# is l2 m \"l>:l_#\"l9_:l9>#[ The relaxation given above when l 9 ad is clearly a special case[ Returning lm to F\\ eqn \"3#\\ yields F\u00bd \u00f0det \"l #:det \"l 9#\u01410:2\\ that is\\ 2 The average \u00f0[ [ [\u0141 can be taken purely over l 0:1 a \\ indeed in its diagonal frame[ Although the whole object l 0:1 a V l \u22120:1 9 is complex and the rotational e}ects of V and l \u22120:1 9 leave the principal elements of l 0:1 a mixed up\\ at most linear combinations of 0:l0:1 >a and 0:l0:1 _a are involved and hence the result depends only on additive combinations of \u00f00:l0:1 >a \u0141 and \u00f00:l0:1 _a \u0141[ Thus\\ \u00f0l \u22120:1 a \u0141 can be averaged in its own frame and then rotated as required[ 3 The remarks of the previous footnote allow the averaging of the tensor l \u22120 a inside the Trace of the product[ The trace is not Tr 2[ Being an invariant and involving only tensors with a common principal frame\\ the Trace trivially reduces to \u00f0l0:1 > \u01411\u00f00:l>\u0141\u00a61\u00f0l0:1 _\u01411\u00f00:l_\u0141[ The constancy of the Trace\\ as l induces rotations of n\\ ensures softness[ the free energy depends on the separate rotational invariants \"the determinants# of the l 9 and l tensors[ This is the additional symmetry[ The tensor order parameter is uniaxial and traceless^ Qij Q\"2 1 ninj\u2212 0 1 dij#[ For weak order \"at high temperatures# l is expandable in powers of Q ] l d \u00a6c0Q \u00a6c1Q Q \u00a6= = = and hence det \"l # 0\u00a6O\u00f0TrQ \u0141\u00a6O\u00f0\"TrQ #1\\ Tr \"Q Q #\u0141 \u00bd 0\u00a6O\u00f0Q1\u0141[ There are accord! ingly no linear terms in F\"Q# and from the Landau theory\\ no high temperature paranematic state[ Because of this symmetry in the free energy\\ heating leads to an isotropic state which one can think of as the reference state for the arguments of the _rst part of this paper[ On the other hand anisotropic formation with ~uctuations\\ rigid crosslinks\\ _nite chain extensibility\\ or other sources of non!ideality destroy the simple dependence on det \"l # and det \"l 9# separately and the additional symmetry is lost["
        ]
    },
    {
        "image_filename": "designv10_10_0003354_icra.2014.6907498-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003354_icra.2014.6907498-Figure4-1.png",
        "caption": "Fig. 4. a) The magnetic manipulation system OctoMag including eight electromagnetic coils. The second version is mechanically more stable and can generate slightly higher magnetic fields than the prototype, which was introduced in [20]. b) The hybrid magnetic-mechanical system with a linear piezoelectric actuator (PEA) and the magnetic manipulation system OctoMag as seen from above.",
        "texts": [
            " The software initializes the positioner and feeds the desired position values to the PEA controller, such that the manipulator moves each step before waiting a determined time t sleep in [ms]. Hence, the longitudinal velocity of the catheter is regulated by the PEA. The actuator allows for maximum velocity of 13 mm/s. The advancing velocity of the catheter was recorded with a vision based blob tracker at different spatial step sizes and with various sleep times, as illustrated in Figure 3. The OctoMag was introduced by Kummer et al. [20] in 2010. A second version was built in 2011, shown in Figure 4a), that is movable and mechanically more stable than the prototype. It also allows for slightly higher magnetic fields of up to 40 mT and magnetic field gradients of 1 T/m. The OctoMag has been shown to successfully guide untethered microrobots during minimally invasive surgery in the posterior eye segment in ex vivo and in vivo applications [21], [22]. The system consists of eight electromagnetic coils with softmagnetic cores in a hemispherical arrangement. The central workspace created by this arrangement is 20 \u21e5 20 \u21e5 20 mm, and by adjusting the currents within the electromagnetic coils the magnetic fields and magnetic gradients can be controlled, guiding magnetic devices with high spatial precision [23]. The lateral motion of the magnetic needle tip of the catheter is observed through a CCD camera at 120 Hz (Grasshopper 03K2C-C, Pointgrey, BC, Canada) and is visually guided in the horizontal plane by a controller, described in section III, through the OctoMag workspace. The complete system consisting of OctoMag and PEA that is utilized for flexible catheter control for capsulorhexis is sketched in Figure 4b). It should be noted, that the OctoMag is capable of 5 degree-of-freedom control, and hence is over actuated for the application described in this work as only lateral motion of the catheter and its pitch are controlled. The catheter tip is equipped with three cylindrical NeFeB magnets with a diameter of 0.5 mm and length 1 mm with total magnetization M in [A/m ]. It is assumed that the magnetization is largest along the longitudinal direction of the catheter while magnetization in the radial direction can be neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003615_978-3-319-27149-1-Figure20-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003615_978-3-319-27149-1-Figure20-1.png",
        "caption": "Fig. 20 Top row: Observed and measured displacements at contact point. Middle row: the 3D deformation structure of the tissue, obtained by our vision approach, plotted at different time instants. Bottom row: comparison between the real force measure and the estimated by the RNN-LSTM architecture and at right by our previous work.",
        "texts": [
            " Challenges in the Design of Laparoscopic Tools 473 Our work consists of a force estimation methodology for Minimally Invasive Surgery based on Recurrent Neural Networks and Long Short-Term Memory model (RNN-LSTM) to analyze the tissue deformation and associate this measurements to the equivalent force applied. The computation of the 3D deformation structure is based on the minimization of energy functional. This information, together with the geometric data (i.e. robot information), constitutes the input to the RNN-LSTM architecture. The results, fig. 20, show that this method works with any tissue model. 474 J. Amat et al. 5.2 The Microsurgery Worm Our department closely collaborates with the prestigious medical center Parc Taul\u00ed, specialized in the revascularization of amputee limbs. One of their demands is the development of a robotized station for microsurgery; a surgical technique which requires operating with high accuracy in small workspaces. Hard training is needed to reach the desired dexterity, although the workspace limitations should not be a handicap for a teleoperated system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.5-1.png",
        "caption": "Fig. 1.5. Angles linking aerodynamic and aircraft coordinate",
        "texts": [],
        "surrounding_texts": [
            "The main distances impacting the aircraft\u2019s equations of motion are shown in Fig. 1.7. 8 M. Jeanneau"
        ]
    },
    {
        "image_filename": "designv10_10_0003748_s11071-016-3218-y-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003748_s11071-016-3218-y-Figure13-1.png",
        "caption": "Fig. 13 Dynamic load distributions on the cracked tooth flanks for Case B: a TC-B1, b TC-B2, c TC-B3, d TC-B4",
        "texts": [],
        "surrounding_texts": [
            "GEAR \u03c9 V RACK (a) (b) For the fillet region, the coordinate of any specific point P at the fillet region is given as [2,17]:{ u p = Rp sin \u03d5 \u2212 ( a sin \u03b1\u2032 + r ) cos(\u03b1\u2032 \u2212 \u03d5) vp = Rp cos\u03d5 \u2212 ( a sin \u03b1\u2032 + r ) sin ( \u03b1\u2032 \u2212 \u03d5 ) (2) where \u03d5 is computed as [2,17]: \u03d5 = a cot \u03b1\u2032 + b Rp (3) where a, b, and r are the dimensions of the rack as shown in Fig. 1, Rp is the radius of the pitch circle, \u03d5 and \u03b1\u2032 are illustrated in Fig. 2b. Detailed discussion about this can be found in Yu et al. [2]. Therefore, the standard spur gear tooth shape is completely defined by the 2 parametric equations. 2.2 Gear tooth plastic inclination model The gear tooth plastic inclination model due to the planar crack with uniform crack depth along the tooth width direction has already been investigated in Shao and Chen [1]. For this type of crack, a two-dimensional (2D)model is capable of defining the crack dimensions. However, for the planar crack with non-uniform crack depth or spatial crack, a 3D model is necessary. Figure 3a shows a spatial crack which propagates along the tooth width through a non-straight curve with a non-uniform crack depth. Figure 3c, d shows the projection of the crackpath on the x\u2013z plane and x\u2013y plane. Figure 3c provides information on how the crack depth (qw) varies along the tooth width, whereas Fig. 3d provides information on how the crack location lw on the tooth outer surface varies along the tooth width. These two variables can be defined as the function ofw in the tooth width direction:{ qw = q(w) lw = l(w) w \u2208 [0,W ] (4) where W is the length of tooth width. All the other parameters are illustrated in Fig. 3. These two equations completely describe how the spatial crack propagates in both the crack depth direction (CD direction as shown in Fig. 3b) and the tooth profile direction (TP direction in Fig. 3b) along the tooth width direction (TW direction in Fig. 3b). However, if we divide the gear tooth into several independent thin pieces [2,9], as shown in Fig. 3b, so that the crack depth qw and the crack location lw at that thin piece can be assumed as constant, if the width of the thin piece \u03b4w is small enough. In this case, a 2D model with a planar crack and a uniform crack depth can be used to investigate the plastic inclination deformation for those thin pieces. Figure 4 shows the schematic for the plastic inclination deformation of the gear tooth thin piece (i.e., Fig. 3b) due to the tooth fillet crack, which is based on the model proposed in Shao and Chen [1]. The solid curve represents the original tooth profile, whereas the dashed curve represents the deformed tooth profile. A global U\u2013V coordinate system is built with its origin at the gear center O , and the V -axis coinciding with the center line of cracked tooth. Point A is the intersection point between the involute profile and fillet profile. Point C is the crack position at tooth profile. Point D and point C are symmetric with the tooth center line (i.e., V -axis). Point B is the crack tip. The crack depth qw and the crack angle \u03b1c (i.e., with respect to the V - axis) are illustrated in Fig. 4. When the plastic inclination happens, it can be assumed that the tooth part above the crack is a cantilever beam with its fixed foundation at straight line BD, and rotates around the middle point o between points B and D. In order to determine the plastic inclination deformation, a local R\u2013S coordinate system is established with its origin at point o and S-axis coinciding with the line BD. Suppose a mesh position E at the original tooth profile, at a given whole tooth plastic inclination angle \u03b8p; it will rotate to the point E \u2032 at the deformed tooth profile. E \u2032\u2032 is the mesh position at the original tooth profile that shares a same line of action (LOA) with E \u2032 at the deformed tooth profile. Therefore, the distance between points E \u2032 and E \u2032\u2032 [i.e., \u03b4w(E)] along theLOA represents the plastic inclination deformation at point E that is acted as the displacement excitation on the gear dynamics. This distance can be calculated based on the geometric relationship shown in Fig. 4. The global coordinates of the points A,C , E , and D on the tooth profiles can be obtained based on the two parametric equations proposed in the previous section. Suppose they are: A(uA, vA), C(uC , vC ), E(uE , vE ), D(uD , vD). Therefore, the global coordinate of point B(uB , vB) can be calculated as: { uB = uC \u2212 qw \u2217 sin(\u03b1c) vB = vC \u2212 qw \u2217 cos(\u03b1c) (5) As a result, the global coordinate of the middle point o (uo, vo) is: { uo = (uB+uD) 2 vo = (vB+vD) 2 (6) The acute angle \u03b8T between U -axis and R-axis can be expressed as [1]: \u03b8T = arctan ( uB \u2212 uD vD \u2212 vB ) (7) This angle can be used to transform the global coordinate to local coordinate through the transform matrix T [1]: T = [ cos(\u03b8T ) \u2212 sin(\u03b8T ) sin(\u03b8T ) cos(\u03b8T ) ] (8) Therefore, the local coordinate of point E (rE , sE ) can be established as: { rE sE } = T\u22121 \u2217 { uE \u2212 uo vE \u2212 vo } (9) When the tooth plastically inclined at an angle of \u03b8p, the local coordinate of point E \u2032(rE \u2032 , sE \u2032) is [1]: { rE \u2032 = \u221a rE 2 + sE 2 cos(arctan(sE/rE ) + \u03b8p) sE \u2032 = \u221a rE 2 + sE 2 sin(arctan(sE/rE ) + \u03b8p) (10) Transforming the local coordinate of point E \u2032(rE \u2032 , sE \u2032) back to global coordinate E \u2032(uE \u2032 , vE \u2032) through the transform matrix T gives:{ uE \u2032 vE \u2032 } = T \u2217 { rE \u2032 sE \u2032 } + { uo vo } (11) Point E \u2032\u2032 on the original tooth profile shares the same LOA with the point E \u2032 on the deformed tooth profile, meaning point E \u2032\u2032 is just on the line T E \u2032 as shown in Fig. 4. Therefore, the mesh angle for point E \u2032\u2032 is: \u03b1E \u2032\u2032 = arccos ( Rb/ \u221a uE \u20322 + vE \u20322 ) \u2212 arctan(uE \u2032/vE \u2032) (12) Substitute this mesh angle into Eq. (1) gives the global coordinate of point E \u2032\u2032 (uE \u2032\u2032 , vE \u2032\u2032). Consequently, the distance between point between points E \u2032 and E \u2032\u2032 along the LOA is obtained as [1]: ew(E) = \u221a (uE \u2032\u2032 \u2212 uE \u2032)2 + (vE \u2032\u2032 \u2212 vE \u2032)2 (13) Based on Eqs. (5)\u2013(13), one can easily deduce the gear tooth plastic inclination deformation along the tooth profile for each thin piece resulting from the spatial crack described by Eq. (4). It should be noted that the proposed method to calculate the plastic inclination deformation by dividing the gear tooth into thin pieces is used based on the assumption that the coupling between the adjacent points of contact is negligible [18]. For wide-faced and thin-rimmed gears, this assumption may not be valid, and further analysis tools are needed to take into account the coupling effect between adjacent contact points [18,19]. 2.3 Gear tooth plastic inclination deformation In this section, we will simulate the gear tooth plastic inclination deformation when a spatial crack exists on one of the driven gear teeth. The main parameters of the spur gear set are shown in Table 1. All the gear teeth except the cracked tooth are ideal without any profile errors. Firstly, we assume that the crack is initiated at the position (i.e., l0) determined by the 30\u25e6 tangential method defined in BS ISO 6336-3:2006 [20], and propagates only in tooth width and tooth depth directions, i.e., Also, suppose the crack depth is distributed as a parabolic function along tooth width as shown in Fig. 5. If the crack extends only a part of the tooth width (i.e., crack length Wc < W ), as shown in Fig. 5a:{ qw = \u2212 q0 W 2 c \u2217 w2 + q0, w \u2208 [0,Wc] qw = 0, w \u2208 [Wc,W ] (15) If the crack extends through the whole tooth (i.e.,Wc = W ), as shown in Fig. 5b: qw = q2 \u2212 q0 W 2 c \u2217 w2 + q0, w \u2208 [0,W ] (16) where q2 is the crack depth at the other end surface of the cracked tooth. All the crack parameters are shown in Table 2. Two groups of tooth damage are considered where the crack inclination angle \u03b1c is kept at a constant 60\u25e6. Group A represents the case where the crack extends through only a part of the tooth width, whereas group B represents the case where the crack extends through the whole tooth. Suppose the plastic inclination angle \u03b8p along the tooth width direction is proportional to the crack depth, and the initial plastic angle \u03b8p0 is increasing from 0 to 0.2, 0.4 and 0.6 degree as shown in Table 2. Figure 6 shows the tooth plastic deformations at each discrete point ranging from the base circle radius to the tip radius for each independent tooth thin piece. For Case A, only the cracked tooth part experiences the plastic deformation, whereas the uncracked part has no deformation at all. It can also be seen that the plastic deformation increases nearly linearly from the base radius to the tip radius, which is consistent with the experimental measured results in Mark et al. [15] and simulation results in Shao and Chen [1]. Besides, the larger the plastic inclination angle \u03b8p, the bigger the plastic deformation at each point. In Case B, the crack extends through the whole tooth with a non-uniform crack depth along the tooth width direction, which results in the non-uniform distributions of the plastic deformations on the cracked tooth flank. These nonuniformly distributed plastic deformations will serve as geometric deviation static transmission error (STE) contributions and lead to non-uniform dynamic load distributions on the cracked tooth flank, and will therefore, significantly affect the gear dynamic performance. We then assume that the crack propagates only in the tooth profile direction with uniform crack depth along the tooth width, i.e., qw = q0, w \u2208 [0,W ] (17) Two growth paths of the spatial crack on the tooth flank are investigated. They are linear and monotonous parabolic, respectively, as shown in Fig. 7. If the crack growth path is linear, as shown in Fig. 7a: lw = l2 \u2212 l0 W \u2217 w + l0, w \u2208 [0,W ] (18) If the crack growth path is parabolic, as shown in Fig. 7b: lw = l2 \u2212 l0 W 2 \u2217 w2 + l0, w \u2208 [0,W ] (19) where l2 is the distance from the crack position in the other end surface to the tooth root as shown in Fig. 7. The crack inclination angle \u03b1c is still kept at a constant 60\u25e6. The initial crack position l0 is still determined by the 30\u25e6 tangential method. The crack depth q0 is kept at 0.4mm, and the tooth plastic inclination angle \u03b8p is assumed as 0.6 degree. Three different crack growth distances along the tooth flank (i.e., l2 \u2212 l0) are shown in Table 3. Figure 8 shows the 3D distributions of the gear tooth plastic deformations on the cracked tooth flank. It is obvious from these figures that as the crack propagates away from the tooth root, the plastic deformation is decreasing along the tooth width direction. A linear crack growth path leads to a linear decreasing trend, whereas a parabolic growth path leads to a parabolic decreasing trend. These demonstrate that aside from the crack depth and plastic inclination angle, the crack position in the fillet region will also affect the plastic deformation distributions. 2.4 Tooth mesh stiffness model The tooth mesh stiffness model proposed in this study is based on thework by Eritenel and Parker [21]. In correspondence with the slicing method introduced in the previous section, the nominal contact line is discretized into a series of segments (as shown in Fig. 9a), and each contact line segment is assigned a linear stiffness kiat its center Mi , which is calculated as: ki = kgkci Hi kg + \u2211n i=1 kci Hi (20) where kg is the global stiffness accounting for all stiffness except the local contact stiffness (i.e., k1g and k2g as shown in Fig. 9a), and is assumed to be the same for all contact segments; kci is the local contact stiffness of the i th segment, and is probably nonlinear depending on the contact function Hi : Hi = { 1, \u03b4i \u2212 ei > 0 0, \u03b4i \u2212 ei \u2264 0 (21) where ei is the profile deviation error of the i th segment (i.e., e1i and e2i as shown in Fig. 9a) which includes the tooth profile manufacturing errors, profile modifications, and the plastic inclination deformations discussed above, \u03b4i is the normal approach at the i th segment. For spur gear pair, \u03b4i is the same for each segment. Hi represents the contact condition at the i th segment. When Hi is 0, it means that there is a contact loss at the i th segment, and the local contact stiffness kci will not contribute to the effective mesh stiffness ki at the i th segment. kg and kci can be obtained from finite element analysis of gears [21,22]. They can also be estimated using analytical approaches [3\u201310]. The effect of the tooth fillet crack does not affect the local contact stiffness kci . However, it will directly influence the global stiffness kg as it can weaken the cracked tooth bending and shearing strength. Detailed discussion about this can be found in [2,7]. 3 Dynamic analysis 3.1 Dynamic model The research objective is a spur gear pair system as shown in Fig. 9a. A Cartesian coordinate system (X\u2013 Y\u2013Z ) is established. The X -axis is in the direction of LOA, and the Y -axis is in the off-line of action (OLOA) direction. The Z -axis is along the axial direction and can be determined by following the right-hand rule. The frictional forces developed between the contact tooth pair are neglected. Therefore, the only translational degree of freedom (DOF) considered is along the X -axis, i.e., x1 and x2. Since the plastic deformations resulting from the spatial crack are non-uniformly distributed on the cracked tooth flank, there will be a tilting moment about the Y -axis. Therefore, the rotational DOF about the Y -axis should be also taken into consideration, i.e., \u03b8y1 and \u03b8y2. The torsional vibration \u03b8z1 and \u03b8z2 should of course be considered. Therefore, a six-degrees-of-freedom (6DOFs) model was built to analyze the influence of the plastic deformations on the dynamics of a spur gear pair. It should be noted that for a helical gear pair set, and/or when it is subjected to misalignments or eccentricities, more DOFs are needed in order to fully study its dynamic behavior. The normal approach at the contact point Mi of the i th segment is calculated as: \u03b4i = VT i q (22) where qT = {x1, \u03b8y1, \u03b8z1, x2, \u03b8y2, \u03b8z2} is degree of freedom vector of the gear pair considered, and Vi is the structure vector defined as: VT i = {\u22121,\u2212ci , Rb1, 1, ci , Rb2} (23) where ci is the distance of Mi to the tooth center along Z -axis, and its value should be between \u2212W /2 and W /2. Suppose tooth profile deviations relative to the perfect geometry are positively defined in the direction of the outer normal and they are small enough to allow the contact to remain on the theoretical base plan [18]. The elastic deformation \u03b5i at Mi is: \u03b5i = \u03b4i \u2212 ei (24) where profile deviation error ei at Mi consists of the profile deviation errors of the driving and driven gears (ei = e1i + e2i ). Therefore, the contact force fi at Mi can be expressed as: fi = ki\u03b5i (25) The total contact force F and the resultant moment about Y -axis acted at the driving gear are: F = n\u2211 i=1 fi , (26a) M = n\u2211 i=1 fi ci (26b) The undamped governing equation can be expressed as: m1 x\u03081 + kBx1x1 \u2212 F = 0 (27a) I1\u03b8\u0308y1 + kB\u03b8 y1\u03b8y1 \u2212 M = 0 (27b) Ip1\u03b8\u0308z1 + kB\u03b8z1\u03b8z1 + FRb1 = T1 (27c) m2 x\u03082 + kBx2x2 + F = 0 (27d) I2\u03b8\u0308y2 + kB\u03b8y2\u03b8y2 + M = 0 (27e) Ip2\u03b8\u0308z2 + kB\u03b8z2\u03b8z2 + FRb2 = T2 (27f) where m j , I j , and Ipj are the mass, the transverse moment of inertia, and the polar moment of inertial of the j th gear ( j = 1, 2 representing the driving gear and driven gear, respectively), respectively; KBx j,KB\u03b8y j and KB\u03b8 z j are the radial stiffness and rotational stiffness along Y -axis and Z -axis of the bearing supporting the j th gear, respectively; Tj is the external torque applied on the j th gear. Equation (27) can be also expressed in matrix form if we substitute Eqs. (22) and (23) into it: Mq\u0308 + [Kg(q) + Kb]q = F0 + F1(q) (28) where: M = diag ( m1, I1, Ip1,m2, I2, Ip2 ) (29a) Kg(q) = \u2211n i=1 kiViVT i (29b) Kb = diag(kBx1, kB\u03b8y1 , kB\u03b8z1 , kBx2 , kB\u03b8y2 , kB\u03b8z2) (29c) FT 0 = {0, 0, T1, 0, 0, T2} (29d) F1(q) = \u2211n i=1 ki eiVi (29e) where the dependence of Kg(q) and F1(q) on q is from ki in Eq. (20). If the damping effect is included, the equations of motion would be: Mq\u0308 + Cq\u0307 + K(q)q = F0 + F1(q) (30) where K = Kg(q) +Kb, and C is the viscous damping matrix of the system, which is normally defined by the Rayleigh-type damping [23], namely C = \u03b1M + \u03b2K (31) where \u03b1 = 2(\u03c92\u03b61 \u2212 \u03c91\u03b62)\u03c91\u03c92 (\u03c92 2 \u2212 \u03c92 1) , \u03b2 = 2(\u03c92\u03b61 \u2212 \u03c91\u03b62) (\u03c92 2 \u2212 \u03c92 1) (32) where\u03c91 and\u03c92 are the first and second undamped natural frequencies (rad/s), respectively, and \u03b61 and \u03b62 are the first and secondmodal damping ratios, respectively. The main parameter values of the spur gear system are given in Tables 1 and 4. The spatial cracks described in Tables 2 and 3 are assumed on one of the driven gear teeth, whereas all the other driven gear teeth and driving gear teeth are totally normal. Supposing there are no manufacturing errors and profile modifications, the only possible geometric deviations come from the plastic deformations e2w (E) of the cracked tooth on the driven gear. It should be noted that e2w (E) is position-dependent (along the tooth width direction) and also time-dependent (along the tooth profile direction). Hence, it can be also written as e2i (t), and ei (t) = e2i (t) (33) 3.2 Effect of the tooth plastic inclination deformations on the gear dynamics In this section, the effect of the tooth plastic inclination deformations on the gear dynamic load factor (ratio of the dynamic tooth load to the static tooth load) is investigated. For simplicity, only the tooth cracks in Case A and Case B described in Table 2 are analyzed. The cracks are assumed on the driven gear teeth. Figures 10 and 11 display the dynamic load factor at the middle tooth width surface for the above-mentioned 8 tooth crack cases. The rotating speed of the driving gear for simulation is 2000 rpm. Therefore, the rotating period of the driven gear for one revolution is 0.025s. In Fig. 10a where the tooth inclination angle \u03b8p is 0, only the reductions in the mesh stiffness caused by the tooth crack are considered in the analysis. In Fig. 10b\u2013d, \u03b8p is 0.2, 0.4, and 0.6 degrees, respectively,whichmeans that the reductions in themesh stiffness together with the tooth plastic inclination deformations both come into play. Compared with the no tooth plastic inclination deformation case, the tooth impact impulse per revolution is more and more obvious as the tooth inclination angle \u03b8p increases. Similar results appear in Fig. 11, except that the dynamic load factor is slightly larger than that of Fig. 10, which is due to the larger crack size in Case B than that of Case A. From the results shown in Figs. 10 and 11, it can be concluded that, instead of the reductions in the mesh stiffness, tooth plastic inclination deformations caused by a tooth crack play a dominant role in the dynamic response of the gear system. This conclusion is consistent with the theoretical findings made by Shao and Chen [1] and the experimental results provided by Mark et al. [15]. In fact, when a tooth fillet crack happens, if only the reductions in mesh stiffness are considered, it can be difficult to identify the defect features by observing the dynamic response shown in Figs. 10a and 11a, especially when the crack size is small. As a result, for the early detection of the initial crack damage, special attention should be paid on the tooth plastic deformations, instead of the reductions in the tooth mesh stiffness, as the latter are likely to cause significantly smaller changes in the dynamic response [15]. 3.3 Effect of the tooth plastic inclination deformations on the dynamic load distributions As explained earlier, the non-uniform distributions of the plastic deformations due to spatial crack will lead to the non-uniform dynamic load distributions on the cracked tooth flank. This point can be verified by Figs. 12 and 13, which display the dynamic load distributions on the cracked tooth flank when subjected the spatial cracks illustrated in Case A and Case B. The rotating speed of the driving gear is 6000 rpm. In Figs. 12a and 13a where there is no tooth plastic deformation, the dynamic load is nearly uniformly distributed along the tooth width direction, just like the case where no tooth crack occurs. However, when the tooth plastic deformation is taken into considera- tion, it can be found that the dynamic load is more and more concentrated on the other end of the tooth width where the plastic deformations are smaller. The larger the tooth plastic inclination angle \u03b8p, the more nonuniformity of the dynamic load distributed along the tooth width direction. This is expected as the tooth thin pieces having smaller plastic deformations will support more load compared with tooth thin pieces having larger plastic deformations. Comparing Case A and Case B, it can also be found that the dynamic load distributions in Case A are more uneven than those in the Case B. A non-uniformly distributed dynamic load along the tooth width direction will cause the tilting moment of the gears along theY -axis. Therefore, the titlingmotion of the driven gear \u03b8y2 (or the driving gear \u03b8y1) can best indicate the non-uniformity of the dynamic load distribution along the tooth width direction. Figures 14 and 15 present the tilting motion of the driven gear \u03b8y2 for various tooth crack cases. It can be seen that the titling motion of the driven gear when there is no plastic motion (i.e., TC-A1 and TC-B1) is always 0, which demonstrates that the dynamic load is always uniformly distributed along the tooth width direction in this case. When the tooth plastic deformation is taken into consideration, the tilting motion is excited whenever the cracked tooth comes into the mesh, whose amplitude quickly decays to 0 as the cracked tooth exits from the mesh zone. The larger the tooth plastic inclination angle \u03b8p, the higher the amplitude of the tilting motion being excited. In addition, comparing Case A and Case B, it can also be found that the tilting motion of Case A is higher in amplitude than that of Case B, which demonstrates again that the dynamic load distribution along the tooth width direction in Case A is more uneven that that of Case B."
        ]
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.13-1.png",
        "caption": "Figure A.13 Line integral of F along the path ab.",
        "texts": [],
        "surrounding_texts": [
            "PRODUCT OF VECTORS 425\nNow\nA . B = I A l O P = B - A\nA . C = C - A = j A / P Q\n... A . B + A . C = IAI(OP+PQ) = IAIOQ\n= A - ( B + C).\nScalar products, particularly in the integral form, are frequently encountered in physical problems.\n1 . Work done by a force F in moving a body of unit mass along a path ab is (Figure A. 13)\nb W = l b d w = .I F - d l . (A.2 1)\n2. Given a volume current density J in a region as shown, the current I through a surface S is (Figure A. 14)\nI = L J - d s . (A.22)",
            "426 VECTORS AND VECTOR ANALYSIS",
            "PRODUCT OF VECTORS 427\nIt follows from the definition of the dot product of two vectors A, B that (1) if OAB = x/2, then A . B = 0 (that is, the dot product vanishes for two orthogonal vectors); and (2) if ~ A B = 0 (that is, when A is parallel to B), then A 1 B = IAl IBI. Hence A . A = a relation used to determine the magnitude of a vector:\n]A] = (A-A) l l2 , (A.23)\nprovided that we know how to evaluate A . A. We will illustrate the general procedure by using the rectangular system of coordinates when (2,fi, 5 ) are the orthogonal set ofunit vectors. By definition, it can be shown that\nTake the two vectors A and B expressed as\nB = ZB, + fiBY + iBz .\n(A.25)\nThen, using (A.23) and (A.24), it could be shown that\nA - B = AxBx+ A,By + A,B,, (A.26)\nwhich gives the algebraic expression for A . B in terms of the components of the vectors.\nFrom (A.26) it follows that with A = B\n(A.27)\nSince the scalar product of two vectors A, B is independent of the coordinate system used, (A.26) can be generalized as\nwhere (Ap , Ab, A,) and (AT, A@, A@) are the cylindrical and spherical components of A and B, respectively."
        ]
    },
    {
        "image_filename": "designv10_10_0001183_robot.1995.525354-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001183_robot.1995.525354-Figure3-1.png",
        "caption": "Figure 3: Modeling of flexible links",
        "texts": [
            " This manipulator has three rigid DOF and three motors, located on the fixed platform, that drive the actuated joints. 2 Modeling of an Individual Link Figure 2 shows the manipulator of Fig. 1 with its legs in their deformed configuration, leg i consisting 627 - of the flexible links i and i + 3. Before modeling the dynamics of link i , some definitions are given. The n: (= 7 + ni)-dimensional vector of generalized coordinates of link i is defined as and the mi(= 6 + ni)-dimensional vector of flexzble twist of the same link is vi = [ wT i-T liT(t) 1\u2019 (2) where, with reference to Fig. 3 , & is the 4-dimensional vector of Euler parameters representing the orientation of the frame X i x Z i ( F ; ) with origin at O;, attached to link i , r; is the position vector of joint Oi in the inertial frame XoYoZO (Fo), and u;(t) is the n;dimensional vector of independent nodal coordinates associated with the link flexibility of link i , ni denoting the number of nodal coordinates of the same link. Furthermore, wi is the angular velocity of the frame F; with respect to Fo. Note that the vector of flexible twist is not simply the time derivative of the vector of generalized coordinates because wi is not a timederivative of any quantity. We have, instead, vi = I?;& or ;li = Aivi (3) where I?; is an mi x ni matrix, while A; is an ni x mi matrix. The forms of I\u2019i-and A; are found from the relation between wi and hi [6]. The position vector, in TO coordinates, of any point Pi on link i can be written from Fig. 3 as pi = ri + Ri[di]; (4) where Ri is the rotation matrix of the frame Fi with respect to the inertial frame, while [di]i is the position vector of point Pi in 3;. coordinates. Moreover, from Fig. 3, where [doi]; is the position vector of point Poi in the undeformed configuration of link i in frame Fi, that can be obtained as explained in [7], while [d,i]i is the elastic displacement of point Pi after the deformation of link i . From now on, a vector a or a matrix A expressed in frame Fi is represented as [a]i or [A]i, respectively, except for the inertial frame Fo, in which neither brackets nor the subscript 0 are used. The elastic displacement [d,i]i of point Pi located on the j t h element of link i in Fig. 3 can be discretized by the finite element method as follows: [dili = [doili + [d,i]i (5) [deili = Li(POi)Ui(t) (6) where Li (poi) is the 3 x ni shape function matrix evaluated at point Poi in the undeformed configuration of link i. The detailed derivation of Li(p0;) is available in [7]. Using eqs.(4), (5) and (6), pi can be expressed as Pi = ri + Ri([doiIi + Li(POi)Ui(t)) pi = + Ri[d;]; + RiLi(po;)&(t) (8) (9) (7) The velocity of point Pi on link i is, then, where Ri[d;]i can be written as Ri[d;]; = wi x di and d; is the position vector of point Pi in F;, expressed in Fo",
            " Then, using simulation,joint angles and their time-rates of change were calculated for the given joint torques using a model containing flexible links. The results show considerable differences between rigid links and flexible links. As an example, Figure 6 shows the deviation between rigid links and flexible links, in the case of joint angle and its timerate of change, for link 1. Significant vibrations are also observed in the flexible links, as shown for link 4 in Pig. 7. It is noted that the tip deflections uy and U , are along the and 2; axes of Fig. 3, respectively. 5 Conclusions In this paper the dynamics of a 3-dof spatial parallel manipulator with flexible links was investigated. The finite-element analysis was used to model the flexible links, while the Euler-Lagrange equations of motion were derived for each isolated link. Moreover, the formulation of kinematic constraints allows us to assemble the equations of motion of all the links to obtain the governing equations of motion of the manipulator. The natural orthogonal complement of Lhe constraint matrix was used to derive the minimum number of equations of motion and to eliminate the nonworking kinematic constraint forces due to the kinematic coupling of the links"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003386_10402004.2014.968699-Figure19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003386_10402004.2014.968699-Figure19-1.png",
        "caption": "Fig. 19\u2014Radial Fr ,b and axial Fx ,b force components from a single ball acting on the tilted inner race.",
        "texts": [
            " In the case of interference, the motion of the ball was sinusoidal, due to the tilt of the inner race, with a frequency of one cage revolution. This was not the circumstance for the motion of the ball with a clearance. As described previously, a ball with clearance loses contact with the IR, at which point it maintains contact with the OR due to centrifugal forces. The motion of the ball was irregular through the unloaded portion of the bearing as it was guided loosely by the cage and the curvature of the OR groove. The normal reaction force presented in Fig. 17 had both an axial and radial component as illustrated in Fig. 19 due to the tilt of the IR. The radial component Fr ,b supports the applied load of 3,000 N. The axial component Fx ,b acts as a moment arm about the IR center of mass. There was a net force acting on the IR in the X direction as seen in Figs. 14c and 14d due to the fact this axial component only occurs in the loaded region. If the IR had pure rotation and no translation, the forces in the axial direction would create coupled moments about the IR center of mass, resulting in a zero net axial force acting on the IR"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002839_s10514-013-9343-2-Figure18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002839_s10514-013-9343-2-Figure18-1.png",
        "caption": "Fig. 18 The robot is pushed with a force of 370 N for a duration of 100 ms, to its right. a Whole Body Inertia Shaping starts when none of the foot placement strategies produces safe fall and b safe fall occurs as a result",
        "texts": [
            " The oscillation of the avoidance angle is the result of the oscillation of the CoP, which is often caused by a rocking motion of the robot when it does not have a firm and stable contact with the ground Fig. 15 The robot is pushed with a backward force of 210 N, for a duration of 100 ms. The default fall direction is already safe. The No Action strategy is chosen in this case Figure 17 shows the safe fall behavior as a result of choosing Take a Step and Partial Inertia Shaping. As expected, we can see significant arm motions in this case, and the robot falls in the forward left direction. In Fig. 18 we consider a case with a stronger push force for which the stepping + PIS strategy was not successful, and the controller resorts to the use of whole body inertia shaping. In Fig. 19, we compare No Action, Take a Step and Partial Inertia Shaping strategies when the robot was pushed with a forward force of 235 N, for a duration of 100 ms. The CoM trajectories show that the safe fall was produced by using Partial Inertia Shaping coupled with Take a Step strategy. All the above results are for cases where the robot was standing stationary upright when pushed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002037_978-3-540-77657-4-Figure4.9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002037_978-3-540-77657-4-Figure4.9-1.png",
        "caption": "Fig. 4.9. Reconfigurable system.",
        "texts": [
            " The productive system has a few working modes (such as economy, sport, winter, etc.). The observer is a simple monitor collecting external sensor data and the driver\u2019s behavior, classifies these inputs and derives a situation indicator. The controller works as a modus selector setting the gearbox into the desired mode. Since we have one productive system and one level of O/C, this is a system of type O/C(single, 1). A reconfigurable system is exemplified by a system on a chip (SoC) such as the experimental system developed by Herkersdorf and Rosenstiel [2] (figure 4.9). It displays a number of subsystems such as CPUs, peripheral units, 4 Controlled Emergence and Self-Organization 99 or memory modules that can be rearranged by switching some of them off or on. It allows for the parameterization of buses adapting the bandwidth to the present needs. The productive system (called functional layer in figure 4.9) is monitored and controlled by an O/C layer (called autonomic layer). The observer not only monitors load data but it has to aggregate these data over time in order to determine the load situation. The controller works as a configurator changing directly the working modes of the subsystems. It could even redefine whole subsystems by loading FPGA data into the circuit. In contrast to the multi-mode systems coexisting without interaction, the subsystems are closely connected. This system can be classified as O/C(multiple, 1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000709_s1350-6307(01)00002-4-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000709_s1350-6307(01)00002-4-Figure10-1.png",
        "caption": "Fig. 10. Finite elements and detail of contact area.",
        "texts": [
            " This figure shows larger values and depths of residual stresses caused by increasing shot-peening intensities. The improved performance of shot-peened gears with increased shot-peening intensity was analysed by finite element analyses, which simulated a meshing cycle of the gears. Starting from the hypothesis that shot-peening has a beneficial effect in stopping microcrack growth but not in preventing initiation [12], the models considered cracked gears, including residual stress profiles caused by different treatment conditions. Fig. 10 shows the computation model, with the dark band indicating the site of the crack and the residual stress field. The elements employed are of \u2018\u2018plane strain\u2019\u2019 type with four nodes and first order shape functions. The total number of elements is 10,224 with 11,226 nodes. The contact was modelled by using the elements provided by the computing program library. The loads of the model are those required by the project, with a torque Mt and inter-axial forces of Fx and Fy (see Fig. 1). The analysis investigated the whole meshing cycle; this allowed one to evaluate the distribution of the forces between the teeth in moving contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001930_j.nonrwa.2008.02.014-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001930_j.nonrwa.2008.02.014-Figure3-1.png",
        "caption": "Fig. 3. The base and the global frame [9].",
        "texts": [],
        "surrounding_texts": [
            "Here we study an offset 3-UPU (Universal\u2013Prismatic\u2013 Universal) parallel manipulator with an equal offset in its six universal joints, as shown in Fig. 1 [9]. A special 3-UPU parallel manipulator with zero offsets in the six universal joints was proposed by Tsai in 1996 [10,11]. Tsai\u2019s 3-UPU manipulator has three extensible limbs (legs) that connect the base to the mobile platform through universal joints, and it can provide a 3-DOF pure translational motion [9]. Due to zero offsets in the universal joints, the kinematics of the manipulator is simple and straightforward [10]. Fig. 2 shows a schema of the i th limb (i = 1, 2, 3), which connects point B on the mobile platform and point A on the base by a passive universal (U) joint, an active prismatic (P) joint, and another passive universal (U) joint. So, it is called a 3-UPU parallel manipulator [9]. For the convenience of kinematics analysis, three local frames, namely; \u03a31 : O X1Y1 Z1, \u03a32 : O X2Y2 Z2, and \u03a33 : O X3Y3 Z3, are set up and attached to the base in order to represent the position and the first axis of a universal joint. Actually, frame \u03a3i (i = 1, 2, 3) is rotated along the X axis by angle \u03b2i from global frame \u03a3 . Besides, \u03b21 = 0 since \u03a31 is already chosen to be parallel to \u03a3 . thus coordinates {X i , Yi , Zi } (i = 1, 2, 3) of a point in a local frames \u03a3 i and its coordinates {X, Y, Z} in the global frame \u03a3 have the following relationship (Figs. 3 and 4) [9]:X i Yi Zi  = 1 0 0 0 cos\u03b2i sin\u03b2i 0 \u2212 sin\u03b2i cos\u03b2i  X Y Z  =  X Y cos\u03b2i + Z sin\u03b2i \u2212Y sin\u03b2i + Z cos\u03b2i  (i = 1, 2, 3). (7)"
        ]
    },
    {
        "image_filename": "designv10_10_0002687_j.apacoust.2013.04.017-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002687_j.apacoust.2013.04.017-Figure10-1.png",
        "caption": "Fig. 10. Scheme of the gearbox. The numbers indicate the tooth number of each gear wheel.",
        "texts": [
            " All data was stored locally on the hard drive of the measurement system. Once the system was dismounted, the data was retrieved for processing and analysis. The gearbox consists of a fixed-shaft, spur bevel reduction stage, followed by two fixed-shaft spur gear stages. The output of the latter stage is connected to the sun gear of the first planetary stage. The carrier plate of the first planetary stage is connected to the sun gear of the second planetary stage. Finally, the carrier plate of the second planetary stage is coupled to the bucket wheel. Fig. 10 shows a scheme of the gearbox, whose total ratio is 349.1:1. The gearbox is driven by an electrical motor whose nominal speed is 990 rpm; at this rotational speed, the bucket wheel rotates at 2.83 rpm. Both planetary stages have three equally-spaced planet gears; all gears are spur gears. The number of teeth of the first planetary stage are ZS1 \u00bc 21, ZP1 \u00bc 64 and ZR1 \u00bc 150, and of the second stage are ZS2 \u00bc 27, ZP2 \u00bc 31 and ZR2 \u00bc 90. It can be demonstrated that all gear meshing of the first stage are in-phase; whereas in the second stage, all planet-ring meshing are in phase, all planet-sun meshing are in phase, but there is a phase difference between the planetring and planet-sun meshing [16]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003392_j.procir.2014.03.066-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003392_j.procir.2014.03.066-Figure4-1.png",
        "caption": "Figure 4: Wire-EDM procedure for gear prototype manufacturing",
        "texts": [
            " Since the gear flanks require a high accuracy finish, they should all be cut and finished in 1 clamping, thus avoiding realignment errors. Therefor the gear tips, which are not that critical in shape accuracy, will be cut in 2 different steps. A base plate will be used for positioning and mounting the preturned forging. The baseplate, made by wire-EDM, consists of an inner ring, connected by 12 thin segments to the rest of the baseplate. These 12 segments will coincide with 12 tooth tips (thus one connection every 30\u00b0). This base plate is illustrated in Figure 4 (a). The turned forging is than glued on top of the baseplate, with the core hole of the turned forging concentric with the hole in the core hole in the baseplate (Figure 4 (b)). In the next step the gear, minus 12 teeth, is cut, using 1 main and 4 trim cuts, in 1 clamping. This is illustrated in Figure 4 (c). In the next step, the gear is repositioned, allowing to machine the 12 remaining tooth tips. This last step is illustrated in Figure 4 (d). A Sodick AQ 537L wire-EDM machine, with water based dielectric, was used for the manufacturing of this gear, using standard steel technology parameters from the machine tool supplier for a workpiece height of 40 mm, including a main cut and 4 trim cuts with constantly reduced discharge energy for finishing. An uncoated brass wire of diameter 0.25 mm was used. 3.2. Results Table 6 lists details about the time needed for preparation and production of the gear prototype using wire-EDM. The total time for manufacturing the finished gear, including the manufacturing of the holder, is 22 h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure5.13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure5.13-1.png",
        "caption": "Figure 5.13 (b) equivalent two-wire line by image. Wire above a ground and image theory: (a) a conducting wire above a ground",
        "texts": [
            " With appropriate excitation, and neglecting the fringe effects, it can be shown [2] that the fields of the TEM mode propagating in the line are E = 533, and H = $Hg, and they carry energy in the z direction. The circuit parameters for the line are + + For the lossless case, R = G = 0, and the characteristic impedance is given by 5.7.4 Circular Wire above a Ground Plane (5.1 10) which by image theory is found to be equivalent to the upper half of a thin 170 TRANSMISSION LINES wire transmission line as shown in Figure 5.13b. The latter can be utilized to determine the circuit parameters for the configuration. It is clear that the capacitance C per unit length from wire above ground can be obtained from (5.103) for the two-wire line as which gives 27rc In 2h/a, C = - Flm (5.1 11) It can now be shown that (5.1 12) in Figure 5.13 is 60 2 h Zo=- ln- 0. & a (5.1 13) 5.7.5 Microstrip Line Microstrip lines (Figure 5 . 2 4 are widely used as transmission lines for microwave integrated circuits and on printed circuit boards (PCBs). They are also used for circuit components such as filters, couplers, and resonators. Being a planar transmission line, they can be fabricated by pholithographic processes and are easily integrated with other passive and active microwave devices. LINE PARAMETERS 171 Figure 5.14 field lines. Transverse view of a microstrip line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure2-1.png",
        "caption": "Figure 2. The Theorem of Three Centres for planar motion, showing the \"ladder' of available ISAs with h = 0 together with transverse ISAs with h = oo that are available when to1,+ t~23 =0.",
        "texts": [
            " If, for three members 1, 2, 3, in relative planar motion, $t2 and $23 are known but definite values are not assigned to ~12 and ~23, ~13 will always be the vector sum, m12 + a~23, and $t3 must lie, according to the theorem, in line with and parallel to $12 and $23- All the ISAs have h=0 . With the magnitudes of ~t2 and ~:a open to choice, member 3 would possess two degrees of freedom relative to member I, and there is available, at the instant, a set of cot S13, s with h=0 , all parallel and in the plane containing both 51, and S23. This single infinitude of available ISAs may be regarded as 'rungs of a ladder' (see Fig. 2). The cylindroid containing all these ISAs becomes infinitely long, but must, nevertheless, (see 2.1. (iii)) still include some other $13's making some angle with those already depicted in the 'ladder'. Moreover (2.1. (ii)), with a cylindroid infinitely long and known to contain ISAs with h=0 , these other $t3's must have h = co. One readily sees that they lie perpendicularly to the plane of the ladder and apply only when the motion of 3 relative to 1 is translational, namely when ~12 + 0).,3 = 0. They are depicted diagrammatically in Fig. 2. All these transverse ISAs with h=co account merely for the possibility of pure relative instantaneous translation between members 1 and 3, and confirm the equivalence between a prismatic pair and a revolute pair at infinity with axis perpendicular to it. Indeed there are other ISAs of finite and infinite h-values going out to infinity to complete the cylindroid, and these can also be regarded as kinematically equivalent to accessible h =oo ISAs. 2.3. Now if $ ~ 2 and $2 a are still parallel but have h-values h 12 and h 2 3 that are not equal to zero $x3 can be located as follows (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of a wide-faced cylindrical geared rotor system.",
        "texts": [
            " The generalized loaded static transmission error for the wide-faced cylindrical gear pair is proposed, and the determination method of mesh misalignment caused by shaft deflection is presented. Section 3 gives the establishment of gear mesh element considering mesh misalignment caused by shaft deflection and dynamic model of the system. Section 4 gives the comparison between the proposed model and the three-dimensional finite element model, and investigates the effect of supporting layout, power transmission path and output torque on quasi-static and dynamic behaviors of a wide-faced spur/helical geared rotor system. Some conclusions are given in Section 5 . Fig. 1 shows a wide-faced cylindrical geared rotor system. The diameters of shaft 1 and 2 are 45 mm and 85 mm respectively, and the lengths of two shafts are both 740 mm. The two shafts are supported using four rolling bearings which are represented using four blue cylinders with 50 mm width. The green cylinder at the left side of shaft 1 denotes the power input location, the red one at the left side of shaft 2 and pink one at the right side of shaft 2 represent the two types of power output locations, respectively",
            " The stiffness of the i th contact point can be determined using k i = F i T LST E \u2212 \u03b5 i (4) The mesh stiffness of the i th sliced helical gear pair along gear width can be calculated using k mi = N \u2211 i =1 k i (5) where N is the number of contact point pairs for a sliced gear pair. For a spur gear pair, N = 1 when the mating sliced gear pair in single-tooth engagement zone, and N = 2 when the mating sliced gear pair in double-tooth engagement zone. According to the shaft structure, power input/output positions and bearing mounting positions, the wide-faced geared rotor system which is given in Fig. 1 is divided into a series of shaft elements and nonlinear contact elements, as shown in Fig. 3 . B g is the gear width, B b is the bearing width. The shaft element is modeled using Timoshenko beam element with 2 nodes and 12 degrees of freedom. The two shafts are coupled using a series of nonlinear contact elements that consist of sliced mesh stiffness and clearance. The model of a Timoshenko beam element with 2 nodes and 12 degrees of freedom is shown in Fig. 4 (a). The generalized coordinate vector of the i th Timoshenko beam element is given as q i s = { x i s , y i s , z i s , \u03b8 i xs , \u03b8 i ys , \u03b8 i zs , x i +1 s , y i +1 s , z i +1 s , \u03b8 i +1 xs , \u03b8 i +1 ys , \u03b8 i +1 zs } T (6) where x i s , y i s , z i s , x i +1 s , y i +1 s , z i +1 s are translational displacements of the i th shaft element along coordinate axis, and \u03b8 i xs , \u03b8 i ys , \u03b8 i zs , \u03b8 i +1 xs , \u03b8 i +1 ys , \u03b8 i +1 zs are rotational angles of the i th shaft element around coordinate axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure11-1.png",
        "caption": "Fig. 11. Comparison of rough-cut geometry of the gear tooth surfaces with regard to the objective geometry for the 5th valid geometry on (a) the concave side and (b) the convex side.",
        "texts": [
            " While running the COBYLA algorithm, every time that zero constraints are violated, a valid rough-cut geometry is saved so that a set of valid rough-cut geometries is obtained. Obviously, the more iterations of the optimization algorithm pass, the lower the maximum deviations between the rough-cut geometry and objective geometry are achieved, and, consequently and according to [23] , the lower the total machining cycle time (including both roughing and finishing operations) will be. Among all valid geometries, the machine-settings obtained for the 5th, 20th and final 40th rough-cut geometry are given in Table 9 . Fig. 11 depicts the distances between the rough-cut geometry and the objective geometry for the 5th valid geometry. As depicted, the maximum stock for the finishing operation is concentrated on the central dedendum area of both concave and convex active surfaces of the rough-cut geometries, whereas the minimum stock is located on the addendum area of concave active surfaces and on the heel and toe areas of convex active surfaces. More concretely, the magnitude of the aforementioned raw material surplus is very limited, being about 360 \u03bcm for the concave side, whereas a minimum stock of 103"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003494_tmag.2016.2572659-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003494_tmag.2016.2572659-Figure14-1.png",
        "caption": "Fig. 14 Prototype.",
        "texts": [
            " From this, it is described that the torque constant of the CSVFRM is lower than that of the CSVFPMM and the permanent magnet in the CSVFPMM assists the magnetic flux due to the DC currents. Fig. 12 shows the N-I characteristics. From this, the tendency of the phase current change is the same with each other. Fig. 13 shows the motor efficiency. From this, it is observed that the motor efficiency of the CSVFRM is lower than that of the CSVFPMM. This means that the permanent magnet in the CSVFPMM assists the magnetic flux due to the DC currents. A. Prototype Machine and Driving Device Measurements using a prototype shown in Fig. 14 were conducted to verify the operational principle of the CSVFPMM. A measuring system is shown in Fig. 15, and the prototype specification is the same as the analysis model shown in Fig. 5. In this chapter, the prototype was rotated by a servo motor, and the static characteristics such as a cogging torque and EMF were measured. B. Cogging Torque Fig. 16 compares the computed and measured cogging torque waveforms when the motor is rotated at 1 rpm. The 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure4-1.png",
        "caption": "Fig. 4. End structure of the 330 MW water-hydrogen-hydrogen turbogenerator.",
        "texts": [
            " 3 that the total loss of the end parts first decreases gradually and then increases gradually with increased relative magnetic permeability of the press plate. When the relative magnetic permeability of the press plate is 30, the total loss of the end parts is minimized. When the relative magnetic permeability of the press plate changes from 1 to 50, the loss of the press plate decreases by 4889 W. When the relative magnetic permeability of the press plate changes from 1 to 50, the loss of the copper screen increases by 3452 W. C. 3-D fluid and thermal analysis model Fig. 4 shows the end structure of this 388 MVA waterhydrogen-hydrogen turbogenerator. The stator end winding, stator core, and water pipes in Fig. 4 correspond to Position E, Position G, and Position F in Fig. 1, respectively. According to the actual structure of this 388 MVA turbogenerator end region, a 3-D fluid and thermal analysis model of the turbogenerator end region is established, as shown in Fig. 5. Fig. 5 (a) shows the end parts in the turbogenerator end region. Fig. 5 (b) shows the inlets and outlets of turbogenerator end region. Press plate Air-gap spacer Stator end winding Stator end core Wind board Copper screen Finger plate Shelter board Water pipes (a) 0278-0046 (c) 2018 IEEE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003296_j.ymssp.2017.05.041-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003296_j.ymssp.2017.05.041-Figure11-1.png",
        "caption": "Fig. 11. Dynamic model of gear system with six DOF.",
        "texts": [
            " In Table 5, it is easy to find that the result of assist-SIF method is more close to the ISO, the relative error of the maximum single-tooth mesh stiffness and average mesh stiffness are 3.9955% and 1.0074%, respectively. In summary, the assist-SIF method can reflect the gear mesh stiffness under the crack states more accurately and effectively. In order to study the feature analysis of gear crack by the simulation signal, based on the mesh stiffness model of the assist-SIF method, a dynamic lumped parameter model of a spur gear system comprising of 6-DOF is established. A schematic of the gear dynamic model is shown in Fig. 11, where the \u2018\u2018y\u201d axis direction is parallel to the meshing line; the \u2018\u2018x\u201d axis is parallel to the direction of the friction force. The equations of motion in the translational direction for the gear and pinion are as follows: mp\u20acxp \u00fe Cpx _xp \u00fe kpxxp \u00bc Ff mg\u20acxg \u00fe Cgx\u20acxg \u00fe kgxxg \u00bc Ff mp\u20acyp \u00fe Cpy _yp \u00fe kpyyp \u00bc N mg\u20acyg \u00fe Cgy _yg \u00fe kgyyg \u00bc N 8>>< >>: \u00f031\u00de The equations of motion in the rotational direction for the gear and pinion are as follows: jp\u20achp \u00feMpN Mpf \u00bc Tp jg\u20achg \u00feMgf MgN \u00bc Tg ( \u00f032\u00de Fig. 10. The gear system rig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure9-1.png",
        "caption": "Figure 9. (a) R-C-R-C and (b) R-C-C-R linkages. (c) A form of (b) that transmits uniform rotational motion from one shaft to another one skew to it,",
        "texts": [
            " So, if the two P-pairs t}st and P45 were removed and replaced by another set of three parallel screws aligned differently from the first set, the same mobility and the same general form of relative curvilinear translation would result. The linkage in Fig. 8(b) depicts such an arrangement. 4.3. Table 4 gives the possible combinations of S-, P-, R- and C-pairs derived from one set of three parallel screw pairs constituting one half of the joints in a six-screw linkage. Two linkages obtained from Table 4 containing two C-pairs and two R-pairs are illustrated in Fig. 9(a) and (b). In Fig. 9(c) is shown a somewhat more generalised form of an often-quoted R-C-C-R linkage that allows the transmission of uniform rotational motion from one shaft to another one placed skew to it. No more than two prsimatic pairs can be included in a closed single loop derived from the screw version of Sarrus's linkage, one prismatic pair being in each set, if the loop is to retain a 'true mobility' of 1. 5. Single-Loop Linkages Containing Four Prismatic Pairs 5.1. If four members 1, 2, 3 and 4 are joined in series by three P-pairs Plz, P-,a, Pa~, randomly orientated with respect to one another, the movement of member 4 relative to member 1 cannot possibly involve any rotation, but may be a curvilinear translation along any chosen track"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003386_10402004.2014.968699-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003386_10402004.2014.968699-Figure8-1.png",
        "caption": "Fig. 8\u2014Finite element rotor supported on each end with DBM ball bearings. Blue arrow indicates the applied load. The blue elements on top of the rotor indicate compressive stresses, whereas the red indicate tensile stresses.",
        "texts": [
            " The dimensions and material properties of the shaft used are given in Table 3, except that the density was adjusted here such that the mass of the rotor would be equivalent to that given by Fukata, et al. (14). The constant radial load used by Fukata, et al. (14) and Mevel and Guyader (15) was 58.8 N and was directly applied to the inner race of the single bearing being examined. In this analysis, the load was applied at the center of the shaft and was doubled such that the total load would be equally supported by the two bearings. Gravitational forces were not considered. The resulting configuration is illustrated in Fig. 8. The displacements of the inner race in the horizontal Y and vertical Z directions are shown in Fig. 9a as presented by Mevel and Guyader (15). Figure 9b illustrates the results from the DBM in the combined rotor\u2013bearing model developed for this investigation and shows that it agrees well with Fig. 9a. Figure 9c depicts the fast Fourier transform of the horizontal and vertical displacement of the inner race shown in Fig. 9b. The VC frequency dominates the spectrum, with the additional harmonics also shown, due to the low operating speed and distance from any critical speeds",
            " The bearing and shaft properties are given in Tables 2 and 3, and the shaft was rotated at 3,000 rpm. A load was gradually applied at the center of the shaft from 0 to 3,000 N in the negative Z direction; therefore, this will be referred to as the centrally loaded case. Two separate simulations were conducted in which the diameter of the balls was varied, resulting in a radial clearance of \u221220 \u03bcm and an interference of +5 \u03bcm. Often deep-groove ball bearings are assembled with clearances, but interferences may occur due to preload or thermal expansion of the bearing elements. Figure 8 illustrates the configuration of the combined system analyzed here. The normalized profile of the applied load is seen in Fig. 11 with the resulting displacements of the inner race (IR) center of mass shown in Fig. 12 for the clearance and interference cases. The displacement in the Z direction was almost identical for bearings 1 and 2 due to the symmetry of the system. At time zero, the IR interference case was in equilibrium with zero displacement, but with an increase of the applied load, the IR began to move downwards with growth in the elastic deformation of the Hertzian contacts between the balls and races"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002545_1350650111433243-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002545_1350650111433243-Figure4-1.png",
        "caption": "Figure 4. Schematic view of the foundation.",
        "texts": [
            " For natural convection, the heat-transfer coefficients of convection are16 for a vertical surface Nu \u00bc 0:28 \u00f0Gr Pr\u00de0:3 \u00f013\u00de for a horizontal surface Nu \u00bc 0:2 \u00f0Gr Pr\u00de0:32 \u00f014\u00de whereas for forced convection, the Nusselt number depends on the air flow direction17 as normal to the wall Nu \u00bc 0:145 Re0:66 \u00f015\u00de tangential to the wall Nu \u00bc 0:27 Re0:63 \u00f016\u00de Since the test gear casing is placed on a foundation, heat not only flows through the lower part of the casing but also through the foundation which is accounted for via an extended surface area in order to estimate Rth 1, 2\u00f0 \u00de. To this end, the foundation is modelled as a rectangular fin (Figure 4) and the following assumptions are introduced: (a) the heat flow in the foundation is unidirectional and (b) both the test gear and the slave gear units can transfer heat through the foundation so that there is a plane of symmetry at x\u00bc l (Figure 4) and the end of the fin is supposed to be insulated. In such conditions, the fin efficiency can be expressed as12 foundation \u00bc th ffiffiffiffiffiffi 2 U k e q :l ffiffiffiffiffiffi 2 U k e q :l \u00f017\u00de at Monash University on December 6, 2014pij.sagepub.comDownloaded from where U is an overall heat-transfer coefficient which takes into account convection and radiation heat exchanges. Since the foundation is supposed to be equivalent to a flat plate, the heat-transfer coefficient for convection is estimated according to the above-mentioned correlations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000775_iros.2000.894664-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000775_iros.2000.894664-Figure4-1.png",
        "caption": "Figure 4: Frames",
        "texts": [
            " A second idea might be to move the tool-center point to the trocar and then to compute X T C P . This demands a calibration for every instrument used. To avoid these drawbacks, we have decided to choose another way. After the instrument has entered the abdomen we are collecting data during the first few seconds. With this data the entry point can be calculated as follows: At each timestep t , we save the joint values 0,. 0i = @(ti) With i E (1,. . . , N } (3) - 566- The frame X L J located at the last joint (see Fig. 4) with respect to the world frame W can be calculated as described in (4). Where is the position a and P i = [ :] i the last joint in the WOI wa = [ If ] a (5) frame W is the vector of the instrument axis in W . So we can define a line g, lying on the instrument axis: ga : iz = p a +A,w, with A, ER (7) If we assume that the entry point does not move, the intersection of the two lines g, and g%+l is the pivot point. Due to noise and slow movement of the entry point these two lines might not have an intersection but pass each other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure5-1.png",
        "caption": "Fig. 5. 3-D fluid and thermal analysis model of the turbogenerator end region. (a) End parts in the turbogenerator end region. (b) Inlets and outlets of the turbogenerator end region.",
        "texts": [
            " When the relative magnetic permeability of the press plate changes from 1 to 50, the loss of the copper screen increases by 3452 W. C. 3-D fluid and thermal analysis model Fig. 4 shows the end structure of this 388 MVA waterhydrogen-hydrogen turbogenerator. The stator end winding, stator core, and water pipes in Fig. 4 correspond to Position E, Position G, and Position F in Fig. 1, respectively. According to the actual structure of this 388 MVA turbogenerator end region, a 3-D fluid and thermal analysis model of the turbogenerator end region is established, as shown in Fig. 5. Fig. 5 (a) shows the end parts in the turbogenerator end region. Fig. 5 (b) shows the inlets and outlets of turbogenerator end region. Press plate Air-gap spacer Stator end winding Stator end core Wind board Copper screen Finger plate Shelter board Water pipes (a) 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 4 In the turbogenerator end region, heat transfer and fluid flow obey energy conservation, momentum conservation, and mass conservation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001283_02640410500520401-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001283_02640410500520401-Figure2-1.png",
        "caption": "Figure 2. Front and side views of the ball \u2013 bridge \u2013 board interactions.",
        "texts": [
            " The simulation switches from the slipping to the nonslipping motion when the tangential velocity of the contact point vanishes. It switches from the nonslipping to slipping motion when the total tangential friction force at the contact point would be greater than the maximum possible Coulomb friction force. Okubo and Hubbard (2002, 2004a) explain the ball \u2013 rim model in detail, and derive the slipping and non-slipping equations of motion using Kane\u2019s method (Kane & Levinson, 1985). Ball \u2013 bridge \u2013 board model A right-handed coordinate system (Figure 2) with origin O at the centre of the hoop has its X axis parallel to the backboard, Y axis perpendicular to the board, and Z axis vertical with unit vectors I, J, and K along the X, Y, and Z axes, respectively. The bridge is a flat slab of width w\u00bc 18 cm for a breakaway type D ow nl oa de d by [ Is ta nb ul U ni ve rs ite si K ut up ha ne v e D ok ] at 0 2: 09 2 6 Ju ne 2 01 3 hoop, whose planar horizontal top surface connects the backboard to the topmost points on the rim in the range \u2013 w/2 x w/2. Note that Rb5Ry Rr (Figure 2), so that it is possible for the ball to remain in motionless equilibrium on top of the bridge. We assume that the ball contacts the bridge and board at variable points on the ball B\u0302y and B\u0302z, respectively. The basketball centre B* lies distances ry from the board and rz from the bridge. The configuration of the ball with radial compliance has six degrees of freedom. Three determine the position of the ball centre: x, y\u00bcRh \u00fe Ry \u2013 ry, and z\u00bc rz \u00fe Rr, where Rh is the radius of the toroidal basketball hoop, Ry is the minimum distance of the rim from the board, and Rr is the radius of the rim"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002026_tmag.2009.2012785-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002026_tmag.2009.2012785-Figure5-1.png",
        "caption": "Fig. 5. Contours of eddy current loss. (a) Without skew and (b) 4/3 slot pitch skewed.",
        "texts": [
            "00 \u00a9 2009 IEEE Here, the distribution of flux density vectors and the losses of the SCIM with the 4/3 slot pitch skewed rotor and that with rotor without skew are calculated. The calculated losses are compared with measured ones to clarify the validity of the 3-D analysis. Further more, the bar-current and the torque are calculated. Fig. 4 shows the distributions of flux density vectors of SCIM with the 4/3 slot pitch skewed rotor. The flux density vectors of the upper section are larger than those of the lower section. The imbalance of the magnetic flux distributions makes the loss distributions imbalanced in the SCIM with skewed rotor. Fig. 5 shows the contours of eddy current loss. The eddy current loss in the tip of teeth and the surface of the rotor is especially large. From Fig. 5(b), the eddy current loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 6 shows the contours of hysteresis loss. The hysteresis loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 7 shows the loss of the SCIM. The iron loss of the SCIM is decreased by the skewed rotor. The calculated total losses agree well with the measured ones. Fig. 8 shows the waveforms of bar-current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001491_1.1876437-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001491_1.1876437-Figure5-1.png",
        "caption": "Fig. 5 Coordinate systems of the hob cutter and CNC hobbing machine",
        "texts": [
            " 8 , the surface equation of the ZN worm-type hob cutter R1 1 , represented in coordinate system S1, can be obtained: R1 1 l1, 1 = rt + l1 cos n cos 1 l1 sin n sin 1 sin \u2212 rt + l1 cos n sin 1 l1 sin n cos 1 sin \u00b1l1 sin n cos \u2212 P1 1 1 , 9 where l1 and 1 are the surface parameters of the hob cutter. In Eq. 9 , the upper sign represents the right-side hob cutter surface while the lower sign indicates the left-side hob cutter surface. The surface normal vector N1 1 of the hob cutter can be ob- tained and represented in coordinate system S1 as follows: N1 1 = R1 1 l1 R1 1 1 , 10 where R1 1 l1 = cos n cos 1 sin n sin 1 sin \u2212 cos n sin 1 sin n cos 1 sin \u00b1sin n cos , and R1 1 1 = \u2212 rt + l1 cos n sin 1 l1 sin n cos 1 sin \u2212 rt + l1 cos n cos 1 \u00b1 l1 sin n sin 1 sin \u2212 P1 . Figure 5 reveals the schematic relationship among coordinate Transactions of the ASME hx?url=/data/journals/jmdedb/27813/ on 03/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F systems S1, Sh, S2, and Sf for the gear generation mechanism. Coordinate system S1 is attached to the hob cutter while coordinate system S2 is attached to the gear blank. Coordinate system Sh is the reference coordinate system and coordinate system Sf is the fixed coordinate system attached to the machine housing. Symbols B and 2 are rotational angles of the hob cutter and gear blank, respectively. A depicts the rotational angle of hob\u2019s swivel axis. The homogeneous coordinate transformation matrix Mij transforms the coordinates from coordinate system Sj to Si. According to the relations as illustrated in Fig. 5, matrices Mh1, M fh, and M2f can be obtained as follows: Mh1 = cos B \u2212 sin B 0 0 sin B cos B 0 0 0 0 1 lh 0 0 0 1 , 11 M fh = \u2212 1 0 0 lx 0 \u2212 sin A \u2212 cos A 0 0 \u2212 cos A sin A \u2212 lz 0 0 0 1 , 12 and M2f = cos 2 sin 2 0 0 \u2212 sin 2 cos 2 0 0 0 0 1 0 0 0 0 1 , 13 where lh = O1Oh , lx = OfQ , and lz = QOh . In Fig. 5, point P is a common point to both hob cutter and work piece. The surface coordinates of the hob cutter can be transformed to the fixed coordinate system Sf as follows: R f 2 = OfP = M fhMh1R1 1 = xfi f + yfj f + zfk f . 14 The velocity of point P attached to the work piece can be obtained by: V f 2 = 2 R f 2 = \u2212 yf 2i f + xf 2j f , 15 where 2= 2k f indicates the angular velocity of the work piece. The velocity of point P attached to the hob cutter can be represented as follows: V f 1 = A + B R f 1 + Vz, 16 where A = \u2212 Ai f , B = \u2212 B cos Aj f + B sin Ak f , and R f 1 = R f 2 \u2212 lxi f \u2212 lzk f = xf \u2212 lx i f + yfj f + zf + lz k f "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure15-1.png",
        "caption": "Fig. 15 \u2013 Location of seats inside the vehicle with the defined residual space.",
        "texts": [
            " Ek \u00bc I v2 2 where I is the moment of inertia relative to the temporary axis of rotation (Table 4), v is the angular velocity relative to the temporary axis of rotation. Therefore v \u00bc 2:558 rad=s Fig. 14 depicts main initial conditions of the analysis. An additional initial condition was the influence of gravity and the contact phenomena occurring on the contact points of the bus bodywork and the tilt plane as well as in the structural elements of the superstructure. Method of performing the strength test of the bus is shown in Fig. 14 while Fig. 15 presents the location of the seats inside the vehicle and the definition of residual space [16]. The results of the performed strength analysis are as follows: contours of deformations, contours of equivalent stress, displacement fields, velocity fields. This paper presents examples of results illustrating the distribution of deformations and stress in the structure at a given moment on a deformed model. Also, the deformation Fig. 16 \u2013 Contours o form is presented at the moment of highest elastic and plastic deformation of bodywork (Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002837_j.mechmachtheory.2013.10.001-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002837_j.mechmachtheory.2013.10.001-Figure1-1.png",
        "caption": "Fig. 1. Needle roller bearing with flanges and inner ring.",
        "texts": [
            " The ends of the needle rollers have smaller diameter or chamfer radius so that they can be located in raceways. Because of higher sliding these bearings have higher coefficient of friction. They are used to take pure radial load. They differ than other bearings in aspects like they have considerably greater length-to-diameter ratio (2.5Dr b le b 10Dr), needle rollers are difficult to manufacture accurately as compared to cylindrical rollers. Needle rollers are difficult to guide and rollers get rubbed against each other. NRB is illustrated in Fig. 1. In NRBs, flanges that are integral to the outer raceway retain rollers. Fig. 2 shows the inner ring that is used with the needle and cage assembly. It is used when the shaft cannot be hardened and grounded to a suitable raceway tolerance. The inner ring is hardened and grounded, and is provided with a chamfer on both sides for assembly. Fig. 3 shows the needle roller which is relieved at ends to prevent edge stresses. Fig. 4 shows the terminology for NRBs. The figure shows different components of the bearing like (1) outer ring, (2) lubrication hole, (3) raceway, (4) needle roller and cage assembly, and (5) open end",
            " The dynamic capacity is defined as \u201cthe constant radial load, which a group of apparently identical bearings can endure for a rating life of one million revolutions of the inner ring (for a stationary load and the stationary outer ring)\u201d and it is expressed as in Eq. (2). For the present optimization case, the maximization of the dynamic capacity of NRB, the objective function is given by, max f X\u00f0 \u00de\u00bd \u00bc max Cd\u00bd \u00f03\u00de f(X) represents the objective function, and X is the design variable vector. Referring to Eq. (2), the NRB design parameter vector has been chosen as Xf g \u00bc Dr ; le;Dm; Z;KDmin ;KDmax ; \u03b5 h iT \u00f04\u00de here Dr, le, Dm and Z (for nomenclatures see Appendix A) are the parameters defining the internal geometry of the bearing (see Fig. 1), while other parameters are used in constraints to give the NRB a feasible design space. These would be defined in the subsequent section. The pitch diameter of the NRB should be selected such that it lies between the inner and outer diameters of the bearing, which ensures the space for the chamfering of sharp corners of the inner and outer rings. d\u00fe 2r\u00f0 \u00de\u2264Dm\u2264 D\u22122r\u00f0 \u00de: \u00f05\u00de The range of mean diameter of the roller is derived from both the strength and geometric considerations. The lower limit of the roller mean diameter is obtained from the contact stress expression and the upper limit is obtained from the geometry",
            "8 mm long [23]. Here, a parameter (\u03c7) defined which gives a constraint on the roller length as given below, where g13 X\u00f0 \u00de \u00bc le\u2212Dr\u03c7\u00f0 \u00de\u22650 with \u03c7 \u00bc le . Dr \u00f015\u00de \u03c7 is the parameter and is having a range of 2.5\u201310. The maximum shear stress occurs at a depth zstatic, below the surface. Hence, the thickness of the outer raceway should be greater than this limit [22]. g14 X\u00f0 \u00de \u00bc 1 2 D\u2212Do\u00f0 \u00de\u22123zstatic\u22650 \u00f016\u00de where zstatic \u00bc 0:626bo where bo \u00bc 3:35 10\u22123 Qo le\u03a3\u03c1o 1=2 : The thickness of the flange tf (see Fig. 1) is taken equal to the thickness of the outer raceway thus imposing a constraint on the length of roller (l = le + 2r) and it is given by t f \u00bc 0:5 D\u2212Di\u22122Dr\u00f0 \u00de or g15 X\u00f0 \u00de \u00bc B\u2212 D\u2212Di\u22122Dr \u00fe l\u00f0 \u00def g\u22650: \u00f017\u00de Both Constraints 13 and 15 are related with the roller length, the first in respect to the radial direction geometrical constraint and the second related to the axial direction geometrical constraint. Since the ratio of needle roller length-to-diameter is recommended in literature in consideration with skewness of roller over races so Constraint 13 comes into force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002486_1.4004225-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002486_1.4004225-Figure3-1.png",
        "caption": "Fig. 3 A Hooke-spherical joint mechanism",
        "texts": [
            " In the first category, the axis intersection-angle d1 needs to be zero as follows: sd1 \u00bc 0 (22) In the second category, the axis intersection-angle d2, axis perpendicular-link parameter a2, and axial link parameter d3 need to satisfy the following constraint: a2 2 \u00fe d2 3s2d2 \u00bc 0 (23) In the third category, axis intersection-angles d2 and d5, axis perpendicular-link parameters a2 and a5, and axial link parameters d2, d3, d5, and d6 needs to satisfy the following constraint: d2 2 \u00fe a2 2 \u00fe d2 3 \u00fe 2d2d3cd2 \u00bc d2 5 \u00fe a2 5 \u00fe d2 6 \u00fe 2d5d6cd5 (24) The three equations present three categories of the 6R double-centered overconstrained mechanisms with a general arrangement. In category 1, the condition sd1\u00bc 0 in Eq. (22) gives a doublecentered mechanism as Hooke-spherical mechanism in Fig. 3. In this category, two joint axes J1 and J2 are coaxial, making one center of the mechanism to become an extended Hooke-joint center. The mechanism is degenerated from a double-spherical linkage to a Hooke-spherical linkage. In category 2, the condition in Eq. (23) gives rise to two mechanisms. In both mechanisms, the axis perpendicular-link parameter a2 needs to be zero. Further to this requirement, the first mechanism follows the axis intersection-angle constraint that d2\u00bc 0. Thus, J2 is collinear to J3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001636_s0263574704000347-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001636_s0263574704000347-Figure3-1.png",
        "caption": "Fig. 3. Feasible and non-feasible \u201czero\u201d configurations.",
        "texts": [
            " Taking into account obvious properties of the parallelograms, the Orthoglide geometrical model can be presented in a simplified form, which consists of three bar links connected by spherical joints to the tool centre point at one side and to the corresponding prismatic joints at another side. Using this notation, the kinematic equations of the Orthoglide can be written as follows (px \u2212 \u03c1x)2 + p2 y + p2 z = L2 p2 x + (py \u2212 \u03c1y)2 + p2 z = L2 p2 x + p2 y + (pz \u2212 \u03c1z)2 = L2 (1) where L is the length of the parallelogram principal links and the \u201czero\u201d position p0 = (0, 0, 0) corresponds to the joints variables 0 = (L, L, L), see Fig. 3a. It should be stressed that the Orthoglide geometry and relevant manufacturing technology impose the following constraints on the joint variables 0 < \u03c1x \u2264 2L; 0 < \u03c1y \u2264 2L; 0 < \u03c1z \u2264 2L, (2) which essentially influence on the workspace shape. While the upper bound (\u03c1 \u2264 2L) is implicit and obvious, the lower one (\u03c1 > 0) is caused by practical reasons, since safe mechanical design encourages avoiding risk of simultaneous location of prismatic joints in the same point of the Cartesian workspace (here and in the following sections, while referring to symmetrical constraints the subscript is omitted, i",
            " However, it is not sufficient, since the lower joint limits http://journals.cambridge.org Downloaded: 15 May 2014 IP address: 186.233.152.15 (2) impose the following additional constraints px > \u2212sx \u221a L2 \u2212 p2 y \u2212 p2 z ; py > \u2212sy \u221a L2 \u2212 p2 x \u2212 p2 z ; (5) pz > \u2212sz \u221a L2 \u2212 p2 x \u2212 p2 y, which reduce a potential solution set. For example, it can be easily computed that for the \u201czero\u201d workspace point p0 = (0, 0, 0), the inverse kinematic equations (3) give eight solutions = (\u00b1L, \u00b1L, \u00b1L), but only one of them is feasible, as shown in Fig. 3. To analyse in details the influence of the joint constraints impact, let us start from separate a study of the inequalities (5) and then summarise results for all possible combinations of the three configuration indices. If sx = 1, then consideration of two cases, px > 0 and px \u2264 0, yields the following workspace set satisfying the constraint \u03c1x > 0 W+x L = {p \u2208 CL|px > 0} \u222a { p \u2208 CL|px \u2264 0; p2 x + p2 y + p2 z < L2 } , (6) which consists of two fractions (1/2 of the cylinder intersection denoted CL and 1/2 of the sphere whose geometric center is (0, 0, 0) and radius is L)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003738_med.2016.7536036-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003738_med.2016.7536036-Figure2-1.png",
        "caption": "Fig. 2. Reference frames and rotor numbering",
        "texts": [
            " In this section, a nonlinear model of the quadrotor dynamics is presented, which is used in section III for the derivation of the linearizing state feedback. Reference frame I is fixed on the ground and assumed to be inertial. It defines a coordinate system with basis vectors in, ie, id pointing north, east, and down. Body frame B is rigidly attached to the quadrotor in its center of mass, defining a coordinate system with basis vectors bx, by , bz pointing towards the front, starboard (right), and bottom of the quadrotor (cf. Fig. 2). Let p denote the position of the quadrotor in reference frame I with north-, east-, down-coordinates pn, pe, pd: p = pnin + peie + pdid (1) The velocity in reference frame I is then represented by v = Idp dt = p\u0307nin + p\u0307eie + p\u0307did . (2) The orientation of the quadrotor is represented by the unit quaternion qI B , which aligns frame B with frame I by rotating frame B by \u03b6 radians about unit vector e [7]: qI B = [q1 q2 q3 q4] T = [ cos \u03b6 2 e sin \u03b6 2 ] (3) The direction cosine matrix CI B , corresponding to qI B , for transforming vector coordinates from frame B to I is [7]: CI B =\u23a1 \u23a3 q21 + q22 \u2212 q23 \u2212 q24 2(q2q3 \u2212 q1q4) 2(q1q3 + q2q4) 2(q2q3 + q1q4) q21 \u2212 q22 + q23 \u2212 q24 2(q3q4 \u2212 q1q2) 2(q2q4 \u2212 q1q3) 2(q1q2 + q3q4) q21 \u2212 q22 \u2212 q23 + q24 \u23a4 \u23a6 (4) The notation clk is introduced to denote the element in row l and column k of CI B ",
            " (8) Each of the four rotors excerts a thrust force Ftk, approximately proportional to the rotor speed squared, and an aerodynamic drag torque about the spinning axis of the rotor Tdk on the quadrotor body. They sum up to a total thrust force Fz pointing in the body fixed upward direction Fz = 4\u2211 k=1 Ftk (9) and torques about the three body axes t = (Ft3 \u2212 Ft4) lbx + (Ft1 \u2212 Ft2) lby +(\u2212Td1 \u2212 Td2 + Td3 + Td4)bz , (10) where l is the distance from the rotor axis to the center of the quadrotor. For motor numbering cf. Fig. 2. Motor dynamics and gyroscopic effects are neglected. A specific total thrust input u1 is introduced as u1 = 1 m Fz , (11) where m is the total mass. Considering the rotor forces acting on the system and gravity pointing down in the ei3 direction, Newton\u2019s equations of motion are formulated as v\u0307 = gid \u2212 u1bz , (12) where v\u0307 = Idv dt and g is the gravitational acceleration. The change of the position p\u0307 = Idp dt is simply p\u0307 = v . (13) With torques t acting on the body, Euler\u2019s rotation equa- tions yield \u03c9\u0307IB = J\u22121 (t\u2212 \u03c9IB \u00d7 (J\u03c9IB)) (14) with \u03c9\u0307IB = Id\u03c9IB dt "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000834_978-94-017-0657-5-Figure130-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000834_978-94-017-0657-5-Figure130-1.png",
        "caption": "Figure 130 Looking for the best u-workspace center locus of 2-DOF Orthoglide",
        "texts": [],
        "surrounding_texts": [
            "To find the best u-workspace center locus, we shift the u-workspace perpendicularly to (L1) and along (L1) (Fig. 13) and the VAF are computed for each configuration. In each case, VAF extrema are located along the sides PiPj: they start from 1 at point S, then they vary until they reach prescribed boundaries on VAF (Fig. 15, section 4.2). Computing the VAF (which analytical expressions Ai (XP,Yp) have been obtained with Maple) along the 4 sides of the square takes only 5 sec. with a Pentium II class PC."
        ]
    },
    {
        "image_filename": "designv10_10_0001937_1.2898730-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001937_1.2898730-Figure13-1.png",
        "caption": "Fig. 13 Biped model\u2019s ascent of an inclined slope: system is rotated by , the biped ascent is equiv \u201emg sin \u2026 that pulls the biped backward.",
        "texts": [],
        "surrounding_texts": [
            "The proposed ZMP-based formulation for motion planning associated with bipedal locomotion satisfies the unilaterality condition with unknown GRFs as well as DE conditions without the necessity of quantifying actuating joint torques. The formulation is highly efficient in that it avoids the time-consuming expense associated with having to solve equations of motion over the time frame of interest. The method poses motion planning associated with walking as an optimization problem. In the sample problems presented, all of the constraints were aggregated into a single equality constraint. This treatment of constraints led to a rapid convergence to feasible and optimal solutions in all three of the examples presented. Although the proposed formulation does not require solving for joint actuating torques, it must be employed with caution. Since ZMP-based DE conditions take care of only two in-plane angular components of resultant forces see Eq. 5 , additional constraints for equilibrium are required for completeness: one for out-ofplane components i.e., yawing moment and another for each of the linear components i.e., two in-plane and one normal forces . In the current formulation, therefore, the magnitude of yawing moment by inertia and gravity forces is assumed to vanish since the yawing moment produced by the frictional components of the ground-reaction forces has a very small moment arm less than the foot-length dimensions about the COP. With yawing moments associated with the very small GRFs, the yawing moments due to inertia and gravity forces should equilibrate themselves. Also, a physical constraint that restricts the magnitude of friction forces to be only a fraction of the normal ground reaction force should be properly applied to three linear components of inertial forces Eq. 36 . Since the ZMP-based formulation explained and demonstrated \u2026 xyz axes are attached to the slope. \u201eb\u2026 When the t to normal walking with fraction of gravity force \u201ea alen herein does not involve joint actuating torques, it is hard to im- JUNE 2008, Vol. 130 / 031002-13 erms of Use: http://www.asme.org/about-asme/terms-of-use p t b e d s s i s p c c m o s o i i i T p a t e g T 1 s s q c h w m t h t h b d t s w f h s h d a m w m n f s f n A D 0 Downloaded Fr ose any constraints or performance measures associated with acuating torques. Nevertheless, even in its current form, the ZMPased formulation can still be an extremely valuable tool for xploring changes in walking parameters i.e., step length, caence, stage durations, foot placement, etc. that keep walking tability. When inverse dynamics is used for motion planning, the moothness in time of the assumed displacement field acts as an mplicit constraint that could perhaps conflict with other contraints and may make the solution domain infeasible. In the proosed methods, the number of control points for cubic B-spline urve approximation is the control parameter for the smoothness onstraint. However, there is no general way of knowing the minium number of control points necessary to secure the feasibility f the problem. Though more control points can increase the moothness of the displacement field and can secure the feasibility f the problem, the computational cost significantly increases with t. When more artificial constraints i.e., to specify travel time, nitial posture or PCOM trajectory come into consideration, it ncreases the potential conflict with the smoothness constraint. hus, by using a minimum number of artificial constraints, the roposed optimization formulation can secure the feasible domain nd minimize the computational cost with a small number of conrol points. The motion planning formulation was exercised on three differnt problems involving walking on a level plane, walking on a ently sloped plane, and walking on a more steeply inclined plane. hese problems were solved in between 840 CPU s and 380 CPU s on a current generation personal computer. As the lope became steeper, more iterations were required to obtain feaible motion-planning solutions; consequently, the CPU time reuired also increased. The cost or objection function values assoiated with walking up an inclined plane were also considerably igher than those for walking on a level plane. These results ould be consistent with the observation that as the feasible doain of a motion planning problem becomes more restricted as is he case for walking up a sloped plane , one can anticipate a igher optimal cost value and more optimization iterations to find he optimum. The authors believe that while the computational times reported ere for the motion-planning computations are quite small i.e., etween 14 CPU min and 22 CPU min , the times can still be reuced by approximately an order of magnitude by keeping both he optimizer and the motion-planning software in the computer\u2019s hared random access memory RAM simultaneously. This ould significantly reduce the time required for information transer functional values and their gradients between the processes. There are a multitude of potential applications for modeling uman walking as described herein. From a biomechanics perpective, a first goal is to better understand normal locomotion in ealthy individuals and to validate the framework\u2019s ability to preict the gaits that constitute normal locomotion. If this can be chieved with a high degree of confidence, then such models ight then be turned to study and address locomotion in humans ith gait pathologies stemming from a wide range of causal echanisms. While the model has been exercised here to explore ormal walking motions, it is foreseen that the model might, with urther development, be very useful in exploring how limb or keletal asymmetries affect or create abnormal locomotion. The ormulation might further be used to devise intervention techiques that would help to restore normal locomotion to patients. cknowledgment This research is funded by the U.S. Army TACOM project: igital Humans and Virtual Reality for Future Combat Systems FCS Contract No. DAAE07-03-Q-BAA1 . 31002-14 / Vol. 130, JUNE 2008 om: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 T"
        ]
    },
    {
        "image_filename": "designv10_10_0001989_s11012-009-9251-x-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001989_s11012-009-9251-x-Figure10-1.png",
        "caption": "Fig. 10 Dynamic tooth force depending on the resonance ratio N",
        "texts": [
            " ISO 6336-1 also defines an intermediate range between resonance range and supercritical range with a linear decrease of Kv\u2212B between N = 1.15 and N = 1.50. Furthermore Fig. 9 shows that the approximation of the dynamic factor in ISO 6336-1 takes into consideration no further resonance except from the main resonance. This is valid in terms of excitation and dynamic response. A consideration of further resonances depending on running speed can be important, especially for operating conditions in the subcritical range. Figure 10 demonstrates the effect of high-order harmonics on the dynamic tooth force depending on the resonance ratio N for a one-mass-oscillator (left-hand side). For example at a resonance ratio of N = 0.2 the fifth harmonic of the tooth contact shows a super elevation in the dynamic tooth force by exciting the system\u2019s natural frequency. Figure 10 also points out, that in the shown example the relative amplification ratio of the dynamic tooth force at different running speeds (=different resonance ratio N ) is equal for different harmonics (1st to 5th) (right-hand side). The absolute value of the dynamic tooth force differs because of the absolute excitation amplitudes of the different harmonics. To sum up, a precise calculation of dynamic tooth force for a real gearing deserves sophisticated models for both, excitation and dynamic response"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002740_iet-cta.2010.0232-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002740_iet-cta.2010.0232-Figure7-1.png",
        "caption": "Fig. 7 Photo of the apparatus",
        "texts": [
            " In this section, an example on the temperature control of an aluminium plate with Peltier element actuator is considered by using the proposed design scheme. Fig. 6 shows the apparatus about the temperature control process of an aluminium plate with Peltier element actuator. The apparatus has roughly two parts connected by LAN: computer PC1 as a controller and the controlled process which is composed of a Peltier-actuated process for cooling the aluminium plate and the serial communication (RS232C) for communication interface between computer PC2 and the micro-computer. The photo of the apparatus is shown in Fig. 7. Peltier device and sensor are installed on both sides of the aluminium plate, respectively. On the heat radiation side of the Peltier device, a heat sink is installed to prevent it from having heat too much. Thus, the model of the aluminium plate can be drawn as Fig. 8, where S3 is a Peltier element, and on the opposite side of it, there exists is a sensor for measuring temperature of the aluminium plate. The parameters of the model are given in Table 1. According to Fourier\u2019s law concerning thermal conduction, Newton\u2019s law of cooling, equation on the variation of heat capacities, Electrothermal amount by Peltier effect, thermal conduction by temperature gradient and Joule exothermic heat by current, a differential equation with regard to heat IET Control Theory Appl"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002596_we.447-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002596_we.447-Figure6-1.png",
        "caption": "Figure 6. RomaxWind model of GRC gearbox.",
        "texts": [
            " Romax Technology is involved in the program and the following sections discuss the application of various simulation technologies and fi ndings related to the program. For more details on the GRC, see Oyague et al.8 The gearbox has been modeled in the RomaxWind software,9 (Romax Technology Ltd, Nottingham, Nottinghamshire, UK) a virtual product development and simulation environment for the design and analysis of wind turbine gearboxes, bearings and drive trains. A model of the GRC gearbox is shown in Figure 6, with some salient features labeled. The gearbox is a single-stage planetary with two parallel helical gear stages\u2014a typical confi guration for medium-sized gearboxes in wind turbines. The gearbox is a speed increaser, with approximately 1:81 ratio and is designed for high-speed shaft speeds of 1200 and 1800 rpm depending on the running confi guration of the two speed (4/6 pole) generator. Some key features of the model include beam fi nite element representation of shafts, solid fi nite element representation of gearbox housing, gear blanks, planet carrier and torque arms and 6 degree-of-freedom spring connections for (elastomeric) trunnion mounts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.9-1.png",
        "caption": "FIGURE 1.9 Simple car model with side force characteristics for front and rear (driven) axle.",
        "texts": [
            "4 will be treated first after which the simple model with two degrees of freedom is considered and analyzed. This analysis comprises the steady-state response to steering input and the stability of the resulting motion. Also, the frequency response to steering fluctuations and external disturbances will be discussed, first for the linear vehicle model and subsequently for the nonlinearmodelwhere large lateral accelerations and disturbances are introduced. The simple model to be employed in the analysis is presented in Figure 1.9. The track width has been neglected with respect to the radius of the cornering motion which allows the use of a two-wheel vehicle model. The steer and slip angles will be restricted to relatively small values. Then, the variation of the geometry may be regarded to remain linear, that is, cos az 1 and sin aza and similarly for the steer angle d. Moreover, the driving force required to keep the speed constant is assumed to remain small with respect to the lateral tire force. Considering combined slip curves like those shown in Figure 1.2 (right), we may draw the conclusion that the influence of Fx on Fy may be neglected in that case. In principle, a model as shown in Figure 1.9 lacks body roll and load transfer. Therefore, the theory is actually limited to cases where the roll moment remains small, that is, at low friction between tire and road or a low center of gravity relative to the trackwidth. This restrictionmay be overcome by using the effective axle characteristics in which the effects of body roll and load transfer have been included while still adhering to the simple (rigid) two-wheel vehicle model. As mentioned before, this is only permissible when the frequency of the imposed steer angle variations remains small with respect to the roll natural frequency. Similarly, as demonstrated in the preceding section, effects of other factors like compliance in the steering system and suspension mounts may be accounted for. The speed of travel is considered to be constant. However, the theory may approximately hold also for quasi-steady-state situations for instance at moderate braking or driving. The influence of the fore-and-aft force Fx on the tire or axle cornering force vs slip angle characteristic (Fy, a) may then be regarded (cf. Figure 1.9). The forces Fy1 and Fx1 and the moment Mz1 are defined to act upon the single front wheel and similarly we define Fy2 etc. for the rear wheel. In this section, the differential equations for the three degree of freedom vehicle model of Figure 1.4 will be derived. In first instance, the fore-and-aft motionwill also be left free to vary. The resulting set of equations of motion may be of interest for the reader to further study the vehicle\u2019s dynamic response at somewhat higher frequencies where the roll dynamics of the vehicle body may become of importance, cf. App. 2. From these equations, the equations for the simple two-degree-of-freedom model of Figure 1.9 used in the subsequent section can be easily assessed. In Subsection 1.3.6, the equations for the car with trailer will be established. The possible instability of the motion will be studied. We will employ Lagrange\u2019s equations to derive the equations of motion. For a system with n degrees of freedom n (generalized) coordinates, qi are selected which are sufficient to completely describe the motion while possible kinematic constraints remain satisfied. The moving system possesses kinetic energy T and potential energy U",
            "41) but with a much smaller relaxation length approximately equal to half the contact length of the tire. For more details, we refer to Chapter 9 that is dedicated to short wavelength force and moment response. From Eqns (1.34b and c), the reduced set of equations for the two-degree-offreedom model can be derived immediately. The roll angle 4 and its derivative are set equal to zero and, furthermore, we will assume the forward speed u (zV) to remain constant and neglect the influence of the lateral component of the longitudinal forces Fxi. The equations of motion of the simple model of Figure 1.9 for v and r now read m\u00f0 _v\u00fe ur\u00de \u00bc Fy1 \u00fe Fy2 (1.42a) I _r \u00bc aFy1 bFy2 (1.42b) with v denoting the lateral velocity of the center of gravity and r the yaw velocity. The symbol m stands for the vehicle mass and I (\u00bc Iz) denotes the moment of inertia about the vertical axis through the center of gravity. For the matter of simplicity, the rearward shifts of the points of application of the forces Fy1 and Fy2 over a length equal to the pneumatic trail t1 and t2 respectively (that is the aligning torques) have been disregarded",
            " Obviously, since za1,2 is usually positive, negative longitudinal accelerations ax, corresponding to braking, will result in a decrease of the degree of understeer. To illustrate the magnitude of the effect, we use the parameter values given in Table 1.1 (p. 34) and add the c.g. height h\u00bc 0.6 m and the cornering stiffness versus load gradients zai \u00bc 0.5Cio/Fzio. The resulting factor appears to take the value l \u00bc 0.052. This constitutes an increase of h equal to 0.052ax/g. Apparently, the effect of ax on the understeer gradient is considerable when regarding the original value ho \u00bc 0.0174. As illustrated by Figure 1.9, the peak side force will be diminished if a longitudinal driving or braking force is transmitted by the tire. This will have an impact on the resulting handling diagram in the higher range of lateral acceleration. The resulting situation may be represented by the second and third diagrams of Figure 1.18 corresponding to braking (or driving) at the front or rear respectively. The problem becomes considerably more complex when we realize that at the front wheels, the components of the longitudinal forces perpendicular to the x-axis of the vehicle are to be taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-20-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-20-1.png",
        "caption": "FIGURE 5-20 Inertia forces acting on engine parts.",
        "texts": [
            " However, this problem can be practically solved by taking the ring radius R to be large enough so that 11m can be made small enough to be negligible. Then, considering the inertia force of the connecting rod, only the inertia forces of the reciprocating mass mel and the rotating mass me2 are taken into account, neglecting 11m. For the inertia couples about the center of gravity, the inertia couple due to !1I must be considered in addition to the couples due to mel and me2. 100 ENGINE DESIGN Inertia Force of Single-Cylinder Engines Taking the origin 0 at the center of the crankshaft and x and y coordinates as shown in figure 5-20(a), the mass mA, consisting of the masses mp and mel of the piston and the upper part of the connecting rod, respectively, has a reciprocating motion producing the inertia force XA in the direction of Ox. Thus (10) The inertia force due to the mass mc2 of the lower part of the connecting rod can be expressed by the components Xr and Yr of the centrifugal force as (11) CRANK EFFORT 101 In figure 5-20(b) the centers of gravity of the masses m,p, m\"n and m,,, of the crankpin, crankarm, and balancing weight respectively are located at the dis tances r, r,n and r\" from the center of the crankshaft. Denoting the inertia forces due to crankpin, crankarm, and balancing weight by F'il' F\"\" and F,,,, then F,/, = m(prw2, F\", = 2m\",raw2, and F(\" = 2m,,7/,w2. Thus the total inertia force F\" of the crankshaft can be expressed in the form where m\" = (m,/,r + 2m\",1'a - 2m,,,l'b)/r is called the equivalent mass of the crankshaft",
            " The problem of piston side thrust can be prac tically solved from design and structural considerations assuming the cylinder is a rigid body. The flexural and torsional vibrations take a complex form, combining natural and forced vibrations. However, the crankshaft of the single-cylinder engine is short, which provides adequate rigidity, and thus the vibration is usually small and negligible. Thus the analysis is made here on the unbalance caused by the centrifugal force and the inertia force. The centrifugal force caused by the rotating mass mB (fig. 5-20) consisting of the equivalent mass me of the crankshaft and the mass mc2 of the lower part of the connecting rod can be balanced by placing a balance weight haying mass mcb at the opposite side of the crankpin. Denoting rb as the distance between the center of the crankshaft and the center of gravity, Gb of the balance weight, the mass mcb, and the distance rb can be determined to satisfy the following relation (22) The inertia force caused by the reciprocating part IS expressed from equation 10 as X"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001376_icca.2005.1528213-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001376_icca.2005.1528213-Figure1-1.png",
        "caption": "Fig. 1. Basic helicopter.",
        "texts": [
            " The outline of this paper is as follows: In the next section, we present the design of a simple UAV helicopter. The components of the simple avionic system will be introduced in Section III. The assembling of the UAV helicopter will be given in Section IV. Finally, we draw some concluding remarks in Section V. In this section, we introduce the detailed components of the UAV helicopter, which include the basic helicopter, the simple avionic system and the supporting system. A. Basic Helicopter An advanced toy radio-controlled (RC) helicopter (Raptor 90), shown in Figure 1, is chosen as the basic aircraft. Such a choice is appropriate for our need as it can be easily upgraded to be a UAV helicopter with a complete auto-pilot system, sensors and a necessary communication modem, which can be utilized for implementation of ight control laws. More importantly, it is cheaper for us to upgrade the RC helicopter than buying a full set of a commercial UAV helicopter system. The Raptor 90 RC helicopter is a high quality toy helicopter in the hobby industry, which is operated manually with a remote control",
            " At rst, the original landing gear of the Raptor 90 helicopter will be revised, and then the designed avionic system will be packed appropriately and installed under the fuselage of the basic helicopter. The assembled UAV helicopter with the necessary components is shown in Figure 8. The original landing gear of the basic helicopter is plastic, which is too weak to undertake amount of bumping momentum when the UAV helicopter is landing on the ground in the automatic or manual mode. There is no enough room in the fuselage of the basic helicopter to install the designed avionic system (see Figure 1). Thus, we have designed and changed the material of the landing gear to aluminum alloy and make a larger room under the fuselage of the basic helicopter for the avionic system. The avionic system is packed in a carbon- ber box. The layout inside the box is shown in Figure 9, which is to set the IMU as close as possible to the center of gravity of the basic helicopter with the avionic system and the avonic system well-balanced. The layout is determined by major considerations of distribution of the weights of the basic helicopter and the avionic system in the horizontal plane as follows, 1) To measure the projected point of the center of gravity of the basic helicopter on the horizontal bottom plane of the carbon- ber box"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001493_j.mechmachtheory.2004.04.006-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001493_j.mechmachtheory.2004.04.006-Figure2-1.png",
        "caption": "Fig. 2. (a) Common tangent plane and polar coordinates. (b) Measurements on surface separation.",
        "texts": [
            "1016/j.mechmachtheory.2004.04.006 Nomenclature ai; bi tool setting of rack cutter P i \u00f0i \u00bc F;P\u00de li variable parameter which determines the location on rack cutter \u00f0i \u00bc F;P\u00de ri radius of pitch circle of gear i \u00f0i \u00bc 1; 2\u00de C0 operational center distance (Fig. 1) DC variation of center distance (Fig. 1) Ri nominal radius of the face mill-cutter \u00f0i \u00bc F;P\u00de Ti number of teeth of gear i \u00f0i \u00bc 1; 2\u00de X \u00f0i\u00de T ; Y \u00f0i\u00de T ;Z\u00f0i\u00de T coordinates of gear tooth surface i \u00f0i \u00bc 1; 2\u00de represented in coordinate system ST (Fig. 2) n\u00f0i\u00dec unit normal vector of surface P i \u00f0i \u00bc F;P\u00de represented in coordinate system Sc R\u00f0i\u00de c position vector of surface P i \u00f0i \u00bc F;P\u00de represented in coordinate system Sc \u00f0r; h\u00de auxiliary polar coordinate system represented on contact tooth tangent plane (Fig. 2) Si\u00f0Xi; Yi; Zi\u00de coordinate system i \u00f0i \u00bc 1; 2; v; h; f;T\u00de with three orthogonal axes Xi, Yi, and Zi Dch horizontal axial misalignment (in degrees, Fig. 1) Dcv vertical axial misalignment (in degrees, Fig. 1) hi variable parameter which determines the location on rack cutter \u00f0i \u00bc F;P\u00de /i rotation angle of gear i \u00f0i \u00bc 1; 2\u00de when gear i is generated by rack cutter /0 i rotation angle of gear i \u00f0i \u00bc 1; 2\u00de when two gears mesh with each other (Fig. 1) D/0 2\u00f0/ 0 1\u00de transmission errors (in arc-second) w\u00f0i\u00de n normal pressure angle of rack cutter P i \u00f0i \u00bc F;P\u00de Subscripts F, P rack cutter surface to generate tooth surfaces of pinion and gear 1, 2 tooth surfaces of pinion and gear located near the middle region of the tooth flank even when the gear set is meshed with axial misalignments",
            " The transmission errors of the curvilinear gear pair can be calculated by using the following equation: D/0 2\u00f0/ 0 1\u00de \u00bc /0 2\u00f0/ 0 1\u00de T1 T2 /0 1; \u00f013\u00de where T1 and T2 denote the tooth numbers of pinion and gear, respectively. /0 2\u00f0/ 0 1\u00de, which represents the actual rotational angle of the gear pair meshing under different assembly conditions, is solved by numerical method. D/0 2\u00f0/ 0 1\u00de expresses the transmission error of the curvilinear gear pair under the given assembly errors. When tooth surfaces are meshed with each other, their instantaneous contact point is spread over an elliptical area owing to elastic deformation. Fig. 2(a) shows that two mating surfaces P 1 and P 2 are tangential to each other at the instantaneous contact point OT, where n represents the common unit normal vector at contact point OT, which can be determined by the TCA computer simulation program. Plane T denotes the common tangent plane of the two mating surfaces. The origin of coordinate system ST\u00f0XT; YT;ZT\u00de and the instantaneous contact point OT are coincident. The direction of axis ZT is defined to coincide with the common unit normal vector n. Thus, the plane XT\u2013YT is the common tangent plane. In this study, the contact ellipses of the gear pair are obtained by using the surface separation topology method. To calculate the separation distance of two mating tooth surfaces, surface coordinates of the mating curvilinear-tooth gear and pinion must be transformed to the same coordinate system ST\u00f0XT; YT;ZT\u00de. Fig. 2(b) shows the separation distances between the surfacesP 1 and P 2 at point P of the tangent plane T . The separation distance of two mating surfaces can be defined by d1 \u00fe d2, where d1 \u00fe d2 is equal to jZ\u00f01\u00de T Z\u00f02\u00de T j, measured from any point P on the tangent plane T along its perpendicular direction. Z\u00f01\u00de T and Z\u00f02\u00de T represent the coordinates of the ZT component of points P1 and P2, respectively. The equal distance-separation line for two mating surfaces, which is found by defining an auxiliary polar coordinate system \u00f0r; h\u00de, can be represented by the following system of nonlinear equations: X \u00f01\u00de T \u00bc X \u00f02\u00de T ; \u00f014\u00de Y \u00f01\u00de T \u00bc Y \u00f02\u00de T \u00f015\u00de tan\u00f0h\u00de \u00bc Y \u00f01\u00de T X \u00f01\u00de T \u00f016\u00de and jZ\u00f01\u00de T Z\u00f02\u00de T j \u00bc 0:00632 mm; \u00f017\u00de where X \u00f01\u00de T , Y \u00f01\u00de T , X \u00f02\u00de T and Y \u00f02\u00de T are coordinates of points P1 and P2 on the tangent plane XT\u2013YT, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-6-1.png",
        "caption": "Figure 11-6 is a free-body diagram of a four-wheel-drive tractor. The only difference from the free-body diagram of the rear-wheel-driven tractor of figure 11-3 is the addition of a gross tractive f?rce F f acting on the front wheels, which are turning at a rotational speed <l>wf.",
        "texts": [],
        "surrounding_texts": [
            "STATIC EQL:ILIBRIL'M Al\\'ALYSIS-DRA WBAR PL'LL 281\ntire and soil parameters. As discussed in the section Traction Prediction from Dimensional Analysis in chapter 10, the gross tractive coefficient iJ-g versus slippage S relation has the following functional form\n(22)\nwhere the dimensionless parameter en incorporates tire and soil parameters as well as the vertical load on the drive wheel. The exponential nature of equation 22 indicates that the maximum value of iJ-g obtainable is iJ-max. For a given drawbar force P, equations 18 and 19 may be used to calculate RI and R, from which the rolling resistance forces TFj and TF, may then be determined. Equation 20 then gives the gross tractive force F, required. Di viding F, by R, determines the required gross tractive coefficient iJ-g. If iJ-g is greater than iJ-ll1ax, it is obvious that the required tractive coefficient cannot be obtained under the given operating conditions. If the required tractive coefficient is less than but close to the value of iJ-ll1ax and if sufficient engine power is available, the given drawbar force may be developed, but the slippage of the drive wheels may be so great that operation under such conditions would be impractical.\nPower Assuming that sufficient traction is available. a check should be made to determine if sufficient engine torque is available for developing the given drawbar force. Starting with the required gross tractive force F\" the ~ngi~.e torque T r\u2022 necessary may be determined from equation 14, where 8 = <D\" = o.\n(23)\nIf Te is less than the maximum torque that can be produced by the engine, the engine has sufficient power for the tractor to pull the given load.\nOperating Conditions To com plete the analysis of the tractor operating conditions for a given draw bar pull, the engine> torque-speed relation may be used to estimate the steady state engine speed <Dr. at which torque Te may be produced. The resulting rear wheel speed, <Du., is then\n(24)\nSince the required gross tractive coefficient iJ-g has already been deter mined, the tractive coefficient (iJ-g)-slippage (S) relation may be used to find the slippage of the drive wheels. For example, using equation 22,\ne - O.:IC\"S 1 - iJ-gl iJ-max\nS = - [In (l - iJ-g1iJ-Il1\"J]/(0.3c,,) (25)",
            "282 MECHANICS OF THE TRACTOR CHASSIS\nGiven the slippage of the drive wheels, equation 13 may be used to calculate the forward velocity of the drive wheels, xw , which is equal to the forward velocity of the tractor.\nEquations 17 and 19 are still applicable to computing forces Rf and Rn which again can be used to compute TFf and TFr- However, equation 20 becomes\nFT + Ff = W, sin ~ + TFf + TFT + P cos a (27)\nEquation 27 has two unknowns, FT and Ff , and the problem is to determine how the two axles divide the total tractive force requirement.\nBy applying equation 22 to both wheels, equation 27 can be written\nj..Lrnax (1 - e - O.3Cn\"sT) RT + j..Lrnax (1 - e - o.3cnf sf) R f = W, sin ~ + TFf + TFT + P cos a (28)\nwhere the subscripts rand f added to the variables en and S denote rear and front, respectively. Equation 28 is now in terms of the unknowns ST and Sf.",
            "LONGITL'DIKAL STABILITY 283\nApplying equation 26 with the constraint that the forward velocities of the front and rear axle centers are equal results in\nXw = r;t>wf(l - Sr) = rr~w>(1 - Sr)\nso that . .\nSf = 1 [( rr<Pu,,)! ( r t<Pu1)] (I - S r)\nLetting NI <PeI<Pu1 and N, = <PeI<Pwn (29)\nEquation 29 can now be used in equation 28 to provide a relationship that can be solved iteratively for Sr. With Sr determined, S r and, hence, F, and Ff can be calculated. The engine torque required becomes\nT = .!. (Frrr + Frrf) e T] N r Nr\nThe engine torque-speed relation can ag~in be us~d to determine the engine speed <p\", and, hence, the wheel speeds <Pwt and <Pur and the forward speed\nEquation 28 indicates that for the same drawbar loading, powering the front wheels of a rear-wheel-driven tractor will reduce the slippage of the rear wheels, resulting in the tractor's ability to pull the given loading at a higher forward travel speed, thus increasing its productivity. Since the rear wheels of a four-wheel-drive tractor usually follow in the tracks left by the front wheels, the rear wheels will usually encounter higher-strength soil. The higher-strength soil is reflected in equation 28 by an increase in the wheel numeric enn which also has the effect of lowering the required rear drive wheel slippage Sr.\nLongitudinal Stability\nThere are several situations in which a tractor may be in danger of rearward overturning. The equations associated with the free-body diagrams of figure 11-1 are particularly useful for the analysis of these situations. In such situ ations in which the front wheels have left the ground, forces Rf and TFf will be zero. With use of D'Alembert's principle, the tractor chassis may be con sidered to be in static equilibrium, allowing moments to be summed about any point. D'Alembert's principle is applied by adding two fictitious forces, often called inertial forces, acting at the chassis center of gravity: m,xc in the - X direction and mJ., in the - Z direction. In addition, a fictitious clockwise moment In)~ is applied to the chassis. Now, with the tractor in the assumed"
        ]
    },
    {
        "image_filename": "designv10_10_0001458_cdc.2003.1271714-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001458_cdc.2003.1271714-Figure1-1.png",
        "caption": "Fig. 1. Finite time stability",
        "texts": [],
        "surrounding_texts": [
            "I. INTRODUCTION\nSince the end of the1 gth and the beginning of the 20th century, various concepts dedicated to the qualitative behavior of the solutions for dynamical systems were introduced (for example the seminal definitions and results from A.M. Lyapunov [14]). But rapidly engineers had to face some more precise time specifications of the behavior of the state variables (or outputs) for real process. This is the reason why Kamenkov [12] and Chetaev [4] probably initiated the analysis of so-called stability over a finite time interval: the attractivity of the motions to the desired target (in general an equilibrium point) take place in a finite time. For example, some finite time stabilizing control design relies upon sliding mode theory (see [20]) and an other one upon optimal control theory (see [18]). In both cases the controller leads to some state discontinuous feedback control laws. Over the years many works were dedicated to this concept, the obtention of some sufficient conditions and the application to the construction of finite-time stabilization control (see for example [l], [2], [3], [6], [5], [ll], [9], [lo], [15], [16], [17]). The main.idea relies on infinite eigenvalue assignation for the closed loop system at the origin. Let us mention the following illustrative example\ni = - IZlasgn(Z),Z E R, . (1)\nfor which the solutions are (a E 10, l[):\n- with s ( t7 20) = sgn(z0) ( (xo~~-' - t ( l - a ) ) and they reach the origin in finite time. In fact, there exists a function called settZing time that performs the time for a solution to reach the equilibrium. This function always depends on the initial condition of a solution. But, for non autonomous systems, it may also depend on time. Lastly, notice from this example, that in order to obtain finite time stability, the right hand side of the ordinary differential equation can not be Lipschitz.\nThe paper is organized as follows. After introducing some notations and defining the notion of finite time stability in section 11, we give necessary and sufficient conditions for finite time stability of autonomous and scalar systems (section 111). Let us mention that this preliminary result appeared without proof in [5] . Here we provide a proof which will be very useful for the given extensions. Then in section IV, we give a generalization for non autonomous systems of any dimension. The idea is to use a Lyapunov function. For this we introduce the notion of upper bounded Lyapunov pair (UB-pair) to obtain sufficient conditions for finite time stability (see subsection IV-A) and the notion of lower bounded Lyapunov pair (LB-pair) to obtain necessary conditions for finite time stability (see subsection IV-B). In fact, these conditions are more general and tractable than conditions given by Bhat and Bemstein in [2]: their sufficient condition is a particular case of our, and their necessary and sufficient conditions depend on the continuity at zero of the settling time function. But, to the best knowledge of the authors, there do not exist any result to check this property without evaluating this function in an explicit form this is without computing the solution.\n0-7803-7924-1/03/$17.00 02003 IEEE 3641",
            "Lastly, using a general results from [SI, the results of the previous sections are given for periodic systems for the property of uniform finite time stability (see section V).\n11. NOTATION Through the paper I = [0, +CO[ and 0 for a > 0, the following function will be used\n0 U denotes a neighborhood of the origin in Rn, a Y denotes a neighborhood of the origin in U.\nPdY) = lYla SW(Y).\nConsider the system:\nx = f ( t , z ) , t E I , z E U (3)\nwhere f : I x U + Rn, then z(t,to,zo) denotes a solution starting from ( t o , 50) . As usually, a continuous function o : [0, U] + [0, +CO[ belongs to class K if it is strictly increasing and ~ ( 0 ) = 0. Moreover, a continuously differentiable function V : I x V + R+ where V is a neighborhood of the origin in U such that: L1. V is positive definite,\nis a Lyupunovfinction for (3). A continuous function U : I x U + R is decrescent if there exists a function $ E K: such that:\nIdt, dl L Q (Ilvll) 7 v, Y) E I x v. The definition of asymptotic stability is well known. In this case, the solutions of the system (3) tends to the origin (but without information about the time transient).\nLet the origin be an equilibrium point of the system (3), the origin is finite time stable for the system (3) if:\n1) the origin is stable for the system (3), 2) Vto E I, 3 6 ( t o ) > 0, if llzoll < 6 ( t o ) then:\na) z(t , t o , zo ) is defined for t 2 t o , b) there exists 0 5 T(t0,zo) < +CO such that\nz(t,to:zo) = 0 for all t 2 t o + T(t0,zo). The notion of finite time stability is illustrated by\nfigure I .\n0 V t 2 t o + T(t0, ZO)}, we say that z(t, t o , ZO) tends to the origin with the settling rime To(to,zo). When the system is asymptotically stable, the settling time may be infinite. In this definition, we see that the settling time depends on t o , but it is possible that it depends only on zo. So, we introduce the definition:\nLet To(t0, zo) = i q q t o , zo) 2 0 ; IlzP, t o , .o)ll =\nDefinition I : Let the origin be an equilibrium point of (3), The origin is un$ormlyjinite rime stable for the system (3) if:\n1) the origin is uniformly stable for system (3), 2) there exists 6 > 0, for all t o E I , if Ilzoll < 6\nthen: a) s(t, t o , 50) is defined for t 2 t o b) there exists 0 5 T(Q) < +CO such that\nLet TO(z0) = inf(T(z0) 2 0; d(z(t , to,zo),K) = 0, Vt 2 to -t T(zo)}, we say that z(t,to,zo) tends uniformly to the origin with the settling time To(z0).\n111. AUTONOMOUS SCALAR SYSTEMS\nz(t,to,zo) = 0 for all t 2 t o + T(z0).\nLet us recall the result given without proof in [5] for autonomous scalar systems of the form\nj . = f(z), z E R, (4)\nwhere f : U 4 R. In this particular case there exists a necessary and sufficient condition for uniform finite time stability:\nProposition I .- Let the origin be an equilibrium point of the system (4) where f is continuous. The origin is uniformly finite time stable if and only if there exists a neighborhood of the origin V such that:\n1 ) VY E v \\ (0) 7 Y f ( Y ) < 0 2) VCYE\u2019V\\{O}, &&<+CO.\nProofi (e) Because of l., V(y) = y2 is a Lyapunov function for the system thus the origin is uniformly asymptotically stable (see 1131). Let z(t , t o , ZO)",
            "be a solution of the system which tends to 0. From the asymptotic convergence of this solution to the origin\nV E > 0) 3T, < +WO; w 2 T,, (z(t , to: zo)l I E. ( 5 )\nLet us denote by TO (20) the settling time of the solution z(t,to,zo). Let us prove that To(z0) < +W. Let 0 5 t , < +CO, the time such that z(t,,to,zo) = a. Because of (3, for t , big enough: a belongs to V\\{O}. Moreover\nTO(XO) To(z0) = itu dt + d t = t , + 1- dt .\n1 Fact 1. implies that - is defined on V \\ (0). Using the change of variables, t I-+ z(t,to,zo): s,\" = f J2(x0) = d t < +CO and thus one concludes that To(z0) < +CO.\n(3) Suppose that the origin is uniformly finite time stable. Let z(t , t o , zg) be a solution which tends to the origin in finite time, and let 6 > 0 given in point 2. of definition 1 (finite time stability property). Suppose there exists yo E 1-6, S[ \\ (0) such that yof(y0) 2 0.\nIf yof(y0) = 0, then f(y0) = 0, and z ( t ) = yo is a solution of (4) which never tends to the origin. If yof(y0) > 0, then one may assume without lose the generality, that yo > 0 and f(y0) > 0 (otherwise one may modify the following proof). From the continuity of f and f(y0) > 0, one get f (y) > 0 for y in a neighborhood of yo. Thus, the solution z( t , t o , yo) is crescent in a neighborhood of to . Because of the continuity, this solution can not go beyond yo and thus can not tend to the origin.\nLet (Y E ] -b ,6 [ \\ (0) and consider the solution z(t,to,a). By assumption, there exists 0 5 T'(a) < +cc such that z( t , t o , a ) = 0 for all t 2 t o + To(a). Since - is defined on 3-6,6[ \\ (0). Using the change of variables t t) z(t, to , a ) one obtains 1 f\nU Remark I : The settling time for a solution z(t,to,zo) is T(zo) = J:o &. By the way we have shown the basic fact that V(y) = y2 is always a Lyapunov function for the asymptotic stable autonomous scalar systems.\nExunzple It Let a E ]0,1[ and consider the system (1). Obviously -ycp,(y) < 0 for y # 0, and let a E R then\nThe assumptions of the theorem 1 are satisfied. Thus the origin is uniformly finite time stable and the solutions z(t,to,zo) tends to 0 in To(z0) = -. These conclusions were directly obtain in the introduction by explicit computation of the solutions (2).\nIV. GENERAL CASE For the more general systems described by (3), a natural extension will invoke the use of Lyapunov functions to give sufficient and/or necessary conditions for finite time stability.\nA. Suflcieiit condition For this, let us introduce the notion of UB-pair. DeJnition 2: (V, r ) is said to be a upper bounded Lyupunovpuir for the system (3) (UB-pair) iff V : I x V -+ R+ is a Lyapunov function for the system (3) and T- is a positive definite function such that the following inequality holds:\nm y ) 5 - - T - ( W , Y ) ) , W , Y ) E I x v. Since the use of Lyapunov function will leads to some scalar differential inequality, the following theorem will give sufficient condition for finite time stability: the existence of UB-pair such that a bounded integral type condition holds:\nTheorem 2: Let the origin be an equilibrium point for the system (3) where f is continuous on I x U, if there exists a UB-pair (V,r) for the system (3) and E > 0 such that\nthen the origin is finite time stable. Moreover, if V is decrescent, then the origin is uniformly finite time stable. Since V is a Lyapunov function (thus satisfy' L1. and L2.), then the origin is asymptotically stable (2nd Lyapunov theorem). Let z(t , to, q) be a solution of (3) which tends to the origin with the settling time To(t0,zo) (0 5 To(t0,zo) 5 +W : from the attractivity of the origin). It remains to prove that To(t0,zo) < +W. Using the asymptotic stability definition, there exists t , < +CO such that z(to + ta,to,zO) = a, where a is chosen small enough to ensure that V(t0 + ta ,a) E [O,e] . Thus To(t0,zo) = Pro08"
        ]
    },
    {
        "image_filename": "designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure7-1.png",
        "caption": "Fig. 7. Particular point Pi on Sw E or Sg at the location given by R and t.",
        "texts": [
            " The equation of meshing [15], satisfied on the envelope to the family of Sw, is represented as follows: f w uw; \u03b8w;\u03d5w\u00f0 \u00de \u00bc \u2202 rEw ! \u2202uw \u2202 rEw ! \u2202\u03b8w 0 @ 1 A \u2202 rEw ! \u2202\u03d5w \u00bc 0: \u00f019\u00de rEw ! is the vector in which the last element of rEw ! is eliminated. Detailed expressions of (17) and (19) for the involute worm gear drive and the K-worm gear drive are provided in Appendix B. The vector rEw ! in Eq. (17) under the condition of Eq. (19) represents the surface Sw E . To calculate the separation between Sw E and Sg, a point P1 on Sw E and a point P2 on Sg are considered. As shown in Fig. 7, it is possible to assume that Pi (i = 1, 2) is located at (R, t), where R is the distance between Pi and the zg-axis and t is the distance between Pi and the xgyg plane. Here, P1 and P2 should satisfy the equations of meshing given by Eqs. (19) and (16), respectively. Thus, from the given values of R and t, the coordinates (xpi, ypi, zpi) of the point Pi in the worm gear coordinate system Cg can be determined from x2pi \u00fe y2pi \u00bc R2 \u00f020\u00de zpi \u00bc t \u00f021\u00de f i \u00bc 0; \u00f022\u00de where rEw ! uw; \u03b8w;\u03d5w\u00f0 \u00de \u00bc xp1 yp1 zp1 1 h iT \u00f023\u00de rg "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure4-1.png",
        "caption": "Fig. 4. Schematic representation of coordinate transformation from S s ( x s , y s , z s ) to S t ( x t , y t , z t ).",
        "texts": [
            " (3) , the centers of the circular arcs O f i and O f o are represented in coordinate system S s , as r ( O f p ) s = M sp r ( O f p ) p = \u23a1 \u23a2 \u23a3 R \u00b1 \u03c1 ( 1 \u2212sin \u03b1 cos \u03b1 ) 0 \u2212\u03c1 1 \u23a4 \u23a5 \u23a6 (7) Finally, the position vector of a point P on the blade edge generating profiles is determined in coordinate system S s by r (P) s (\u03bb) = \u23a1 \u23a2 \u23a3 R \u00b1 \u03c1 [( 1 \u2212sin \u03b1 cos \u03b1 ) \u2212 cos \u03bb ] 0 \u03c1( sin \u03bb \u2212 1 ) 1 \u23a4 \u23a5 \u23a6 (8) 2.2. Geometry of head-cutter generating surfaces The geometry of the face-milling cutter generating surfaces is obtained as the locus of the cutting blades in their rotation motion about the cutter-head axis. They are derived by coordinate transformation from coordinate system S s ( x s , y s , z s ), fixed to the face-milling cutter, to coordinate system S t ( x t , y t , z t ), fixed to the cradle. Fig. 4 shows the previously mentioned coordinate transformation from S s to S t . The angular parameter \u03b8 represents the angular position of the head-cutter blades in their rotation motion around the cutter axis of rotation, z t , and constitutes the second surface parametric coordinate of the head-cutter generating surfaces. Transformation matrix M ts , given by Eq. (9) , represents the coordinate transformation from S s to S t . M ts (\u03b8 ) = \u23a1 \u23a2 \u23a3 cos \u03b8 \u2212 sin \u03b8 0 0 sin \u03b8 cos \u03b8 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5 \u23a6 (9) The inside and outside cutter generating surfaces constitute a pair of conical surfaces represented by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000714_4233.826856-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000714_4233.826856-Figure3-1.png",
        "caption": "Fig. 3. (a) Block diagram of data flow in the automated tool. (b) The automated tool. (c) The configuration of the needle and syringe.",
        "texts": [
            " A 16-gauge Tuohy needle was selected as it is a commonly used size. As described above, needles were deployed by the following two methods. 1) Within the laboratory, an automated handheld device was used on deceased porcine specimens. The needle was driven by a lead screw, its position determined by a linear potentiometer. The feed force and pressure within the needle were measured using strain gauged force and pressure transducers, respectively. Feed rate and data acquisition were controlled via an AD/DA interface board in a personal computer. Fig. 3(a) and (b), respectively, show the control block diagram for velocity feed control and the device. The feed rate, force, and pressure data were continuously used in a tissue interface identification function capable of detecting membrane rupture, which is described in Section III-B. 2) The above equipment was unsuitable for use outside the laboratory, and, in such cases, the needles were deployed manually in a fluid-filled syringe. This suited requirements for recently deceased humans. Pressure in the fluid was sensed using a diaphragm piezoresistive sensor connected to the fluid via a three-way tap and arterial pres- sure tubing. The arrangement is shown in Fig. 3(c). Feed displacement measurements were obtained by using a reflective optoelectronic sensor mounted on the body of the syringe, in close proximity to the fixation point of the needle. In the second method, feed force was derived from pressure measurement, similar to Holloway and Telford [8]. There is a slight difference between the pressure and force functions, principally due to seal friction, as shown by the offset in Fig. 4(a). Otherwise, the relationship is linear. Fig. 4(b) shows the relationship between signal intensity and proximity to the skin resulting from the optoelectronic sensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001636_s0263574704000347-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001636_s0263574704000347-Figure1-1.png",
        "caption": "Fig. 1. Orthoglide kinematic architecture.",
        "texts": [
            " joints; (ii) regular workspace shape properties with a bounded velocity amplification factor; and (iii) low inertia effects. This paper analyses the kinematics and the workspace of the Orthoglide. Section 2 describes the Orthoglide geometry. Section 3 proposes new solutions for its inverse and direct kinematics. Sections 4 and 5 present a detailed analysis of the workspace and jointspace, respectively. Section 6 contains an exhaustive singularity study. And, finally, Section 7 summarises the main contributions of the paper. 2. MANIPULATOR GEOMETRY The kinematic architecture of the Orthoglide is shown in Fig. 1. It consists of three identical kinematic chains that are formally described as PRPaR, where P , R and Pa denote the prismatic, revolute, and parallelogram joints, respectively. The mechanism input is made up of three actuated orthogonal prismatic joints. The output body (with a tool mounting flange) is connected to the prismatic joints through a set of three kinematic chains. Inside each chain, one parallelogram is used and oriented in a manner that the output body is restricted to translational movements only"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002324_tia.2010.2057391-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002324_tia.2010.2057391-Figure10-1.png",
        "caption": "Fig. 10. Impaired cooling by blocking ventilation (motor 2).",
        "texts": [
            " 9 that, by using (8), the proposed thermal protection scheme is capable of providing accurate estimation of the stator temperature under variable-load conditions. As stated in Section I, it is crucial that the stator temperature can be accurately estimated when the motor\u2019s cooling capability is deteriorated so that the user can be warned for inspection or repair of the motor with impaired cooling. To test the feasibility of the proposed stator temperature estimation scheme in the case of impaired cooling, a paper foil is attached to the end of motor 2 to partly block the ventilation, as shown in Fig. 10. For comparison purposes, the motor is operated again under variable-load conditions (no load \u2192 100% \u2192 50% \u2192 75% of the rated load). The stator temperature estimation results are shown in Fig. 11. It can be observed that the proposed stator temperature estimation scheme can provide accurate estimation of the stator temperature for determining whether the cooling capability of the motor is healthy or impaired. It can be observed from the comparisons of Figs. 9 and 11 that impaired cooling induces an increased stator temperature rise under the same load condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000764_s0094-114x(97)00022-0-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000764_s0094-114x(97)00022-0-Figure7-1.png",
        "caption": "Fig. 7. For the derivation of determination of angle ~t.",
        "texts": [
            " 3) Er-- instantaneous value of the shortest center distance between the pinion and the grinding disk (Fig. 3) l~d i sp l acemen t of the grinding disk in the direction of the pinion axis (Fig. 3) a~--parabola coefficient of the parabolic function Si--coordinate system u~0k~--surface parameters of the shaper 0o~--angular width of the space of the shaper on the base circle (Fig. 5) r ,~posi t ion vector in system S,(i = s, 1, 2) rh~--radius of the base circle of the shaper (Fig. 5) ~o--pressure angle [Fig. 6 (b)] ~--proflle angle for determination of pointing (Fig. 7) n,, N~--unit normal and normal (Fig. 5) to the shaper surface Mj~--matrix of coordinate transformation from system S~ to system S, E,--shaper (i = s), pinion (i = 1) or gear (i --- 2) tooth surface ~,--angle of rotation of the shaper (i = s) or face gear (i = 2) (Fig. 2) v,m~--~relative velocity vector ~c~-'~--relative angular velocity vector E--shortes t center distance between the shaper and the face gear (Fig. 2) X,, Y,, Z,---coordinates of the axis of meshing m.,,--gear ratio R,--inner (i = 1) and outer (i = 2) radii of face gear free of undercutting and pointing (Fig",
            " Considering the conditions of tangency of the cross-section profiles of the shaper and the face-gear, we can make the following conclusions: (i) such points of tangency are M, and M2 in plane HI, and N~ and N2 in plane 1-12 [figs 6(b) and 7]; (ii) the common normals to the cross-section profiles pass through these points and the points of axis of meshing Pi (i = 1, 2); (iii) the common tangents to the cross-section profiles form an angle c\u00a20 and ~, respectively. (4) We assume now that plane 1-I2 is the plane where the pointing of the cross-section profiles of the face gear occurs. Our investigation shows that the cross-section profiles of the face-gear deviate only slightly from the straight lines. Therefore, we assume that point K (Fig. 7) of the intersection of the tangents to the profiles is the point of intersection of the real cross-section profiles of the face gear. (5) Using the consideration discussed above, we are able now to derive the equations for the determination of the outer radius R2 of the face gear for the zone of pointing. Step I: Vector equation (Fig. 7) yields that [4]: O~A + ANI + N t K = OsK - t a n ~ - - w h e r e 0o~ is represented by equation (4). (13) 2Pdrm _ 0o~ (14) N~ Meshing of orthogonal offset face-gear drive 95 Step 2: We consider that point P~ belongs to the pitch cylinder of the shaper [Fig. 6(a)], and the location of P2 with respect to P~ is determined with segments AI and Aq [fig. 6(a)]. Drawings of Figs 6(a), 6(b) and 7 yield Aq = O~P: - O~P, = rb~ rb~ _ N~ / c o s a zo _-- cos ~'] (15) cos~ cos~0 2 / '~ \\ cos~ / AI= Aq (16) tan y~ Step 3: The location of plane H2 is determined with parameter L2 [Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure13-1.png",
        "caption": "Fig. 13. Comparison of rough-cut geometry of the gear tooth surfaces with regard to the objective geometry for the 40th valid geometry on (a) the concave side and (b) the convex side.",
        "texts": [
            " As depicted, the maximum stock for the finishing operation is concentrated on the central dedendum area of both concave and convex active surfaces of the rough-cut geometries, whereas the minimum stock is located on the addendum area of concave active surfaces and on the heel and toe areas of convex active surfaces. More concretely, the magnitude of the aforementioned raw material surplus is very limited, being about 360 \u03bcm for the concave side, whereas a minimum stock of 103.8 \u03bcm is obtained at the concave side, which meets the requirement of 100 \u03bcm stock allowance for the rough-cut geometry. Additionally, Fig. 12 shows the results of comparison of the rough-cut geometry and the objective geometry for the 20th valid geometry and Fig. 13 shows the corresponding results for the 40th and final valid geometry before the COBYLA algorithm returns after 500 iterations. In Figs. 11\u201313 , the rough-cut geometry is represented as solid body and the objective geometry as a wireframe model. Comparison of normal distances corresponding to the three reached roughcut geometry reveals, firstly, similar tendencies, and secondly, negligible differences among them. Fig. 14 shows the stock material distribution corresponding to the 40th valid geometry for both the concave and convex sides of the pinion tooth surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure7-3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure7-3-1.png",
        "caption": "FIGURE 7-3 Mechanical governor built into a distributor-type diesel injection pump. (Courtesy Roosa Master.)",
        "texts": [
            " The assumption that the flyweights on governors have their masses con centrated at their centers of gravity is an approximation for spherical weights. However, few governors are made in this manner because they are designed for ease of manufacture and compactness of the assembly. For a more nearly correct solution, the flyweights should be assumed as broken down into simple shapes and the moment should be found for each separately. These moments may then be summed to obtain the total moment for any position. A phantom view of a distributor-type diesel fuel pump is shown in figure 7-3. The governor for the engine is an integral part of the distributor pump. 160 ENGINE ACCESSORIES Spark Arresters Fires may result from contact between dry vegetation and hot exhaust pipes or from the emission of hot carbon particles in the exhaust stream. Carbon particles have been found to ignite at a minimum temperature of about 480\u00b0 to 540\u00b0C. Because temperatures within the cylinder may be from 1650\u00b0 to 2200\u00b0C, loose carbon particles will be burning as they leave the exhaust system. Field tests indicate that fires may be started consistently in dry vegetation by glowing carbon particles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001916_s00604-007-0872-2-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001916_s00604-007-0872-2-Figure4-1.png",
        "caption": "Fig. 4. The reaction principle of enzyme biosensor",
        "texts": [
            " The phenolic compounds being oxidized to free radicals will decay to non-radical products through polymerization reactions: AH \u00fe AH ! AH2 \u00fe A AH \u00fe AH ! AH AH AH \u00fe \u00fe AH ! Polymers According to above scheme, 2,4-DCP will loss an electron and forms a radical in the presence of HRP [2, 13]. Because the electrochemical reduction of the radicals is very rapid, furthermore, the MWNTs provides excellent reaction interface for the electrochemical reaction, the HRP-MWNTs-GC electrode should be a sensitive biosensor for the 2,4-DCP. The response of HRP-MWNTs-GC electrode on 2,4-DCP can be depicted in Fig. 4. In this experiment, S1 and S2 were used to denote H2O2 and 2,4-DCP, respectively. In order to predigest the discussion of catalytic reaction of 2,4-DCP in the presence of HRP, here we deal with the two steps of reaction as one-step kinetic mechanism of enzyme biosensor [30]. According to the Marko-Varga [31] and Chen et al. [32], the oxidation of organic substrates (AH2) catalyzed by peroxidase involving two kinetically distinct enzyme intermediates (CompoundI and Compound-II), is a ping-pong reaction, and the Lineweaver-Burk curves are straight lines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000700_rsta.1997.0049-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000700_rsta.1997.0049-Figure3-1.png",
        "caption": "Figure 3. Cross-section of edge of strip with rounded corners. Points a, b, c, d indicate contact with surface of liquid for increasing weights of strip. Arrows indicate direction of surface tension.",
        "texts": [
            " The angle \u03a6 depends on physical characteristics of the object, liquid and gas, and is governed by Young\u2019s equation, namely S sin \u03a6 = Ssl \u2212 Ssg, (2.29) where Ssl, Ssg are, respectively, the interfacial tensions between the solid and liquid, and the solid and gas. In contrast, the angle \u03c6 between the horizontal and the free surface of the liquid depends primarily on considerations of equilibrium and in what follows we determine the influence of \u03a6 on \u03c6 for the single uniform strip of rectangular section. Figure 3 depicts cross-sections of differently weighted strips of rectangular section with, for demonstration purposes, rounded corners. The arrowed lines are tangents to the surface of the liquid. For rectangular sections with no rounded corners the points a, b coalesce, as do the points c, d. Furthermore, it is apparent that when \u03c6 < \u03a6 the free surface of the liquid coincides with the lower edges of the strip, while if \u03c6 > \u03a6 it coincides with the upper edges of the strip. Finally, if \u03c6 = \u03a6 the surface of the liquid meets the sides at some intermediate point, see below, where the three cases are analysed by the linear theory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003640_j.cirp.2014.03.124-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003640_j.cirp.2014.03.124-Figure1-1.png",
        "caption": "Fig. 1. Transmission gear box noise path [1].",
        "texts": [
            " Bernard (1)d a AIRBUS HELICOPTERS, Ae\u0301roport de Marseille Provence, 13700 Marignane, France b Universite\u0301 de Toulouse, INSA, ICA (Institut Cle\u0301ment Ader), 135 avenue de Rangueil, F-31077 Toulouse, France c Aix-Marseille Universite\u0301, CNRS, ISM UMR 7287, 13288 Marseille Cedex 09, France d Ecole Centrale de Nantes, IRCCyN UMR CNRS 6597, BP 92101, 1 rue de la Noe\u0308, 44321 Nantes Cedex 3, France 1. Spiral bevel gear optimization for noise reduction In accordance with the conclusions of Coy and al in their study on behalf of NASA [1], it is established that the noise generated by a helicopter gear box is principally due to the meshing of the gears. The path of the waves is shown schematically in Fig. 1. The vibrations propagate from the gearbox to the cabin through the air and through the airframe. The noise impacts the comfort for pilots and passengers. Different isolations devices can be installed on a Helicopter in order to limit the propagation of the noise. It is now even possible to imagine active noise control systems in the cabin to counteract directly the noise in the passengers environment. However all these devices have significant weight and cost. In addition, Coy [1] highlights two trends related to evolution of the Helicopter design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure13-1.png",
        "caption": "Fig. 13 Some 3-DOF PPR-PMs of family 13.",
        "texts": [],
        "surrounding_texts": [
            "Virtual chains have been introduced to represent the motion patterns of 3-DOF motions. A procedure for the type synthesis of Copyright  2004 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Dow 3-DOF PPR-PMs has also been proposed. Using the proposed procedure, 3-DOF PPR-PMs are synthesized in three steps: (a) Type synthesis of legs, (b) Type synthesis of 3-DOF PKCs and (c) Selection of actuated joints. In addition to all the 3-DOF PPR-PKCs and 3-DOF PPR-PMs proposed in the literature, a number of new 3-DOF PPR-PKCs and 3-DOF PPR-PMs have also been identified. It has also been found that there are no 3- DOF PPR-PMs with identical types of legs. Due to the introduction of the virtual joints, the type synthesis of legs for an f -DOF PKC or PM generating a specified motion pattern is reduced to the type synthesis of f -DOF single-loop kinematic chains. This leads to that the proposed method is more straightforward and efficient than the current approaches for the type synthesis of PMs [9, 10, 13, 16\u201319, 27, 29\u201332] at their current state of the art. The proposed approach is also applicable to the type synthesis of PMs generating other 3-, 4- and 5-DOF motion patterns. However, the classification of V-chains is still an open issue."
        ]
    },
    {
        "image_filename": "designv10_10_0001930_j.nonrwa.2008.02.014-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001930_j.nonrwa.2008.02.014-Figure4-1.png",
        "caption": "Fig. 4. The mobile platform and its frame [9].",
        "texts": [],
        "surrounding_texts": [
            "Here we study an offset 3-UPU (Universal\u2013Prismatic\u2013 Universal) parallel manipulator with an equal offset in its six universal joints, as shown in Fig. 1 [9]. A special 3-UPU parallel manipulator with zero offsets in the six universal joints was proposed by Tsai in 1996 [10,11]. Tsai\u2019s 3-UPU manipulator has three extensible limbs (legs) that connect the base to the mobile platform through universal joints, and it can provide a 3-DOF pure translational motion [9]. Due to zero offsets in the universal joints, the kinematics of the manipulator is simple and straightforward [10]. Fig. 2 shows a schema of the i th limb (i = 1, 2, 3), which connects point B on the mobile platform and point A on the base by a passive universal (U) joint, an active prismatic (P) joint, and another passive universal (U) joint. So, it is called a 3-UPU parallel manipulator [9]. For the convenience of kinematics analysis, three local frames, namely; \u03a31 : O X1Y1 Z1, \u03a32 : O X2Y2 Z2, and \u03a33 : O X3Y3 Z3, are set up and attached to the base in order to represent the position and the first axis of a universal joint. Actually, frame \u03a3i (i = 1, 2, 3) is rotated along the X axis by angle \u03b2i from global frame \u03a3 . Besides, \u03b21 = 0 since \u03a31 is already chosen to be parallel to \u03a3 . thus coordinates {X i , Yi , Zi } (i = 1, 2, 3) of a point in a local frames \u03a3 i and its coordinates {X, Y, Z} in the global frame \u03a3 have the following relationship (Figs. 3 and 4) [9]:X i Yi Zi  = 1 0 0 0 cos\u03b2i sin\u03b2i 0 \u2212 sin\u03b2i cos\u03b2i  X Y Z  =  X Y cos\u03b2i + Z sin\u03b2i \u2212Y sin\u03b2i + Z cos\u03b2i  (i = 1, 2, 3). (7)"
        ]
    },
    {
        "image_filename": "designv10_10_0002358_j.optlaseng.2010.12.008-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002358_j.optlaseng.2010.12.008-Figure1-1.png",
        "caption": "Fig. 1. 3D model and mesh division.",
        "texts": [
            " QTR is the latent heat of phase transformations. LSM process accompanies phase transformation. The latent heat produced from phase transformation is expressed as the form of enthalpy: H\u00bc Z r\u00f0T\u00deC\u00f0T\u00dedT \u00f02\u00de In one temperature incremental interval, all the produced latent heat of phase transformation can be described as the superposition of each value: HP \u00bc X i HiDVi \u00f03\u00de where Hi is the latent heat of ith phase, DVi is the volume phase transition ratio of ith phase. The 3-D FE model and mesh division mesh are shown in Fig. 1. The geometry of the melt structure was modeled with eight-node hexahedral elements including 13 563 notes and 16 532 elements. Determination of optimal time stepping and mesh is essential for solution of these nonlinear and coupled governing equations. A FE mesh was refined in the melting area and HAZ, which have a large temperature gradient and phase transformations (Fig. 2). In the region far from melting area, temperature gradient is not so large and the mesh is coarse. Variation of temperature in the component is the main driving force for phase transformations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002433_ja204891v-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002433_ja204891v-Figure1-1.png",
        "caption": "Figure 1. A schematic representation of a SAMmodified gold electrode with fluorescently labeled, copper-containing L93C NiR on top. The bold arrow signifies the quenching of the fluorescent dye (red star) through FRET to the type-1 site (yellow). The dashed arrows illustrate the ET process from the electrode surface via type-1 Cu to type-2 Cu site (green), where the nitrite reduction to nitric oxide takes place. In this schematic representation, one of the monomers (1/3) is closer to the electrode than the other two (2/3). Therefore, two interfacial ET rates (kET 1/3 and kET 2/3) are distinguished.",
        "texts": [
            "ublished: August 24, 2011 r 2011 American Chemical Society 15085 dx.doi.org/10.1021/ja204891v | J. Am. Chem. Soc. 2011, 133, 15085\u201315093 \u2019 INTRODUCTION Copper-containing nitrite reductase (NiR) catalyzes an oneelectron reduction of nitrite to nitric oxide: NO2 + 2H+ + e f NO + H2O in denitrifying organisms.1 NiR is a homotrimer, in which each subunit contains a type-1 and a type-2 copper site (Figure 1).2,3 The type-1 Cu site, which is located close to the protein\u2019s surface, accepts electrons from its natural donor, pseudoazurin, and transfers them to the buried type-2 Cu site where nitrite is reduced.2,4 9 In the type-1 copper center of green NiR from Alcaligenes faecalis, the copper atom is coordinated by two histidines, one methionine, and one cysteine.10 A ligand-tometal charge transfer (LMCT) from the sulfur (cysteine) to the oxidized copper (Cu2+) gives rise to absorption bands around 450 and 590 nm, which disappear when the copper gets reduced (Cu1+)",
            " At both pH values, two monomers within the trimer have an approximately 25-fold smaller kET rate than the third monomer (compare kET 1/3 to kET 2/3 in Table 1). Assuming an exponential ET rate decay value of \u03b2 = 0.9 \u00c5 1, this difference in kET rate corresponds to a 3.6 \u00c5 difference in distance.46,47 This distance illustrates how much further an electron has to travel from the electrode to the type-1 copper site. The relatively small difference in distance indicates that all type-1 copper sites of a trimer face the electrode surface (Figure 1). The enzyme does not bind \u2018side on\u2019, as this would result in at least one monomer being spaced apart from the electrode by more than 35 \u00c5 (a distance between type-1 Cu sites taken from NiR crystallographic structure).10 Model. Our spectroelectrochemistry data can be only explained by the full model (route A + route B) of Figure 7. In this study we have also constructed models based on either routes A or B only. Neither of these was able to explain two fundamental findings of NiR enzyme catalysis: substrate inhibition at low pH and substrate activation at high pH (Figure 6)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-33-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-33-1.png",
        "caption": "FIGURE 12-33 Method of force analysis on three-point hitch of tractor. (From R. W. Wilson, Paper 1'\\0. 960, SAE meeting, Sept. 14- 17,1959.)",
        "texts": [
            " The dimensions of categories I, II, III, and IV three-point hitches have been standardized by ASAE and SAE. Figure 12-32 illustrates the stan dard three-point hitch. Details of the standard are shown in ASAE S217.1 0 (also SAEJ715 SEP83). Another standard, ASAE S320.1, describes the three point hitch standard for lawn and garden tractors having less than 15 kW of power. 354 HYDRAULIC SYSTEMS AND CONTROLS The design of the three-point hitch has carefully considered the effect on both the implement and the tractor. Figure 12-33 describes a graphical method of determining the resultant of all forces acting upon the hitch. Note that a bend ing force, b, exists on the lower link, thus affecting the location of the virtual center f'. With the free-link or floating-type, no bending force can exist except that resulting from friction in the pin-connected joints. Most tractors employ some means of holding the lower links in a fixed vertical position (position con trol) or holding the lower links at a vertical position regulated by the force on either the upper or lower links (draft control). These systems were discussed in the section Classification of Hydraulic Controls. ,--------- Upper hitch point adjustment area ~ Center line pto Upper link point Tire clearance of lower hitch point at max height -+, _--- Lower hitch point (max) QCICK-ATTACHING COUPLER FOR THREE-POINT HITCHES ~55 I t is obvious from figure 12-33 that the virtual center, J', of the forces on the hitch system will be higher if a downward bending force exists on the lower links. I f it is desired to determine all the forces in the three links, it is necessary to measure simultaneously the bending and tension forces in the lower links and the compression (or possibly tension) force in the top link, while at the same time recording their position relative to the tractor. If it is desired to determine the vertical and transverse forces plus the longitudinal forces acting upon a three-point hitch, it will be necessary to equip each of the bottom links with strain gages that will independently mea sure tension and bending forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001967_0094-114x(78)90041-1-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001967_0094-114x(78)90041-1-Figure6-1.png",
        "caption": "Figure 6. Masses fixed in and assigned to a link in a counterweight chain from other such chains.",
        "texts": [
            " Provision must be made in eqn (1) for masses which are either fixed in or assigned to the links of these counterweighted chains. The masses can be divided into three groups. The first consists of those assigned to the joints connecting a link to the remainder of the chain. The second consists of masses assigned to other revolute joints in the link whilst the third is formed by those masses assigned via prismatic joints in the link. Consider the kth link which lies within a counterweighted chain and is shown in Fig. 6. The two joints that connect this link to the other links in the chain are denoted by the subscripts of the links they connect. Let there be x masses, Mr, assigned to or fixed in joint k / k - 1 as a result of a dependent link and/or another counterweighted chain being incident at or assigned to either this joint or links higher up in the chain. Assume also that the link has u other revolute joints, one of which is denoted by q and let there be yq masses, Ma, assigned to the qth joint. In this case the qth joint is offset from the lkth arc by an angle 8q and separated from the joint k/k + 1 by the distance lq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003000_j.measurement.2012.07.005-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003000_j.measurement.2012.07.005-Figure2-1.png",
        "caption": "Fig. 2. Schematic view of absolute position for gravity center.",
        "texts": [
            " Assume that the shaft can be considered to be massless and flexible whereas the element E can be approximated by a particle of mass m. This particle is attached to the shaft at the geometric center (C) of the element E. The center of gravity G is displaced by l from the geometrical center of the shaft cross-section C. The distance l represents eccentricity for imbalance of the disc E and can be considered to have a small magnitude. To analyze the motion of this system, it is introduced the inertial system of coordinates XY as shown in Fig. 2. The instantaneous position of the center C is defined by the position vector rc. Since the angular velocity is constant, the relative instantaneous position of the center of gravity G is determined by the angle (Xt), that is, eccentricity l (vector rGC). The absolute position of the center of gravity G in Fig. 2 is denoted by rG. Since the internal and external damping are neglected, the equation of motion of the gravity center (G) is governed by the Newton\u2019s second law, m\u20acrG \u00bc R \u00f01\u00de where \u20acrG represents second derivation of the position vector of the gravity center (G) with respect to time. As seen from Fig. 2, rG \u00bc \u00f0x\u00fe l cos Xt\u00dei\u00fe \u00f0y\u00fe l sin Xt\u00dej R \u00bc k\u00f0xi\u00fe yj\u00de \u00f02\u00de In the above equation, k denotes the stiffness of shaft, x and y are the position coordinates of the point C. Substituting of Eq. (2) into Eq. (1), the equation of motion of the gravity center (G) can be obtained as follows [24]. \u20acx\u00fex2 nx \u00bc q cos Xt \u00f03\u00de \u20acy\u00fex2 ny \u00bc q sin Xt \u00f04\u00de where the natural frequency (xn) xn \u00bc ffiffiffiffi k m r ; k \u00bc 3EIL a2b2 and q \u00bc lX2 When the influence of whirling for the shaft-bearing system is considered, the equation of motion of the right bearing for y-direction is defined, mb\u20acy\u00fe kby \u00bc Fby \u00f05\u00de where mb and kb denote the mass and stiffness of bearing, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002924_1.4023208-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002924_1.4023208-Figure3-1.png",
        "caption": "Fig. 3 (a) Detail of investigated HCR gear wheels and (b) fixation of the accelerometer to the gearbox",
        "texts": [
            " A schematic drawing as well as a picture of the device used in experiments is shown in Fig. 2. The test rig consists of two gearboxes, the first one equipped with test gears and the second one with so-called power return gears. Gearboxes are connected with two shafts to close the power flow between them. The loading of the system is ensured by a prestress of the shaft using a load coupling. Input power is delivered by an electromotor [6]. Both gearboxes are equipped with high contact ratio (HCR) spur gearwheels (with the number of teeth z1\u00bc 21 and z2\u00bc 51, respectively, Fig. 3(a)). The HCR gear wheels differ from commonly used spur gears by a higher value of contact ratio, ea\u00bc 2.003 [7]. These types of gears provide a higher contact area and therefore, higher life length, as well as lower noise levels [8, 9]. When the frequency analysis of the new well produced gearbox without necessary manufacturing faults (a reference state) is carried out, one can identify from frequency spectra: \u2022 the excessive amplitude as a result of allowable imbalances in the gearwheels, rotational frequency of shafts with gears \u2022 mesh frequency (the first, second, and third harmonics and to investigate the possibilities using the fourth, eventually the fifth harmonics) with smaller sideband amplitudes with the interval of rotational frequency of the gear sets \u2022 the faults of load coupling (imbalance, i",
            " The signal was picked up by a uniaxial piezoelectric accelerometer (either B&K 4391 used with B&K 2515 or B&K 4514-001 used with B&K PULSE) and processed by a data acquisition unit. For older measurements (set 1) B&K 2515 was used, newer measurements were analyzed by B&K PULSE 3560. Data processed were recorded and analyzed using a laptop with B&K LabShop and MATLAB software. The accelerometer was fixed into the gearbox\u2019s body by a stud in order to ensure a firm fixation and the same measurement position throughout the experiment (Fig. 3(b)). 4.2 Settings. The frequency spectra were obtained by processing the time signals through an FFT analyzer with the settings listed in Table 2. The span was chosen to be 1.6 kHz in order to capture at least the first four tooth mesh frequencies and their sidebands. A bandwidth of 1 Hz is sufficient to distinguish the Table 1 List of apparatus used Type Device Notes Data acquisition 1 Frequency analyzer Bruel & Kjaer 2515 Software used\u2014B&K WT9324 Data acquisition 2 Bruel & Kjaer PULSE 3560 Software used\u2014B&K PULSE LabShop Accelerometer 1 Bruel & Kjaer 4391 UniGain Uni-axial piezoelectric accelerometer with build-in preamplifier, fixed to structure by a studAccelerometer 2 Bruel & Kjaer 4514-001 Postprocessing software Bruel & Kjaer WT9324 \u2014 Bruel & Kjaer PULSE LabShop v14 MATLAB r2010a Journal of Vibration and Acoustics APRIL 2013, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001382_bf02460302-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001382_bf02460302-Figure2-1.png",
        "caption": "Figure 2. The motion of the organism and the Frenet trihedron. (a) The motion of the organism ijk. The trajectory is traced by the organism's center of mass, which is the origin of ijk. The trajectory is determined by the organism's translational velocity V and rotational velocity co. (b) The motion of the Frenet trihedron TNB. The origin of the Frenet trihedron also traces the trajectory, so the origin of TNB also is the organism's center of mass. The unit tangent vector T is always tangent to the trajectory, so it points in the direction ofV. TNB rotates with rotational velocity d (the Darboux vector).",
        "texts": [
            " A right-hand helical trajectory is given by: H(t) = r cos(Tt)I + r sin(Tt)J + \\ 2nJ K (1) where IJK is a reference frame fixed to the helix such that K is the axis of the helix; p is the pitch; r is the radius; and 7 is the angular frequency (radians/time) (Fig. 1).* around the cylinder. The organism is considered a rigid body represented by an orthogonal reference frame ijk. The organism moves in three-dimensional space with translational (linear) velocity V and rotational (angular) velocity o~. As the organism moves, the origin of ijk describes a curve in space (Fig. 2a). The Frenet trihedron TNB also follows this curve such that the origin of TNB * For left-hand helical motion the sine and cosine terms are interchanged. This analysis uses the equation for a right-hand helix, but the results also apply to left-hand helices. 200 H . C . CRENSHAW a and ijk are the same point (Fig. 2b). Consequently, ijk and T NB translate and rotate with respect to XYZ and to each other. The first step in this analysis is to describe the unit vectors of the Frenet trihedron and the curvature and torsion of the trajectory in terms of V and co. This will permit description of the parameters of helical mot ion in terms of V and co. I begin with the conventional arrangements of V and co being described relative to the body of the organism, ijk (subscript b), and the unit vectors of the Frenet trihedron being described relative to space, XYZ (subscript s)",
            " Furthermore, the translational velocity of the Frenet trihedron is by definition: u = VT~ (2) KINEMATICS OF HELICAL MOTION 201 i.e. the speed of the Frenet tr ihedron equals that of the organism, and the Frenet tr ihedron translates in the direction of T~. The rotational velocity of the Frenet tr ihedron is given by a vector known as the Darboux vector ds, which is given by Goetz (1970, pp. 63-64) as: ds =-cTs + ~cB s (3) where z and ~c are the torsion and curvature, respectively, of the trajectory (Fig. 2b). The unit vectors of the Frenet tr ihedron are described in space as follows: = (4) dTJds N s - i d T j d s I (5) V s x 'V s (6) B s - iV ~ x *sl where the dots indicate derivatives with respect to time (see Gillett, 1984, pp. 693-696). It is now possible to describe these unit vectors relative to ijk. T is parallel to Vb (7) T , , - v 9 N b can be determined using equation (5) and the following operator for the time derivative of a vector in a rotating reference frame: \u2022 (8) (see Symon, 1971, p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003296_j.ymssp.2017.05.041-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003296_j.ymssp.2017.05.041-Figure7-1.png",
        "caption": "Fig. 7. Modeling of the calculate SIF. (a) Different regions near the crack tip. (b) Location of the nodes near the crack tip.",
        "texts": [
            " (24) can be written as: dc \u00bc @U @F \u00bc W E @ @F Z q 0 K2 I \u00fe K2 II dq \u00f025\u00de dc \u00bc 2W E Z q 0 K I @ @F K I \u00fe K II @ @F K II dq \u00f026\u00de dc \u00bc 2W FE Z q 0 K2 I \u00fe K2 II dq \u00f027\u00de Therefore, the mesh stiffness of cracked teeth can be expressed as: kc \u00bc F2E 2W ,Z q 0 K2 I \u00fe K2 II dq \u00f028\u00de The SIF is used to define the stress distribution intensity at the crack tip affected by crack shape and load size. From the literature [31], the region near the crack tip is divided into three regions, namely, region-1, region-2 and region-3. They are shown in Fig. 7(a). In the previous research, it is certain that the locality field is hard to express in the region-1, in which exists stress singularity because the region-1 is close to the crack tip. The SIF calculation in the region-3 is also not the valid region due to large number of unknowns required in the series mathematical model. Thus region-2 is the optimum field for accurate SIF calculation. Dally and Sanford [32] adopted three unknown coefficients approach, which assumed that the region-2 can be expressed with sufficient accuracy by three series equations. The stress filed in the region-2 can be expressed as: rx \u00bc A0r 1=2 cos h 2 1 m \u00f01\u00fe m\u00de sin h 2 sin 3h 2 \u00fe 2B0 \u00fe A1r1=2 cos h 2 1 m \u00f01\u00fe m\u00de sin2 h 2 ; ry \u00bc A0r 1=2 cos h 2 1 m \u00f01\u00fe m\u00de sin h 2 sin 3h 2 2mB0 \u00fe A1r1=2 cos h 2 1 m \u00f01\u00fe m\u00de sin2 h 2 ; sxy \u00bc A0r 1=2 sin h cos 3h 2 A1r1=2 sin h cos h 2 \u00f029\u00de where A0, A1 and B0 are unknown coefficients which can be appraised with the help of geometry and boundary conditions of the point P\u00f0r; h\u00de as shown in Fig. 7. Among them, r is the crack tip to any point near the distance. h is the angle of crack surface and any point. m is the Poisson\u2019s ratio. According to the linear elastic fracture mechanics, the type-1 SIF K I is related to A0 coefficient, which can be written as [32]: K I \u00bc ffiffiffiffiffiffi 2p p A0 \u00f030\u00de In order to ensure the accuracy of gear contact analysis, in this paper a 3-D FEM is used for unknown coefficient A0 calculation. Aiming at the stress singularity at the crack tip, Barsoum et al. [33] pointed out that the intermediate nodes of the second-order element\u2019s near the crack tip moves to the 1/4 nodes along the crack tip, as shown in Fig. 7(b). It is clear that the point P\u00f0r; h\u00de is replaced by any 1/4 nodes which has the same radial location r and different orientation angles h for the crack tip. In order to raise its calculation efficiency and lower the cost, a 3-D involute gear contact model is generated using the parameters of gear listed in Table 3, as shown in Fig. 8(a), which only have five teeth and the rim length is 4m (m is modular). Besides, in order to meet the needs of the tooth root crack tip stress singularity, the meshing and elements around the crack tip are set as binomial singular elements whose intermediate node moves to the position which is at the 1/4 length of the crack tip"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001274_robio.2004.1521816-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001274_robio.2004.1521816-Figure8-1.png",
        "caption": "Fig. 8. Variable ZMP in walking. (a) ZMP at heel as landing and at toe as lifting (b) ZMP is a linear function of time in single support phase",
        "texts": [
            " 1) The height of the COG is constant, i.e., z = 0. 2) Height of support foot is neglected and foot ankle joint is at the center of foot. 3) The origin of local coordinate system is always set at the sole center of support foot. Therefore, for ZMP fixed case, the origin is identical to ZMP. 4) The equivalent foot length of two feet is b. Thus, the variable range of ZMP for variable ZMP case is b. 5) At landing and lifting, the angle of robot sole with floor is so small that it can be neglected (Fig. 8.a). 6) ZMP moves at constant velocity in single support phase as shown in Fig. 8.b. 7) The robot moves with constant velocity in double support phase. 8) Robot starts its walking from rest as shown in Fig.2 and Fig.3, i.e., x(0) = 0, y(0) = 0 and \u00b1 = 0, y = 0. In local system frame, the ZMP is expressed as ..z XZMP = - ..__ yz YZMP = YC- . \u00b1 g (1) (2) C. Stable walking condition With the above assumptions and (1), the following walking condition ([11]) can be obtained, pg < = ((x-xzMP) = gtanO <pg (3) z where, p is coefficient of friction between the sole of robot and support floor",
            " With the initial conditions x(O) = 0 and NO() = Vil, the motion equation can be expressed as x(t)= Vi sinh(wt) (18) w And with the terminal condition x(toa) Sai, the motion time tal and terminal velocity at time toa are respectively tal --In( j (I +l\u00b1( Vi )2) (19) Vahl = \u00b1Vl+ (WSal )2 (20) Note that BCDE is a whole walking cycle which consists of a double support phase, a deceleration phase, and a acceleration phase. After acceleration phase, the robot will enter into double support phase and start a new walking cycle again. B. Walking Pattern with Variable ZMP In this case, ZMP is variable in both of double support phase and single support phase. In double support phase, ZMP rapidly moves from the toe of the former support leg to the heel of new support leg as described in above subsection; while in single support phase, ZMP moves from the heel to toe of support leg with a constant velocity as shown in Fig.8.b. S_1 ~~~~ XZMp(t) b b t (21) 2 td\u00b1+ta where, td and La are respectively the motion time of deceleration and acceleration phase in single support phase. The moving velocity of ZMP is b/(td\u00b1ta) in single support phase. Similar to the above subsection III-A, biped walking with variable ZMP can also be divided into initial acceleration, double support, deceleration, and acceleration phases, where the latter three phases compose a whole COG traj.ectory as ZMP is movable from heel to toe 1) Initial acceleration phase: From (21) and initial conditions x(0) = 0, \u00b1(0) = 0, and td = 0, (5) is changed to b b b b x(t) -- -t + - cosh(wLt)- sinh(wt) (22) 2 taO 2 &JtaO where, taO is motion time of this initial acceleration phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001653_j.snb.2006.05.013-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001653_j.snb.2006.05.013-Figure1-1.png",
        "caption": "Fig. 1. Circuit diagram and three dimensional representation (3D) of the transmitter unit. The amperometric module comprised a buffered voltage follower (a), a single OPA potentiostat (b), a current-to-voltage converter (c) and a single supply differentiator/amplifier (d). The +5 Vcc voltage was stabilized by the power supply m mmab a oltage t",
        "texts": [
            " The serial-to-USB conerter was a FTDI-FT232BM module (ELT) with a 6 MHz quartz nd a 93C46 E2PROM. All resistors were precision metal oxide hick film (250 mW, 0.1% tolerance, Ohmite, Rolling Meadws, IL). All capacitors were NP0-type multilayer ceramic (low ass filter, decoupling) or electrolytic (decoupling). The compoents were soldered on a single side PCB board (eurocard size 160 mm \u00d7 100 mm). Emilac\u00ae, Positiv\u00ae and Plastic\u00ae technical prays were from Cramolin (Mu\u0308hlacker, Germany). .3. Transmitter unit circuit description The transmitter unit (Fig. 1) comprised four different modles. The amperometric module was built around the interated circuit (IC) LMC6064, a quad single-supply operational mplifier (OPA). National Semiconductors designed this CMOS amily of OPA for micropower applications with low input ias current (10 fA) and high input resistance (>10 T ). The T a a w ators B 122 (2007) 118\u2013126 119 MC6064 can operate from a single-supply voltage with \u201crailo-rail\u201d inputs and outputs. One OPA (Fig. 1a) serves as voltage ollower connected to the wiper of 1 M multiturn trimmer otentiometer. This circuit produces the voltage necessary to olarize the working electrode (WE) between 0 and +1.25 V hile the single OPA potentiostat (Fig. 1b) controls the reference RE) and the auxiliary (AE) electrodes. The current-to-voltage I/V) converter (Fig. 1c) is a single-supply adaptation of a classic ransimpedance amplifier [12] with a three-position adjustable ain varied by a rotary switch. The transfer function of the I/V onverter is: out1 = \u2212(ioxRf) + Vapp (1) here iox is the oxidation current flowing through the WE, Rf is he feedback resistor and VApp is the potential applied to the WE. he resistors have capacitors in parallel to complete a low pass lter with a cut-off frequency (Fcut-off) of 10 Hz for each range. he capacitor values (CF) were calculated in Farads according o the equation: F = 1/(Fcut-off2 \u03c0Rf) (2) n which Rf is the resistor value for each range. The values of F are shown in Fig. 1c. The difference amplifier circuit (Fig. 1d) has the dual role of ubtracting the potential applied to the WE [12] while amplifyng ten times the resulting signal. The transfer function of the ifferentiator is: out2 = (Vout1 \u2212 Vapp)(R2/R1) + Vref(R2/R1) (3) here: Vout1 and Vapp are the signals applied to the inputs and he values of R1 and R2 are respectively 1 and 10 M . Vref is qual to 0 V because the 10 M resistor is grounded, then: out2 = 10 (Vout1 \u2212 Vapp) (4) he combination of the two stages of amplification (Fig. 1c nd d) provides three different full scales, ranging from 1 nA/V 100 M ) up to 100 nA/V (1 M ), with the global transfer funcion: out = \u221210 (ioxRf) (5) The low tolerance resistors (0.1%) reduce the error in the I/V nd differentiator circuits. With a power supply of +5 V the maxmum input current is almost 500 nA (494 nA in the observed rail-to-rail\u201d output). In this range of amplifications it is possile to calibrate accurately a glucose biosensor (Pt disk, 125 m iameter) in vitro. The power supply module (Fig. 1e) was constructed using a P2950-5.0, +5 V voltage regulator, and two decoupling capactors. This IC has very low quiescent current (75 A), low rop-out voltage (40\u2013100 mV) and excellent linear regulation 0.05%). The PIC12F683 is the heart of the digital module (Fig. 1f). his is a 8-bit CMOS IC with low power features equipped with n internal variable clock (31 KHz\u20138 MHz, software selectable) nd a 10 bit ADC with four multiplexed channels. The MCU, orking at 4 MHz, performed the ratiometric A/D conversion 120 P.A. Serra et al. / Sensors and Actuators B 122 (2007) 118\u2013126 o d d 4 p i i c r s p odule equipped with a low drop out voltage regulator (e). The in-circuit progra nalog lines: I/V converter output (1), applied voltage monitor (2) and battery v o the input pin of the transmitter module (g). f Vout (Fig. 1 1\u20133), Vapp and battery voltage (Vbatt). After the igital signal processing (DSP) of acquired raw data, a serial ata packet was generated and sent to the transmitter (Fig. 1 ). The in-circuit-serial-programming (ICSP) bus provides the ossibility of programming the IC \u201con-board\u201d in a few seconds. The miniaturized transmitter (17.8 mm \u00d7 10.16 mm; Fig. 1g) s a thick film AM module, with SAW controlled oscillator and ntegrated antenna, running at the frequency of 433.92 MHz. In onjunction with the MCU, this hybrid component allows the 2 m le digital module (f) was equipped with a PIC-12F683 MCU connected to three monitor (3). The serial data output (4) from the MCU was directly connected ealization of a serial data transmitter working at the maximum peed of 2400 baud. A rechargeable 8.4 V Nickel\u2013Metal hydride (Ni\u2013Mh) Battery ack (3300 mA/h) provided the power to the transmitter unit",
            " This odule was built around the FT232BM, clocked at 6 MHz and onnected to an external 93C46 E2PROM (used to store USB ID arameters, resource configuration, etc.). A LED provided direct isualization of received packets. A few resistors and decoupling apacitors completed the USB interface and the +5 V power upply, derived from the USB. .5. PCB design and construction The components placement was simulated using a graphic oftware (KiCAD). The three-dimensional (3D) reconstructions f the transmitter and receiver units are illustrated in Fig. 1, 3D nd Fig. 2, 3D. 2 a AM signal was decoded by the receiver unit (a) connected to a 17.28 cm \u201cwhip\u201d d to the personal computer (c). The unit was powered by the USB bus without The printed circuit board (PCB) tracks were designed with freely available software (KBan 2.0) and printed on a trans- arency using a HP Laserjet 1200. The PCB board was cleaned ith sandpaper (3 M, Microfine-1500 grit) and rinsed with water nd acetone before applying a coating of positive photoresist Positiv\u00ae). After 45 min the board was coupled with the printed ransparency, using removable tape, and exposed to direct UV ight for 5 min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure17-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure17-1.png",
        "caption": "Fig. 17 \u2013 Contours of plastic hinges \u2013 interior view.",
        "texts": [],
        "surrounding_texts": [
            "The results of the performed strength analysis are as follows: contours of deformations, contours of equivalent stress, displacement fields, velocity fields. This paper presents examples of results illustrating the distribution of deformations and stress in the structure at a given moment on a deformed model. Also, the deformation Fig. 16 \u2013 Contours o form is presented at the moment of highest elastic and plastic deformation of bodywork (Figs. 16\u201319). To fulfil the requirements of the Regulation No. 66 of UN/ ECE, for the algorithm and simulation programme the whole energy balance was needed to be plotted. The comparison of the kinetic, internal, hourglass and total energies for the FE bus model is depicted in Fig. 20, which illustrates the kinetic f plastic hinges. energy conversation to internal energy of the whole bus structure. Moreover, the non-physical energy components introduced by the process of finite element modelling and simulating was also plotted. According the Regulation No. 66 of UN/ECE it shall not exceed 5% of the total energy at any time [3]. Since the maximum hourglass energy is 3.5% of the total energy the stated requirement is met."
        ]
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure12-1.png",
        "caption": "Figure 12. Overview of time domain simulation models. (a) Six-dof model, (b) FE-model for MNF creation, (c) I16 MNF model with dark interface nodes visualized, and (d) I16 time domain simulation model with shaft and bearings.",
        "texts": [
            " In this study, the bearing rings are connected to the housing/shaft elements using bonded contact formulation but other mounting setups such as thermal shrink fit and frictional contact could be modelled. The time-domain models are simulated in ref [26]. The pressure pre-processing described in the section on Contact pre-processing has been implemented in a stand-alone executable file called when the bearing is added to the model and the contact computations described in the Tapered roller bearing model section are included in two dynamic-link libraries, one for the six-dof model and one for the multi-degree model, available for the time-domain solver. Figure 12(a) shows the six-dof bearing model where the bearing outer rings are fixed to the ground and the housing is thus omitted. The overall housing stiffness can be included by connecting each bearing surface to one interface node in the bearing centre using a multi-point constraint (MPC) or beam element approach. Such modelling will, however, still include the limitation that the bearing outer rings remain circular and are not considered in this study. The flexibility of the shaft is included using a Timoshenko beam element. The rollers are only at Eindhoven Univ of Technology on June 17, 2014pik.sagepub.comDownloaded from included for visualization and can either be a single separate body, if the rotational inertia is to be considered, or belong to either the inner or outer ring. The creation of the multi-dof models is initiated with a FE model in ref [25] as shown in Figure 12(b) where the bearing outer rings are included. A number of nodes are selected on the centre of the outer raceway surface, and each node is connected to an appropriate number of local nodes using a MPC formulation in order to distribute the contact loads calculated in the Interface node reactions section on the nodes on the axial line of contact. In this study, four different numbers of interface nodes, 10, 16, 23 or 46, are used for each bearing and in all cases only the six constraint modes for each interface node are included as this is sufficient for capturing the load distribution. The different models are designated I10,I16,I23,I46 where the subscript refers to the number of interface nodes in each bearing. In all cases, the interface nodes are uniformly distributed along the circumference of the raceway. This is not a necessity, it could be beneficial to have smaller spacing where the housing stiffness has large deviations, but has the drawback that the visualized forces cannot be compared. Figure 12(c) shows a wireframe visualization of the generated modal neutral file (MNF) housing model where each interface node is highlighted. The final multi-dof model with a shaft including a beam element, two multi-dof bearings, constraints and external loading is shown in Figure 12(d). Two different loading scenarios are considered and in both cases the results of the FE model are compared with the six-dof bearing model and the four different multi-dof models. No flange-induced tilt moments are considered as well as roller inertial forces in order to allow for a comparison with the FE results that do not include these aspects. In this study, a full revolution of a radial force of 5 MN is applied at the load node. Referring to the coordinate system in Figure 12(d), the applied loads are as follows Fx\u00f0 l \u00de \u00bc cos\u00f0 l \u00de 5MN , l 2 \u00bd0, 360 \u00f040\u00de Fy\u00f0 l \u00de \u00bc sin\u00f0 l \u00de 5MN, l 2 \u00bd0, 360 \u00f041\u00de mx \u00bc my \u00bc 0 \u00f042\u00de where l refers to the direction of the load, as indicated in Figure 12(d), that starts in downwards direction and loads the bearing in a full clockwise revolution. The results of the FE model consist of series of simulations with a 15 increment of l. A detailed load distribution and relative raceway misalignment comparison for l\u00bc 0 is shown in Figure 13(a) and (b). It should be noted that for the FE model, misalignments are only calculated for loaded rollers. Figure 13(c) shows the time-domain simulation model and Figure 13(d) shows the interpolated pressures for the highest loaded roller, which is not necessarily the same roller for the different designs. While the comparison in Figure 13(a) to (d) only includes a single load case/time step, Figure 13(e) shows the bearing fatigue life calculated for a full azimuthal revolution of the radial force. Due to symmetry, only the angles from 0 to 180 are shown. In this study, a full revolution of a moment of 10 MNm is applied at the load node. Referring to the coordinate system in Figure 12(d), the applied loads are Fx \u00bc Fy \u00bc 0 \u00f043\u00de mx\u00f0 l \u00de \u00bc sin\u00f0 l \u00de 10MNm, l 2 \u00bd0, 360 \u00f044\u00de my\u00f0 l \u00de \u00bc cos\u00f0 l \u00de 10MNm, l 2 \u00bd0, 360 \u00f045\u00de A detailed load distribution and relative raceway misalignment comparison for l \u00bc 90 is shown in Figure 14(a) and (b). The small deviation between at Eindhoven Univ of Technology on June 17, 2014pik.sagepub.comDownloaded from the results of the I46 and the FE model can easily be explained by the model differences discussed previously. Figure 14(c) shows the time-domain simulation model and Figure 14(d) shows the interpolated pressures for the highest loaded roller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001140_1.2168467-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001140_1.2168467-Figure3-1.png",
        "caption": "Fig. 3 Dynamic state of the ball under the bea",
        "texts": [
            " Therefore, Ci sustains the same displacement with respect to the outer ring and we have a = CifCip 2 Each ball is supposed to be submitted to the elementary load F p /Z directed along the Y axis.The preload is made with use of a spring with much lower an axial stiffness than those of the bearing. Therefore, Fp can be considered as constant and not influenced by rotational speed and angle variations. The distance between raceway groove curvature centers becomes rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/07/201 CopCip = af + p 3 In Fig. 3 a , we consider that the bearing has a constant rota- tional speed around the Y axis. A stationary motion without vibration is considered. Because of inertial forces, outer and inner contact angles have now two different values, o and i. Balls follow the cage orbital motion around the Y axis at the speed c that will be later calculated in Eq. 38 . No sliding motion is supposed to appear at points A and B. At points A and B the outer and inner contact actions are sup- posed to be reduced to resultant forces F o and F i see Fig. 3 b . These forces are respectively decomposed into normal loads Q o and Q i and tangential loads T o and T i. The resultant of centrifugal forces F c is directed along the Z axis and is applied at the point G as shown on Fig. 3 b . Each ball is also submitted to a gyroscopic moment M g which will be calculated later in Eq. 48 . 2.3 Contact Model. Ball deformations are supposed to be mainly concentrated in the vicinity of the contact points A and B. These deformations account for those of the raceways and of the ball in accordance with Hertzian 9 contact model 13,12,8 . Neither configuration change nor elastic deformation at the inner and outer raceways occur except at the ball contact area. o and i being the deformations at points A and B, respectively, under the action of normal forces Qo and Qi ; deformation laws are given by the following nonlinear contact laws 6,8,16 ring rotational speed and the preload Fp MARCH 2006, Vol",
            "org/ on 05/07/201 V B b/c = b/c \u00d9 GB 25 V B ir/c = ir/c \u00d9 OB = ir/or \u2212 c/or \u00d9 OB 26 where V P S1/S2 is the speed of a point P belonging to part S1 with respect to the part S2, and S1/S2 is the rotational speed of part S1 with respect to part S2. Subscript b, c, or, and ir, respectively, refer to ball, cage, outer ring, and inner ring motion. For further calculation and to simplify the expressions, we will use the following notations ir/or = Y 27 c/or = cY 28 b/c = b \u2212 cos Y + sin Z 29 In the same manner as in Ref. 8 , we assume that the deformations are negligible and we have also GA = GB db 2 30 With the notation given in Fig. 3 GA = db 2 sin oY + cos oZ 31 GB = db 2 \u2212 sin iY \u2212 cos iZ 32 and OA \u00b7 Z = dm 2 + db 2 cos o 33 OB \u00b7 Z = dm 2 \u2212 db 2 cos i 34 Assuming no sliding motion at points A and B see Fig. 3 a , we can write the condition of speed equality of the two contacting points at both outer and inner contact, which gives V A b/or = V A b/c \u2212 V A or/c = 0 35 Substituting Eqs. 23 , 24 , and 31 into Eq. 35 yields b db 2 cos o \u2212 = c dm 2 + db 2 cos o 36 With the same analysis applied to the inner contact at point B, we obtain b db 2 cos i \u2212 = \u2212 c dm 2 \u2212 db 2 cos i 37 Finally, using Eqs. 36 and 37 , we obtain the expression of the cage rotational speed c c = dm \u2212 dbcos i cos o \u2212 dm cos o \u2212 + cos i \u2212 + db sin i \u2212 o sin 38 The relative motion of the ball regarding the outer ring is as- sumed to be pure rolling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure7-1.png",
        "caption": "Fig. 7. Dynamic model of gear mesh element.",
        "texts": [
            " The establishment and solution of the quasi-static contact analysis model for widefaced cylindrical gears is given in Fig. 6 . After the mesh misalignment distribution on the tooth flank caused by shaft deflection is determined, the composite mesh stiffness and composite mesh error of the wide-faced cylindrical gear pair can be obtained based on LTCA model [23] . Introducing composite mesh stiffness, composite mesh error and gear mesh damping, the lumped gear mesh element model with 2 nodes and 12 degrees of freedom is established, as shown in Fig. 7 . k m and e m are the composite mesh stiffness and composite mesh error considering mesh misalignment caused by shaft deflection, respectively. x j , y j , z j ( j = p, g ) are the translational degree of freedom along coordinate axis of gear mesh element. \u03b8 xp , \u03b8 yp , \u03b8 zp ( j = p, g ) are the rotational degree of freedom around coordinate axis of gear mesh element. The meanings of other symbols are the same as that in Fig. 4 (b). The generalized coordinate vector of gear mesh element is defined as q m = { x p , y p , z p , \u03b8xp , \u03b8yp , \u03b8zp , x g , y g , z g , \u03b8xg , \u03b8yg , \u03b8zg } T (14) The relative displacement of driving and driven gear along normal line of action can be given as \u03b4m = V q m (15) where V is the projective vector from generalized coordinate to normal line of action, as given in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003012_tmag.2012.2197189-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003012_tmag.2012.2197189-Figure5-1.png",
        "caption": "Fig. 5. Flux density distribution due to .",
        "texts": [
            " The subdivision in the plane of the full 3-D mesh is the same with that of the 2-D eddy current analysis of the motor. The subdivision in the PM of the full 3-D mesh is also the same with that for the 3-D eddy current analysis of only the PM. The gap widths and shown in Fig. 2 are both 0.1 mm. For each model, the steady state is analyzed with step length of electrical angle deg. The distribution of the flux density generated by , obtained by subtracting the flux density for from that for in double 2-D eddy current analyses is shown in Fig. 5. This figure shows that the improvements described above are required for an SPM motor. First, the reluctance of the equivalent gap should be variable in space by VEG because the flux distribution in PM generated by the uniform is not uniform. Moreover, the effect of the flux generated by in the neighboring PM on the flux distribution in the PM itself should be also taken account of in the 2-D eddy current analysis because the flux by passes through the other PM. Fig. 6 shows the variation in the equivalent relative permeabilities with the rotor position at points p and q in the equivalent gap shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002791_0954406211404853-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002791_0954406211404853-Figure7-1.png",
        "caption": "Fig. 7 The view of the test rig",
        "texts": [
            " Although a reasonable rank is obtained, FS, however, failed to select as many useful features as possible, whereas the proposed RBS selected a subset containing 11 features and achieved an even higher classification accuracy of 96.15%. Proc. IMechE Vol. 225 Part C: J. Mechanical Engineering Science IN PLANETARY GEARBOXES This section presents the problem of feature selection for classifying damage degree in planet gears. Descriptions of our test rig and how our experiments were conducted are given in Subsection 5.1. The features to be studied for the given problem are introduced in Subsection 5.2. The datasets used are established and the results are analysed in Subsection 5.3. The test rig shown in Fig. 7 was designed to fully enable performing controlled experiments for developing a reliable diagnostic system for planetary gearboxes. The planetary gearbox has an over-hung floating configuration that mimics the support used in the field by Syncrude\u2019s mining operations. Its main components include one 20-HP drive motor, one stage bevel gearbox, two stages of planetary gearboxes, two stages of speed-up gearboxes, and one 40-HP load motor. Table 5 lists the number of teeth and the speed ratio achieved by each gearbox"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001288_j.optlastec.2004.04.009-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001288_j.optlastec.2004.04.009-Figure1-1.png",
        "caption": "Fig. 1. Schematic of LDM for thin wall.",
        "texts": [
            " Therefore, for investigation of effects of powder concentration distribution on fabrication of thin-wall parts, it is necessary to understand the relationship between powder concentration distribution and power density. In this paper, the relationship between powder concentration distribution and power density was studied, and model of effects of powder concentration distribution on fabrication of thin-wall parts was presented. A metallic thin-wall part is usually fabricated with laser scanning along a single row, and the wall thickness, t; is equal to the width of the molten pool created in laser cladding. As shown in Fig. 1, a laser beam moves in the positive x-direction at velocity, v: The origin of the system of coordinates is on the centerline of the laser beam. In laser cladding, a coaxial nozzle is usually applied. The following assumptions can be made: 1. The coaxial jet flow is treated as a steady-state turbulent flow with constant velocity distribution in the inlet boundary, and the powder concentration distribution per unit time in the stream is independent of time. 2. Only the powder blown into the melt pool is molten to clad on the substrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-32-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-32-1.png",
        "caption": "FIGURE 5-32 Method of metering fuel to injectors with in-line system. (Courtesy Robert Bosch GmbH.)",
        "texts": [
            " The three systems most commonly used on tractors are: 1. Individual or in-line injection pumps of the timed, metered type (figs. 5- 31 and 5-32) 2. The distributor system in which one injection pump serves all the injection nozzles by delivering a metered fuel charge at the correct instant through a distributor (fig. 5-33) 3. The unit injector system in which the fuel-injection pump is combined with the injection nozzle in one assembly on the cylinder head (fig. 5-36) The pumping principle of the in-line type is shown in figure 5-32. This pump is of the constant-stroke, lapped-plunger type and is operated by a cam. Fuel enters the pump from the supply system through the inlet con nection and fills the fuel sump surrounding the barrel. With the plunger at the bottom of the stroke, the fuel flows through the barrel ports, filling the space above the plunger and also the vertical slot cut in the plunger and the cutaway area below the plunger helix. As the plunger moves upward, the barrel ports are closed. As it continues to move upward, the fuel is discharged through the delivery valve into the high-pressure line to the injector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001020_s0039-9140(01)00377-0-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001020_s0039-9140(01)00377-0-Figure1-1.png",
        "caption": "Fig. 1. Exploded view of the disposable glucose sensor strip used in this work.",
        "texts": [
            " (Tokyo, Japan); hexamineruthenium (III) chloride from Aldrich (Milwakee, WI, USA); carbon paste (TU-15ST) and silver paste (LS-405) from Asahi Chemical Research Laboratory (Tokyo, Japan); insulator paste was from Seoul Chemical Research Laboratory (Shiheung, Korea); flexible polyester film from Korea 3M (Seoul, Korea); and nitrocellulose (NC) membranes from Whatman International Ltd.(Maidstone, England). All aqueous solutions were prepared with deionized water (18 M cm). The glucose stock solution was prepared and allowed to stand 24 h before use to allow equilibration between the and anomers. 2.3. Disposable strip sensors fabrication The strip-type electrodes on a polyester film were fabricated as illustrated in our previous report: briefly, as shown in Fig. 1, three lines of silver conductors (1\u00d720 mm), two square carbon electrode sites (2\u00d72 mm) on the top of the conductors, and a dielectric layer were screen printed sequentially exposing 2\u00d78 mm channel area. The Ag/AgCl reference electrode was formed by applying 0.3 M FeCl3 solution on the silver electrode. The carbon paste working electrodes were electrochemically activated in a saturated Na2CO3 solution at 1.2 V versus SCE for 5 min before assembling the whole strip. The enzyme solution was prepared by thoroughly mixing GOx, [Ru(NH3)6]3+, 0.5 wt.% CMC and 0.2 wt.% Triton X-100 in 0.1 M PBS, pH 7.4. The NC membrane (2 mm in width), which was washed in 10 v/v.% methanol for 5 min, deionized water for three times, and dried at room temperature, was dipped in the prepared cocktail solution for 5 min. It was then allowed to dry in a decicator at room temperature. The NC membrane which contains GOx/[Ru(NH3)6]3+ was placed on the electrodes exposed on the strip, and covered with another polyester film using double-side adhesive tape (Fig. 1). 2.4. Measurement of the sensor performance To characterize the electroanalytical properties of the assembled sensor system, standard solutions containing 11.1 mM glucose were applied at one edge of the reagent strip and equilibriated for 30 s before applying a given potential. Applied potentials were varied from \u22120.1 to +0.2 V, and the corresponding chronoamperometric responses to the [Ru(NH3)6]3+-meditated enzymatic glucose oxidation were recorded. Optimum applied potential (vs Ag/AgCl) that begins to result in near constant response was determined from the I-E curve (the anodic current values read at 30 s vs the applied voltage)",
            " The optimum working pH, and the enzyme and mediator compositions added to the reagent strip were determined by chronoamperometry as described in our previous report [24]. The current responses to 0\u20135 mM interfering substances, e.g. ascorbic acid, uric acid, acetaminophen, dopamine, salicylate and creatinine, were examined at a given potential. Calibration curves for glucose determination were acid and the reduction of hexamineruthenium (III) are not affected. The same type of CVs were observed with other interfering substances. 3.2. Optimization of electroanalytical performance for the sensor system As shown in Fig. 1, samples applied at one side of the glucose sensor are taken into the working electrode through the NC membrane while separating particulate and large molecules. The level of glucose in the sample is usually determined by chronoamperometric method. To find the optimum operating potential for the sensor, a series of chronoamperometric measurements for the 11.1 mM glucose sample was made and the change in currents at 30 s was recorded as a function of applied potential. In this experiment, we also examined the effect of dissolved oxygen on the catalytic current changes using the standard glucose samples bubbled with nitrogen, air and oxygen for 30 min (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001360_0003-2670(92)85134-r-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001360_0003-2670(92)85134-r-Figure2-1.png",
        "caption": "Fig 2 Schematic diagram of the \"dipstick\" electrode",
        "texts": [
            " Acta 269 (1992) 65-73 application to clinical measurement of alkaline phosphatase (ALP) in serum EXPERIMENTAL Most experiments were performed using a chloride-phosphate buffer (pH 74) containing 2 44 g NaH 2PO4 4H 20, 7 5 g Na2HPO4 , 3 0 g NaCl and 0 6 g EDTA per litre Na 2SO3 (6%, w/v) was added to prevent oxidation of catechol and hydrocaffeic acid solutions when the buffer pH was adjusted to alkaline conditions Other chemicals were of analytical-reagent grade For ALP assay, the buffer was 2-amino-2-methylpropanol (AMP) [9,10], based on the IFCC recommended method for ALP assay [9,10] For the interference voltammograms, the chloride-phosphate buffer was used Bovine intestinal ALP, type VII-S (E C 3131) was obtained from Sigma (Poole) 4-Aminophenyl phosphate was synthesized as described previously [9] Polycarbonate membranes of pore size 0 03 and 0 05 \u00b5m were obtained from Nuclepore (Pleasanton, CA) Cuprophan dialysis membranes were removed from a haemodialysis cartridge (Gambro, Lund, Sweden) Cellulose acetate membranes were prepared by dissolving 2 0 g of polymer (39 8% acetyl content) in 100 ml of acetone A 10-m1 volume of this solution was spread on a 5 X 5 cm2 glass plate and the plate was rotated manually for 2 min (ca 30 rpm) Membranes were left to dry at room temperature for 1 h Cellulose acetate was used with a covering polycarbonate membrane, pore size 0 03 \u00b5m Both polycarbonate alone and the cellulose acetate-polycarbonate membrane were evaluated in the amperometric cell Casting of PVC membranes A 10-ml volume of tetrahydrofuran (THF) (Fisons, Loughborough) was placed in a beaker and plasticizer added [8,11] The plasticizers used were dioctyl phthalate (DOP) and isopropyl myristate (IPM), in volumes of 50-300 \u00b5l A 0 06-g amount of PVC powder (MW 200000) (BDH, Poole) was added to the THF and plasticizer and the mixture stirred until the PVC had fully dissolved A 9-cm Petri dish was rinsed with THF, then the PVC solution (10 ml) was poured in and the lid replaced The dish was left at room temperature (20 \u00b1 2\u00b0C) for 2-3 days, until the THF had evaporated, leaving a film of PVC on the glass dish A 15 x 15 cm piece of the thin membrane (ca 0 05 mm) was cut out, overlaid with a matching dialysis membrane and the membrane pair lifted from the glass with a scapel blade PVC membranes could also be cast directly on dialysis membranes A piece of dialysis membrane was stuck to a sheet of paper with adhesive tape, further tape was stuck over the dialysis membrane to form a window (15 x 15 cm) A 15-\u00b5l volume of PVC solution (10 ml of THF, 0 06 g of PVC, 0 15 ml of IPM) was pipetted and spread on the dialysis membrane The tape window confined the solution to the desired area, and also prevented curling of the resulting membrane When dry, after evaporation of the THF, the membrane sandwich was cut within the window, allowing ready removal of the PVC-coated dialysis membrane The discrete PVC films could be peeled off the dialysis membranes, but normally the membranes were used in combination 5mm 1 PVC Tube Epoxy Rein AV Cathode Pt Anode Polyaerylamido gel PVC Coating Assembly of electrodes Composite membranes were used m an amper- ometnc cell designed for oxygen measurement (Rank, Bottisham, Cambridge) [5] This consisted of a platinum working electrode and a silver cathode functioning as a pseudo-reference electrode Before use the electrodes were polished with alumina powder, then conditioned by polarization at +0 65 V vs Ag, in phosphate buffer until a baseline was achieved To assemble the cell, the electrode was covered with a small volume of aqueous buffer and the membrane composite was placed on top In some instances this involved a combination of polycarbonate membrane overlying cellulose acetate, polycarbonate alone or a dialysis membrane alone For the PVC system, the final arrangement is as shown in Fig 1, the PVC being used in conjunction with the dialysis membrane The sample chamber and 0- ring were then mounted over the electrode, this served to stretch the membrane over the raised anode, and the locking ring was tightened The sample chamber was then rinsed and filled with any chosen solution Dipstick configuration sensor To avoid possible damage to the thin PVC membrane when the electrode was assembled, a \"dipstick\" configuration was also studied, whereby the PVC was cast directly over an in-house electrode (Fig 2) For this, a piece of platinum wire 1 mm diameter and 10 mm long was sol- 67 68 dered to one lead of a two-core coaxial cable The platinum and lead were covered in epoxy resin over a length of 30 mm from the tip A section of PVC tubing (Gallenkamp) of 2 5 mm i d was pushed over the platinum-epoxy resin, and resin was inserted to fill any air pockets, with adjustments made to position the platinum and lead fully within the epoxy After the epoxy resin had set, the PVC was removed leaving the platinum embedded in a cylinder of epoxy resin A silver wire, 0 5 mm diameter, looped around the end of the cast cylinder, served as the pseudo-reference electrode and was itself fixed in position with epoxy resin moulded to a PVC tube (6 5 mm id) A 25-mm length of 6 5 mm i d PVC tube was fitted over the epoxy resin so that it projected 0 5 mm beyond the end face of the electrode Polyacrylamide gelling solution [12] was prepared by mixing aqueous solutions of 30% acrylamide (electrophoresis grade) (300 \u00b5l), 2 6% N,N'methylenebisacrylamide (electrophoresis grade) (100 \u00b5l) and 2% N',N',N',N-tetraethylmethylenediamme (TEMED) (100 \u00b5l) and then adding 100 \u00b5l of 2 8% potassium peroxodisulphate solution After mixing, 10 \u00b5l were immediately spread on the end face of the upturned dipstick to form an electrolytic gel layer, and allowed to set for several hours A 40-\u00b51 volume of PVC solution containing 0 024 g of PVC and 0 06 ml of IPM in 15 ml of THF was then spread on top of the gel, ensuring film continuity with the PVC tubing After evaporation of the THF overnight and conditioning in phosphate buffer, the electrode was ready for use Measurements were made with the platinum anode polarized at + 0 65 V vs Ag after a 2-h conditioning period at this voltage in buffer A potentiostat, constructed by the School of Chemistry Workshops, University of Newcastle-upon Tyne, allowed polarization of the cell in the range + 12 to -12 V and continuous current measurements from 0 1 nA to 2 0 mA to be made via a strip-chart recorder (SE 120, Goertz-Metrawatt, Vienna) Generally, measurements were made by adding small volumes of stock buffered solutions to the assay buffer, changes in current output were I M Chnstre et a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003495_s00332-016-9294-9-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003495_s00332-016-9294-9-Figure5-1.png",
        "caption": "Fig. 5 Shell boundary loads: \u03d2, \u03d1 , and Q are the surface traction, the moment, and the shear, respectively. T denotes the outward in-plane normal",
        "texts": [
            "14c) 8 We denote by F\u2212A a the components of F\u22121, the inverse of F. See Appendix 7 for the details of the derivation of (4.13) and (4.14) following (4.7). where T is the outward in-plane vector field normal to the boundary \u2202H. Remark 4.2 Note that we canmodify the Lagrange\u2013d\u2019Alembert\u2019s principle in order to prescribe non-vanishing initial and boundary conditions on \u2202H. Let\u03d2 be the boundary surface traction, \u03d1 be the boundary moment, Q be the boundary shear, and V t0 be the initial velocity vector field (see Fig. 5). We write the Lagrange\u2013d\u2019Alembert\u2019s principle as \u03b4S(\u03d5, G, B) + \u222b t1 t0 \u222b H (FG :\u03b4G + FB :\u03b4B) dSdt + \u222b t1 t0 \u222b \u2202H ( J\u03d2agab\u03b4\u03d5 b + J\u03d1a\u03b4\u03d5n ,AF \u2212A a + JQ\u03b4\u03d5n ) dLdt + \u222b H \u03c1V t0 .\u03b4\u03d5t0dS = 0, and from (4.14) we have \u2202L \u2202\u03d5\u0307 \u2223\u2223\u2223\u2223 t=t0 = \u03c1V t0 , ( 2 \u2202L \u2202CAB Fc Agac + 2 \u2202L \u2202 AB Fc A\u03b2ac ) TB = Jgab\u03d2 b, [( \u2202L \u2202 AC Fb A ) |C F\u2212B b + ( \u2202L \u2202N ) b gabF\u2212B a ] TB = JQ, \u2202L \u2202 AB Fa ATB = J\u03d1a . We introduce the following surface tensors: Second Piola-Kirchhoff stress tensor: S = 2 \u2202W \u2202C , in components, SAB = 2 \u2202W \u2202CAB ; First Piola-Kirchhoff stress tensor: P = 2F \u2202W \u2202C , in components, PbB = 2 \u2202W \u2202CAB Fb A; Cauchy stress tensor: \u03c3 = 2 J F \u2202W \u2202C FT, in components, \u03c3 ab = 2 J \u2202W \u2202CAB Fa AF b B; Material couple-stress tensor: M = \u2202W \u2202 , in components, MAB = \u2202W \u2202 AB ; Two-point couple-stress tensor: M = F \u2202W \u2202 , in components, MbB = \u2202W \u2202 AB Fb A; Spatial couple-stress tensor: \u03bc = 1 J F \u2202W \u2202 FT, in components, \u03bcab = 1 J \u2202W \u2202 AB Fa AF b B "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002773_tpas.1966.291548-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002773_tpas.1966.291548-Figure13-1.png",
        "caption": "Fig. 13. Polar plot of total reference phase stator current as a function of slip. A, parallel configuration, V = 247; B, back-to-back configuration, V = 247, + = 162.3; C, parallel configuration, V= 220; D, back-to-back configuration, V = 247, + = 124.4; E, backto-back configuration, V = 247, 0 = 86.5; F, back-to-back configuration, V = 247, 4 = 48.6.",
        "texts": [
            " A polar plot of the individual stator currents with slip as variable and 4 as parameter is shown in Fig. 12. This is the measured counterpart of the theoretical results illustrated in Fig. 7 and shows that under some circumstances stator 128 FEBRUARY P 2 4' SMITH: TWIN STATOR INDUCTION MACHINE 1 can operate at leading power factor and also, as seen from Fig. 10, that stator 2 may deliver power to the supply. The total line current under the various conditions of operation is shown, plotted in polar form, in Fig. 13. Curve A shows the total line current as a function of slip for parallel operation of the machines fed with 247 volts and corresponds to the arc ABB' in Fig. 6, which is the locus of I1p/2. Curves B, D, E, and F (but not C) show the total line current as a function of slip for the back-to-back configurationwhen + = 162.3\u00b0, 124.4\u00b0, 86.5\u00b0, and 48.60, respectively, and correspond to the arc AEE' in Fig. 6, which is the locus of I1/2. Curve C in Fig. 13 is the locus of the total stator current for the parallel configuration when fed with a voltage of ./1 - cos 124.40 X 247 = 220 volts 2 and should be compared with curve D in Fig. 13. As shown in Fig. 8, the torque slip curves are practically identical for the two cases to which curves C and D correspond. Thus, curves C and D confirm the conclusion reached in the sec- 1966 129 IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS tion on \"Comparison of Power Factor.\" The dashed lines in Fig. 13 correspond to AB in Fig. 6. Measured Efficiency When arranged to give identical output power, the total input power in the back-to-back configuration, in terms of the total input power for the parallel configuration, is given by (33) Pin \u00b1P\u00b1in+ RS,2(I +cos 4)). When V8, = 247 volts and 4 = 124.4\u00b0, the term (R, IV,,12/ tZ I2) (1 + cos 4) = 5 watts for the machines under test. No significant difference was measured in the efficiency of the two cases. In practice, the difference would be somewhat greater than this because of the reduction in core losses associated with the reduced voltage applied to the parallel configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-16-1.png",
        "caption": "FIGURE 13-16 Conventional bevel gear dif ferential.",
        "texts": [
            " It is the preferred profile because constant rotational velocity is transmitted. Even though a perfect involute profile will transmit constant rotational ve locity, the machining and heat-treating processes will leave some profile errors that will result in impact stresses and noise. Figures 13-14 and 13-15 show some of the terminology used to describe involute gears. The kinematic details of gears are presented more completely by Mabie and Ocvirk (1975). Bevel Gears Bevel gears are used to connect shafts with intersecting axes (fig. 13-16). Usually the shafts intersect at right angles, but there are many bevel gear applications that require shaft angles greater or less than a right angle. The pitch surface of a bevel gear forms a cone. Several types of bevel gears are available. The straight bevel gear is the bevel gear equivalent of the spur gear, with load transferring abruptly from tooth to tooth. Therefore, straight bevel gears are noisy at high power and high speed. Spiral bevel gears have curved teeth that are angled like helical gear teeth so that the load is gradually transferred from tooth to tooth",
            " The number of teeth in the planet pinion is not important for assembly, as long as it will mesh properly with both the sun and the ring gear. Compound planetary gear systems are much more complex, except when the number of teeth in all the sun and ring gears is divisible by the number of planet pinions. Simple inspection will show that proper assembly will be obtained when this is the case. Other combinations may be available that will assemble properly, but the correct indexing of the planet gears must be found by trial methods, as described by Myers. Differentials A differential such as shown in figure 13-16 is necessary to allow tractors to be steered. The differential assembly normally includes a large spiral bevel gear that drives the differential housing and the small bevel gears. The torque driving the larger output bevel gears must be the same on each side to maintain the smaller bevel gears in static equilibrium. Thus, the output gears can rotate at any speed as required for turning but will deliver equal torque to both wheels. Note that when turning occurs, the power delivered to the wheels will not be equal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002650_tec.2012.2200898-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002650_tec.2012.2200898-Figure9-1.png",
        "caption": "Fig. 9. Prototype machine.",
        "texts": [
            " It should be noted that \u03b4\u2217 is a negative value, indicating generating mode and the phase angle of \u21c0 \u03c8s(k+1) lags behind that of \u21c0 \u03c8e(k+1) . In Fig. 8, the DTLC scheme employs SVPWM to achieve smooth and direct regulation of the instantaneous torque, which substitutes the hysteresis control of the DTC scheme. As can be seen, both the DTC and DTLC need the instantaneous torque information. To verify the improved estimation method, experimental tests have been carried out on a PHESF generator dc power system. Fig. 9 shows the prototype machine and the machine dimensions and parameters are shown in Table II. The phase currents ia , ib , ic are obtained by current sensors LA28-NP and phase voltages ua , ub , uc are acquired as follows [14]: ua = udc 3 (2DA \u2212 DB \u2212 DC ) ub = udc 3 (2DB \u2212 DA \u2212 DC ) uc = udc 3 (2DC \u2212 DA \u2212 DB ) (20) where DA , DB , and DC are the duty ratios of leg A, leg B, and leg C, respectively, and the dc bus voltage udc is acquired by a voltage sensor LV28-P. Fig. 10(a) and (b) shows the estimated stator flux linkages using the pure integrator and the improved estimation method, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001450_detc2006-99628-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001450_detc2006-99628-Figure3-1.png",
        "caption": "Fig. 3 3-R\u030b(RRR)ER\u030b parallel mechanism with both spherical and translational modes in (a) a general configuration in the translational mode, (b) a lockup\u2194translation configuration, (c) a lockup configuration, (d) a lockup\u2194rotation configuration, and (e) a general configuration in the spherical mode.",
        "texts": [
            " Since the wrench system of each leg varies with the change of its configuration, we make the assumption that such conditions are met as long as a 3-DOF parallel mechanism with both spherical and translational modes is composed of at least three legs with a 1- wrench-system listed in Table 4 with/without legs with a wrench system of order 0 (Fig. 2). The geometric constraints among legs of a parallel mechanism can be clearly shown in a configuration of the parallel mechanism in which all the legs with a 1-wrench-system are in their transitional configurations. The above configuration of the parallel mechanism is called (a) a lockup configuration [Fig. 3(c)] if the linear combination of all the leg-wrench systems is a 6-wrench-system, (b) a lockup\u2194translation configuration Copyright  2006 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Down Table 4 Legs for parallel mechanisms with both spherical and translational modes. ci Class No. Type 1 5R 1 R\u030bR\u030cR\u0300R\u0300R\u030b 2 R\u030bR\u0300R\u030cR\u0300R\u030b 3 R\u030bR\u0300R\u0300R\u030cR\u030b 4 R\u030bR\u0301R\u030cR\u0300R\u030b 5 R\u030bR\u0301R\u0300R\u030cR\u030b 6 R\u0301R\u030bR\u030cR\u0300R\u030b 7 R\u0301R\u030bR\u0300R\u030cR\u030b 8 R\u030bR\u030cR\u0300R\u0301R\u030b 9 R\u030bR\u0300R\u030cR\u0301R\u030b 10 R\u030bR\u030cR\u0300R\u030bR\u0301 11 R\u030bR\u0300R\u030cR\u030bR\u0301 12 R\u030b(RRR)ER\u030b 4R1P 13 R\u030bPR\u030cR\u0300R\u030b 14 R\u030bPR\u0300R\u030cR\u030b 15 PR\u030bR\u030cR\u0300R\u030b 16 PR\u030bR\u0300R\u030cR\u030b 17 R\u030bR\u030cR\u0300PR\u030b 18 R\u030bR\u0300R\u030cPR\u030b 19 R\u030bR\u030cR\u0300R\u030bP 20 R\u030bR\u0300R\u030cR\u030bP 21 R\u030bR\u030cR\u0301R\u030bP 22 R\u030bR\u030cR\u0301PR\u030b 23 R\u030bR\u030cPR\u0301R\u030b 24 R\u030bPR\u030cR\u0301R\u030b 25 PR\u030bR\u030cR\u0301R\u030b 26 R\u030bR\u0301R\u030cR\u030bP 27 R\u030bR\u0301R\u030cPR\u030b 28 R\u030bR\u0301PR\u030cR\u030b 29 R\u030bPR\u0301R\u030cR\u030b 30 PR\u030bR\u0301R\u030cR\u030b 31 R\u030b(RRP)ER\u030b 32 R\u030b(RPR)ER\u030b 33 R\u030b(PRR)ER\u030b 3R2P 34 R\u030bR\u030cPR\u030bP 35 R\u030bPR\u030cR\u030bP 36 R\u030bR\u030cPPR\u030b 37 R\u030bPR\u030cPR\u030b 38 PR\u030bR\u030cPR\u030b 39 R\u030bPPR\u030cR\u030b 40 PR\u030bPR\u030cR\u030b 41 R\u030b(RPP)ER\u030b 42 R\u030b(PRP)ER\u030b 43 R\u030b(PPR)ER\u030b 0 omitted omitted omitted 6 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 03/11/2018 T [Fig. 3(b)] if there are no more than two independent \u03b60 \u2014whose axes pass through the centre of rotation of the moving platform\u2014 in the linear combination of all the leg-wrench systems, or (c) a lockup\u2194rotation configuration [Fig. 3(d)] if there are no more than two independent \u03b6\u221e in the linear combination of all the leg-wrench systems. In the lockup configuration [Fig. 3(c)], the DOF of the moving platform of the parallel mechanism is 0. In the lockup configuration [Fig. 3(c)], lockup\u2194translation configuration [Fig. 3(b)], or lockup\u2194rotation configuration [Fig. 3(d)], each leg can rotate about the axes of its R\u030b joints. Let us take the 3-R\u030b(RRR)ER\u030b parallel mechanism with both spherical and translational modes shown in Fig. 2(a) as an example. In the lockup\u2194translation configuration shown in Fig. 3(b), the axes of the second joints of all the legs are parallel to a plane. The axis of the \u03b60 of each leg is in fact parallel to the axis of the second joint within the same leg. Thus, there are two indepen- Copyright  2006 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Dow 7 Copyright  2006 by ASME nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 03/11/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use Dow dent \u03b60 in the linear combination of all the leg-wrench systems. In this configuration, the moving platform can translate along a direction which is perpendicular to the above plane. In the lockup\u2194spherical configuration shown in Fig. 3(d), three vectors, each perpendicular to the axes of the first two joints within a same leg, associated with all the legs are parallel to a plane. The direction of the \u03b6\u221e of each leg is in fact parallel to the above vector. Thus, there are two independent \u03b6\u221e in the linear combination of all the leg-wrench systems. In this configuration, the moving platform can rotate about an axis that is perpendicular to the above plane. In the lockup configuration shown in Fig. 3(c), the wrench system of each leg is a 2-wrench-system instead of a 1-wrench-system in a regular configuration. The base of the wrench system of each leg is composed of (a) a \u03b6\u221e whose direction is perpendicular to the axes of the first two joints within a same leg and (b) a \u03b60 whose axis is parallel to the axis of the second joint within the same leg. It is noted that neither the set of directions of the three \u03b6\u221e nor the set of axes of the three \u03b60 is parallel to one common plane. Thus, the linear combination of all the leg-wrench systems is a 6-wrench-system, and the DOF of the moving platform is 0 in such a configuration. For a parallel mechanism with both spherical and translational modes to change from the translational mode [Fig. 3(a)] to the spherical mode [Fig. 3(e)], it must go through a lockup\u2194translation configuration [Fig. 3(b)], the lockup configurations [Fig. 3(c)], and a lockup\u2194rotation configuration [Fig. 3(d)] in sequence. For the parallel mechanism to change from the spherical mode [Fig. 3(e)] to the translational mode [Fig. 3(a)], it must go through a lockup\u2194rotation configuration [Fig. 3(d)], the lockup configurations [Fig. 3(c)], and a lockup\u2194translation configuration [Fig. 3(b)] in sequence. The axes of the two R\u030b joints within a leg, which are coaxial in a transitional configuration, are parallel to each other if the parallel mechanism works in the translational mode or intersect each other at the centre of rotation of the moving platform if the parallel mechanism works in the spherical mode. By assembling the legs listed in Table 4, their variations, and legs with a wrench system of order 0, a large number of parallel mechanisms with both spherical and translational modes such as the two parallel mechanism shown in Fig",
            " According to the validity condition for actuated joints of translational parallel mechanisms [19] and spherical parallel mechanisms [8], one can find that the three joints located on the base can be used as actuated joints in both the translational mode [Fig. 4(a)] and the spherical mode [Fig. 4(b)] of the 3- R\u030b(RRR)ER\u030b parallel mechanism. However, these three actuated joints are not sufficient to change the parallel mechanism from one operation mode to another since they cannot fully control the motion of the moving platform in the lockup\u2194translation configuration [Fig. 3(b)] or the lockup\u2194rotation configuration 8 nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 03/11/2018 T [Fig. 3(d)]. In order to change operation modes, four joints, including the three joints located on the base and the second joint in one of the legs, should be actuated [Figs. 4(c) and 4(d)]. It is noted that the DYMO proposed in [2,3] is a specific case of the 3-R\u030b(RRR)ER\u030b parallel mechanism with both spherical and translational modes (Figs. 2(a) and 3). In DYMO, it is further required that (a) the axes of the R joints denoted by (RRR)E are perpendicular to the axes of the R\u030b joints within a same leg, and (b) the axes of the R joints on the moving platform are coplanar"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002427_iros.2011.6095091-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002427_iros.2011.6095091-Figure6-1.png",
        "caption": "Fig. 6. Standing strategy.",
        "texts": [
            " Another disadvantage is that the air compressor can\u2019t be built into the robot because of its big size. A pneumatically actuated robot is difficult to control in standing posture because of the compliance and nonlinearity of the actuators. We developed a control method for the pneumatic system and conducted a standing control experiment to evaluate the performance of the robot. Before explaining the control law, we describe human standing control. There are three human standing strategies: ankle strategy, hip strategy, and stepping strategy (Fig. 6). Ankle strategy and hip strategy, in particular, are performed not only individually but also in combination [13]. Of these three strategies, we selected only ankle strategies this time for simplicity. The ankle strategy is a basic strategy for static standing. In the static standing posture, there is a hypothesis that the central nervous system does not work as a linear PD controller but intervenes in an intermittent or on-off way, and it keeps the state of the system in a bounded region around the equilibrium, remaining in asymptotic instability [14]",
            " This musculoskeletal robot can use its whole body to perform static balancing and its powerful pneumatic actuators for dynamic tasks such as dynamic walking. For the standing experiment, we have developed a control method for pneumatic artificial muscles, mimicking the human standing control to some extent. For the walking experiment, we utilized human muscle activation patterns to take advantage of the highly-similar musculoskeletal body structure and performed dynamic walking making the robot take a few steps. For future work, we will apply the other standing strategies, hip strategy and stepping strategy, to the robot as shown in Fig. 6. We will also develop an integrated strategy for them with the aim to realize more stable standing. Furthermore, we have to develop a feedback control method for more stable walking. We aim to realize multimodal locomotion and investigate the human musculoskeletal system using this robot. [1] J.van Soest and Maarten F.Bobert. The contribution of muscle properties in the control of exprosive movements. Biological Cybernetics, 69:195\u2013204, 1993. [2] M. Kumamoto, T. Oshima, and T. Yamamoto. Control properties induced by the existence of antagonistic pairs of bi-articular muscles\u2013 mechanical engineering model analyses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000901_irds.2002.1041594-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000901_irds.2002.1041594-Figure1-1.png",
        "caption": "Figure 1: Kinematic and dynamic parameters of Bicycle",
        "texts": [
            " In the computer simulation, we also adopt a low pass filter in the control loop which can reduce the chattering problem without loosing the stability property. This checking is important for the implementation of the proposed control strategy to real system. 0-7803-7398-7/02/$17.00 02002 IEEE 2200 2 Unmanned Elec t r i c Bicycle In this section, we consider the kinematic and dynamic model of electric bicycle which has the load mass balance mechanism which plays important role in controlling the direction of bicycle. 2.1 Kinematic and Dynamic Models A bicycle is depicted in Fig. 1. The main problem discussed in this paper is to find the control strategy for controlling the load mass, steering angle and driving wheel speed which makes bicycle go forward without falling down. The geometric view of the bicycle model is shown in Fig. 2. Let pf denote the center point of the steering front wheel and p, the center point of the driving rear wheel. Let L be the distance between pf and p,. We assume that the mass center of bicycle is located in the middle b e tween center points of the steering and the driving rear wheel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001602_421-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001602_421-Figure1-1.png",
        "caption": "Figure 1. Sketch of the interaction between two filaments, a cross-link and a molecular motor. After the interaction, the motor (shown as a red sphere moving in the direction of the red arrow) aligns the filaments along the bisector n\u0304, but the midpoint positions do not coincide due to the cross-link (blue sphere).",
        "texts": [
            " Near the threshold of the orientation instability mentioned above, \u03c1 & \u03c1c, the master equation can be systematically reduced to equations for the coarse-grained local density of filaments \u03c1 and the coarse-grained local orientation \u03c4 \u03c1 = \u222b \u03c0 \u2212\u03c0 P(r, \u03c6, t) d\u03c6 , \u03c4 = \u3008n\u3009 = 1 2\u03c0 \u222b n P(r, \u03c6, t) d\u03c6, (13) by means of a bifurcation analysis. The effect of cross-links on the motor-induced interaction of filaments is twofold. Firstly, the simultaneous action of a static cross-link, serving as a hinge, and a motor moving along both filaments results in a fast and complete alignment of the filaments, as shown in figure 1. This justifies the assumption of fully inelastic collisions for the rods\u2019 interaction. Note that without cross-links the overall change in the relative orientation of the filaments is much smaller: the angle between filaments decreases only by 25\u201330% in average, see the discussion in [19]. Complete alignment also can occur for the case of simultaneous action of two motors moving in opposite direction, as in experiments on kinesin\u2013NCD mixtures reported in [12]6, and even for two motors of the same type moving in the same direction but with a different speed due to variability of the properties and the stochastic character of the motion",
            " As we have verified, this simplified approximation did not change the results on a qualitative level, affecting only numerical prefactors of some nonlinear terms. 6 In these experiments, multimeric motor complexes have been prepared from kinesin (a plus-end directed motor) and NCD (a minus-end directed motor), see [12] for details. New Journal of Physics 9 (2007) 421 (http://www.njp.org/) presence of a cross-link the midpoints of the rods will not coincide after the interaction. In fact, the distances S1,2 from the midpoints to the cross-link point do not change, as it is shown in figure 1. To describe the interaction rules in the presence of a cross-link, we express the radiusvector of an arbitrary point on a filament Ri via the position of its midpoint ri , the filament orientation ni , and the distance from the center of mass S, Ri = ni Si + ri . The intersection point of two rods is given by the condition R\u2217 = R1 = R2, which fixes the values of S1,2 to S1,2 = (r2 \u2212 r1)\u00d7n2,1 n1 \u00d7n2 . (14) Due to the cross-link, the values of S1,2 do not change during the interaction. Since the filaments become oriented along the bisector direction n\u0304, the distance of the two filament midpoints from the total center of mass will be 1S = (S1 \u2212 S2)",
            " Thus in the experiments, even if without cross-links the motor density was not high enough to trigger the orientation transition, due to the cross-linking by ATP-depleted motors the system is likely driven beyond the threshold of orientation transition. Moreover, the oriented state is typically unstable with respect to a transverse instability leading to bundle formation, implying that bundles are competing with aster-like structures as the experimental pictures suggest. We have shown that a small amount of cross-links (in the order of one crosslink per filament pair) can be easily included in the microscopic theory based on instantaneous collisions [17], see the sketch in figure 1. Another microscopic theory, based on phenomenological motor-induced active currents, has been proposed earlier [15]. However, the implementation of cross-links in the active currents is less obvious than in the collision rules equation (16). For higher filament/cross-link densities than can be captured by a binary interaction approach, either the phenomenological active gel theory introduced in [16] or statistical models [6, 8, 22] should be used. While pattern formation can be studied also in the framework of the active gel theory, the statistical models are focused on the viscoelastic properties, and so far have not been used to address patterns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000968_3516.868924-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000968_3516.868924-Figure8-1.png",
        "caption": "Fig. 8. Backlash nonlinearity N .",
        "texts": [
            " It usually slows down systems and can cause the limit cycle instability. Therefore, it is desirable to suppress the adverse effect of backlash in systems. In our second example, we show that a disturbance observer can suppress limit cycles caused by backlash. Consider an inverted pendulum driven by a motor and gear system, where the gears have backlash. A simplified model of an inverted pendulum can be represented by P (s) = 1 s2 1 : (12) Let the gear backlash, denoted by N , be that shown in Fig. 8. Clearly, the graph of N lies in the region between or on two parallel lines G+(u) = u + 0:5 and G (u) = u 0:5 for all u 2 . Hence, N can be decomposed as (1), where the transfer function of the linear part is H(s) = 1 and is a nonlinearity whose output d is bounded by 0.5. Therefore, the nonlinear system S(N; P ) can be represented S(H; P ), and S(N; P ; DOB), denoted by y , y , and y , respectively, in the absence of measurement noise . It is evident that y and y overlap and converge to zero. That is, the disturbance observer has suppressed the limit cycles caused by the backlash"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001310_tmag.2004.832157-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001310_tmag.2004.832157-Figure1-1.png",
        "caption": "Fig. 1. Schematic of moving-magnet linear actuator with cylindrical Halbach array.",
        "texts": [
            " Manuscript received October 15, 2003. This work was supported by the MOCIE under a grant from the IERC program, Korea. S.-M. Jang, J.-Y. Choi, H.-W. Cho, and W.-B. Jang are with the Department of Electrical Engineering, Chungnam National University, Daejeon 305-764, Korea (e-mail: smjang@cnu.ac.kr; aramis76@cnu.ac.kr; hwcho@cnu.ac.kr; wbjang@hanmail.net). S.-H. Lee is with the LG Digital Appliance Laboratory, Seoul, Korea (e-mail: iemechas@lge.com). Digital Object Identifier 10.1109/TMAG.2004.832157 Fig. 1 shows the schematic of moving-magnet linear actuator. It consists of the permanent magnet (PM) as a mover, a coil-wrapped hollow bobbin, and an iron core as a pathway for magnet flux. Fig. 2 shows the two regions analytical model of moving-magnet linear actuator sketched in Fig. 1. This paper assumes that the stator current flows through an extremely thin sheet on the inner surface of the stator, at , and both iron permeability and actuator length are infinite. Since there is no free current in the magnet region, . So, . The magnetic vector potential is defined as . By the geometry of the tubular structure, the vector potential has only -components [3]. Therefore, The Poisson\u2019s equation, in terms of the Coulomb gauge, , is given by (1) 0018-9464/04$20.00 \u00a9 2004 IEEE where denotes the free space permeability, is the spatial wavenumber of the harmonic, and is the pole pitch of the actuator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003154_s11071-013-1125-z-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003154_s11071-013-1125-z-Figure1-1.png",
        "caption": "Fig. 1 (a) Bevel gear FE model, (b) detail of the groove",
        "texts": [
            " By means of the proposed contact element, the static normal preload pressing the damper to the gear is no more computed with a preliminary static analysis as in [8], where the classical uncoupled formulation [15] of the contact element was used, but it is the result of a coupled static/dynamic analysis of the vibrating assembly in the frequency domain with the HBM. The method is applied to a test case, where the forced response of a bevel gear is calculated, and the effect of the principal design parameters of the ring damper that affect the dynamics of the gear is also highlighted. The dynamic system that includes friction contacts is usually the assembly of two or more substructures, which are modeled by FEM. In this paper, the primary structure is the gear, shown in Fig. 1a, made of NS identical sectors, while the secondary structure is the ring damper (Fig. 2), characterized by a circular shape and by a cut along its axial direction, performed to insert it into the rectangular groove located under the rim of the gear and shown in Fig. 1b. The gear is a cyclic symmetric structure, and its mode shapes (Fig. 3) have special features: \u2013 The modal amplitudes of points located at the same relative position of different sectors have a harmonic distribution along the hoop direction and form an integer number of waves along that direction. \u2013 For this reason, mode shapes can be grouped according to the number of nodal diameters nd, i.e., nodal lines crossing the axis of rotation where the modal displacement is null. Also, nodal circles are a common feature of modes of cyclic symmetry structures; in this case, the nodal line is a circle centered on the axis of rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002791_0954406211404853-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002791_0954406211404853-Figure9-1.png",
        "caption": "Fig. 9 The diagram of two-stage planetary gearboxes",
        "texts": [
            " Its main components include one 20-HP drive motor, one stage bevel gearbox, two stages of planetary gearboxes, two stages of speed-up gearboxes, and one 40-HP load motor. Table 5 lists the number of teeth and the speed ratio achieved by each gearbox. The two-stage planetary gearboxes are our study object. There are four accelerometers located on the housing of the two-stage planetary gearboxes including two identical low sensitivity accelerometers (LS1 and LS2) and two identical high sensitivity accelerometers (HS1 and HS2), as shown in Fig. 8. Figure 9 provides a schematic diagram for the structures of the planetary gearboxes. The experiments were conducted using planet gears with different degrees of pitting damage. The pitting damage was artificially created on one planet gear of the second stage planetary gearbox. To mimic the pits observed on actual pitted gears, circular holes were created along the pitch line of the gear tooth surface. The number of holes was varied for different degrees of damage. Four damage degrees were considered: baseline, slight, moderate, and severe"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003385_12.2010577-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003385_12.2010577-Figure4-1.png",
        "caption": "Figure 4. Examples of incorrect positionings of the prototype on the building platform.",
        "texts": [
            " However, this is possible only theoretically given the fact that the prototype needs additional elements to be supported during the building process. Therefore, positioning should be decided in a proper way so that the supports do not affect the surface finishing condition on key areas of the blade, as well as do not result in a complex removal which may damage the part. A wide user experience is vital at this stage of the study, since any rapid prototyping tool is not able to evaluate an optimal positioning taking all the above issues into account. In particular, as an example, incorrect positionings are shown in Figure 4. Supports are in light grey while the prototype is in dark grey. In the first case (left), the airfoil is fully hidden being it completely embedded within the support, which is needed to build the platform and would hamper a proper removal; it also results in a longer processing time due to the fact that additional powder has to be sintered to create the support itself. In the second case (right), a support would be necessary inside and along the airfoil so affecting a key surface of the element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000932_027836499701600206-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000932_027836499701600206-Figure3-1.png",
        "caption": "Fig. 3. A 3-DOF manipulator.",
        "texts": [
            " The unit vector n, which is orthogonal to those vectors, is For a small perturbation 0e about the point qo and along the normal h(qO), the coordinates of the perturbed point are For the perturbed point to exist inside the workspace, it must satisfy eq. (3), subject to inequality constraints of eq. (6). Thus, a solution is sought to the following system of equations: The subsurface ~i(q) is an internal surface if and only if there exists a solution for eq. (44) for both perturbations ::i:8\u00a3, consistent with the equalities of eq. (45). 3. A General 3-DOF Mechanism To illustrate the foregoing analysis, consider the threedegree-of-freedom manipulator depicted in Fig. 3 which has three revolute joints. The boundary surfaces to the workspace generated by the point Ox,, = [ 0 0 0 ]T will be studied. 3.1. Determining First-Order Singularities For this manipulator, the three homogeneous transformation matrices using the Denavit-Hartenberg representation of joints 1, 2, and 3 are where ql , q2, and q3 are the generalized variables representing joint displacements. at LAKEHEAD UNIV on March 18, 2015ijr.sagepub.comDownloaded from 204 Multiplying the matrices 1-13 i=l iT2,_ and extracting the (3 x 3) rotation matrix yields The position vector is For a general point x = x y z ]T , the equation of constraint, eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000676_robot.1997.620040-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000676_robot.1997.620040-Figure2-1.png",
        "caption": "Fig. 2 Zero Moment Point (ZMP)",
        "texts": [
            " This structure is strong against falling down of the robot and it looks smart and more similar to human. 3 Conditions for Continuous Walking In this section, we consider the conditions for stable walking. Biped locomotion robots must be controlled under the possibility of falling down. Therefore the reference trajectory of biped locomotion robots must be generated without falling down. We must consider many kinds of conditions for Continuous walking without falling down as follows; 0 Conditions of Zero Moment Point (ZMP) The moment is generated by the floor reac- tion force and torque. Figure 2 shows the concept of Zero Moment Point, where p is the point that T, = 0 and Ty = 0 , T,,T, represent the moments around x axis and y axis generated by reaction force F,. and reaction torque T,. respectively. The point p is defined as the Zero Moment Point(ZMP). When the ZMP exists within the domain of the support surface, the contact between the ground and the support leg is stable. where pzmp denotes a position of ZMP. S denotes a domain of the support surface. This condition indicates that, no rotation around the edges of the foot occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001598_j.ijmecsci.2006.06.013-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001598_j.ijmecsci.2006.06.013-Figure1-1.png",
        "caption": "Fig. 1. Gear set and line of contact in reference position.",
        "texts": [
            " Results of the maximum contact stress are compared and contrasted with those obtained by the analytical model. Section 4 presents the experimental work by using the photoelasticity techniques with a prototype of the gear set. Results are compared with those obtained through the analytical model. Finally, conclusions for the contact problem are then discussed. Essentially, an internal gear pump type gerotor consists of a pair of gear: an inner rotor with external teeth called inner/internal gear and an outer ring with internal teeth called outer/external gear (Fig. 1). The two gears are mated Nomenclature Latin symbols a contact band distance cv volumetric capacity d normal distance to contact force e eccentricity F contact force per unit length G radius of circle to complete external gear H gear thickness I instantaneous centre of relative motion m distance IPs (Fig. 1) O gear centre r pitch circles P fluid pressure Ps singular point centre of the arc radius S Pk contact point k \u00bc 1, 2,y,Z Qk centre of curvature Qs specific flow R2 distance O2Ps (Fig. 1) S arc radius of the external gear tooth Vk volume of a generic chamber xpc, ypc coordinates of the contact point x, y coordinates of the gear profile X, Y absolute reference Z, (Z 1) number of external, internal teeth Greek symbols apc angle of the contact point ag angle of generation dQ irregularity flow index f pressure angle g tangent to the contact point l contraction index r vector ray u equidistant index o angle of rotation c rotation of external gear relative to internal gear Subscripts 1 i inner/internal gear 2 e outer/external gear A,B contact points dividing low and high-pressure (Fig. 1) k generic contact point pc contact point P.J. Gamez-Montero et al. / International Journal of Mechanical Sciences 48 (2006) 1471\u201314801472 so that each tooth of the internal gear is always in sliding contact with the external gear, which are known as contact points. The external gear has Z teeth, one tooth more than the internal gear and then, there are Z contact points. The idea underlying this method based on Colbourne\u2019s theory is to equalize the hydraulic and stress moments, and thus, the first goal is to calculate the positions of each contact point",
            " Therefore, it puts forward to introduce another methodology to estimate the line of contact and gear geometry in the present analytical model. It was Nervegna et al. [2,3] who defined the line of contact, xpc apc \u00bc R2 cos apc S m R2 cos apc r2 , ypc apc \u00bc R2 sin apc S m R2 sin apc , m \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r22 \u00fe R2 2 2r2R2 cos apc q , \u00f01\u00de where the sign is taken negative for the reference position of Fig. 1. Internal gear contains all the contact points during a complete rotation of the gear set, so the line of contact describes its profile xi(agi), yi(agi) \u00bc f(R2,S, e,Z 1), which is in turn the function of four geometrical parameters. To determine the external gear, its profile must be determined geometrically by parts xe(age),ye(age) \u00bc f(R2,S,G,Z), which is in turn the function of four geometrical parameters. Both profiles are shown in the reference, set forth in Fig. 1. For any other position of the gear set, profiles can be generated by the applying rotation equation, xr;j\u00f0oj\u00de \u00bc xj agj cos oj yj agj sin oj, yr;j\u00f0oj\u00de \u00bc xj agj cos oj \u00fe yj agj sin oj, \u00f02\u00de where j \u00bc i for the internal gear and j \u00bc e for the external gear [4]. Fig. 2 shows a kinematic inversion in which the entire system has been given a counter clockwise rotation of (Z 1)c, where c is the counter clockwise rotation of the external gear relative to the internal gear. Once the coordinates of the contact points are known at any position of the gear set, the idea behind this method is to bring all the contact points to the first quadrant of the external gear reference through a kinematic inversion",
            " Thus, when a couple is applied to the internal gear, it will rotate a small amount about its axis, until the tooth deformations are large enough to provide forces whose combined moments about O2 are equal to the stress moment on the external gear. A small rotation of Doi is given to the internal gear and the penetration Dv caused in each tooth is calculated. Hence, Hertz\u2019s equations are used to find the contact stress forces, and with an iterative procedure the maximum contact stress is given by syy max \u00bc 2F pa . (4) The chamber volume reaches either maximum or minimum values when it is symmetrical over the X-axis. Two contact points, A and B of Fig. 1, form the seals that separate the high-pressure fluid of the outlet port and low-pressure fluid of the inlet port. Thus, once all coordinates of the contact points are known, the Energetic method can be used (Table 2) to calculate the fluid moment on the external gear about O2. The force caused by the fluid pressure will have components PDY and PDX, and it acts through the midpoint of the line joining the two contact points. A specific unit of gerotor pump has been studied in this work. The trochoidal-gear set is named PZ9e285 and its geometrical parameters are presented in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003219_1350650114557710-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003219_1350650114557710-Figure4-1.png",
        "caption": "Figure 4. Scheme of the increased cage pocket clearance by 4% tangential elongation.",
        "texts": [
            " Tribofilm properties greatly depend on the nature of the rolling surfaces (grain boundaries, microdents, thermal stress, energy, etc.)41 and on lubricant formulation, as, for example, excessive amounts of detergents could partially inhibit tribofilm formation.10,58 Moreover, lubrication regimes highly influence tribofilm tribochemical wear and structure, therefore affecting the effectiveness of the chemical barrier against hydrogen permeation. To illustrate this point, the fore-detailed ACBB tests have been also conducted using two types of cages: the standard design and an increased pocket clearance design (Figure 4) to avoid excessive friction and scrapping of the balls on the cage bridges. While WECs have been reproduced on all IR for the standard cage design (Table 1), reproducibility rate was lowered to 50% for the increased pocket clearance. SEM EDX analyses have been performed, after the fore-detailed cleaning procedure, along the contact ellipse major axis: typical tribofilm characterizations corresponding to the two types of cages are presented in Figure 5. It can be observed that no tribofilm is detected for the standard cage design presenting a high WEC reproduction rate (Figure 5(a)), while heterogeneous and irregularly stripped tribofilm (Figure 5(b) to (d)) has been formed for the modified cage design at the contact center, probably because, as they might be less scrapped of by cage bridges,36 more lubricant additives remain available in the contact area to form tribofilm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000786_1.1518501-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000786_1.1518501-Figure4-1.png",
        "caption": "Fig. 4 Ruled hyperboloidal pitch surface with instantaneous generator $pi and tangent to tooth surface Sci \u201ealso perpendicular to null plane\u2026. The spiral angle c is defined such that the tooth surface normal is reciprocal to the ISA \u201eregardless of pressure angle\u2026.",
        "texts": [
            " The use of axodes as reference surfaces for the specification of gear teeth can result in nonpractical dimensions of gear teeth necessary for power transmission ~e.g., hypoid, spiroid\u2122, and worm gearing!. Further, the use of axodes limits the gear teeth to \u2018\u2018spur\u2019\u2019 type gear teeth. The orientation of the gear tooth on the hyperboloidal pitch surface must be specified to ensure reciprocity or that the desired gear ratio is maintained. A relationship is developed between the tooth surface normal ~i.e., the line of action! and the displacements of the input and output gear elements as parameterized using a system of cylindroidal coordinates. Shown in Fig. 4 is a segment of a hyperboloidal pitch surface. Illustrated in Fig. 4 is an instantaneous generator $pi of the pitch surface, a tooth spiral, and the corresponding spiral angle c. Fig. 5 provides an enlarged view of a gear tooth relative to the hyperboloidal pitch surface. The spiral angle at a given point between two hyperboloidal pitch surfaces in mesh is obtained by specifying that the tooth contact normal $ l is reciprocal to the instantaneous twist $is for any pressure angle. The independence of pressure angle from spiral angle is explained in terms of the linear line complex defined by the instantaneous twist $is ~see @22#"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001123_152091504773731375-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001123_152091504773731375-Figure1-1.png",
        "caption": "FIG. 1. Schematic of fluorescence generation by NIR fluorescence sensor. A: In the absence of glucose, the binding of dextran to immobilized ConA results in a close proximity of the donor and quencher dyes conjugated to the respective macromolecules, and fluorescence emission of the donor dye is quenched because of FRET. B: In the presence of glucose, dextran is competitively displaced from ConA binding sites, resulting in an increase in donor dye fluorescence.",
        "texts": [
            " The sensor combines a fluorescence resonance energy transfer (FRET)-based assay with immobilized ConA for fast signal generation, and a glucose-insensitive reference dye for signal independence from optical interference like variations in light source intensity or skin matrix effects. FRET, a process in which dipole\u2013dipole type interac- tions between donor and acceptor dyes result in attenuation of the donor dye fluorescence when both dyes are in close proximity (20\u201370 \u00c5),32 is represented schematically in Figure 1. To demonstrate the feasibility of the FRETbased sensing scheme, we prepared a hollow fiber-based sensor capsule made of regenerated cellulose (o.d. 210 mm, membrane thickness 20 mm), which consisted of three sensor fibers filled with a suspension of QSY21\u2122 ConASepharose and Alexa Fluor\u00ae 647 (both from Molecular Probes, Eugene, OR) dextran, and two fibers containing the reference dye LD800 (Molecular Probes) embedded in polysulfone (see Fig. 2). This combination of fibers generated adequate fluorescence yield with an optimal emission peak ratio (675 nm vs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001909_cjoc.200790183-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001909_cjoc.200790183-Figure1-1.png",
        "caption": "Figure 1 Schematic diagram of HPLC-CL system. A: mobile phase, B: K3Fe(CN)6, C: luminol, P1: high pressure pump, P2: peristaltic pump, S: sample, V: injection valve, E: chromatographic column, F: flow cell, W: waste, D: detector, PC: personal computer.",
        "texts": [
            " Working solutions were made by dilution of these stock solutions. A 0.01 mol/L luminol solution was prepared by dissolving 1.772 g of luminol in 1 L of 0.01 mol/L NaOH solution and a NaHCO3-NaOH mixture solution was used to dilute it to the corresponding concentration. Other solutions were K3Fe(CN)6 (1.0\u00d710\uff0d2 mol/L), potassium hydrogen phthalate (0.01 mo/L) and methanol (HPLC grade, B&J USA). The serum sample was from a patient provided by the hospital of Southwest Normal University. The flow system used in this work is shown in Figure 1. PTFE tubing of 0.8 mm i.d. was used to connect all components in the flow system. A peristaltic pump was used to deliver the chemiluminescence reagents at a flow rate of 2 mL/min on each flow line. The eluent carrying sample was delivered by a high pressure pump of a D-7000 HPLC (Hitachi, Japan). The volume of the sample loop was 20 \u00b5L. The CL signal was transformed into an electrical signal by an photomultiplier tube and then recorded with an MCFL-A multifunctional chemiluminescence/biochemiluminescence analytic system (Ruimai Electron Science and Technology Ltd., Xi\u2019an). An ultrafilter tube (VIVASPIN 100 \u00b5L) was employed to remove large molecules in the serum samples. The schematic diagram of HPLC-CL system was showed in Figure 1. Flow lines were inserted into the luminol solution, K3Fe(CN)3 solution and the eluent respectively. The pumps were started to wash the whole system until a stable baseline was recorded. Then the standard solution or sample was injected through the injection valve of the HPLC, and was carried by the eluent into the column. As having different retention time, E, NA and DA were separated and after being mixed with the CL reagent in the spiral flow cell, each of them produced different CL signal peak"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001259_j.talanta.2003.08.023-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001259_j.talanta.2003.08.023-Figure2-1.png",
        "caption": "Fig. 2. Absorption spectra of the mixture of DAB and NB with 0.20 g ml\u22121 hydrazine at 5 min after mixing in: (1) neutral media at room temperature, (2) neutral media at 75 \u25e6C, (3) 0.016 M HCl at 75 \u25e6C, (4) 0.016 M HCl at room temperature; and with 5 g ml\u22121 phenylhydrazine in: (5) 0.016 M HCl at room temperature, (6) neutral media at room temperature, (7) 0.016 M HCl at 75 \u25e6C and (8) neutral media at 75 \u25e6C.",
        "texts": [
            " Condensation of DAB with hydrazine and NB with phenylhydrazine affording azine and phenylhydrazone products, respectively, proceed according to stoichiometric equations given below: (1) (2) SDS micellar media strongly enhance the rate and equilibrium constants of the above reactions [7]. The absorption spectra of produced azine and phenylhydrazone is shown in Fig. 1. As Fig. 1 shows, the spectra of the azine and phenylhydrazone overlap, and each compound interferes in the spectrophtometric determination of another one. But the system is suitable for simultaneous determination of hydrazine and phenylhydrazine using HPSAM. It was observed that the rate of the reactions of hydrazine and phenylhydrazine with DAB and NB were different in each condition. Fig. 2 shows the absorption spectra of products of the reaction of hydrazine and phenylhydrazine with a mixture of DAB and NB in different conditions. The reaction of phenylhydrazine with NB was completed after 5 min in neutral media at 75 \u25e6C, while the reaction of hydrazine with NB was very slow. But the reaction of hydrazine with DAB was very fast and completed by 5 min in acidic media at room temperature while the reaction of phenylhydrazine with NB was very slow. To take full advantages of the procedure, the reagent concentrations and reaction conditions must be optimized"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001491_1.1876437-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001491_1.1876437-Figure4-1.png",
        "caption": "Fig. 4 Relations between the hob cutter and cutting blade coordinate systems. \u201ea\u2026 Relationship between coordinate systems Sc and Sf . \u201eb\u2026 Relationship between coordinate systems S1 and Sf .",
        "texts": [
            " In Fig. 3 c , the symbols ro, r1, and rf represent the outside radius, pitch ra- dius, and root radius of the ZN type-worm hob cutter, respec- SEPTEMBER 2005, Vol. 127 / 983 hx?url=/data/journals/jmdedb/27813/ on 03/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F tively. The cutting blade width bn equals the normal groove width of the hob cutter. Then, the design parameter rt can be obtained from Figs. 3 c and 3 d as follows: rt = r1 2 \u2212 bn 2 4 sin2 \u2212 bn 2 tan n . 7 Figure 4 shows the relations among coordinate systems Sc Xc ,Yc ,Zc , S1 X1 ,Y1 ,Z1 , and Sf Xf ,Y f ,Zf , where coordinate system Sc is the blade coordinate system, coordinate system S1 is rigidly connected to the hob cutter\u2019s surface, and coordinate system Sf is the reference coordinate system. Axes Zc and Zf form an angle that is equal to the lead angle on the worm pitch cylinder as shown in Fig. 4 a . Figure 4 b shows that the movable coordinate system S1 performs a screw motion with respect to the fixed coordinate system Sf. Z1-axis is the rotation axis of the hob cutter. The locus of the cutting blade can be represented in coordinate system S1 by applying the following homogeneous coordinate transformation matrix equation: R1 1 = M1fM fcRc B , 8 where M fc = 1 0 0 0 0 cos \u2212 sin 0 0 sin cos 0 0 0 0 1 , and 984 / Vol. 127, SEPTEMBER 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000711_s0094-114x(02)00066-6-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000711_s0094-114x(02)00066-6-Figure4-1.png",
        "caption": "Fig. 4. 3-UPU wrist.",
        "texts": [
            " The result of their investigation is that a mechanism architecture, called 3-UPU (Fig. 3) and used already for translational manipulators [4], under some mounting and manufacturing conditions, can be used to obtain manipulators able to make the platform perform infinitesimal spherical motions. In the 3-UPU manipulators, the platform and the base are connected to each other by three legs of type UPU in which the prismatic pair is the actuated joint (Fig. 3). The mounting and manufacturing conditions enunciated by Karouia and Herv e [13] are as follows (see Fig. 4): (i) the three revolute pair axes fixed in the platform (base) must converge at a point fixed in the platform (base), (manufacturing condition); (ii) in each leg, the intermediate revolute pair axes must be parallel to each other and perpendicular to the leg axis which is the line through the universal joints centers (manufacturing condition); (iii) the platform s point located in the intersection of the platform s revolute pair axes must coincide with the base s point located in the intersection of the base s revolute pair axes (mounting condition)",
            ", it is not overconstrained and it does not need a passive spherical pair joining platform and base. This paper will demonstrate that the geometric conditions matched by the 3-UPU wrist s architecture are sufficient to make the platform perform finite spherical motions when the prismatic pairs are actuated. Moreover, it will show that the 3-UPU wrists may reach singular configurations (translation singularities) in which the spherical constraint between platform and base fails. Finally, the singularity condition is written in explicit form and is geometrically interpreted. Fig. 4 shows a 3-UPU wrist. With reference to Fig. 4, the points Ai, i \u00bc 1; 2; 3, are the centers of the universal joints which connect the legs to the base; the points Bi, i \u00bc 1; 2; 3, are the centers of the universal joints which connect the legs to the platform and the point P is the common intersection of the revolute pair axes fixed in the platform. The 3-UPU wrist is mounted so as to make the platform s point P coincide with the base s point located by the intersection of the revolute pair axes fixed in the base. Fig. 5 shows the ith leg, i \u00bc 1; 2; 3, of the 3-UPU wrist",
            " 5), forbids the displacement along the w2i s direction of the platform point (point P in Fig. 5) instantaneously coinciding with the intersection of the revolute pair axes at the leg endings. When this point (point P in Fig. 5) goes to infinity, i.e., w1i and w4i (Fig. 5) are parallel to each other, the forbidden displacement becomes a forbidden platform rotation around the direction of the free vector w2i w4i [18]. The position analysis of the 3-UPU wrist focused on the mechanism configurations that keep the platform s point P (Fig. 4) at rest is identical with the one of the Innocenti and ParentiCastelli s parallel wrist (Fig. 1) [11]. Thus, with reference to the demonstration reported in [11], it can be stated that the platform orientations compatible with a given set of values of the three parameters di, i \u00bc 1; 2; 3, are at most eight, whereas only one triplet of di values is compatible with a given platform orientation. In order to find the 3-UPU wrist s singularity conditions the relationship between the platform s velocities, x and _P , and the time derivatives _di, i \u00bc 1; 2; 3, of the actuated joint coordinates is required",
            " From an analytic point of view, the unit vectors w2i, i \u00bc 1; 2; 3, depend on the links geometry and the platform s orientation. If the links geometry is given, Eq. (26) will be a scalar equation in the three variables chosen to parameterize the platform s orientation. The solutions of a scalar equation in three unknowns lie on a surface, when they are reported in a three-dimensional Cartesian diagram whose coordinates are the three unknown variables of the scalar equation. From a geometric point of view, with reference to Fig. 4, condition (26) is verified when the planes the three triangles AiBiP , i \u00bc 1; 2; 3, lie on have a straight line through the point P as common intersection (Fig. 6). In fact, in this case, the unit vectors w2i, i \u00bc 1; 2; 3, are all perpendicular to the line common to the three planes and are all parallel to any plane perpendicular to the same line. When this geometric condition occurs, the platform s point P can undergo an infinitesimal displacement along the line common to the three planes and the platform can undergo an infinitesimal rotation around the same line in both of the possible directions after any infinitesimal variation of the lengths di, i \u00bc 1; 2; 3, is given (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001721_tac.2007.900825-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001721_tac.2007.900825-Figure3-1.png",
        "caption": "Fig. 3. Constant sampling step = 0:2 s, noise magnitude \" = 0:1 m.",
        "texts": [
            " The tracking accuracy was calculated as maximal absolute values of , , during the last 25% of the simulation time. The results are summarized in Table I. The system performance with in the absence of noises is shown in Fig. 2. It cannot be distinguished from the performance with full exact measurements of all derivatives [23]. The system is fully destroyed already with the noise magnitude . The system performance with the noise magnitude 0.1 m is practically the same as in the absence of noises with (Fig. 3). Note that the magnitude of the actual control is about 16 and the vibration frequency is about 0.5 , which is quite feasible. Mark that is close to the typical human reaction time. Note also that the real performance might be measured by the maximal steady-state distance of the car trajectory from the desired one, which is much smaller than (Fig. 3(a)). Performance with the variable measurement step in the absence of noises with and is shown in Fig. 4. The accuracy is obtained with [Fig. 5(a) and (b)]. The performance of the controller is slightly improved by the restriction (15) of the measurement step from above. With large noises the restriction actually provides for the same performance of the controller as with the constant sampling interval [Fig. 5(c) and (d)]. The demonstrated performance of the controllers does not significantly change when the noise frequency varies in the range from 10 to 100000"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003263_tmag.2014.2320446-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003263_tmag.2014.2320446-Figure8-1.png",
        "caption": "Fig. 8. Various winding configurations for 18-slot 14-pole machine. (a) Three-phase. (b) Six-phase. (c) Nine-phase.",
        "texts": [
            " Assuming that the currents in each three-phase set are independently controlled, the hth-order MMF harmonic can be canceled out, if the combined phase shift angles, \u03b8 f w and \u03b8bw, for the forward and backward MMF harmonics satisfy \u03b8 f w = \u03b2(k+1)h \u2212\u03b2kh +\u03b8 =\u00b1360\u00b0/K +q f 360\u00b0, q f \u2208 Z (7) \u03b8bw = \u03b2(k+1)h \u2212\u03b2kh \u2212\u03b8 =\u00b1360\u00b0/K + qb360\u00b0, qb \u2208 Z (8) where K is the number of three-phase sets and Z denotes any integer. The above conditions lead to the second summation in (5) and (6) becoming zero, and hence the hth-order harmonic is eliminated. By way of example, the 18-slot 14-pole windings can be configured into a one three-phase, two three-phase, or three three-phase system, as shown in Fig. 8. To eliminate unwanted harmonics, the current phase shift angle \u03b8 needs to be chosen according to (7) and (8). Table I lists the spatial shift angle \u03b2(k+1)h \u2212 \u03b2kh for MMF harmonic orders up to 29 of the 18-slot 14-pole nine-phase (three three-phase) windings. The spatial shift of the first-order MMF harmonic is \u2212260\u00b0 because phase A2 is 13 slots lagging phase A1 and each slot occupies 20\u00b0 mechanical degrees in space, as shown in Fig. 8(c). When the current phase shift angle \u03b8 is selected to be 20\u00b0, the combined MMF harmonic phase shift angle \u03b8 f w = \u03b2(k+1)h \u2212 \u03b2kh + \u03b8 becomes \u2212240\u00b0 (or 120\u00b0), and satisfies (7). Hence, the first-order forward rotating harmonic is eliminated. It should be noted that the first-order backward rotating harmonic does not exist in the machine, and this is denoted by \u00d7 in Table I. Similarly, the combined phase shift angles \u03b8 f w and \u03b8bw of the fifth-, 13th-, 17th-, 19th-, 23rd- \u00b7 \u00b7 \u00b7 order MMF harmonics satisfy (7) and (8), and therefore they are canceled out"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001572_ichr.2007.4813852-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001572_ichr.2007.4813852-Figure2-1.png",
        "caption": "Fig. 2. Grasp model",
        "texts": [
            " qndof  C is the transformation matrix between T and velocity of all the bodies (V Rbody body : twist of body expressed in its own frame Rbody)[17]. [ Vroot V1 . . . Vndof ]T = C \u00b7T Coulomb friction formalism, extended to polyarticular, is inspired from T. Liu and M.Y. Wang [13]. Friction can be formulated through the strict inequality: | f t c|< \u00b5 \u00b7 f n c with f n c , f t c and \u00b5 being the normal contact force, the tangent contact force and the dry-rub factor. We offer two grasp models. Firstly, as a damped spring between the hand and the object (Fig. 2(a)). They can be actived / inactived at any time in the simulation. A damped spring link is composed of a spring (mapping from SE (3) to se(3)\u2217) and a damper (mapping from se(3) to se(3)\u2217). We choose for the spring a formulation derived from a potential (E. D. Fasse and P. C. Breedveld [7]). Secondly, by modeling the hand\u2019s kinematics (Fig. 2(b)), the clenching efforts are the contact efforts between the hand and the object. To find a control law, we need an adapted model, most often a simplification of the physical model. The physical simulation uses Coulomb\u2019s friction model, which is a non linear model. As we need a linear formulation for our QP, we use a linearized coulomb model. Like J.C. Trinkle et al. [21], we linearize contact cones into multifaceted friction cones in order to obtain linear constraints (Fig. 3). The linearized contact force of the k-th contact is denoted: f k c/linearized = l f k c \u00b7\u03be k with \u03be k = [ \u03be k 1 . . . \u03be k ne ]T (2) with ne, the number of edges, l f k c , the linearized friction cone, \u03be k the forces to every line direction of the k-th linearized friction cone. The contact forces computed by our control law must be inside the friction cone which means: \u2200i\u2208 [1,ne],\u03be k i \u2265 0. Our first grasp model is a damped spring between the hand and the object (Fig. 2(a)). When the hand is close enough to the object, the damped spring is activated in the control law (and simulation), which is similar to a clenching effort. The second grasp model are based on hand\u2019s kinematics (Fig. 2(b)). The clenching effort is the contact efforts between hand and object. The hands\u2019 DoF take part in the grasping effort but not in any way in the manikin\u2019s balance control. To grasp an object from an initial posture (Fig. 2(c)), we compute torques as an articular control towards final posture (Fig. 2(d)). We use a robotic approach and more precisely joint control to handle VH dynamic. As in [22] [1], we formulate a constrained optimization problem (Quadratic Programming: QP). This method deals with a great number of DoF and solves simultaneously all constraint equations. We introduce the following notation, Y : unknown vector, Y des: desired but not necessarily accessible solution, Q: quadratic norm and A, b, C and d matrices and vectors which express linear equality and inequality constraints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002201_j.aca.2009.03.045-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002201_j.aca.2009.03.045-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the FIA apparatus (1) carrier (0.1 M KH2PO4/Na2HPO4",
        "texts": [],
        "surrounding_texts": [
            "A a\nY D\na\nA R R A A\nK B P A O\n1\nc i n o m c e s s c\na c b h e A b r n\n0 d\nAnalytica Chimica Acta 643 (2009) 13\u201318\nContents lists available at ScienceDirect\nAnalytica Chimica Acta\njourna l homepage: www.e lsev ier .com/ locate /aca\nnovel biosensor based on photoelectro-synergistic catalysis for flow-injection nalysis system/amperometric detection of organophosphorous pesticides\ninyin Wei, Ying Li, Yunhe Qu, Fei Xiao, Guoyue Shi, Litong Jin \u2217\nepartment of Chemistry, East China Normal University, 3663 Zhong Shan Road North, Shanghai 200062, China\nr t i c l e i n f o\nrticle history: eceived 15 December 2008 eceived in revised form 10 March 2009 ccepted 26 March 2009 vailable online 5 April 2009\na b s t r a c t\nIn this study, a highly sensitive amperometric biosensor based on photoelectro-synergistic catalysis for detecting organophosphorus pesticides (OPs) in flow-injection analysis (FIA) system has been developed. The acetylcholinesterase enzyme (AChE) was immobilized by adsorption into the nanostructured PbO2/TiO2/Ti, which also acted as the working electrode. This strategy was found to catalyze the oxidative reaction of thiocholine effectively, make the AChE/PbO2/TiO2/Ti biosensor detect the substrate at 0.30 V\neywords: iosensor hotoelectro-synergistic catalysis cetylcholinesterase rganophosphorus pesticides\n(vs. SCE), hundreds milli-volts lower than others reported. PbO2/TiO2/Ti and TiO2/Ti electrodes were prepared and investigated with atomic force microscope (AFM). Factors influencing the performance were optimized. The resulting flow system offered a fast, sensitive, and stable response. A value of 1.34 mM for the apparent Michaelis\u2013Menten constant (Kapp\nM ) was obtained. A wide linear inhibition response for trichlorfon was observed in the range of 0.01\u201320 M with the detection limit of 0.1 nM. The results using this biosensor agreed very well with chromatographic method and we also examined the real samples successfully in this work.\n. Introduction\nOrganophosphorous pesticides are well known as highly toxic ompounds which are widely used in agriculture and for chemcal warfare agents [1]. Because of the inherent toxicity of these eurotoxic compounds, there is a considerable interest in the develpment of highly sensitive, selective, rapid and reliable analytical ethods in their detection. Current analytical techniques like gas hromatography (GC), liquid chromatography (LC), mass spectromtry (MS) or combinations thereof (GC\u2013MS or LC\u2013MS/MS), are very ensitive and reliable, but they are very time-consuming and expenive and can be only performed by highly trained technicians and urrently not suitable for field use [2].\nEnzyme-based biosensors have emerged in the past few years s the most promising alternative for direct monitoring of pestiides [3,4]. Various inhibition and noninhibition biosensor systems, ased on the immobilization of acetylcholinesterase (AChE) or OP ydrolase (OPH) onto various electrochemical or optical transducrs, have been proposed for field screening of OP neurotoxins [5\u20139]. lthough OPH-based noninhibition biosensors provide a direct iosensing route (OPH catalyzes the hydrolysis of OP compounds, esulting in electroactive species, such as p-nitrophenol), OPH is ot commercially available, which limits widespread applications.\n\u2217 Corresponding author. Tel.: +86 21 62232627; fax: +86 21 62232627. E-mail address: ltjin@chem.ecnu.edu.cn (L. Jin).\n003-2670/$ \u2013 see front matter \u00a9 2009 Elsevier B.V. All rights reserved. oi:10.1016/j.aca.2009.03.045\n\u00a9 2009 Elsevier B.V. All rights reserved.\nA preferred indirect electrochemical biosensing route based on the inhibition of target enzymes has been widely developed by different groups [10\u201318]. Because of their high sensitivity, amperometric transducers have been the transduction principle of choice in many of these biosensors [10].\nIn the AChE enzyme system (Eq. (1) and (2)), thiocholine (TCh) ester, acetylthiocholine (ATCh), are preferred as substrate.\nAcetylthiocholine + H2O AChE\u2212\u2192thiocholine + acetic acid (1)\n2Thiocholine anodic oxidation\u2212\u2192 dithio-bischoline + 2H+ + 2e\u2212 (2)\nThe amperometric response of the AChE biosensors, i.e. the anodic oxidation current resulting from the thiocholine formed in the enzymatic hydromantic hydrolysis of acetylthiocholine, is inversely proportional to the concentration of organophosphorus pesticides (OPs) in samples, and the exposed time as well.\nThere are many efforts to develop these inhibition biosensors, certain analytical characteristics of these systems require further improvement to meet the required specifications, such as higher sensitivity, selectivity, and stability.\nOne approach to improve the performance characteristics of the AChE-based inhibitor biosensors would be the design and production of the appropriate enzymes with characteristics more suitable for biosensor applications. It was only recently that biotechnology allowed the highly efficient production of pure AChE from different sources thus enabling their thorough study [11] and use [12]. Initial biochemical studies revealed that Drosophila melanogaster acetyl-",
            "1 himica Acta 643 (2009) 13\u201318\nc [ t\na d e t b s\ns a i A y i t c d d w T c s\n2\n2\ne r ( w e T c C u\n2\nF b C c t A S e ( o w w p p 1\n2\nm d t\n4 Y. Wei et al. / Analytica C\nholinesterase (Dm. AChE) is the most sensitive enzyme toward OPs 13]. The Dm. AChE-based inhibitor biosensors show great promise o improve the sensitivity of the biosensor system.\nAnother possible approach for improving the performance charcteristics of the AChE-based inhibitor biosensors is to improve the esign of the biosensor and the electrochemical detection of the nzymatic product. Most of the approaches for AChE immobilizaion on electrode surfaces in the reported literature are covalent inding [14], direct adsorption [15,16], or entrapment in different ubstrate materials [17,18]\nHere, we describe for the first time the application of a biosenor based on photoelectro-synergistic catalysis, a combination pproach of photocatalysis and electrocatalysis, together with flownjection analysis (FIA) for highly sensitive insecticide detection. n AChE/PbO2/TiO2/Ti biosensor was prepared and its electrocatalsis, photocatalysis and photoelectro-synergistic catalysis were nvestigated. Electrochemical technique was adopted to collect he electrical signals produced during photoelectro-synergistic atalytic oxidation, which also succeeded in determining OPs irectly. As an example, we used the organophosphate insecticide, imethyl 2,2,2-trichloro-1-hydroxyethylphosphonate (trichlorfon), hich has been widely used as an insecticide for more than 40 years. he PbO2/TiO2/Ti based on AChE biosensor was found to effectively atalyze the oxidative reaction of thiocholine with no loss of the ensitivity and with the detection limit 0.1 nM of trichlorfon.\n. Materials and methods\n.1. Materials\nPurified acetylcholinesterase (VI-S, 1000 IU mg\u22121) from electric el, pyridine 2-aldoxime methiodide (PAM), acetylthiocholine chloide and chitosan were purchased from Sigma\u2013Aldrich. Trichlorfon [2,2,2- trichloro-1-hydroxyethyl]-phosphonic acid dimethyl ester) as purchased from Dr. Ehrenstorfer Co. Titanium rod (99.7%, diamter 2.5 mm) was purchased from the Far East Ti Equipment Co. itanium tetraisopropoxide, ethanol, polyglycol, lead nitrate, perhloric acid were purchased from Shanghai Chemical Reagent Co., hina. All of other chemicals were analytical grade. All solutions sed in experiments were prepared with doubly distilled water.\n.2. The experimental setup\nThe setup of the FIA system for OPs detection is shown in ig. 1. The flow carrier which was held in a reservoir was propelled y a D100B/C peristaltic pump (Huxi Instrumental Co., Shanghai, hina) through an injector (7520, Rheodyne) and a photochemical ell with a three-electrode unit installed, before being transported o a waste tank. The three-electrode unit was composed of an ChE/PbO2/TiO2/Ti photoelectro-synergistic catalysis biosensor, a CE electrode and a Pt electrode, serving as the working, refernce and counter electrode, respectively. A 12-W quartz UV lamp max = 253.7 nm) was used as an excitation source. The surface f the photoelectro-synergistic catalysis cell facing the UV lamp as made of quartz, and the inlet, outlet and the salt bridge ere all connected to the interlayer (0.5 mm in thickness). The hotoelectrocurrent produced by the working electrode during hotoelectro-synergistic catalysis process was recorded with a CHI030 electrochemical station (CHI, America).\n.3. AChE/PbO2/TiO2/Ti biosensor preparation\nTitanium tetraisopropoxide (12 mL) and ethanol (48 mL) were ixed under an inert atmosphere. Subsequently, a solution of\niethanolamine (4 mL) and water (0.5 mL) were added to the mixure under stirring for 60 min at ambient temperature, which led\n(PBS), pH 8.0)); (2) pump; (3) injector; (4) a thin-layer amperometric detector (a: flow inlet, b: counter electrode, c: working electrode, d: flow outlet, e: reference electrode, f: quartz window); (5) CHI-1030 electrochemical system; (6) personal computer.\nto the formation of a sol\u2013gel of TiO2 [19]. Then, polyglycol was added to the sol\u2013gel solution before dip-coating the bare Ti rod. The TiO2-coated Ti rod was then dried at 100 \u25e6C for 5 min. The operation of coating and drying was repeated three times. Then it was heated at 400 \u25e6C for 3 h. After that, the PbO2 film was formed in 1 M HClO4 solution containing 0.01 M Pb(NO3)2 by cycling the potential between 1.4 and 1.8 V at low scan rate for 10 min. After modification, the electrode was removed from the modifying solution and rinsed with doubly distilled water.\nThe 0.1 M KH2PO4/Na2HPO4 (PBS, pH 8.0) was used to dissolve the enzyme (2.2 mg in 0.5 mL PBS). The resulting solution was stored at 4 \u25e6C in refrigerator. The AChE was immobilized by casting a 5 L droplet of AChE mixed with 1.0 L 1.0 mg mL\u22121 chitosan onto the PbO2/TiO2/Ti working electrode surface and air dried. The enzymatic membrane was subsequently gelatinized completely in the refrigerator (4 \u25e6C) for 24 h. All the prepared AChE/PbO2/TiO2/Ti biosensors were stored in PBS (pH 8.0) in the refrigerator (4 \u25e6C) when not in use.\n2.4. Flow-injection amperometric detection of trichlorfon\nFlow-injection amperometric detection of trichlorfon was performed with the above-mentioned flow-injection system. First, 20 L 1.0 mM ATCh substrate was injected to obtain the initial response under UV irradiation (A0: peak area of the oxidation current) of the biosensor after a steady-state value was obtained. Then, 20 L of a specific concentration of trichlorfon was injected. After the pesticide reached the cell, the flow was stopped to let the biosensor incubated with the OPs for 10 min. Following the inhibition step, the response of the AChE/PbO2/TiO2/Ti biosensor to the same concentration substrate (Ai) was recorded again. It was noted during the inhibition that the electrochemical record of current via time and UV irradiation were paused. The inhibition percentage was calculated from the remaining activity after each inhibition step and was plotted against the log [trichlorfon].\n3. Results and discussions\n3.1. Atomic force micrographs of the electrodes\nThe surface of the electrodes which was characterized by atomic force microscope (AFM, Shanghai AJ Nanoscience Development Co., Ltd.) as shown in Fig. 2(A) illustrates the diameter of the prepared TiO2 particle was about 50 nm. Meanwhile, PbO2 particles whose",
            "Y. Wei et al. / Analytica Chimica Acta 643 (2009) 13\u201318 15\n(A) an\nd e t t\n3 b\ng s t c c r a\nr b A t w e I a d i I\nF 0 i\niameter was around 100 nm were formed on the surface of the lectrode, as shown in Fig. 2(B). Fig. 2 provides strong evidence for he formation of PbO2/TiO2/Ti nanocomposite which can be used o catalyze the oxidative reaction of thiocholine effectively.\n.2. Photoelectro-synergistic catalysis on AChE/PbO2/TiO2/Ti iosensor\nWhen TiO2 particles were irradiated by UV (<387.5 nm), they enerated h+/e\u2212 pairs and these species migrated to the solid urface. It was accepted commonly that the strong oxidant, phoogenerated hole could oxidize water adsorbed on TiO2 surface to reate another oxidizing agent hydroxyl radical (\u2022OH) [20]. The thioholine could be oxidized by the photogenerated hole and hydroxyl adicals which were generated from the anodic discharge of water dsorbed on PbO2 surface at a certain potential.\nFig. 3 shows the effect of UV illumination to the curent responses of AChE/TiO2/Ti biosensor and AChE/PbO2/TiO2/Ti iosensor. In Fig. 3(A), at a working potential of 0.30 V (vs. SCE) ChE/TiO2/Ti biosensor had a larger amperometric response with he injection of ATCh (arrows in figure) with UV irradiation than ithout it. This was because the production of photo-generated lectrons could catalyze the oxidative reaction of thiocholine. n Fig. 3(B), AChE/PbO2/TiO2/Ti biosensor had a great larger mperometric response with UV irradiation than without it. It emonstrates the photoelectro-synergistic catalysis has largely mproved the oxidation current than that just of electrocatalysis. t could be summarized that the photoelectro-synergistic catalysis\nig. 3. The influence of biosensor on the current response in the FIA system (ATCh concen .30 V vs. SCE) (A) AChE/TiO2/Ti sensor (a) without UV illumination, (b) with UV illum llumination.\nd PbO2/TiO2/Ti (B) electrodes.\nof AChE/PbO2/TiO2/Ti biosensor can enlarge the oxidation current of thiocholine effectively, thus it can detect largely lower concentration of OPs.\n3.3. Kinetic characteristics of AChE/PbO2/TiO2/Ti biosensor in FIA\nThe kinetic response of AChE/PbO2/TiO2/Ti biosensor in FIA system was tested to investigate the enzymatic activity retained on the surface of PbO2/TiO2/Ti electrode. Fig. 4 shows the dependence of the current on the concentration of ATCh. The Kapp\nM value of the immobilized AChE was calculated by fitting experiment data to the Michaelis\u2013Menten equation [21] using the Lineweaver-Burk electrochemical representation of \u2013 [peak area] vs. [ATCh]. At pH 8.0 and at room temperature (about 25 \u00b1 2 \u25e6C), the Kapp\nM of the immobilized AChE was of 1.34 mM and the linear correlation coefficient r2 was of 0.9969. It demonstrates that the immobilized AChE is suitable for the Michaelis\u2013Menten kinetic equation. Besides, 1.0 mM ATCh was already used in the following experiments by using AChE-based biosensors to detect anticholinesterase pesticides considering that it was within the linear response range with high sensitivity.\n3.4. Optimal operating conditions\nThe proposed AChE/PbO2/TiO2/Ti biosensor was used as an amperometric detector in an FIA system. Accordingly, an optimization study involved the best experimental parameters was performed. Fig. 5 shows the influences of both the working potential and the pH value of PBS on the response to substrate ATCh. It can\ntration: 1.0 mM; flow rate: 0.50 mL min\u22121; carrier: PBS, pH 8.0; working potential: ination; (B) AChE/PbO2/TiO2/Ti sensor (c) without UV illumination, (d) with UV"
        ]
    },
    {
        "image_filename": "designv10_10_0000932_027836499701600206-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000932_027836499701600206-Figure11-1.png",
        "caption": "Fig. 11. Workspace of (A) RRR, (B) RPR, (C) RRP, (D) RPR.",
        "texts": [],
        "surrounding_texts": [
            "211 at LAKEHEAD UNIV on March 18, 2015ijr.sagepub.comDownloaded from",
            "212\nReferences\nAbdel-Malek, K. 1995. Dexterity of manipulator arms at an operating point. Proc. 21st Advances in Design Automation Conf., Vol. 82(1). ASME, pp. 781-788.\nAgrawal, S. K. 1990. Workspace boundaries of in-parallel manipulator systems. Int. J. Robot. Automat. 7(2):94- 99.\nAllgower, E. L., and Georg, K. 1990. Numerical Continuation Methods: An Introduction. Berlin: SpringerVerlag.\nCecarelli, M., and Vinciquerra, A. 1995. On the workspace of general 4R manipulators. Int. J. Robot. Res. 14(2):152-160.\nDenavit, J., and Hartenberg, R. S. 1955. A kinematic notation for lower-pair mechanisms based on matrices. J. Appl. Mech. 22:215-221.\nEmiris, D. M. 1993. Workspace analysis of realistic elbow and dual-elbow robot. Mech. Machine Theory 28(3):375-396.\nGosselin, C., and Angeles, J. 1990. Singularity analysis of closed loop kinematic chains. IEEE Trans. Robot. Automat. 6(3):281-290.\nGupta, K. G., and Roth, B. 1982. Design considerations for manipulator workspace. J. Mech. Des. 104(4):704- 711.\nHaug, E. J., Adkins, R., and Luh, C. M. 1994. Numerical algorithms for mapping boundaries of manipulator workspaces. Proc. 23rd ASME Mechanisms Conf. (Minneapolis, MN).\nHaug, E. J., Wang, J. Y., and Wu, J. K. 1992. Dexterous workspaces of manipulators: I. analytical criteria. Mech. Struct. Mach. 20(3):321-361.\nKeller, H. B. 1987. Lectures on Numerical Methods in\nBifurcation Problems. Berlin: Springer-Verlag.\nKleinfinger, J. F. 1986. Modelisation dynamique de robots a chaine cinematique simple, arborescente ou ferm&eacute;e, en vue de leur commande. Ph.D. thesis, Universit&eacute; de Nantes.\nKumar, V 1985. Robot Manipulators&mdash;Workspaces and Geometric Dexterity. Master\u2019s thesis, Ohio State University.\nKumar, A., and Waldron, K. J. 1981. The dexterous workspace. ASME Special Paper 80-DET.\nLai, Z. C. 1986. On the Dexterity of Robotic Manipulators. Ph.D. dissertation, University of California, Los Angeles, CA.\nLai, Z. C., and Menq, C. 1988. The dexterous workspace of simple manipulators. IEEE J. Robot. Automat. 4(1):99-103.\nat LAKEHEAD UNIV on March 18, 2015ijr.sagepub.comDownloaded from",
            "213\nLucaks, G. 1990. Simple singularities in surface-surface intersections. In Gregory, J. A., (ed.), The Mathematics of Surfaces. Oxford: Clarendon Press. McKerrow, P. J. 199I. Introduction to Robotics. Reading, MA: Addison-Wesley. Muellenheim, G. 1991. On determining start points for a surface/surface intersection algorithm. Computer Aided Geometric Design 8(5):401-408. Nutbourne, A. N., and Martin, R. R. 1988. Differential Geometry Applied to Curve and Surface Design, Volume 1: Foundations. Chichester, UK: Ellis Horwood.\nPennock, G. R., and Kassner, D. J. 1993. The workspace of a general planar three-degree-of-freedom platformtype manipulator. ASME J. Mech. Des. 115(2):269- 276.\nPratt, M. J., and Geisow, A. D. 1986. Surface/surface intersection problems. In Gregory, J. A., (ed.), The Mathematics of Surfaces. Oxford: Clarendon Press. Qiu, C. C., Luh, C. M., and Haug, E. J. 1995. Dexterous workspaces of manipulators, part III: calculation of continuation curves at bifurcation points. Mechanics of Structures and Machines 23(1):115-130.\nQiulin, D., and Davies, B. J. 1987. Surface Engineering Geometry for Computer-Aided Design and Manufacturing. Hampstead, UK: Ellis Horwood.\nRheinboldt, W. C. 1986. Numerical Analysis of Parameterized Nonlinear Equations. New York: John Wiley and Sons.\nRoth, B. 1975. Performance evaluation of manipulators from a kinematic viewpoint. National Bureau of Standards Special Publications no. 459, pp. 39-61. Tsai, Y. C., and Soni, A. H. 1981. Accessible region and synthesis of robot arm. ASME special paper 80-DET101, pp. 803-811. Vinagradov, I. et. al. 1971. Details of kinematics of ma-\nnipulators with the method of volumes. (Russian). Mexanika Mashin No. 27/28: 5-16.\nWang, J. Y., and Wu, J. K., 1993. Dexterous workspaces of manipulators, part 2: computational methods. Mech. Structures and Machines 21(4):471-506. Wilf, I., and Manor, Y. 1993. Quadric-surface intersection curves: shape and structure. Computer Aided Design 25(10):633-643. Yang, D. C. H., and Lai, Z. C. 1985. On the dexterity of robotic manipulators-service angle. Trans. ASME J. Mech. Transm. Automat. Design 107(2):262-270. Yang, D. C. H., and Lee, T. W. 1983. On the workspace of mechanical manipulators. J. Mech. Trans. Automat. Design 105(1):62-69.\nat LAKEHEAD UNIV on March 18, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_10_0003109_978-0-8176-4893-0_6-Figure6.3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003109_978-0-8176-4893-0_6-Figure6.3-1.png",
        "caption": "Fig. 6.3 Kinematic car model",
        "texts": [
            " u D \u02db'3;4=N3;4 where '3;4 D \u00ab C 3 2 R C 4=3 j P j C 0:5 j j3=4 1=3 P C 0:5 j j3=4 sign. / j R j C 4=3 j P j C 0:5 j j3=4 2=3 1=2 and N3;4 D j\u00ab j C 3 2 j R j C 4=3 j P j C 0:5 j j3=4 2=3 1=2 Consider a simple kinematic model of car control Px D v cos.'/ (6.36) Py D v sin.'/ (6.37) P' D v=l tan. / (6.38) P D u (6.39) where x and y are the Cartesian coordinates of the middle point of the rear axle, ' is the orientation angle, v is the longitudinal velocity, l is the length between the two axles, and is the steering angle (i.e., the control input) (Fig. 6.3). The task is to steer the car from a given initial position to the trajectory y D g.x/, where g.x/ and y are assumed to be available in real time. Define D y g.x/. Let v D const D 10m=s, l D 5 m, x D y D ' D D 0 at t D 0, g.x/ D 10 sin .0:05x/ C 5. Obviously the control appears for the first time explicitly in the third derivatives of x and y. Thus the relative degree of the system is 3 and both the nested (Sect. 6.6.1) and quasi-continuous (Sect. 6.6.2) 3-sliding controllers solve the problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001967_0094-114x(78)90041-1-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001967_0094-114x(78)90041-1-Figure5-1.png",
        "caption": "Figure 5. A dependen t link incident on another.",
        "texts": [
            " In such cases there exists only a simple problem in vector addition, since they meet on either a common link or, for a degenerate link, a common joint which must be at least a double joint. Counterweighted chains incident on one another merge to form one chain. The other case occurs when a counterweighted chain of one dependent link is incident on another dependent link. To examine this consider the zero-length chain, i.e. point W, of the dependent link G being incident on the dependent link P, see Fig. 5. From the previous section, the mass mg fixed in link G at Z can be represented by two assigned masses, one at W and the other at X. The assigned mass at W, from eqn (2), is lg As noted previously, this can be considered as fixed at W for force balance purposes. Consequently, it can be re-assigned to points R and S in the dependent link P using eqns (2) and (3) respectively. The mass assigned to R is mg'lg -[pp\" and to S is r t ~ . G lp e ~ . From this, it is seen that in transferring counterweighted chains over dependent links the factors for the masses are multiplicative whereas the offset angles are additive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000956_0890-6955(95)00073-9-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000956_0890-6955(95)00073-9-Figure3-1.png",
        "caption": "Fig. 3. Equivalent vibratory system.",
        "texts": [
            " After an initial upward deflection (displacement) or an initial horizontal deflection was given to the leaf spring by the adjusting screw and the rod indicated in the figure, the rod was removed instantaneously by a hammer. The vibratory displacement of the leaf spring at this time was detected using an eddy current-type sensor. In this manner, the free damped vibration of the leaf spring with an impact damper could be observed. The vibratory system consisting of the leaf spring and the impact damper used in this experiment can be represented as the equivalent vibratory system illustrated in Fig. 3. As the leaf spring vibrates, the free mass m collides with the main mass M (actually the shank area indicated just below the bolt head in Fig. 2). Accordingly, the thickness of the leaf spring T was varied widely in order to investigate the damping effect of the impact damper when vibratory characteristics of the main vibratory system were different (mainly the main mass and the spring constant). Furthermore, in order to investigate the effects of the free mass m and the clearance CL on the damping capability of the impact damper, m and CL were varied greatly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002363_j.conengprac.2009.03.001-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002363_j.conengprac.2009.03.001-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed, reference-parallel and body-fixed frames.",
        "texts": [
            " The process plant model, which simulates as close as possible the real physics of the plant dynamics including process disturbances, sensor outputs and control inputs, is used for numerical simulations and analysis of the stability and performance of the closed-loop system. The control plant model, which is simplified from the process plant model, is used for controller design and analytical stability analysis (e.g. in the sense of Lyapunov). In this section, the process plant model including the kinematics and dynamics is discussed. In station keeping, the motions and state variables of the control system are defined and measured with respect to some reference frames or coordinate systems as shown in Fig. 1 (S\u00f8rensen, 2005a). The Earth-fixed reference frame is denoted as the XEYEZE-frame, in which the vessel\u2019s position and orientation coordinates are measured relative to a defined origin. The body frame XYZ is fixed to the vessel and thus moving along with it. The hydrodynamic frame, XhYhZh-frame, is generally moving along the path of the vessel. In station keeping operations about the coordinates xd, yd, and cd, the hydrodynamic frame is Earth-fixed and denoted as the reference-parallel frame XRYRZR"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001572_ichr.2007.4813852-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001572_ichr.2007.4813852-Figure6-1.png",
        "caption": "Fig. 6. Balance control in two phases",
        "texts": [
            " Then, it analyses its state and chooses a strategy. We consider two global strategies: reaction to disturbance and task. In the first strategy, HR can have different reactions (simple/complex subsection V-B.1). Thanks to stability criteria, HR uses complex reaction to disturbance if necessary. In task mode, HR can realize task sequences (Fig. 7). Finally, thanks to subsection IV-C, we can formulate and solve two QP (Static and Dynamic) in order to compute the HR articular torque. 1) Towards Multi-Phase Balance Control: In these examples (Fig. 6), HR contacts are activated/deactivated as the simulation carries on. It is a more high-level control. We implement a two phase balance control. At the beginning of the scene, the HR is upright and its hand contacts are deactivated. On account of a disturbance force applied on its back, its CoM moves away from itsgoal position \u2016xgoal G \u2212xG\u2016> dist (dist is an arbitrary distance). In the first case (Fig. 6(a)), hand contacts are activated and try to come in touch with the environment. Thanks to its hands, the HR can maintain its balance. Finally, its hand contacts are deactivated in order to meet up with its starting posture. We note that it is a non-coplanar multi contact problem and the Static QP of our algorithm allows us to stabilize the motion. The HR converges to a stable CoM and posture. In the second case (Fig. 6(b)), contact accelerations of the right feet have a new goal so that HR makes one step forward. 2) Strategies Linking: In this example (Fig. 7), HR must grasp a brush and realize the task of painting the wall. In order for its hand to reach the brush, we use the previously evoked joint limit control (Eq. 17). When HR is close enough, we activate the damped spring in the simulation (Fig. 7(b)). A disturbance hits the floor, at an unpredicted time. Though it does not qualitatively know the nature of the disturbance, it knows that one was applied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001989_s11012-009-9251-x-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001989_s11012-009-9251-x-Figure2-1.png",
        "caption": "Fig. 2 Slice model and mesh stiffness of spur and helical gears [8]",
        "texts": [
            " Furthermore it can be assumed, that in many cases a reduction of the excitation level will lead to a direct reduction of noise and vibration of the complete gearbox, even with varying operating conditions in terms of running speed. In theory zero excitation means zero dynamic response. The excitation caused by the gear mesh is mainly the result of: \u2013 the periodical change of the mesh stiffness \u2013 the elastic deflection of the teeth under load leading to mesh interference at the beginning and the end of the line of action, which is also known as the engagement impact Figure 2 shows schematically the changeover from spur to helical gears, by means of the so called \u201cslice model\u201d. Below the illustration of the \u201cslice model\u201d the course of the stiffness of a single tooth pair and the resulting mesh stiffness depending on the path of contact for the spur and for the helical gears is displayed. As shown in Fig. 2 the course of the mesh stiffness for helical gears is more even than that for spur gears. The discontinuity of the mesh stiffness for both gear types is marked by arrows. Because of the greater discontinuity of mesh stiffness, the spur gears have a higher excitation level. To evaluate the excitation of a gear, the function of mesh stiffness under load can be developed in a Fourier-series [7]. The example in Fig. 3 illustrates this by a sinus and a trapezoidal function. The lower the excitation amplitude is the lower is the answer by the system in the corresponding natural frequency",
            " analytic model, FEsolver, is necessary to introduce accurate sub models into the simulation. A single gear stage can be simplified to a model with two degrees of freedom\u2014one for the pinion and one for the wheel [4]. With a further simplification it can be modified to the one-mass-oscillator with the system coordinate x\u2014the deflection of the teeth (see Fig. 7). The one-mass-oscillator shows the characteristic properties of a parameter-excited oscillation system with the consideration of the variable mesh stiffness (see Fig. 2) and the damping. Other properties of the oscillation system are not taken into consideration, e.g. backlash or multi-body model of the shafts. The attenuation constant DZE for the tooth contact can be calculated depending on the viscosity of the injected oil (\u03b7 in mPas), the centre distance (a in mm) and the running speed (vt in m s ) with (1) according to [4] DZE = 0.00022 \u00b7 (a \u2212 23)0.55 \u00b7 (\u03b7 + 39)0.27 \u00b7 (vt \u2212 5)0.53 (1) Therefore Fig. 8 shows on the left-hand side the attenuation constant DZE for a gearing related to the oil viscosity for two different centre distances at a con- stant running speed of vt = 22 m s "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000703_s0013-4686(98)00294-1-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000703_s0013-4686(98)00294-1-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammogram of a poly (1-2) electrode, obtained by oxidative electropolymerization (G 1+ 2=2.2 10\u00ff9 mol cm\u00ff2) in CH2Cl2+0.1 M TBAP. The scan rate is 100 mV s\u00ff1.",
        "texts": [
            "4, does not induce the appearance of the electrochemical response of the polypyrrole matrix while the current intensity of the oxidation peak decreases. This probably indicates the formation of an insulating polymer on the electrode surface. A convenient way to improve the electropolymerization capacity of 1 and the electroactivity of the polymeric \u00aelm is to copolymerize 1 with a pyrrole ammonium (2). Electropolymerization of a mixture of 1 and 2 was carried out by controlled potential electrolysis (0.5 mC) at 1.25 V. Fig. 1 shows the cyclic voltammogram exhibited by the resulting modi\u00aeed electrode upon transfer into a CH2Cl2+0.1 M TBAP solution free of monomers. The reversible oxidation wave around 0.55 V corresponds to the electrochemical response of the polypyrrole matrix. The apparent surface coverage of electropolymerized 1 and 2 monomers, G 1+ 2=2.2 10\u00ff9 mol cm\u00ff2, was determined from the charge recorded under the polypyrrole wave. The possibility to immobilize biotin-labeled biomolecules on the resulting modi\u00aeed electrode has been examined through the avidin\u00b1biotin system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002346_tee.20393-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002346_tee.20393-Figure1-1.png",
        "caption": "Fig. 1 Components of harmonic drive gearing",
        "texts": [
            " Published by John Wiley & Sons, Inc. Keywords: harmonic drive gearing, angular transmission error, nonlinear elastic deformation, modeling, compensation Received 1 September 2008 1. Introduction Harmonic drive gearings are widely used in a variety of industrial applications, e.g. industrial and/or humanoid robots, precision positioning devices, etc., because of their unique kinematics and high-performance attributes such as simple and compact mechanism, high gear ratios, high torque, and zero backlash. As shown schematically in Fig. 1, this transmission system is generally comprised of just three components: a wave generator (WG) with an elliptical shape, a flexspline (FS) of an elastic thin-walled steel cup, and a circular spline (CS) of a rigid steel ring with internal teeth, which was developed to take advantages of the elastic dynamics of metal. The basic principles of motion are as follows: FS is deflected by WG into an elliptical shape and the inscribed ellipse contacts with internal teeth of CS at two points. Then, the tooth engagement position moves by turns relative to CS, while FS moves by two teeth relative to CS because of two fewer teeth of FS than that of CS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003952_c4an00975d-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003952_c4an00975d-Figure7-1.png",
        "caption": "Fig. 7 The manufactured screen-printed carbon electrode containing TCNQ on a glass\u2013epoxy substrate.",
        "texts": [
            " Since the inhibition of AChE is known to be directly related to the amount of organophosphorous pesticides,10,11 the result shows that we can effectively This journal is \u00a9 The Royal Society of Chemistry 2014 detect as low a concentration of methamidophos as 60 ppb by getting about 8% inhibition. Development of the working prototype of an enzyme sensor Since the AChE\u2013(F127-MST) sensor unit was successfully made and its stability and sensitivity were well evaluated, development of an actual enzyme sensor with this unit was considered as a next step. We manufactured screen-printed carbon electrodes (SPCEs) containing TCNQ as seen in Fig. 7 in the same way as has been previously reported.32 External views of the sensor unit (7 8 5 cm) composed with SPCE are also shown in Fig. 8. AChE\u2013(F127-MST) cut into f 4.5 mm by excimer laser irradiation was simply placed to the working carbon electrode without further xing. A sampling unit was xed to SPCE, and then 90 ml of 0.1 M phosphate buffer (pH 7.4) was poured into the unit. Using this sensor, amperometric measurements were performed with a PalmSens handheld potentiostat (Palm Instruments BV, Netherlands) at room temperature (25 C), by applying a constant potential (150 mV) to the working electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001349_s00707-006-0329-4-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001349_s00707-006-0329-4-Figure3-1.png",
        "caption": "Fig. 3. Goldak double ellipsoidal heat source",
        "texts": [
            " In this work a 2D approximation of the heat source is used, therefore a double ellipsoidal model is preferred since the error associated with the 2D approximation can be minimized by using a double ellipsoidal heat source [26]. The most widely accepted model for simulation of arc welding processes is the so called double ellipsoidal heat sourcemodel, presentedbyGoldaket al. [27], and it is used in the presentwork.This model has the excellent feature of power density distribution control in the weld pool and HAZ. The heat input is defined separately over two regions; one region in front of the arc center and the other behind the arc center, shown in Fig. 3. The spatial heat distribution in a moving frame of reference can be calculated using qf \u00bc 6 ffiffiffi 3 p gQ ff p ffiffiffi p p afbc e h 3 x2 a2 f \u00fey2 b2\u00fez2 c2 i ; \u00f01\u00de qr \u00bc 6 ffiffiffi 3 p gQfr p ffiffiffi p p arbc e h 3 x2 a2 r \u00fey2 b2\u00fez2 c2 i ; \u00f02\u00de where, Q \u00bc VI and ff \u00fe fr \u00bc 2. The origin of the coordinate system is located at the center of the moving arc. A user subroutine is used to calculate the centroidal distance of elements from the moving arc center corresponding to the arc position at any instant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.4-1.png",
        "caption": "FIGURE 1.4 Vehicle model showing three degrees of freedom: lateral, yaw, and roll.",
        "texts": [
            " Chiesa and Rinonapoli (1967) were among the first to employ effective axle characteristics or \u2018working curves\u2019 as these were referred to by them. Va\u030agstedt (1995) determined these curves experimentally. Before assessing the complete nonlinear effective axle characteristics, we will first direct our attention to the derivation of the effective cornering stiffnesses which are used in the simple linear two-wheel model. For these to be determined, a more comprehensive vehicle model has to be defined. Figure 1.4 depicts a vehicle model with three degrees of freedom. The forward velocity u may be kept constant. As motion variables, we define the lateral velocity v of reference point A, the yaw velocity r, and the roll angle 4. A moving axes system (A, x, y, z) has been introduced. The x-axis points forwards and lies both in the ground plane and in the plane normal to the ground that passes through the so-called roll axis. The y-axis points to the right and the z-axis points downward. This latter axis passes through the center of gravity when the roll angle is equal to zero",
            "16) together yields the total steer angle for each of the wheels. The effective cornering stiffness of an axle Ceff,i is now defined as the ratio of the axle side force and the virtual slip angle. This angle is defined as the angle between the direction of motion of the center of the axle i (actually at road level) when the vehicle velocity would be very low and approaches zero (then also Fyi / 0) and the direction of motion at the actual speed considered. The virtual slip angle of the front axle has been indicated in Figure 1.4 and is designated as aa1. We have, in general, Ceff;i \u00bc Fyi aai (1.17) The axle side forces in the steady-state turn can be derived by considering the lateral force and moment equilibrium of the vehicle: Fyi \u00bc l ai l may (1.18) The axle side force is the sum of the left and right individual tire side forces. We have FyiL \u00bc \u00f01=2CFai \u00fe zaiDFzi\u00de\u00f0ai jio\u00de \u00fe \u00f01=2CFgi \u00fe zgiDFzi\u00de\u00f0gi gio\u00de FyiR \u00bc \u00f01=2CFai zaiDFzi\u00de\u00f0ai \u00fe jio\u00de \u00fe \u00f01=2CFgi zgiDFzi\u00de\u00f0gi \u00fe gio\u00de (1.19) where the average wheel slip angle ai indicated in the figure is ai \u00bc aai \u00fe ji (1",
            " Pevsner (1947) studied the nonlinear steady-state cornering behavior at larger lateral accelerations and introduced the handling diagram. One of the first more complete vehicle model studies has been conducted by Pacejka (1958) and by Radt and Pacejka (1963). For more introductory or specialized study, the reader may be referred to books on the subject, cf. e.g.: Gillespie (1992), Mitschke (1990), Milliken and Milliken (1995), Kortu\u0308m and Lugner (1994), and Abe (2009). The derivation of the equations of motion for the three degree of freedom model of Figure 1.4 will be treated first after which the simple model with two degrees of freedom is considered and analyzed. This analysis comprises the steady-state response to steering input and the stability of the resulting motion. Also, the frequency response to steering fluctuations and external disturbances will be discussed, first for the linear vehicle model and subsequently for the nonlinearmodelwhere large lateral accelerations and disturbances are introduced. The simple model to be employed in the analysis is presented in Figure 1",
            " However, the theory may approximately hold also for quasi-steady-state situations for instance at moderate braking or driving. The influence of the fore-and-aft force Fx on the tire or axle cornering force vs slip angle characteristic (Fy, a) may then be regarded (cf. Figure 1.9). The forces Fy1 and Fx1 and the moment Mz1 are defined to act upon the single front wheel and similarly we define Fy2 etc. for the rear wheel. In this section, the differential equations for the three degree of freedom vehicle model of Figure 1.4 will be derived. In first instance, the fore-and-aft motionwill also be left free to vary. The resulting set of equations of motion may be of interest for the reader to further study the vehicle\u2019s dynamic response at somewhat higher frequencies where the roll dynamics of the vehicle body may become of importance, cf. App. 2. From these equations, the equations for the simple two-degree-of-freedom model of Figure 1.9 used in the subsequent section can be easily assessed. In Subsection 1.3.6, the equations for the car with trailer will be established",
            " For a system with n degrees of freedom n (generalized) coordinates, qi are selected which are sufficient to completely describe the motion while possible kinematic constraints remain satisfied. The moving system possesses kinetic energy T and potential energy U. External generalized forces Qi associated with the generalized coordinates qimay act on the system. Internal forces acting from dampers to the system structure may be regarded as external forces taking part in the total work W. The equation of Lagrange for coordinate qi reads d dt vT v _qi vT vqi \u00fe vU vqi \u00bc Qi (1.25) The system depicted in Figure 1.4 and described in the preceding subsection performs a motion over a flat level road. Proper coordinates are the Cartesian coordinates X and Y of reference point A, the yaw angle j of the moving x-axis with respect to the inertial X-axis and finally the roll angle 4 about the roll axis. For motions near the X-axis and thus small yaw angles, Eqn (1.25) is adequate to derive the equations of motion. For cases where j may attain large values, e.g., when moving along a circular path, it is preferred to use modified equations where the velocities u, v, and r of the moving axes system are used as generalized motion variables in addition to the coordinate 4",
            " We may need to take the effect of combined slip into account The longitudinal forces are either given as a result of brake effort or imposed propulsion torque or they depend on the wheel longitudinal slip which follows from the wheel speed of revolution requiring four additional wheel rotational degrees of freedom. The first Eqn (1.34a) may be used to compute the propulsion force needed to keep the forward speed constant. The vertical loads and more specifically the load transfer can be obtained by considering the moment equilibrium of the front and rear axle about the respective roll centers. For this, the roll moments M4i (cf. Figure 1.4) resulting from suspension springs and dampers as appeared in Eqn (1.34d) through the terms with subscript 1 and 2 respectively, and the axle side forces appearing in Eqn (1.34b) are to be regarded. For a linear model the load transfer can be neglected if initial (left/right opposite) wheel angles are disregarded. We have at steady state (effect of damping vanishes) DFzi \u00bc c414\u00fe Fyihi 2si (1.35) The front and rear slip angles follow from the lateral velocities of the wheel axles and the wheel steer angles with respect to the moving longitudinal x-axis The longitudinal velocities of the wheel axles may be regarded the same left and right and equal to the vehicle longitudinal speed u",
            "34) may be further linearized by assuming that all the deviations from the rectilinear motion are small. This allows neglecting all products of variable quantities which vanish when the vehicle moves straight ahead. The side forces and moments are then written as in Eqn (1.5) with the subscripts i \u00bc 1 or 2 provided. If the moment due to camber is neglected and the pneumatic trail is introduced in the aligning torque, we have Fy1 \u00bc Fyai \u00fe Fygi \u00bc CFaiai \u00fe CFgigi Mzi \u00bc Mzai \u00bc CMaiai \u00bc tiFyai \u00bc tiCFaiai (1.37) The three linear equations of motion for the system of Figure 1.4 with the forward speed u kept constant finally turn out to read, if expressed solely in terms of the three motion variables v, r, and 4: m\u00f0 _v \u00fe ur \u00fe h0\u20ac4\u00de \u00bc CFa1f\u00f01\u00fe csc1\u00de\u00f0ud\u00fe e _d v ar\u00de=u\u00fe csr14g \u00fe CFa2f\u00f01\u00fe csc2\u00de\u00f0 v\u00fe br\u00de=u\u00fe csr24g \u00fe \u00f0CFg1s1 \u00fe CFg2s2\u00de4 (1.38a) Iz _r\u00fe \u00f0Izqr Ixz\u00de\u20ac4 \u00bc \u00f0a t1\u00deCFa1f\u00f01\u00fe csc1\u00de\u00f0ud\u00fe e _d v ar\u00de=u\u00fe csr14g \u00f0b\u00fe t2\u00deCFa2f\u00f01\u00fe csc2\u00de\u00f0 v\u00fe br\u00de=u\u00fe csr24g \u00fe \u00f0aCFg1s1 bCFg2s2\u00de4 (1.38b) \u00f0Ix \u00fe mh02\u00de\u20ac4\u00fe mh0\u00f0 _v\u00fe ur\u00de \u00fe \u00f0Izqr Ixz\u00de _r \u00fe\u00f0k41 \u00fe k42\u00de _4\u00fe \u00f0c41 \u00fe c42 mgh0\u00de4 \u00bc 0 (1.38c) In these equations, the additional steer angles ji have been eliminated by using expressions (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002136_tmech.2010.2089530-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002136_tmech.2010.2089530-Figure1-1.png",
        "caption": "Fig. 1. 3D-LIPM on inclined plane in pitch and roll directions.",
        "texts": [
            " In the single support phase, the primary dynamics of the humanoid robot on a flat plane can be modeled as a single inverted pendulum, which is called the 3D-LIPM [19]. It is assumed that the support leg is a weightless telescopic limb, and the mass is concentrated as a single point without vertical motion. Consequently, it is possible to decouple the equations of motion for sagittal and lateral planes. The 3D-LIPM can be extended to on the inclined plane in pitch and roll directions, as shown in Fig. 1. Using the extended model, the CoM trajectory for stable walking on the inclined plane can be obtained. The dynamic equation of the 3D-LIPM for the angular momentum taken around the contact point between the pendulum model and ground surface in the frame {R}, which lies on the inclined plane is written as follows: Tgr + rcom \u00d7 Fgr = d dt (rcom \u00d7 L) (1) where Tgr = [Tx Ty Tz ]T represents the torque created by the ground reaction force, rcom = [x y z]T represents the vector from the contact point to the CoM, and L is the linear momentum of the CoM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002497_j.conengprac.2010.02.014-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002497_j.conengprac.2010.02.014-Figure8-1.png",
        "caption": "Fig. 8. Three dimensional view of the CATIAs model of the helicopter. Six hundred and eighty parts are modeled and kinematically linked together. The obtained model is pictured in Fig. 8. Payload, landing-gear, sensors, electronic devices, Li-Po batteries, and numerous add-ons are modeled to obtain accurate estimates of inertia matrix and position of the center of gravity.",
        "texts": [],
        "surrounding_texts": [
            "One particularity of the presented helicopter is that a rigid rod connects the two blades of the main rotor. This features rules out any possibility of \u2018\u2018coning effect\u2019\u2019. This effect, commonly found on full-sized helicopters (see Padfield, 2007; Prouty, 2003), has an important impact on the thrust generated by the rotor. Because of the relative rigidity of the mentioned rod, it was decided to neglect this phenomenon. Yet, the vertical flapping b generates a torque Mb."
        ]
    },
    {
        "image_filename": "designv10_10_0003605_j.aej.2018.07.010-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003605_j.aej.2018.07.010-Figure1-1.png",
        "caption": "Fig. 1 Terminology",
        "texts": [
            " Because of the direct proportionality between stress and tooth load, it is observed that the bending failure will occur when the stress on the teeth reaches or exceeds the yield strength of gear teeth material because the stress is directly proportional to the tooth load. The stress developed at the contact of the two gears is directly proportional to the square root of the applied tooth-load. Contact stress is a function of Hertzian contact equation. In general, the contact failure will occur when the contact stress on the teeth reaches or exceeds the surface endurance strength. Fig. 1 illustrates the basic terminology of the spur gear. In 1892, Wilfred Lewis formulated an equation called Lewis bending equation to determine the tooth stress of the gear teeth by considering the tooth profile. It is one of the oldest and significant design equations to consider for the design of gear, especially for spur gears. It is the primary and easiest way to design the spur gear. While deriving the bending equation, Lewis considered few assumptions: gear teeth are independent of gear mesh; apply of transmitted load at the tip of the teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000956_0890-6955(95)00073-9-Figure15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000956_0890-6955(95)00073-9-Figure15-1.png",
        "caption": "Fig. 15. Application of impact damper to drill.",
        "texts": [
            " It is clear from Table 4 that using the impact damper, the damping capability of the main vibratory systems can be improved at least eight-fold for both vertical and horizontal vibrations. When the impact damper used in this experiment was applied to cutting tools, the following additional experiment was carried out in order to investigate to what degree the damping capability of cutting tools can be improved and what should be considered in the actual setting. The cutting tool used was a drill. As shown in Fig. 15, the drill was fixed to the tail spindle of a lathe by a three-jaw chuck, therefore the drill was in the state of a cantilever, with one end free and the other end fixed. A ring-shaped free mass with a diameter of 30 mm and a width of 15 mm was positioned a certain distance from the end of the drill using a jig, as illustrated in the figure. In the same manner as described in Fig. 2, after an initial displacement was given to the end of the drill by a rod, a free damped vibration was given to the drill by suddenly releasing the rod",
            " The free damped vibration near the end of the drill was measured using an eddy current-type sensor. The drill used in this experiment had a diameter of 10 mm and an overhang of 260 mm. The free mass, the clearance and the initial displacement used were m = 0.049 kg, CL = 0.4 mm and Yo = 0.6 mm, respectively. These values were chosen by taking into consideration the equivalent spring constant of the drill (9.1 kN/m), the ratio of the free mass to the main mass (the equivalent mass of the drill containing the jig shown in Fig. 15), and the relationships between the optimum clearance and the free mass shown in Table 3. The drill was made of high speed tool steel and the free mass was of brass (70% Cu and 30% Zn). 4.2. Experimental results Figures 16, 17 and 18, respectively, show the frequency of the drill f , the critical amplitude Yo and the corresponding logarithmic decrement \"y when the setting position of the impact damper was varied widely. From Fig. 16, as the setting position of the impact damper is apart from the end of the drill, the frequency increases in spite of the existence of the impact damper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure14-5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure14-5-1.png",
        "caption": "FIGURE 14-5 Shop-type or agricultural dynamometer. (Courtesy A. W. Dyna mometer Co.)",
        "texts": [
            " In either arrangement, the power put into or developed by the unit is 410 TRACTOR TESTS AND PERFORMANCE 2-rrCFn Power = 60,000' kW which is the same as for the Prony brake (equation 3). Shop-Type Dynamometers (5) It is often desirable to measure the pto power of a tractor in the field or in an implement dealer's repair shop. Since dynamometers, such as are shown in figure 14-3 or 14-4, are much too expensive and difficult to use except in laboratories, there have been developed several inexpensive and portable devices generally classified as shop-type or agricultural dynamometers. An example is shown in figure 14-5. This type of dynamometer is used primarily as an indicator of the condition of the engine. It is also used in the process of adjusting or tuning an engine and in indicating to customers the improve ment in a tractor engine as a result of an overhaul, maintenance, or adjust ment. DRAWBAR DYNAMOMETERS 411 The principle of operation of shop-type dynamometers is generally sim ilar to a hydraulic or a Prony brake dynamometer. Hydraulic pumps are also sometimes used. Since shop-type dynamometers are not constructed with the precision nor maintained with the care of laboratory dynamometers, they cannot be expected to have the accuracy attained by dynamometers used in engineering laboratories"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002098_j.mechatronics.2008.11.013-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002098_j.mechatronics.2008.11.013-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the 6-dof parallel seismic simulator.",
        "texts": [
            " So how to implement the actuator redundancy and improve the performance for the parallel manipulator, especially used for the application of the large load requirement, is a very interesting problem. It is also one of motivation for us to write this paper. This paper presents the development of 6-dof parallel seismic simulator with novel redundant actuation used for the application of large load requirement. The structure is presented firstly. Then, the kinematics analysis is carried out. In the following, the consideration for the prototype building is illustrated. Finally, the paper is finished with conclusions. The schematic of the 6-dof seismic simulator is shown in Fig. 1 and Fig. 2. As shown in Fig. 1. The parallel seismic simulator is composed of a moving platform and six sliders. In each kinematic chain, the platform and the slider are connected via spherical ball bearing joints by a strut of fixed length. Each slider is driven by Dc motor via linear ball screw. The detail of the implementation of the actuation is presented in the Section 4. The lead screw of B1, B2 and B3 are vertical to the ground. The lead screw of B4, B5 and B6 are parallel with the ground and are orthogonal to lead screw of B1, B2 and B3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002695_6.2012-1733-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002695_6.2012-1733-Figure3-1.png",
        "caption": "Figure 3. Fatigue test specimen geometry (in mm) unnotched (A) and notched (B).",
        "texts": [
            " Hence, the material density of the SLM parts equals the density of the VAR material. This will not only drastically improve the fatigue properties of the SLM-parts, it also eliminates the pores as driving force for fatigue failure. D ow nl oa de d by M O N A SH U N IV E R SI T Y o n N ov em be r 26 , 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /6 .2 01 2- 17 33 American Institute of Aeronautics and Astronautics 4 The geometry of the notched and the unnotched fatigue specimens is shown in Figure 3. Multiple oversized specimens were build up layer by layer using the in-house SLM machine, the optimal scanning parameters, the bidirectional scanning strategy and building direction (z) as illustrated in Figure 3. After this, Electrical Discharge Machining (EDM) was used to remove the excess of material and to machine the notch. The EDM-process was executed in deionised water through seven consecutive gradually finer steps leading to a surface roughness (Ra) of 0.85\u03bcm. Three different geometries were created with the same nominal cross section of 18mm\u00b2. The unnotched specimens were manufactured with an elliptical transition instead of a circular one in order to reduce the influence of the so called stair effect",
            " 15 For the production of these test samples, a bidirectional scanning strategy was used in combination with the optimal scan parameters as indicated in Table 1. The plain specimen fatigue limit (\u2206\u03c30) was determined according to the method described in subsection A. Apart from this analytical method, LC can also be found using a graphical procedure as shown in Figure 4. For the three different fatigue specimen geometries, the linear elastic FE-model was used to plot the maximum principle stresses along a line drawn from the root of the notch in a direction normal to the loading direction (z-direction in Figure 3). Using the linear-elastic material hypothesis, these three lines were then vertically shifted until the maximum values were equal to the local range of the respective endurance limits as determined in subsection A. The critical distance can then be found as the intersection between these three stress gradient curves. 27 D ow nl oa de d by M O N A SH U N IV E R SI T Y o n N ov em be r 26 , 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /6 .2 01 2- 17 33 American Institute of Aeronautics and Astronautics 7 IV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003763_s10846-017-0545-2-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003763_s10846-017-0545-2-Figure1-1.png",
        "caption": "Fig. 1 The goal of the MORUS project is to design a cooperative autonomous robotic system comprised of a UAV and an AUV, working together in a maritime environment",
        "texts": [
            " Bogdan Laboratory for Robotics and Intelligent Control Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia e-mail: tomislav.haus@fer.hr M. Orsag e-mail: matko.orsag@fer.hr S. Bogdan e-mail: stjepan.bogdan@fer.hr a Gazebo based simulator and experimental results of the testbed. Both results confirm the findings of our mathematical analysis. Keywords UAV \u00b7 Internal combustion engine \u00b7 Moving mass \u00b7 Root locus The work presented in this paper fits within the scope of an ongoing project called MORUS that aims to build a cooperative autonomous robotic system able to work both in air and underwater (Fig 1). To that end, an unmanned aerial vehicle (UAV) and an autonomous underwater vehicle (AUV) are brought to work together on a common goal, maritime surveillance. In the envisioned scenario, the UAV has to be capable of lifting the AUV and carrying it to a designated drop-off point. Ever since they were introduced to the mainstream [1], quadrotors have emerged as a number one research platform used in aerial robotics. Since then, numerous linear and nonlinear control algorithms have been proposed and tested",
            "1 Nonlinear Dynamical Model of the UAV with MMC Moving Mass Control (MMC) is a concept that relies on the change of CoG of the vehicle to ultimately distribute torque around the body in order to control its attitude. In total, a multirotor has 6 DOF, and in our implementation MMC controls only two of them, roll and pitch angle. Since the underlining physics of MMC cannot effectively control its other degrees of freedom, classical rotor speed control is applied to yaw angle and height control. The only two DOFs left (i.e. x-axis and y-axis) are controlled through high level controllers, and thus fall out of scope of this paper. The control structure is presented in Fig 1. Mathematical modelling starts with the well known formula for the time derivative of an arbitrary vector r0 expressed in the moving reference frame L0 (body frame), w.r.t. the inertial frame [13]: d\u03c9 dt (r0) = r\u03070 + \u03c9 \u00d7 r0, (1) where r\u03070 is vector rate of change in the moving reference frame. On the right side of the equation, \u03c9 represents angular velocity of the moving reference frame w.r.t. the inertial frame. In this paper \u03c9 represents the quadrotor\u2019s angular velocity. Note that d\u03c9 dt denotes the time derivative of a vector expressed in the moving frame w"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003640_j.cirp.2014.03.124-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003640_j.cirp.2014.03.124-Figure2-1.png",
        "caption": "Fig. 2. Linear spectrum of helicopter gearbox vibrations [1].",
        "texts": [
            " In pract modifications of the relative direction of the rotation axes of f conjugate surfaces may cause contacts on the edges of the fla This implies a significant increase of the noise and of the con pressure that finally will lead to the reduction of the efficiency the life time of the gear. That is one of the reasons why the flank a Gleason spiral bevel gear are not conjugate surfaces. They h systematically a transmission error without load, also ca kinematic transmission error. It directly affects the noise genera by the meshing. Coy [1] therefore suggests working on how decrease its amplitude without canceling it completely. The identification of the origin of noise is based on the result various vibration and acoustic measurements. Fig. 2 shows observed vibration spectrum nearby a helicopter gear box. spiral bevel gear generates the highest peaks in that case. 2. Transmission error analysis of the spiral bevel gear Numerous papers are dealing with the study of the transm sion error, this phenomenon playing a leading role on performance of gears. The earlier studies focus on the unloaded transmission er Vogel [2] determines it without generating the tooth flanks A R T I C L E I N F O Keywords: Optimization Finite element method Transmission error A B S T R A C T New methods and tools have been developed the last years to improve the understanding of meshing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001562_20.105039-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001562_20.105039-Figure2-1.png",
        "caption": "Figure 2 : Description of a coil",
        "texts": [],
        "surrounding_texts": [
            "In this paper the authors present the modelling of an induction machine using a non-linear magnetodynamic complex method coupled with the circuit equations .\nThe squirrel cage rotor is a polyphase circuit with connection between bars and end-rings . Eddy currents induced in the bars are important and the end-ring resistances have a considerable influence on the reaction of the rotor.\nNormally, we take into account the effect of the end-ring by calculating an equivalent conductivity on the bar, but in using this method we make an error on the distribution of induced current density in the bar of the rotor and in fact, we forget the effect of the end-ring inductance.\nIn using a formulation which combines the analysis of magnetic fields with electrical circuit equations taking the squirrel cage as a polyphase cycling circuit , we can model an induction squirrel cage machine [ 11 .\n1 - INTRODUCTION :\nThe magnetic vector potential form of Maxwell's equations yields to the solution of equation (1)\naA curl v curl A + (T- t (T grad V = 0\nat\nOhm's law is written as :\n(1)\nJ=-o (2 -+gradV) (2)\nWith the following notations : A : Magnetic vector potential v : Reluctivity of materials (T : Electricalconductivity J : Currentdensity V : Electricpotential One method that takes the term representing the eddy currents in a solid conductor, consists of solving equation (1) by means of complex variables. As a matter of fact we have [2] :\n(3) aA . =JWOA at\nAs a consequence of the non linearity of the magnetic materials of the iron sheets, the magnetic reluctivity is variable with respect to the field. To solve this problem, an iterative Newton - Raphson method has been used [2].\nThe presence of sinuso'idal sources, with non linear materials leads to a time variation of the stored magnetic energy. In order to compute the magnetic energy corresponding to a given maximum value of the induction, an equivalent B(H) curve, previously prepared, has been used[2] .\nIn the case of an induction motor, the rotor currents have the pulsation g o where g represents the slip of the rotor. In order to be able to model the induced currents in the cage, the pulsation g o will be considered in the rotor.\nThis hypothesis, however, leads to a wrong representation of the space harmonics, the pulsation of which is then :\n(1 - n (1 - g)) o (4)\nn being the rank of the harmonic. All these hypothesis yields to solve the two following\nequations.\ncurl veq curl A + j (T g o A + (T grad V = 0\nJ = - j (T g o A - (T grad V\n(5)\n(6)\nTo represent a voltage fed induction motor, circuit equations must be coupled with field equations. Furthermore, because the rotor cage is a polyphase, tridimen:ional circuit, a specific coupling method has been developped.\nThus, there is obtained a tool in which the resistances and the reactances of the end rings and of the end windings may be introduced. These quantities are computed analytically and complete the finite element analysis of the induction machine.\n2 - ROTOR EQUATIONS :\nThe finite element formulation of equations (5 ) and (6) leads to the following system of equations in the case of solid conductors [l].\n( [SI + jgw[Ll I [AI - [Cl [AV1 = 0\n- j o g [RI KIT [AI + [AV1 = [RI ID1 J\n(7)\n(8)\nWith\nJ.\nJ r\nJ\n0018-9464/91$01.00 0 1991 IEEE",
            "E E E TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 5, SEPTEMBER 1991\nBut the rotor cage bars are solid conductors connected together by means of the end rings. Every portion of the ring located between two bars may be considered as an extemal impedance. The rotor cage is then described by the polyphase Circuit of figure 1.\nL L L L I r r I\nAVa2 AVai AVai+l\nAV1 9 V 2 RcrroR AVbi-1 AVbi\nI1 12 l i - 1 I i l i t 1\nBARS d L d L r L t L\nA A A A -\n4247\nb\nAVbi+l 1 L\nLet ra and xa be respectivelly the resistance and the reactance of a portion of the ring. With reference to Fig 1, we obtain the following equations.\nAVbi-1 = 2AVai + AVbi (9)\nThe two equations (10) and (9) give the two following matrix equations.\n[Kl = [MINI (13)\n[AVa] = - 1/2[MIt[AVb] (14)\n(15)\nWhen substituting equation (1 1) with equations (13) and (14) one yields to.\n( ra + jgxa ) [rl = -[Tl[AVl\nWhere Finally, equauon (8) becomes, in the case of a rotor cage.\n[I = 1/2[M][M]f is a symemc band matrix.\n-jwg[RItClt[Al + ( 1 + [R l [ I /('a + M a 1 )[AV1 = O (16)\nThe currents in the bars may be obtained by the relation (15) . The resistance and the reactance of the end-rings are computed\nusing analytical methods.\n3 - STATOR EQUATIONS :\nStator coils are made of thin conductors in which the skin effect may be considered as negligible. In this particular case, it is possible to find a formulation that represents a voltage fed coil .\nLet us consider an N identical tum, coil connected to an extemal impedance q x t an2 supplied by a sinusokial voltage source\nOhm's law writes as follows :\nNS E = Zext I + (Av1.k - Av2.k) (17)\nk= 1\nWhen applying equation (2) on the NS conductors, NS\n-jw[C'lT[A1 + [R]-l[AV] = p] I\nequations are obtained leading to the following formulation [ 11.\n(18)\nA linear combination of equations (17) and (18) yields finally to\njw[DlTtC'lT[A1 + (Gxt + Rk) I = E (19) Ns\nk+ 1\nwith C.. ' - i j - N ssk L 1,I.i d n\nSince the conductors are thin, the potential difference across each conductor simply writes with respect to I.\nThe field equation (3) then becomes :\n[S][A] - [C][D] I = 0 (20)\nZext is the impedance of the end windings analytically computed.\n4 - RESULTS :\nComputations have been performed on a three phase motor, 4 poles, 50 Hz with a double cage rotor, the slots of which are not skewed (Fig 3) .\nThe measurements have been done by running the machine at a given speed, then coupling to the network .",
            "4248\nIEEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 5, SE\u20ac'EMBER 1991\nOn figure 4 are compared computed and measured values. The e m r on the absorbed current and on the power is less than 5 %. The error on the torque is some times greater than 5 % which shows the influence of the space harmonics that are not correctly represented by this model.\nThe study of the motor under 380 V, at ambient temperature gives the motor characteristics with respect to the rotor speed as represented in figure 7.\nI1 is the current in one phase of the stator and I2 is the current of the rotor seen by one phase of the stator . R2 is the dynamic resistance see by one phase of the stator.\nWhen modelling this motor at high temperature, the influence of the thermal effects on the electrical characteristics may be put into evidence (Fig 8) . All characteristics of the motor decrease with the temperature .\n5 - CONCLUSION :\nThe method presented in this paper is an extension to the harmonic solution of non-linear magnetodynamic problems of the nowadays classical finite element method.\nThe coupling of the circuit equation completes the 2D finite element method by introducing the possibility to take into account the 3D part of the motor. Another advantage is the abilite to include voltage sources .\nThis new method may be applied in induction machines with good approach of global values if spatial harmonics can be neglected .With this method we can have a good approach of all characteristics of the motor. This method can be used to build and to optimise new motors with less prototypes than a classical analysis .\nAKNOWLEDGMENT\nThe authors gratefully aknowledge LEROY-SOMER and Electricire De France for financial supporting part of the research.\nREFERENCES :\n[ 11 D.Shen,G.Meunier,J.L.Coulomb,J.C.Sabonnadi&re. \"Solution of magnetic fields and elecmcal circuits combined problems\", IEEE Trans. on Mag.,vol. MAG-21,N06, pp 2288-2291.1985 . [2] E.Vassent, G.Meunier, J.C.Sabonnadi&re,\" Simulation of induction machine operation using complex magnetodynamic finite elements Method.\" IEEE Trans. on mag, Vol MAG 25, No 4, july 1989. [ 31 D.Shen,G.Meunier.\"Modeling of squirrel cage induction machines by the finite elements method combined with the circuits equations\", Proc. of the Int. Conf. on Evolution and Modern Aspects of Induction Machines,Torino, pp 384-388.8-1 1 July 1986 .\nOn the field maps of figures 5 and 6, the double cage effect on the flux penetration during the starting up of the rotor, may be observed. The skin effect is very strong and the rotor resistance is multiplied by a factor of 2,5 when starting (Fig 7)."
        ]
    },
    {
        "image_filename": "designv10_10_0002600_1.4004962-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002600_1.4004962-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of a rolling element bearing",
        "texts": [
            " Elastic deformation between race and ball gives a nonlinear force deformation relation, which is obtained by using Hertzian theory. Other sources of stiffness variation are the positive internal radial clearance, the finite number of balls whose position change periodically, and waviness at the inner and outer race; all causes periodic changes in stiffness of bearing assembly. Taking into account these sources of stiffness variation the governing differential equations are obtained. A schematic diagram of rolling element bearing is shown in Fig. 1. In the mathematical model, the ball bearings are considered as a mass-spring system and contact act as nonlinear contact spring. Since the Hertzian forces arise only when there is contact deformation, the springs are required to act only in compression. In other words, the respective spring force comes into play when the instantaneous spring length is shorter than its unstressed length; otherwise the separation between ball and race takes place and the resulting force is set to zero. An unbalance force (Fu) is acted due to rotating of rotor with inner race"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure4-1.png",
        "caption": "Fig. 4 \u2013 Lateral arrangemen",
        "texts": [
            " The location of residual space depends on the location of the suspension of vehicle, its shape and the location of seats. The space may not be smaller than as defined by the regulation but the manufacturer may define a bigger residual space than is required to simulate the worst case and thus increase the safety margins in the case of emergency load and enable the maximum protection of passengers. The envelope of the vehicle's residual space is defined by creating a vertical transverse plane within the vehicle which has the periphery described by the regulation (Fig. 4) through the length of the vehicle. The characteristic points of the space, which define it, are SR points, through which a vertical transverse plane is moved through the length of the vehicle along straight lines (Fig. 5). The SR point is located on the seatback of each outer forward or rearward facing seat (or assumed seat position), 500 mm above the floor under the seat, 150 mm t of residual space [3]. from the inside surface of the side wall. No account should be taken of wheel arches and other variations of the floor height"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002831_1350650112462324-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002831_1350650112462324-Figure1-1.png",
        "caption": "Figure 1. A meshing helical gear pair.",
        "texts": [
            " In this work a steady-state thermal finite line contact EHL model is developed for the application of helical gears with a non-unity transmission ratio and three typical mesh locations are chosen to study the 1State Key Laboratory of Mechanical Transmission, Chongqing University, People\u2019s Republic of China 2School of Engineering, University of Warwick, UK Corresponding author: Huaiju Liu, State Key Laboratory of Mechanical Transmission, Chongqing University, Shazheng St. 174, Shapingba, Chongqing 400044, People\u2019s Republic of China. Email: huaijuliu@qq.com variation of lubrication details in a mesh cycle. Effect of load, speed and addendum modification coefficient on lubrication performance during the engaging are investigated. Figure 1 shows the engagement diagram of a helical gear pairs, and the base helix angle b is expressed as the angle between the contact line K1K 0 1 and the rotation axis. The ideal engaging surface is N1N 0 1N2N 0 2. The length of contact line K1K 0 1 first increases when engaging in and then turns out to be decrease when engaging out. The helical gear pair is assumed as two cones with the same conical degree, as shown in Figure 2. N1N 0 1, N2N 0 2 are the rotation axis of the two equivalent cones, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.8-1.png",
        "caption": "Fig. 1.8. Aerodynamic loads and moments expressed in aircraft-axis",
        "texts": [
            " These aerodynamic loads and moments depend on the status of the system (velocities, attitude, altitude), external conditions (velocity and direction of the wind, etc.), the The AIRBUS On-Ground Transport Aircraft Benchmark 11 configuration of the aircraft (slats, flaps, spoilers, etc.) and the position of the aerodynamic control surfaces (ailerons, rudder, elevators, etc.). Their determination is based on the identification of aerodynamic coefficients. In the model these loads are expressed in the aircraft coordinate system as illustrated in Fig. 1.8. The aerodynamic loads and moments are usually represented in the form of functions proportional to the dynamic pressure \u03c1, to the reference surface of the aircraft S, to the square of the air velocity Vair and to aerodynamic coefficients Cx, Cy, Cz, Cl , Cm, Cn Fxaero = \u22121 2 \u03c1SV 2 airCx Fyaero = 1 2 \u03c1SV 2 airCy Fzaero = \u22121 2 \u03c1SV 2 airCz Mpaero = 1 2 \u03c1S eaeroV 2 airCl Mqaero = 1 2 \u03c1S caeroV 2 airCm Mraero = 1 2 \u03c1S eaeroV 2 airCn (1.9) with eaero the wing span and caero the aerodynamic chord. The aerodynamic coefficients are determined from the angles of attack, sideslip, pitch, roll and yaw rates, deflection of the rudder, ailerons, elevators and the configuration of the aircraft, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000700_rsta.1997.0049-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000700_rsta.1997.0049-Figure12-1.png",
        "caption": "Figure 12. Notation for discs of oval shape.",
        "texts": [
            " Problems of this nature may be considered in a later paper but in what follows we present an inverse type of analysis that yields a numerical solution for pairs of touching discs of oval shape, the boundaries of whose flat lower surfaces meet the surface of the liquid. (b ) Inverse method of analysis for touching pairs of oval discs We assume that the pair of touching discs, whose shape is at present undetermined, exhibit symmetry both about their common tangent at the point of contact and about a horizontal line orthogonal to this tangent. With the notation of figure 12, C is the point of contact and D,D\u2032 are on each boundary diametrically opposite C; the points O1, O2 are at the centres of the diameters CD,CD\u2032, each of length 2\u03c7. We adopt polar coordinates \u03c11, \u03b81 and \u03c12, \u03b82 centred on O1 and O2 respectively but we focus attention on the right-hand disc. Guided by the results of \u00a75 and to satisfy all the symmetry conditions, we take the deflexion of the liquid surface to be given by \u03b6 = \u03b61 + \u03b62, (6.12) Phil. Trans. R. Soc. Lond. A (1997) where \u03b61 = A{K0(\u03c11) + \u00b5K1(\u03c11) cos \u03b81}, \u03b62 = A{K0(\u03c12)\u2212 \u00b5K1(\u03c12) cos \u03b82}, and A,\u00b5 are constants"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.7-1.png",
        "caption": "FIGURE 1.7 The influence of load transfer on the resulting axle characteristic.",
        "texts": [
            " The effective axle characteristic for the case of roll steer can be easily established by subtracting jri from ai. Instead of using the linear relationships (1.8) and (1.13), nonlinear curves may be adopted, possibly obtained from measurements. For the case of roll camber, the situation becomes more complex. At a given axle side force, the roll angle and the associated camber angle can be found. The cornering characteristic of the pair of tires at that camber angle is needed to find the slip angle belonging to the side force considered. Load transfer is another example that is less easy to handle. In Figure 1.7 a three-dimensional graph is presented for the variation of the side force of an individual tire as a function of the slip angle and of the vertical load, the former at a given load and the latter at a given slip angle. The diagram illustrates that at load transfer, the outer tire exhibiting a larger load will generate a larger side force than the inner tire. Because of the nonlinear degressive Fy vs Fz curve, however, the average side force will be smaller than the original value it had in the absence of load transfer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001823_bf00265715-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001823_bf00265715-Figure2-1.png",
        "caption": "Fig. 2. Free body diagram of forearm segment",
        "texts": [
            " The acceleration of the double linkage unit is produced by muscular forces acting across the elbow and wrist Y.-S. Hang et al.: Biomechanical Study of the Pitching Elbow joints. By measuring the acceleration of the centre of mass of the two segments [9] we can calculate the resultant inertial force component along the forearm segment at the elbow joint by solving the dynamic equilibrium equation. This is based on Newton's Law of F --- ma and d 'Alembert 's principle which stated, 'All external forces and inertial forces form an equilibrium system'. In the forearm segment (Fig. 2), a force mf~ generated by the muscle to produce forearm motion exerted a joint reaction force at the elbow Fe and at the wrist Fw respectively. This force also produced a t o r q u c If(Jr, which likewise exerted a moment M e at the elbow and a moment Mw at the wrist. By the same token, the moving handball segment (Fig. 3), produced a force mh~h which acted across the wrist joint Fw, together with a torque lhSh, which exerted an angular momentum across the wrist joint with a magnitude of Mw. From Newton's Second Law and the Angular Momentum Principle, the differential equations of Y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002860_s12239-013-0077-0-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002860_s12239-013-0077-0-Figure3-1.png",
        "caption": "Figure 3. Free body diagram of a full-toroidal CVT including one roller and two disks.",
        "texts": [
            " In ideal situation, there is no slippage between disk and roller. Therefore ideal velocity ratio is . Spin r1\u03c91 r2\u03c92\u2013 r1\u03c91 ------------------------= Spout r2\u03c92 r3\u03c93\u2013 r2\u03c92 ------------------------= e r0 --- Sr \u03c93 \u03c91 ----- 1 Spin\u2013( ) 1 Spout\u2013( ) r1 r3 --- 1 Sp\u2013( ) r1 r3 ---== = SrID r1 r3 ---= Therefore, speed efficiency could be obtained by (Carbone et al., 2004): (6) SP is the slip coefficient. As stated in equation (6) the slippage between disks and roller causes a decrease in speed efficiency. Figure 3 shows the free body diagram of a full-toroidal CVT. A kinetic analysis of this system can be found in (Carbone et al., 2004): (7) (8) Where FN is the normal force at the contact point, and are traction forces that exert input torque to roller and output disk, respectively. These traction forces are obtained by integrating the shear stress in the oil film over the contact area. Considering equations (7) and (8), to increase moment transfer ability, either normal force must grow or a type of oil with higher traction coefficient must be used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001598_j.ijmecsci.2006.06.013-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001598_j.ijmecsci.2006.06.013-Figure7-1.png",
        "caption": "Fig. 7. Geometry of the assembled gear set PZ9e285.",
        "texts": [
            " Both the software have been developed at the International Centre for Numerical Methods in Engineering of Barcelona (CIMNE). The software used in this work is accurate enough to make stress predictions. However, new finite element techniques can be found in the bibliography [7]. The profiles of the gears have to be defined very accurately in order to obtain a correct geometry of the assembled gear set. Initial penetration has to be avoided because a virtual interference would appear producing unreal results. That phenomenon is illustrated in Fig. 7. Fig. 8 shows the FEM mesh of the assembled gear set. The mesh is constructed by 26,270 unstructured P.J. Gamez-Montero et al. / International Journal of Mechanical Sciences 48 (2006) 1471\u201314801476 triangles with 17,845 nodes. The elements have been more concentrated on the gear profiles. That is because the entire internal gear profile becomes a contact point at any time of one complete revolution and the curvature of its teeth. Hence, the mesh density increases the required CPU time extremely and this has to be taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001880_j.mechatronics.2007.10.004-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001880_j.mechatronics.2007.10.004-Figure2-1.png",
        "caption": "Fig. 2. (a) First maneuver and (b) second maneuver.",
        "texts": [
            " Then, according to the value of , the maximum allowed reference vertical jerk \u20aczr is estimated in order to have the asymptotic amplitude of the signal n( ) sufficiently small to fulfill the restriction highlighted in Section 3.4. A final refinement of the value of KP can be done by possibly increasing its value in order to decrease the asymptotic effect on the tracking errors of the term De according to (37). We tested the control law on two possible desired maneuvers whose executions require aggressive attitude configurations. In the first scenario (see Fig. 2) we design a reference trajectory simulating an aggressive maneuvers realized with constant heading. Lateral and longitudinal dynamics have to follow a circular fast reference signal whose tracking requires very aggressive roll and pitch angles (near to 60 ). The overall reference trajectory of the first maneuver is precisely set to xr\u00f0t\u00de \u00bc 3S2t ; yr\u00f0t\u00de \u00bc 3C2t ; zr\u00f0t\u00de \u00bc 0; wr\u00f0t\u00de \u00bc 0: \u00f038\u00de The second reference signals have been chosen to test the control algorithm in a different scenario (see Fig. 2). More precisely we first ask the helicopter to track a fast ascendent trajectory with constant yaw and a aggressive pitch angle carrying the helicopter rapidly to a certain altitude with zero final speed. Then, in the second part of the trajectory, we ask the helicopter to move backward at a constant altitude without changing yaw attitude. Analytically we designed the following trajectory: xr\u00f0t\u00de \u00bc 16t 2t2; t < 4; 32; 4 6 t < 8; 32 8 3 \u00f0t 8\u00de; t P 8; 8>< >: zr\u00f0t\u00de \u00bc t2; t < 4; 16; t P 4: ( \u00f039\u00de The control algorithm has been tuned according to the procedures described in the previous sections using, as helicopter\u2019s nominal parameters, the values reported in Table 1 (which refer to MIT\u2019s X-Cell "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000956_0890-6955(95)00073-9-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000956_0890-6955(95)00073-9-Figure2-1.png",
        "caption": "Fig. 2. Experimental apparatus (setting for vertical vibration).",
        "texts": [
            " In this experiment, leaf springs with a width of 30 mm and an overhang of 165 mm were used as the main vibratory system. The leaf springs were vibrated in the direction of gravity and perpendicular to it. The case in which the leaf springs vibrate in the direction of gravity is called vertical vibration, while the case in which the leaf springs vibrate in the direction perpendicular to gravity is called horizontal vibration. In vertical vibration, a leaf spring was fixed on the table by two bolts as shown in Fig. 2. For the horizontal vibration, the leaf spring was fixed on the table by means of an auxiliary block in a state in which the leaf spring was rotated 90 \u00b0 around the center axis. To diminish the influence of the fixing condition of the leaf spring clamping part on the damping characteristics of the system, the thickness of the clamping part was kept at 20 mm, which was thicker than the thickness of the overhang, and the clamping torque was kept at a constant value of 29.4 Nm. A ring-shaped free mass indicated by the hatching was attached to the end of the leaf spring by the bolt shown in Fig. 2. The diameter of the bolt beneath the head is slightly smaller than the hole diameter of the free mass (12 mm), so that the free mass can move within a certain range (clearance). This range of free mass motion is called clearance CL herein. After an initial upward deflection (displacement) or an initial horizontal deflection was given to the leaf spring by the adjusting screw and the rod indicated in the figure, the rod was removed instantaneously by a hammer. The vibratory displacement of the leaf spring at this time was detected using an eddy current-type sensor. In this manner, the free damped vibration of the leaf spring with an impact damper could be observed. The vibratory system consisting of the leaf spring and the impact damper used in this experiment can be represented as the equivalent vibratory system illustrated in Fig. 3. As the leaf spring vibrates, the free mass m collides with the main mass M (actually the shank area indicated just below the bolt head in Fig. 2). Accordingly, the thickness of the leaf spring T was varied widely in order to investigate the damping effect of the impact damper when vibratory characteristics of the main vibratory system were different (mainly the main mass and the spring constant). Furthermore, in order to investigate the effects of the free mass m and the clearance CL on the damping capability of the impact damper, m and CL were varied greatly. The amount of free mass m was controlled by varying the diameter of the free mass D, indicated in Fig. 2; the size of the clearance CL was controlled by varying the diameter of the bolt d beneath the bolt head. The thickness of the leaf spring T, the free mass m, the clearance C L and the initial displacement Yo used in the experiment are listed in Table 1. The leaf springs were made of carbon steel for machine structural use (0.45% C) and the free mass was made of brass (70% Cu and 30% Zn). Figures 4 and 5 show the amplitude reduction of a leaf spring obtained from free damped vibrations. Figure 4 is the result for the vertical vibration and Fig",
            " The results of the natural frequency f , and the logarithmic decrement \"/o obtained from free damped vibrations of the leaf spring without a free mass are summarized in Table 2. The logarithmic decrement ~/o of the same leaf spring is affected by the initial displacement, but a mean value of logarithmic decrements is presented in the table. Furthermore, the values for the equivalent spring constant K and the equivalent mass M of the leaf springs are listed in the table. The equivalent spring constant K was obtained by applying a static bending load at the position (which coincides with the overhang of 165 mm in Fig. 2) where an initial displacement was given to make the leaf spring a free damped vibration. The equivalent mass M was calculated from the natural frequency f , and the equivalent spring constant K. On the other hand, the amplitude decrements of the leaf spring with a free mass differ considerably from those of the leaf spring without a free mass. In the case of the vertical vibration shown in Fig. 4, the amplitude linearly decreases from point A (first cycle) to point B (13th cycle). However, only a very small amplitude is maintained after point D (15th cycle)",
            " This equation has already been clarified in a previous report [9], and was introduced from an assumption that a free mass separates from a main mass and begins to collide with a main mass when the vibratory acceleration of a leaf spring becomes greater than the acceleration of gravity. With respect to the horizontal vibration, the critical amplitude has no relation to the natural frequency and remains low for the following reasons. The impact damper functions effectively when the amplitude of the leaf spring is large, because the vibratory energy is absorbed by the collision between the free mass and the main mass. As the amplitude of the leaf spring decreases, the free mass begins to contact the main mass (actually with the shank below the bolt head in Fig. 2) in a certain period of the vibration. At this time, as the vibratory direction of the horizontal vibration deviates 90 \u00b0 from the direction of gravity, Coulomb's friction occurs in the contacting area of the free mass and the main mass due to the relative motion between them. This frictional force always acts as a damping force on the system while the leaf spring vibrates. Therefore, the critical amplitude when the leaf spring vibrates in the horizontal direction has no relation to the natural frequency as shown in the figure and is smaller than the critical amplitude of the vertical vibration",
            " When the impact damper used in this experiment was applied to cutting tools, the following additional experiment was carried out in order to investigate to what degree the damping capability of cutting tools can be improved and what should be considered in the actual setting. The cutting tool used was a drill. As shown in Fig. 15, the drill was fixed to the tail spindle of a lathe by a three-jaw chuck, therefore the drill was in the state of a cantilever, with one end free and the other end fixed. A ring-shaped free mass with a diameter of 30 mm and a width of 15 mm was positioned a certain distance from the end of the drill using a jig, as illustrated in the figure. In the same manner as described in Fig. 2, after an initial displacement was given to the end of the drill by a rod, a free damped vibration was given to the drill by suddenly releasing the rod. The free damped vibration near the end of the drill was measured using an eddy current-type sensor. The drill used in this experiment had a diameter of 10 mm and an overhang of 260 mm. The free mass, the clearance and the initial displacement used were m = 0.049 kg, CL = 0.4 mm and Yo = 0.6 mm, respectively. These values were chosen by taking into consideration the equivalent spring constant of the drill (9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001110_cdc.2001.980449-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001110_cdc.2001.980449-Figure1-1.png",
        "caption": "Figure 1: The Inertia Wheel Pendulum",
        "texts": [
            "roceedings of the 40th IEEE Conference on Decision and Control Orlando, Florida USA, k e m k r 2001 FrAOl-3 Global Stabilization of a Flat Underactuated System: the Inertia Wheel Pendulum Reza Olfati-Saber California Institute df Technology Control and Dynamical Systems 107-81 Pasadena, CA 91125 olfati@cds.caltech.edu Abst rac t Inertial Wheel Pendulum (IWP) is a planar pendulum with a revolving wheel (that has a uniform mass distribution) a t the end. The pendulum is unactuated and the wheel is actuated. Our main result is to address global asymptotic stabilization of the inertia wheel pendulum around its up-right position. Simulation results are provided for parameters taken from a real-life model of the IWP. 1 Introduct ion Inertia Wheel Pendulum, depicted in Fig. 1, is a planar inverted pendulum with a revolving wheel at the end. The wheel is actuated and the joint of the pendulum at the base is unactuated. The inertial wheel pendulum was first introduced by Spong et al. in 131 where a supervisory hybrid/switching control strategy is applied to asymptotic stabilization of the IWP around its upright equilibrium point. Here. we show that based on a recent result of the author in [l], the dynamics of the inertia wheel pendulum can be transformed into a cascade nonlinear system in strict feedback form using a global change of coordinates in an explicit form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001593_15502280590923612-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001593_15502280590923612-Figure4-1.png",
        "caption": "FIG. 4. Inverted pendulum system.",
        "texts": [
            " Then, we can obtain the following positive definite matrices P(=W \u22121) and the feedback gains C\u03b2(=Y\u03b2 W \u22121): P = [ 2.7632 \u22121.0422 \u22121.0422 2.6941 ] , C1 = [\u22120.4927 4.7539], C2 = [\u22121.507 5.2238]. [40] Therefore, based on Theorem 3.1, the model-based fuzzy controller described in Eq. (38) can stabilize the nonlinear system N and the H\u221e control performance is guaranteed. The simulation result is illustrated in Fig. 3 with initial conditions, x1(0) = 2.5 and x2(0) = \u22121.9. 5.2. Example 2 Consider the problem of balancing an inverted pendulum on a cart shown in Fig. 4 to illustrate the control methodology. The dynamic equations of motion of the pendulum are given as following [5]:   x\u03071 = x2 x\u03072 = g sin(x1) \u2212 amlx2 2 sin(2x1)/2 \u2212 a cos(x1)u 4l/3 \u2212 aml cos2(x1) [41] where x1 denotes the angle (in radian) of the pendulum from the vertical and x2 is the angular velocity. g = 9.8 m/s2 is the gravity constants, m is the mass of the pendulum, M is the mass of the cart, 2l is the length of the pendulum, and u is the force applied to the cart (in Newtons). a = 1/(m + M)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.19-1.png",
        "caption": "Figure 6.19 Small antenna of length dP illuminated by an incident field.",
        "texts": [
            " We have seen earlier that under matched conditions, the power received by the load is (see (6.165)) (6.170) where it is assumed that RL = RA E Rr, Rr being the relation resistance of the antenna (i.e., we are assuming that the antenna is lossless, and Voc is given by (6.169)). 254 ANTENNAS AND RADIATION We assume a plane wave incident on an elementary receiving antenna I dl oriented along the z axis and receiving antenna oriented along the i axis and receiving, an incident linearly polarized field E' as shown in Figure 6.19. We have in this case the open-circuit induced voltage for (6.169), V& = h* . E' = Eo sin 6 d l (6.171) and By definition, the equivalent area is power received by the load incident power density at the antenna &(Q, $) = 7 (6.172) (6.173) Note that the effective area generally depends on the incident field direction. From (6.172) and (6.173) we obtain (6.174) EQUIVALENT CIRCUITS OF ANTENNAS 255 We know from (6.47) that for a current element I de radiating in an infinite medium of intense impedance 7, R, = p2 d12 7/67r"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001765_tsmcb.2007.913600-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001765_tsmcb.2007.913600-Figure1-1.png",
        "caption": "Fig. 1. Two-axis inverted-pendulum servomechanism. (a) Entire framework. (b) Spherical coordinate system.",
        "texts": [
            " Moreover, the major control designs of the cascade CTC and DAFC schemes are presented in Section III. In Section IV, numerical simulations and experimental results are performed to demonstrate the efficiency and applicability of the proposed methodology for the stabilizing and tracking control of the nonlinear two-axis inverted-pendulum servomechanism. Finally, some conclusions are drawn in Section V. In this paper, a nonlinear two-axis inverted-pendulum servomechanism that was established by Wai and Chang [15] is used for the controlled subject, as shown in Fig. 1(a). In this servomechanism, the inverted-pendulum mechanism, which is a combination of a cart, a pendulum, and a stick, is driven by two permanent-magnet (PM) synchronous servo motors through screw gears. The corresponding spherical coordinate system is depicted in Fig. 1(b), in which \u03b8 and \u03c6 represent the rotating angles of the stick in the X-axis and Y -axis directions. According to the Newtonian law and energy conservation principle, the entire dynamic model introduced from [15] can be organized by the following vector form in the stick angle and cart position coordinates: a\u0308 =f1(\u03b8, \u03b8\u0307, \u03c6, \u03c6\u0307) + G1(\u03b8, \u03c6)fv (1) p\u0308 =f2(\u03b8, \u03b8\u0307, \u03c6, \u03c6\u0307) + G2(\u03b8, \u03c6)u (2) where a = [\u03c6 \u03b8]T and p = [y x]T express the stick angle and cart position vectors, in which x and y are the displacements of the cart in the X-axis and Y -axis directions, respectively; fv denotes the control effort vector; u = [ux uy]T denotes the control force vector, in which ux and uy are the control forces in the X-axis and Y -axis directions, respectively; the detailed elements of the vectors and matrices f1(\u03b8, \u03b8\u0307, \u03c6, \u03c6\u0307), G1(\u03b8, \u03c6), f2(\u03b8, \u03b8\u0307, \u03c6, \u03c6\u0307), and G2(\u03b8, \u03c6) in (1) and (2) are given in Appendix I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000803_s0020-7403(03)00140-1-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000803_s0020-7403(03)00140-1-Figure3-1.png",
        "caption": "Fig. 3. Schematic of a laser cladding work-piece in analysis.",
        "texts": [
            " The work-piece is subjected to a laser beam striking uniformly and perpendicularly on a rectanglearea (3 mm \u00d7 3 mm) of the work-piece surface at a constant velocity, v = 3:33 mm=s along the longitudinal direction. As regards clad powders, those are mixed to the desired composition and adhered as a powder bed in the substrate so that the thickness of powder bed is a constant hc = 0:4 mm. Besides, the incident laser power is P = 456 W, only 60 percent of which is absorbed into the work-piece at ambient temperature 298 K. Since the loading is symmetric, only half the actual problem is modeled with adiabatic boundary applied along the symmetry plane (Fig. 3), discretized into eight-node brick elements as shown in Fig. 4, in which (a) and (b) are cross-section meshes on appropriate coordinates in the transverse and longitudinal directions, respectively. In the process, a quasi-steady state thermal !eld is attained within seconds soon after the laser beam starts to scan the surface. Fig. 5 shows a three-dimensional quasi-steady state temperature contours at a cladding time t = 20:0 s. Fig. 6 presents the shape and size of melt pool and the temperature contours near pool in the transverse cross section of y=16 mm at the instance t=4:8 s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001009_an9921701839-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001009_an9921701839-Figure1-1.png",
        "caption": "Fig. 1 (a) General scheme for a sequential injection set-up: HC, holding coil; D, detector. (6) Schematic representation of two zones being stacked in the holding coil next to each other and their mutual dispersion after the flow reversal",
        "texts": [],
        "surrounding_texts": [
            "Novel Single Standard Calibration and Dilution Method Performed the Sequential Injection Technique Alan Baron, Miguel Guzman, Jaromir R&Wka* and Gary D. Christian* Department of Chemistry BG- 10, Center for Process Analytical Chemistry, University of Washington, Seattle, WA 98195, USA 1839 bY A novel single standard calibration and dilution method utilizing the sequential injection analysis (SIA) technique is described. The SIA manifold employs a dilution conduit for storing a concentration gradient of an injected analyte, which provides for a variable calibration and dilution scheme suitable for both single and multizone analyses by taking selected aliquots from the gradient. This paper describes the principles of the method, the experimental characterization of the SIA manifold with Bromothymol Blue dye using a spectrophotometric detector and the application of the method to glucose determination using glucose oxidase by sensor injection analysis and by multizone stopped-flow analysis. Keywords: Flow injection; sequential injection; dilution, single standard calibration The use of flow injection (FI) techniques provides effective calibration and dilution schemes applicable to a variety of analytical methodologies.l.2 Recent developments in flowinjection analysis (FIA) have concentrated on the refinement of calibration techniques to accompany the wide range of analytical applications. A variety of dilution and single standard calibration schemes have been investigated, including calibration along the falling concentration gradient of an FIA peak,3.4 gradient scanning standard additions,5 and calibration according to the exponential dilution of a mixing chamber.6 A limitation of these methods, however, is the fact that none of them is valid for multizone analyses because the sample : reagent ratio changes with position along the tailing FIA peak. Sample dilutions for multizone FIA procedures require an initial dispersion of the analyte before merging with the reagent zone. In conventional FIA systems, the amount of dispersion is fixed for each flow manifold configuration and cannot be altered without changing some of the parameters of the manifold. Clearly, a variable dilution and calibration scheme suitable for both single zone and multizone analyses will bring a significant improvement to the current methodology. In the present study, a method was developed to generate a set of precisely diluted aliquots from a single standard using the sequential injection analysis (SIA) technique. This method applies not only to calibration set generation but also to dilution of analytes the concentrations of which exceed the working range of a detector. The diluted aliquots can be used for a variety of analytical procedures, including sensor injection, multizone analysis and stopped-flow analysis. A typical SIA set-up utilizes a multi-port injection valve coupled with a bidirectional flow pump7 [Fig. l(a)]. In order to perform an analysis with the SIA technique, well defined reagent and sample zones are sequentially aspirated adjacent to each other in a holding coil. After the valve has been moved to the detector position, the flow is reversed and the zones mutually disperse and penetrate each other as they pass through a reaction coil to the detector [Fig. l(b)]. An important advantage of the SIA technique is the versatility that the multiposition valve provides. Each port at the valve is dedicated to a specific purpose and the combinations of sample, standards, reagents and detectors around the valve are easily modified to suit a particular analysis. This paper describes a set of experiments where one port on a multiposition valve is dedicated to holding a dilution conduit, a tube where a concentration gradient of the analyte * Authors to whom correspondence should be addressed. is stored. This gradient is then used to generate a set of diluted standard aliquots. Aspiration of a sample from valve position 2 into the holding coil, followed by transfer of the zone into the dilution conduit at position 3, generates a concentration gradient along the physical length of the dilution conduit (Fig. 2). The concentration gradient along the conduit resembles a typical FIA peak. Subsequent aspiration of equal volume aliquots from the dilution conduit back into the holding coil, and then propelling them to the detector, effectively takes slices of the concentration profile established in the dilution conduit. At the detector, each sequential aliquot elicits a response which reflects the changing sample : carrier ratio of a portion of the concentration profile placed in the dilution conduit. Control over the magnitude and range of dilution for a particular conduit is effected with three volume parameters: sample volume, Vs, transfer volume, VT, and analysis volume, VA. The sample volume (V,) is the amount of sample or standard which is withdrawn into the holding coil via the sample port (see Fig. 2). The transfer volume (V,) describes the volume of sample plus accompanying wash in the holding coil and tubing which is transferred into the dilution conduit Pu bl is he d on 0 1 Ja nu ar y 19 92 . D ow nl oa de d by U ni ve rs ity o f Il lin oi s at C hi ca go o n 28 /1 0/ 20 14 1 8: 34 :5 6. View Article Online / Journal Homepage / Table of Contents for this issue"
        ]
    },
    {
        "image_filename": "designv10_10_0001604_iros.2005.1545594-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001604_iros.2005.1545594-Figure6-1.png",
        "caption": "Fig. 6. (a) The megabitty board and the sensors board used in the prototype of a microrobot; (b) 6-directional sensor system for directional communication and proximity sensing.",
        "texts": [
            " The current IF of IR emitters was limited to 20 mA, that corresponds to I/O ports of the microcontroller. Experiments have been done by measuring a voltage Vo on the emitter of phototransistor. The emitter resistance are chosen so that at a maximal reflection the max. voltage equals Vo \u2248 5V . Measurements have been done with the digital voltmeter \u201dVoltcraft M-3850\u201d. We purchased also only such devices that provide analog output signal, therefore such popular sensors as IS471F or Sharp\u2019s GP2Dxxx with binary output are not considered. In Fig. 6 we show some tested sensors (from over 30 pairs). The IR based signal transmission is actually not problematic, because a direct receiver-emitter optical connection provides enough IR radiation for stable communication channel. The points, that we have to be care about, are 60o opening angle with good sector coverage and communication distance. In experiments we used the following pairs TEST2600:TSSS2600, TEFT4300: (IRL80A, TSKS5400FSZ, LD271L), integrated sensors SFH9201, TCNT1000, TCRT1000, QRB1134, QRD1113",
            " For color sensing we tested TSLB257, TSLG257, TSLR257 color-light-to-voltage convertors. The main problem we encountered is that the color perception as well as a communication by color LEDs cannot be done in a presence of any ambient light. The sensor cannot differentiate whether the light comes from color emitter (or reflected light from colored object) or it is an ambient light. This problem is remained unsolved. The sensors used for communication and sensing are prototyped on the sensors board, shown in Fig. 6. Experimenting with this optical prototype, we encounter several problems with optical isolation. Tubes on the receivers and montage of both boards restrict opening angle too much so that communication-dead zones appear in the corner areas. This prototype is currently under redesigning. After describing the IR hardware solution, we focus on the \u201dsoftware support\u201d of communication and perception. Communication. As already mentioned, a propagation of information through a swarm represents the main problem (see for details [8])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001443_robot.2005.1570700-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001443_robot.2005.1570700-Figure5-1.png",
        "caption": "Fig. 5: Model of the handshaking simulation.",
        "texts": [
            " The amplitude of the oscillation depends on Input2, and then an adaptation occurs on the amplitude of handshaking motion. The relationship between signals in a neural oscillator is shown in Fig. 4. We determine typical values of parameters of the neural oscillator as follows, 0.2=iS \uff0c 5.2=ib \uff0c 8.0=ija , 1.0=rT , 05.0=aT , 2.1=iK , 024.0=iL , 02.0=iC . In order to examine the synchronization between humanrobot motions, we make computer simulations of handshaking. We assume that a parson shake hands using neural oscillators. Figure 5 shows an arm model for handshaking simulations. Each arm has three degrees of freedom in two dimensional space. Joints 1, 2 and 3 are shoulder, elbow and wrist joints, respectively. We assume that A arm is a robot arm, and B arm is a human arm. Input2Input1)1( )))()((()1( ')( 1 21 1 +\u2212+ \u2212\u2212+ +\u2212\u2212=+ \u2212 \u2260 \u2212 \u2260 \u2211 \u2211 j il lli j jk ijijijikikij ij r xgxgK sxbxgax dt dx T ),0max()( )(' ' ijij ijij ij a xxg xgx dt dx T = =+ (A arm is a robot arm, and B arm is a human arm.) The dynamic equation of the model is written by (7) where, M is the inertial matrix, h is the Coriolis force and centrifugal term, g is the gravity term, A\u03bb is the constraint force term between A and B arms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.29-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.29-1.png",
        "caption": "FIGURE 1.29 Single track model of car-trailer combination.",
        "texts": [
            " More specifically, we will study the possible unstable motions that may show up with such a combination. Linear differential equations are sufficient to analyze the stability of the straight-ahead motion. Wewill again employ Lagrange\u2019s equations to set up the equations of motion. The original Eqn (1.25) may be employed because the yaw angle is assumed to remain small. The generalized coordinates Y, j, and q are used to describe the car\u2019s lateral position and the yaw angles of car and trailer respectively. The forward speed dX/dt (zV z u) is considered to be constant. Figure 1.29 gives a top view of the system with three degrees of freedom. The alternative set of three variables v, r, the articulation angle 4, and the vehicle velocity V (a parameter) which are not connected to the inertial axes system (O, X, Y) has been indicated as well and will be employed later on. The kinetic energy for this system becomes, if we neglect all the terms of the second order of magnitude (products of variables), T \u00bc 1 2 m\u00f0 _X2 \u00fe _Y 2\u00de \u00fe 1 2 I _j 2 \u00fe 1 2 mc n _X 2 \u00fe \u00f0 _Y h _j f _q\u00de2 o \u00fe 1 2 Ic _q 2 (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure3-1.png",
        "caption": "Fig. 3. Illustration of the K-worm surface SwK.",
        "texts": [
            " Because the hob surface ShI is an involute helicoid, as is the worm surface SwI, ShI can be represented in the same manner as SwI by changing the subscript w to h for all parameters used for SwI. Therefore, as in the case of SwI, a position vector rhI ! of ShI can be represented in the coordinate system of the hob Ch[xh, yh, zh] as follows: rhI ! uh; \u03b8h\u00f0 \u00de \u00bc cos \u03b8h \u2212 sin \u03b8h 0 0 sin \u03b8h cos \u03b8h 0 0 0 0 1 \u03bdh 0 0 0 1 2 664 3 775 \u2212uh sin invh\u00f0 \u00de uh cos invh\u00f0 \u00de 0 1 2 64 3 75; \u00f02\u00de where invh = tan \u03c1h \u2212 \u03c1h, \u03c1h = cos\u22121(rbh/uh) and \u03bdh \u00bc \u03b8hlh 2\u03c0 . rbh is the base radius of the hob and lh is the lead of the hob. 2.1.2. Klingelnberg worm and hob surfaces As shown in Fig. 3, a surface of the conical grinding wheel to process the K-worm can be represented in the coordinate system Cc[xc, yc, zc] as follows: rc ! uc; \u03b8c\u00f0 \u00de \u00bc \u2212uc sin \u03b8c uc cos \u03b8c \u03b6 c 1 2 64 3 75; \u00f03\u00de where \u03b6 c \u00bc \u03c3\u00f0uc\u2212uc0\u00de\u2212 snc 2 and \u03c3 = tan \u03b1n. snc is the normal tooth thickness of the grinding wheel; uc0 is the pitch radius of the grinding wheel; and \u03b1n is the normal pressure angle. The family of the grinding wheel surfaces Sc is represented in the coordinate system of the worm Cw[xw, yw, zw] as follows: rwK "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure10-1.png",
        "caption": "Fig. 10 \u2013 Geometric model of bus frame \u2013 front view.",
        "texts": [],
        "surrounding_texts": [
            "The object of study was a bus structure based on Volkswagen LT vans type: 2DX0AZ model LT produced by Automet in Sanok, Poland (Fig. 9). The basic technical specifications of the vehicle are presented in Table 2. The body of the bus was made of steel characterized by the following properties (Table 3): yield limit, Re_min = 198 MPa, tensile strength, Rm_min = 364 MPa, elongation, A5 = 22% Table 3 \u2013 Tensile characteristics for the material of the body. Strain [ ] Stress (MPa) 0.005 210.3 0.01 222.5 0.02 245.2 0.04 277.5 0.06 299.8 0.08 316.6 0.10 328.8 0.12 341.0 0.14 347.8 0.16 353.1 0.18 357.5 0.20 361.1 0.22 363.7 According to the manufacturer (VW) the frame of the vehicle was made of steel St 12.03 and St 37-2, whose strength properties are listed in table: St 12.03 yield limit, Re_min = 210 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% St 37-2 yield limit, Re_min = 235 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% Taking into account the quantitative changes in the material, i.e. the strain rate, the material model based on the assumed viscoplasticity of the material was obtained. A broad review of this characteristic is included in works [10,11]. The hardening velocity \u00c7 e equals elastic hardening velocity \u00c7 eel and viscoplastic hardening velocity, \u00c7 ev p \u00c7 e \u00bc\u00c7 eel \u00fe \u00c7 ev p; whereas the value of stress equals: s \u00bc E \u00c7 e \u00c7 ev p ; where E is the elasticity module. The finite element method uses the models of hardening at deformation velocity based on the abovementioned model, e. g. Cowper\u2013Symonds model [12]: s \u00bc\u00c5 s0 1 \u00fe \u00c7 e D 0 @ 1 A 1= p2 64 3 75; where \u00c5 s0 is the static yield limit, p, D are material constants, equalled to 5 and 40 s 1 respectively. The bodywork is supported by a frame on wheels (twin wheels in the rear). The bodywork was furnished with basic elements of bus interior, i.e. seats, seats frame, reinforcement of side wall, reinforcement of back wall, reinforcement of roof with a support structure for the emergency compartment, shelves and ventilation shaft and the air-conditioning system. It also includes glass panes which are glued to the reinforced body structure. All these elements constitute a load to the bodywork structure but do not alter its original shape. The first stage was to prepare the geometric model of the external shape of the structure. The strength calculations [13] were conducted using specialized software which implements an explicit algorithm for computing simultaneous differential equations [14]. The geometric model served as a basis for a discreet model of the bus bodywork, which was used for calculations using the finite element method. The body and frame were modelled using shell elements. These are rectangular four-node shell elements with 6 degrees of freedom in the node. The average size of the finite element is approximately 20 mm. Due to the fact that during a strength test the material may be subject to partial plastification (material nonlinearity) and large hinges may cause the configuration to change significantly (geometric nonlinearity), all finite elements are adapted to calculations with both types of nonlinearity [15]. The geometric model of the bus is shown in Figs. 10 and 11. The discrete model with division into finite elements is presented in Figs. 12 and 13. In total the discreet model comprises 105 151 finite elements on 102 879 nodes. The complete model has approximately 617 000 degrees of freedom. Since there are two rows of seats on the left side of the bus, the centre of gravity is somewhat moved leftwards relative to the axis of the vehicle. Its coordinates relative to the system, whose beginning is on the tilting edge above the rear wheel, are presented in Table 4. By tilting the bus on its right side the worst case was analysed (greater kinetic energy). From the law of conservation of energy: Ep \u00bc Ek; Table 4 \u2013 Moments of inertia relative to the edge of tilt (the Z axis along the tilting edge) (kg T m2). Ixx Iyy Izz 28130 28840 7226 Ixy Iyz Izx 2586 4036 6493 where Ep is the potential energy, Ek is the kinetic energy of rotational motion. Thus, in accordance with point the Regulations Ep \u00bc M g h1 \u00bc M g 0:8 \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 0 \u00fe B t\u00f0 \u00de2 q where M = Mk is the unladen kerb mass of the vehicle type if there are no occupant restraints, or Mt is the total effective vehicle mass when occupant restraints are fitted, and, Mt = Mk + k*Mm, where k = 0.5. h0 is the height (in metres) of the vehicle centre of gravity for the value of mass (M) chosen, t is the perpendicular distance (in metres) of the vehicle centre of gravity from its longitudinal vertical central plane, B is the perpendicular distance (in metres) of the vehicle's longitudinal vertical central plane to the axis of rotation in the rollover test, g is the gravitational constant, h1 is the height (in metres) of the vehicle centre of gravity in its starting, unstable position related to the horizontal lower plane of impact. Ek \u00bc I v2 2 where I is the moment of inertia relative to the temporary axis of rotation (Table 4), v is the angular velocity relative to the temporary axis of rotation. Therefore v \u00bc 2:558 rad=s Fig. 14 depicts main initial conditions of the analysis. An additional initial condition was the influence of gravity and the contact phenomena occurring on the contact points of the bus bodywork and the tilt plane as well as in the structural elements of the superstructure. Method of performing the strength test of the bus is shown in Fig. 14 while Fig. 15 presents the location of the seats inside the vehicle and the definition of residual space [16]."
        ]
    },
    {
        "image_filename": "designv10_10_0000991_s0022112003005147-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000991_s0022112003005147-Figure5-1.png",
        "caption": "Figure 5. Variation with \u03bb of dimensionless average swimming velocity of axisymmetric cells (B = 0.8) at Pe= 0, 15 and 100 and (a) \u03c6f = 0\u25e6, (b) 60\u25e6, (c) 95\u25e6 and (d) 120\u25e6. , locations of stable nodes of the deterministic problem at indicated values of \u03bb; *, corresponding e\u0304 for Pe= 100.",
        "texts": [
            " Between these \u2018small\u2019 and \u2018large\u2019 values of \u03bb, there may exist an intermediate domain whose extent depends on both \u03c6f and the intrinsic shape parameter B . In this domain, multiple stable attractors may simultaneously coexist or else orientation space may be divided into separate domains wherein different modes of rotary motion occur. These differences in the deterministic rotary motion show up in the following description of the effective phenomenological transport coefficients. 4.1. U\u0304 , the average swimming velocity Figure 5 presents the effect of \u03c6f , the azimuthal direction of external field on the variation of U\u0304/U = e\u0304 with \u03bb. The solid curves describe the variation of e\u0304 in the plane of shear at Pe =0+, 15 and 100 and the arrows indicate the sense of increasing \u03bb. The open circles denote the projections on the plane of shear of the stable nodes of the corresponding deterministic rotary motion together with the relevant values of \u03bb. The corresponding locations of e\u0304 are marked by asterisks on the respective curves pertaining to Pe =100",
            " Similarly to spheres, the largest values of the component of U\u0304 perpendicular to F\u0302 (which is essential in gyrotactic focusing) occur at \u03bb slightly larger than those corresponding to the first appearance of stable equilibrium orientations. With the exception of \u03c6f = 95\u25e6 these, however, take place at \u03bb considerably smaller than 1/2. Figure 6 presents the variation of |U |/U , the (dimensionless) average swimming speed, with \u03bb at Pe =15 (figure 6a) and 100 (figure 6b). At both values of Pe, the average swimming speed at \u03c6f = 95\u25e6 is significally smaller than at all other values of \u03c6f presented. Furthermore, at Pe =100 the ascent of |U |/U is non-monotonic for \u03bb 0.7. Referring back to figure 5(c), we note that for 0.71 \u03bb 0.9, a pair of stable nodes simultaneously coexist. This has a profound effect on the resulting orientation distribution and hence on the average swimming speed (as well as the effective rate of dispersion, see figure 9 and the discussion pertaining thereto.) (Also in this context, Pedley & Kessler (1987, 1992) speculate on potential implications of the existence of a pair of stable equilibria in pure straining flows.) 4.2. D\u0304, the Taylor dispersivity Similarly to the dispersion of spheres, we here focus also on the eigenvalue \u03bd and the corresponding eigenvector u\u0302 characterizing D\u0304",
            " This difference originates from the orientation distribution of axisymmetric particles at large Pe and arbitrarily small \u03bb becoming increasingly concentrated in a boundary layer about the stable attractor (e.g. a limit cycle) of the corresponding deterministic problem (Almog & Frankel 1998). Less intuitive is the appearance of respective maxima in the variation with \u03bb. Apparently we anticipate that, with growing intensity of external field, P \u221e 0 becomes increasingly concentrated about the average orientation (which, in turn, approaches F\u0302, see figure 5). This is expected to result in the diminishing of the forcing term of the B-field equation (2.15) and consequently of B and D\u0304 as well. While for very large values of \u03bb, \u03bd indeed eventually vanishes (approximately as (\u03bbPe)\u22122, Manela 2002), for Pe sufficiently large this process is non-monotonic. Some insight into this behaviour is gained by considering the fields P \u221e 0 , B2 (the component of B in the direction of ambient fluid velocity) and the product P \u221e 0 (\u2207eB2) 2. Numerical evidence indicates that this product forms the main contribution to \u03bd within the present range of parameter values",
            " To simplify the description, figure 8 presents only the variation of these fields with the azimuthal direction \u03c6 for particle orientations within the plane of shear (\u03b8 = \u03c0/2), i.e. along the equator of the unit sphere. Figure 8(a) presents the corresponding sections of P \u221e 0 . At \u03bb= 0, this distribution consists of two identical peaks \u03c0 apart from each other (the entire distribution being invariant under \u03c0-translation in \u03c6, cf. Almog & Frankel 1998). With increasing intensity of external field, it, on the average, transfers particles from the vicinity of the right-hand peak to that of the left-hand one (being closer to \u03c6f , cf. the discussion of figure 5). This enhancement of the left-hand peak is accompanied by only a slight shift towards \u03c6f . Figure 8(b) depicts the effect of \u03bb on B2. Two maxima of \u2202B2/\u2202\u03c6 are discernible. With increasing \u03bb, the relatively milder slope on the right-hand side changes only slightly in magnitude and remains nearly in phase with the right-hand peak of P \u221e 0 . The sharper left-hand slope is ever steepening with increasing \u03bb. At the same time, this peak is shifting to smaller \u03c6, thus becoming out of phase with the corresponding peak of P \u221e 0 ",
            " Rather, significant densities occur over a wide interval of azimuthal angles. Furthermore, with increasing Pe, a secondary peak is emerging. These unique features are related to the occurrence of the abovementioned \u2018intermediate domain\u2019 of external field directions and magnitudes in which domain of \u03c6f and \u03bb the deterministic rotary motion of spheroids is affected by the simultaneous coexistence of multiple stable equilibrium orientations. Thus, at \u03c6f = 95\u25e6 a pair of stable nodes exist for \u03bb between 0.710 and 0.907 (cf. figure 5 and the discussion pertaining thereto). Figure 10(c) for \u03c6f =95\u25e6 shows in the same interval of \u03c6, large gradients of B2 which are still intensifying with Pe. Owing to the peculiar nature of the corresponding P \u221e 0 , these gradients appear where significant densities exist (unlike all other cases, when the B2 gradients only appear at the outer margins of P \u221e 0 ). As shown in figure 10(f ), the combination of these P \u221e 0 and B2 results in large values of the product P \u221e 0 (\u2202B2/\u2202\u03c6)2 throughout a considerable portion of orientation space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-25-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-25-1.png",
        "caption": "FIGURE 5-25 Diagram of a two-stroke-cycle diesel engine showing cycle of events. (Courtesy Detroit Diesel Division, General Motors Corp.)",
        "texts": [
            " Ignition of the charge of fuel and air. 4. Power stroke. In this step the heat energy in the fuel is converted into mechanical energy. 5. Exhaust stroke. In this step the burned gases are pushed out by one stroke of the four-stroke engine. In the case of the two-stroke engine, a Roots blower, or some other positive displacement air pump, scavenges the burned gases out of the cylinder by forcing clean air into the cylinder after the gases expand far enough to expose the air intake ports in the side of the cylinder (see fig. 5-25). Construction of Diesel Engines The major difference between a spark igmtlOn engine and a compression ignition engine is the compression ratio. Theoretically, there is a wide range in the type or kind of fuel that can be used in a diesel engine. However, in 1986 the fuels most commonly used in diesel engines were the heavy hydro carbon (petroleum) fuels called distillates, which, when used in diesel engines, are called diesel fuels. Because diesel fuels require a temperature above their autoignition temperature in order to ignite, it has been necessary to build diesel engines with a compression ratio of 14: 1 or greater"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure10-1.png",
        "caption": "Figure 10. Baseline geometry. (a) Full view, (b) sliced view and (c) front view.",
        "texts": [
            " Using this method, the excessive number of degrees of freedom of typical finite element (FE) models is reduced to a number of mode shapes that can be superpositioned to reproduce the total structural deformation. Loads can be applied to flexible bodies through interface nodes. The flexibility of the supporting structure of the outer ring is included by creating a FE model of the bearing housing and outer bearing ring. The shaft is assumed to remain circular, which is a good assumption even for hollow shafts, as the one analysed in this study and shown subsequently in Figure 10. In the final model evaluations, a hollow shaft is used with very limited errors. Along the circumference of the outer raceway, a number of interface nodes are added for subsequent transfer of roller contact loads to the outer raceway. The roller loads of the six-dof model are summarized into three forces and two moment components, whereas the multi-dof model has a number of single component forces andFigure 2. Bearing azimuth cut view. at Eindhoven Univ of Technology on June 17, 2014pik.sagepub",
            " 1 4:5 \u00f032\u00de According to ref [11], the basic bearing reference life is calculated as the statistical combination of the predicted life of the bearing outer raceway and the predicted life of the bearing inner raceway L10 \u00bc Xns k\u00bc1 qc,1k qe,1kt 4e \u00fe qc,2k qe,2kt 4e\" # ! 1 e \u00f033\u00de at Eindhoven Univ of Technology on June 17, 2014pik.sagepub.comDownloaded from where e is the Weibull slope approximated as 9/8 according to ref [21]. The presented multi-dof bearing model is evaluated in a comparison with a FE model. This section presents the model setup, the FE model and the time-domain simulation model. The presented bearing model is evaluated using the wide spread back-to-back mounted tapered roller bearing housing shown in Figure 10. The housing and shaft are made from cast iron using the elastic properties E\u00bc 170GPa and \u00bc 0.275. Despite the large distance from the bearing to the supporting feet, the setup is indeed appropriate for demonstrating the effect of an uneven stiffness of the bearing housing. Besides the overall bearing dimensions shown, the basic properties of the two identical bearings are listed in Table 1. The shaft is loaded in the centre of the front bearing and the axial preload is zero. Using zero preload is not realistic but used in the frame of demonstration only"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002705_acc.2011.5990793-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002705_acc.2011.5990793-Figure1-1.png",
        "caption": "Fig. 1. Boundary layer nonlinearities We find the DF of the nonlinearity )(\u03c3f as follows [11]:",
        "texts": [
            " We apply the describing function (DF) method [11] to the analysis of motions in the system (1), (2) having the control (6), (7) or another single-valued monotone odd-symmetric continuous function f(\u03c3) fully located in the 1st and 3rd quadrants and satisfying the following conditions: hf \u2264)(\u03c3 , (8) \u03a6 = = hf 0d )(d \u03c3\u03c3 \u03c3 (9) 0 d )(d 2 2 < \u03c3 \u03c3f (10) The first condition specifies that the function must be saturating, and the second condition sets the limit on the derivative of this function, matching it with the derivative of the linear approximation (5). The nonlinearity satisfying conditions (8)-(10) is fully located in the area defined by the saturation function (6) (Fig. 1). \u222b= \u03c0 \u03c8\u03c8 \u03c0 0 )sin(2)( daf a aN , (11) Because the function is odd-symmetric, we rewrite (11): \u222b= 2/ 0 )sin(4)( \u03c0 \u03c8\u03c8 \u03c0 daf a aN , (12) It follows from (8)-(10) that the DF of the nonlinearity )(\u03c3f is a monotone function of amplitude a satisfying         \u03a6 \u2212 \u03a6 + \u03a6 \u03a6 \u2264< \u2212 2 2 1 1sin2)(0 aaa haN \u03c0 , (13) \u03a6= /)0( hN (14) For the nonlinearity given by (7), \u03b5 \u03c3 \u03c3 \u03c3 hNf == = )0( d )(d 0 that falls into the definition (8)- (10) when \u03a6=\u03b5 . The condition of the absence of chattering as self-excited oscillations in the closed-loop system that includes the plant (with possible parasitic dynamics), the sliding surface, and the considered nonlinear controller can be formulated as the absence of solution of the harmonic balance equation: )(/1)(0,0 aNjWa l \u2212\u2260\u2265\u2265\u2200 \u03c9\u03c9 , (15) where )( \u03c9jWl is the frequency response of the linear part (plant and sliding surface)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002122_s0263574708004256-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002122_s0263574708004256-Figure5-1.png",
        "caption": "Fig. 5. Geometrical determination of dexterous workspaces of the manipulators.",
        "texts": [
            " The geometrical workspace can be obtained by examining each branch individually and taking the intersecting regions of the reachable workspace of all three branches.1 For each branch of the 3-PRR, link DiBi can rotate about point Di as this point slides with the prismatic joint. Since each point of the dexterous workspace must be able to rotate from 0 to 2\u03c0 , the radius of the circle at all positions must be li \u2212 ri .19 This creates an oval shape for each leg. Their intersection constitutes the dexterous workspace as shown in Fig. 5(a). For the 3-RPRR, since branch i can also rotate around point Ai , the dexterous workspace is obtained by rotating the oval shapes for branch i around points Ai when the latter are located at a zero length prismatic stroke, as shown in Fig. 5(b). The geometric parameters of the 3-PRR and the 3-RPRR manipulators based on Fig. 1 are: A1A2 =A2A3 = A3A1 = 1.0 m, B1B2 = B2B3 = B3B1 = 0.10 m, ri = 0.0577 m, li = 0.25 m, \u03c81 = 7\u03c0 6 , \u03c82 = 11\u03c0 6 , \u03c83 = \u03c0 2 , \u03c1maxi = 0.577 m and \u03c1mini = 0 m. Based on Figs. 5(a) and 5(b), the 3-PRR nonredundant manipulator dexterous workspace is 0.196 m2 and the redundant 3-RPRR manipulator dexterous workspace is 0.261 m2, an increase of more than 33%. The increase in the area of the dexterous workspace of the redundant versus http://journals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003820_1.4039386-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003820_1.4039386-Figure11-1.png",
        "caption": "Fig. 11 The hydraulic variable preload spindle",
        "texts": [
            " fTg is the temperature vector of all nodes, and fQg is the heat generation vector of all nodes. For the given spindle-bearing system, the heat generation vector fQg are all from bearing nodes, which can be obtained by Eqs. (31)\u2013(35). Therefore, the temperature of any node as shown in Fig. 9 can be obtained by solving the matrix Eq. (37). 4.1 The Test Rig. In order to validate the proposed model in this paper, an experimental setup for the hydraulic preload spindle with rated rotational speed of 12,000 rpm has been built. As shown in Fig. 11, the 7014C bearings with the duplex back to back arrangement were used, and the initial preload 2160 N (1080 N for a single bearing) was applied by the compression springs. Four Pt100 temperature sensors with resolution of 0.1 C were used to measure the temperature of bearing outer rings, and the preload levels can be adjusted by the oil pressure in hydraulic oil 053301-8 / Vol. 140, MAY 2018 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 03/22/2018 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003164_s12283-012-0084-9-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003164_s12283-012-0084-9-Figure7-1.png",
        "caption": "Fig. 7 Top view of same bat swing (subject A) showing set, downswing, impact, and follow through phases of the swing. The bat aim angle at impact is noted",
        "texts": [
            " For instance, the bat is at rest and the end of the barrel is located at the origin of the field-fixed frame at the start of the swing and returns to this state at the end. Moreover, the location of the ball on the tee is also known relative to the field-fixed frame and, at impact, the barrel of the bat contacts the ball at/near the sweet spot \u2018\u2018s\u2019\u2019. These known kinematic conditions can be exploited to reduce/identify drift error in arriving at the following animations of threedimensional bat motion. Figure 7 illustrates the bat motion for the previous example (subject A) as viewed in the horizontal plane from a top view perspective looking down onto the batter. The bat in the middle of the set phase (dark blue image), the downswing, at impact (red image), and during the follow through are notated. These images are constructed every 10 ms with the exception of the ten (dark) images surrounding impact which are constructed every millisecond. This 10 ms period centered about impact is denoted as the \u2018\u2018hitting zone\u2019\u2019 in which the bat remains in a well-defined \u2018\u2018swing plane\u2019\u2019 (see below) just prior to, during and just after ball impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-22-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-22-1.png",
        "caption": "FIGURE 12-22 Hydraulic system for a White 2-155 tractor. (Courtesy White Farm Equipment Co.)",
        "texts": [
            " F is the feedback loop, which might be either a mechanical linkage at tached to an \"error bar\" (see fig. 12-18) or a pressure line to sense the load on, or the position of, the output of the cylinder, as in hydrostatic power steering. Further information on automatic control theory can be obtained from the references at the end of the chapter. A concise and yet complete treatise on automatic hydraulic, or fluid power, control systems is provided by Merritt ( 1967). The method of automatically controlling a three-point hitch can be vis ually grasped by a thorough study of figure 12-22. This illustration shows the hydraulic system controlling the three-point hitch on a series of large tractors by a major manufacturer. Complete Hydraulic System The complete hydraulic system used on one tractor is shown schematically in figure 12-23 and is illustrated using symbols in figure 12-24. This system includes a circuit for a remote cylinder, a circuit for the three-point hitch servo valve, a circuit for steering, a circuit for brakes, a circuit for the pto clutch, a circuit for the differential lock, and several circuits for lubrication since most of the power train is lubricated by hydraulic fluid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.5-1.png",
        "caption": "Figure 6.5 Geometry of the spherical surface S with origin at 0 and the antenna at 0.",
        "texts": [
            " Note that the assumption de << A is satisfied. Again, the near and far zone type of variations of field are evident in Figure 6.4. Note that for this case the fields for 100 kHz are entirely in the near zone within the range of T shown. Also in the near field region the field strength is greater at lower frequencies, and it increases with increase of frequencies in the far field region. 208 ANTENNAS AND RADIATION In an unbounded medium, the total power radiated by the current element is given by Prad = 3;, s a v . ds, (6.39) where (Figure 6.5) S is a closed spherical surface in the far zone surrounding the antenna, S a v = .i.ISavI is the power flow density or the radiation density produced by the antenna at the location of an elementary vector surface ds located on S at (0,$): ds = i d s = i r 2 s i n 0 d0 d$ = ? r 2 dR with dR as the solid angle subtended by ds at the origin 0 of S (Figure 6.5). We now rewrite (6.39) as (6.40) RADIATION FROM A SHORT CURRENT ELEMENT 209 where = T ~ Wholid angle 2rl (6.41) is defined as the radiation intensity of the antenna in the direction 8 , 4, which physically represents the power radiated from the antenna per unit solid angle. Note that U ( 8 ) , as defined, is independent of T and in general is a function of 8 and 4. Using (6.40) and (6.38), we find in the present case ~ ( 8 ) = UO sin2 8 (6.42) with (6.43) as the maximum radiation intensity produced by the current element in the direction 8 = r / 2 ",
            " Wherever possible we utilize the dipole results given earlier as an illustration. Our discussion will be brief; more detailed description can be found in textbooks on antennas, for example, in [ 1-61. We will assume that a given antenna is radiating in a linear, lossless, isotropic, and homogeneous medium of infinite extent. We will hrther assume that the FUNDAMENTAL ANTENNA PARAMETERS 219 antenna is radiating TEM spherical waves and its phase center, assumed to be somewhere in the antenna, is located at the origin 0 of a spherical coordinate system as shown in Figure 6.5. The far zone radiation fields E and H of the wave produced by the antenna are orthogonal to each other, and they are each orthogonal to the radiation direction from an antenna that is also the direction of propagation of the waves. Thus, most generally, the radiation fields of the antenna can be written as with (6.71) (6.72) With the fields given above, the time average power flow for the wave is S , = R e ___ [ \"2\"*] = Re [ ~ ( E o H ; - EdH,*)5.] (6.73) 220 ANTENNAS AND RADIATION In view of (6.72) we obtain from (6.73) (6.74) The power flow in the radial direction (6 ' ,$ ) and through an elementary vector surface ds located on a large spherical surface S having its origin at 0 (see Figure 6.5) is dP(B, 6) = Sav. dS = ISavlr2 sin 6' d6' d$ = ISavlT2 do, (6.75) where dR is the solid angle included by the surface dS as shown in Figure 6.5. We now define the radiation intensity U(6',$) in a direction (6 ' ,$ ) as the power radiated in that direction per unit solid angle and has the units of watts per square radian (or steradian). Thus symbolically the radiation intensity is given by = r2 1 S a v 1 , Wlsteradian (6.76) where we have used (6.75). Note that since for a spherical wave ISavI 0: (1/r2), U(6',$) is independent of distance T , but in general, it is a function U(B,$ ) versus ( B , $ ) is called the power pattern of the antenna"
        ],
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    },
    {
        "image_filename": "designv10_10_0003199_05698196208972467-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003199_05698196208972467-Figure2-1.png",
        "caption": "FIG. 2. Test appara tus",
        "texts": [
            " The five-ball fati gue test er consists essent ially of a driven test ball pyramided upon four lower support ball s positioned by a separa tor and free to rot at e in an an gular-contact raceway. Specimen load ing and dri ve is supplied through a vertical sha ft. By va ry ing th e pitch diameter of the four lower suppor t balls, th e bearing contac t angle ['l IFi g. 2 (b) 1 may be contro lled . The an gular spin velocity (J) \" can be approxi mat ed by th e pr odu ct of th e sha ft angular veloci ty Wi and th e sine of th e contac t angle ~ . The five-ball fa t igue test er was also designed to ac commoda te a 204-size full-scale bearing in place of th e test specimen assembly [Fig. 2 (a ) 1. Loading and drive for th e bearing are th e same as for the test specimen. In strumentation provides for automa tic fai lure det ecti on and shutdown when a bearing or ball specimen fati gue spall occurs, makin g possible long-t erm unm onitored test s. In all test s , th e ball specimens and the 204-size bearin zs were lubrica ted bv a svnthe tic diest er fluid mee ting th e ~ IIL-L- 7 808C -specifica t ion, int rodu ced in mist form. OPEHATING-T EMPERATUHE l\\I EASUHING D EVICE T he five-ba ll fa tigue test er was modifi ed in order to measure th e temp era ture near th e contact area of a mod ified test specimen during ope ra tion"
        ],
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    },
    {
        "image_filename": "designv10_10_0000579_s0094-114x(98)00043-3-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000579_s0094-114x(98)00043-3-Figure1-1.png",
        "caption": "Fig. 1. A Stewart platform mechanism with octahedral arrangement.",
        "texts": [
            " However, the derivation of this 16thorder polynominal equation is a quite arduous and time-consuming task, because it would involve complicated variable transformations and require one to employ Bezout's method [10] to perform complicated algebraic manipulation. In addition, even such a 16th-order polynominal equation has been successfully derived, to search all of its possible solutions once again becomes another challenging and time-consuming task. The purpose of this paper is just to establish a mathematical algorithm which could e ciently solve the direct displacement kinematic problem of parallel mechanisms. A special type of the Stewart platform mechanisms with an octahedral arrangement, as shown in Fig. 1, is studied. Numerical results have shown that not only is the present algorithm simple and e cient, but the computer program can also be easily implemented. Most of all, the solution of the direct displacement kinematic problem can be obtained just requiring a few iteration steps. The octahedral Stewart parallel mechanism considered in this paper is illustrated in Fig. 1. This mechanism consists of a top platform, a base platform, and six extensible links. The six extensible links are arranged so that they are connected to the top platform at three distinct points R, S and T with spherical kinematic pairs, and to the base platform at three distinct points A, B and C with universal joint pairs. This arrangement makes this mechanism an octahedron, and provides the top platform with 6 dof. The dimensions of this mechanism required in the following calculations are: for the base platform, the lengths of lines AB, BC and CA are denoted as LA, LB, and LC, respectively; for the top platform, the lengths of lines RS, ST and TR are denoted as b1, b2 and b3, respectively; for the actuating devices, the lengths of the six links are denoted as L1, L2, . . . , L6, respectively. Now, consider the mechanism in Fig. 1 with the top platform RST being removed for the moment. In the triangle ARB, point R must be located on a sphere G 1 with its centre at B and with a radius equal to L1. In addition, R must also be located on another sphere G 2 with its centre at A and with a radius equal to L2. Thus, the actual locus of point R must be located on the intersection of the two spheres G 1 and G2. From the knowledge of geometry, it is known that the locus of this intersection will be a circle with its centre at Or, and Or must be located on the line joining the points A and B",
            " Similarly, the linkages ATC and BSC can now be replaced by the links OtT and OsS, with the revolute joints at Os and Ot and spherical joints at S and T, respectively. These replacements are shown in Fig. 2. Next, consider the mechanism shown in Fig. 2 with the top platform RST being placed. This con\u00aeguration leads to a three-arm, parallel mechanism as shown in Fig. 3. As compared with Fig. 2, Fig. 3 reveals that additional constraints on the movement of the joints R, S and T will be imposed. These additional constraints state that the distances between joints R and T, R and S, and S and T, should be \u00aexed. As compared with Fig. 1, Fig. 3 shows that the present three-arm parallel mechanism is kinematically equivalent to the octahedral Stewart platform mechanism of Fig. 1. As the determination of the locations of the revolute joints Or, Os and Ot of Fig. 3 is a ected by the displacements of the six links of Fig. 1, thus in Fig. 3 we use the lengths r1, s1 and t1 to locate the positions of the revolute joints of Or, Os and Ot, and, also, the lengths of OrR, OsS and OtT are denoted as mr, ms and mt, respectively. It is also noted that r1, s1 and t1 can be regarded as another three variables, these three variables contribute to additional degrees of freedom. The relationships between the variables of r1, s1, t1, mr, ms, and mt in Fig. 3, and the link lengths L1, L2, . . . ,L6 in Fig. 1, are derived \u00aerst. As shown in Fig. 4, in the triangle ARB, because the line OrR is perpendicular to the line AB, according to the Pythagorean theorem, one can derive the following expressions: r1 L2 A L2 1 \u00ff L2 2 =2LA; r2 LA \u00ff r1; mr L2 1 \u00ff r21 1=2: 1a Similar procedures could also be applied in the triangles BSC and CTA, and one can lead to the expressions: s1 L2 B L2 6 \u00ff L2 5 =2LB; s2 LB \u00ff s1; ms L2 6 \u00ff s21 1=2; 1b t1 L2 C L2 4 \u00ff L2 3 =2LC; t2 LC \u00ff t1; mt L2 4 \u00ff t21 1=2: 1c Next, it is necessary for us to de\u00aene the position vectors of the revolute joints of Or, Os and Ot",
            " This iteration process is repeated to solve the associated incremental quantities (Df n r , Df n s, Df n t ), where the superscript ``n`` indicates the step number in the iteration procedure, until the three incremental quantities (Df n r , Df n s, Df n t ) simultaneously become a value smaller than a prescribed value, say x. Typically, this procedure could be converged within a few iteration steps. The problem studied here is to determine the inclination angles (fr, fs, ft) of an octahedral Stewart platform mechanism illustrated in Fig. 1, with the lengths of the six links given. The associated coordinates and dimensions which are required in the calculations are listed in Table 1a The X- and Y-coordinates of the joints A, B and C on the base platform; Table 1b link lengths of the actuating devices of the octahedral Stewart platform mechanism; and Table 1c dimensions of the top platform Table 1a. Joint I/D A B C X-coordinate \u00ff5.1 1.4 3.6 Y-coordinate \u00ff5.9 9.0 \u00ff1.0 Table 1b Link I/D L1 L2 L3 L4 L5 L6 Length 9.18 9.14 5.64 8.93 7.73 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000830_s0736-5845(96)00023-3-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000830_s0736-5845(96)00023-3-Figure11-1.png",
        "caption": "Fig. 11. Intersection of singular surfaces R 4, R 6 and R s.",
        "texts": [
            " Therefore, continuation curves, previously unexplained in physical space, are now identified as the trace of a singular surface at which the manipulator loses at least one degree of freedom. The intersection of two singular surfaces, cut by a plane, specified by method I as a bifurcation point, is now identified in physical space as the projection of the intersection of two singular surfaces on to a plane. Since at a bifurcation point there may exist two singular surfaces, the manipulator loses at least two degrees of freedom. To illustrate, consider the intersection of singular surfaces R s, R 4 and R 6 as shown in Fig. 11, for which the singularities are s4 = {q3 = n, q4 = 20}, s6 = {q2 = 20, q3 = re} and Ss = {q2 = 20, q4 = 20}. The common constant generalized coordinates are q2=20, q3=n and q4=20. Therefore, the actual intersection in space yields a curve for which only joint 1 (q0 is allowed to rotate generating a curve. The projection of this curve on a cutting plane used in method I, yields the so-called bifurcation point (point 2 on Fig. 2). Robotics & Computer-Integrated Manufacturing \u2022 Volume 13, Number i, 1997 a symbolic manipulator (MATHEMATICAl) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001713_13552540710719172-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001713_13552540710719172-Figure3-1.png",
        "caption": "Figure 3 Test part and direction of measurements",
        "texts": [
            " The dimensions of the part were according to the ASTM standards for testing Plywood, since Plywood has a similar behaviour to the paper used in LOM, because of the limitation of the working envelope of the LOM machine, the test part was scaled down by a factor of 0.739, so that it could fit on the platform of the machine. Additionally, in each experiment, 20 layers of paper were set on the platform before starting the process. This results in obtaining the desirable temperature of the surface. In addition, chamfer temperature was kept constant. Surface roughness (Ra) measurements were executed in Z direction as shown in Figure 3 with the appliance, DIAVITE DH-5. The nose transverse length was 4.8mm. The Taguchi design method is a simple and robust technique for optimizing the process parameters. In this method, main parameters, which are assumed to have an influence on process results, are located at different rows in a designed orthogonal Volume 13 \u00b7 Number 1 \u00b7 2007 \u00b7 17\u201322 D ow nl oa de d by N or th er n A lb er ta I ns tit ut e of T ec hn ol og y A t 1 5: 07 2 3 Fe br ua ry 2 01 5 (P T ) array. With such an arrangement randomized experiments can be conducted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001450_detc2006-99628-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001450_detc2006-99628-Figure2-1.png",
        "caption": "Fig. 2 Some parallel mechanisms with both spherical and translational modes at their lockup configurations.",
        "texts": [
            " In this section, we will discuss how to obtain parallel mechanisms with both spherical and translational modes by assembling these legs. In assembling a 3-DOF parallel mechanism with both spherical and translational modes, it should satisfy both the assembly conditions for the spherical parallel mechanisms that guarantee the moving platform can undergo at least the spherical motion [8] and the assembly conditions for the translational parallel mechanisms [19] that guarantee the moving platform can undergo at least the translational motion. This requires that all the axes of R\u030b joints and the R\u030c intersect at one common point (Fig. 2). To guarantee that the DOF of the parallel mechanism with both spherical and translational modes is three and not greater than three at a regular configuration, the linear combination of all its leg-wrench systems should be a 3-\u03b60-system if the parallel mechanism works in the spherical mode or a 3-\u03b6\u221e-system if the parallel mechanism works in the translational mode. From the previous section, it is found that a leg for parallel mechanisms with both spherical and translational modes has a wrench system of order 1 or 0 in a regular configuration (Table 4). Since the wrench system of each leg varies with the change of its configuration, we make the assumption that such conditions are met as long as a 3-DOF parallel mechanism with both spherical and translational modes is composed of at least three legs with a 1- wrench-system listed in Table 4 with/without legs with a wrench system of order 0 (Fig. 2). The geometric constraints among legs of a parallel mechanism can be clearly shown in a configuration of the parallel mechanism in which all the legs with a 1-wrench-system are in their transitional configurations. The above configuration of the parallel mechanism is called (a) a lockup configuration [Fig. 3(c)] if the linear combination of all the leg-wrench systems is a 6-wrench-system, (b) a lockup\u2194translation configuration Copyright  2006 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Down Table 4 Legs for parallel mechanisms with both spherical and translational modes",
            " 3(d)] if there are no more than two independent \u03b6\u221e in the linear combination of all the leg-wrench systems. In the lockup configuration [Fig. 3(c)], the DOF of the moving platform of the parallel mechanism is 0. In the lockup configuration [Fig. 3(c)], lockup\u2194translation configuration [Fig. 3(b)], or lockup\u2194rotation configuration [Fig. 3(d)], each leg can rotate about the axes of its R\u030b joints. Let us take the 3-R\u030b(RRR)ER\u030b parallel mechanism with both spherical and translational modes shown in Fig. 2(a) as an example. In the lockup\u2194translation configuration shown in Fig. 3(b), the axes of the second joints of all the legs are parallel to a plane. The axis of the \u03b60 of each leg is in fact parallel to the axis of the second joint within the same leg. Thus, there are two indepen- Copyright  2006 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Dow 7 Copyright  2006 by ASME nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 03/11/2018 Terms of Use: http://www.asme",
            " The axes of the two R\u030b joints within a leg, which are coaxial in a transitional configuration, are parallel to each other if the parallel mechanism works in the translational mode or intersect each other at the centre of rotation of the moving platform if the parallel mechanism works in the spherical mode. By assembling the legs listed in Table 4, their variations, and legs with a wrench system of order 0, a large number of parallel mechanisms with both spherical and translational modes such as the two parallel mechanism shown in Fig. 2 can be obtained. Without considering the variation of legs, as it can be seen from Table 4, one can obtain 43 types of 3-legged parallel mechanisms with both spherical and translational modes with identical types of legs. According to the validity condition for actuated joints of translational parallel mechanisms [19] and spherical parallel mechanisms [8], one can find that the three joints located on the base can be used as actuated joints in both the translational mode [Fig. 4(a)] and the spherical mode [Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001523_j.optlastec.2005.08.012-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001523_j.optlastec.2005.08.012-Figure1-1.png",
        "caption": "Fig. 1. Schematic of laser direct formation (LDF).",
        "texts": [
            " Laser cladding provides a route to generate metal parts directly from CAD drawings. It is originally a surface treatment process. During this process, an alloy is fused onto the surface of a substrate [1]. In fact, laser cladding can be considered as a type of material additive manufacturing technology. Laser cladding devices, including powder feeder, CNC workstation table, laser unit, and shielding gas controller, are integrated to make automatically any cladding profile possible. As shown in Fig. 1, metal powder is e front matter r 2005 Elsevier Ltd. All rights reserved. tlastec.2005.08.012 ing author. ess: liujichang2003@sohu.com (J.C. Liu). transmitted through a nozzle to a substrate, and some powder is heated by a focused laser, melted and clad on the substrate. The work table is moving in x, y and z directions, driven by instruction from a computer according to a layered scanning trajectory from a stl. file-in-which a CAD file of a part is transferred to, or directly from the CAD file"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000707_0167-6911(95)00075-5-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000707_0167-6911(95)00075-5-Figure3-1.png",
        "caption": "Fig. 3. A V/STOL aircraft.",
        "texts": [
            " The initial tracking errors are Ax(O) = 1000 m, Ay(O) = 0 and A~O(0) = ~z/2. Despite the large initial errors, the trajectory converges on the reference quickly and gracefully. Fig. 2 contains the corresponding control (bank angle) history. The control bounds are enforced as in (18). Example 5.2 Control of a V/STOL Aircraft. Consider the planar jet-borne flight control of a vertical/short takeoff and landing (V/STOL) aircraft [4]. A schematic for such an aircraft in a vertical plane is shown in Fig. 3. During the jet-borne flight, the nozzles o f the aircraft engine can be rotated down to provide thrust (u]) directed out the bottom of the aircraft. A reaction control system (RCS) can provide the rolling moment to produce proper roll angle (u2). I f we use ul and u2 as the controls, the point-mass equations of motion of the aircraft in dimensionless variables can be written as \u00a3 = - u l sin uz, (48) y = - I + ul cosu2, (49) where x and y are the position coordinates, ' - 1 ' is the gravitational acceleration, ul the thrust acceleration in 9 and u2 the roll angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.14-1.png",
        "caption": "Figure A.14 Current I through the surface S is the integral of J through a surface S.",
        "texts": [],
        "surrounding_texts": [
            "PRODUCT OF VECTORS 425\nNow\nA . B = I A l O P = B - A\nA . C = C - A = j A / P Q\n... A . B + A . C = IAI(OP+PQ) = IAIOQ\n= A - ( B + C).\nScalar products, particularly in the integral form, are frequently encountered in physical problems.\n1 . Work done by a force F in moving a body of unit mass along a path ab is (Figure A. 13)\nb W = l b d w = .I F - d l . (A.2 1)\n2. Given a volume current density J in a region as shown, the current I through a surface S is (Figure A. 14)\nI = L J - d s . (A.22)",
            "426 VECTORS AND VECTOR ANALYSIS",
            "PRODUCT OF VECTORS 427\nIt follows from the definition of the dot product of two vectors A, B that (1) if OAB = x/2, then A . B = 0 (that is, the dot product vanishes for two orthogonal vectors); and (2) if ~ A B = 0 (that is, when A is parallel to B), then A 1 B = IAl IBI. Hence A . A = a relation used to determine the magnitude of a vector:\n]A] = (A-A) l l2 , (A.23)\nprovided that we know how to evaluate A . A. We will illustrate the general procedure by using the rectangular system of coordinates when (2,fi, 5 ) are the orthogonal set ofunit vectors. By definition, it can be shown that\nTake the two vectors A and B expressed as\nB = ZB, + fiBY + iBz .\n(A.25)\nThen, using (A.23) and (A.24), it could be shown that\nA - B = AxBx+ A,By + A,B,, (A.26)\nwhich gives the algebraic expression for A . B in terms of the components of the vectors.\nFrom (A.26) it follows that with A = B\n(A.27)\nSince the scalar product of two vectors A, B is independent of the coordinate system used, (A.26) can be generalized as\nwhere (Ap , Ab, A,) and (AT, A@, A@) are the cylindrical and spherical components of A and B, respectively."
        ]
    },
    {
        "image_filename": "designv10_10_0001368_icar.2005.1507466-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001368_icar.2005.1507466-Figure6-1.png",
        "caption": "Fig. 6. A downview of a force-transfer-mechanism",
        "texts": [
            " A MECHANISM OF FORCE TRANSMISSION In this section, we describe a mechanism of transmitting force to a basketball as a spherical tire. We show a force-transfer-mechanism, which we developed, in Fig.5 and 6. However, forces are friction forces between wheels and a basketball. In Fig.5, a drive axis and a free rotation axis are shown. A drive axis is to transmit force on a basketball, and a free rotation axis isn\u2019t to transmit force on it. Two axes are orthogonal. And a wheel is sliced on both sides. In Fig.6, two wheels are shown. A DC-motor drives two frames, which have a drive axis, respectively. Then, a chain synchronizes two frames and a DC-motor. And wheels, which frames have, contact on a basketball, either-or or both. It\u2019s no problem that wheels contact both. Since, wheels are synchronized, and they transmit the same forces and velocities. We don\u2019t need to know which wheels contact. This useful feature is used in calculations of motors\u2019 torques and angler velocities. Those methods are described in next section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure4.8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure4.8-1.png",
        "caption": "Figure 4.8 rectangular pulse signal. Pulse width 7 and time period T = l / f o . (a) amplitude spectrum, ( b ) phase spectrum, and (c ) spectral intensity of a",
        "texts": [
            "J71w0T/2 sin(nworl2) T riwor/2 a, = - Taking the results, we obtain (4.22) (4.23) (4.24) (4.25) n = 0 , 1 1 , f 2 , . . . , where we have expressed the coefficients in terms of the fundamental frequency f o . Equations (4.24) and (4.25) give the two-sided amplitude and phase spectrum for the rectangular pulse signal. The one-sided spectral intensity of the same signal is given by for n = 0 for n # 0, that is. (4.26a) (4.26 b) POWER SIGNALS 127 Various spectra for the rectangular pulse signal are shown in Figure 4.8, where we have indicated the use of a continuous frequency variable f = nfo. Note that the envelopes of the amplitude spectrum and spectral intensity can be expressed in terms of the sin x/x function. For example, (4.27) with f as a continuous variable. Equation (4.27) indicates that the zero a,\u2019s occur at f = - , m = *1\u2019*2,.. . . (4.28) \u2019m 7 and for the spectral intensity shown in Figure 4 . 8 ~ . and Figure 4.8: The following observations are made from an examination of (4.27), (4.29) 1. All component frequencies or spectral lines are located at integer multiples of the fundamental frequency, i.e., they are given by nfo = $. 2. As the fundamental frequency increases (or T decreases), the density of spectral lines decreases and the amplitude of the lines increases. 3. The shapes of the envelopes of the amplitude spectrum and the spectral intensity are primarily of the form 9. We consider a special case having application to clock signals used in digital systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001721_tac.2007.900825-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001721_tac.2007.900825-Figure4-1.png",
        "caption": "Fig. 4. Variable measurement interval, noise magnitude \" = 0.",
        "texts": [
            "1 m is practically the same as in the absence of noises with (Fig. 3). Note that the magnitude of the actual control is about 16 and the vibration frequency is about 0.5 , which is quite feasible. Mark that is close to the typical human reaction time. Note also that the real performance might be measured by the maximal steady-state distance of the car trajectory from the desired one, which is much smaller than (Fig. 3(a)). Performance with the variable measurement step in the absence of noises with and is shown in Fig. 4. The accuracy is obtained with [Fig. 5(a) and (b)]. The performance of the controller is slightly improved by the restriction (15) of the measurement step from above. With large noises the restriction actually provides for the same performance of the controller as with the constant sampling interval [Fig. 5(c) and (d)]. The demonstrated performance of the controllers does not significantly change when the noise frequency varies in the range from 10 to 100000. The simulation data listed in Table I confirm the asymptotics claimed in Theorems 3\u20136"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001672_j.robot.2007.06.001-Figure18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001672_j.robot.2007.06.001-Figure18-1.png",
        "caption": "Fig. 18. Nonlinear spring\u2013damper model between the foot and the ground.",
        "texts": [
            " This is a very useful characteristic because there are usually errors involved in modeling robots. Even though we assumed that the supporting foot is fixed on the ground in the previous simulations, the supporting foot is not fixed on the ground in reality, and there is a dynamic interaction between the feet and the ground during walking. Here, we will incorporate this dynamic feature in the simulation for more realistic environments. The contact between the supporting foot and the ground was modeled by nonlinear springs and dampers as shown in Fig. 18 [44]. Its dynamics is f = \u2212\u03bb\u03b4\u03b4\u0307 \u2212 K \u03b4, where f is the ground reaction force, \u03b4 is the penetration depth, K is the spring coefficient and \u03bb is the nonlinear damping coefficient [43]. In the contact model, K was 5 \u00d7 105 N/m and \u03bb was 7.5 \u00d7 106 N s/m2 [44]. Fig. 19 shows that the ZMP errors oscillate and are bigger compared to those in Fig. 9. In the sagittal plane, the ZMP errors in MMIPM and VHIPM are smaller than 20 mm but those in IPM, GCIPM and TMIPM are greater than 60 mm as shown in Fig. 19(a)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5\u00b719-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5\u00b719-1.png",
        "caption": "FIGURE 5\u00b719 Equivalent dynamic system for a connecting rod.",
        "texts": [],
        "surrounding_texts": [
            "PISTON CRANK KINEMATICS 97\n5 - r[ (l - COS 8) + ~-l sin2 8 J\n= r[ (1 - cos 8) + ~l (l - cos 28) J (5)\nThe piston velocity (i at a given crank angle can be derived by differ entiating equation 5 ,,-ith respect to time t to obtain\nds ds d8 ( r ) v = dt = d8 dt = rw sin 8 + 21 sin 28 (6)\n,,-here w is the angular velocity of the crank. The maximum velocity of the piston is attained when\nd8 rw (cos 8 + 7 cos 28 ) o\nfrom \\\\\"hich\n(7)\nIt is noted that the values of 8 at which the piston velocities are maximum or minimum depend upon the connecting-rod-to-crank ratio. Usually the piston attains its maximum velocity at 75\u00b0 to 80\u00b0 from top dead center at which the angle between the crank arm and connecting rod is close to being perpen dicular.\nThe acceleration of the piston can be obtained by differentiating the expression for the piston velocity with respect to time. Thus\ndv dv d8 , ( r ) a = dt = d8 dt = rw 2 cos 8 + I cos 28\nThe maximum and minimum values for acceleration are attained when\nda = 0 d8\nfrom which we obtain\nor\nsin 8 = 0\n. 2r . sm 8 + I S1l1 28 = 0\nand cos 8 = 4r\n(8)\nThen at the angles of 8 = 0 and 8 = 27T, ,,\u00b7hich correspond to top and bottom dead center respectively, the maximum accelerations are attained.\nThe piston and the upper part of the connecting rod are assumed to",
            "98 ENGINE DESIGN\nhave a reciprocating motion. If the mass of the reciprocating part is denoted as M, the inertia force F acting on the mass can be expressed as\nr F = Ma = Mrw2 (cos 8 + l cos 28) (9)\nIn equation 9, the terms containing cos 8 and cos 28 are called the first and second harmonics of the inertia force respectively. It is noted that the inertia force F increases in proportion to the square of the angular velocity, resulting in a large value for a high-speed engine.\nInertia Force of Connecting Rod\nIn order to obtain the inertia force of the connecting rod, an equivalent dynamical system having the same inertia force and couple as the connecting rod is considered. The upper part of the connecting rod is considered to have a reciprocating motion and the lower part of the rod is assumed to have a rotating motion. The connecting rod shown in figure 5-19( a) is considered",
            "INERTIA FORCE OF CONNECTING ROD 99\nto be equivalent to the system with two concentrated masses, mel and me2, located at distances a and b apart from the center of gravity G as shown in figure 5-19( b). For the system (b) to be dynamically equivalent to the system (a) in figure 5-19, the following conditions must be satisfied:\n1. Total masses for the two systems are equal. 2. Locations of the centers of gravity are the same. 3. Moments of inertia for both systems about the center of gravity are equal.\nFrom the conditions 1 and 2 the following expressions are derived, noting that a + b = l .\nmeb mel l or b\nmel I me\nme2l a\nmea = or me2 = T me\nThus the mass me of the connecting rod can be divided into two masses, mel and mc2, located at distances a anJ b, respectively, from the center of gravity_ For condition 3 the moment of inertia f for the equivalent system is expressed in the form\nIf fa is the moment of inertia of the original system [fig. 5-19(a)], the inequality fa < h holds in general. To compensate, a ring of radius R and mass 11m will be placed about the center of gravity as shown in figure 5-19(c). Then the moment of inertia !1I of the ring about G is expressed as\n!1I = I1mR2\nHence !1I can be determined to satisfy\nfa = fb - !1I\nAddition of !1I increases the total mass of the system by 11m and results in condition 1 not being satisfied. However, this problem can be practically solved by taking the ring radius R to be large enough so that 11m can be made small enough to be negligible. Then, considering the inertia force of the connecting rod, only the inertia forces of the reciprocating mass mel and the rotating mass me2 are taken into account, neglecting 11m. For the inertia couples about the center of gravity, the inertia couple due to !1I must be considered in addition to the couples due to mel and me2."
        ]
    },
    {
        "image_filename": "designv10_10_0002766_s11044-011-9281-8-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002766_s11044-011-9281-8-Figure1-1.png",
        "caption": "Fig. 1 The 3-PRS parallel manipulator",
        "texts": [
            " The origin of this coordinate central system is located just at the center G of the moving triangle. The kinematical constraints of each leg limit the motion of spherical joint of each limb to a plane perpendicular to the axis of the revolute joint and containing the spherical joint. In the symmetrical version of the manipulator, the first leg A is typically contained within the Ox0z0 vertical plane, whereas the remaining two legs B,C make angles \u03b1B = 120\u00b0, \u03b1C = \u2212120\u00b0 respectively, with the first leg (Fig. 1). To simplify the graphical image of the kinematical scheme of the mechanism, in the follows we will represent the intermediate reference systems by only two axes, so as used in most of books [1, 3, 9]. The zk axis is represented for each element Tk . It is noted that the relative rotation with \u03d5k,k\u22121 angle or relative translation of Tk body with \u03bbk,k\u22121 displacement must always be pointing about or along the direction of zk axis. In the following we consider that the moving platform is initially located at a central configuration, where the platform is not rotated with respect to the fixed base and the mass center G is located at an elevation OG = h above the origin O of fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002355_j.triboint.2009.05.023-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002355_j.triboint.2009.05.023-Figure1-1.png",
        "caption": "Fig. 1. Test specimens, upper and lower disc of twin disc equipment.",
        "texts": [
            " The tests were carried out to study the effect of steel material, surface treatment, surface roughness, DLC coating and lubricant type on micropitting and friction performance. Umetrics Modde 4.0 software was used for design of experiments (DOE) and statistical analysis of the test results. In the twin disc equipment used, the two discs were in rolling/ sliding contact against each other under controlled load. The lower disc was partly submerged in the oil and provided the lubricant also into the contact (Fig. 1). Friction force was measured during the tests from the axial torque of the lower shaft. The twin disc equipment makes it possible to test the lubricant properties by varying the contact pressure, surface properties and rotational speeds and measuring the axial torque and oil temperature. The tests were performed using parameters favouring micropitting failure propagation. The lower disc (radius 21.5 mm) was a cylindrical one and the upper disc (radius 22.6 mm) had a barrel shaped surface to provide controlled elliptical contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001433_dia.2006.8.312-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001433_dia.2006.8.312-Figure5-1.png",
        "caption": "FIG. 5. Schematic of the hand-held photofluorometer: ocular to fit against orbital rim isolating eye from ambient light (1); housing for ocular (2); set screw to adjust alignment of ocular (3); lens to focus blue Cree light emitting diode (LED) array on the eye (4); blue (488 nm) LED circular array (5); main body housing (6); back housing (7); set screw to adjust alignment of the back housing (8); rear housing for sensor diode, battery, and integrated circuits (9); sensor diode and rechargeable battery power supply (10); 500 nm high-pass barrier filter (11); slit to direct blue LED on the eye (12); integrated circuit for signal averaging and locking (13); red central fixation LED to stabilize eye movement (not shown) (14); integrated circuits to subtract 574 nm signal from 514 nm signal (15); slit at eye to restrict blue light to cornea and reduce autofluorescence (16); telemetry transmitter (optional and not shown) (17); telemetry receiver at insulin pump (optional and not shown) (18); digital read-out (19).",
        "texts": [
            "10 This ultraviolet light also served to sterilize the formulation, and the remaining process and packaging were performed under sterile conditions. Polymerization was considered complete after 6 h, and the molds were then soaked in MilliQ water (Millipore, Bedford, MA) overnight to remove any unpolymerized monomers and any TRITC-Con A or FITC-dextran adherent to the surface. The final lenses were employed within 2 weeks of manufacture. The optical diagram of the hand-held photofluorometer is shown in Figure 5. The device is held directly in front of the eye, resting on the orbital rim, thus excluding most ambient light. To further ensure no interference from ambient light, the light is modulated at 2.6 MHz and signal locked. An array of Cree blue (488 nm) light-emitting diodes are arranged in a circle (Power Technology, Inc., Little Rock, AR), focusing their exciting light on the contact lens. The light-emitting diodes are modulated at 2.6 MHz. The green (514 nm) fluorescence and yellow (574 nm) fluorescence then pass through a collector lens and a barrier filter (excluding blue light in a 500 nm high pass filter) to a diode detector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001173_20.106473-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001173_20.106473-Figure1-1.png",
        "caption": "Figure 1: Test motor laminations",
        "texts": [
            " The philosophy behind choosing a time step on the basis of a maximum permitted change in flux linkages, is that flux linkages change when the magnetic field changes, so that a non-linear field solution is carried out only when the magnetic field has changed. The authors have found that 30 time-steps are required per supply cycle using this technique, whilst other authors have reported 100- 200 steps per cycle. EXPERIMENTAL VERIFICATION The procedure outlined above was verified by means of tests canid out on a 415V, 4 kW, 4-pole cage motor. The stator and rotor laminations for this motor are shown in Figure 1, and other details are summarised in Table 1. Figures 2(a) and 2(b) show the computed and measured variations of red and blue phase current during a direct-on-line start with the rotor coupled to an inertial load. Figure 3 shows the computed variation of electromagnetic torque during the same test. Direct experimental verification of the transient torque is not available, but as an alternative Figure 4 compares the computed variation of speed with the output from an a.c. tachogenerator coupled to the rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002454_melcon.2010.5476026-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002454_melcon.2010.5476026-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor helicopter configuration frame system",
        "texts": [
            " In Section V the efficacy of the proposed scheme are presented, while the conclusions are drawn in the last Section VI. The model of the UqH utilized in this work, assumes that the structure is rigid and symmetrical, the center of gravity and the body fixed frame origin coincide, the propellers are rigid and the thrust and drag forces are proportional to the square of propeller\u2019s speed. The electro\u2013mechanical structure 978-1-4244-5795-3/10/$26.00 \u00a92010 IEEE 1411 of the UqH under study, and the relative coordinate systems are presented in Figure 1. The aerodynamic forces and moments acting on the UqH during a hovering flight segment are the thrust, hub forces and the drag moment due to vertical, horizontal and aerodynamic forces respectively, and the rolling moment which is the integration over the entire rotor of the lift of each section acting at a given radius. An extended formulation of these forces and moments can be found at [10] and the system can be described by a set of a twelve order nonlinear ODE of the form X\u0307 = f(X,u) with u the input vector, and X the state vector, where: X = [\u03c6 \u03c6\u0307 \u03b8 \u03b8\u0307 \u03c8 \u03c8\u0307 z z\u0307 x x\u0307 y y\u0307]T (1) u = [U1 U2 U3 U4 \u03a9r] (2) The control inputs in (2) are produced by the following combinations of the angular velocities \u03a9i of the four UqH\u2019s rotors as: U1 = b(\u03a92 1 + \u03a92 2 + \u03a92 3 + \u03a92 4) U2 = b(\u2212\u03a92 2 + \u03a92 4) U3 = b(\u03a92 1 \u2212 \u03a92 3) (3) U4 = d(\u2212\u03a92 1 + \u03a92 3 \u2212 \u03a92 3 + \u03a92 4) \u03a9r = \u2212\u03a91 + \u03a92 \u2212 \u03a93 + \u03a94 where b is the thrust coefficient and d the drag coefficient; the input U1 is related with the total thrust and the inputs U2, U3, U4 are related with the rotations of the quadrotor and \u03a9r is the overall propellers\u2019 residual speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000834_978-94-017-0657-5-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000834_978-94-017-0657-5-Figure11-1.png",
        "caption": "Figure 11. Two orientations for the 2-DOF Orthoglide u-workspace",
        "texts": [
            " The variation of the VAF along the isotropy continuum is limited (Fig. 10), which is interesting as it shows that isotropy brings homogeneousness to kinetostatic performances, which is prefered for this application. The Biglide isotropy continuum is not studied here because it has few consequences on the VAF homogeneousness inside the u-workspace. See section 4.1 for more details on its location. The 2-DOF Orthoglide u-workspace is first arbitrarily centered on the point S where the VAF are equal to 1 (Fig. 11). Changing the u workspace center position will be discussed in section 4. Two possible u workspace orientations are studied (Fig. 11) and it appears that orientation A has a bad ratio between the u-workspace and the C workspace, which yields a poor machine compactness because of the larger joint ranges. 325 Furthermore in the case of orientation A, singular configurations may appear inside the C-workspace, which is not acceptable. Indeed, the u workspace is used for the machining task, but the C-workspace can be used for changing the tool position between two machining operations. Singularities are then strictly prohibited. Thus orientation B is selected for the 2-DOF Orthoglide",
            " But for moving from one workspace of the direct kinematics to another workspace of the direct kinematics a singularity has to be passed. To make that possible special effort is necessary, concerning the control and the design of the manipulator. Four conditions have to be fulfilled to pass such a singularity. First of all, the passive and actuated joints have to allow motion on both sides of the singularity. This is an additional design condition, that could be easily fulfilled for the discussed planar PRRRP parallel manipulator (Fig. 11). It is a crucial condition when the approach is to be adapted to spatial mechanisms. Secondly, the control system has to allow an on-line change of the kinematic equations. The algebraic sign of the square roots in the kinematic equations have to be adapted after each crossover into another workspace. This can be realized by implementing the algebraic signs (kt, k2 and ks in Eq. 1, 2 and 8) that have to be changed as additional variable parameters in the control system. Thirdly, a sensor has to be added, which allows to recognize the active workspace in a way, that a known and secure reference position can be reached from any unknown pose",
            " When the manipulator is moved into the singularity with one drive disabled the inertia of the links slides the manipulator through the singularity. The implementation of this approach to cross singularities is explained in the next chapter. The crossing of singularities using the inertia of the machine elements has been implemented to the manipulator control system (DSP-based) in eight steps. It is programmed as one function and can be called during any motion cycle. 355 from its actual pose to a pose close to the singularity (e.g. Fig. 11). As the second step, one drive is disabled (idle, not braked). In step three, the still enabled drive moves the manipulator into the singularity. When the singularity is reached a minimum speed is obligatory. If the minimum speed could not be obtained, the friction forces in the joints are higher then the inertia forces of the masses moved and the singularity will not be crossed. Immediately when reaching the singularity the drive has to decelerate to prevent an oscillation about the singularity",
            " As step five, the kinematic equations are adjusted in the control software. In the sixth step, the disabled drives are enabled. This is done by increasing the proportional parameter of the drive controller from zero to its optimal value with an exponential function. In step seven, the manipulator is moved in articulated coordinates to the target pose. In the last step, the crossover is reported successful, and the manipulator controller continues with its prior program. A sample path through the workspace is shown in Fig. 10. Figure 11. Prototype on both sides of a singularity 356 First experiments with the prototype show that the method is very reliable. Mter the minimum speed and the deceleration parameters for the active drive had been determined by experiments, the crossover itself has not once been unsuccessful. The time that is required for the crossover is mainly determined by the power up time of the disabled drives. The main difference to moving in only one workspace is that not any path is possible. But this is no restriction for handling tasks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001840_s11249-007-9215-z-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001840_s11249-007-9215-z-Figure4-1.png",
        "caption": "Fig. 4 Measurements location",
        "texts": [
            " 3) Mechanical parameters Functional parameters Points Rx (mm) |u1 + u2| (m/s) |u1\u2013u2| (m/s) W (N) hm (lm) P0 (Mpa) u1 u2 u1\u00feu2 A 5.788 0.504 0.202 132.5 0.095 219.15 0.40 B 8.138 0.549 0.033 265 0.107 261.38 0.06 I 8.376 0.556 0.006 265 0.109 257.64 0.01 C 8.661 0.566 0.032 265 0.112 253.36 0.056 D 9.103 0.610 0.202 132.5 0.132 174.75 0.33 Experimental measurements The wear is evaluated by a thickness loss measurement. A gear tooth vernier, apparatus with double reading was used for the various tooth thicknesses measurements. Measurements were taken in three different places (Fig. 4), at the tooth root, at its tip and its pitch diameter. For the pinion, the measurement locations correspond, respectively, to points A, D and I on line of action. On the other hand, for the gear, correspond to the points D, A and I. Measurements were reproduced on three teeth, separated by 120 , on the pinion as well as the gear. The average value was considered. The temperature was evaluated at the tooth root. An infrared thermocouple was used for the temperature measurements. The roughness is evaluated before and after the operation in zones, which represents a high rate of sliding (tooth root)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000772_s0094-114x(99)00068-3-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000772_s0094-114x(99)00068-3-Figure2-1.png",
        "caption": "Fig. 2. Balancing elastic system with \u00aexed cam and translation follower.",
        "texts": [
            " The moving axes system x1Oy1 is supposed to be rigidly connected with the arm 1, so that y1G1 0: The ordinate YC of point C and its derivative dYC=dj are the solutions of the following di erential equation that expresses the equilibrium condition: g OG1m1 OAm4A cos j FsOA sin j\u00ff y YCR31sin a 0, 1 where g represents the gravity acceleration magnitude, and the reaction force between the cam 1 and the roll 3 has the following expression: R31 Fssin y m2 m3 m4B g P YC ; XA OA cos j; YA OA sin j; XB 0; YB YC BC; a arctan dYC=dj YC ; y arctan YB \u00ff YA \u00ffXA ; Fs F0 k AB\u00ff l0 ; AB XA \u00ff XB 2 YA \u00ff YB 2 q : The mass m4 of the helical spring 4 is considered as being concentrated in the end points A and B, m4A and m4B, respectively. The masses m1, m2, m3 and m4 of the bodies, the dimensions OA, BC, OG1 and the helical spring characteristics F0, l0, k are considered as known. The initial conditions for solving Eq. (1) are considered in a convenient mode, adequate to a known equilibrium position. In the kinematics scheme shown in Fig. 2, the cam 1 is \u00aexed to frame and the follower 2 I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b11311 1301 slides along the robot arm. The balancing helical spring 4 is joined with its A end to the follower 2. The parametrical equations of the directrix curves of the cam active surfaces are: x1 XC3 R dOC=dj sin j XC Q , y1 YC2 R dOC=dj cos j\u00ff YC Q , where XC OC cos j; YC OC sin j; Q dXC=dj 2 dYC=dj 2 q : The distance OC and its derivative dOC=dj are calculated by integrating the following di erential equation: Fs YB OC AC cos j AB \u00ff R02OC cos j\u00ff a \u00ff g \u00ff m1OG1 m4A OC AC m2 OC CG2 cos j 0, 2 where: R02 g m2 m4A \u00ff Fscos j\u00ff y cos j\u00ff a ; a arctan dOC=dj OC : Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure1-1.png",
        "caption": "Fig. 1. Kinematical model of the cradle-style hypoid gear generator.",
        "texts": [
            " Mathematical model of computerized generation of face-milled spiral bevel gear drives In this section, a mathematical model of derivation of gear tooth surfaces corresponding to face-milled spiral bevel gears is presented. Fundamentally, it is based on a matrix formulation [24] and follows the approach proposed in [3,4,7,8] , which in turn is based on the kinematic model corresponding to the traditional cradle-style generator employed in both spiral bevel and hypoid gear manufacturing, and is represented in Fig. 1 . As depicted in Fig. 1 , the primitive generator requires eight motions in order to machine either spiral bevel or hypoid gears, which are described in Table 1 . The first four motions, represented by i, j, q and S r , constitutes the cutter head positioning settings, while the last four motions, represented by E m , X B , X D and \u03b3 m , let positioning the work head. Additionally, \u03c9 t , \u03c9 w and \u03c9 c represent the tool (face-milling cutter), work and cradle rotation velocities, respectively. In this work both tilt angle i and swivel angle j will not be taken into account, since their effect will be compensated with the search for the pressure angles corresponding to the inner and outer cutter blade profiles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000722_1.2794209-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000722_1.2794209-Figure1-1.png",
        "caption": "Fig. 1 Simple mass-spring system shown at landing and takeoff",
        "texts": [
            " The next section introduces a simple model for a quadruped and devel ops the dynamic model for the quadruped. Section 4 extends the results of Section 2 to quadruped trot and examines the energy exchange in the gait. Sections 5 and 6 describe the method used to generate periodic solutions for quadruped bound and gallop. Section 7 compares the results for quadru ped trot, bound, and gallop. The last section summarizes the results. Before the details of the model of the quadruped gait are presented, it is essential to start from a simple mass and spring system. This system is shown in the Fig. 1. It consists of a simple point mass which represents the body mass and a single leg modeled as a massless linear spring. A typical gait of this system would consist of alternating stance phases and aerial phases. The stance phase refers to the period of the gait when the leg is in contact with the ground. When none of the feet are in contact with the ground, the phase will be referred to as the aerial phase. A combination of a stance phase followed by an aerial phase would be considered as a step",
            " (2) with the conditions given in Eqs. (3) and (4). The solution procedure for these set of equations will be cumbersome and computationally expensive. An alternative to the above strategy is to solve the differential equations with the appropriate initial conditions. The appro priate initial conditions will be the one's that will automatically guarantee that the Eqs. (3) and (4) are satisfied. These initial conditions can be obtained by using symmetry arguments. The vertical velocity at the end of the stance phase in Fig. 1 is negative of the vertical velocity at the beginning of the stance phase. Thus, the vertical velocity at the middle of the stance phase should be zero. Similarly, the point mass should be lo cated at the top of the foot in the middle of the stance phase. These conditions are shown in Fig. 2 and can be stated mathe matically as: Journal of Biomechanical Engineering NOVEMBER 1995, Vol. 1 1 7 / 4 6 7 Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000786_1.1518501-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000786_1.1518501-Figure1-1.png",
        "caption": "Fig. 1 Nomenclature to define right-angle gear drive",
        "texts": [
            " Dooner and Seireg @22# recognized these limitations and used the theory of screws to provide a universal methodology for the integrated design and manufacture of generalized gears. Three laws of gearing were presented as part of their original work. The three laws formulated below are modified from their original presentation where it is believed that the following presentation better discloses the significance of these three laws. The objective of a direct contact mechanism is to achieve a desired motion relationship between two bodies. For gear pairs this is achieved by two teeth or surfaces in direct contact. Depicted in Fig. 1 are an input and output hyperboloidal gear body in mesh and some nomenclature used to define the topology of these bodies. Shown is the shaft center distance E between the two axes of rotation $ i and $o along with the included angle S between these two axes. The relationship between the angular position n i of an input element and the corresponding angular position no of an output element is defined as the transmission function. The instantaneous gear ratio g is the ratio between the infinitesimal displacement dno of the output and the corresponding infinitesimal angular displacement dn i of the input, thus g5 dno dn i "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-32-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-32-1.png",
        "caption": "FIGURE 12-32 Standard three-point hitch for agricultural trac tors. (From ASAE S 217.10.)",
        "texts": [
            " Space considerations preclude a detailed discussion of all the systems that have been and are being used. Because the three-point hitch is used by almost every manufacturer of tractors in the world, it would seem advisable to devote most of the discussion to it. As the plow in figure 12-31 enters the soil, the virtual hitch point J' continues to rise until the plow reaches equilibrium. The three-point hitch was developed in 1935 by the late Harry Ferguson (Gray 1954). The dimensions of categories I, II, III, and IV three-point hitches have been standardized by ASAE and SAE. Figure 12-32 illustrates the stan dard three-point hitch. Details of the standard are shown in ASAE S217.1 0 (also SAEJ715 SEP83). Another standard, ASAE S320.1, describes the three point hitch standard for lawn and garden tractors having less than 15 kW of power. 354 HYDRAULIC SYSTEMS AND CONTROLS The design of the three-point hitch has carefully considered the effect on both the implement and the tractor. Figure 12-33 describes a graphical method of determining the resultant of all forces acting upon the hitch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003533_978-3-319-60916-4_17-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003533_978-3-319-60916-4_17-Figure4-1.png",
        "caption": "Fig. 4 Contacts are maintained unless their position is too far, or the environment prevents it",
        "texts": [
            " The contact is broken if an inverse kinematics solver fails to find a collision free limb configuration which satisfies joint limits [2]. If the solver fails, the contact is broken and a collision free configuration is assigned to the limb. Once a first candidate configuration is taken for all limbs, the quasi-static balance is tested by whether the weight wrench is in the gravito-inertial cone (i.e. there exists valid contact forces that compensate for the weight of the robot), using the geometric approach described in [19]. If the balance is not obtained, new contacts are randomly generated using the following procedure (Fig. 4). Creating a contact: We consider a configuration where some limbs are in contact, some are free and quasi-static balance is not enforced. To enforce balance,we proceed in the followingmanner: we randomly select a contact free limb; if there is no contact free limb, we select the limb that made contact first. Using the contact generator introduced in [22], we project the configuration of this limb into a contact that enhances balance, if it exists (Fig. 5); If balance is not achievable and a contact is possible, it is generated anyway; If balance is not achieved, the next limb is selected and projected into a contact configuration, and so on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure8-9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure8-9-1.png",
        "caption": "FIGURE 8-9 Action of journal bearing (exaggerated). (a) At rest. (b) Partial lubrication, just starting. (c) Fluid film lubrication.",
        "texts": [
            " Journal Bearing Design The coefficient of friction of a journal bearing is a function of several variables. For any given bearing, the only three variables that may be changed are the 196 LUBRICA nON absolute viscosity of the lubricant, fl, the speed n of the journal, and the bearing pressure p (force/projected area). These three factors are commonly combined into the nondimensional quantity \u00b7fln/p. The action of a bearing in starting from rest and passing through the region of unstable or thin-film lubrication is shown in figure 8-9. When at rest, the journal is as shown in figure 8-9( a}. The clearance space is filled with oil. At the beginning of operation, the shaft tends to roll up one side of the bearing. However, since some oil adheres to the journal and is carried between the load-carrying surfaces, the rotation tends to build up a supporting oil film, after which the journal moves to the right, as shown in figure 8-9(c}. Note that the shaft during operation is displaced to the side opposite the one that it tends to roll up during starting. So that no metal-to-metal contact may occur between the journal and bearing, a film of oil sufficiently thick must be kept between the two. The thickness of the film required will depend on how smooth the surfaces are, since no bearing is perfectly smooth. When the layer of oil is thick enough to prevent any metal-to-metal contact, the bearing is said to be operating in the region of thick-film or stable lubrication. Under conditions of thin-film or unstable lubrication, the projections touch so that the bearing materials and the conditions of the surfaces affect the frictional loss. Referring to figure 8-9(c}, note that the oil flows toward the point of minimum thickness. The oil film is built up by the rotation of the journal, and since the film thickness increases with the speed of rotation, the load that the bearing can carry also increases with the speed of rotation. The coefficient of friction has been found to be a straight-line function of the quantity IJ-nlp except at low values, which usually indicate either high loads or low speeds (fig. 8-10). Operation of the bearing to the right of the point of minimum coefficient of friction tends to be stable as an increase in bearing temperature lowers the oil viscosity and decreases the coefficient of friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003615_978-3-319-27149-1-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003615_978-3-319-27149-1-Figure13-1.png",
        "caption": "Fig. 13 Sheathed cables with decoupled movement.",
        "texts": [
            " Solutions based on rods or gears admit then only few variants, hence we were forced to skip solutions based on these technologies. The technology chosen has thus been that based on cables, as that of the currently hegemonic manufacturer. Both designs, though, are clearly differentiated because ours do not use pulleys to guide the cable in each joint interposed, but flexible cable-sheath, fig. 12. Sheathed cables are useful to transmit the movement through a joint, without varying the longitude of the cable, fig. 13. Hence, the movement becomes decoupled, contrarily to the case of pulleys shown in fig. 11. Challenges in the Design of Laparoscopic Tools 469 This solution has been used for decades and thus it is not subject to IP claims. Although conceptually simple, this solution is difficult to be implemented at reduced scale. For this reason, it has been necessary to solve the problem of confronting the cable when leaving the sheath towards the actuation drum of the joint or the gripper. Although not optimal, this solution relies on the design of frictionbased deflection nozzles, fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002596_we.447-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002596_we.447-Figure10-1.png",
        "caption": "Figure 10. RomaxWind model showing planet positions at nominal carrier rotation.",
        "texts": [
            "1002/we 641 (putting the blades askew to the wind), yawing of the machine and wind shear. Most dynamometer tests only load the drive train with torque, and it is important to understand that the loading and defl ections of the gearbox may be markedly different in the two installations; particularly for three-point mounting arrangement (main bearing and two torque arm supports). For the given load case, a nonlinear static analysis has been performed and the contact and stress in the planetary stage is calculated at a certain carrier rotation. Planet positions are shown in Figure 10, and subsequent results focus on the planet/sun gear mesh and the planet and carrier bearings indicated in the fi gure. Wind Energ. 2011; 14:637\u2013651 \u00a9 2011 John Wiley & Sons, Ltd. DOI: 10.1002/we 642 Examining the three-point mounting arrangement, it is clear that moments about the main bearing must be supported by the gearbox mounts and the load path is then through the carrier bearings and housing. The load as well as clearance in these bearings can misalign the carrier to the housing and ring gear and affect the gear contact",
            " For many wind turbine gearbox designs, the alignment of the planetary stage is sensitive to the magnitude of the clearances in the planet carrier bearings (i.e. the bearings that support the carrier). For this model (Figure 9), with the gearbox installed in the turbine, a full factorial study has been performed where the radial internal clearance of the upwind and downwind planet carrier bearings are varied, and the misalignment and face load distribution factor (F\u00dfX and KH\u00df 11) are calculated for each planet position of Figure 10. Note, for the results of Figures 11, 15\u201317, the clearance was assigned as 260 \u00b5m for both carrier bearings. The factorial study (Figure 17) demonstrates how sensitive the misalignment of the sun and planet is to these bearing settings, and designers can use such models to optimize the settings of the bearings. The best clearance specifi cation would be the subject of a full design review; however, a brief example is provided here where the carrier clearances are set to an optimal value so that the planet/sun misalignments are consistent with position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002238_iros.2010.5653006-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002238_iros.2010.5653006-Figure7-1.png",
        "caption": "Fig. 7 Schematic diagram of parameters",
        "texts": [
            " This chamber can be pressurized through an air vent. Flange Artificial muscle Pressure supply Contraction force Air vent Amount of contraction Pressureless Pressurize Fig.8 Relationship between pressure and closing area rate 0 20 40 60 80 100 0 0.01 0.02 0.03 0.04 Pressure [MPa] g C lo sin g ar ea ra te [% ] n A. Performance Evaluation Parameters The prototype is shown in Fig. 6, and its specifications are shown in Table 1. In this study, we define the closing area and volume exclusion rates as performance evaluation parameters of the unit. Fig. 7 shows the schematic diagram of the closing area and volume exclusion rates. The closing area rate Ca is defined using the percentage as where S0 is the unit-opening space viewed from the axial direction at the initial state, and S is the unit-opening space viewed from the axial direction at the time of pressurization. The closing area rate shows the performance of the unit as a valve. The volume exclusion rate E is defined using the percentage as where V0 is the internal volume of the unit at the initial state, and V is the internal volume of the unit at the time of pressurization"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003495_s00332-016-9294-9-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003495_s00332-016-9294-9-Figure6-1.png",
        "caption": "Fig. 6 Visualization of a few stress-free material evolutions of an initially planar sheet with the prescribed evolving fundamental forms such that the in-plane growth is uniform, i.e., \u03c9A = \u03c9A(t) for A = X, Y , the Gaussian curvature is vanishing, i.e., KX KY = 0, and the nonzero principal curvature is such that KX = KX (X, t) or KY = KY (Y, t). We assume for these figures that KY = 0 and a KX = KX (t) to grow to a cylindrical portion, b KX (X, t) = k1(t) sin(k2(t)X), where k1 = k1(t) and k2 = k2(t) are some arbitrary functions of time resulting in a sheet with sinusoidal rippling, and c KX (X, t) = k(t) \u221a X , for X > 0, where k = k(t) is some arbitrary function of time",
        "texts": [
            " In the case of an initially flat morphoelastic simplyconnected shell, the growth is stress-free if and only if e2\u03c9X [( \u2202\u03c9Y \u2202Y \u2212 \u2202\u03c9X \u2202Y ) \u2202\u03c9X \u2202Y \u2212 \u22022\u03c9X \u2202Y 2 ] + e2\u03c9Y [( \u2202\u03c9X \u2202X \u2212 \u2202\u03c9Y \u2202X ) \u2202\u03c9Y \u2202X \u2212 \u22022\u03c9Y \u2202X2 ] = KX KY e 2\u03c9X e2\u03c9Y , \u2202KX \u2202Y = (KY \u2212 KX ) \u2202\u03c9X \u2202Y , \u2202KY \u2202X = (KX \u2212 KY ) \u2202\u03c9Y \u2202X . Now we consider the following simplifying assumptions: \u2022 If we assume that the in-plane growth is uniform, i.e., \u03c9A = \u03c9A(t) for A = X,Y , we find that the growth is stress-free if and only if KX = KX (X, t), KY = KY (Y, t), and KX KY = 0. This case includes the stress-free growth of a planar sheet into a cylindrical portion. See Fig. 6 for examples of evolutions of planar sheets into flat surfaces with stress-free growth. \u2022 If we assume that the evolving curvatures KX and KY are uniform, i.e., KA = KA(t) for A = X,Y , we distinguish the following cases: \u2013 If KX = KY , then the growth is stress-free if and only if \u03c9X and \u03c9Y are uniform and KX KY = 0. This is precisely the case of a planar sheet evolving to a cylindrical portion with a stress-free growth (see Fig. 6a). \u2013 If K = KX = KY , then the growth is stress-free if and only if e2\u03c9X [( \u2202\u03c9Y \u2202Y \u2212 \u2202\u03c9X \u2202Y ) \u2202\u03c9X \u2202Y \u2212 \u22022\u03c9X \u2202Y 2 ] + e2\u03c9Y [( \u2202\u03c9X \u2202X \u2212 \u2202\u03c9Y \u2202X ) \u2202\u03c9Y \u2202X \u2212 \u22022\u03c9Y \u2202X2 ] = K 2e2\u03c9X e2\u03c9Y . \u2022 If we assume that the in-plane growth is isotropic, i.e., \u03c9 = \u03c9X = \u03c9Y , we distinguish the following cases: \u2013 If K = KX = KY , then the growth is stress-free if and only if K is uniform and \u22022\u03c9 \u2202Y 2 + \u22022\u03c9 \u2202X2 = \u2212K 2e2\u03c9. In particular, if KX = KY = 0, then the growth is stress-free if and only if \u03c9 is harmonic. See Example 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002746_asjc.504-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002746_asjc.504-Figure4-1.png",
        "caption": "Fig. 4. Illustration of the state and input variables.",
        "texts": [
            "1 Dynamic model of the unmanned rotorcraft We have obtained a complete flight dynamics model for HeLion in [8] using the first-principles approach. The complete structure of the nonlinear model is depicted in Fig. 3, which includes four key components: (i) kinematics; (ii) 6-DOF rigid-body dynamics; (iii) main rotor flapping dynamics; and (iv) factory-installed yaw rate feedback controller dynamics. This flight dynamics model features minimum complexity and contains fifteen states and four inputs, which are illustrated in Fig. 4 and summarized in Table I. In the modeling procedure, some unique features of the hobbybased helicopters, such as stabilizer bar configuration and the yaw rate feedback controller, have been included. The necessity has been well proven in some documented work (see, for example, [8,24]). 2.1.1 Kinematics The Kinematics part includes two equations, which describe the relative motions between the two coordinate frames adopted, i.e., the body frame and the local north-eastdown (NED) frame. More specifically, the one relative to the translational motion is given by P V R Vn n n b b= = , (1) and the relative rotational motion is expressed by \u03c6 \u03b8 \u03c8 \u239b \u239d \u239c \u239c\u239c \u239e \u23a0 \u239f \u239f\u239f = \u2212S 1wb n b , (2) where Pn is the NED-based position vector, Vn is the NED-based velocity vector, Vb is the body-frame velocity vector, wb n b is the angular rate vector, Rn/b and S are the \u00a9 2012 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society transformation matrices and are, respectively, given as (see also, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003250_s10846-015-0301-4-Figure24-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003250_s10846-015-0301-4-Figure24-1.png",
        "caption": "Fig. 24 Proposed tilting mechanism",
        "texts": [
            " After some research, within these specs in the bag, the relatively easier and robust way to turn a regular quadrotor into a tilt-roll rotor quadrotor is achieved by using auto- matic car wing mirror actuators. They are easy to use, can be run by using simple electronics tools within a proven robustness level. Not only these but also they already have both of tilt and roll control system in the box once their operational plane lay-out is rotated 90 degrees along x axis. A simple lay out of the wing mirror is given in Fig. 24. Figure 24a shows the top view of the tilting platform. Lift generating motor and rotor sets will be placed on each platform. The points P and R, are where the platform is actuated to have pitch and roll motions, respectively. The mechanism will tilt with respect to the center point O. Each motor shaft has a worm which attached to a worm gear as shown in the top view in Fig. 24c. This arrangement reduced rotational speed and allows higher torques to be transmitted to the tilting mechanism. The worm gear has a ball screw inside as shown in side view of Fig. 24b, which will rise and lower the platform as required. The height of the ball screw mechanism and the distance between points O, R and P determine the pitch and roll limits of the mechanism. Please see Figs. 25 and 26 for the 2 DC motor driven schematics of wing mirror actuator design. Figure 25 shows the proposed quadrotor with the tilting mechanisms are mounted. Figure 26 shows inner view of one of these tilting mechanisms. Each mechanism requires two micro DC motors for tilt and roll motions. In this project, the tilting mechanism of the proposed tilt-roll rotor quadrotor is based on Mirror Controls International (MCI) wing mirror actuators"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002559_humanoids.2011.6100862-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002559_humanoids.2011.6100862-Figure7-1.png",
        "caption": "Fig. 7. The 3D CAD section and the physical prototype of the compact SEA module",
        "texts": [
            "9 kg, and the waist section, including the hip flexion motors, weighing 5.5 kg. The leg of COMAN incorporates two series elastic (SEA) actuation units, which are placed at the knee flexion and the ankle dorsiflexion joints. The actuation structure used in the COMAN is based on a compliant actuation unit developed in [15]. To minimize dimensions while achieving high rotary stiffness, the compliant module of the unit is a mechanical structure consisting of a three spoke output component (Output pulley, Figure 7), a circular input pulley, and six linear springs. More details on the actuator can be found in [15]. Figure 8 shows the stiffness curve of the module within the range of the deflection angle for the compliant actuation unit used in the joints of the COMAN. The compliant joints have a passive deflection range of approximately 0.2 rad. Using the reconstructed CoM trajectories, COMAN successfully performed a stable, highly dynamic, human-like walking (in Figure 9 some snapshots from the video of the robot walking)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001444_icassp.1979.1170793-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001444_icassp.1979.1170793-Figure4-1.png",
        "caption": "Fig. 4. 2 for one sinusoid, 0>0, SNR=Odb, 2nd order.",
        "texts": [
            " \u2014 The problem here is related to that encountered in 2\u2014D spectral factorization (7), where it is found that a single\u2014quadrant filter is not suf\u2014 (5) ficient to realize a general 2\u2014D magnitude response. That is, the spectral estimate should in- corporate a second inverse filter H2(zl,z2) corresponding to second\u2014(or fourth)\u2014quadrant prediction, i.e., I H2(z1,z2) = (10) The coefficients bk ore found to be bik = geWT (11) withg given, as before, by (8). The corresponding S2(w1,w) for the case in Fig. 1 is shown in (7) Fig. 4.ond ms seen to be the mirror image of Fig. 2 about the axis. One might now expect the appropriate spectral estimate to be (12) (13) The associated 2\u2014D spectral estimate is = jw1T jw2d 2. H(e ,e where K is a normalizing constant. 0 For the case of the monochromatic plane wave in white noise, the space\u2014time correlation function is given by R(p,q) = + a2 cS(pq) (6) where a2 is the noise power. The corresponding solution to the normal equations is simply \u2014 j(iT + kD) \u2014 \u00b0ik \u2014 e (a00 1) where the are real\u2014valued constants"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003768_tia.2017.2694798-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003768_tia.2017.2694798-Figure1-1.png",
        "caption": "Fig. 1. Cross section and winding configurations of 6s/4r VFRM.",
        "texts": [
            " The sections are organized as follows: In section II, the torque production of 6s/4r VFRM is analyzed based on the instantaneous torque equation and harmonic analysis. In section III, two harmonic field current generation methods are proposed to calculate the magnitude of injected harmonic current. In Section IV, the experimental validation is given. Additionally, the influence of magnetic saturation and machine rotating speed is investigated in section IV. II. INSTANTANEOUS TORQUE EQUATION OF 6S/4R VFRM Fig. 1 shows the cross section and winding configurations of 6s/4r VFRM. Its main specifications are listed in TABLE I. V 0093-9994 (c) 2016 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. Both field and armature windings are in concentrated type and wounded on each stator tooth. Additionally, the series turns of all coils are identical. In this case, the phase self-inductance of armature winding is equal to the mutual inductance between field and armature windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003109_978-0-8176-4893-0_6-Figure6.2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003109_978-0-8176-4893-0_6-Figure6.2-1.png",
        "caption": "Fig. 6.2 Fifth-order differentiation",
        "texts": [
            "z2 v1/ C z3 Pz3 D v3; v3 D 2L1=3 jz3 v2j2=3 sign .z3 v2/ C z4 Pz4 D v4; v4 D 1:5L1=2 jz4 v3j1=2 sign .z4 v3/ C z4 Pz5 D 1:1L sign .z5 v4/ ; \u02c7\u030c f .6/.t/ \u02c7\u030c L It is applied, with L = 1, for differentiating the function f .t / D sin.0:5t/ C cos.0:5t/ \u02c7\u030c f .6/.t/ \u02c7\u030c 1 The initial values of the differentiator variables are taken zero. In practice it is reasonable to take the initial value of z0 equal to the current sampled value of f .t/, significantly shortening the transient. Convergence of the differentiator is demonstrated in Fig. 6.2. The fifth derivative is not exact due to the software restrictions (the number of decimal digits of the mantissa). In fact, higher-order differentiation requires special software development. Introducing the differentiator of order r 1 given above in the feedback loop, one obtains an output-feedback r-sliding controller u D \u02db '.z0; z1; : : : ; zr 1/ (6.30) where Pz0 D v0; v0 D r 1L 1=r jz0 j.r 1/=r sign .z0 / C z1 Pz1 D v1; v1 D r 2L 1=.r 1/ jz1 v0j.r 2/=.r 1/ sign .z1 v0/ C z2 ::: Pzr 2 D vr 2; vr 2 D 1L 1=2 jzr 2 vr 3j1=2 sign "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000764_s0094-114x(97)00022-0-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000764_s0094-114x(97)00022-0-Figure8-1.png",
        "caption": "Fig. 8. Limitations of the face gear.",
        "texts": [
            " 5) to the shaper surface Mj~--matrix of coordinate transformation from system S~ to system S, E,--shaper (i = s), pinion (i = 1) or gear (i --- 2) tooth surface ~,--angle of rotation of the shaper (i = s) or face gear (i = 2) (Fig. 2) v,m~--~relative velocity vector ~c~-'~--relative angular velocity vector E--shortes t center distance between the shaper and the face gear (Fig. 2) X,, Y,, Z,---coordinates of the axis of meshing m.,,--gear ratio R,--inner (i = 1) and outer (i = 2) radii of face gear free of undercutting and pointing (Fig. 8) Pj---diametral pitch A/, Aq--segments for the determination of pointing [Fig. 6 (a)] vd~---velocity of contact point that moves over the tooth surface of the shaper L,----limiting line on the shaper tooth surface (i = s) (Fig. 9), or face-gear tooth surface (i = g) L--fillet line (Fig. 10) 87 88 F.L. Litvin et al. 0k,.--shaper parameter at the addendum cylinder r~,~--radius of the addendum cylinder of the shaper L,--limiting length of the shaper for avoidance of undercutting (Fig. 8) 7 shaft angle 05/ angles of rotation of pinion (i = l), and face gear (i = 2) being in mesh A~--transmission errors [Figs 14 (a), (b), (c)] v~(s)--velocity vector of the shaper in S~ v;2--velocity vector of the face gear in S~ o,'\"--angular velocity vector of the face gear in S~ p--screw parameter 1. INTRODUCTION The face-gear drive is an invention of the Fellows Company. The theory of face-gear drives was represented in the Russian literature in works [1] and [2]. The importance of face-gear drives was recognized when such gear drives with torque splitting [3] were proposed for application in helicopter transmissions",
            " The second approach is based on the application of the axis of meshing and the respective equation used for derivations is X ~ - x ~ _ Y~--y~=Zs-z~ (11) N,s N,~ N:~ Equation (l 1) describes that normal Ns passes through the axis of meshing; X,, Y~, and Z are the coordinates of the axis of meshing; xs, ys, and zs are the coordinates of a current point of the shaper tooth surface. After transformations, equation (1 l) yields the equation of meshing. Using one of the described approaches, we obtain that f (u, Ok~, \u00a2~) = m2sUs cos(\u00a2~ _ (0k~ + 0o0) - rb~ = 0 (k = 7, fl) (12) In equation (12) m2s = Ns/N2 is the gear ratio. The top land width of a face-gear tooth is not constant (Fig. 10). There is an area where the top land width becomes equal to zero, which means that the tooth becomes pointed. Our goal is to determine the outer radius R2 (Fig. 8) of the face gear for the area of pointing B (Fig. 10). Two approaches were proposed in [2] and [4] for the determination of area of pointing. The first one requires simultaneous consideration of the equations of the surfaces of both sides of the face-gear tooth and the determination of the area where both surfaces have a common point. The other one is based on the consideration of cross-sections of tooth profiles of the shaper and the face gear. Both approaches have been applied by the authors; the results are compared but only the second one, the simpler one, is presented in this paper",
            " (13) 2Pdrm _ 0o~ (14) N~ Meshing of orthogonal offset face-gear drive 95 Step 2: We consider that point P~ belongs to the pitch cylinder of the shaper [Fig. 6(a)], and the location of P2 with respect to P~ is determined with segments AI and Aq [fig. 6(a)]. Drawings of Figs 6(a), 6(b) and 7 yield Aq = O~P: - O~P, = rb~ rb~ _ N~ / c o s a zo _-- cos ~'] (15) cos~ cos~0 2 / '~ \\ cos~ / AI= Aq (16) tan y~ Step 3: The location of plane H2 is determined with parameter L2 [Fig. 6(a)], where L2 = rp + Aq = Nscos ~o (17) tan 7s 2PdCOS ~ tan y~ where tan 7~ = 1/m2s. The outer radius R2 of the face gear (Fig. 8) is represented as R: =,j-k-;+ L~ (18) M M T 33/I-2 D 96 F.L. Litvin et al. Undercutting can be avoided if the face-gear tooth surface is free of singularities. This can be achieved by limiting of the inner radius of the face gear. An effective approach for the determination of singularities of the generated surface is proposed in [2] and [4]. The approach is based on application of the following equations \u00a5~s ) + \u00a5~s2) = 0 (19) 0fdu 0f 00ks 0fd4,s OUs dt + dOks dt t- 0dpl d t = 0 (20) Vectors of equation (19) are represented in coordinate system Ss; v~ ~ is the velocity of a contact point that moves over the tooth surface of the shaper; v~ ~21 is the relative velocity of a shaper point with respect to the face gear",
            " 9) using the equations r~ = rdu~, OkO, f(u,~, O,s, (a,,) = O, F(U~, Ok~, (as) = O, (k = 7, fl) (26) Line L~ contains regular points of surface \u00a3~, but generates singular points on surface \u00a32. Knowing one of the two limiting lines, say L,, we may also determine Ls using a coordinate transformation from, & to $2. Due to asymmetry of the face-gear tooth surfaces, both surfaces have to be checked for undercutting. The dimensions of the blank that is used for manufacturing of the face gear are determined using the larger value of the inner radius R~ (Fig. 8) that is determined from conditions 98 F. L. Litvin et al. of undercutting for the generating profiles 7 and ft. The research results show that, for a positive offset (E > 0), the critical shaper surface that will cause undercutting in the surface with cross-section as curve fl-fl, and it is the opposite for negative offset (E < 0). The point of intersection of line L (Fig. 10) with the addendum cylinder of the shaper is critical for undercutting. The shaper parameter 0ks that corresponds to the addendum is determined by the equation 0* = , (27) rbs where r,s and rbs are the radii of the addendum and the base cylinder of the shaper. Substituting the value of 0~ into equation (3), we obtain the coordinates (x*, y*, z*) of the point of intersection of the limiting line with the addendum cylinder of the shaper. Knowing these values, the limiting inner radius of the face gear (R,) and the limiting length of the shaper (L,) (Fig. 8) are determined as R, = ~ + y~ (28) L, = z, (29) sin 2 ~ks + rn~O~ ~ + sin ~k~ -T- O~ cos ~ks cos 3 G~ = 0 (30) where Oh is the value of shaper surface parameter at the addendum cylinder, and ~ks is represented by equation ~=~s+_(O~+Oo~) k=?,/~ (31) Meshing of orthogonal offset face-gear drive 99 5. COMPUTERIZED SIMULATION OF MESHING AND CONTACT The procedure of simulation of meshing is directed at the determination of transmission errors and the shift of the contact path caused by misalignment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003585_b978-0-12-803766-9.00007-5-Figure5.2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003585_b978-0-12-803766-9.00007-5-Figure5.2-1.png",
        "caption": "FIGURE 5.2 Torque versus exoskeleton ankle joint angle relationship with motor position fixed and the ankle joint being passively flexed for one hundred strides.",
        "texts": [
            " \u2022 Bowden Cable Nonlinearities and Stiction Bowden cables are often used as a part of the transmission in robotic legged locomotion systems. For simplicity, we modeled the Bowden cable as a frictionless linear spring, but its stiffness is actually nonlinear and there are substantial frictional effects. The cable is stiffening, exhibiting greater local stiffness at high loads. This can be seen in the torque versus ankle angle curves generated by fixing the motor and passively flexing the device joint during walking (Fig. 5.2). The cable warms over the course of a many strides, which decreases its overall stiffness. It exhibits creep, which increases the slack length. If the cable is allowed to go slack, the state corresponding to reengagement is uncertain. There is substantial friction in the cable, including dissipation with characteristics of Coulomb friction, viscous damping, and stiction, some of which are visible in Fig. 5.2. The cable heats over the course of many strides, which increases overall friction. Stiction leads to sudden changes in cable force, and propagation of the slipping point along the length of the cable makes these changes unpredictable. These transmission properties are complex, nonlinear and time varying. \u2022 Human\u2013Robot Interaction and Human Adaptation In the case of exoskeletons and prostheses, the robot device works together with the human body. The device often contacts the soft tissues and muscles of the human body, often using flexible straps",
            " During tuning we found very similar suitable low-level control parameters across high-level controllers, and so used identical values within each low-level controller for consistency. Tuning was performed on a separate day from data collection. For model-based compensation, the value of R\u0303 was based on measurements of the motor output pulley radius, motor gear ratio, and exoskeleton lever arm. K\u0303c was estimated based on measurement of the passive relationship between exoskeleton torque and exoskeleton joint angle measured during walking experiments (Fig. 5.2). For each high-level controller, all low-level control conditions were tested on the same day, without removal of the exoskeleton between trials. A table of condition order is presented in Supporting Materials1 Table SI. For each combination of low-level torque control and high-level assistance control, we collected data from 100 steady-state strides. Steady state was typically reached after about 20 strides. The subsequent 100 strides were then decomposed into individual strides, each beginning at heel strike as detected by a shoe-embedded switch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002880_s12647-013-0045-1-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002880_s12647-013-0045-1-Figure2-1.png",
        "caption": "Fig. 2 Photograph of inner race of bearing having groove defect width of a 0.4714 mm, b 1.0220 mm, c 1.4954 mm and d 1.8145 mm",
        "texts": [
            " A Labview based data acquisition system (Make: National Instrument, Model: SCXI-1000 having 4 channel input) was used for acquiring the signal obtained from the accelerometer. The signal was stored in the hard disk of computer for further processing and subsequent analysis. Following the procedure mentioned in Sect. 2 for obtaining wavelet, the collected data was processed in Matlab environment [13]. In the present study experiments were carried out on four sets of the specified bearing (NBC 30205) but having different defect width (of 0.4714, 1.0220, 1.4954 and 1.8145 mm) on the inner race respectively. The defects as shown in Fig. 2 were generated using laser engraving technique [14]. Experiments were conducted at shaft speed of 2050 rpm. Both inner race defect frequency and outer race defect frequency have distinct values and give an indication of the defect lying on inner race and outer race accordingly but they can\u2019t give size of the defect present therein. The measurement of the defect width can be determined from the variation in amplitude of the bursts present in the signal. The amplitude of the raw signal from the defect free bearing falls in the range of -1 to "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002831_1350650112462324-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002831_1350650112462324-Figure2-1.png",
        "caption": "Figure 2. Diagram of the equivalent contacting cones.",
        "texts": [
            " Effect of load, speed and addendum modification coefficient on lubrication performance during the engaging are investigated. Figure 1 shows the engagement diagram of a helical gear pairs, and the base helix angle b is expressed as the angle between the contact line K1K 0 1 and the rotation axis. The ideal engaging surface is N1N 0 1N2N 0 2. The length of contact line K1K 0 1 first increases when engaging in and then turns out to be decrease when engaging out. The helical gear pair is assumed as two cones with the same conical degree, as shown in Figure 2. N1N 0 1, N2N 0 2 are the rotation axis of the two equivalent cones, respectively. The radius of the left side of the driving gear is expressed as r1d \u00bc N1K1. Since the theoretical length of engaging line is the distance N1N2, and suppose the contact line length K1K 0 1 \u00bc l, then the radius r1, r2 along the contact line K1K 0 1 are r1 \u00bc r1d y sin b r2 \u00bc N1N2 r1 \u00f01\u00de The equivalent radius ry can then be expressed as ry \u00bc r1r2 r1 \u00fe r2\u00f0 \u00de cos b \u00f02\u00de The rolling velocities ui, the entrainment velocity ue and the sliding velocity us can be expressed as u1 \u00bc "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003154_s11071-013-1125-z-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003154_s11071-013-1125-z-Figure2-1.png",
        "caption": "Fig. 2 FE model of the ring damper",
        "texts": [
            " The method is applied to a test case, where the forced response of a bevel gear is calculated, and the effect of the principal design parameters of the ring damper that affect the dynamics of the gear is also highlighted. The dynamic system that includes friction contacts is usually the assembly of two or more substructures, which are modeled by FEM. In this paper, the primary structure is the gear, shown in Fig. 1a, made of NS identical sectors, while the secondary structure is the ring damper (Fig. 2), characterized by a circular shape and by a cut along its axial direction, performed to insert it into the rectangular groove located under the rim of the gear and shown in Fig. 1b. The gear is a cyclic symmetric structure, and its mode shapes (Fig. 3) have special features: \u2013 The modal amplitudes of points located at the same relative position of different sectors have a harmonic distribution along the hoop direction and form an integer number of waves along that direction. \u2013 For this reason, mode shapes can be grouped according to the number of nodal diameters nd, i.e., nodal lines crossing the axis of rotation where the modal displacement is null. Also, nodal circles are a common feature of modes of cyclic symmetry structures; in this case, the nodal line is a circle centered on the axis of rotation. The maximum number of nodal diameters is nd = int(NS/2); see Fig. 2a and Fig. 2b, showing two mode shapes at nd = 1 and nd = 2, respectively. \u2013 Due to the cyclic symmetry, the mode shape of the whole structure can be obtained from the mode shapes of one of its sectors, the commonly defined fundamental sector. The eigenvalues associated to the eigenvectors with nd = 0 and NS/2 (if NS is even) correspond to a single natural frequency, i.e., standing mode shapes are found, while the double eigenvalues are found for those modes characterized by nd different from 0 and NS/2. In this case, the corresponding two mode shapes are orthogonal, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002906_j.mechmachtheory.2013.01.010-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002906_j.mechmachtheory.2013.01.010-Figure2-1.png",
        "caption": "Fig. 2. Geometry of a ball and inner and outer raceways in case of two-point ball bearing with zero clearance.",
        "texts": [
            " In [15] load distribution of bearing without clearance is investigated, in [16] static capacity and load distribution of bearing with and without clearance is investigated, and in [17] load distribution and static capacity of bearing with clearance and predefined irregular geometry is investigated. The calculation procedure presented in this paper is given only for ball bearings but it can be extended for roller bearings as well. Furthermore, since such computational model is especially appropriate for computer implementation it can also be easily integrated into expert computer systems for complete design of bearing connections, such as described by Prebil and Kaiba [18] or Rao [19]. Geometry of the ball and raceways in case of two-point ball bearing without clearance is shown in Fig. 2. Here O0, O, Oi and Oo stand for the centres of the bearing, ball, inner raceway and outer raceway, respectively, and d, D, ri, ro and \u03b10 stand for ball track diameter, ball diameter, inner and outer raceway radius and nominal contact angle, respectively. Ci and Co stand for contact points on inner and outer raceways, respectively, and oi,a, oi,r, oo,a and oo,r stand for nominal axial and radial distances between the centres of the ball and inner/outer raceways, respectively. The word nominal refers to the geometry of the bearing in case of zero clearance. Radii ri and ro are usually the same, hence ri=ro=r, and are most often defined in terms of the diameter of the ball and the osculation S, which is defined as: S \u00bc D 2r : \u00f01\u00de The nominal distances between the centres of inner and outer raceways and the centre of the ball are usually the same, hence oi,a=oo,a=oa and oi,r=oo,r=or. Considering the aforementioned definitions and Fig. 2 the distances oa and or are defined as: oa \u00bc D 2 sin\u03b10 1 S \u22121 \u00f02\u00de or \u00bc D 2 cos\u03b10 1 S \u22121 : \u00f03\u00de In case of oa=or the nominal contact angle \u03b10=45\u00b0, which is the most common case. Furthermore, in most cases the osculation is between 0.95 and 0.97. Irregular bearing geometry is specified by means of irregular geometry of the raceways' centres as schematically shown in Fig. 3, which shows the tracks of balls' and inner raceways' centres. For each ball along the ball track the distance from the ball centre to the raceway centre is defined as a sums of nominal axial and radial distances between the ball centre and the raceway centre in case of bearing with zero clearance, i",
            " As already explained in the introduction the idea behind this is that \u2013 to some degree \u2013 such geometry can be used as a basis for studying the influence of the bearing deformation on the contact load distribution on the bearing raceways. Hence, hereinafter the bearings with such geometry are referred to as deformed bearings or bearings with deformed geometry. The geometry of the raceway centre, which describes the deformation, was defined by the following sine wave function, \u0394o;a \u03c8 \u00bc Asin B\u03c8\u2212C\u00f0 \u00de: \u00f021\u00de The function describes axial shift of the outer raceway's centre, i.e. axial shift of the point Oo in Fig. 2. The calculations were done for amplitudes A=[0.05, 0.10] mm, hence for approximately a quarter and a half of the clearance 0.25 mm. These seem to be somehow sensible values, though it has to be noted that they were chosen completely arbitrarily. Phases of the sine wave function were chosen as C=[0,45,90,180,270,315]\u00b0 whilst the angular frequency was always B=2. Angular frequency was chosen to be B=2 since most catalogues of large slewing bearings mention that the maximum flatness deviation of the connecting surfaces on the substructure of the bearing in the circumferential direction can appear only once per 180\u00b0, which is basically a sine wave with frequency 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001227_s11663-003-0071-4-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001227_s11663-003-0071-4-Figure1-1.png",
        "caption": "Fig. 1\u2014Schematic illustration of electron beam cold-hearth melting: 1 through 4\u2014electron-beam guns, 5\u2014consumable billet, 6\u2014cold hearth, 7\u2014mold, 8\u2014ingot, and 9\u2014hearth.",
        "texts": [
            " To develop a mathematical model for aluminum evaporation during the actual EBCHM process, the aluminum and titanium material balance equations for each zone in which metal is in the molten state must also be derived, and the relations for the mass flows between zones must be formulated. Moreover, the kinetic Eq. [6] must be applied in accordance with the specific processing parameters of the equipment used. To derive the material balance equations, consider the electron-beam melting of a consumable billet with a cross section area S0 (m 2) into the hearth and then the mold (Figure 1). It is assumed that molten metal flows into the hearth and mold in a continuous fashion. Let the billet be fed into the melting zone at a speed m0 (kg/s). The concentration of aluminum here is denoted as [Al]0 (mass fraction) and titanium as [Ti]0 (mass fraction). During the melting process, the aluminum content of the molten metal varies, ranging from [Al]1 at the melting tip of the billet to [Al]2 in the cold hearth and [Al]3 in the mold; the concentration of titanium in liquid metal varies from [Ti]1 at the melting billet tip to [Ti]2 in the cold hearth and [Ti]3 in the mold"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001875_s00707-008-0037-3-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001875_s00707-008-0037-3-Figure1-1.png",
        "caption": "Fig. 1 Cross section along membrane radius in dimensional terms",
        "texts": [
            " It is assumed in Sects. 2\u20138 that the circumferential displacement V (R) is zero (i.e., there is no torsion), and that the radial and transverse displacements are rotationally symmetric. It is assumed that the membrane is taut. The onset of wrinkling is determined by the condition that the minimum principal stress resultant reduces to zero [8]. The self-weight of the membrane is neglected in the equilibrium analyses. 2.1 Generalized Reissner (GR) theory A cross section along a radius of the membrane is depicted in Fig. 1. The membrane is assumed to be isotropic, homogeneous, and linearly elastic with modulus of elasticity E , Poisson\u2019s ratio \u03bd, and constant thickness h. It is subjected to a distributed load with tangential and normal components Pt and Pn per unit of deformed area, respectively. The radial coordinate is R, with A \u2264 R \u2264 B . The radial displacement is U (R), the downward displacement is W (R), and the meridional rotation is \u03c6(R). The circumferential coordinate is \u03b8 . For an incremental change in arc length in Fig. 1, the horizontal projection is dR + dU and the vertical projection is dW . Hence [9] W \u2032 = (1 + U \u2032) tan \u03c6. (1) The arc length of an element in the deflected membrane is [\u03b12 r dR2 + \u03b12 \u03b8d\u03b82]1/2, where [5,10] \u03b1r = [(1 + U \u2032)2 + (W \u2032)2]1/2 = 1 + \u03b5r , \u03b1\u03b8 = R + U = R(1 + \u03b5\u03b8 ). (2a,b) Using Eqs. (1) and (2), the meridional and circumferential strains may be written as \u03b5r = [(1 + U \u2032)/ cos\u03c6] \u2212 1, \u03b5\u03b8 = U/R. (3a,b) The use of the rotation \u03c6 in Eqs. (3) instead of the square root in Eq. (2a) is convenient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure5-1.png",
        "caption": "Fig. 5 \u2013 Longitudinal arrangement of residual space [3].",
        "texts": [
            " The space may not be smaller than as defined by the regulation but the manufacturer may define a bigger residual space than is required to simulate the worst case and thus increase the safety margins in the case of emergency load and enable the maximum protection of passengers. The envelope of the vehicle's residual space is defined by creating a vertical transverse plane within the vehicle which has the periphery described by the regulation (Fig. 4) through the length of the vehicle. The characteristic points of the space, which define it, are SR points, through which a vertical transverse plane is moved through the length of the vehicle along straight lines (Fig. 5). The SR point is located on the seatback of each outer forward or rearward facing seat (or assumed seat position), 500 mm above the floor under the seat, 150 mm t of residual space [3]. from the inside surface of the side wall. No account should be taken of wheel arches and other variations of the floor height. These dimensions should also be applied in the case of inward facing seats in their centre planes. If the SR point of rearmost outer seat is less than 200 mm behind the rear wall, then the residual space is the inner face of the rear wall of the vehicle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001117_robot.1994.350931-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001117_robot.1994.350931-Figure1-1.png",
        "caption": "Figure 1: A two link manipulator a t the end points of a specified path.",
        "texts": [
            " The iteration on a single parameter is computationally quite inexpensive compared to the dynamic programming search used in (Shin and McKay 1986, Singh and Leu 1987, Vukobratovic and Kircanski 1982). The method was implemented for two planar manipulators. It is first demonstrated numerically for a two link manipulator, followed by an experimental example for the UCLA Direct Drive Arm. 5.1 A Two link Planar Manipulator In this example, the task is to move the two link manipulator, with the parameters given in Table l, along the specified path shown in Figure 1. Figure 2 shows a family of time-energy optimal trajectories in the phase plane, s - S, for various values of E . Also shown in Figure 2 is the time optimal trajectory. Clearly, as E approaches zero, the corresponding trajectory approaches the time optimal one. Figure 3 shows the variations in the motion time as a function of 6\u2019. From Figure 3 it is clear that trajectories for a small E can be computed by starting with a large E , then solving the problem repeatedly for progressively smaller E\u2019S , using the solution for XI(0) at each iteration as the initial guess for the next iteration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-36-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-36-1.png",
        "caption": "FIGURE 12-36 Simple hydraulic system.",
        "texts": [
            "01 mm Oil viscosity, v, is 5 centistokes Oil density, p, is 0.88 kg/L 4. A hydraulic pump has an inlet pressure of - 34 kPa vacuum and a discharge pressure of 3440 kPa. The diameter of the suction line is 32 mm and the discharge line is 19 mm. The pump discharges oil at 1.15 Us and the density, p, of the oil is 0.88 kg/L. Neglect friction and efficiency. Determine the power in kilowatts required to rotate the py.mp. 5. In problem 4, how much power must be added if the kinetic energy of the fluid is also considered? 6. Refer to figure 12-36. (a) What is the minimum pressure setting that would be acceptable for the coun terbalance valve? (b) If the piston must be capable of a velocity downward of 5 cm/s, what minimum pump capacity is required? (c) If the piston must provide a net force downward of 1.11 X 103 N, what is the minimum setting for the pressure relief valve? (d) If the pump is 90 percent efficient, what power is required? (e) If 3 m/s is the maximum fluid velocity acceptable in the lines, what size tubing should be used? (j) What porting configuration would you suggest for the centered position of the valve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002755_tsmcc.2011.2182609-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002755_tsmcc.2011.2182609-Figure1-1.png",
        "caption": "Fig. 1. Comanche STG.",
        "texts": [
            "ndex Terms\u2014Acoustic emission (AE) sensor, ant colony optimization (ACO), gear fault location detection, split torque gearbox (STG), wavelet transform (WT). I. INTRODUCTION THE requirement for higher energy density transmissions (lower weight) in helicopters has led to the development of the split torque gearbox (STG) to replace the traditional planetary gearbox by drive drain designers [1]. A typical STG transmission system is shown in Fig. 1. As stated in [2], in a traditional planetary gear transmission train, the output shaft is driven by several planet gears. Torque is transmitted from the central sun gear through the planets to the planet carrier. In a split torque gear train design, multiple pinions connected by a Manuscript received April 13, 2011; revised July 20, 2011; accepted December 13, 2011. Date of publication February 15, 2012; date of current version December 17, 2012. This paper was recommended by Associate Editor T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003820_1.4039386-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003820_1.4039386-Figure3-1.png",
        "caption": "Fig. 3 Ball-raceway contact analysis",
        "texts": [
            "org/about-asme/terms-of-use where dik and dok are the ball-raceways contact deformations, and hik and hok are oil film thicknesses in contact areas. The ballraceways contact forces can be expressed by the Hertz contact theory Qik \u00bc Kikd 1:5 ik Qok \u00bc Kokd 1:5 ik 8< : (4) where Kik and Kok denote the deflection coefficients of ball-raceways contacts. In order to determine the oil film traction forces in ball and raceways contacts, the relative sliding velocities between ball and raceways should be first obtained. Figure 3 illustrates the surface velocities of ball-raceways contacts. As shown in Fig. 3(a), at any contact point (xo, yo) in ball-outer raceway contact ellipse, the relative sliding speeds in the minor axis and major axis directions of contact ellipse can be written as Dvn o \u00bc \u00f0xx0 cos ao \u00fe xz0 sin ao xm cos ao\u00de n \u00f0R2 o x2 o\u00de 1=2 \u00f0R2 o a2 o\u00de 1=2 \u00fe \u00bd\u00f00:5D\u00de2 a2 o 1=2 o 0:5dmxm Dvg o \u00bc xy0 n \u00f0R2 o x2 o\u00de 1=2 \u00f0R2 o a2 o\u00de 1=2 \u00fe \u00bd\u00f00:5D\u00de2 a2 o 1=2 o 8>>>>>< >>>>: (5) where ao is the major semi-axis of ball-outer raceway contact ellipse, the superscripts n and g are, respectively, the directions of minor axis and major axis in contact ellipse, and the equivalent curvature radius Ro can be written as Ro \u00bc 2roD 2ro \u00fe D (6) As shown in Fig. 3(a), the spinning angular velocity between the ball and the outer raceway can be expressed as xs o \u00bc xx0 sin ao xz0 cos ao xm sin ao (7) Similarly, the relative sliding speeds at any contact point (xi, yi) in ball-inner raceway contact ellipse can be written as Dvn i \u00bc \u00f0xx0 cos ai \u00fe xz0 sin ai \u00f0xi xm\u00decos ai\u00de n \u00f0R2 i x2 i \u00de 1=2 \u00f0R2 i a2 i \u00de 1=2 \u00fe \u00bd\u00f00:5D\u00de2 a2 i 1=2 o 0:5dm\u00f0xi xm\u00de Dvg i \u00bc xy0 n \u00f0R2 i x2 i \u00de 1=2 \u00f0R2 i a2 i \u00de 1=2 \u00fe \u00bd\u00f00:5D\u00de2 a2 i 1=2 o 8>>>< >>>: (8) Journal of Mechanical Design MAY 2018, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003843_s12206-018-0635-5-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003843_s12206-018-0635-5-Figure1-1.png",
        "caption": "Fig. 1. Illustration of a three-dimensional ball movement.",
        "texts": [
            "com \u2020 Recommended by Associate Editor Young Whan Park \u00a9 KSME & Springer 2018 The ball typically undergoes rolling without slipping in the race under common, mid-speed operations. Therefore, the proposed wear model is based on the following assumptions: (1) All friction-inclusive materials are isotropic and their friction properties remain invariant during the analysis period; (2) The surface roughness of the components remains constant and the post-wear profiles of both inner and outer races remain circular. 2. Quasi-dynamic analysis of rolling bearings 2.1 Revolution, rotation, and spin of rolling elements The three-dimensional rotation of the ball is shown in Fig. 1, where \u2018{x,y,z}\u2019 is an inertial frame and \u2018{x\u2019,y\u2019,z\u2019}\u2019 is the local coordinate with its origin located at the center of the ball. Axis x\u2019 is parallel to axis x, and the coordinate system rotates about axis x at the revolution speed of the ball. O\u2019U is the rotation axis of the ball. The three components of the angular velocity bw are \u2019 \u2019,bx byw w and \u2019,bzw respectively: 2 1/2 ' ' ' 2 2( )b bx by bzw w w w= + + , (1) among which, ' cos cos 'x bw w b b= \u00d7 , (2) ' cos sin 'y bw w b b= \u00d7 , (3) ' sinz bw w b= "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001562_20.105039-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001562_20.105039-Figure5-1.png",
        "caption": "Figure 5 : Flux lines for V= 0 p.m , and zoom on the teeth.",
        "texts": [],
        "surrounding_texts": [
            "E E E TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 5, SEPTEMBER 1991\nBut the rotor cage bars are solid conductors connected together by means of the end rings. Every portion of the ring located between two bars may be considered as an extemal impedance. The rotor cage is then described by the polyphase Circuit of figure 1.\nL L L L I r r I\nAVa2 AVai AVai+l\nAV1 9 V 2 RcrroR AVbi-1 AVbi\nI1 12 l i - 1 I i l i t 1\nBARS d L d L r L t L\nA A A A -\n4247\nb\nAVbi+l 1 L\nLet ra and xa be respectivelly the resistance and the reactance of a portion of the ring. With reference to Fig 1, we obtain the following equations.\nAVbi-1 = 2AVai + AVbi (9)\nThe two equations (10) and (9) give the two following matrix equations.\n[Kl = [MINI (13)\n[AVa] = - 1/2[MIt[AVb] (14)\n(15)\nWhen substituting equation (1 1) with equations (13) and (14) one yields to.\n( ra + jgxa ) [rl = -[Tl[AVl\nWhere Finally, equauon (8) becomes, in the case of a rotor cage.\n[I = 1/2[M][M]f is a symemc band matrix.\n-jwg[RItClt[Al + ( 1 + [R l [ I /('a + M a 1 )[AV1 = O (16)\nThe currents in the bars may be obtained by the relation (15) . The resistance and the reactance of the end-rings are computed\nusing analytical methods.\n3 - STATOR EQUATIONS :\nStator coils are made of thin conductors in which the skin effect may be considered as negligible. In this particular case, it is possible to find a formulation that represents a voltage fed coil .\nLet us consider an N identical tum, coil connected to an extemal impedance q x t an2 supplied by a sinusokial voltage source\nOhm's law writes as follows :\nNS E = Zext I + (Av1.k - Av2.k) (17)\nk= 1\nWhen applying equation (2) on the NS conductors, NS\n-jw[C'lT[A1 + [R]-l[AV] = p] I\nequations are obtained leading to the following formulation [ 11.\n(18)\nA linear combination of equations (17) and (18) yields finally to\njw[DlTtC'lT[A1 + (Gxt + Rk) I = E (19) Ns\nk+ 1\nwith C.. ' - i j - N ssk L 1,I.i d n\nSince the conductors are thin, the potential difference across each conductor simply writes with respect to I.\nThe field equation (3) then becomes :\n[S][A] - [C][D] I = 0 (20)\nZext is the impedance of the end windings analytically computed.\n4 - RESULTS :\nComputations have been performed on a three phase motor, 4 poles, 50 Hz with a double cage rotor, the slots of which are not skewed (Fig 3) .\nThe measurements have been done by running the machine at a given speed, then coupling to the network .",
            "4248\nIEEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 5, SE\u20ac'EMBER 1991\nOn figure 4 are compared computed and measured values. The e m r on the absorbed current and on the power is less than 5 %. The error on the torque is some times greater than 5 % which shows the influence of the space harmonics that are not correctly represented by this model.\nThe study of the motor under 380 V, at ambient temperature gives the motor characteristics with respect to the rotor speed as represented in figure 7.\nI1 is the current in one phase of the stator and I2 is the current of the rotor seen by one phase of the stator . R2 is the dynamic resistance see by one phase of the stator.\nWhen modelling this motor at high temperature, the influence of the thermal effects on the electrical characteristics may be put into evidence (Fig 8) . All characteristics of the motor decrease with the temperature .\n5 - CONCLUSION :\nThe method presented in this paper is an extension to the harmonic solution of non-linear magnetodynamic problems of the nowadays classical finite element method.\nThe coupling of the circuit equation completes the 2D finite element method by introducing the possibility to take into account the 3D part of the motor. Another advantage is the abilite to include voltage sources .\nThis new method may be applied in induction machines with good approach of global values if spatial harmonics can be neglected .With this method we can have a good approach of all characteristics of the motor. This method can be used to build and to optimise new motors with less prototypes than a classical analysis .\nAKNOWLEDGMENT\nThe authors gratefully aknowledge LEROY-SOMER and Electricire De France for financial supporting part of the research.\nREFERENCES :\n[ 11 D.Shen,G.Meunier,J.L.Coulomb,J.C.Sabonnadi&re. \"Solution of magnetic fields and elecmcal circuits combined problems\", IEEE Trans. on Mag.,vol. MAG-21,N06, pp 2288-2291.1985 . [2] E.Vassent, G.Meunier, J.C.Sabonnadi&re,\" Simulation of induction machine operation using complex magnetodynamic finite elements Method.\" IEEE Trans. on mag, Vol MAG 25, No 4, july 1989. [ 31 D.Shen,G.Meunier.\"Modeling of squirrel cage induction machines by the finite elements method combined with the circuits equations\", Proc. of the Int. Conf. on Evolution and Modern Aspects of Induction Machines,Torino, pp 384-388.8-1 1 July 1986 .\nOn the field maps of figures 5 and 6, the double cage effect on the flux penetration during the starting up of the rotor, may be observed. The skin effect is very strong and the rotor resistance is multiplied by a factor of 2,5 when starting (Fig 7).",
            "IEEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 5, SEPTEh5BER 1991 4249\n30880\n20000\ni I I I i\n0 200 400 600 800 1000 1200 1400\n'1 50\n4\nFigure 7 : Characteristics at ambiant temperature\nFigure 8 : Characteristics at high temperature ."
        ]
    },
    {
        "image_filename": "designv10_10_0002949_978-3-642-19457-3_7-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002949_978-3-642-19457-3_7-Figure3-1.png",
        "caption": "Fig. 3 For basic analysis of static stability, we consider a robot with single actuators per hip, similar to the RHex-style robot shown. With such a model, the stability margin of gaits is computed.",
        "texts": [
            " In the figure we highlight potentially dangerous cells that recirculate 2 or 3 of the legs together at the same time. The cell where all legs are in stance, or only a single leg recirculates, would be considered safe cells. We utilize Stancen[T] to define in general the global properties of static stability for an n-legged robot. This approach allows us to evaluate gait stability simply by studying the cells through which a given gait passes. Figure 4 shows analysis of the Stance Complex on T 4. Using our simple model of a quadrupedal robot (Fig. 3), each cell is tested for static stability, consisting of a total of 160, 000 tested configurations for the 16 cubical cells, taking into full consideration the entire gait space of T 4. Cells with more legs in stance offer greater static stability. Similarly, certain cells with two legs in stance perform better than others, for instance showing that the cells corresponding to a trot gait, cells 6 and 9, have greater stability than those for pace and bound gaits. Utilizing both the Gait Complex and Stance Complex, we develop a mixed planning and control approach to automate safe switching between gaits",
            ": Testing static equilibrium for legged robots. IEEE Transactions on Robotics 24(4), 794\u2013807 (2008) 2. Cohen, F., Koditschek, D.E.: Hybrid control over the coordination complex (2009) (in preparation) 3. Cohen, F.R.: On Configuration Spaces (2008) (in preparation) 4. Farley, C., Taylor, C.: A mechanical trigger for the trot-gallop transition in horses. Sci- ence 253, 306\u2013308 (1991) 2 For an example of a more complicated family of reference gait generators capable of producing such \u201cwinding\u201d limit cycles, consider the example in Fig. 3 of [20]. 5. Griffin, T., Kram, R., Wickler, S., Hoyt, D.: Biomechanical and energetic determinants of the walk-trot transition in horses. Journal of Experimental Biology 207, 4215\u20134223 (2004) 6. Hatcher, A.: Algebraic topology. Cambridge University Press, Cambridge (2002) 7. Haynes, G.C.: Gait regulation control techniques for robust legged locomotion. Ph.D. thesis, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA (2008) 8. Haynes, G.C., Khripin, A., Lynch, G., Amory, J., Saunders, A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001440_008-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001440_008-Figure2-1.png",
        "caption": "Figure 2. Experimental set-up.",
        "texts": [
            " It can be seen that the attenuation of laser power is an exponential function and determined by process variables such as the powder feed rate, m\u0307p, grain moving velocity, vp, grain radius, rp, half spraying angles of the laser beam and powder flow stream, \u03d5 and \u03c6, radii of their waists, 1 tan \u03d5 and 2 tan \u03c6, their waist position, z0, and run of the laser beam through the powder flow stream, z\u2032. In equation (15), since 2 arctan(A 1 + B) < {arctan[A( 1 + z0) + B] + arctan[A(z\u2032 + 1 \u2212 z0) + B]}, attenuation increases with the powder feed rate or run of the laser beam through the powder flow and decreases with a rise in the grain diameter or in the moving velocity. The impacts of the other variables on the attenuation of laser power are complicated. The experimental set-up is shown in figure 2. A portable power meter is placed under the coaxial nozzle and used to measure the laser power which has been attenuated by powder. The gaspowder flow and laser beam go through the coaxial nozzle to the power meter. In the experiment presented, the diameter of the laser spot on the surface of the power meter is required to be over 4.0 mm in order to protect the power meter from being damaged by laser. Because no melt pool exists on the power meter, the powder particles are blown away after arriving at the power meter by the gas flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure5-1.png",
        "caption": "Fig. 5. Cutting force of single-feed technique.",
        "texts": [
            " The forces F cs and F cr , exerted on the chip from the shear plane of the workpiece and the rake face of the tool, can be expressed respectively in S s and S r as: F cs = [ \u2212F s cos \u03b7s F s sin \u03b7s N s ]T (28) F cr = [ N c \u2212F r sin \u03b7c \u2212F r cos \u03b7c ]T (29) Transformed to the base S n , the forces F cs and F cr can be expressed respectively as: F (n ) cs = M ns \u00b7 F cs = \u23a1 \u23a3 F (n ) cs _ x F (n ) cs _ y F (n ) cs _ z \u23a4 \u23a6 = [ \u2212F s cos \u03b7s cos \u03c6n \u2212 N s sin \u03c6n F s sin \u03b7s \u2212F s cos \u03b7s sin \u03c6n + N s cos \u03c6n ] (30) F (n ) cr = M nr \u00b7 F cr = \u23a1 \u23a3 F (n ) cr _ x F (n ) cr _ y F (n ) cr _ z \u23a4 \u23a6 = [ N r cos \u03b3n + F r cos \u03b7c sin \u03b3n \u2212F r sin \u03b7c N r sin \u03b3n \u2212 F r cos \u03b7c cos \u03b3n ] (31) where, M ns is the transfer-matrix from S s to S n and M nr is the transfer-matrix from S r to S n M ns = [ cos \u03c6n 0 \u2212 sin \u03c6n 0 1 0 sin \u03c6n 0 cos \u03c6n ] (32) M nr = [ cos \u03b3n 0 \u2212 sin \u03b3n 0 1 0 sin \u03b3n 0 cos \u03b3n ] (33) The equilibrium of the forces applied to the chip in a stationary process can be expressed in S n as: F (n ) cs + F (n ) cr = 0 (34) Thus the normal forces N s , N r and the friction force F r , exerted on the chip from the shear plane of the workpiece and the rake face of the tool, can be expressed in S n as: F r = F s \u00b7 sin \u03b7s sin \u03b7c (35) N s = F s \u00b7 cos \u03b7s sin ( \u03c6n \u2212 \u03b3n ) + F s \u00b7 sin \u03b7s cot \u03b7c cos ( \u03c6n \u2212 \u03b3n ) (36) N r = \u2212F s \u00b7 cos \u03b7s cos \u03c6n + N s \u00b7 sin \u03c6n + F r \u00b7 cos \u03b7c sin \u03b3n cos \u03b3n (37) The cutting graph in gear skiving with single-feed technique is shown in Fig. 5 (a), from which we can see the recess edge removes most of the material of the tooth space, followed by the top edge and the approach edge. The calculation result of cutting force density (cutting force divided by the length of the cutting edge) of the tool in gear skiving with single-feed technique, based on the basic parameters in Table 1 , is shown in Fig. 5 (b). As shown in Fig. 5 (b), the largest force density locates at the top-recess nose of the cutter tooth when it moves out of the tooth space of the workpiece, which may result in a rapid wear of the cutter tooth. The cutting work done by the cutting edge element can be described as: W = \u222b t 1 t 2 v c \u00b7 M 2 n \u00b7 F (n ) r + v (2) n \u00b7 N (n ) r d t (38) where, t 1 and t 2 are the cut in time and cut out time of the edge element and M 2 n is the transfer matrix from S n to S 2 M 2 n = [ v (2) n | v (2) n | t (2) c | t (2) c | n (2) c | n (2) c | ] (39) The calculation result of cutting works done by the edge elements in gear skiving with single-feed technique using the basic parameters in Table 1 are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001105_robot.2001.933160-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001105_robot.2001.933160-Figure4-1.png",
        "caption": "Figure 4: Top view of two Conro configurations and their connectivity graph",
        "texts": [
            " This graph describes the topology of a robot but cannot be used to uniquely identify configurations with modules that can be connected to each other using different ports, i.e., if a module with n ports can be connected to any of the n ports of another module, then there are n! ways in which the two modules can be connected, many of which might be topologically different. The Conro module is a multiport module and thus, we cannot use a connectivity graph to uniquely identify a configuration. For example, the two configurations shown in Figs. 4.a-b have the same connectivity graph shown in Fig. 4.c (a module has been colored for visualization purposes). A way to distinguish between configurations of multiport modules is to use the labels of the ports in the representation. In this case a suitable representation of the module is that shown in Fig. 3.c, where tlie module is represented by its ports, i.e., a vertex represents a port while an edge indicates that two ports either belong to the same module or belong to two connected modules. Our goal is to find a graph-only representation of a robot that would allow us to distinguish between dif- ferent configurations regardless of their labelings, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5\u00b79-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5\u00b79-1.png",
        "caption": "FIGURE 5\u00b79 Valve rotator mechanism. (Cour tesy Thompson Products.)",
        "texts": [],
        "surrounding_texts": [
            "86 ENGINE DESIGN\nIn certain instances, where valve materials or requisite properties to obtain the desired durability are not available or cannot be used economically, various means of valve fortification are employed. The most important of these are as follows:\n1. Face Coatings-These are welded overlays applied to valve faces and intended to develop optimum corrosion and wear resistance at the valve seating surface. Cobalt-, nickel-, and iron-base alloys are usually chosen for this purpose. 2. Head Coating-These coatings are applied to the tops of the heads of exhaust valves to inhibit corrosion. Because hot hardness is not required, nickel chromium alloys are most frequently chosen for this purpose. 3. Aluminizing-This is a special case of a protective coating. It comprises a thin layer of aluminum applied to the face and sometimes to the valve head. Aluminum, when diffused, alloys with the base material and provides a thin hard corrosion-resistant coating. 4. Internal Cooling-Hollow valves, partially filled with metallic sodium or so dium-potassium mixtures, transfer heat by convection from the hot head end of valve to the stem. Internal cooling reduces maximum valve temperatures to about 175\u00b0C. 5. Stem and Tip Welding-Occasionally, the valve tip or the entire stem is made of martensitic steel. The stem material is welded to the head section of the valve and heat-treated to provide better scuff resistance. 6. Valve Rotators-These are mechanical devices [see fig. 5-9] which cause the valve to turn in the opening portion of the cycle. Rotation tends to ensure good heat transfer from the valve face to the seat. Several types are in use. Valve rotators have been responsible for durability improvements of from two to ten times of the same material without rotation. 7. Hydraulic Valve Lifters-Hydraulic valve lifters [see fig. 5-10] compensate for wear and for thermal changes in the valve train. Their use tends to avoid excessive stresses resulting from too large a clearance, as well as excessive valve temperatures resulting from too small a clearance.\nValves are subjected to high acceleration forces. For example, in an en gine operating at 2400 rpm, an exhaust valve must open, permit the burned mixture to escape, and then close, all within about 0.01 s. During this cycle the exhaust valves and seats are exposed to temperatures that may be as high as 2500\u00b0C during the combustion and may be about 650\u00b0C during the exhaust.\nThe temperature to which exhaust valves are subjected is shown clearly in figure 5-11. The exhaust temperature is decreased by increasing the compression ratio of the engine, although at the same time the maximum temperature will increase within the combustion chamber. Since the top of the valve is within the combustion chamber, it is obvious that a valve is sub jected to increased thermal stresses as the compression ratio is increased. The",
            "VALVE TIMING\n87\nmethod by which a valve is cooled is shown in figure 5-12. Some heat flows through the valve seats, and the remainder is lost through the valve stem, which is cooled by lubricating oil and by contact with the valve stem guide.\nValve Timing\nIt would seem at first thought that the intake valve should open on head dead center and close on crank dead center, whereas the exhaust valve should open on crank dead center and close on head dead center. With a large and very slow-speed engine this procedure might operate satisfactorily. The proper valve timing is a function of several factors, including engine speed. With an increase in engine speed the intake valve must be closed later and the exhaust opened earlier. The best valve timing for any given engine can be determined only by actual tests because it depends greatly on the design of the intake and the exhaust passages. A given timing results in maximum compression pres sure at some given speed. An ideal arrangement would be one in which the valve timing was automatically changed with the speed. Such an arrangement has recently been put into practical use, but it is limited to some gasoline engines and large diesel engines producing more than 1000 kW. With the rapid advancement of electronic control technology, the application of au-",
            "88\nENGINE DESIGN\ntomatic control of valve timing and independent valve control system de pending on load conditions may be put into practice for tractor engines in the near future.\nFigure 5-13 shows the results of a test on an engine to determine the optimum valve timing at a given rpm. The data plotted are air consumption in kilograms per minute for varying inlet valve opening (ivo) and inlet valve closing (ivc). They are also a comparative measure of volumetric efficiency for different inlet valve timings. The curves represent combinations of inlet"
        ]
    },
    {
        "image_filename": "designv10_10_0001703_bfb0036159-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001703_bfb0036159-Figure12-1.png",
        "caption": "Figure 12: A three-dimensional passive biped. Like the original 2D model it has straight legs and semicircular feet. Orientation of the stance leg relative to the ground coordinates is determined by the yaw (\u00a2), roll (\u00a2), pitch (8) sequence of rotations about the axes indicated. The swing and stance legs have the same yaw and roll angles, but can pitch independently. Mass centres are shown for the legs and hip; those on the legs have 3D rotational inertia, while the hip axle c~rries only a point mass.",
        "texts": [
            " Several models of walking machines are discussed and experimented. The paper by A. Sano and J. Furusho presents a control method for quadrupeds at a pace gaits. The locomotion is hence dynamic since only two feet, on the same side, touc~ the ground together. The approach is based on a discrete-time model and experimental results show its effrectiveness. Passive Dynamic Biped Catalogue, E-marl to USERTMCG@cc.sfu.ca 1991 R o m a n C C I g m R ~'gyr rg vg Vwg VW, lg T g V W Whip x (relevant formulae are referenced in Greek axial position of mass centre (figure 12) matrix of control gains (22) identity matrix gravitational acceleration angular momentum parentheses) leg length mass foot radius radius of gyration stride function (1) jacobian of g (6) first row of VS (23) gradient of ~ w.r.t, g (25) gradient of ff w.r.t. TH (20) first element of Vrff (23) torque vector of control variables (25) translational velocity forward offset from link axis to mass centre (Ay in figure 12) hip width (figure 12) coordinate normal to the ground (figure 12) coordinate along the slope (figure 12) eigenvalue (7); lateral coordinate (figure 12) ao leg pitch angle at support transfer fl torso inclination 7 slope, positive downhill 7~ slope for gravity-powered walking Ay forward offset from link axis to mass centre (figure 12) Az lateral offset from link axis to mass centre (figure 12) 0 pitch angle (figure 12) ff start-of-step state vector (1) a dimensionless pendulum frequency (9) r dimensionless time t V ~ v0 step period \u00a2 roll angle (figure 12) \u00a2 yaw angle (figure 12) rotation rate in pitch w rotation rate Subscripts 0 steady cycle conditions C stance leg F swing leg H at the hip k step index T torso or hip 466 r a x l e l l I J l Jl r l ~ II I 1 ~ II I 1 ~ i~ I l l ..... / ! 1 1 / i / / / / / / / / _ Figure h A bipedal toy which walks passively down shallow slopes. Energy gained by descending the slope is balanced by energy dissipated each time the swing foot hits the ground. The illustration is adapted from McMahon [8]. Abstract Passive dynamic bipeds walk and run by virtue of physics inherent in the interaction of their legs and the ground; they need no motor control",
            " Following this observation we might expect out-of-plane stability to benefit from lateral leg separation. Lateral separation, however, raises the question of whether and how a passive model might counter the unsupported weight of the swing leg. One can certainly attempt to reason out a scheme, but for those whose 3D intuition is unreliable there is also the option of blind recourse to numerical methods. We conceded membership in the latter category and so developed a new stride function for the 3D model sketched in figure 12. This model has seven start-of-step variables: yaw, roll, and stance pitch angles (swing pitch is determined by the contact condition) plus rates about the three stance leg axes, plus interleg pitch rate about the hip. The motion is calculated using fully nonlinear dynamics (which for security we derived once by hand and again using the Autolev program [10]). End-of-step conditions are conservation of the angular momentum vector H of the whole machine about the point of heel strike, and o f / t ",
            " This combination is surprising in view of the exactly opposite strategy of our introductory toy. Its cycle develops pronounced roll but little yaw; in fact a quadrupedal cousin of the toy cannot yaw at all. The differences between the models can be ascribed to foot design. In the sagittal plane the toy's feet form a circular section centred above the overall mass centre. Lateral rocking then reduces to a lightly-damped pendulum oscillation, and to make the toy work well the body-rock and leg-pitch pendulums should be tuned with frequencies roughly in the ratio 3:4 [3]. The model of figure 12, on the other hand, has blade feet and so cannot rock without dissipating a lot of energy. It therefore eliminates rocking~ and instead arranges for lateral balance by exploiting centrifugal effect in a turn. The balance can be demonstrated as follows. The centrifugal acceleration of each mass centre is V~, V being the local speed tangent to the turn and \u00a2 the yaw rate. The net centrifugal torque, when normalised by mgl, is therefore roughly V~ (2m,~gc + roT) ~ 2ao 2A\u00a2 (2m,~gc + mT) (12) r0 To where ao is the excursion of the stance leg in pitch, and A\u00a2 the excursion in yaw"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-28-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-28-1.png",
        "caption": "FIGURE 5-28 Schematic diagrams of four basic combustion chambers used in diesel engines. (a) Direct injection. (b) Precom bustion chamber. (c) Turbulence chamber. (d) Auxiliary chamber. (Standard Oil Co. Engr. Bull., TB-218.)",
        "texts": [
            " Thus, if the fuel were injected directly into the combustion chamber, there would be an unnecessarily long delay before ignition begins, resulting in a very high initial pressure. However, direct injection (fig. 5-27) of the diesel fuel into the combustion chamber is the most common method used. High-speed diesel engines employ several methods to reduce the ignition lag and improve the combustion. Four 113 114 COMBUSTION CHAMBER DESIGN 115 types of combustion chambers used in diesel engmes are shown in figure 5-28. The open-chamber, or direct-injection, combustion chamber generally em ploys a concave piston head. Mixing of the fuel and air is often aided by an induction-produced air swirl or by a movement of air from the outer rim of the piston toward the center of the piston commonly known as \"squish.\" The precombustion chamber is sometimes a part of the injection nozzle, or it may be part of the cylinder head. The entire fuel charge is injected into the precombustion chamber, which contains 25 to 40 percent of the clearance volume"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003464_we.1940-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003464_we.1940-Figure6-1.png",
        "caption": "Figure 6. Seeded faults: (a) sun gear fault, (b) planet gear fault, and (c) ring gear fault.",
        "texts": [
            " The corresponding fault frequencies are represented as follows: f f ;sun \u00bc s f sun f carrier\u00f0 \u00de \u00bc f sunzrings zsun \u00fe zring (14) f f ;planet \u00bc 2 f planet \u00fe f carrier \u00bc 4nsunzsunzring z2ring z2sun (15) f f ;ring \u00bc s f carrier \u00bc f sunzsuns zsun \u00fe zring (16) where ff,i indicates the fault frequency at gear component i and s represents the number of planet gears in the gearbox. For more details, see Bartelmus and Zimroz.36 Tables III and IV present the structural information and characteristic frequencies of the PGB used in this paper. Wind Energ. (2015) \u00a9 2015 John Wiley & Sons, Ltd. DOI: 10.1002/we Three types of PGB faults were created: sun gear partial tooth cut, planet gear partial tooth cut, and ring gear tooth breakage. Each type of gear fault was artificially created by damaging a tooth on a sun gear, planet gear, and ring gear as shown in Figure 6. Both healthy and faulty gearboxes were tested under 20 combinational conditions of four varying loading conditions: 0% loading, 25% loading, 50% loading, and 75% loading out of the rated torque of the PGB, and five varying shaft speeds: 10, 20, 30, 40, and 50Hz. Vibration data were collected from each fault seeded gearbox sequentially. After switching one gearbox to another, the vibration sensors were mounted in the same location on the PGB to preserve the experimental consistency. Figure 7 provides an overview of the experimental procedure that was used to generate the validation results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000694_0094-114x(96)84593-9-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000694_0094-114x(96)84593-9-Figure6-1.png",
        "caption": "Fig. 6. 3-RPS mechanism with intersecting axes.",
        "texts": [
            " 3, at the initial position there is a translation along the Z axis, and since $~ and $~ are in a same base plane and the intersecting point is E, any lines in the base plane that are parallel with $~ and all the connecting lines between point E and any point on $~ can be the rotational axes. This mechanism is different from those discussed in the previous sections. The axes of three revolute joints intersect at the same point. It is assumed that the upper and lower triangle platforms are equal, as shown in Fig. 6. At the initial position, the upper and lower platforms are parallel with each other. The three force line vectors passing through a, b and c points are in a common plane and intersect at a common point. They are linearly related. Only two of the line vectors are linearly independent. The mechanism has four degrees of freedom at this moment. The translations in the X and Y directions are restricted. The possible motions are the translation along the Z direction and three rotations. Any lines in the upper platform plane and lines passing through the intersecting point can be the rotational axes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure1-1.png",
        "caption": "Fig. 1. Numerical model of angular contact ball bearing B7008C/ZYS.",
        "texts": [
            " The outer ring is static, the inner ring, the cage and balls rotate around the axis at their own speed. Besides, balls also suffer from spinning effect. For cage rotation, generally there are three guiding methods, the inner ring guiding, the outer ring guiding and the balls guiding. Only the outer ring guiding condition was discussed in this paper, due to its widely use for angular contact ball bearing, especially at high rotation speed. The structure parameters and model of B7008C bearing can be seen in Table 1 and Fig. 1. The whole computation fluid domain was denoted in a rotating coordinate system with rotation speed nc. The outer ring was static surface in inertial system or with a rotation speed nc in the rotating coordinate system. Balls\u2019 surface and inner raceway were set as rotating wall with rotation speed \u2013nw nc and ni nc, respectively. During bearing internal air flow analysis (without lubrication device, seen in Fig. 1(a)), according the bearing symmetry in peripheral direction, only 1/18 of the entire model was calculated for efficiency purpose, seen in Fig. 1 (b). For oil\u2013air two phase flow analysis stage, the structure of lubrication device was considered, seen in Fig. 1(c) and (d). Taking the real work condition into account, the lubrication unit contains one or two inlet(s) and six outlets. Here the sliding mesh plane method was adopted to describe the interfaces between the rotating inner raceway and the static lubrication unit, the air\u2013oil nozzle and bearing cavity. The geometry model was divided with ICEM unstructured mesh method. In the contact area, the gridding was intensified to adapt the geometry features and improve the result precision, seen in Fig. 1 (b). During the calculation, the standard k\u2013e model was employed for turbulence flow simulation, because it is quick in convergence and precise enough for engineering analysis. For air\u2013oil two phase flow, the VOF model was chose in order to clear the interface of air\u2013oil flow. The PISO scheme with Skewness Correction and Neighboring Correction was chose for pressure velocity coupling. The Second Order Upwind scheme was adopted for turbulent kinetic energy and momentum spatial discretization, and Geo-Reconstruct scheme was applied for oil\u2013air phase interface tracking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003289_jjap.56.06hf03-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003289_jjap.56.06hf03-Figure1-1.png",
        "caption": "Fig. 1. (Color online) Schematic illustration of ICP-CVD system.",
        "texts": [
            " The CFP used as a substrate in the present study was Toray carbon paper EC-TP1-060T.29) Carbon fibers of about 7 \u00b5m diameter are randomly woven and the density of CFP used is 0.44 g=cm3. The high porosity (about 78%) of the CFP facilitates gas and liquid flow. The CFP was cut into 2 \u00d7 2 cm2. The CFP has itself a large surface area; the effective surface area of CFP is roughly estimated to be 50 times as large as that of a flat sample. CNWs were grown on the CFP by ICP-CVD using a CH4= Ar gas mixture.30,31) A schematic illustration of the ICP-CVD system is shown in Fig. 1. A one-turn coil antenna was set on the quartz window at the top of chamber. An RF (13.56MHz) power of 500W was applied to the coil antenna to sustain the plasma generated in the chamber. A mixture of CH4 with a flow rate of 50 sccm and Ar with a flow rate of 20 sccm was introduced in the chamber, and the total gas pressure was maintained in the range from 15 to 20mTorr by manually controlling the conductance valve. Growth experiments were carried out for 90min typically. The temperature of the heater for sample heating was maintained at 720 \u00b0C during CNW growth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002889_j.triboint.2013.05.002-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002889_j.triboint.2013.05.002-Figure2-1.png",
        "caption": "Fig. 2. Bearing house with heaters.",
        "texts": [
            " For each oil tested, a new rolling bearing sample was used in order to reduce the influence of the surface finish and possible chemical interactions between oils tested. The surface finish of different new samples was measured and similar finishing was found on the rolling bearing ring (Table 3). The rotational speeds were chosen considering the available range of our machine and also the rotational speeds usually used in the wind turbines. For example, the low speed planetary shaft is about 1 m/s and the high speed shaft is about 6.5 m/s. The heater (Fig. 2) is used to increase and maintain a constant operating temperature at a desired value (80 1C for the study case). The thermocouple (III) is used to control the oil operating temperature, because the heater control system is a PID with feedback. All thrust ball bearing tests were performed applying an axial load of 7000 N or 700 N and rotational speeds in the range 75\u20131200 rpm. A detailed presentation of the test procedure can be found in [25]. The machine was started at the desirable speed and ran until it reached a constant operating temperature (80 1C), induced by the heaters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003250_s10846-015-0301-4-Figure26-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003250_s10846-015-0301-4-Figure26-1.png",
        "caption": "Fig. 26 A car mirror tilting mechanism [29]",
        "texts": [
            " This arrangement reduced rotational speed and allows higher torques to be transmitted to the tilting mechanism. The worm gear has a ball screw inside as shown in side view of Fig. 24b, which will rise and lower the platform as required. The height of the ball screw mechanism and the distance between points O, R and P determine the pitch and roll limits of the mechanism. Please see Figs. 25 and 26 for the 2 DC motor driven schematics of wing mirror actuator design. Figure 25 shows the proposed quadrotor with the tilting mechanisms are mounted. Figure 26 shows inner view of one of these tilting mechanisms. Each mechanism requires two micro DC motors for tilt and roll motions. In this project, the tilting mechanism of the proposed tilt-roll rotor quadrotor is based on Mirror Controls International (MCI) wing mirror actuators. These wing mirrors are used on some Ford vehicles. The 2D drawings of the actuator system and the specifications obtained from the datasheet of the wing mirror actuation system are given in Fig. 27 and Tables 2 and 3. As this actuator system will be driven to hold the quadrotor in desired positions according to the feedback control loop explained in the control section of this paper, the product specifications and limits should be understood well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure3-1.png",
        "caption": "Fig. 3 Generated surface of the shaper",
        "texts": [
            " Therefore, the transformation matrix from Ss to S2 is derived as follows: Mms \u00bc cos\u03d5s \u2212sin\u03d5s 0 sin\u03d5s cos\u03d5s 0 0 0 1 2 4 3 5 \u00f01\u00de Mpm \u00bc 1 0 0 0 0 \u22121 0 1 0 2 4 3 5 \u00f02\u00de Ms2 \u00bc cos\u03d52 sin\u03d52 0 \u2212sin\u03d52 cos\u03d52 0 0 0 1 2 4 3 5 \u00f03\u00de Where Mms represents the transformation matrix from Ss to Sm, and so on. Therefore, the transformation matrix from Ss to S2 is derived M2s \u00bc M2p\u22c5Mpm\u22c5Mms \u00bc cos\u03d52cos\u03d5s \u2212cos\u03d52sin\u03d5s \u2212sin\u03d52 \u2212sin\u03d52cos\u03d5s sin\u03d52sin\u03d5s \u2212cos\u03d52 sin\u03d5s cos\u03d5s 0 2 4 3 5 \u00f04\u00de Where, \u03d52 \u00bc i2s\u03d5s \u00f05\u00de The surface of the shaper is established in the coordinate system Ss, as shown in Fig. 3. The position vector rs * of the shaper surface is given as \u21c0rs us; \u03b8s\u00f0 \u00de \u00bc rbs sin \u03b8os\u00fe \u03b8s\u00f0 \u00de\u2212\u03b8scos \u03b8os\u00fe \u03b8s\u00f0 \u00de\u00bd \u2212rbs cos \u03b8os\u00fe \u03b8s\u00f0 \u00de \u00fe \u03b8ssin \u03b8os\u00fe \u03b8s\u00f0 \u00de\u00bd us 2 4 3 5 \u00f06\u00de Where rbs represents the base circle radius of the shaper, \u03b8S and uS represent, respectively, the angle parameter and the axial parameter in the shaper, and \u03b8OS represents the angle between the starting point of the involute and the symmetry line of the gullet which can be calculated as follows: \u03b8os \u00bc \u03c0 2Ns \u2212inv\u03b10 \u00f07\u00de Where Ns represents the number of teeth of the shaper, and \u03b10 represents the pressure angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure23-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure23-1.png",
        "caption": "Fig 23 Effect of oil hole position on predicted feed pressure flow (for NELl VEB data)",
        "texts": [
            " The comparison with the NEL results is good, suggesting that the feed pressure flow predictions may, at least for a circumferentially grooved bearing, be adequate for design purposes. A more commonly used oil feed arrangement for big end connecting rod bearings is through a drilling in the shaft. The actual position of the drilling is very important, as this affects the oil flow and the resultant film pressures. One can get a direct appreciation of this effect by simply superimposing on the journal orbit relative to the shaft (eg, from load diagram as Fig 1 (c)) the lines for constant values of feed pressure flow, using the Martin/Lee equations s , see Fig 23. By rotating the two 'maps' independently one can visually judge the best position of the crank drilling for maximum flow conditions. This analysis supplements the film extent map technique. Film extent maps for this same NEL/VEB study case are shown in Figs 24(a) and (b). In Fig 24(a) the oil hole position at TDC (0 = 0 \u00b0) on the journal is shown to be favourable since it hardly cuts across any high film pressure regions. In contrast to this a crank drilling at 180 \u00b0 to TDC position is extremely unfavourable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003435_0959651814566040-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003435_0959651814566040-Figure1-1.png",
        "caption": "Figure 1. Frame of quadrotor.",
        "texts": [
            " Meanwhile, the complex flight condition, high nonlinearities and strong coupled properties of UAV render the trajectory tracking control design much more challenging. In practical operations, vertical take-off and landing (VTOL) vehicle is a very promising vehicle for its stationary flight capability. The quadrotor unmanned vehicle presented here is a kind of VTOL vehicle with more properties. It consists of four rotors of \u2018\u2018X\u2019\u2019 arrangement, which is divided into two pairs, rotating in the opposite directions, as shown in Figure 1. Therefore, the quadrotor is an under-actuated vehicle which can maneuver in all 6 degrees of freedom with only four commands.1 Among different types of rotary-wing UAVs, quadrotor helicopters can usually afford larger payload than conventional helicopters due to four rotors. Moreover, small quadrotor helicopters possess a great maneuverability and are potentially simpler to manufacture. For these advantages, quadrotor helicopters have received much interest in UAV research.2 Fault-tolerant control system (FTCS) is a control system with the ability to tolerate faults automatically and continue its operation in the event of a failure in some of its components",
            " The multiple time-scale analysis is presented in section \u2018\u2018Time-scale analysis of multiple loops\u2019\u2019 to make the loops realizable. In section \u2018\u2018Simulation,\u2019\u2019 several simulation experiments under certain conditions (parameter uncertainties, highfrequency noise and abrupt actuator faults) are conducted to illustrate the effectiveness of the proposed strategy, and conclusions are given in section \u2018\u2018Conclusion.\u2019\u2019 at MICHIGAN STATE UNIV LIBRARIES on February 20, 2015pii.sagepub.comDownloaded from Model description and multi-loop control structure of a quadrotor The quadrotor dynamic model in Figure 1 is described below _P=V \u00f01\u00de _V= gez CdV Vj j+ T m Rez \u00f02\u00de J _O= O3 JO+ X4 1 1\u00f0 \u00deivijr h i O3 e3 + ta \u00f03\u00de jr _vi = ti kv2 i cvvi \u00f04\u00de Io = fex, ey, ezg is the inertial frame and Ao = fe1, e2, e3g is the frame attached to the vehicle, as shown in Figure 1. P= \u00bdx, y, z T denotes the position of the gravity center of a quadrotor. V= \u00bdu, v,w T represents its velocity in frame I and V= \u00bdp, q, r T denotes its angular velocity (pitch, roll and yaw) in frame A. The orientation of the vehicle depends on three Euler angles F= \u00bdf, u,c T, which represent pitch, roll and yaw angles, respectively. m is the mass of the quadrotor, J= diagfJx, Jy, Jzg is the inertia symmetric matrix, and g is the gravitational acceleration. The rotational velocity of rotor i is vi and its inertia symmetric matrix is jr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003640_j.cirp.2014.03.124-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003640_j.cirp.2014.03.124-Figure9-1.png",
        "caption": "Fig. 9. Load contact pressure after optimization (MPa).",
        "texts": [],
        "surrounding_texts": [
            "r to ved The der atic out ded del s in her ude\nJ. Astoul et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx\u2013xxx 3\nThe design data of the workpieces are given in Table 1. The pinion tooth flanks are grinded separately with the Simplex method. The gear tooth flanks are grinded simultaneously with the Duplex method. Table 2 gives the tool geometries and provides the machine settings with Klingelnberg format. The load cases are presented in Table 3. All of the following data are required to define the model. They are given with the necessary precision to model the right tooth flank topographies.\n3.3. Results and model validation\nThe recordings of the encoders are post-processed in orde identify the transmission error. The measurements are achie for three load cases. Figs. 5\u20137 show the results of the tests. measured transmission error is characterized by the first or undulations of the curve. The first order is the quasi-st component. In Fig. 5, the model runs like a gear meshing with contact and tooth distortions. Its curve corresponds to an unloa transmission error. The gap in amplitude shows that the mo stiffness is too high. The higher is the torque, the better it fit amplitude with the simulated transmission error. The hig orders of undulation may be due to dynamic effects, its amplit increases with the torque.\n4. Reduction of the transmission error\nRef. ial the ank\nto ent the\nLoad case Pinion torque (Nm) Pinion speed (tr min 1)\n1 65 154 2 130 154 3 260 154\nPlease cite this article in press as: Astoul J, et al. New methodology to - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cir\n4.1. Methodology\nThe method used to optimize the tooth flank is detailed in\n[18]. The variables are the six coefficients of the polynom function which defines the roll ratio between the cradle and workpiece. This enables accurate corrections of the tooth fl topography. Only the pinion is modified. The objective is minimize the contact pressure computed with the finite elem model previously exposed. The initial meshing conditions of\nreduce the transmission error of the spiral bevel gears. CIRP Annals p.2014.03.124",
            "gear QUA\n4.2.\nA pres esta pres 11 min the opti shar quas the\nJ. Astoul et al. / CIRP Annals - Manufacturing Technology xxx (2014) xxx\u2013xxx4\nPle - M\nhave to be free from critical edge contact. The software BOSS TTRO drives the optimization process.\nApplication case\nlink between the minimization of the maximal contact sure and the improvement of the load sharing has been blished [18]. Actually, there is also a link between the contact sure and relative curvature of the contacting surfaces. Figs. 8\u2013 show that a correlation can be established between the imization of the maximal contact pressure and the reduction of quasi-static transmission error, which is the basis of the mization strategy. Indeed, the improvement of the load ing increases the contact ratio and, therefore, reduces the i-static transmission error. Fig. 11 shows a 30% reduction in quasi-static transmission error.\n5. Conclusion\nThe meshing simulation is based on a finite element analysis using a solver commonly available in the industry. The models of the two parts are meshed with a very high accuracy. Their unloaded meshing positions are defined with the method presented in Ref. [4]. The spiral bevel gear optimization method is based on the links between the maximal contact pressure, the load sharing, the contact ratio and the quasi-static transmission error. The simulation results are consistent with the measurements. The simulated and measured transmission error curves fit quite reasonably. Nevertheless our optimization process still requires good initial conditions without critical edge contacts. These are today avoided by anticipating the edge contacts before the optimization process through a preliminary contact pattern check. This work shows promising results regarding noise optimization of spiral bevel gears.\nReferences\n[1] Coy JJ, Handschuh RF, Lewicki DG, Huff RG, Krejsa EA, Karchmer AM (1987) Identification and Proposed Control of Helicopter Transmission Noise at the Source. NASA/Army Rotorcraft Technology Conference, Moffett Field, Calif, 17\u201319 March. [2] Vogel O, Griewank A, Ba\u0308r G (2002) Direct Gear Tooth Contact Analysis for Hypoid Bevel Gears. Computer Methods in Applied Mechanics and Engineering 191:3965\u20133982. [3] Vimercati M (2007) Mathematical Model for Tooth Surfaces Representation of Face-Hobbed Hypoid Gears and its Application to Contact Analysis and Stress Calculation. Mechanism and Machine Theory 42:668\u2013690. [4] Astoul J, Sartor M, Geneix J, Mermoz E (2012) A Simple and Robust Method for Spiral Bevel Gear Generation and Tooth Contact Analysis. International Journal on Interactive Design and Manufacturing 7/1:37\u201349. [5] Gosselin C, Cloutier L, Nguyen QD (1995) A General Formulation for the Calculation of the Load Sharing and Transmission Error Under Load of Spiral Bevel and Hypoid Gears. Mechanism and Machine Theory 30:433\u2013450. [6] Litvin FL, Chen JS, Lu J, Handschuh RF (1996) Application of Finite Element Analysis for Determination of Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis. Journal of Mechanical Design 118:561\u2013567. [7] Kolivand M, Kahraman A (2009) A Load Distribution Model for Hypoid Gears Using Ease-Off Topography and Shell Theory. Mechanism and Machine Theory 44:1848\u20131865. [8] Litvin FL, Lee HT (1989) Generation and Tooth Contact Analysis of Spiral Bevel Gears with Predesigned Parabolic Functions of Transmission Errors. NASA CR \u2013 4259. [9] Litvin FL, Fuentes A, Mullins BR, Woods R (2002) Design and Stress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears. NASA CR \u2013 2002- 211344. [10] Litvin FL, Wang AG, Handschuh RF (1998) Computerized Generation and Simulation of Meshing and Contact of Spiral Bevel Gears with Improved Geometry. Computer Methods in Applied Mechanics and Engineering 158:35\u201364. [11] Wang PY, Fong ZH (2006) Fourth-order Kinematic Synthesis for Face-Milling Spiral Bevel Gears with Modified Radial Motion (MRM) Correction. Journal of Mechanical Design 128:457\u2013467. [12] Su J, Fang Z, Cai X (2013) Design and Analysis of Spiral Bevel Gears with Seventh-Order Function of Transmission Error. Chinese Journal of Aeronautics 26:1310\u20131316. [13] Argyris J, Fuentes A, Litvin FL (2002) Computerized Integrated Approach for Design and Stress Analysis of Spiral Bevel Gears. Computer Methods in Applied Mechanics and Engineering 191:1057\u20131095. [14] Simon V (2009) Design and Manufacture of Spiral Bevel Gears with Reduced Transmission Errors. Journal of Mechanical Design 131:041007-1\u2013041007-11. [15] Simon V (2013) Design of Face-Hobbed Spiral Bevel Gears with Reduced Maximum Tooth Contact Pressure and Transmission Errors. Chinese Journal of Aeronautics 26:777\u2013790. [16] Artoni A, Kolivand M, Kahraman A (2010) An Ease-Off Based Optimization of the Loaded Transmission Error of Hypoid Gears. Journal of Mechanical Design 132:011010-1\u2013011010-9. [17] Artoni A, Gabiccini M, Guiggiani M, Kahraman A (2011) Multi-Objective EaseOff Optimization of Hypoid Gears for Their Efficiency, Noise, and Durability\nase cite this article in press as: Astoul J, et al. New methodology to anufacturing Technology (2014), http://dx.doi.org/10.1016/j.cir\nPerformances. Journal of Mechanical Design 133:121007-1\u2013121007-9. [18] Mermoz E, Astoul J, Sartor M, Linares J-M, Bernard A (2013) A New Methodol-\nogy to Optimize Spiral Bevel Gear Topography. CIRP Annals \u2013 Manufacturing Technology 62/1:119\u2013122. [19] Icard Y (2005) Engrenage spiroconique: Mode\u0301lisation sous charge applique\u0301e au domaine ae\u0301ronautique., Institut National des Sciences Applique\u0301es de Lyon. PhD thesis in mechanical engineering.\nreduce the transmission error of the spiral bevel gears. CIRP Annals p.2014.03.124"
        ]
    },
    {
        "image_filename": "designv10_10_0003768_tia.2017.2694798-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003768_tia.2017.2694798-Figure10-1.png",
        "caption": "Fig. 10. Comparison of the measured torque waveforms at If = 1 A, I1 = 2 A. (a) Without torque ripple reduction. (b) With proposed method I. (c) With proposed method II.",
        "texts": [],
        "surrounding_texts": [
            "For the experimental validation, the proposed methods are applied to the prototype 6s/4r VFRM in dSPACE platform. Fig. 8(a) shows the VFRM control block diagram with external field current control configuration. The armature currents are controlled by a conventional three-phase inverter, and the field current is controlled by an external field current converter. For the three-phase armature current control, the PI controllers are used in synchronous dq-axis frame. For the PI controller parameter selections, the proportional gain KP is set to 2\u03c0fcL1 and the integral gain KI is set to 2\u03c0fcRs, in which fc is the current control loop bandwidth. The switching frequency is set to 10 kHz for the inverter and the converter. The PI controller bandwidths are selected to 3,141 rad/s. In case of the field current control, the modified field current contains the constant component and additional multiples of the third harmonic, which cannot be effectively controlled by PI controller. Hence, the PIR controller is applied in order to track the reference field current having alternating components as shown in Fig. 8(b) [20]. Each resonant controller operates in parallel configuration so that the dc, third, sixth, and ninth harmonic components are regulated, respectively. In every resonant controller, the resonant coefficients KR are set to 50, which affect the dynamic performance. The resonant frequencies of PIR controller are adjusted as the machine speed changes. 0093-9994 (c) 2016 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. Table III compares the measured average torque per field rms current (the rms value of total field current, including both dc and injected harmonic currents) ratio under different load conditions. It should be noted that the fundamental component of the armature current is set to 1.414If for the minimum copper loss operation [21]. By comparing the results with/without applying the proposed methods, it can be seen that the rms current is only slightly increased despite of the injected field harmonic currents. Additionally, similar average torque is produced under all the load conditions. Consequently, the average torque/field rms current ratio is maintained at a similar level. TABLE III. COMPARISON OF AVERAGE TORQUE/FIELD RMS CURRENT RATIO Field current (A) Average torque (Nm) Torque ripple (Nm) Field current (Arms) Tavg/Irms 1.0 w/o 0.18 0.15 1.00 0.18 w 0.06 1.01 0.18 1.5 w/o 0.41 0.21 1.50 0.27 w 0.09 1.52 0.27 2.0 w/o 0.68 0.39 2.00 0.34 w 0.19 2.02 0.34 2.5 w/o 0.91 0.75 2.50 0.36 w 0.42 2.53 0.36 0093-9994 (c) 2016 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. V. INFLUENCE OF MAGNETIC SATURATION AND MACHINE ROTATING SPEED A. Influence of magnetic saturation The magnetic saturation will be directly reflected on the inductance variation of VFRMs. For the proposed method I, it relies on FEA calculation. In this case, the saturation effect can be taken into account by calculating the field current waveforms for all the load conditions. However, since the proposed method II utilizes the machine inductance parameters calculated under unsaturated condition, the inductance variation will surely affect the torque ripple reduction performance. From (9), the harmonic field current with inductance variation can be presented as   * 1 1 1 2 1 ( ) ( ). 3f e ripple ei T P L L I       (10) where \u0394L1 is the error in the fundamental inductance component estimation. When the cores are saturated, the fundamental component will drop and \u0394L1 is negative. Since (L1+\u0394L1) is placed in the denominator, the underestimated fundamental component may cause high field current, consequently undesirable torque ripple. In order to evaluate the influence of saturation, the torque ripple reduction performance is analyzed when the nominal value of the fundamental component inductance varies from 20 % to 200 %. The torque ripple comparisons are conducted by 2D-FEA calculation and experiments by injecting the harmonic current considering the parameter variation. Fig. 12 shows the torque ripple performance under the parameter variation at (If = 1 A, I1 = 1.414A) and (If = 2.5 A, I1 = 3.535A). It can be found that the torque ripple reduction performance will not be influenced much unless the nominal inductance is below 50%. Meanwhile, by using frozen permeability method [22], the actual inductance is calculated. The variation of nominal inductance component against field current is shown in Fig. 13. It can be found that L1 will only drop down to 90% even under over-saturated situation. In this case, method II is expected to be effective even under saturated condition, albeit with degraded performance due to the error in inductance estimation. This is also confirmed by the measured variation of torque ripple for different load condition as shown in Fig. 14. B. Influence of machine rotating speed Fig. 15 shows the influence of the speed increase on the torque ripple reduction performance. Since the measurement of the torque ripple is inaccurate in high speed operation due to the limited bandwidth of the torque transducer, the dynamic simulation results are presented. The dynamic simulation in MATLAB/Simulink considers controller models, inverter model with pulse width modulation (PWM), and machine model based on the derived torque equation. The machine is controlled under current control at 2 A of if and I1. When the proposed method is not applied to the machine, the torque ripple is around 0.2 Nm. At 100 rpm, the torque ripple is around 0.05 Nm, and the torque ripple reduction performance is degraded as the machine speed increases. Although the PIR controller is implemented, the current controller performance will be limited due to the limited bandwidth."
        ]
    },
    {
        "image_filename": "designv10_10_0001851_978-1-4020-8600-7_24-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001851_978-1-4020-8600-7_24-Figure3-1.png",
        "caption": "Fig. 3 Reflection of Lam\u00e9 curve with respect to a line x2 = z2.",
        "texts": [
            " (2) can be expressed as lc = \u222b dl = \u222b \u221a dx 2 2 + dz 2 2 (5) in which dx2 and dz2 are the infinitesimal versions of the increments x2 and z2. Eqs. (4) are used to slightly rearrange Eq. (5), thus obtaining lc = \u222b \u03c0/2 0 \u221a x \u20322(\u03b8)2 + z\u20322(\u03b8)2d\u03b8 = \u222b \u03c0/2 0 1+ tan2 \u03b8 (1+ tan3 \u03b8)4/3 \u221a d2 tan4 \u03b8 + e2d\u03b8 (6) However, there is a problem when using Eq. (6) as it is expressed, since, when \u03b8 \u2192 \u03c0/2, tan \u03b8 \u2192 \u221e, which poses a numerical problem when computing the integral. To circumvent this problem, the integral computation is divided in two parts by using a reflection, with respect to a line x2 = z2, transforming the curve F into a curve F (see Figure 3). This affine transformation creates an intersection point P , for which \u03b8 = 45\u25e6 = \u03c0/4. Obviously, because of the reflection properties, the length of the curve segment between points P and C is identical to the length of the curve segment between points P and C . Therefore, the total Lam\u00e9 curve length lc can be computed as lc = \u222b \u03c0/4 0 1+ tan2 \u03b8 (1+ tan3 \u03b8)4/3 \u221a d2 tan4 \u03b8 + e2d\u03b8 (7) + \u222b \u03c0/4 0 1+ tan2 \u03b8 (1+ tan3 \u03b8)4/3 \u221a d 2 tan4 \u03b8 + e 2d\u03b8 where d = e and e = d . 228 Optimization of a Test Trajectory for SCARA Systems To generate a motion along a trajectory, two important steps are required [5]: (1) to define a geometry parameterized with respect to the displacement s along the trajectory; and (2) to define a velocity profile stating the relation of this displacement over time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-12-1.png",
        "caption": "FIGURE 11-12 (a) Free-body diagram of a tractor about to overturn laterally as a result of making a steady-state turn, (b) Plane containing the tipping motion of the tractor. (c) Top view of tractor.",
        "texts": [
            " For an oversteering vehicle, the speed at which the required steer angle or becomes zero is termed the critical speed, u(\" From equation 56, u~ - Lg/(W/ICar - W)C\",). By examining the eigenvalues of equations 52 and 53, it can also be shown that an oversteering vehicle is directionally unstable above the critical speed. Lateral Stability in a Steady-State Turn The geometric configuration of tricycle tractors, combined with their ability, aided by individual brakes on the drive wheels, to make sharp turns at mod erately high travel speeds, can result in a potential lateral overturning situ ation. Figure 11-12 illustrates a tricycle tractor in the steady-state circular turn analyzed in the previous section. 296 MECHANICS OF THE TRACTOR CHASSIS Assuming that the lateral tire forces are sufficient to generate the assumed acceleration, D'Alembert's principle may be applied by assuming the presence of a force mtu 21R acting at the center of gravity and in a direction opposite to the lateral acceleration of the center of gravity. The tractor may now be considered to be in static equilibrium. Assume that the forward speed U of the tractor is gradually increased as the center of gravity traverses the circle of radius R",
            " Assuming the tire force com ponents all act through the tipping axis, a summation of moments about that axis produces Thus u2 mt ~ cos \"/ Zeg - WtA 0 rgAR Us = 'J~ (57) where g is the acceleration of gravity. ,,/, the angle between the assumed force mtu21R and the tipping plane, is given by tan-l(yIIL). Equation 57 indicates Us is decreased as the radius of the turn or the moment arm A of the tractor weight is decreased or as the height Zeg of the center of gravity is increased. To use equation 57, a relation for A must be determined from the tractor geometry. Let the xyz coordinate system and associated unit vector system i,j, and k shown in figure 11-12 have its origin at the point on the ground surface directly beneath the center of the left rear wheel. Relative to this coordinate system, the tipping axis is defined by the unit vector l. 1 = (LlB)i + (yIIB)j (58) where Land Yl locate the point directly beneath the left front wheel center where the corresponding tire forces are assumed to act and B = VL 2 + y1. The plane containing the motion of the center of gravity as it rotates about the tipping axis intersects the tipping axis at point D. The vector from the origin of the xyz system to point D is denoted El"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002130_978-3-540-71364-7_22-Figure21.1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002130_978-3-540-71364-7_22-Figure21.1-1.png",
        "caption": "Fig. 21.1. Schematic exposition of the situation in MIS: The instrument is moved around an invariant fulcrum point. In consequence the surgeon can command only four degrees of freedom (\u03b1, \u03b2, \u03b3, l) inside the patient\u2019s body.",
        "texts": [
            "com c\u00a9 Springer-Verlag Berlin Heidelberg 2007 In this section the peculiarities of manual minimally invasive surgery (MIS) are described and advantages as well as disadvantages are discussed. Subsequently, a short introduction in minimally invasive robotic surgery (MIRS) is given which illustrates the research needs. Minimally invasive surgery is an operation technique which was established in the 1980s. In contrast to conventional, open surgery there is no direct access to the operating field and the surgeon employs long, slender instruments. These are inserted into the patient through narrow incisions which are typically slightly bigger than the instrument diameter (see Fig. 21.1). The main advantages of MIS, compared to open surgery, are reduced pain and trauma, shorter hospitalisation, shorter rehabilitation time and cosmetic advantages. However, MIS is faced with at least three major disadvantages [1]: (a) As the surgeon does not have direct access to the operating field the tissue cannot be palpated any more. (b) Because of the relatively high friction in the trocar1 and due to the torques which are necessary to rotate the instrument around the entry point, the contact forces between instrument and tissue can hardly be sensed. This is especially true when the trocar is placed in the intercostal space (between the ribs). (c) As the instruments have to be pivoted around an invariant fulcrum point (see Fig. 21.1), intuitive direct hand-eye coordination is lost. Furthermore, due to kinematic restrictions only four degrees of freedom (DoF) remain inside the body of the patient. Therefore, the surgeon cannot reach any point in the work space at arbitrary orientation. This is a main drawback of MIS, which makes complex tasks like knot tying very time consuming and requires intensive training [2, 3]. As a consequence MIS did not prevail as desired by patients as well as by surgeons and while most standard cholecystectomies (gall bladder removal) are performed minimally invasively in the industrialised world, MIS is hardly used in any other procedure to this extent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure8-1.png",
        "caption": "Fig. 8. Fluid velocity distribution around the surface of the press plate and position of the shelter board. (a) Fluid velocity distribution. (b) Position of the shelter board. (c) Size of the finger plate and shelter board.",
        "texts": [
            " 7, the z component of the fluid velocity is positive along the positive z direction, and vice versa. It can be seen from Fig. 7 that the highest fluid velocity component along the z-axis around the surface of the statorend winding is 28.7 m/s, which occurs near the center of the stator-end winding. The press plate can be used to axially clamp the stator core and reduce the magnetic flux leakage in the end region. It is of great significance to study the fluid velocity distribution around the surface of the press plate. Fig. 8 shows the distribution of the fluid velocity around the surface of the press plate and position of the shelter board. In Fig. 8, since the axial distance between the press plate and stator end core is large, the cooling fluid distribution is relatively uniform and the cooling fluid velocity is low around the C region of the press plate. Due to the blocking effect of the shelter board located between the press plate and stator end core in the outer diameter of the long finger plate, the axial distance (50 mm) between the press plate and the stator end core suddenly reduces to the axial distance (3 mm) between the press plate and stator end core, as shown in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002109_j.rcim.2009.10.002-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002109_j.rcim.2009.10.002-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of HPDM.",
        "texts": [
            " It provides a new way to directly manufacture parts made of difficult-to-machine materials with short process, low cost and high quality. A flowchart to interpret the HPDM process is shown in Fig. 1. The STL file of the 3D CAD model of a product is imported into the HPDM software system, then the processing path and NC instructions are automatically generated by the software. Based on the NC instructions, the combination of PDM and NC milling is realized by the hybrid machine [12]. The schematic diagram of the HPDM machine is shown in Fig. 2. The PDM subsystem includes five main parts: the plasma power generator, the powder supply unit, the system control equipment, the plasma torch and the cooling equipment. The plasma torch is fixed on HPDM machine and the working platform moves in X\u2013Y plane. As planned, molten metal powder is deposited on the substrate and solidifies quickly. After one layer of deposition, the working platform moves in Z direction ahead with a displacement of one layer thickness, and the surface of the progressively deposited layers are machined timely with the NC"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure14-1.png",
        "caption": "Fig. 14. Stock material distribution for the 40th valid geometry for the concave side (left) and convex side (right).",
        "texts": [
            " 12 shows the results of comparison of the rough-cut geometry and the objective geometry for the 20th valid geometry and Fig. 13 shows the corresponding results for the 40th and final valid geometry before the COBYLA algorithm returns after 500 iterations. In Figs. 11\u201313 , the rough-cut geometry is represented as solid body and the objective geometry as a wireframe model. Comparison of normal distances corresponding to the three reached roughcut geometry reveals, firstly, similar tendencies, and secondly, negligible differences among them. Fig. 14 shows the stock material distribution corresponding to the 40th valid geometry for both the concave and convex sides of the pinion tooth surfaces. In the end, Fig. 15 shows the geometry of the rough-cutting blades for the 5th geometry and 40th rough-cut geometry. As presented, those obtained geometries are valid due to the constraint represented by Eq. (38e) . 5. Conclusions Based on the performed research work, the following conclusions can be drawn: 1. The application of the COBYLA algorithm is very suitable to search for the machine-tool settings for the rough-cut oper- ation generated by the so-called Five-Cut method for spiral bevel gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003035_20120829-3-mx-2028.00056-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003035_20120829-3-mx-2028.00056-Figure1-1.png",
        "caption": "Fig. 1. Definition of the Qball-X4 attitude",
        "texts": [
            " The quadrotor UAV used in the paper is also known as Qball-X4. All the designs and experiments have been carried out in this physical Qball-X4 system. The groundwork of a controller designing process is always based on a mathematical model of the system to be controlled. In this paper, a dynamic model is needed because forces generated by four propellers are the main reasons that the quadrotor flies and these propellers need to be controlled in appropriate ways for different flight modes and flight conditions. Fig.1 shows more clearly on the relation between movements and forces. Positive direction of pitch, roll and yaw angles have been presented as marked in the figure. Qball-X4 is a rigid body, and two sets of reference frames have been used to formulate the system dynamic equations. One frame is the body-fixed frame in which the origin is located at the centre of the mass of the Qball-X4, as shown in Fig. 1. The other reference frame is the earth-fixed frame (or known as global frame) in which the origin can be chosen as desired. The coordinates , ,q q qx y z are defined in body-fixed 978-3-902823-09-0/12/$20.00 \u00a9 2012 IFAC 1317 10.3182/20120829-3-MX-2028.00056 frame, and , ,x y z are defined in earth-fixed frame. Qball-X4 can be considered as a local frame rotating and translating in the global coordination. Euler rotation and translation matrix has been introduced here to generate the general transformation",
            " Using the rotation matrix (1), forces in earth-fixed frame can be found as: x xq y yq z zq F F F F F F \u23a1 \u23a4\u23a1 \u23a4 \u23a2 \u23a5\u23a2 \u23a5 = \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5\u23a3 \u23a6 \u23a3 \u23a6 R (3) By Newton\u2019s second law of motion, ,F ma= and taking friction factor f into consideration, the acceleration of each axis in earth-fixed frame can be extracted as F fa m \u2212= , or c s c s s 1 1s s c s c c c x x x zq y y y z z z x F f f F y F f f m m m z F G f G f \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03c8 \u03b8 \u03c6 \u03c6 \u03c8 \u03b8 \u03c6 \u2212 +\u23a1 \u23a4 \u23a1 \u23a4 \u23a1 \u23a4 \u23a1 \u23a4 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5= \u2212 = \u2212 \u2212\u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5\u2212 \u2212 +\u23a3 \u23a6 \u23a3 \u23a6 \u23a3 \u23a6 \u23a3 \u23a6 (4) where m is the mass of the Qball-X4, and G mg= represents the gravity of the Qball-X4. The drag forces xf , yf , and zf are defined according to aerodynamics (Anderson, 2007) as, x xf d x= , y yf d y= , z zf d z= . Positions, velocities and accelerations are variables governing motion of the Qball-X4, which are caused by the change of the attitude of the QballX4 through pitch, roll, and yaw angles. Attitude is determined directly from the force generated by each propeller. For instance, from Fig. 1, if forces 1F and 2F change, the torque of y axis in body-fixed frame will be changed by the difference 1 2 ,F F\u2212 so as to the change of pitch angle \u03b8 . Similarly, roll angle \u03c6 will be changed by the difference 3 4F F\u2212 , and yaw angle \u03c8 will be changed by 1 2 3 4F F F F+ \u2212 \u2212 . A translational momentum M of the Qball-X4 rigid body can be written as (Stevens and Lewis, 2003): = = + \u00d7 = + \u00d7qM H H H Hq q q q\u03c9 J \u03c9 \u03c9 (5) and in terms of qM in a body-fixed frame, one has: ( ) [ ( )]= \u2212 \u00d7 = \u2212 \u00d7q q qM H Mq q q q q q q\u03c9 J \u03c9 J \u03c9 J \u03c9-1 -1 (6) whereH is the matrix of the angular momentums in earthfixed frame, qH is the matrix of the same momentums in body-fixed frame, q\u03c9 contains all the angular velocities of body-fixed frame, and qJ is the inertia matrix about axes , ,q q qx y z of the body-fixed frame: xx xy xz xy yy yz xz yz zz J J J J J J J J J \u23a1 \u23a4\u2212 \u2212 \u23a2 \u23a5= \u2212 \u2212\u23a2 \u23a5 \u23a2 \u23a5\u2212 \u2212\u23a3 \u23a6 qJ (7) From the principle of axes theory and Eq",
            " The experimental tests have also been carried out in the Qball-X4 quadrotor helicopter testbed available at the Networked Autonomous Vehicles (NAV) Lab of Concordia University. The testbed includes six cameras as the in-door GPS system for providing position of the Qball-X4 during flight in real-time, a joystick as the safety control, and a desktop computer as the ground station. The reason for the name of Qball-X4 is because of the ball-shape protection cage surrounding the quadrotor to protect the four propellers. Four propellers are lined up orthogonally as shown in Fig. 1. The black-box at the centre has all the control hardware devices that send control signals to control the attitude and motion of the Qball-X4 during flight, to generate different pulses to each rotor for pitch, roll, and yaw commands with the control algorithm implemented in software format in the on-board Gumstix single-chip micro-computer (control device). For the UAV system, not only are the inertial sensors on HiQ board which is located inside the black-box, but also vision sensors are in use"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002676_1.4006791-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002676_1.4006791-Figure2-1.png",
        "caption": "Fig. 2 The geometrical quantities of the double full-toroidal vairator (DFTV in (a)) and of the half-toroidal variator (SHTV in (b))",
        "texts": [
            " This in principle should allow to get much better efficiency. We observe that the toroidal variators can be provided with a number m of cavities and n rollers (or pair of rollers in the case of the DFTV). 2.1 Geometric Description. The geometry of the toroidal drive is characterized by the radii of curvature of the rollers and of the cavity: the first principal radius of curvature of the input and output disks is the cavity radius r0, whereas the second principal radii of curvature are r11 and r33 for the input and output disks, respectively (see Fig. 2), and r2 is the rolling radius of the rollers. The ratio between the second principal radius of the rolled r22 and the cavity radius r0 is referred to as the conformity ratio CR\u00bc r22/r0, which in the case of full-toroidal traction drives varies between 0.3 and 0.5, larger values would lead to a strong decrease of the transmission efficiency [22,23] because of increased values of spin losses. The aspect ratio k\u00bc e/r0 is defined as the ratio between the eccentricity e (see Fig. 2) and the radius of the toroidal cavity r0. Shifting is obtained by tilting the power roller of an angle c about the tilting point O. The radial coordinates r1 and r3 of the roller disks contact points change and so does the geometric ratio srID defined as srID \u00bc r1 r3 (1) The radii of curvature of the disks at the roller\u2013disks contacts can be expressed in a dimensionless form as a function of the cone angle h and the tilting angle c (see Fig. 2) as ~r11 \u00bc ~r1 cos\u00f0h\u00fe c\u00de (2) ~r33 \u00bc ~r3 cos\u00f0h c\u00de (3) where, the dimensionless wrapping radii ~r1 and ~r3 of the input and output disks are simply written as ~r1 \u00bc r1 r0 \u00bc 1\u00fe k cos\u00f0h\u00fe c\u00de (4) ~r3 \u00bc r3 r0 \u00bc 1\u00fe k cos\u00f0h c\u00de (5) The expression of the roller rolling radius r2 is r2\u00bc r0 sin h in the case of the single-roller variator, whereas, using the condition of zero spin at unit speed ratio the rolling radius for the DFTV is r2\u00bc (r0\u00fe e)sin(a/2). 2.2 Kinematic Quantities. Figure 3 shows the angular velocities triangles for the DFTV (see Fig",
            " 134, JULY 2012 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use coordinate of the disk\u2013roller contact point. In Ref. [7], the equilibrium equation for the case of SHTV and SFTV has been already derived, here we focus only on the DFTV. By referring to Fig. 6, the torque balance equation gives FTin r2 FTC rC \u00feMSin cos hDT TBa \u00bc 0 (18) FTC rC FTout r2 \u00feMSout cos hDT TBb \u00bc 0 (19) where the angle hDT\u00bc (p a)/2 (see Fig. 2(a)). In Eqs. (18) and (19), FTC represents the resultant vector of the tangential forces at the roller\u2013roller interface, while the term TB includes the torque losses due to roller bearings (TBR) and to the thrust axial bearing (TBL), namely TB\u00bc TBL\u00fe TBR. According to Refs. [7] and [11], we have expressed the axial bearing loss TBL as TBL \u00bc 4:6 10 5F1:03 R (20) with FR\u00bc 2FN cos h. We have also taken into account the loss torque due to the internal friction of needle bearings, which are assembled on the shaft of each roller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002925_j.triboint.2013.06.008-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002925_j.triboint.2013.06.008-Figure1-1.png",
        "caption": "Fig. 1. Plane sketch of a bearing inner ring.",
        "texts": [
            " Second, several parameters, such as radial load, moment and RGCR, are varied to study SIFs, crack growth rates and crack initiation angles. The results are helpful for better understanding the effect of material defects on RCF of bearings. In this paper, the inner ring of a 6208 (bearing designation, SKF) deep groove ball bearing is considered as the RCF research object. The basic geometric data are shown in Table 1. A plane sketch of the geometric model used for the RCF analysis is presented in Fig. 1. The material defect is modeled as a quadrate pore located at a depth (0.5 mm) below the raceway surface and its size is assumed to be 0.5 mm. The symbol \u03b8 indicates the rotation angle of the inner ring. The rotation angle is defined to be negative when the contact position is to the left of the pore. The moment M is exerted on the inner ring in the anticlockwise direction. The numerical model was developed as shown in Fig. 2. The material used in this study was AISI 52100 steel, and the main parameters are: Young's modulus E\u00bc2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003792_icuas.2017.7991321-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003792_icuas.2017.7991321-Figure1-1.png",
        "caption": "Fig. 1. Top view for a standard hexacopter motor distribution.",
        "texts": [
            " In [2], the study of fault tolerant controls has been carried out for multi-rotor vehicles with different number of rotors. The minimum number of rotors needed to achieve a fault tolerant control for multi-rotor MAVs, is an issue that has been discussed in [3], [4], [5], [6], among others. In [5], a study on the trade off between number of rotors, maneuverability, efficiency and redundancy is carried out. As it is shown in these works, in the case of failure on a rotor, an hexagon shaped hexarotor without its motors tilted (see Fig. 1), will see its performance degraded, due to the fact that the attitude controller will be unable to reject disturbance torques in certain directions. This means that this kind of vehicle is not fault tolerant. There are some known solutions to the full controllability problem for fault tolerant multirotors. The octocopter solution [7] requires more actuators, increasing the mechanical redundancy; other mechanical designs make use of servomotors in order to change the position and orientation of the motors [8]; bidirectional rotating motors are proposed as well [5], with the disadvantage of generating thrust in the opposite direction",
            " Most frequently, multirotor helicopters such as the classical quadrotor, the hexagon shaped hexarotor, or the octagon shaped octocopter, have the spinning direction of their motors set in an alternated fashion. Namely the adjacent motors have reverse spinning direction with respect to one another. A \u201cde facto\u201d notation is usually employed to describe this, where \u201cP\u201d denotes clockwise spinning direction of a motor and \u201cN\u201d denotes a counterclockwise one. With this notation in hand, the hexagon shaped hexacopter studied within this article, will have a NPNPNP setup for the spinning direction of its rotors, from number 1 to number 6 (see Fig.1). Another spinning direction setup for hexacopters proposed in the literature, is to reconfigure the spinning direction of the motors, for instance a PPNNPN configuration. This allows to maintain full controllability for total rotor failures, but only in the first four actuators of the PPNNPN setup ([3], [9], [10], [11]). In this work we assume that failures are identically likely to appear in any motor, then this configuration can not be considered fault tolerant. To overcome the lack of fault tolerance of the standard hexagon shaped hexarotor, in [6], instead of the standard design with rotors pointing in the vertical direction, an alternative is proposed, which turns out to be completely controllable even in case of failure in one rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001161_la0503449-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001161_la0503449-Figure1-1.png",
        "caption": "Figure 1. (a) Sample features, (b) experimental setup for preparation of preordered stripe pattern of wrinkles, and (c) experimental setup for mechanical perturbation (lateral compressive loading and unloading). The small vise is used for compression.",
        "texts": [
            " Finally, we describe the dynamics of domain growth and shrinkage due to strain changes, namely the shapes of domains and their changes. We discuss them in terms of the characteristic geometry of the domain shapes and the configuration of the topological defects, both of which are related to the misfit angle and stripe wavelength. 2.1. Preparation of a Preordered Wrinkle Pattern. A 5-mm-thick elastomeric poly(dimethylsiloxane) (PDMS) of a right circular cylinder with a diameter of 8 mm are prepared (Dow Corning Sylgard Elastomer 184) (Figure 1a). To obtain the preordered microwrinkle pattern, the surface is modified through Pt deposition by applying a uniaxial compressive strain (7%) (Figure 1b). The deposition of Pt with a thickness of approximately 8 nm is conducted over a flat surface with a circular shape. An ion sputter (E-1030, Hitachi) is used for the deposition with a current of 5 mA, a pressure of 10 Pa, a distance of 30 mm between samples and the Pt target, and a deposition time of 180 s. During the deposition under uniaxial compression, the PDMS surface is assumed to be modified to have a silica-like rigid nature16-19 due to the collision energy of active species. Uniaxial compression anisotropically deforms the PDMS surface, where expansion in the perpendicular direction also spontaneously takes place",
            "20,30 Thus, an irreversible process, such as material flow or plastic deformation, possibly occurs during pattern formation. This suggests that the pattern is stable or fixed, i.e., the waves of wrinkles do not travel, under ambient conditions without any mechanical perturbation. Although the stripe pattern might be modulated by applying compressive strain, the original ordered stripe is expected to recover after unloading, which is described later. 2.2. Loading and Unloading. Our experimental setup for the mechanical perturbation is similar to that used previously (Figure1b).20 Uniaxial compressivestrain isexertedandunloaded stepwise to the PDMS cylinder with the preordered pattern in a direction with the misfit angle \u03c6, using a small vise under the optical microscope at 293 K. The rate of changing strain is (1%/ min. The step size is (1%, thus it takes one minute for changing strain for a step. The system is equilibrated for 5 min after every strain change. The images are acquired after equilibrations. The observations are conducted in the same area near the center of the sample surface during a loading-unloading cycle to avoid edge effects which caused anomalous stripes16 and a nonuniform stress distribution",
            " Phys. Rev. Lett. 1998, 80, 3228. (32) Bazen, A. M.; Gerez, S. H. IEEE Trans. Pattern Anal. Mach. Intell. 2002, 24, 905. y). The local orientation of the wave \u03b8(x, y) is defined through the relation exp[i\u03b8(x, y)] ) k(x, y)/|k(x, y)|, where k ) kx + iky. In a real field, the wave vector (kx, ky) is equivalent to (-kx, -ky), so their signs are chosen to hold a condition, kx g 0, resulting in wave orientation values ranging from -90 to +90\u00b0. Note that the strain direction, i.e., the x direction (see Figure 1c), corresponds to the orientation expressed by \u03b8 ) 0. The histograms of the area corresponding to the various stripe orientations at each degree of strain during a loading-unloading cycle are analyzed. To investigate how the original stripe orientation changes, an image showing spatial domain distribution is created for each microscopy image. This is conducted by extracting the points that show \u03b8 within the range of -\u03c6 ( 10\u00b0, whitening them in the image, and blackening the rest. That is, the surface with pattern is decomposed in domains containing stripes with two different orientations, namely the orientation of the original stripes and an orientation that is more parallel to the applied strain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001947_j.ijmecsci.2007.08.002-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001947_j.ijmecsci.2007.08.002-Figure8-1.png",
        "caption": "Fig. 8. (a) Geometry of the housing elastic face and coordinate system and (b) localization of a planes containing points for evaluation the sound pressure.",
        "texts": [
            " For the computation of the noise radiated by the elastic face of the gearbox, the classical Helmholtz integral will be used to develop the RI method combined with structural FE model. Assume a rectangular thin-plate radiator in flexural vibration is mounted on a flat rigid baffle of infinite extent. The acoustic pressure radiated can be obtained by evaluating the Rayleigh surface integral where each elemental area on the plate surface is regarded as a simple point source of an outgoing wave and its contribution is added with an appropriate time delay [15]. Referring to Fig. 8(a), the acoustic pressure P(M,t) at the observation point M with Cartesian coordinates (x0,y0,z0) at time t ARTICLE IN PRESS M. Slim Abbes et al. / International Journal of Mechanical Sciences 50 (2008) 569\u2013577574 caused by the vibration of the plate is given by P\u00f0x0; y0; z0; t\u00de \u00bc r0 2p Z a 0 Z b 0 \u20acw\u00f0x; y; t R c \u00de 1 R dxdy, (22) where r0 and c are, respectively, the mass density and wave velocity of the acoustic field, \u20acw\u00f0x; y; t\u00de is the acceleration time history of the plate obtained previously, and R is the distance between the observation point M and the infinitesimal element at (x,y) on the plate surface",
            " Ri;j \u00bcffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x0 iDx\u00de2 \u00fe \u00f0y0 j Dy\u00de2 \u00fe z20 q is the distance between the observation point (M) and the grid point of coordinates iDx, jDy on the plate. It is well known that a car gearbox is situated in a confined environment. Therefore, the acoustic field under interest for the study has been chosen sufficiently near the gearbox housing. It is assumed that the elastic face was inserted in a rigid baffle and radiates in a half-space full of air (V2f ). By applying Eq. (22), the pressure is calculated at a large number of spatial points. Fig. 8(b) shows the gearbox system and an example of perpendicular planes containing points where the pressure is evaluated. The plane (p1) is parallel to the housing elastic face, whereas (p2) is perpendicular. The proprieties of the Fig. 9. Three-dimensional acoustic pressure distribution on the planes (p1) and (a) fe \u00bc 594.3Hz and (b) fe \u00bc 614.4Hz. acoustic field are density r0 \u00bc 1.2 kg/m3 and sound speed c \u00bc 340m/s. It has been chosen to study the acoustic radiation of the gearbox housing, in free field, for two of its structural eigenmodes 594"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-13-1.png",
        "caption": "FIGURE 13-13 Involute tooth profile. (From Browning 1978.)",
        "texts": [
            " Spur gears have teeth that are parallel to the axis of rotation of the gear, whereas the teeth of helical gears are at an angle to the axis of rotation. Spur gears are somewhat less expen sive to manufacture than helical gears and often can be supported in the transmission much more simply and inexpensively because there is no axial thrust force as there is with helical gears. However, helical gears gradually transfer the tooth loads from one tooth to the next and generally generate much less noise. An involute tooth profile is used. This profile is the form that is generated by a point on a string as the string unwraps about a cylinder (fig. 13-13). It is the preferred profile because constant rotational velocity is transmitted. Even though a perfect involute profile will transmit constant rotational ve locity, the machining and heat-treating processes will leave some profile errors that will result in impact stresses and noise. Figures 13-14 and 13-15 show some of the terminology used to describe involute gears. The kinematic details of gears are presented more completely by Mabie and Ocvirk (1975). Bevel Gears Bevel gears are used to connect shafts with intersecting axes (fig",
            " The relationship between the gear module, gear pitch diameter, and number of teeth is where m D N m = DIN tooth size, module nominal pitch diameter number of teeth (9) For helical gears, m is the module in the transverse plane and is related to the normal or cutter module mn by m = mnlcos IjJ (10) where IjJ = the helix angle The general range of tooth modules for various gears in the drive train is as follows: 1. Transmission gears-4 to 5 2. Power shift planetary gears-2.5 to 3.5 GEAR DESIGN 381 3. Spiral bevel gears-8 to 12 4. Final drive gears-5 to 7 Usually cutters of nominal size and pressure angle are used, but often center distances and tooth numbers are chosen so that the nominal pitch diameters will not touch, as shown in figure 13-13. This only means that the operating or working pitch diameter is different from the nominal pitch diameter shown in equation 9. There is a corresponding working pressure angle, which is given by where <1>\", m N1,N2 CD <1>1 <1>\" _ [ m (N1 + N2) cos <1>1 <1>\" = cos 2 CD (11) the working pressure angle the gear module in the transverse plane from equation 10 the number of teeth in gear 1 and gear 2 shaft center distance the transverse pressure angle = tan -[ (tan <l>n1cos tV) the nominal or cutter pressure angle Gear geometry and stress calculations are too complex to be done man ually now that computers are readily available"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001821_emed_jour_1980_009_022_02-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001821_emed_jour_1980_009_022_02-Figure1-1.png",
        "caption": "Fig. 1 A diagram ofpart of a leg, with the foot on the ground. Further explanation is given in the text",
        "texts": [
            " The maximum stresses which occur in jointsare probably of the same order of magnitude in mammals of all sizes and also in insects of all sizes, but the stresses in insects are probably larger than the stresses in mammals and other vertebrates. This paper reviews the forces which act in strenuous activities, in the major joints of animals. Only vertebrates and arthropods are considered though some other animals such as bivalve molluscs and echinoderms also have skeletons with joints. The forces have been estimated by simple calculations, often from data which may not be very accurate. The resulting errors are not serious as the differences between animals which will be demonstrated are extremely large. Figure 1 illustrates the method of calculation which has been used. It represents a free body diagram of those parts of a leg which are distal to the joint being considered. The ground exerts a force G on the foot. The required joint force is J, and muscles acting across the joint exert a force M. The antagonists of these muscles might simultaneously exert a force M' but it will be assumed unless there is evidence to the contrary that antagonistic muscles are not active simultaneously. The forces W and f are the weight of the limb segment and the inertia force on it, and T is the inertial torque",
            " The mass and moment of inertia of the limb segment can be determined from a dead specimen, and the linear and angular accelerations of the segment can be obtained by kinematic analysis of the film. Hence W, I and T can be evaluated if necessary. However it can often be shown by simple arguments that they are small enough to ignore. The direction of M and the points of application of M andJ are known from anatomy. Hence M and J can be calculated by considering the equilibrium of the segment. In some of the cases which will be considered they are so large compared to the other forces that they are approximately equal in magnitude. Figure 1 represents a simple situation in which all the muscles which are likely to be active are collinear. When knees are considered, account has to be taken of three groups of muscles, the gastrocnemius and plantaris, the quadriceps and the hamstrings. The forces in the gastrocnemius and plantaris have been estimated by considering moments about the ankle and the force in the hamstrings has been estimated by considering moments about the hip as explained for dogs by Alexander (1 974). Some joints in the legs of spiders are operated hydraulically by blood pressure, and so do not resemble Fig. 1 (Parry and Brown, 1959). This paper considers only more typical joints, which are operated directly by muscles. Data The data have been collected from various sources which are cited in Table 1. Bibliographic references will not be given unnecessarily in the text if they appear in this table. The data will be reviewed in approximate order of increasing size of animals, starting with insects. Only a few species of insect jump but several of them have been studied closely. The examples in Table 1 are fleas, flea beetles and click beetles which jumped to heights of 35 mm, 200 mm and 260 mm, respectively, and a locust which jumped distances of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000856_s0956-5663(97)00138-3-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000856_s0956-5663(97)00138-3-Figure8-1.png",
        "caption": "Fig. 8. Schematic depiction of biosensor.",
        "texts": [
            " To test for the potential utility of these electrocatalysts in biosensors, we employed GC electrodes modified with films of either 3,4-DHB or with the iron complex in the construction of biosensors based on A1DH or ADH immobilized on a nylon mesh (see experimental section). In this approach enzyme immobilization takes place preferentially on the fibers of the mesh, without occlusion of the pores. Under these conditions transport of substrate and products is not impeded, making this immobilization procedure superior to direct protein immobilization on the electrode surface. Moreover in this assembly the enzyme is physically separated, thus allowing for its reuse with other electrodes. The working principle of the biosensor (see Fig. 8) involves oxidation of the substrate (aldehyde or ethanol) by the immobilized enzyme in the presence of NAD +. This cofactor acts as an acceptor of electrons generated in the enzymatic reaction and is transformed to its reduced form NADH which, in turn, diffuses to the electrode, where it is catalytically reoxidized back to NAD* by the layer of 3,4 DHB or the Fe-complex. The modified electrode serves as a secondary acceptor of electrons able to regenerate the cofactor (NAD +) used in the enzymatic reaction, so that the magnitude of this catalytic current can be employed as the analytical signal in the determination of the substrate (aldehyde or ethanol) concentration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002121_007-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002121_007-Figure5-1.png",
        "caption": "Figure 5. The forces on a soccer ball. The gravitational force points down; the drag force is opposite to the ball\u2019s velocity; the lift force is perpendicular to the ball\u2019s velocity (shown here for a ball with backspin) and in the plane formed by the velocity and the ball\u2019s weight. A sideways force is possible if the spin axis is not perpendicular to the plane of this page.",
        "texts": [
            " 4 Our in-house software was developed by Richard Dignall and Simon Goodwill at the University of Sheffield. There are other commercially available software packages that allow one to analyse trajectories from movies. A good one sold primarily in the USA is VideoPoint. (This figure is in colour only in the electronic version) Once we have analysed a given camera 1 movie, we have a set of Cartesian coordinates for the first 0.07 s of the ball\u2019s trajectory. We then need to match those experimental data to a numerical solution of Newton\u2019s second law. Figure 5 shows a free-body diagram of the soccer ball in flight with the gravitational, drag and lift forces acting on the ball. Using the free-body diagram, we set up Newton\u2019s second law as m a = Fg + FD + FL, (5) where a is the Teamgeist ball\u2019s linear acceleration. Equation (5) is a second-order nonlinear differential equation. The speed dependence of the drag and lift forces means that the components of equation (5) are coupled. Such an equation can only be solved with the help of a computer. We fit a computational solution of equation (5) to the camera 1 data with a lift coefficient chosen to minimize the least-squares deviation between the data and the computational fit",
            " We feel this procedure helps eliminate errors we introduced while trying to determine the location of the ball\u2019s centre of mass in each frame of the camera 1 movie. As for the physics content in figure 7, we see that as the spin parameter increases, the lift coefficient appears to level off (we certainly cannot apply that conclusion for Sp > 1, where we have no data). We noted that trend with our work on 32-panel balls (see figure 6). To understand why CL does not increase at the same rate for 0.5 < Sp < 1 as it does for 0 < Sp < 0.5, we look on the opposite sides of the ball and examine the speed of the air relative to the ball\u2019s surface. The sketch in figure 5 shows a ball with backspin because the lift force has a vertical component. If the ball is spinning with an angular speed \u03c9 and moving with the centre-of-mass speed v, the relative air speed near the top of the ball (where the FL vector emerges from the ball in figure 5) is roughly v \u2212 r\u03c9, were r is the ball\u2019s radius. On the opposite side of the ball, the relative air speed is roughly v + r\u03c9. We use the word \u2018roughly\u2019 because in the ball\u2019s reference frame, the speed of the air rises from zero at the ball\u2019s surface to nearly the free-stream speed just outside the boundary layer. But, using v \u00b1 r\u03c9 gives us an idea of what might make CL level off for 0.5 < Sp < 1. We can validate this idea with our camera 1 movies. For Sp 1, meaning v \u2212 r\u03c9 0, the ball in the camera 1 movie appears to roll without slipping on an invisible inclined plane",
            " Now, as the spin rate increases for a given centre-of-mass speed, v \u2212 r\u03c9 decreases, meaning it may decrease below the critical speed, vc. If the ball spins fast enough, the v \u2212 r\u03c9 side of the ball will experience a laminar boundary layer separation, while the v + r\u03c9 side has a turbulent boundary layer separation. Because laminar separation does not occur as far back on the ball as turbulent separation [19], the v \u2212 r\u03c9 side of the ball does not whip the air around as much as it would if the separation were turbulent. If top of the ball in figure 5 has laminar flow because v \u2212 r\u03c9 < vc, air will not be whipped downwards as much as if the top of the ball had turbulent separation. That makes for smaller lift in the former case compared to the latter. To better understand this idea, consider the side of the ball with a relative air speed given by v \u2212 r\u03c9. If v \u2212 r\u03c9 < vc, we may expect laminar separation on that side of the ball. Because Sp = r\u03c9/v, we write the aforementioned condition as Re < Rec 1 \u2212 Sp , (6) where speeds have been changed to Reynolds numbers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002026_tmag.2009.2012785-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002026_tmag.2009.2012785-Figure4-1.png",
        "caption": "Fig. 4. Distributions of flux density vectors in SCIM with 4/3 slot pitch skewed rotor. (a) lower section and (b) upper section.",
        "texts": [
            " 1(b)]: (2) In the same way, the potential in the air gap region is calculated under conditions that the potential obtained by step (iii) is given to nodes in the rotor region and the potential zero is given to nodes in the stator region. iv) The coordinates of nodes in the rotor region [see Fig. 1(c)] and the air gap region is skewed according to the each potential . 0018-9464/$25.00 \u00a9 2009 IEEE Here, the distribution of flux density vectors and the losses of the SCIM with the 4/3 slot pitch skewed rotor and that with rotor without skew are calculated. The calculated losses are compared with measured ones to clarify the validity of the 3-D analysis. Further more, the bar-current and the torque are calculated. Fig. 4 shows the distributions of flux density vectors of SCIM with the 4/3 slot pitch skewed rotor. The flux density vectors of the upper section are larger than those of the lower section. The imbalance of the magnetic flux distributions makes the loss distributions imbalanced in the SCIM with skewed rotor. Fig. 5 shows the contours of eddy current loss. The eddy current loss in the tip of teeth and the surface of the rotor is especially large. From Fig. 5(b), the eddy current loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure8-7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure8-7-1.png",
        "caption": "FIGURE 8-7 Operational temperatures of typical tractor engine in reasonably hard service, but not overloaded, at 75 percent of rated drawbar power and at an average speed of 4.8 km/h. (Courtesy Standard Oil Co. of Indiana.)",
        "texts": [
            " 3, Texaco, Inc., 1966.) 189 CLASSIFICATION OF OIL BY VISCOSITY 191 perature. An oil with a high viscosity index (VI) has less change in viscosity with a change in temperature than an oil with a low VI. Refineries have no problem producing oil of the correct viscosity for a constant operating tem perature, but the necessity of starting an engine at a low temperature and running it at a higher temperature complicates the problem. The variation of temperature within the engine also adds to the problem (fig. 8-7). There fore, an oil with a high viscosity index is desirable. When the system of calculating the viscosity index was first developed, it was based upon a crude oil \"L\" (naphthenic), which was assigned an index of 0, and a crude oil \"H\" (paraffinic), which was assigned an index of 1 00. It was assumed that the \"L\" oil possessed the absolute maximum limit of viscosity temperature sensitivity and that the \"H\" oil was the least sensitive. Although the system is still in use, the upper and lower limits of 100 and o no longer contain all of the oils"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003763_s10846-017-0545-2-Figure19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003763_s10846-017-0545-2-Figure19-1.png",
        "caption": "Fig. 19 Laboratory testbed - the UAV mounted on a gimbal and constrained to 2DOF (roll and pitch angle). Four stepper motors are used to move masses. Showing also a DLE111, an internal combustion engine which will be used to power the propulsion system",
        "texts": [
            " For that gain, the vehicle remains airborne, but exhibits high frequency oscillations due to the saturation limits on mass positions (see Fig. 18). The theoretical critical gain, determined from root locus in Fig. 14b, equals 8.2, which suggests a satisfactory agreement between a linearized model used for root locus analysis and the nonlinear Gazebo model. The video showing simulation experiments can be found in [25]. For the experimental testbed we use a full scale vehicle mounted on a gimbal (Fig. 19) whose motion is constrained to 2DOF (roll and pitch angle). To satisfy conditions (45) for gimbal dynamics, we have mounted the axes of rotation as close as possible to the vehicle CoG. While in [15] we used a small scale gimbal with Dynamixel motors as a mass servo system, the full scale vehicle uses MIS231 stepper motors with a rack and pinion mechanism transforming rotational to linear motion. A Pixhawk flight controller is attached to the vehicle main body and we utilize its IMU to measure attitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002791_0954406211404853-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002791_0954406211404853-Figure1-1.png",
        "caption": "Fig. 1 An example of feature mapping enabling linear data separation (adapted from [10])",
        "texts": [
            " A separating plane (SP) in the input space can be expressed as follows, if the training data are linearly separable f \u00f0x\u00de \u00bc wTx \u00fe b \u00bc 0 \u00f01\u00de where w2R n is a weight vector, b is a scalar, and T means the transpose operator. The parameters of w and b which define the location of SP are determined during the training process. When the training data are non-linearly separable, equation (1) is no longer applicable. In SVM theory, one can introduce a mapping function, ( ), which projects the original feature space onto a highdimension feature space in which the training data can be linearly separated again. Figure 1 shows an example of such mapping. The SP for non-linearly separable data can still be expressed in a linear form but only with the addition of the mapping, ( ) f \u00f0x\u00de \u00bc wT \u00f0x\u00de \u00fe b \u00bc 0 \u00f02\u00de A distinct SP should satisfy the following constraints yif \u00f0x i\u00de \u00bc yi\u00f0w T \u00f0xi\u00de \u00fe b\u00de 1, i \u00bc 1, 2, . . . , M \u00f03\u00de where an underlying constraint applied is that the predicted f(x) value of data point x should have the same sign as its virtual class label. Figure 2 is an example of a linearly separable classification problem in a two-dimensional feature Proc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001636_s0263574704000347-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001636_s0263574704000347-Figure8-1.png",
        "caption": "Fig. 8. Orthoglide workspace.",
        "texts": [
            " Hence, the decision equation may be derived by analysing the dot-product of the plane normal vector (\u03c1\u22121 x , \u03c1\u22121 y , \u03c1\u22121 z ) and the vector directed along any of the bar links (for instance, (px \u2212 \u03c1x, py, pz) for the first link): m = sgn ( px \u03c1x + py \u03c1y + pz \u03c1z \u2212 1 ) (19) which for the positive joint limits is equivalent to m = sgn(px\u03c1y\u03c1z + \u03c1xpy\u03c1z + \u03c1x\u03c1ypz \u2212 \u03c1x\u03c1y\u03c1z) (20) It should be stressed that the feasible solutions for the inverse/direct kinematics, located in the neighbourhood of the \u201czero\u201d point, have the following configuration indices: sx = sy = sz =+1 and m =\u22121. 4. WORKSPACE ANALYSIS The robot workspace is an important criterion in evaluating manipulator performance. As follows from the equation (10), the Orthoglide workspace WL is composed of two fractions (Fig. 8): (i) the sphere SL of radius L and centre point (0, 0, 0), and (ii) the thin non-convex solid GL, which is located in the first octant and bounded by the surfaces of the sphere SL and the cylinder intersection CL. These surfaces can be generated by applying the following algorithm based on the expressions from SubSection 3.2: Algorithm 1. Orthoglide Workspace (3D Mesh) Input: \u03d5, \u03b8 (grid steps of angles \u03d5, \u03b8) Output: X, Y , Z (2D arrays of 3D Face nodes) for \u03d5 = 0 to 2\u03c0 step \u03d5 for \u03b8 =\u2212\u03c0/2 to \u03c0/2 step \u03b8 ex = cos \u03d5 cos \u03b8 ; ey = cos \u03d5 sin \u03b8 ; ez = sin \u03d5 if (ex < 0) or (ey < 0) or (ez < 0) k = 1; else k = max {\u221a e2 x + e2 y ; \u221a e2 x + e2 z ; \u221a e2 y + e2 z } end if X(\u03d5, \u03b8) = exL/k; Y (\u03d5, \u03b8) = eyL/k; Z(\u03d5, \u03b8) = ezL/k; next \u03b8 next \u03d5 where (ex, ey, ez) are the components of a unit direction vector, which are expressed via two angles \u03d5, \u03b8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure7-4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure7-4-1.png",
        "caption": "FIGURE 7-4 Centrifugal separator-type spark arrester. (a) Spark arrester onlv. (b) Combined with muffler. (Courtesy Hasco Manufacturing Co.)",
        "texts": [
            " Because temperatures within the cylinder may be from 1650\u00b0 to 2200\u00b0C, loose carbon particles will be burning as they leave the exhaust system. Field tests indicate that fires may be started consistently in dry vegetation by glowing carbon particles. Spark arresters are generally of two types, a centrifugal separator and a screen type. The chief criticisms of the screen type have been insufficient retention of smaller particles and clogging, which results in increased back pressure. SPARK ARRESTERS 161 Figure 7-4 shows a cross-sectional view of a typical centrifugal-type spark arrester. Exhaust gases entering at A are channeled to the outer walls by the baffles at B. Centrifugal force causes the carbon particles to go to the outside wall, where they are collected. The exhaust gases turn and go out the top of the exhaust pipe. The U.S. Forest Service requires all vehicles to use approved spark arrest ers in specified forests. The Forest Service specifies the method of testing and the requirements that each spark arrester must meet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002664_s10999-012-9181-y-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002664_s10999-012-9181-y-Figure4-1.png",
        "caption": "Fig. 4 The simulation trajectory of mass centre",
        "texts": [
            " Firstly, the model is imported into the ADAMS software by adding various constrains; secondly, the driving forces data is imported into motion of the ADAMS model, their driving functions as below: SFORCE_1: AKISPL (time, 0, spline_F1, 0), SFORCE_2: AKISPL (time, 0, spline_F2, 0), SFORCE_3: AKISPL (time, 0, spline_F3, 0), SFORCE_4: AKISPL (time, 0, spline_F4, 0), SFORCE_5: AKISPL (time, 0, spline_F5, 0), SFORCE_6: AKISPL (time, 0, spline_F6, 0), Import the above six driving functions into the six forces driving respectively, we can get the parallel mechanism trajectory, shown as Fig. 4. The relationship of velocity, acceleration and displacement of mass centre of moving platform with time are shown in Figs. 5, 6 and 7. From above Figs. 4, 5, 6 and 7, we can see that, the simulation trajectory and other kinds of motion parameters are consistent with the planned ones, which proves the correctness and feasibility of inverse dynamics mathematic model. Cross-producting and dot-producting are main computing means in dynamic model which are suitable for computer solving and with high speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002348_j.talanta.2009.10.016-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002348_j.talanta.2009.10.016-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of a basic FIA system.",
        "texts": [
            " The systematic nomenclature of porphyrins, metalloporphyrins nd related molecules is detailed by IUPAC [33] and a World Wide eb version [34], while Fisher numeration [33], trivial names [33] nd abbreviations [16] are also found in literature. Flow-injection analysis (FIA), introduced in 1975 [35], marked n important breakthrough in unsegmented automatic continuous ow analysis and has developed over three decades as a simple, onvenient, feasible analytical technique with the capability of a igh sample frequency and degree of automation [36\u201346]. FIA is an nalytical technique that is based on injecting a known volume of ample, with a well-defined shape, into a moving, unidirectional nsegmented carrier or reagent stream (Fig. 1). In this moving tream, the sample is physically and chemically transformed into detectable specie that causes a detector response downstream of he injection point. If all critical parameters (reproducible injection, ontrolled reaction time, and controlled dispersion) are held within ertain tolerance levels, the result will be reproducible [36,40]. The asic instrumentation needed for an FIA system are a multichanel pump, an injection valve, a flow-through detector, and a signal utput device (originally a recorder, lately a computer)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001778_ecc.2007.7068863-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001778_ecc.2007.7068863-Figure1-1.png",
        "caption": "Figure 1. The Asymmetric Spring Loaded Inverted Pendulum (ASLIP).",
        "texts": [
            " It is emphasized that the practical consequences of these results lie in the fact that they allow the direct use of controllers obtained for the SLIP in a more complete model. This model is called the Asymmetric Spring Loaded Inverted Pendulum (ASLIP), and can be used to study the sagittal plane running of bipedal robots. Despite its importance, to the best of the authors\u2019 knowledge, no formal studies of the ASLIP exist. Proposing and formally analyzing control laws for the stabilization of the ASLIP that take advantage of SLIP controllers constitutes the goal of this paper. A schematic for the Asymmetric Spring Loaded Inverted Pendulum (ASLIP) is presented in Fig. 1. The hip joint does not coincide with the center of mass (COM) of the torso, which is modeled as a rigid body with mass m and moment of inertia J about the COM. The leg is assumed to be massless. The ASLIP is controlled by two inputs: a force 1u acting along the leg, and a torque 2u applied at the hip. In what follows, the subscripts \u201cf\u201d and \u201cs\u201d denote \u201cflight\u201d and \u201cstance,\u201d respectively. A. Flight Phase Dynamics The flight phase dynamics corresponds to a point mass undergoing ballistic motion in a gravitational field together with a double integrator governing the pitch motion",
            " The rest of the proof is a consequence of the fact that the flight flow of the ES-SLIP is the same as the translational part of the flight flow of the ASLIP. Equations (65) and (66) ensure that, not only the flight flows, but also the corresponding reset maps, are identical. C. Proof of Theorem 1 The proof of Theorem 1 follows from Lemmas 1, 2 and 3. This section presents a simulation of the controller described above. The mechanical properties of the ASLIP correspond to preliminary designs of a biped robot that is currently under construction, and are given in Table I (see Fig. 1). The desired pitch angle \u03b8 , the nominal leg length 0l and the touchdown angle td\u03d5 are specified a priori, based on gait requirements and design constraints. Then the nominal leg length of the ES-SLIP is calculated through 2 2 0 0 0 td2 sinr l L l L \u03d5= + \u2212 . (67) The ES-SLIP mass coincides with the ASLIP mass while the spring constant k is arbitrarily specified. Table I presents the parameter values used in the simulations. Given these parameters, an exponentially stable fixed point for the Poincar\u00e9 return map of the ES-SLIP is calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003558_s12206-017-0627-x-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003558_s12206-017-0627-x-Figure1-1.png",
        "caption": "Fig. 1. Global coordinate systems, loading and displacements.",
        "texts": [
            " To this end, a four DOF quasi-static model for D-CRBs was developed and verified that is capable of providing a fully-occupied stiffness matrix, bearing displacements, and contact loads between rollers and raceways for aligned, as well as misaligned bearings. The contact pressure distribution in rolling elements was then derived using a three dimensional (3D) elastic contact method and used for fatigue life estimation. The performances of one D-CRB and a pair of S-CBRs were comprehensively compared. Finally, an extensive parametric study on the effect of bearing loading, radial clearance and misalignment on bearing stiffness and fatigue life was conducted. Fig. 1 shows the global coordinate systems Oxyz. The origin point is located at the center of the inner ring. In this study, it is assumed that the inner ring can freely rotate around the bearing axis and move in the axial direction. Therefore, only four DOF of loading and displacement are considered. The external load and displacement vectors of the bearing are written, respectively, by. {F}T = {Fy, Fz, My, Mz} (1) {d}T = {dy, dz, gy, gz}. (2) Fig. 2(a) shows the local coordinate systems defined for a particular roller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001051_s00170-005-0032-y-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001051_s00170-005-0032-y-Figure11-1.png",
        "caption": "Fig. 11 Ball-type pull-in mechanism",
        "texts": [
            " Spring force reduction due to the centrifugal-force is less than 5% of the total spring force at a speed up to 15,000 rpm. 5.2 Force amplification mechanism As mentioned before, the ball-type pull-in mechanism can amplify the disc spring force by proper geometric parameters designed at the static state. In practice, the centrifugal force of the ball at high speed will add another force on the final draw force. Therefore, it is necessary to predict and control the additional centrifugal force. A balltype pull-in mechanism is shown in Fig. 11(a). At the pullin status, the spring force is amplified through the contact geometry of the steel ball. A simplified model is shown in Fig. 11(b). The input force is the spring force and the output is the draw force. Geometrical parameters of the contacted ball of the pullin mechanism are defined in Fig. 12(a). Free body diagram of the steel ball is depicted in Fig. 12(b). Friction of the ball contact interface is assigned as \u03bck. At static state, the force and moment equivalent conditions must be satisfied as:X Fx \u00bc 0 ) F3 sin \u00fe \u00f0 \u00de \u00fe ukF3 cos \u00fe \u00f0 \u00de \u00feukF1 sin \u00f0 \u00de F1 cos \u00f0 \u00de \u00fe f2 \u00bc 0 (11) X Fy \u00bc 0 ) F2 \u00bc F3 cos \u00fe \u00f0 \u00de ukF3 sin \u00fe \u00f0 \u00de F1 sin \u00f0 \u00de ukF cos \u00f0 \u00de (12) X M0 \u00bc 0 ) f2 \u00bc uk F3 F1\u00f0 \u00de (13) Pin \u00bc F1 sin \u00fe uk cos \u00bd (14) Pout \u00bc F3 cos uk sin \u00bd (15) Solving the Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003385_12.2010577-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003385_12.2010577-Figure3-1.png",
        "caption": "Figure 3. Example of support structure.",
        "texts": [
            " Positioning is therefore a key element managing a laser sintering process. As no pre-heating of the powder is performed, the prototype may suffer from thermal strain if full cross-sections are sintered just after lattice support structures. Therefore, a tilting angle of the part on the platform has to be provided, so that a gradual growth is performed. Furthermore, parts with steep curvatures are required to be placed in a way that the recoater does not hinder their growth while providing the powder. The use of lattice supports (Figure 3) which are processed with different parameters and scanning techniques is required when parts are directly sintered in SLM. Two kinds of supports are allowed: blocks to fix the part to the building platform and conduct excess heat away from the part; gussets to prevent sintering on loose powder for embossed zones. More tight meshes are needed for blocks compared to gussets. Supports structure features are suggested by Materialise software considering the prototype geometry and positioning on the building platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002755_tsmcc.2011.2182609-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002755_tsmcc.2011.2182609-Figure6-1.png",
        "caption": "Fig. 6. Location of the gears on the output side of the gearbox.",
        "texts": [
            " To collect AE burst signals, wideband type AE sensors were used. The operating frequency range for this type of sensors is between 100 kHz and 1 MHz. It covers the AE source frequency range. The schematic of the data acquisition system is shown in Fig. 5. The data acquisition board is a two-channel data acquisition card with 18-bit resolution and the maximum sampling rate is 40 MHz, which is 40 times the highest response frequency of the AE sensors. The location of the gears on the output side of the gearbox, called ODG, is shown in Fig. 6. To setup the experiments for the validation of the presented method, a seeded gear fault on ODG2 was created by chipping a tooth of the gear by 20%. Two AE sensors were placed on the surface of the gearbox as close as possible to the ODGs: one by ODG2 and one by ODG3. In this paper, AE sensor 1 represents the sensor located near ODG2 and AE sensor 2 the sensor located near ODG3. During the experiments, AE burst type signals were collected based on the trigger value set in the data acquisition board"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure8-11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure8-11-1.png",
        "caption": "FIGURE 8-11 Bypass engine oil filtering system. (Courtesy Fram Corp.)",
        "texts": [
            " In the future, agricultural tractors may have to meet the same EPA (Environmental Protection Agency) require ments now required of highway vehicles. See SAE J900 (Nov. 1980) (Crank- OIL FILTERS 199 case Emission Control Test Code) for the standard method of measuring the crankcase emissions. Oil Filters Lubricating oil in an engine becomes contaminated with various materials: dirt, metal particles from the engine, carbon from fuel and oil that have burned, water, and fuel dilution. An ideal filter should remove all contami nants larger than engine clearances. The majority of oil filters are classified as bypass filters (fig. 8-11) in that only a percentage of the oil that is pumped by the oil pump passes through the filter. The remainder bypasses the filter and goes directly to the oil dis tributor lines. The rate of How through a filter depends on several factors, the most important being the pressure on the filter, the viscosity and tem perature of the oil, the size of orifice, and the area of the filter. Rather extensive tests (Univ. Nebraska Agr. Expt. Sta. Bull. 334, 1941) reveal some interesting information about oil filters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-16-1.png",
        "caption": "FIGURE 12-16 Piston concen tric in cylinder.",
        "texts": [
            " Close-fitting surfaces in relative motion occur in most hydraulic components. If the viscosity of the fluid is too low, leakage flows increase; if the viscosity is too large, component efficiencies decrease because of additional power loss in fluid friction. Viscosity is of such significance that it is common practice to designate the fluid by its viscosity at a certain temperature; for example, oil with 150 SCS at 54\u00b0C might be such a fluid designation. Referring to the piston and cylinder of figure 12-16 in which the radial clearance C is filled with a fluid, ~ ewton observed that a force was necessary to cause relative motion. This force is a measure of the internal friction of the fluid or its resistance to shear; it is proportional to the area in contact and to the velocity and is inversely proportional to the film thickness. Therefore, x F = /-LA C, The constant of proportionality /-L is known as the absolute viscosity (the terms \"dynamic viscosity\" and \"coefficient of viscosity\" are also used) of the fluid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003010_imece2014-36661-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003010_imece2014-36661-Figure4-1.png",
        "caption": "Figure 4. EBAM Machine: (a) overall outside, and (b) inside of the build chamber.",
        "texts": [
            " The objective of this research is to attempt temperature measurements in EBAM using an NIR thermal imager and to achieve better understanding of process temperatures that may be applied for the validation of EBAM thermal models. An NIR with a spectral range of 0.78-1.08 \u03bcm was employed to acquire thermal images during EBAM fabrications using Ti-6Al-4V powder. A CAD was designed and built to evaluate the spatial resolution and temperature distributions around a melt pool during melt scans. Post-processing data of NIR images was analyzed to quantify the maximum temperatures and melt pool sizes. EXPERIMENTAL DETAIL \u00a0 An Arcam S12 EBAM system, shown in Figure 4, at NASA\u2019s Marshall Space Flight Center (Huntsville, AL) was used to fabricate parts of a designed model in conjunction with temperature measurement experiments. Ti-6Al-4V powder from Arcam was used. The part designed for was a simple block: 50 mm long, 25 mm wide and 30 mm tall (x\u00d7y\u00d7z), with notches on the edge along the build direction, shown in Figure 5.\u00a0 The EBAM primary settings used were default values typically employed for Ti-6Al-4V powders. The layer thickness was 0.07 mm. A set of parameters called a build theme are suggested to dynamically control the electron beam speed and current as well as the raster spacing during the part fabrication process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001310_tmag.2004.832157-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001310_tmag.2004.832157-Figure6-1.png",
        "caption": "Fig. 6. (a) Halbach arrays with the ideal radial magnetized ring and (b) parallel magnetized arc segments.",
        "texts": [
            " In particular, the analytical results of back EMF are compared with FE results in case of mover velocity . The results are shown in good agreement with those obtained from finite-element analysis (FEA). Fig. 5(a) shows the photograph of cylindrical Halbach array mover and single-phase stator windings. Fig. 5(b) shows the experimental system that consists of load cell, indicator, dc power supply, and moving-magnet linear actuator with cylindrical Halbach array to measure static thrust. Specifications of manufactured moving-magnet linear actuator are presented in Table I. Fig. 6(a) shows the cylindrical Halbach array composed of ideal radial and axial magnetized ring. In case of a ring magnet, a geometry-specific impulse magnetizing fixture is required to impart the magnetization, whereas arc segments can be magnetized with a parallel magnetization such as in Fig. 6(b) [4]. So, this paper introduces parallel magnetized arc segments as a mover, which offers advantages not only reducing burden in ideal radial magnetized PM\u2019s manufacture, but cutting down manufacture expenses. Fig. 7 shows the comparison of air-gap flux density distributions according to composition methods of cylindrical Halbach array using the three-dimensional FEA. It can be seen that air-gap flux density due to parallel magnetized arc segments makes little difference it due to ideal radial magnetized PM\u2019s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001900_978-1-4020-8829-2_11-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001900_978-1-4020-8829-2_11-Figure3-1.png",
        "caption": "Fig. 3. Sum of dual vectors",
        "texts": [
            " The computational steps are described in the following and are justified by the geometry depicted in Fig. 2. 1. Compute the dual vectors E\u0302i = A\u0302i\u2225\u2225\u2225A\u0302i \u2225\u2225\u2225 , (i = 1, 2). (8) 2. Compute their cross product E\u03023 = E\u03021 \u00d7 E\u03022\u2225\u2225\u2225E\u03021 \u00d7 E\u03022 \u2225\u2225\u2225 . (9) 3. Compute cosine and sine of the dual angle \u03b8\u0302 between the two line vectors cos \u03b8\u0302 = E\u03021 \u00b7 E\u03022 , (10a) sin \u03b8\u0302 = E\u03021 \u00d7 E\u03022 \u00b7 E\u03023 . (10b) 4. Compute dual angle \u03b8\u0302 = atan2 ( sin \u03b8\u0302, cos \u03b8\u0302 ) = \u03b8 + \u03b5h . (11) The procedure is not valid if line vectors are parallel. In this case, there is an infinite set of dual vectors E\u03023. With reference to the geometry of Fig. 3, we want to compute the sum A\u0302 = A\u03021 + A\u03022 . (12) One can observe that the direction of A\u0302 is obtained by prescribing a screw motion to A\u03021 defined by the screw axis E\u030212 and dual angle \u03b1\u03021. On the basis of this observation, the following algorithm can be stated: 1. Compute the dual vectors E\u03021 = A\u03021\u2225\u2225\u2225A\u03021 \u2225\u2225\u2225 , E\u03022 = A\u03022\u2225\u2225\u2225A\u03022 \u2225\u2225\u2225 , where \u2016\u00b7\u2016 denote the Euclidean norm. 2. Compute the dual angle \u03b8\u0302 and the dual vector E\u030212 perpendicular to both A\u03021 and A\u03022 (see previous section). 3. Compute the module of the dual vector sum A = \u221a A\u03021 \u00b7 A\u03021 + A\u03022 \u00b7 A\u03022 + 2A\u03021 \u00b7 A\u03022 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001127_rob.4620120903-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001127_rob.4620120903-Figure7-1.png",
        "caption": "Figure 7. Stability margin for a discontinuous crab gait.",
        "texts": [
            " Figure 5 shows the diagonal that determines the stability margin for a crab gait (solid lines) and the diagonal for a non-crab body motion (dotted lines). Observe that for the first leg motion, that of leg 4, the LSM is the same in both cases (crab and non- Gonzalez de Santos and Jimenez: Generation of Discontinuous Gaits 605 crab gait); but when leg 2 moves, the LSM decreases for the crab gait motion. When leg 3 moves after a body motion, the LSM is the same as in a non-crab motion. Finally, when leg 1 moves, the LSM is better than the one for the non-crab gait (for the crab angle considered in the figure). Figure 7 shows the LSM as a function of the crab angle for each leg in its transfer subphase. In this figure the following parameters have been considered; P, = 60 cm, P, = 120 cm, R, = 60 cm, R, = 40 cm, and a takes values from -45 degrees to 45 degrees. Leg 2 presents the smallest LSM for positive crab angles; hence, this is the LSM of the locomotion cycle. Substituting leg position values into Eq. (l), when leg 2 is in transfer and a meets the case A constraints, yields: Considering a negative crab angle, the minimum LSM is achieved when leg 1 is in transfer. In this case the value of the LSM is given by: PYX, + 2P,R, tan a - R: tan a LSMA- = (11) 4p, From the last two equations, it is obvious how the expression for the largest crab angle for a specified LSM may be found. When the crab angle meets case B constraints, Eq. (1) provides the LSM expressions for both positive and negative crab angles given by: and: -2P,R, - 2P,R, + R,R, - 2P,R, cotan a LSMB- = 8P, For those parameters considered, Figure 7 shows that the permitted crab angle falls into the range running from -30 degrees to 26 degrees. 3.2. TPDC Gait with Change in Initial Position The maximum crab angle that a quadruped can achieve with stability can be augmented if the foot trajectories of support legs pass over the center of the working area. This is equivalent to locating the initial foot positions as shown in Figure 8(a). After the leg 2 and leg 4 transfer phase, the body will move half a cycle\u2019s displacement along the x and y axes",
            " The main interest of the gaits studied here is to connect them to follow a given trajectory. In this study, for the sake of simplicity, the initial and final leg locations, in the body reference frame, will be the same for all gaits considered. Hence, it is quite simple to join different gaits at the end of a locomotion cycle. Different possibilities for discontinuous crab walking have already been analyzed. Note that the two-phase discontinuous gait coincides with the zero crab angle discontinuous gait. The employment of one or the other depends on working area constraints. Figure 7 and Figure 9 show the LSM and the maximum crab angle achieved by each gait mode. Each graph shows one mode with two different cases defined by its foot trajectories. The switch from one trajectory to the other occurs at the point where the slope of the curve suddenly changes. The TPDC, with a change in the initial position, can achieve greater crab angles (from -64 degrees to 64 degrees) than the TPDC mode with no change in its initial position (which is restricted to between -30 degrees and 26 degrees)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003606_jas.2018.7511267-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003606_jas.2018.7511267-Figure1-1.png",
        "caption": "Fig. 1. The structure of the SIP.",
        "texts": [
            " Based on the application of the BBBC algorithm, the third objective of this paper is to realize the optimization of the multiple PID controllers with the BBBC algorithm for the SIP. This paper is organized as following six sections. Section II introduces the modelling procedure of the SIP step by step. Section III gives the control structure with multiple PID controllers for the SIP. Section IV shows the optimization of the multiple PIDs with BBBC algorithm. Section V gives some comparisons and discussions. And Section VI concludes the work presented in this paper. The structure of the SIP is given in Fig. 1. The pivot of the SIP is activated by three control forces, which are Fx, Fy , and Fz . Three control forces are along the direction of the x-axis, y-axis and z-axis in the spatial coordinate system, respectively. We assume the pivot point is at o\u2032(x, y, z) in the xyz spatial coordinate system, and the origin point of x\u2032y\u2032z\u2032 spatial coordinate system is set at pivot point o\u2032(x, y, z). The x\u2032, y\u2032 and z\u2032 axes are parallel with x, y and z axes, respectively. The center of mass of the pendulum is at p(xp, yp, zp) in the x\u2032y\u2032z\u2032 spatial coordinate system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000861_b103044m-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000861_b103044m-Figure1-1.png",
        "caption": "Fig. 1 Biosensing film.",
        "texts": [
            " On the surface of the composite films of PB and N-substituted polypyrroles, reactive groups are present and the materials are acceptable as ready-to-use supports for enzyme immobilization.23 The carboxy groups of the organic component (PPyrBAc) allow the chemical binding of biomolecules to the film surface using a simple one-step carbodiimide method. The method leads to the formation of a monomolecular layer of enzyme molecules bound covalently directly to the surface of the PB film, as shown in Fig. 1. Owing to the lack of any intrinsic absorption near 700 nm, the biolayer does not change the absorbance of the film. After enzyme immobilization, the films are still transparent and show no sign of turbidity. In contrast to turbid enzyme membranes utilizing pre-activated supports, the extremely thin monomolecular enzyme layers are fully transparent, which is particularly advantageous in the case of optical measurements in transmission mode. These covalently linked enzyme molecules form a stable layer exhibiting high biocatalytic activity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000717_robot.1997.620131-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000717_robot.1997.620131-Figure1-1.png",
        "caption": "Figure 1: Model of a compass-like biped robot",
        "texts": [
            " A typical gait patterin is then briefly discussed in Section 3 . The limit of the linearizing approach is identified in Section 4. Section 5 is devoted to a systematic numerical analysis of the compass gait, with a special emphasis on complex gaits (asymmetric and chaotic gaits). Section 6 presents finally the future lines of research that we intend to pursue. 2 Governing equation, normalization 2.1 Model description The biped robot considered here, hereafter called compass, consists of two identical legs jointed at the hip, see Fig. 1. The mass is concentrated at 3 points: at the hip, m H , and on each leg, m, at distances a and b respectively from the leg tip and the hip. For forthcoming simulation trials, the mass ratio ,U = and the length ratio ,O = will be varied from 0.1 to 10 when total mass m C = 2m + m H and leg length 1 = a+b are constant and equal, respectively, to 20 Kg and 1 meter. This compass walks down on a plane surface possessing a constant slope 4. The compass gait consists of two stages: - Swing: the compass hip pivots around the point of support of its support leg on the ground",
            " The compass state vector is then - Transition: the support is transferred, instantaneously, from one leg to the other. The impact of the swing leg with the ground is assumed to be inelastic and without sliding. The half-inter leg angle CY will be used to characterize transition. A knee-less compass with a rigid leg cannot however clear the ground. This conceptual problem is avoided by including below point mass m a prismatic-jointed knee with a telescopically retractable massless lower leg, see Fig. 1. This obviously solves the problem of foot clearance without affecting compass dynamics. The simplifying assumptions described here are not unique to this work, they are routinely made in the biped robot literature and compass prototypes have also been actually developed, see [17], [ll]. 2.2 The governing equations = [e , e]? The computational details regarding the derivation of the compass equations and the proofs of the normalization properties can be found in [14]. Swing stage The dynamic equations of the swing stage are similar to the well-known double-pendulum equations",
            " The chaotic gait, represented by a continuous distribution of points in Figures 3(a) and 3(b), is omitted for the sake of clarity in all subsequent bifurcation diagrams. Finally, Figs. 3 (d), 4 (d) and 5 (d) present several phase plane diagrams. These numerical simulations show that the compass takes longer and faster steps when 4 or p are increased and longer but slower steps when ,f3 is increased. This behavior can also be summarized as follows: where L and U denote respectively the step length, i.e. L = 21sina, (cf. Fig. 1) and the average velocity, i.e. U = L. The evolution of v can be made more precise using Figs. 3 (d), 4 (d) and 5 (d): when 4 is increased, phase plane diagrams are enlarged in both directions. Therefore v clearly increases. When p and /3 are increased, phase plane diagrams are compressed in {,he T 2whose arithmetic average is represented by the dotted line. #-direction, but enlarged in the #-direction. We deduce immediately that the maximum angular velocity decreases when p and p are increased"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002768_j.msec.2012.06.020-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002768_j.msec.2012.06.020-Figure2-1.png",
        "caption": "Fig. 2. CVs of 0.5 mMPhH at (a) bare CPE, (c) BHCPE and (d) BHTCPE; (b) shows the CVs of blank solution at BHTCPE. Electrolyte is 0.1 M phosphate buffer solution (pH 8.0) and scan rate is 20 mVs\u22121.",
        "texts": [
            " In the present work, for the first time we investigate the catalytic oxidation of PhH at BHTCPE by some electrochemical techniques in buffered solutionwith pH 8.0 as optimum pH for electrocatalysis of PhH. Also thismodified electrodewas used as a sensor for determination of PhH and HZ concentrations simultaneously. The utility of the modified electrode for oxidation of PhHwas evaluated by cyclic voltammetry. The cyclic voltammetric response of a bare carbon paste electrode in 0.1 M phosphate buffer (pH 8.0) with PhH is shown in Fig. 2 (curve a). Curves b and c of Fig. 2 show cyclic voltammograms of modified electrode in the buffer solution without and with 0.5 mM PhH, respectively. The results show that the nanostructured sensor produces a large anodic peak current in the presence of PhH without a cathodic peak (Fig. 2, curve c). At the surface of a bare electrode, PhH was oxidized around 700 mV. However, the oxidation of PhH at the BHCPE was around 180 mV vs. Ag/ AgCl electrode (Fig. 2 curve c). Thus, a decrease in overpotential and enhancement of peak current for PhH oxidation are achieved with the modified electrodes. Such a behavior is indicative of an EC\u2032 mechanism [30]. Therefore with increasing the peak current of PhH oxidation (i.e. increasing of electroanalytical signal) the sensitivity of PhH measurement can be increased by the modified electrode. Also with decreasing the overpotential of PhH oxidation at the modified electrode the interference of some analytes which can be oxidized at high potentials will be eliminated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003748_s11071-016-3218-y-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003748_s11071-016-3218-y-Figure4-1.png",
        "caption": "Fig. 4 Schematic for plastic inclination deformation of the gear tooth thin piece due to root crack [1]",
        "texts": [
            " Mechefske Department of Mechanical and Materials Engineering, Queen\u2019s University, Kingston, ON K7L 3N6, Canada e-mail: wennian.yu@queensu.ca M. Timusk Bharti School of Engineering, Laurentian University, Sudbury, ON P3E 2C6, Canada 2D Two dimensional (or 2 dimensional) 3D Three dimensional (or 3 dimensional) 6DOFs Six degrees of freedom (or 6 degrees of freedom) DOF Degree of freedom FEA Finite element analysis GMS Gear mesh stiffness LOA Line of action OLOA Off-line of action STE Static transmission error TC Tooth crack A, B, C , D, E , E \u2032, E \u2032\u2032 Point labels defined in Fig. 4 T , P , Q Point labels defined in Fig. 2 F Total tooth contact force F0, F1 External excitations due to static load Tj and tooth profile deviations ei Hi Contact function at Mi M Moment about Y -axis due to total contact force F M, C, K Overall system mass, viscous damping ,and stiffness matrices Kg, Kb Stiffness matrices regarding to bearing and gear pair Rb, R f Radii of the gear base circle and reference circle, respectively T Transform matrix between the U\u2013V coordinate and R\u2013 S coordinate system Tj ( j = 1, 2) Torques appliedon thedriving ( j = 1) and driven ( j = 2) gear, respectively V i Structure vector at Mi W , Wc Length of the tooth width and the crack along tooth width a, b, c, f , \u03b1 Geometries of the rack in Fig",
            " 3b) and the tooth profile direction (TP direction in Fig. 3b) along the tooth width direction (TW direction in Fig. 3b). However, if we divide the gear tooth into several independent thin pieces [2,9], as shown in Fig. 3b, so that the crack depth qw and the crack location lw at that thin piece can be assumed as constant, if the width of the thin piece \u03b4w is small enough. In this case, a 2D model with a planar crack and a uniform crack depth can be used to investigate the plastic inclination deformation for those thin pieces. Figure 4 shows the schematic for the plastic inclination deformation of the gear tooth thin piece (i.e., Fig. 3b) due to the tooth fillet crack, which is based on the model proposed in Shao and Chen [1]. The solid curve represents the original tooth profile, whereas the dashed curve represents the deformed tooth profile. A global U\u2013V coordinate system is built with its origin at the gear center O , and the V -axis coinciding with the center line of cracked tooth. Point A is the intersection point between the involute profile and fillet profile. Point C is the crack position at tooth profile. Point D and point C are symmetric with the tooth center line (i.e., V -axis). Point B is the crack tip. The crack depth qw and the crack angle \u03b1c (i.e., with respect to the V - axis) are illustrated in Fig. 4. When the plastic inclination happens, it can be assumed that the tooth part above the crack is a cantilever beam with its fixed foundation at straight line BD, and rotates around the middle point o between points B and D. In order to determine the plastic inclination deformation, a local R\u2013S coordinate system is established with its origin at point o and S-axis coinciding with the line BD. Suppose a mesh position E at the original tooth profile, at a given whole tooth plastic inclination angle \u03b8p; it will rotate to the point E \u2032 at the deformed tooth profile. E \u2032\u2032 is the mesh position at the original tooth profile that shares a same line of action (LOA) with E \u2032 at the deformed tooth profile. Therefore, the distance between points E \u2032 and E \u2032\u2032 [i.e., \u03b4w(E)] along theLOA represents the plastic inclination deformation at point E that is acted as the displacement excitation on the gear dynamics. This distance can be calculated based on the geometric relationship shown in Fig. 4. The global coordinates of the points A,C , E , and D on the tooth profiles can be obtained based on the two parametric equations proposed in the previous section. Suppose they are: A(uA, vA), C(uC , vC ), E(uE , vE ), D(uD , vD). Therefore, the global coordinate of point B(uB , vB) can be calculated as: { uB = uC \u2212 qw \u2217 sin(\u03b1c) vB = vC \u2212 qw \u2217 cos(\u03b1c) (5) As a result, the global coordinate of the middle point o (uo, vo) is: { uo = (uB+uD) 2 vo = (vB+vD) 2 (6) The acute angle \u03b8T between U -axis and R-axis can be expressed as [1]: \u03b8T = arctan ( uB \u2212 uD vD \u2212 vB ) (7) This angle can be used to transform the global coordinate to local coordinate through the transform matrix T [1]: T = [ cos(\u03b8T ) \u2212 sin(\u03b8T ) sin(\u03b8T ) cos(\u03b8T ) ] (8) Therefore, the local coordinate of point E (rE , sE ) can be established as: { rE sE } = T\u22121 \u2217 { uE \u2212 uo vE \u2212 vo } (9) When the tooth plastically inclined at an angle of \u03b8p, the local coordinate of point E \u2032(rE \u2032 , sE \u2032) is [1]: { rE \u2032 = \u221a rE 2 + sE 2 cos(arctan(sE/rE ) + \u03b8p) sE \u2032 = \u221a rE 2 + sE 2 sin(arctan(sE/rE ) + \u03b8p) (10) Transforming the local coordinate of point E \u2032(rE \u2032 , sE \u2032) back to global coordinate E \u2032(uE \u2032 , vE \u2032) through the transform matrix T gives:{ uE \u2032 vE \u2032 } = T \u2217 { rE \u2032 sE \u2032 } + { uo vo } (11) Point E \u2032\u2032 on the original tooth profile shares the same LOA with the point E \u2032 on the deformed tooth profile, meaning point E \u2032\u2032 is just on the line T E \u2032 as shown in Fig. 4. Therefore, the mesh angle for point E \u2032\u2032 is: \u03b1E \u2032\u2032 = arccos ( Rb/ \u221a uE \u20322 + vE \u20322 ) \u2212 arctan(uE \u2032/vE \u2032) (12) Substitute this mesh angle into Eq. (1) gives the global coordinate of point E \u2032\u2032 (uE \u2032\u2032 , vE \u2032\u2032). Consequently, the distance between point between points E \u2032 and E \u2032\u2032 along the LOA is obtained as [1]: ew(E) = \u221a (uE \u2032\u2032 \u2212 uE \u2032)2 + (vE \u2032\u2032 \u2212 vE \u2032)2 (13) Based on Eqs. (5)\u2013(13), one can easily deduce the gear tooth plastic inclination deformation along the tooth profile for each thin piece resulting from the spatial crack described by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-18-1.png",
        "caption": "FIGURE 13-18 Planetary gear set with two clutches and two brakes to provide three forward speeds and one reverse speed. (Courtesy J. I. Case.)",
        "texts": [],
        "surrounding_texts": [
            "384",
            "PLAI\\'ETARY GEAR SYSTEMS 385\nPlanetary design requires some special techniques to calculate gear ratios and efficiency and to ensure the gears will mesh properly. The large amount of literature available on planetary systems indicates that planetaries are con sidered challenging to design. However, only a few basic engineering prin ciples of statics and kinematics are needed to design planetary systems.\nPlanetary Ratio Engineers use many techniques (Mihal 1978; Hanson 1981) to determine the planetary ratio. A simple and effective method is to use the kinematic principle:\nThe absolute velocity of any planetary member is equal to the absolute velocity",
            "386 TRANSMISSIONS AND DRIVE TRAINS\nof the planet carrier plus the relative velocity of the member with respect to the carrier.\nFor example, the planetary ratio of the simple planetary shown in figures 13-17 (a) and 13-19 can be determined as follows:\nns = nc - (nr - nc)NrIN<,\nwhere ns = the rpm of the sun gear ne = the rpm of the carrier nr = the rpm of the ring gear\nN r = the number of teeth in the ring gear Ns = the number of teeth in the sun gear\n(12)\nThe ring gear is fixed in the final drive so that nr = O. The equation can be rearranged to yield the planetary ratio in which the sun gear is the input and the carrier is the output. Thus the planetary ratio is\nrpm input = ns = 1 + N r\nrpm output nc N, (13)\nSpeed ratios for more complex planetary systems can be determined by si multaneous solution of the equations of motion for each planetary.\nPlanetary Efficiency An efficiency analysis of a planetary system is very simple when basic engi neering principles are used. The same gear efficiencies given previously can be used. However, the power flow through the gear mesh will be different from the input power. Therefore, one should use the basic definition of efficiency\npower out e = .\npower III (14)\nwhere power out = output torque x output rpm power in = input torque x input rpm\nThus, for a planetary final drive with sun input, carrier output, and fixed ring gear\nPower out = Tene Power in = T,n,\nwhere T represents torque, n represents rpm, the subscript s represents the input sun gear, and c represents the output carrier as defined previously for equation 12. Thus, from equation 14, the efficiency equation is\npower out e =\npower in (15)"
        ]
    },
    {
        "image_filename": "designv10_10_0002745_pime_proc_1966_181_036_02-Figure27-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002745_pime_proc_1966_181_036_02-Figure27-1.png",
        "caption": "Fig. 27. The kinematic diagram of the rolling motion",
        "texts": [
            " Lower and upper threshold points of Tangential tractional force. Coefficient of traction (= F/N). Average film thickness; critical film thick- Correlation coefficient, equation (5). Normal load, lb. Load carried by direct contact; that by hydrodynamic pressure. Nominal maximum Hertzian pressure. Primary transition region. Cylinder radius, toroid \u2018track\u2019 radius and Force per unit area pertaining to bound- Secondary transition region. Difference and mean of surface-velocity Mean of surface-velocity vectors, cmh. Kinematic parameters (Fig. 27). Pressure-viscous coefficient, cm2/dyne. Film thickness, arbitrary unit, see equa- e.h.1. respectively. ness. minimum toroid radius, in. ary lubrication and viscous drag. vectors, ft/min ( U - = U tan j?). tion (6). Proc Instn Mech Engrs 1966-67 \u201ch 7; 7 0 Fraction of contact area in metal-tometal contact. Viscosity, P; initial viscosity at surface temperature. Coefficient of boundary friction; that of viscous drag. Ratio of measured voltage to applied potential difference. Dimensionless film thickness, S/S,, or (hO-hc)/uh in Appendix 4",
            " R1wfl w2 = -; the rolling component; the R2 spin component. Apparatus The rig, shown schematically in Fig. 26, consists of a circular base A, supporting a roller By and a semicircular vertical ring C to which the toroid is attached. The semicircular ring is perpendicular to the plane of the base and is constrained by an extended strain-gauge ring D which allows movement in the plane of the ring. It can be shown (38) that the kinematic relation between general types of ball motion can be specified by two \u2018angle\u2019 parameters, as shown in Fig. 27. The spin ratio is given by tan a and the slide/sweep ratio by tan ,8. By adjusting the vertical and the base rings any orientation of the ball axis with respect to the track can be achieved. Both angles can be read directly from the vernier scales to within one-tenth of a degree. It was found necessary, however, to subdivide the vernier scale by means of a micrometer screw to 0.001 of a degree in order to have the degree of accuracy required. The rig when used for sliding experiments is not dissimilar to that used by Smith (33) and Misharin The extended octagonal ring D with eight strain gauges is mounted on the adjustable platform by means of two flexible cross-springs",
            " It is one of the lubricants which has been extensively used by earlier investigators and a great deal is known about its physical properties (32) (43). Its viscosity varies from 3.30 to 0.66 P between 18 and 40\u00b0C. The corresponding variation of the pressure viscosity coefficient y is estimated to be from 2-98 to 2.5 x cm2/dyn. In this section the tangential force arising from rolling with spin (44) and rolling with slide is considered and related to the rolling speed. The mean surface velocity U for a given kinematic relation between the rolling elements can be derived from Fig. 27. However, for a small angle /3 (say /3 < 6\") it is approximately R,wl, where w1 is the angular velocity of the cylinder. This is true provided no gross slip takes place between the ball and the roller in Results and discussions To illustrate the general pattern of the frictional behaviour of rolling with spin and slide some of the results are plotted in Figs 32a and 32b. Despite the difference in their kinematics, the two families of curves look strikingly similar and the region to the left of the 'knee' or sharp change which occurs in the neighbourhood of U = 480 ft/min has been termed the primary transition region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001900_978-1-4020-8829-2_11-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001900_978-1-4020-8829-2_11-Figure5-1.png",
        "caption": "Fig. 5. Spherical motion (left) and screw motion about axis h (right)",
        "texts": [
            " The Principle of Transference can be stated as follows [10,18,24]: All valid laws and formulae relating to a system of intersecting unit line vectors (and hence involving real variables) are equally valid when applied to an equivalent system of skew vectors, if each variable a, in the original formulae is replaced by the corresponding dual variable a\u0302 = a + \u03b5ao. By virtue of the Principle of Transference, formulas for the composition of spherical motions can be extended to the general helicoidal motion case by simply substituting the angle of rotation \u03b8 with the dual angle \u03b8\u0302 = \u03b8 + \u03b5s, where s is the displacement of the body along the screw axis. Extension of Rodrigues\u2019 Formula With reference to the geometry of Fig. 5, let r2 be the position of vector r1 after a rotation about axis of versor u of an angle \u03b8. The well known Rodrigues\u2019 formula, in vector notation, can be rewritten in the form r2 = r1 + 2\u03c4 1 + t2 \u00d7 (r1 + \u03c4 \u00d7 r1) , (28) where t = tan \u03b8 2 and \u03c4 = tu. When \u03b8 = \u03c0 the previous expression cannot be applied and the following should be adopted r2 = 2 (u \u00b7 r1) u \u2212 r1 . (29) By applying the principle of Transference, the Rodrigues\u2019 formula (28) can be generalised to define a screw motion about the line vector defined by E\u0302 as follows R\u03022 = R\u03021 + 2T\u0302 1 + tan2 \u03b8\u0302 2 \u00d7 ( R\u03021 + E\u0302 tan \u03b8\u0302 2 \u00d7 R\u03021 ) , (30) where \u2013 \u03b8\u0302 = \u03b8 + \u03b5s is the dual angle whose primary part is the angle of rotation and s the displacement along the screw axis (see Fig. 4); \u2013 R\u03021 and R\u03022 are the initial and final positions of a line vector framed to the rigid body, respectively (see Fig. 5). Composition of Finite Screw Motions Let us specify two spherical rotations: the first one of an angle \u03b81 about the axis u1 and the second of an angle \u03b82 about the axis u2. Hence, the components of the vectors \u03c4 i = tan \u03b8i 2 ui, (i = 1, 2) , (31) can be computed. It can be demonstrated [19, 20] that the resultant spherical motion is defined by the following vector \u03c4 3 = \u03c4 1 + \u03c4 2 \u2212 \u03c4 1 \u00d7 \u03c4 2 1 \u2212 \u03c4 1 \u00b7 \u03c4 2 . (32) Consider two finite screw motions about the axes located by the unit line dual vector E\u0302i (i = 1, 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure10-18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure10-18-1.png",
        "caption": "FIGURE 10-18 (a) European-style tire with wider lugs for improved road wear. (Courtesy Goodyear Tire and Rubber Co.) (b) Japanese-style tire for rice soil conditions. (Courtesy Bridgestone Tire Co., Japan.)",
        "texts": [],
        "surrounding_texts": [
            "TREAD DESIGN\n261\nThe decision as to which tire tread performs best is also dependent on the criteria being used. Some of the criteria are;\n1. Tractive efficiency 2. Net tractive coefficient 3. Tire life 4. Soil compaction",
            "262",
            "Effect of Lug Spacing\nA study was made by Taylor (1974) on the effect of lug spacing on 11.0-38 (279-965 mm) tires. The number of lugs per side on the five tires tested was 20, 23,. 26, 29, and 32, which gave a pitch (in millimeters) of 238, 207, 178, 164, and 148. Taylor found (see fig. 10-19) that when the tires were tested on sad the maximum pull occurred when using the 23-lug tire. On the other soil conditions tested, lug spacing had little effect.\nTraction Improvement\nFor certain soil conditions, traction aids are helpful. Table 10-4 shows the relative improvement of three traction aids. Strakes and half tracks are more commonly used in Europe. Table 10-5 shows the relative effect of adding weight and increasing the contact area (larger tires).\nTractors with both rubber tires and wheel extensions (strakes) are com monly used on weak surfaces such as rice paddy soils.\nRubber traction tires, as compared to steel traction wheels, have greatly improved the tractive efficiency, maneuverability, and comfort of farm trac tors. Except on very firm soils, however, rubber tires have not increased the traction. In fact, under some conditions, such as when the surface of the soil is very wet and slick or when the soil is covered with a thick cover crop, the traction of rubber tractor tires is poor."
        ]
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure11-1.png",
        "caption": "Figure 11. FE modelling of bearing housing, bearing and shaft. (a) Roller spring modeling approach, (b) complete FE-model sliced view and (c) spring stiffness comparison.",
        "texts": [
            " Rolling element bearings constitute a significant FEmodelling challenge due to the high number of contacts between the rollers and raceways. Efficient approaches for FE-modelling of roller bearings, where each roller is approximated as a number of axially distributed non-linear springs connecting the bearing inner and outer raceway are presented in refs [22,23]. Apart from the high generality of this method, it does not involve contact elements, which again allows for relative coarse modelling mesh, short solution time and good convergence performance. Figure 11(a) shows a sketch of nine uniformly distributed springs connecting the inner and outer raceway in a tapered roller bearing. In the simplified modelling, the flange contact is neglected and the springs are perpendicular to the outer raceway. The effect of the flange induced roller tilt moment can easily be included in the pressure post-processing of the roller/raceway contacts by including the necessary flange force and moment on each roller in the pressure calculation. Many different theoretical and empirical expressions exist for the roller/raceway contact deflection, see ref [5] for an overview of several commonly used relationships",
            "comDownloaded from The springs are uniformly distributed along the roller length and the position of each spring is calculated as xk \u00bc l 2 \u00fe l nk \u00f0k 0:5\u00de \u00f038\u00de The roller profile defined in equation (28) is now included in the spring stiffness definition by subtracting the profile from the spring deflection. Since rollers only transfer forces in compression, the force deflection relationship for spring k is qk \u00bc kk k 2 Cp\u00f0xk\u00de 10 9 if jk 4 2 Cp\u00f0xk\u00de 0 if jk42 Cp\u00f0xk\u00de 8< : \u00f039\u00de To verify the inner and outer raceway contact stiffness using the relationships in equations (34) and (39), the agreement with the results shown in Figure 8(a) (for i\u00bc 0 and the equivalent results for the outer raceway) is compared in Figure 11(c). In this comparison, only the inner and outer raceway contact stiffness is compared and equation (34) is directly inserted in equation (39), where the profile is only multiplied with one to consider only one raceway contact. This comparison shows that using a discrete number of springs, the stiffness relationship from ref [24] and subtracting the profile has an excellent stiffness agreement with the detailed approach used to calculate the resultant contact force shown in Figure 8(a). The FE model, shown in Figure 11(b), is created in ref [25] and consists of approximately 90,000 elements and 386,000 nodes. A total of 30 springs are used to represent each roller, which has shown to be well above what is required to achieve converged results. The solid mesh consists of twenty-node hexahedral elements. It is assumed that the bearing rings are properly mounted without clearance, misalignment, etc. In this study, the bearing rings are connected to the housing/shaft elements using bonded contact formulation but other mounting setups such as thermal shrink fit and frictional contact could be modelled"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003487_tmag.2016.2526614-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003487_tmag.2016.2526614-Figure7-1.png",
        "caption": "Fig. 7 Flux density and loss distribution of PMSM. (a) Flux density for Id=0 and SF=20kHz; (b) Flux density for Id=-8.32 and SF=3.59kHz; (c) Iron loss for Id=0 and SF=20kHz; (d) Iron loss for Id=-8.32 and SF=3.59kHz.",
        "texts": [
            " In order to validate the proposed ABC efficiency improvement, the experimental setup shown in Fig.5 has been employed. Fig. 6 shows overall efficiency improvement of the motor-inverter system during full power range based on ABC algorithm proposed in this paper. And the optimum SFs and Ids for are operation points are shown in TABLE II. Both the original phase current and optimal current are measured and assigned into 2D FE model of the motor in JMAG. The flux density distribution and iron loss at 1500rpm and 24N are shown in Fig.7. The optimal flux density is smaller than the original one under the same load power condition. Therefore, 0018-9464 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. GJ-07 4 the iron loss reduces from 52.13W to 44.73W for Id=-8.32 and Fs=3.59kHz. Meanwhile, the decreases of copper loss and inverter loss are 18.48W and 365.5W obtained by measured, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003120_ifs-2012-0569-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003120_ifs-2012-0569-Figure1-1.png",
        "caption": "Fig. 1. Inverted pendulum system.",
        "texts": [
            " We used PSO algorithm in this paper because this algorithm has very simple structure and the equations are simpler other than algorithms such as Genetic. This characteristic causes to speed our system\u2019s capability. Computational speed is very important item for considering in industrial applications. 8. Simulation results In this section, illustrative numerical simulation examples are provided to demonstrate the effectiveness and robustness of the proposed approach. The problem to be considered is a pole-balancing of an inverted pendulum as shown in Fig. 1. The system is represented by \u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 x\u03071 = x2 x\u03072 = mlx2 2 sin(x1) cos(x1) \u2212 (M + m)g sin(x1) ml cos2(x1) \u2212 ( 4 3 )l(M + m) + \u2212 cos(x1) ml cos2(x1) \u2212 ( 4 3 )l(M + m) u(t) + d(t) (38) Where x1angle \u03b8 (in radians) of the pendulum from the vertical, M mass of cart, m mass of the pole, u(t) force applied to the cart and d(t) is an external disturbance. The parameters employed in this simulation are given as follows: M = 1 kg , m = 0.3 kg, l = 0.5 m and g = 9.8 m / s2. In this simulation, the known parts of f (X(t))and g(X(t)) are listed as follows:\u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 f\u0302 (X(t)) = m\u0302l\u0302x2 2 \u2212 (M\u0302 + m\u0302)g\u0302 m\u0302l\u0302 \u2212 4 3 l\u0302(M\u0302 + m\u0302) g\u0302(X(t)) = \u22121 m\u0302l\u0302 \u2212 4 3 l\u0302(M\u0302 + m\u0302) (39) The values of parameters m\u0302, l\u0302, M\u0302 and g\u0302 are considered to be 90 percent of their real values"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002665_iet-epa.2011.0092-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002665_iet-epa.2011.0092-Figure1-1.png",
        "caption": "Fig. 1 Configuration of the investigated SRM",
        "texts": [
            " The mechanical formula of SRM is given by the following equation Te = J du2 j dt2 + D duj dt + TL (2) where Te is electromagnetic torque of SRM, J is the moment of inertia of rotor, D is coefficient of viscosity and TL is load torque. The above two equations are correlated with following instantaneous electromagnetic torque formula Tj = \u2202 \u2202u \u222bij 0 cj di (3) where Tj is instantaneous torque of phase j, Tj is generated when phase winding is excited and the phase inductance varies with the rotor position. Fig. 1 shows the configuration of the prototype SRM. The numbers of stator and rotor poles are 12 and 8, respectively. The details of the SRM parameters are shown in the Appendix. Training data of NN can be acquired through direct measurement of SRM in operation or by FEA [15]. In this paper, the data of phase current, flux-linkage and rotor position are obtained by FEA to train NN. Fig. 2 shows the relationship between rotor position, phase current and fluxlinkage. As presented in this figure, the rotor angle ranges from aligned position 08 to unaligned position 222"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure3-1.png",
        "caption": "Fig. 3. Fully plastic stress distributions for a hollow disc rotating at maximum speed according to (a) von Mises and (b) Tresca",
        "texts": [
            " Tresca also predicts a greater spread of plasticity (rep 136:875 mm, rep=ri 2:738) than von Mises at similar speeds. These differences influence the normalised distributions of residual stress sRq =Y and sRr =Y for each criteria in the manner shown. We shall see later how residual stress are put to advantage when a disc rotates at its normal elastic speed. Figs. 3a, b present further comparisons between the two criteria for a fully plastic disc of similar dimensions. Here the von Mises numerical solution (Fig. 3a) gave a maximum speed of 1311.6 rad/s (12525 rev/min). The speed by Tresca (Fig. 3b) is found from eq. (21a) to be a lower value 1244.3 rad/s (11882 rev/min). There are also differerences in the stress magnitudes since Tresca conforms to sq Y and von Mises obeys eq. (2). According to the latter the residual hoop stress within the bore has exceeded its compressive yield value sRq =Y < \u00ff1 , i.e., reversed yielding has occurred in the bore fibres. A pre-speed should be selected to induce residual stress without reversed yielding occurring. This is to avoid the Bauschinger effect as the hoop stress becomes tensile at subsequent elastic speeds. The numerical solution confirmed that sRq \u00ffY at the bore when rep 150 mm for a Mises disc rotating at a speed of 12000 rev/min. As a rule of thumb when rep coincides with the mean radius the bore stress will be close to the reversed yield point. In contrast, with Tresca, a reversed yield condition arises only when rep ro (see Fig. 3b). The high speeds found are a consequence of the rather large radius ratio ro=ri 5 chosen to make these comparisons. 3.2 Solid disc Next consider a thin, solid steel disc with outer radius 250 mm of similar material properties rotating at a speed of 13000 rev/min. This lies between the initial yield speed of 11930 rev/min and a fully plastic (Tresca) speed of 13232 rev/min from eqs. (20b) and (21b), respectively. In this case a von Mises numerical solution to the interior elastic-plastic stress distribution was initialised for N 50 (h 5 mm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003354_icra.2014.6907498-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003354_icra.2014.6907498-Figure5-1.png",
        "caption": "Fig. 5. The catheter is anchored at the anchor shaft A, it describes a circular path with radius R with parameters l j and a j . The length of the catheter l j is governed by the PEA while orientation a j is controlled by the OctoMag.",
        "texts": [
            " To simulate the control of the magnetic catheter tip on a circular path, a kinematic model is derived in MATLAB that calculates the motion parameters of the catheter. It is assumed that there is zero curvature along the length of the catheter, i.e. that it is a straight line at all times. The user defines the anchor point A of the catheter, at which a shaft restricts the lateral motion of the catheter, corresponding to the insertion point in a physical procedure. To approach the circular path, described by points Kj = (x j ,y j ), the catheter travels a predefined longitudinal distance of length L, as illustrated in Figure 5. The length l j of the catheter at point Kj is given by l j = kAKjk whereas the angle of orientation of the catheter tip a j is given by a j = arcsin x j kAKjk ! (5) Figure 6 illustrates the parameters a j and l j versus time. In this example, a circle with radius R= 5 mm is circumscribed by the simulated catheter tip within a time of 10 s where distance L = 3 mm. For model based closed loop control the catheter tip is visually tracked at all times using a blob tracking algorithm, which detects the current position (x t ,y t ) of the catheter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002718_978-3-642-22164-4_1-Figure1.4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002718_978-3-642-22164-4_1-Figure1.4-1.png",
        "caption": "Fig. 1.4 Solving the harmonic balance equation for TA",
        "texts": [
            "15) where a is the generic amplitude of the oscillation at the input of the nonlinearity and W ( j\u03a9) is the complex frequency response characteristic (Nyquist plot) of the plant. Using the notation of the twisting algorithm this equation can be rewritten as follows: W ( j\u03a9) =\u2212 1 N(a1) , (1.16) where the function on the right-hand side is given by: \u2212 1 N = \u03c0a1 \u2212c1 + jc2 4(c2 1 + c2 2) . Equation (1.15) is equivalent to the condition of the complex frequency response characteristic of the open-loop system intersecting the real axis at the point (\u22121, j0). The graphical illustration of the technique of solving equation (1.15) is given in Fig. 1.4. The function\u2212 1 N is a straight line, the slope of which depends on the c2/c1 ratio. This line is located in the second quadrant of the complex plane. The point of intersection of this function and the Nyquist plot W ( j\u03d6) provides the solution of the periodic problem. This point gives the frequency of the oscillation and the amplitude a1. Therefore, if the transfer function of the plant (or plant plus actuator) has relative degree higher than two, then a periodic motion may occur in such a system. For that reason, if an actuator of first or higher order is added to the plant of relative degree two driven by the twisting controller a periodic motion may occur in the system. The conditions for the existence of a periodic solution in a system with the twisting controller can be derived from the analysis of Fig. 1.4. Obviously, every system with a plant of relative degree three or higher would have a point of intersection with the negative reciprocal of the DF of the twisting algorithm and, therefore, a periodic solution would exist. Fig. 1.5 Block diagram of the system governed by STA This is applicable to so called \u201c twisting as a filter\u201d algorithm. The introduction of the integrator in series with the plant makes the relative degree of this part of the system equal to two. As a result, any actuator introduced in the loop increases the overall relative degree to at least three"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000764_s0094-114x(97)00022-0-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000764_s0094-114x(97)00022-0-Figure4-1.png",
        "caption": "Fig. 4. Location and orientation of axes of meshing.",
        "texts": [
            " AXES OF M E S H I N G Litvin [2] has proven the following theorem: tooth surfaces are in line contact at every instant and one of the interacting surfaces is a helicoid. Then, there are two straight lines I-I and II-II that lie in parallel planes, have constant location and orientation during the process of meshing, and the normal to the interacting surfaces at any regular point of surface tangency passes through I-I and II-II. These lines are called the axes o f meshing. parameter p of the helicoid approaches to infinity. The location and orientation of the axes of meshing in this particular case is as shown in Fig. 4. Axis of meshing I-I lies in plane x~ ~) = 0, and its orientation is determined as Z \") N2 y~l) Ns (2) Meshing of orthogonal offset face-gear drive 91 Axis of meshing II-II is parallel to Zh but lies in a plane x~ \") that approaches infinity along the negative direction of Xh. 4. EQUATION OF TOOTH SURFACES 4.1. Applied coordinate systems Movable coordinate systems Ss and $2 are rigidly connected to the shaper and the face gear, respectively (Fig. 2). Coordinate systems Sh and S~ are the fixed ones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure10-21-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure10-21-1.png",
        "caption": "FIGURE 10-21 Lug wheels used in paddy fields. (a) Open lug wheel; (b) float-type lug wheel. (From Tanaka 1984.)",
        "texts": [
            " Cone indices will typically be less than 50 N/cm. Performance of regular rubber-tired wheels is not acceptable because of high slippage and adhesion of sticky soil. Specially designed high-lug rubber tires as shown in figure 1 0-18( b) are commonly used in paddy fields. Farm tractors and other farm vehicles that are operated in these condi tions often require special devices used with tires or in place of tires. As an example of some typical devices, an open lug wheel and a float lug wheel are shown in figure 10-21. Figure 10-21(a) shows the open lug wheel for a two wheeled power tiller. The average weight of a power tiller is in the 200- to 300-kg range, with average engine power of7.0 Kw. The lug plates are welded to a circular rim. Many types and shapes of lug plates are in use for paddy field operations. Figure 10-21(b) shows a lug wheel used as an auxiliary device with a tractor tire. Float-type lugs are connected to the circular ring plate, and the lugs can be folded toward the center of the wheel when the tractor operates on a hard surface or paved road. Development of traction and transport performance prediction equa- TRACTION DEVICES FOR PADDY FIELDS 267 tions for paddy field conditions is extremely challenging. Tanaka (1984) provides a state-of-the-art overview of analytical work and an extensive bib liography"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001943_0141-0229(81)90031-4-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001943_0141-0229(81)90031-4-Figure1-1.png",
        "caption": "Figure 1 Oxygen-stabilized enzyme electrode. A, Electrode glass body; B, oxygen electrode output; C, oxygen electrode Teflon membrane; D, Pt-gauze with immobilized enzyme (electrolysis anode); E, dialysis membrane; F, Pt-coil wired around the electrode (electrolysis cathode); G, electrolysis electrode terminals",
        "texts": [
            "35 glucose oxidase units/rag (~0.6 units/rag) and 1 mg catalase from beef liver, (United States Biochemical Corp., Ohio, USA) containing 5755 units/mg, were dissolved with 20 mg bovine serum albumin (BDH Chemicals Ltd, England) in 0.25 ml 25 my phosphate buffer, pH 7. To this was added 0.1 ml of a 2.5% solution of glutaraldehyde, (Merck, W. Germany) and the Pt-gauze was wetted with the mixture, and then placed in a refrigerator for polymerization overnight. Electrode design The glucose electrode (Figure 1) was built on a galvanic oxygen electrode, according to Johnson e t al. 16 modified only with respect to the membrane, which was a 0.025 mm thick Teflon membrane (Habia, Knivsta, Sweden). A thin Pt-wire was tied to the N-gauze which was then pressed against the Teflon membrane of the oxygen electrode by means of a dialysis membrane (regen. cellulose, 24 A, Union Carbide) and kept in place by an O-ring. The Pt-wire, which was used as electrical connector to the N-gauze, was isolated against the glass tube of the oxygen electrode with a polyolefin heat-shrinking tube. Mound this tube, close to the sensitive surface of the enzyme electrode, another Pt wire, ((/50.1 ram, length 500 ram), was wired around the tube to form an electrolysis cathode, as shown in Figure 1. Electronic circuit The enzyme electrode was connected to a similar oxygen electrode to give a differential potential as shown in Figure 2. Zero differential potential was used as the set value for electrolysis in the enzyme electrode, where the enzymecovered N-gauze was the anode and the other N-wiring was the cathode. The voltage difference was amplified and fed E F G J.( H a i l i i i i Figure2 Principle of the electronic circuit used for the oxygenstabilized enzyme electrode. A, Enzyme electrode; B, reference electrode; C, reference electrode potential, used also as a measure of the dissolved oxygen tension in the broth; D, differential partial pressure of oxygen between the two electrodes (z3~OO~); E, differential amplifier; F, PI-regulator; G, current controller consisting of an LED and a photoresistor mounted in an aluminium block; H, Pt-gauze with immobilized enzyme, I, Pt-coil; J, microammeter (electrolytic current) to a Pl-regulator which controlled the current through the electrolysis cell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001758_robot.2008.4543731-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001758_robot.2008.4543731-Figure2-1.png",
        "caption": "Fig 2: Forces acting on a cable element",
        "texts": [],
        "surrounding_texts": [
            "A. System Governing Equation Consider an infinitesimal cable segment [x, x+dx] with negligible inertia and Coulomb friction acting on it due to contact with the conduit. For this small segment the radius of curvature can be assumed to be constant R(x), where x is the distance of a point along the conduit. Define u(x,t) as the axial displacement of the cable, T(x,t) as the axial cable tension in the. N(x,t) denotes the normal force between the cable and the conduit and f(x,t) denotes the frictional force acting on the cable. When the net axial tension force T(x+dx,t)-T(x,t) = T'(x,t)dx is less than the limiting value of friction the cable segment will not move due to the Coulomb friction, i.e. T . . > T'(x,t) ( , ) 0 ( , ) T'(x,t)dx R x s t u x t and f x t \u00b5 \u2200 \u21d2 = =\u027a (1) On the other hand, when the cable segment moves due to the net axial tension, by force balance along the axial direction: ( , ) ( ) 0 T T x t dx sign u dx when u R \u00b5 \u2032 = \u2260\u027a \u027a (2) To calculate the cable strain Hooke\u2019s law of elasticity is used, modeling cable-conduit system as a linear spring with stiffness keq. The governing strain equation is given by: (x,t) (x,t) T K \u03b5 = (3) where eq k defines the equivalent stiffness of the cable- conduit system give by: 1 1 1 eq cable conduit k k k = + (4) B. Discrete Element Model Partial differential equations in (1) to (3) define the dynamics of the system. However, due to the discontinuous nature of the friction present in the system, it is difficult to solve the equations. Therefore, for computational simplicity, a discrete element formulation is used by dividing the cable into n segments and calculating the displacement and tension of each node at discrete time instants. Consider the i th cable segment between nodes i and i+1. Let T(xi,tj) and u(xi,tj) be the tension and the displacement of the i th node, respectively at time tj. We neglect small variations in radius of curvature over the cable segment, and denote the radius by R(xi). Based on the motion, cable segments can be divided into three different categories. Case 1: When the entire cable segment is moving, since ( ), 0u x t \u2260\u027a , (2) can be integrated to relate the tension and displacements at the two ends as: ( ) ( ) ( ) ( ) ( )1 1 1, , exp ( , ) ( , ) i i i j i j i j i j i x x T x t T x t sign u x t u x t R x \u00b5 + + \u2212  \u2212 = \u22c5 \u2212     (5) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 ( , ) ( , ) ( , ) ( , ) , exp ( , ) ( , ) , , 2 i i j i j i j i j eq i i i j i j i j i i j i j i i eq R x u x t u x t sign u x t u x t k x x T x t sign u x t u x t R x T x t T x t x x k \u00b5 \u00b5 + \u2212 + \u2212 + + \u2212 = \u2212  \u2212 \u2212     + \u2212 \u2248 i (6) Case 2: When the entire cable segment is stationary, the strain and therefore the tension of the segment will not change, i.e. -1 1 1 -1 -1 1 1 -1 ( , ) ( , ) ( , ) ( , ). ( , ) ( , ) ( , ) ( , ). i j i j i j i j i j i j i j i j T x t T x t and T x t T x t u x t u x t and u x t u x t + + + + = = = = (7) Case 3: A part of the cable segment is moving, while the rest of it is stationary. Assume that node i is moving, while node i+1 is stationary. From (7), for the stationary section of the cable segment, j j-1 j j-1 T(x,t ) = T(x,t ) and u(x,t ) = u(x,t ) . The displacement of the stationary section can be approximated by the displacement of the last moving point of the cable segment. Therefore, we can approximate that (6) holds true. On moving one end of the cable initially only a part of the cable moves, and as the tension at the input end changes, motion gradually propagates across the cable. If the first k nodes are moving at some time instant tp, we need to solve for the cable stretch and tension of the first k segments, solving 2k-1 equations simultaneously for tension of the first k nodes, and displacement of node 2 to node k. When the k th cable segment satisfies eq. (5), motion propagates to the next node and node k+1 becomes the last moving node. C. Single Cable Simulation Before simulating the closed loop system, simulations were carried out to characterize the tension transmission across a single cable. A desired motion profile is provided to the actuator end of the cable, and the tension at the two ends of the cable is calculated. Simulation results are plotted in Fig. 4 for two cases: 1. Pretension is high such that the cable does not slack; 2. Pretension is low, such that the cable becomes slack during the motion. These simulation results are similar to the lumped mass model and experimental results performed Kaneko et al. [5, 6], which also justifies the assumption of negligible cable inertia. It has been shown that due to tension losses across the cable, tension transmission may not be continuous across the cable. This leads to a period during which the movement of one end of the cable does not lead to the movement of the other end. The other end starts to move only when the tension change on the first end is significant enough to overcome friction. Thus it follows a backlash type of force transmission profile. D. Closed loop cable-conduit Simulation We extend the simulation of single cable to the case of closed loop system, assuming no slacking at the two pulleys. One end of each cable (cable A and cable B as shown in Fig 5) is fixed to the drive pulley while the other end is anchored to the follower pulley. Apart from the assumption of small cable motion, we can also assume that the nodes on one side of the pulley do not move to the other side. This assumption is reasonable since we always have some part of cable exposed without a conduit where no friction is acting, and therefore can be taken towards the compensation for the cable motion. Similar to the case of single cable described above, the simulations are carried out with the constraints for torsional spring and no slacking at the pulleys, 4 2 ( ) o e o o K T T R\u03c4 \u03b8= \u2212 = \u2212 (8) 3 2 2 o o x x R \u03b8\u2212 = (9) 2 3 x x L+ = (10) where \u03c4o is the torque being applied by the load motor, o \u03b8 is its angular rotation, Ro is the radius of the pulley at the load motor, Ke is the simulated environment stiffness, L is the sum of two cable lengths (with pretension), T1,2,3,4 denote the tension at the four ends of the cable, and x1,2,3,4 denote the position of the corresponding ends. The input motor is provided with a sinusoidal oscillatory motion profile. For each time step the motion of the input motor is calculated and based on that, we determine the \u2018last moving node\u2019 on each side of the pulley, and the tension and displacements of all the nodes up to the last moving node. Consider the time period when one end cable A is moving, while the other end is stationary, i.e. there is some intermediate node on the cable A which is the last moving node. During this period, cable A will act as an independent cable, the motion of which will not affect the motion of cable B. Therefore during the time period when the last moving nodes of the two cables do not coincide, there is no interaction between the two cables and the motion of the two cables can be solved independently. Once the last moving nodes of the two segments coincide, the entire system follows a collective motion. Based on the above analysis, the motion of the system can be divided in two categories, both sides of cable taut, or either side of cable slack. When one side of the cable goes slack the other side still moves as an independent cable. E. Simulation Results Analysis Apart from the backlash profile in motion and torque transmission, several other atypical phenomena are observed. Fig. 6 shows the variation in the tension at the two ends of the cable for both cables, input (load) torque vs output (drive) torque profile, and input vs output angular rotation. For the ease of understanding, various time instances in the motion and the sequence of motion propagation have been marked in Fig. 6, which are described as follows: 1. Drive motor starts to rotate counterclockwise such that cable A is getting stretched, while cable B is released. 2. Motion has propagated across cable B and it starts to move load pulley. Motion has only been propagated in cable A till some intermediate point, and a part of cable A is still stationary. 3. Motion has propagated to the end of cable A, and both cables start to move. 4. Cable B goes slack. 5. Input motor reverses its direction of motion, while cable B still remains slack, load pulley is not moving. 6. Cable B starts to move after getting taut again, and it moves the load pulley. Motion has only propagated in cable A till some intermediate point. Similar to stage 2. 7. Both cables start to move, but in direction opposite to that of stage 3. 8. Cable A goes slack. 9. Cable A remains slack, input motor changes direction of motion, similar to stage 5, but slack cable and direction of motion has been changed. 10. Cable A starts to move after becoming taut, and starts After stage 11, next stage coincides with stage 3, and stages 3-11 keep on repeating thereafter. Based on these stages the motion can be divided into following phases: I. Output pulley not moving (Time interval between stages 1-2, 5-6, 9-10) \u2013 Motion has not propagated to the distal ends (i.e. the load pulley) in either of the cable. The load pulley remains stationary, and it translates to the backlash region in the transmission profile. II. One cable pulling another cable (Intervals 2-3, 6-7, 10-11) \u2013 The tension variation at the two ends of the cable are opposite to each other, i.e. when tension at one end of the cable is increasing (or decreasing), but on the other end it is decreasing (increasing). This translates to the small slope in the torque backlash profile, which has also been referred as soft spring [3]. The motion of the output pulley is influenced only by one cable, while the other cable remains inactive. In this phase one of the cables is not moving, but it is not slack, i.e. the pretension is high enough to avoid any slacking. III. Both cables moving (Intervals 3-4, 7-8, 11-3) - Entire system is moving collectively. This translates to the directly proportional part of the transmission profile. IV. One cable goes slack while other cable keeps moving (Intervals 4-5, 8-9) - Since the motion is governed by one motor, similar to phase II, the slope in the torque as well as theta profile reduces. V. Change of direction of motion of one cable, while From these plots, it is evident that friction not only causes a backlash type of tension transmission profile, but also results in other phenomenon, such as changes in the slope of the transmission, introduction of small slopes in the torque transmission (intervals 6-7, 1-11), as well as opposite tension variations at two ends of the cable. Apart form the transmission profile, all these phases are most predominantly visible in the plot of input torque versus input theta (Fig 7). This also provides evidence that if the state of the system friction is know, the motion of the load pulley and cables can be predicted based on the motion of the drive pulley."
        ]
    },
    {
        "image_filename": "designv10_10_0003515_tasc.2016.2602500-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003515_tasc.2016.2602500-Figure2-1.png",
        "caption": "Fig. 2. (a) 2-D FE model for the BLDCM, (b) 2-D FE models for the winding C- with mesh.",
        "texts": [
            " Section V gives the results and the conclusions. Fig. 1 shows the structure and the cross section of the ironless BLDCM and Table I gives the basic specifications. The BLDCM includes an iron-less armature (fixed in a fiber frame), an iron core and the permanent magnets. In this paper, the AC copper losses are carried out by using two-dimensional (2D) FE model. In order to consider the skin effect and proximity effect for the windings, the models with a large number of winding wires inside the slots are created, as shown in Fig. 2. To consider the effect of the winding wire diameter, several winding models with different wire diameter in parallel are created. The total cross-sections of the winding wires are the same. The motor runs in the specific speed (fm = 2 kHz), and three phase sinusoidal currents ia = Ia \u00b7 sin(2\u03c0fa \u00b7 t + \u03b8a) 1051-8223 \u00a9 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001162_20050703-6-cz-1902.00489-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001162_20050703-6-cz-1902.00489-Figure1-1.png",
        "caption": "Fig. 1. A Schematic of the Turbofan in MAPSS",
        "texts": [
            " A basic tracking controller can be used in place of (11) to improve the tracking error. )()1( 1100 )()( n n n n YZYKZYKU \u2217\u2212\u2217 \u2212 \u2217 +\u2212++\u2212= L (15) The Modular Aero-Propulsion System Simulation (MAPSS) package, developed by (Parker and Guo, 2003) at the NASA Glenn Research Center, was used for this demonstration because of its flexibility and availability. A component-level model (CLM) within MAPSS consists of a two-spool, high pressure ratio, low bypass turbofan with mixed-flow afterburning. The engine schematic from Mattingly (1996) is illustrated in Fig 1. The model consists of hundreds of coupled equations and look-up tables that ensure mass, momentum, and energy balances throughout while modeling gas properties effectively. Mathematical details are found in books by Mattingly (1996), Boyce (2002), and Cumpsty (2002). A simplified top-level diagram is illustrated in Fig. 2. In general, the CLM is defined by two nonlinear vector equations ),,,,( ),,,,( xmaltpuxgy xmaltpuxfx CLMCLMCLM CLMCLMCLM = =& (16) that are functions of a 3\u00d71 state vector (xCLM), a 7\u00d71 input vector (uCLM), a 10\u00d71 health parameter vector (p), altitude (alt), and Mach number (xm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003719_tmag.2016.2524589-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003719_tmag.2016.2524589-Figure1-1.png",
        "caption": "Fig. 1. Simplified geometry of a two\u2013pole toroidally\u2013wound brushless dc machine.",
        "texts": [
            " The theory is applied to a two\u2013pole toroidally-wound brushless DC (BLDC) motor, but the resulting force model can be used for any two\u2013pole uniform\u2013gap permanent\u2013magnet synchronous motor. Since no prior literature exists that applies the perturbation theory to the machine type dealt in this paper, the air gap magnetic field without eccentricity is first summarized. Then the perturbation theory is applied to obtain the eccentric air gap magnetic field. Using this distorted magnetic field solution, analytical model for the radial forces are derived. The validity of the model is verified against finite\u2013 element analysis (FEA). Illustrated in Fig. 1 is the simplified geometry of a two\u2013 pole toroidally\u2013wound brushless dc machine. It consists of a permanent\u2013magnet rotor and a stator carrying three pairs of coils. The theory developed here is applicable not only to this type of toroidally\u2013wound machine but also to any two\u2013pole non\u2013salient permanent\u2013magnet machine (for example [8]). The air gap magnetic field for this machine without eccentricity is well studied in the literature (e.g. [9], [10]). Only the final form of the air gap field is included here as a starting point for modeling the case with eccentricity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001179_s0263574701004039-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001179_s0263574701004039-Figure1-1.png",
        "caption": "Fig. 1. Configuration of the parallel manipulator.",
        "texts": [
            " Section 2 describes the architecture of a parallel manipulator and its dynamic modeling. Section 3 gives an active damping method for vibration of linkages and Section 4 gives simulation results. Finally, conclusions are given in Section 5. Robotica (2002) volume 20, pp. 329\u2013339. \u00a9 2002 Cambridge University Press DOI: 10.1017/S0263574701004039 Printed in the United Kingdom http://journals.cambridge.org Downloaded: 06 Jul 2014 IP address: 129.174.21.5 The architecture of the parallel mechanism considered is illustrated in Figure 1. The platform has a regular triangular shape and is supported by three intermediate links assumed to exhibit structural flexibility. Therefore, vibration of the linkage gives a direct influence on motions of the platform. Both ends of the intermediate link are composed of nonactuated revolute joints. A slider connecting with the linkage is driven by a linear actuator. The proposed planar manipulator is categorized as a PRR type, because one closed chain consists of the prismatic joint and two consecutive revolute joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000792_s1361-8415(98)80006-6-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000792_s1361-8415(98)80006-6-Figure8-1.png",
        "caption": "Figure 8. Principle of the rotational CVT and application to serial kinematic robots. Two drive rollers are attached to two successive links and two passive rollers stabilize the central sphere. The CVT orients the steering roller to the controlled angle \u03b3 (called \u03b8 in the left-hand figure) such that tan \u03b3 = \u03c92/\u03c91.",
        "texts": [
            " It can however enforce a constraint surface, which, in this example, should be understood as a constraint curve in the planar workspace. It can enforce this constraint simply by steering the wheel parallel to it. Because the rolling wheel at each moment can only be moved in the direction in which it is aimed, the user perceives an impenetrable boundary at the constraint surface. In practice, this illusion is convincing. Since the constraint arises mechanically, it is smooth and frictionless. CVTs have been also designed for arm-like cobots with revolute joints. By analogy a rotational CVT (cf. Figure 8) holds two angular joint velocities in proportion T = \u03c92/\u03c91. T = tan \u03b3 is computer controlled using a steering roller. For an n-joints cobot, (n \u2212 1) CVTs are necessary to couple the n-joints such that a trajectory in space may be executed. Since the CVT rolling wheels must roll without skidding, there could be a practical design limitation on the constraining force that can be applied. Cobot very naturally allows the execution of trajectories in space. \u2018Free motion\u2019 and \u2018motion in a region\u2019 modes are not the intrinsic modes and must be achieved through computer control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-11-1.png",
        "caption": "FIGURE 11-11 Tractor making a steady-state turn of radius R at constant forward speed u.",
        "texts": [
            " To find the trajectory of the center of gravity of the tractor in the X, Y space fixed system, one must first transform the velocity of the 292 MECHANICS OF THE TRACTOR CHASSIS center of gravity from the vehicle fixed system to the space fixed system. Since the vehicle x, y system makes an angle IjJ with the X, Y system, X, = u cos IjJ - v sin IjJ y, = u sin IjJ + v cos IjJ Integration of the velocities X\" y\" and r = ~ determines the location of the center of gravity in the space fixed system and yaw angle, 1jJ, of the tractor as functions of time. Let us now turn to an analysis of a steady-state turning situation. In figure 11-11, the tractor shown is traveling on level ground at a constant forward velocity u in such a manner that the center of gravity of the tractor is traversing a circle of radius R. Although both the front and rear slip angles are negative (resulting in positive lateral forces), the absolute values of the angles are used in the geometric analysis. From figure 11-11, LlR = asr + '6f - asf or '6f = LlR + asf - asr But, for this steady-state situation, iJ = r = 0 and r ulR. Thus, with '6f small, equations 50 and 51 become m, (iJ + ur) = m, u2/R = Lf + Lr (54) I zz, r = 0 = Lfxfw - L,xcg (55) From equation 55, Lr = Lf (xfJxcg ). Substituting in equation 54, (xcg + xfw) L m, u2/R = Lf (1 + xfJxcg) = Lf = Lf - Xcg Xcg Thus, 2 W 2 -~ ~-~~~ Lf - L m, R - L g R But xcgW,IL = Wf is the portion of the tractor weight, W,' statically supported at the front axle so thatLf = (Wlg)(u 2/R)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-24-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-24-1.png",
        "caption": "FIGURE 12-24 Basic component arrangement for a hy drostatic power steering. (From Wittren 1975.)",
        "texts": [
            " A concise and yet complete treatise on automatic hydraulic, or fluid power, control systems is provided by Merritt ( 1967). The method of automatically controlling a three-point hitch can be vis ually grasped by a thorough study of figure 12-22. This illustration shows the hydraulic system controlling the three-point hitch on a series of large tractors by a major manufacturer. Complete Hydraulic System The complete hydraulic system used on one tractor is shown schematically in figure 12-23 and is illustrated using symbols in figure 12-24. This system includes a circuit for a remote cylinder, a circuit for the three-point hitch servo valve, a circuit for steering, a circuit for brakes, a circuit for the pto clutch, a circuit for the differential lock, and several circuits for lubrication since most of the power train is lubricated by hydraulic fluid. Power Steering* Tractors having 30 kW or more power generally will have power steering. A quarter-century of power-steering development on farm tractors has focused almost completely on two basic fluid power types",
            " The two most important advantages of the hydrostatic system are: 1. Flexibility of installation 2. Lower cost The most distinguishing feature common to hydrostatic steering systems is the use of a positive displacement How metering or measuring device cou- 336 HYDRAULIC SYSTEMS AND CONTROLS pled to the steering wheel shaft. Hydrostatic systems can be conveniently categorized by the manner in which this metering device operates in the control loop. At least four basic types can be identified, as shown in figure 12-24. Type 1 The metering unit is mechanically linked to the steering shaft and control valve and is hydraulically connected in series to the actuator. With this arrangement, the metering unit is an extension or slave of the actuator, the two always moving together in lockstep fashion because the high-pressure oil is routed through the metering unit on its way to the load. It provides the remote monitoring of actuator position at the control valve location, known as position feedback. An input error between the steering shaft and the me tering unit is measured and translated into control valve displacement by a suitable mechanical means",
            "60, the maximum possible drawbar power is 18 kW, the rear wheels weigh 14,7001\\, and the front wheels weigh 7350 K (a) Compute the kinetic energy to be absorbed in stopping the tractor. (b) If the tractor is stopped (not declutched) in 15 cm by a drawbar spring, what is the increase in the drawbar pull above the maximum tractive ability? Neglect rolling resistance of the tractor. Show all calculations and quote sources of information. 2. For an assigned tractor, obtain descriptive literature of its complete hydraulic system. From the descriptive literature (e.g., technical articles, operator's manuals, and service manuals), prepare a diagram similar to that in figure 12-24 of the complete hydraulic system, using symbols. 3. Compute the force to move a piston in a hydraulic cylinder at a velocitv of 25 cm/s. Assume pressure is zero and cylinder is full of oil. Given: Piston diameter is 50 mm Piston length is 50 mm 358 HYDRAULIC SYSTEMS AND CONTROLS Cylinder diameter is 50.01 mm Oil viscosity, v, is 5 centistokes Oil density, p, is 0.88 kg/L 4. A hydraulic pump has an inlet pressure of - 34 kPa vacuum and a discharge pressure of 3440 kPa. The diameter of the suction line is 32 mm and the discharge line is 19 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.7-1.png",
        "caption": "Fig. 1.7. Main geometrical elements used in the model",
        "texts": [
            " For a perfectly horizontal pavement, such a coordinate system can be deduced from the earth\u2019s coordinate system by a rotation around the vertical axis so as to orientate it in the wheel plane. For the main landing gear wheels, this orientation angle can be taken as equivalent to the aircraft heading. Because the nose landing gear is movable, its angle of deflection must be taken into account for the nose wheels. Finally there are two \u201cwheel\u201d coordinate systems: one NW (Nose Wheel) coordinate system and one MLG (Main Landing Gear) coordinate system. The AIRBUS On-Ground Transport Aircraft Benchmark 7 The main distances impacting the aircraft\u2019s equations of motion are shown in Fig. 1.7. 8 M. Jeanneau The core of the model is based on differential equations derived from the fundamental principle of dynamics and the Euler angle formalism. Applying Newton\u2019s second law of motion gives the following equations: F = m ( \u2202V \u2202t +\u2126 \u2227V ) (1.3) M = \u2202(I \u00b7\u2126) \u2202t +\u2126 \u2227 (U \u00b7\u2126) (1.4) With \u2126 = \u23a1\u23a3p = roll rate q = pitch rate r = yaw rate \u23a4\u23a6 and V = \u23a1\u23a3Vx Vy Vz \u23a4\u23a6 the centre of gravity displacement velocity projected into the aircraft coordinate sys- tem. F represents the sum of the external forces applied to the system and M the sum of the moments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003033_s00170-012-4406-7-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003033_s00170-012-4406-7-Figure11-1.png",
        "caption": "Fig. 11 Virtual machine simulation results for BC type table-tilting five-axis machine tool",
        "texts": [
            " Toolpath is generated in Siemens NX6 CAM software. For postprocessing, programmed zero is located at the bottom center of the workpiece and part is directly mounted on the C axis table, therefore workpiece offset distance is set to W \u00bc 0i\u00fe 0j\u00fe 80k mm. Selected tool and the holder have a tool offset length of 150 mm. The distance from the machine home position to the workpiece zero is 365i\u2212255j\u2212640k mm. Virtual machine simulation module user interface and close-ups for 300th CL points are shown in Fig. 11. In Fig. 12, sample output of the NC code and the code postprocessed with a commercial postprocessor generated by NX6 Post Builder is shown. From Figs. 11 and 12, it can be seen that programmed five-axis motion in the NC code matches perfectly with the CL data positions; therefore, it may be concluded that the validity of the presented postprocessor and virtual machine simulation module is proved. A second verification test is performed on an AC-type table-tilting five-axis machine tool in order to demonstrate that presented approach is generic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000851_1.1415739-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000851_1.1415739-Figure1-1.png",
        "caption": "Fig. 1 Coordinate system of a shaft element",
        "texts": [
            " Rotating shafts are modeled as Timoshenko beams with effects of shear deformation and gyroscopic moment taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set and the transmission error is simulated by a displacement excitation at the mesh. The transfer matrix of a gear mesh is developed. Effect of the time-varying stiffness of the gear mesh is investigated. Free vibrations and forced vibrations due to mass unbalance, gear mesh errors, and force coupling effect are studied. A fixed reference frame (X-Y -Z), shown in Fig. 1, is used to describe the motions of the system. The X-axis is collinear with the axis of the non-deflected rotor. The Y -Z plane perpendicular to the X-axis is the whirl plane of the system. With the axial displacement neglected, there are at each node five degrees of freedom, viz., y, uy , z, uz , and f. A schematic diagram of a geared rotor system is shown in Fig. 2. The system consists of two shafts, a spur gear pair, and several bearings supporting the shafts. Rotating shafts are modeled as Timoshenko beams with effects of shear deformation and gyroscopic moment taken into account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure33-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure33-1.png",
        "caption": "Fig 33 Cleazanee space displacement - GMT 1060 engine",
        "texts": [
            " More recently, with co-operation between Grandi Motori Triesti; Glacier Metal Company and Cornelt University, Booker has carried out an analysis on the 1060 engine 4s'49 . Fig 32 shows an exaggerated view of the bearing arrangement with the bearings (rather than the journals) as the oscillating members 47 . The main squeezing action is taken on the inner bearings while the outer bearings are being pulled away from the journal (by rocking action) allowing more oit in. The rocking principle of aitemately squeezing and lifting on the inner and outer bearings is i~Austrated in Fig 33. The lower diagram shows the sequence of events during one cycle of operation and the upper drawing shows the relative position of the two journal centres (A and B) in their respective clearance spaces (note that the offsets of the centres are greater than the bearing clearance). One can see the generally large film thicknesses on the outer lift bearing at crank angles of 0, 90 and 180 \u00b0. At 270 \u00b0 the clearance space in the inner bearing has a chance to replenish its oil for subsequent squeeze actiom The change in predicted film thickness throughout the load cycle,, Fig 34, shows the successive support between the inner (mai~) bearing and the outer (lift) bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001825_3.55753-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001825_3.55753-Figure2-1.png",
        "caption": "Fig. 2 Ball fuze configuration, showing the circular motion radius e, the polar angle 06 and the position vectors of the body c.m. and the component c.m. relative to the body-plus-component c.m.",
        "texts": [
            " D ow nl oa de d by U N IV E R SI T Y O F O K L A H O M A o n Ja nu ar y 29 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .5 57 53 MARCH-APRIL 1978 INFLUENCE OF MOVING PARTS ON PROJECTILE ANGULAR MOTION 119 The motion of the c.m. of the internal component will be assumed to be a circular motion of amplitude e and constant phase angle </>e with respect to the angle-of-attack plane. If the vectors locating the c.m. of the component and body with respect to the body-plus-internal-component c.m. are denoted by rc and rbf this motion of the component relative to the body (Fig. 2) is specified by the vector equation \u2014 rb = he1 \u2014e(e2 cos0e -I- e3 sin0e) (6) (7) Since these vectors are defined in terms of the c.m. of the combination, (8) (9) (10) and, therefore, rb=xbe,+eb(e2 cosO\u20ac+e3 sin0e) rc=xce1 \u2014 ec(e2 cosdf+e3 sin0e) where xc \u2014 mbhlm ec =mbe/m xb= \u2014mch/m eb = mce/m The angular momentum vector of the body, Lb, can now be computed from its definition7 in terms of a large number of small submasses, dm, with position vectors rb+Rb. (ID The rotational symmetry of the body can be best exploited by expressing the position vectors of the submasses in cylindrical coordinates: Rb=xbe1+rb[e2 (12) Since the body is spinning with respect to the aeroballistic axes, it should be noted that <j>b is not zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002548_13506501jet790-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002548_13506501jet790-Figure1-1.png",
        "caption": "Fig. 1 Hydrodynamic force and moment",
        "texts": [
            " Engineering Tribology at UNIV OF PITTSBURGH on March 13, 2015pij.sagepub.comDownloaded from F x t = \u2212 1 2R \u222b+\u221e \u2212\u221e H (X ) dP (X ) dX dX T y n = \u222b+\u221e \u2212\u221e XP (X ) dX T x n = \u2212 \u222b+\u221e \u2212\u221e ( 1 + H0 \u2212 H (X ) R 2 ) P (X ) dH (X ) dX dX T y t = \u2212 1 2R 2 \u222b+\u221e \u2212\u221e XH (X ) dP (X ) dX dH (X ) dX dX T x t = \u22121 2 \u222b+\u221e \u2212\u221e ( 1 + H0 \u2212 H (X ) R 2 ) H (X ) dP (X ) dX dX (23) The equivalent integrals for the classical dimensionless parameters are presented in equation (48) in Appendix 2. Finally, one is interested in the resultant force and moment plotted in Fig. 1 ( f x l , f y l , and tl)\u2211 F x\u2211 F y\u2211 T 2.3 Power losses Power losses due to viscous shearing can be defined using equation (22) and the shear rate defined below \u03b3\u0307 = \u03c4 \u03b7 = 1 \u03b7 dp dx ( y \u2212 h 2 ) + u h (24) The power losses per unit area \u03b8 read \u03b8 = \u222bh 0 \u03c4 \u03b3\u0307 dy = \u222bh 0 \u03c4 2 \u03b7 dy = \u03b7 u2 h + 1 12 \u03b7 ( dp dx )2 h3 (25) For pure-rolling conditions, one obtains \u03b8 = 64 b p5 H E \u20323\u03b70 1 12 \u03b7\u0304 ( dP dX )2 H 3 = 64 b p5 H E \u20323\u03b70 (26) Thus, the power losses per unit length is \u222b+\u221e \u2212\u221e \u03b8 dx = 64 b2 p5 H E \u20323\u03b70 \u222b+\u221e \u2212\u221e dX (27) 3 RESULTS AND DISCUSSION 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001800_j.jmatprotec.2006.11.149-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001800_j.jmatprotec.2006.11.149-Figure2-1.png",
        "caption": "Fig. 2. The schematic diagram of three different forming modes. (a) Titanium a e h",
        "texts": [
            " Forming result prediction and control of forming efects Numerical simulation is an effective method to predict formng results, but the simulation of MPF process is much more omplicated than that of conventional pressing. Here LS-DYNA ith an explicit solver is introduced to simulate the MPF of itanium alloy cranial prosthesis, including the creation of FE d e s echnologic computation; (c) convex\u2013concave shape cavity. odel, the choice of material model, the establishment of boundry conditions and the treatment of contact friction. Forming efects such as wrinkles and dimples can be predicted by differnt forming technique modes with this software. Fig. 2(a) is a schematic diagram that titanium alloy retiary heet is contacted with the element groups directly in MPF press. F.X. Tan et al. / Journal of Materials Processing Technology 187\u2013188 (2007) 453\u2013457 455 F t d t b t w s s s t w w t m d p e p r b r l h b k r a a 1 a p i w t g t p f e o lloy retiary sheet is contacted with the element groups directly; (b) polyurethane lastic cushion is used; (c) polyurethane elastic cushion, steel padding and blankolder device are used. ig. 3(a) shows the simulation result of the forming mode when itanium alloy retiary sheet is contacted with the element groups irectly",
            " The simuation result shows that the stress maximum value (987 MPa) as surpassed the tensile strength of Ti\u20136Al\u20134V, the part may e torn. In other words, the obvious dimples and serious wrinles will appear when the forming mode in which titanium alloy etiary sheet is contacted with the element groups directly is dopted, the qualified 3D curved surface of prosthesis can\u2019t be cquired. In order to eliminate above-mentioned forming defects, 0 mm polyurethane elastic cushion is used between titanium lloy retiary sheet and element groups when the new forming lan is constituted. The schematic diagram of the forming plan s shown in Fig. 2(b). Fig. 3(b) shows the simulation result of the forming mode hen polyurethane elastic cushion is used, it can be seen that he dimples has been suppressed. During the forming process, reat elastic deformation takes place in the elastic cushion, and he elastic cushion will fill in the blank spaces between element unches and distributes the concentrated loads, causes stressul condition to become average, so the dimples is suppressed fficaciously. From the simulation result, it can be seen that not nly dimples has been suppressed effectively but also average lastic deformation can be realized, and the wrinkles has been educed, though it still exist",
            " If the blank-holder device takes pressure o bear on the retiary sheet when adopting the above standard, t will waste partial expensive material, moreover, the forming rea is too small to satisfy the surgery\u2019s need. In order to solve his problem, steel padding whose material is 08AL and whose ize is larger than that of retiary sheet is considered; it is sandiched between polyurethane elastic cushions and retiary sheet, he press take blank-holder pressure to bear on the steel padding hen forming. During the forming process, the titanium alloy etiary sheet is held tightly by the two piece of steel padding nd they are deformed together. This schematic diagram of the orming plan is shown in Fig. 2(c). Fig. 3(c) shows the simlation result of the forming mode when polyurethane elastic ushion, steel padding and blank-holder device are used. From he simulation result of Fig. 3(c), it can be seen that dimple and rinkle defects have been suppressed primely. So using good igid characteristic steel padding, the titanium alloy retiary sheet s constrained to be not wrinkle. In conclusion, the 3D curved urface of prosthesis can be eligibly shaped with this forming ode. In Fig. 4, a comparison of the sectional node displacement vertical direction) of 3D curved surface simulated with above hree different MPF modes, the three lines are assembled by ome nodes of transversals of the three simulation results, they how the surface quality of the simulated 3D curved surface of rosthesis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001562_20.105039-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001562_20.105039-Figure3-1.png",
        "caption": "Figure 3 : Geometry of the motor",
        "texts": [
            " (18) A linear combination of equations (17) and (18) yields finally to jw[DlTtC'lT[A1 + (Gxt + Rk) I = E (19) Ns k+ 1 with C.. ' - i j - N ssk L 1,I.i d n Since the conductors are thin, the potential difference across each conductor simply writes with respect to I. The field equation (3) then becomes : [S][A] - [C][D] I = 0 (20) Zext is the impedance of the end windings analytically computed. 4 - RESULTS : Computations have been performed on a three phase motor, 4 poles, 50 Hz with a double cage rotor, the slots of which are not skewed (Fig 3) . The measurements have been done by running the machine at a given speed, then coupling to the network . 4248 IEEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 5, SE\u20ac'EMBER 1991 On figure 4 are compared computed and measured values. The e m r on the absorbed current and on the power is less than 5 %. The error on the torque is some times greater than 5 % which shows the influence of the space harmonics that are not correctly represented by this model. The study of the motor under 380 V, at ambient temperature gives the motor characteristics with respect to the rotor speed as represented in figure 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003494_tmag.2016.2572659-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003494_tmag.2016.2572659-Figure1-1.png",
        "caption": "Fig. 1. Current superimposition variable flux reluctance machine.",
        "texts": [
            " Due to this, the torque constant of the VFRM can be controlled and its power band can be increased. However, since two separate sets of windings are required, the size of the motor is large and it becomes more complicated to manufacture. Under such circumstances, a study to eliminate the field winding has been done [20]. In this method, the direction of the phase current is one way. Therefore, there are some constraints in the pole and slot combination. In order to solve these problems, we have developed a current superimposition variable flux reluctance machine (CSVFRM) shown in Fig. 1, which requires only a single set of windings that can perform both the armature and field winding functions simultaneously [21] - [23]. The advantages of the CSVFRM compared with the VFRMs that use field windings are as follows [22]. 1: The output power density of the CSVFRM is much higher because the allocation between the DC and AC currents can be controlled electrically. (In the conventional VFRMs, the maximum current density is set to each coil. Therefore, the operation range of the VFRMs becomes narrow due to the limited current density of either field or armature coils"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000943_j.finel.2004.02.002-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000943_j.finel.2004.02.002-Figure5-1.png",
        "caption": "Fig. 5. A solid model of an involute gear tooth sector.",
        "texts": [
            " For a complicated 3D geometry such as a gear tooth sector, this process is very diHcult, and it is preferable to create the FE model by meshing a solid model. Fig. 4c shows a Iowchart of the program CrtFEMod, which together with the subroutines CrtSections (see Fig. 4b) and FindBnd (see Fig. 4a) create a FE model of an involute gear tooth sector (an FE model of a spur, helical or straight conical involute gear sector can be generated more e/ectively if additional logic is added to the processes). The solid model (see Fig. 5) is built from the bottom up, i.e. points are !rst created and then these points are used to de!ne lines. Surfaces are de!ned from the lines and !nally these surfaces are used to de!ne the volumes. The six volumes are owned by the solid model and have common surfaces at the interfaces. Partitioning of the solid model with these interior surfaces enables the use of a semi-automatic mesh generation method [9], which will result in a mapped mesh (or structured grid). This approach gives one considerably more control over the FE mesh than an approach in which the solid model is not partitioned and is meshed using a fully automatic method (or free meshing method)",
            " (42), (43) and (20) we obtain that the interval size of the parameter \u2019Rj is O\u2019Rj = |\u2019Rj(sr ; w) \u2212 \u2019Rj(uFR ; w)| = 2 m [ sr 2 \u2212 ha tan n + cos n (sin n \u2212 1) ] : (44) According to the standard ISO 53-1974, n = 20\u25e6, ha = 1:25 m and = 0:38 m. Expression (44) now becomes O\u2019Rj = 1:29\u00d710\u22121=z, which shows that the sum of O\u2019R+ and O\u2019R\u2212 is only about 4% of the angular pitch 2 =z. As a result, the root surface of the gear is not represented as an own surface, but only as part of the !llet surface, which therefore is extended to the boundary where uRj = sr (otherwise the tooth sector is not a characteristic sector and could not be used to generate a gear). A point on this boundary is designated as an end root point (see Fig. 5) and is determined using (20) (with uRj = sr), (31) and (32). A rim end point (see Fig. 5) is also determined using (20) and (31), but the inner rim radius rr is used instead of the root radius rf . The shared points (see Fig. 5) join the right and left tooth pro!les together and are located on the symmetry line of a tooth section if the tooth is symmetric, i.e. the gear is a spur, helical or straight conical involute gear. By substituting Ij(\u2019Ij; w) = \u2019Ij \u2212 (w) into (28) we get rgIj(\u2019Ij; w) =   cos (w) \u2212sin (w) 0 0 sin (w) cos (w) 0 0 0 0 1 0 0 0 0 1     x0 Ij y0 Ij z0 Ij 1   =Mg0r0Ij( Ij; w); (45) where r0Ij( Ij; w) =   r cos Ij + (r Ij \u2212 jsj(w)=2) cos tj sin( Ij \u2212 j tj) r sin Ij \u2212 (r Ij \u2212 jsj(w)=2) cos tj cos( Ij \u2212 j tj) w 1   : (46) Expressions (45) and (46) indicate that rgIj may be obtained by describing the vector r0Ij in coordinate system Sg that has been rotated counter-clockwise about the z0-axis by the angle (w). Vectors r0Fj and r0Rj can be determined in a similar way. As a consequence, an arbitrary transverse section, which is de!ned by w, may be considered to have rotated clockwise about the zg-axis by (w). This circumstance is used to determine the coordinates of the shared points. Upper and lower shared points (see Fig. 5) are calculated by transforming the coordinates (ra; 0; w) and (rr ; 0; w) respectively in coordinate system S0 to coordinate system Sg using expression (45). Intermediate shared points are determined by the vector rgM = rgIF+ \u2212 (rgIF+ \u2212 rgIF\u2212); (47) where is a scalar with an appropriate length, rgIFj is the position vector of a boundary point and rgM and the unit vector [cos (w) sin (w) 0]T lay in a plane that is orthogonal to a transverse plane. Multiplication with the unit vector [sin (w) \u2212 cos (w) 0]T, which is normal to this plane, gives us "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002779_c1sm05998j-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002779_c1sm05998j-Figure2-1.png",
        "caption": "Fig. 2 (a) The minimalist model: Consider an elliptical shell with long axis b, short axis a, and uniform thickness t. The magnitude distribution of the unconstrained differential strain field is also illustrated. (b) Typical FEM mesh of the minimalist model (front view).",
        "texts": [
            " The curves of strain components are obtained as the average of all measured directions from all samples, and the error bars indicate respective data scatter. Pu bl is he d on 0 3 O ct ob er 2 01 1. D ow nl oa de d by U ni ve rs ity o f R eg in a on 2 6/ 10 /2 01 4 11 :3 6: 20 . View Article Online Representative effects of the vein modulus and density are illustrated. Future outlooks are discussed in Section 4. In order to capture some of the most essential features of the wrinkling morphology of a dried leaf, a minimalist model of the leaf blade is established in Fig. 2(a), which resembles an elliptical membrane thin film with short axis a, long axis b, and thickness t. The thickness is assumed uniform, and the veins are excluded from the minimalist model and their roles will be discussed in Section 3. As a first-order approximation, the mechanical properties of the thin shell are assumed to be homogeneous, isotropic, and linear elastic; its Young\u2019s modulus and Poisson\u2019s ratio are denoted as E and n, respectively. In most parts of this paper, n is fixed at 0.48 unless otherwise denoted",
            " Furthermore, when the strain compo- nents are plotted as a function of the normalized distance with respect to the leaf center in Fig. 1(d), the results indicate that the radial and circumferential strains are of the same magnitude, and more importantly, the distribution of the shrinking strain is approximately linear. Therefore, in our minimalist model, we assume that the spatial distribution of the differential dehydration (and the associated shrinking strain) is linear.\u2020 Based on the observation and experiments above, the magnitude of the unconstrained differential strain field is assumed to take the following form (see Fig. 2(a)): 3\u00f0x; y\u00de \u00bc DaT x2 a2 \u00fe y2 b2 (1) where at the rim, the unconstrained excessive strain (with respect to that at the center) is assumed to be DaT in both radial and hoop directions, and the strain gradient is assumed to be linear in the minimalist model (according to Fig. 1(d)). With the differential unconstrained strain field (eigen-strain), the excessive shrinking near the rim causes the interior region to be compresses, andbeyonda critical strainbuckling instability occurs so as to minimize the strain energy of the system. The buckling of the model leaf is investigated numerically using finite element method (FEM) using software ABAQUS, where the membrane thin film is discretized by 4-node general purpose shell elements with reduced integration and accounting for large rotation; a representativemesh is given in Fig. 2(b) and amesh convergence study is carried out to ensure appropriate mesh density. The unconstrained differential contraction strain field (eqn (1)) can be conveniently implemented using the equivalent thermal strain in simulation.A very small initial defect is introduced so as to initiate the out-of-plane buckling, whose magnitude is a very small fraction of the sheet thickness and confirmed to have no influence on the resulting configuration.Noboundary constraint is imposed on the model except limiting the rigid body displacement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure6-1.png",
        "caption": "Fig. 6. Relationship between the coordinate systems of the worm and the worm gear.",
        "texts": [
            " In general, the transmission function \u03d5g(\u03d5w) can be obtained by TCA [3,15]. In the case of involute worm gear drive, \u03d5g = \u03d5g(\u03d5w) can be replaced by \u03d5g \u00bc \u03d5w g \u00fe \u03d5g0 because there is no transmission error in involute worm gear drives [7]. \u03d5g0 is an offset angle to describe the contact between Sw and Sg. The interference between Sw and Sg can be examined by calculating the surface separation between Sw E and Sg, where Sw E is the envelope to the family of Sw in the coordinate system Cg, which is attached to Sg. The family of worm surfaces Sw can be represented in Cg (Fig. 6) as follows: rEw ! uw; \u03b8w;\u03d5w\u00f0 \u00de \u00bc Mgw \u03d5w;\u03d5g \u03d5w\u00f0 \u00de rw ! uw; \u03b8w\u00f0 \u00de; \u00f017\u00de where Mgw is the transformation matrix from Cw to Cg and is defined as follows: Mgw \u00bc 0 0 1 0 cos\u03d5g sin\u03d5g 0 0 \u2212 sin\u03d5g cos \u03d5g 0 0 0 0 0 1 2 664 3 775 \u22121 cos \u03d5w sin\u03d5w 0 0 \u2212 sin\u03d5w cos \u03d5w 0 \u2212d0 0 0 1 0 0 0 0 1 2 664 3 775: \u00f018\u00de Here, d0 is the center distance of the worm and the worm gear. The equation of meshing [15], satisfied on the envelope to the family of Sw, is represented as follows: f w uw; \u03b8w;\u03d5w\u00f0 \u00de \u00bc \u2202 rEw ! \u2202uw \u2202 rEw "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000615_20.573842-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000615_20.573842-Figure7-1.png",
        "caption": "Fig. 7. The magnetic flux distributions of the 11 kW skewed motors after a rotation of 30 (Number of slices = 4): (a) at the first slice and (b) at the fourth slice.",
        "texts": [
            " The results computed using the proposed method show very good correlation with the test data. The presented method has been used to simulate the steadystate operation of two identical 11 kW, skewed rotor cage induction motors (380 V, 50 Hz, connected, 4 poles, 48 slots in stator, 44 slots in rotor, and a skewing of 1.2 rotor slot pitch) carrying approximately full load. The programs are run on a Pentium/90 MHz personal computer. The size of each time step is 0.039 ms. The computed flux distributions after a rotation of 30 are shown in Fig. 7. The computed stator phase currents when different numbers of slices are chosen are shown in Fig. 8. The stator phase current waveforms obtained by experiment are shown in Fig. 9. The comparison of CPU time required for the computation of one step as well as the errors which are defined by (19) is as shown in Table I, where is the th harmonic magnitude of current obtained experimentally and is the computed result. From Figs. 8, 9, and Table I, one can see the following. 1) If nonskewed model is used to simulate skewed motors, a big error will appear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001493_j.mechmachtheory.2004.04.006-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001493_j.mechmachtheory.2004.04.006-Figure1-1.png",
        "caption": "Fig. 1. Simulation of gear meshing with assembly errors.",
        "texts": [
            " Gear edge contact can thus be avoided because the contact paths on gear tooth surfaces are * Corresponding author. Tel./fax: +886-35-728-450. E-mail address: cbtsay@mail.nctu.edu.tw (C.-B. Tsay). 0094-114X/$ - see front matter 2004 Published by Elsevier Ltd. doi:10.1016/j.mechmachtheory.2004.04.006 Nomenclature ai; bi tool setting of rack cutter P i \u00f0i \u00bc F;P\u00de li variable parameter which determines the location on rack cutter \u00f0i \u00bc F;P\u00de ri radius of pitch circle of gear i \u00f0i \u00bc 1; 2\u00de C0 operational center distance (Fig. 1) DC variation of center distance (Fig. 1) Ri nominal radius of the face mill-cutter \u00f0i \u00bc F;P\u00de Ti number of teeth of gear i \u00f0i \u00bc 1; 2\u00de X \u00f0i\u00de T ; Y \u00f0i\u00de T ;Z\u00f0i\u00de T coordinates of gear tooth surface i \u00f0i \u00bc 1; 2\u00de represented in coordinate system ST (Fig. 2) n\u00f0i\u00dec unit normal vector of surface P i \u00f0i \u00bc F;P\u00de represented in coordinate system Sc R\u00f0i\u00de c position vector of surface P i \u00f0i \u00bc F;P\u00de represented in coordinate system Sc \u00f0r; h\u00de auxiliary polar coordinate system represented on contact tooth tangent plane (Fig. 2) Si\u00f0Xi; Yi; Zi\u00de coordinate system i \u00f0i \u00bc 1; 2; v; h; f;T\u00de with three orthogonal axes Xi, Yi, and Zi Dch horizontal axial misalignment (in degrees, Fig. 1) Dcv vertical axial misalignment (in degrees, Fig. 1) hi variable parameter which determines the location on rack cutter \u00f0i \u00bc F;P\u00de /i rotation angle of gear i \u00f0i \u00bc 1; 2\u00de when gear i is generated by rack cutter /0 i rotation angle of gear i \u00f0i \u00bc 1; 2\u00de when two gears mesh with each other (Fig. 1) D/0 2\u00f0/ 0 1\u00de transmission errors (in arc-second) w\u00f0i\u00de n normal pressure angle of rack cutter P i \u00f0i \u00bc F;P\u00de Subscripts F, P rack cutter surface to generate tooth surfaces of pinion and gear 1, 2 tooth surfaces of pinion and gear located near the middle region of the tooth flank even when the gear set is meshed with axial misalignments. The transmission error (TE) of a mating gear pair is an important factor for gear noise and vibration criteria. Litvin and Tsay [3] simulated the meshing and bearing contact of circular arc helical gears",
            " The circular-arc imaginary rack cutter surface P PL used to produce the right-side curvilinear-tooth gears and its unit normal vector are expressed as R\u00f0P\u00de c \u00bc lP cosw \u00f0P\u00de n \u00fe aP \u00f0lP sinw\u00f0P\u00de n \u00fe bP aP tanw \u00f0P\u00de n \u00de cos hP \u00fe RP\u00f01 cos hP\u00de \u00f0lP sinw\u00f0P\u00de n \u00fe bP aP tanw \u00f0P\u00de n \u00de sin hP \u00fe RP sin hP 2 64 3 75 \u00f06\u00de and n\u00f0P\u00dec \u00bc sinw\u00f0P\u00de n cosw\u00f0P\u00de n cos hP cosw\u00f0P\u00de n sin hP 2 64 3 75: \u00f07\u00de Therefore, the mathematical model of the right-side of the curvilinear gear tooth surface P 2R can also be developed by the same process and represented as follows: f2\u00f0lP; hP;/2\u00de \u00bc \u00bdlP aP\u00f0cosw\u00f0P\u00de n \u00fe tanw\u00f0P\u00de n sinw\u00f0P\u00de n \u00de \u00fe bP sinw \u00f0P\u00de n cos hP \u00fe \u00f0RP\u00f01 cos hP\u00de r2/2\u00de sinw\u00f0P\u00de n \u00bc 0; \u00f08\u00de R \u00f0P\u00de 2 \u00bc cos/2 sin/2 0 r2\u00f0cos/2 \u00fe /2 sin/2\u00de sin/2 cos/2 0 r2\u00f0sin/2 /2 cos/2\u00de 0 0 1 0 0 0 0 1 2 664 3 775R\u00f0P\u00de c : \u00f09\u00de The unit normal vector of the generated gear tooth surface can be obtained by n \u00f0P\u00de 2 \u00bc cos/2 sinw \u00f0P\u00de n \u00fe sin/2 cosw \u00f0P\u00de n cos hP sin/2 sinw \u00f0P\u00de n \u00fe cos/2 cosw \u00f0P\u00de n cos hP cosw\u00f0P\u00de n sin hP 2 64 3 75: \u00f010\u00de Substituting Eq. (8) into Eq. (9) yields the mathematical model of the right-side curvilinear gear tooth surface P 2R, and Eq. (10) expresses its unit normal vector represented in coordinate system S2\u00f0X2; Y2; Z2\u00de. The model for gear meshing with assembly errors can be simulated by changing the settings and orientations of the coordinate systems Sh\u00f0Xh; Yh;Zh\u00de and Sv\u00f0Xv; Yv;Zv\u00de with respect to the fixed coordinate system Sf\u00f0Xf ; Yf ; Zf\u00de as shown in Fig. 1, where coordinate systems S1\u00f0X1; Y1;Z1\u00de and S2\u00f0X2; Y2; Z2\u00de are attached to the pinion and gear, respectively. The axes Z1 and Z2 are rotational axes of the pinion and gear, respectively. Coordinate systems Sv\u00f0Xv; Yv; Zv\u00de and Sh\u00f0Xh; Yh; Zh\u00de are the reference coordinate systems for the misaligned gear assembly simulations. The simulation of horizontal axial misalignment of the gear may be achieved by rotating the coordinate system Sh\u00f0Xh; Yh;Zh\u00de about the Xh axis through an angle Dch with respect to the coordinate system Sf\u00f0Xf ; Yf ;Zf\u00de"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002202_b717694e-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002202_b717694e-Figure9-1.png",
        "caption": "Fig. 9 Schematic illustration of structure and electron transport in the cyt c\u2013SO multilayer. After the oxidation of the sulfite to sulfate occurring at the Moco domain of the SO (white balls), the electrons are first delivered to the heme b5 domain and then transferred to the closest molecule of cyt c, which transfers electrons further to the electrode via other cyt c molecules while re-oxidizing itself.",
        "texts": [
            " This may be due to an increased probability for productive collisions in the densely packed assembly because the conductive negatively charged polyelectrolyte in parallel increases the dielectric constant of the medium surrounding cyt c and reduces the heme edge-to-edge distance by interacting with the positively charged His-18 residues, which are important for establishing the optimum distance.34 This is also in correspondence with earlier reports on long distance ET in cyt c\u2013PASA multilayers.19,20 Thus the functional assembly can be schematically illustrated (Fig. 9). This journal is \u00aa The Royal Society of Chemistry 2008 For the first time a SO\u2013cyt c multilayer was successfully formed as a fully electroactive assembly with the help of a self-assembly process and the polyelectrolyte PASA. The proteins, which are communicating via direct ET, constitute an artificial ET chain and have been immobilized from a protein mixture. The accumulation of the mass on the surface of a gold electrode has been followed by QCM and cyclic voltammetry showing for each deposition round an increase in mass and electroactive cyt c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure7-1.png",
        "caption": "Fig. 7. Three-dimensional streamline inside bearing cavity (without additional oil\u2013 air device).",
        "texts": [
            " 6(f) indicate their weak heat dissipation and air flow performance, which verified the existence of air flow vortexes in Fig. 6(e). It should be particularly noted that, at high rotation speed, a small new vortex appears near the entrance of inner ring contact area, which directly blocks oil\u2013air flowing into the contact area, and leads to the decline of lubrication performance. Based on the streamline monitoring technology, vortexes near the ball and inner ring were analyzed in three dimensional streamline view, seen in Fig. 7. Influenced by the ball\u2019s motion, chaotic streamline appears in front and behind the contact area, where the high pressure areas form (seen in Fig. 4). Due to the combined effect of ball and inner ring\u2019s interaction, the streamline of the contact area is sparse. As mentioned above, at high rotation speed, the air flow in the A side cavity is regular and intense while in B side it is weak, which are consistent with the streamline distribution. Near the entrance of the contact area, the streamline is curved, which indicates the existence of the secondary vortex"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002243_ac101303s-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002243_ac101303s-Figure1-1.png",
        "caption": "Figure 1. Schematic drawing of a gold-gold sensor-modulator junction electrode with a negative potential applied to the modulator electrode in order to produce locally alkaline conditions in the micrometer interelectrode gap.",
        "texts": [
            " In this study, a nonenzymatic glucose sensor for neutral media is proposed on the basis of a symmetric pair of adjacent gold electrodes. The interelectrode gap is approximately 500 nm.24 The electrochemical oxidation of glucose in aqueous media, which is possible at gold electrodes under bulk alkaline conditions,25 is demonstrated here in neutral solution. One electrode (the \u201cmodulator\u201d electrode) is employed to generate hydroxide from water (see eq 1), and the second electrode (the \u201csensor\u201d electrode) is employed to oxidize glucose to gluconic acid25 (see eq 2, Figure 1). 2H2O + 2 e- f H2 + 2 OH- (1) glucose + 2 OH- f gluconic acid + H2O + 2 e- (2) For small electrode junctions, the localized production of hydroxide is feasible when the diffusional transport of OH- across the interelectrode gap occurs rapidly on the time scale of a cyclic voltammetry or pulse voltammetry experiment. Preliminary data are presented to show that pulse voltammetry in junction electrodes will be feasible in robust miniaturized glucose sensors and of interest in a wider range of sensing problems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003033_s00170-012-4406-7-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003033_s00170-012-4406-7-Figure10-1.png",
        "caption": "Fig. 10 Impeller roughing toolpath",
        "texts": [
            " CL data is used for the illustration of the toolpath in the simulation. Validity of the NC code is proved by comparing CL data (toolpath in simulation) and tooltip position of the machine. If tooltip position and the corresponding CL point match, then NC code is verified. The virtual machine simulation module described in Section 4 is implemented in Visual Studio C++ using the Coin3D graphics development API. Implementation of the proposed approach and virtual machine simulation module is verified on an impeller roughing toolpath which is shown in Fig. 10. Toolpath is generated in Siemens NX6 CAM software. For postprocessing, programmed zero is located at the bottom center of the workpiece and part is directly mounted on the C axis table, therefore workpiece offset distance is set to W \u00bc 0i\u00fe 0j\u00fe 80k mm. Selected tool and the holder have a tool offset length of 150 mm. The distance from the machine home position to the workpiece zero is 365i\u2212255j\u2212640k mm. Virtual machine simulation module user interface and close-ups for 300th CL points are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000694_0094-114x(96)84593-9-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000694_0094-114x(96)84593-9-Figure1-1.png",
        "caption": "Fig. 1. Distribution of screw pitch.",
        "texts": [
            " The number of independent line vectors is also three if all the vectors are parallel with each other. I f all the line vectors are in a common plane, and intersect at the same point or are parallel with each other, the number of independent line vectors will be two. 3. THE RECIPROCAL SCREW AND POSSIBLE MOTION If the reciprocal screw $r of a known motion screw system is a line vector, it is a constraining force. To analyse the motion of a body under this constraining force, the coordinate system is chosen in the way as shown in Fig. 1. Therefore, $ ~ = ( 0 1 0;0 0 O) if the motion is expressed as, Sm=(~;~o)=(l m n;p q r) Let ~ . ~ = 1, ~ - ~o :# 0, it can be deduced from equation (1) that q = 0, and the pitch of the motion screw can be calculated as, h l~+mq +nr + m2 + n2 (2) Because we have, g o = l / x g + h g and l ~ = ( x y z ) v (3) (~- lh I :Yn-Zm\\ = | Z I - X n I \\ r -nh / \\ X m - YI/ (4) Since there are nine unknowns which are l, m, n, p, r, h, X, Y, Z, and only three equations, we can choose any five parameters among the nine for determination of Sm considering that the square sum of the direction cosine is 1. In order to further understand the distribution of the possible motions in the space, we obtained the value of h under different direction at x = + 1 as shown in Fig. 1. It can be seen that all the direction lines on the same plane with $r have zero pitch, that is h = 0. These direction lines can be rotational axes when the motion is rotational. In the direction in which the pitch h = oo, the motion can only be translation. I f h has a value other than 0 or oo, the motion will be the screw motion. It can be concluded that if a body is subjected to a reciprocal screw $~, i.e. a constraining force, its rotations will be restricted, except for those around the axes sharing the same plane with Sr",
            " The difference of two line vectors is, therefore, f = x/~, h = 1/2, (l m n) T = (0 - 1 / x / ~ 1/x/~) T, (p q r) T = (0 -m/x/~ 0) T, and acting point R = (1/2 0 0) r. These two reciprocal screws $~ and $~ are perpendicular and intersect with each other. Four motion screws are, $ ~ = ( 0 1 1;0 0 1), h=\u00bd l $\u2022=(0 - 1 1;0 0 --1), h = - ~ $~ '=(1 0 0;0 0 0), h = O $ ~ = ( 0 0 0;1 0 0), h = oo Any other possible motions are the linear combination of these four screws. Another method for determination of the motion screws is the observation method. From Fig. 1, it can be seen that translation is possible in the direction orthogonal to $~ and $L and the axis intersecting with $~ and $~ can be the rotating axis, as shown in Fig. 2. We can verify the agreement of these two methods, for example, $ ~ = $ ~ + $ ~ n = 2 ( 0 0 1;0 0 0), rotation $ ~ = $ ~ + $ T + 2 5 ~ = 2 ( 0 0 1;1 0 0), rotation $ ~ = $ ~ + $ ~ = ( 1 0 1;0 0 0), rotation When the body is subjected to three reciprocal screw line vectors, i.e. three constraining forces, all its translational motions in three-dimensional space are constrained, and its possible motions are three rotations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003748_s11071-016-3218-y-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003748_s11071-016-3218-y-Figure7-1.png",
        "caption": "Fig. 7 Crack model at gear tooth fillet region: a Case C b Case D",
        "texts": [
            " These nonuniformly distributed plastic deformations will serve as geometric deviation static transmission error (STE) contributions and lead to non-uniform dynamic load distributions on the cracked tooth flank, and will therefore, significantly affect the gear dynamic performance. We then assume that the crack propagates only in the tooth profile direction with uniform crack depth along the tooth width, i.e., qw = q0, w \u2208 [0,W ] (17) Two growth paths of the spatial crack on the tooth flank are investigated. They are linear and monotonous parabolic, respectively, as shown in Fig. 7. If the crack growth path is linear, as shown in Fig. 7a: lw = l2 \u2212 l0 W \u2217 w + l0, w \u2208 [0,W ] (18) If the crack growth path is parabolic, as shown in Fig. 7b: lw = l2 \u2212 l0 W 2 \u2217 w2 + l0, w \u2208 [0,W ] (19) where l2 is the distance from the crack position in the other end surface to the tooth root as shown in Fig. 7. The crack inclination angle \u03b1c is still kept at a constant 60\u25e6. The initial crack position l0 is still determined by the 30\u25e6 tangential method. The crack depth q0 is kept at 0.4mm, and the tooth plastic inclination angle \u03b8p is assumed as 0.6 degree. Three different crack growth distances along the tooth flank (i.e., l2 \u2212 l0) are shown in Table 3. Figure 8 shows the 3D distributions of the gear tooth plastic deformations on the cracked tooth flank. It is obvious from these figures that as the crack propagates away from the tooth root, the plastic deformation is decreasing along the tooth width direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002858_mra.2011.943231-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002858_mra.2011.943231-Figure1-1.png",
        "caption": "Figure 1. Three robot kits: (a) VEX, (b) Fischertechnik, and (c) LEGO Mindstorms. (Photo courtesy of Steven Canvin from LEGO Mindstorms.)",
        "texts": [
            " The hands-on approach, coupled with accessible and affordable robot kits, has greatly aided the teaching of science, technology, engineering, and mathematics (STEM) concepts within the curriculum. The use of robots in the classroom spans a wide variety of topics, of which only a snapshot of what is possible is provided here: l mathematics of gearing l levers, pulleys, and simple machines l electronics l sensors and actuators l software flowcharting and artificial intelligence l datalogging l automated systems. Three of the robot kits have been widely used by Fischertechnik, VEX, and LEGO (Figure 1). More information can be found at their respective Web sites: l VEX: http://www.vexrobotics.com/ l LEGO Mindstorms: http://mind storms.lego.com l Fischertechnik: http://www.fischer technik.de/en/. Alternatives to these popular kits fall into two categories: expensive/modular and inexpensive/single configuration. l Expensive/modular kits such as the Kondo (kondo-robot.com/EN) and Bioloid (robotis.com/xe/bioloid_en) kits have impressive specifications with sophisticated processors interfacing to, and in some cases, a dozen servomotors and multiple sensors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003128_j.jtbi.2015.10.013-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003128_j.jtbi.2015.10.013-Figure9-1.png",
        "caption": "Fig. 9. A detailed resolution of the temporal dynamics near a sphere for the virtual turbot sperm with the early activation stage waveform, as parameterised in Table 1 and with prescribed bending conditions at the head-tail junction. In particular, results are presented for an egg with a radius of R\u00bc 43L and R\u00bc 44L, together with different parameter values for the surface repulsion force. (a) A schematic picture, not to scale, of the swimming sperm near an egg, illustrating the plotted parameters in (b) and (c). (b) Time evolution of the distance between the head surface and the head-tail junction for the model sperm, which corresponds to the magnitude of the red arrow in (a). (c) Time course for the angle of the sperm head orientation, as defined by the head axis of symmetry passing through the head\u2013flagellum junction, with respect to the tangential plane of the egg surface, which is perpendicular to the red arrow of (a) and passes through head\u2013flagellum junction. This angle is illustrated in green in (a). (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)",
        "texts": [
            ", 2009a; Ishimoto and Gaffney, 2014). Table 2 Reference parameters for the turbot fish sperm flagellar waveform for late stage motility, between about 40\u201380 s after activation, using Fig. 1b as a guide as well as data from the late-stage motility observations of Chauvaud et al. (1995) and the late Since the transition to stable sperm swimming near an egg occurs at a larger sphere radius than observed, we proceed to examine the model predictions of transient versus stable swimming in more detail, via Fig. 9. Here, the time course for the distance between the sperm head-tail junction and the sphere surface is plotted, together with the angle of the sperm head orientation to the tangential plane of the sphere, as depicted and detailed in Fig. 9a. In particular, the virtual turbot sperm has an early activation stage waveform with a parameterisation via Table 1; in addition it starts at x\u00bc R and z\u00bc 15L with an initial velocity in the positive \u00fex direction and thus swims towards a spherical egg, which has a radius of either R\u00bc 43L or R\u00bc 44L. Finally, different values of g and d, respectively the strength and lengthscale of the repulsive force are considered, with plots presented for \u00f0g=\u03c9\u03bc; d=L\u00deA \u00f0200;1=100\u00de; \u00f0200;1=200\u00de; \u00f0400;1=100\u00de : Table 1 Reference parameters for the fish sperm flagellum with a beat pattern in the early stage of activation, together with reference egg sizes",
            " Trajectories of model turbot sperm with prescribed bending conditions at the hea swimming direction given by the black arrows and the eggs depicted using a meshed sph there is no stable sperm surface swimming, even with surface repulsion forces for an swimming is observed. (b) With the early stage activation parameters for the flagellar b virtual turbot spermwhen the egg radius is R\u00bc 50L\u00bc 2:15 mm. Here virtual sperm swim the trajectories are very similar for virtual turbot sperm with the late stage flagellar be extended, swimming near the egg surface when R=12L. The first two plots of Fig. 9b and c with the reference surface repulsive potential parameters, \u00f0g=\u03c9\u03bc; d=L\u00de \u00bc \u00f0200;1=100\u00de, demonstrate that the transition to stable swimming occurs within the range of sphere radii, RA\u00f043L;44L\u00de, i.e. about 2.5 times larger in radius than a turbot egg. Furthermore, the angle of these trajectories in Plot 9c demonstrate that sperm align with the sphere in a very similar manner, becoming oriented to swim away from the sphere, with the angle becoming positive. Nonetheless the angle is very small and hence any given sperm swims close to the sphere for an extended period even if it eventually leaves. In particular, such a sperm is still under the influence of hydrodynamic attraction of the sphere, which is longer ranged than the surface repulsion potential. Hence the sperm starts to turn, though the hydrodynamic attraction is weak so the turning takes a significant number of beat periods. Whether the sperm swims stably, as with the green trajectory of Fig. 9b, or transiently near the surface, as with the red trajectory, xy 0 10 20 )Lfotinu( z xy R=12L d-tail junction, swimming near an egg with radius R\u00bc 12L, and R\u00bc 50L, with the erical surface. (a) For a sperm exhibiting the early activation beat pattern of Table 1, egg radius of R\u00bc 12L. However an extended, albeit ultimately transient, surface eat pattern presented in Table 1, stable surface swimming can be observed for the along the egg surface, and do not be separate from the egg. (c) One can observe that at parameters of Table 2 and, in particular, that there is again only transient, albeit stage controls of Dreanno et al",
            " Note that the reduction in frequency with late stage motility does not alter the sperm trajectory due to the effective absence of inertia in sperm swimming. Parameter Interpretation Value V Sperm head volume 7:36 \u03bcm3 a Flagellar radius 0:125 \u03bcm L Flagellar length 56 \u03bcm kL Wavenumber 3\u03c0 A Flagellar envelope parameter 0.1087 B Flagellar envelope parameter 0.0543L \u03c9 Angular frequency 14 Hz appears to hinge onwhether the sperm turns sufficiently for it to be attracted back towards the egg. If it is, there is a damped oscillation in the radial distance and the sperm swims stably near the egg. Otherwise, it drifts away, as in the red trajectory of Fig. 9b. Note also that these observations occur for the blue and purple trajectories associated with further parameter choices in Fig. 9b and c illustrating that this aspect of the dynamics is not specific to detailed parameter choices. In summary, these plots illustrate that the question of whether the swimming near the egg is stable or transient is about a competition between two influences. The first is the small exit angle of the initial close-scale interaction of the sperm and the egg, which initiates a slow drift away from the egg. The second is the weak hydrodynamic force attracting the sperm back. In this study, we have considered the behaviour of virtual sperm swimming in the vicinity of smooth spherical fish eggs by modelling the mechanical interactions of a sperm with its surroundings, with the implicit assumption that mechanical feedback, such as the subtle change in viscous drag near a surface, does not alter the flagellar beat pattern",
            " However, it is important to note that the predicted transience of swimming near spheres the size of turbot eggs is not consistent with the observation that, in practice, turbot sperm swim stably adjacent to their eggs. In particular, spheres with radii of about a 1.8 millimetres or larger are required for predictions of stable surface swimming, as indicated in Figs. 8b and 9. Thus effectively, we have a disagreement between the modelling and observation; however it is with regard to the quantitative details, rather than the qualitative principles. Furthermore, inspection of Fig. 9 indicates that whether transient or stable swimming is observed is due to a competition between two driving influences, one is the small positive exit angle of the initial sperm\u2013egg interaction causing the sperm to drift away from the egg; the second is the weak hydrodynamic attraction between the sperm and the egg. Hence the question of stability versus transience in sperm swimming next to a sphere may be sensitive to modelling approximations that induce small changes in the scattering angle or the hydrodynamic attraction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure1-11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure1-11-1.png",
        "caption": "FIGURE 1-11 Phantom view of a modern tractor showing the design complexity. (Courtesy Ford Motor Co.)",
        "texts": [
            " Four-wheel-drive, or simply 4WD, tractors have been developed so as to be able to produce more drawbar power. The size of 4WD tractors varies in the United States and Canada from 100 kW to more than 300 kW. In Europe, 4WD tractors may be as small as 15 kW and are used especially in vineyards. Four-wheel-drive tractors can be steered by pivoting the tractor in the center (frame steer) or steering the wheels (as in fig. 1-10). 8 DEVELOPMENT OF THE TRACTOR The complexity of a modern tractor is illustrated by figure 1-11, which shows such features as power steering, epicyclic gear reduction in the front wheels, wet disk brakes, power shift transmission and an ROPS type cab. Some World Variations in Tractors 1. Tractors made and used inJapan are usually equipped with riceland tires. 2. The power-to-mass ratio is greater for Japanese tractors than for others. 3. European tractors more commonly use radial-ply tires for traction. 4. Tractors made outside of North America may have as many as four different speeds on the power takeoff"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003227_s11071-014-1701-x-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003227_s11071-014-1701-x-Figure1-1.png",
        "caption": "Fig. 1 Schematic illustration of a the gear-rotor\u2013bearing system under nonlinear suspension, b model of force diagram between pinion and gear and c model of rub-impact force diagram between rotor and stator",
        "texts": [
            " Section 2 derives dynamic mod- els for the gear-rotor\u2013bearing system with a nonlinear suspension effect, strongly nonlinear rub-impact force, strongly nonlinear gear mesh force and strongly nonlinear couple-stress fluid film force. Section 3 describes the techniques used in this study to analyze the dynamic response of the gear-rotor\u2013bearing system and presents the numerical analysis results obtained for the behavior of the gear-rotor\u2013bearing system under various operational conditions. Finally, Sect. 4 presents some brief conclusions. Figure 1a presents a dynamic model to simulate the gear-rotor\u2013bearing system under the assumptions of nonlinear rub-impact force, nonlinear fluid film force, nonlinear suspension effect and nonlinear gear meshing force. Figure 1b presents a schematic illustration of the dynamic model considered between gear and pinion. Figure 1c is the model of rub-impact force diagram between rotor and stator. Og and Op are the center of gravity of the gear and pinion, respectively, and Or is the center of gravity of the rotor; O1 and O2 are the geometric centers of the bearing 1 and bearing 2, respec- tively; Oj1 and Oj2 are the geometric centers of the journal 1 and journal 2, respectively; M1 is the mass of the bearing housing for bearing 1, M2 is the mass of the bearing housing for bearing 2, and Mr is the mass of the rotor; Mp is the mass of the pinion and Mg is the mass of the gear; K is the stiffness coefficients of the shafts; K11, K12, K21 and K22 are the stiffness coefficients of the springs supporting the two bearing housings for bearing 1 and bearing 2; C1 and C2are the damping coefficients of the supported structure for bearing 1 and bearing 2, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002496_icorr.2011.5975415-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002496_icorr.2011.5975415-Figure1-1.png",
        "caption": "Fig. 1. Experimental setup showing treadmill, body weight support system and additional mass attached to the subject.",
        "texts": [
            " Therefore, different walking speeds were incorporated into the tests to permit such an effect. The 6 walking conditions for each subject are summarised in Table II. The order of these conditions was randomised for each person. The static weight of the additional mass was compensated for using the body weight support system Levi (Hocoma AG, Volketswil, Switzerland), so that the overall effect was an increase in inertia, but not static weight, of the walking subject. The experimental set-up is illustrated in Fig 1. The body weight support system will tend to produce a horizontal force, since deviations from the vertical position of the cable will produce a lateral force component towards the centreline, as shown in Fig 2. With the force acting in opposite direction to the subject\u2019s lateral movement, the body weight support system acts as a spring which provides assistance in the lateral balance task. Data from the front plate of the treadmill were used to calculate the CoP for the first portion of each step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002122_s0263574708004256-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002122_s0263574708004256-Figure3-1.png",
        "caption": "Fig. 3. Examples of direct singularities for the 3-RPRR manipulator with linear dependency between columns/rows.",
        "texts": [
            " Thus, the singularity conditions described above can be expanded to the distal links being parallel to one another regardless of their alignment with any of the axes. Therefore, for the 3-RPRR manipulator, direct kinematic singular configurations only depend on relative positions and orientations of the distal links. The third column of Jxr becomes zero when all three distal links meet at point P , the origin of the end-effector. Again, since singularities are not frame dependent, the direct singularities can take place when all three distal links meet at a common point regardless of where this is located (Fig. 3(a)). Linear dependency between the rows of Jxr have the same meaning as between the columns. Linear dependency between any two rows happens when two distal links are aligned with the side of the end-effector located in between. Figure 3(b) illustrates such a configuration for the first and second limbs. Since for this configuration \u03b11 = \u03b12 \u2212 \u03c0 = \u03c6 http://journals.cambridge.org Downloaded: 02 Feb 2015 IP address: 128.59.222.12 the direct Jacobian Jxr in Eq. (8) can be rewritten as: Jxr |\u03b11=\u03b12\u2212\u03c0=\u03c6 = \u23a1 \u23a2\u23a3 l1c\u03b11 l1s\u03b11 \u2212l1r1s\u03c81 \u2212l2c\u03b11 \u2212l2s\u03b11 l2r2s\u03c82 l3c\u03b13 l3s\u03b13 l3r3s(\u03b13\u2212\u03c6\u2212\u03c83) \u23a4 \u23a5\u23a6 3\u00d73 . (10) Considering Fig. 3(b) with P at the centre of the moving platform, it is evident that r1s\u03c81 = r2s\u03c82 , therefore, the first and second rows are linearly dependent. The same can be shown for any other two limbs of the 3-RPRR. The same argument can be given for the 3-PRR non-redundant manipulator. For redundant parallel manipulators, inverse singularities occur when the determinant of Jqr J T qr is zero.1 This implies that inverse singularities take place when all the nonredundant manipulators, extracted from the 3-RPRR by locking three of the active joints at the time, are in a singular configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.20-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.20-1.png",
        "caption": "FIGURE 1.20 Construction of stability boundary (upper diagram, from Figure 1.17). On the isolated branch a stable range may occur (large steer angle as indicated in middle diagram). The lower diagram shows the case with complete understeer featuring a stable main branch.",
        "texts": [
            "84) may be violated when we deal with tire characteristics showing a peak in side force and a downward sloping further part of the characteristic. The second condition corresponds to condition (1.65) for the linear model. Accordingly, instability is expected to occur beyond the point where the steer angle reaches a maximum while the speed is kept constant. This, obviously, can only occur in the oversteer range of operation. In the handling diagram the stability boundary can be assessed by finding the tangent to the handling curve that runs parallel to the speed line considered. In the upper diagram of Figure 1.20 the stability boundary that holds for the right part of the diagram (ay vs l/R) has been drawn for the system of Figure 1.17 that changes from initial understeer to oversteer. In the middle diagram, a number of shifted V-lines, each for a different steer angle d, has been indicated. In each case, the points of intersection represent possible steady-state solutions. The highest point represents an unstable solution as the corresponding point on the speed line lies in the unstable area. When the steer angle is increased, the two points of intersections move toward each other",
            " For the six tire/axle configurations, the parameter values have been given in the table below. axle case m cFa C E front a,b 0.8 8 1.2 2 c 0.78 8 1.3 2 rear a 0.9 11 1.2 2 b 0.9 6 1.2 2 c 0.65 11 1.5 1 Determine, for each of the three combinations (two dry, one wet), 1. The handling curve (cf. Figure 1.17). 2. The complete handling diagram (cf. Figure 1.17). 3. The portion of t curves where the vehicle shows an oversteer nature. 4. The stability boundary (associated with these oversteer ranges) in the (ay/g versus l/R) diagram (\u00bc right-hand side of the handling diagram) (cf. Figure 1.20). 5. Indicate in the diagram (or in a separate graph): a. the course of the steer angle d required to negotiate a curve with radius R \u00bc 60 m as a function of the speed V. If applicable, indicate the stability boundary, that is, the critical speed Vcrit, belonging to this radius. b. the course of steer angle d as a function of relative path curvature l/R at a fixed speed V \u00bc 72 km/h. If applicable, assess the critical radius Rcrit. For the vehicle systems considered so far, a unique handling curve appears to suffice to describe the steady-state turning behavior",
            " The domain of Figure 1.22 appears to be open on two sides which means that initial conditions, in a certain range of (r/v) values, do not require to be limited in order to reach the stable point. Obviously, disturbance impulses acting in front of the center of gravity may give rise to such combinations of initial conditions. In Figures 1.23 and 1.24, the influence of an increase in steer angle d on the stability margin (distance between stable point and separatrix) has been shown for the two vehicles considered in Figure 1.20. The system of Figure 1.23 is clearly much more sensitive. An increase in d (but also an increase in speed V) reduces the stability margin until it is totally vanished as soon as the two singular points merge (also the corresponding points I and II on the handling curve of Figure 1.17) and the domain breaks open. As a result, all trajectories starting above the lower separatrix tend to leave the area. This can only be stopped by either quickly reducing the steer angle or enlarging d to around 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001183_robot.1995.525354-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001183_robot.1995.525354-Figure4-1.png",
        "caption": "Figure 4: Geometric Configuration of manipulator",
        "texts": [
            ", six, and wc and c denoting the angular velocity of the M P and the position vector of point C , the center of mass of the MP, with respect to the inertial frame, respectively, as depicted in Fig. 2, that can be obtained as explained in [5]. Matrix A is the p x m' twist-constraint matrix, and 0, is the p-dimensional zero vector, with p defined as the number of twist-constraint equations. Moreover, w ; and i-i can be expressed, in light of eq.(lO), as where i = 1 ,2 ,3 and ai is the vector shown in Fig. 2, while zj is the unit vector parallel to the joint axis Z j , depicted in Fig. 4. Here, U k =: U k ( t ) is as defined in eq.(l), and L k is the shape function matrix evaluated at point Ok+3 in link k . Moreover, w;,;+3 is the angular velocity of Fi+3 with respect to Fi, resulting from the elastic deformation of link i , that can be written for small displacements as - 629 - with IjaOiII being the Euclidean norm of the position vector of point Oi+3, depicted in Fig. 2 , in the undeformed configuration of link i, ( . ) j being the j t h component of vector (.I, while L; and ui are defined in eqs",
            " Upon differentiation of the loop-constraint equations, the dependent generalized speeds can be expressed in terms of the independent generalized speeds . Then, v can be expressed in terms of the independent generalized speeds . Finally, using eq.(24) leads to N, which is the linear transformation mapping the independent generalized speeds into the generalized flexible twist. Vector ti, for the manipulator at hand, can be written as where 81, 82 and 83 are the actuated-joint angles measured in radians, as shown in Fig. 4, and ui is as defined in eq.( l ) . Upon substitution of the values w j and ij from eqs.(22) into eq.(21), and expansion o i the equation thus obtained, vector v is derived in terms of ti and three dependent joint rates, 84, 85 and 86. Three constraint equations are required to eliminate the dependent joint rates from these equations. They are obtained by equating to zero the time-derivatives of the magnitudes of vectors a78, a 7 9 and a 8 9 , which are nothing but the lengths of the sides of the rigid triangle 0 7 0 8 0 9 , i.e., a&&78 = o aT92 i79 = o i28b) a&&89 = o (28c) Here, a 7 8 , a 7 9 and a89 are obtained by writing three loop equations, using Fig. 4, namely, 01 + a1 + a4 + a78 - a5 - a 2 - 0 2 = 0 2 (29a) 01 + a1 + a4 + a 7 9 - a6 - a3 - 03 = 0 2 (29b) 02 + a2 + a5 + a 8 9 - a 6 - a3 - 03 = 0 2 (29c) where oi is the position vector of the origin Oi, as depicted in Fig. 2. Therefore, upon eliminating the dependent joint rates, v can be expressed as a linear transformation o f t ; , which leads to N. Upon assembling of the dynamics models of all links together, we obtain the dynamics model of the overall manipulator as Mi. = bs + bE + bo + b K + b~ (30) where M is the m\u2019 x m\u2019 generalized extended mass matrix of the system, given by M = d i a g ( MI Ma "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001530_iccima.2007.228-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001530_iccima.2007.228-Figure3-1.png",
        "caption": "Figure 3 : Turn angle fuzzy set",
        "texts": [
            " The values are fuzzified with designated linguistic terms (near, medium, and far). Among three output fuzzy sets, the turn-angle fuzzy set has been uniquely defined. The angle lies between -30\u00b0and 30\u00b0 act as a default .The total angle of 60\u00b0 is divided into six amplitudes represented by six member functions, and each of which is associated with the following linguistic terms: positive-left (PL), negative-left (NL), positive-center (PC), negativecenter (NC), positive-right (PR), and negative-right (NR) as shown in Figure 3 . 4.2.2 Pit Detection Sensor: An apparatus and method for uniquely detecting pits on a smooth surface by irradiating an area of the surface; separately sensing radiation scattered from the surface in the near-specular region indicative of a pit and in the far-specular region indicative of a flaw and producing signals representative thereof; normalizing the near-specular signal with respect to the far-specular signal to indicate a pit [5]. 1. Color detection : Identifying the presence or absence of a specific color; 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001796_ac50031a031-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001796_ac50031a031-Figure3-1.png",
        "caption": "Figure 3. Calibration curve of nitrite and nitrate obtained from the soluble enzyme system. All measurement conditions (see text). (0 - 0) nitrate, (0 - 0) nitrite",
        "texts": [
            " This effect becomes especially apparent a t low substrate concentrations, (5 x M to 5 x lo4 M), where poor response times were obtained (>7 min), if the layer was too thick. T o make the layer thinner, a tissue was used to absorb the excess electrolyte. The return of the signal t o a steady, well-defined baseline (the recovery time) was almost instantaneous, provided that the electrolyte layer is renewed between measurements. Cal ibra t ion C u r v e of S t a n d a r d Solu t ions . According - % error observed NO,- N O 3 - to the procedures described above, standard curves for nitrite and nitrate were obtained and are shown in Figure 3. The diverse of diverse linear range is between 5 x 1 x 10 * M NO3- and NO2 . ions ions, M Ca2+ 5 x 10-3 -3 .2 + 1.9 with a slope of 1.10-1.12 pH units/decade. The fact that the Zn2+ 5 x 10-3 - 2.6 -3.5 curve levels off a t high concentrations is possibly due to (1) the oxidation of reduced methyl viologen by molecular oxygen Mn2+ 5 x 10-3 t 1.9 -4.2 CUZ' 5 x 10-3 -80.6 - 75.4 - 1.6 before completion of the enzyme rea( tion. ( 2 ) The equation COZ' 5 x 1 0 - 3 -2.7 NiZ+ 5 x 10-3 + 1.7 - 2.6 by Ruzicka and Hansen (14) does not hold a t high concenMg2+ 5 x 10-3 -3 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002145_physreve.79.051503-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002145_physreve.79.051503-Figure1-1.png",
        "caption": "FIG. 1. Picture of a ferromagnetic filament.",
        "texts": [
            " It may be interesting to remark that thermal fluctuation effects are important for the chains of the ferromagnetic nanoparticles which persistence length may be estimated by lp = d /2 12 =m2 /d3kBT is magnetodipolar interaction parameter of these particles with magnetic moment m and diameter d . Investigation of working of nanomachines formed by ferromagnetic nanoparticles is pending for future publications. Equations for the superparamagnetic and ferromagnetic filaments are derived in 4,11 . Here we are considering twodimensional case. The tangent and normal vectors are = cos , sin ; n = \u2212sin , cos , where is the angle between the tangent and the external field H = \u2212cos t ,0 Fig. 1 . The curvature of the filament 1 /R reads 1 /R=\u2212d /dl l is the arclength of center line . The normal and tangential components of the stress are here and further subscript,\u2026 denotes the derivative Fn = C 1 R ,l \u2212 MH \u00b7 n 1 and F = \u2212 C 1 2R2 \u2212 . 2 Here C is bending modulus, M is the magnetization of fila- ment per unit length that is parallel to the tangent vector, H is the strength of applied magnetic field, and is the Lagrange multiplier enforcing inextensibility of the filament. To have self-propulsion it is necessary to take into account in the theoretical model the anisotropy of the hydrodynamic drag"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003402_j.ymssp.2015.04.006-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003402_j.ymssp.2015.04.006-Figure3-1.png",
        "caption": "Fig. 3. (a) Tyre rolling over straight cleat road and (b) tyre rolling over 451 inclined cleat road.",
        "texts": [
            " The contact pressures are observed before and at the time of cleat impact across the treadband. Fig. 2(b) shows that the pressure distribution is symmetric across the contact patch that ensures flat contact of tyre during straight rolling as it approaches the cleat. The line contact shown in Fig. 2(c) ensures impulse excitation across the treadband, which is responsible for flat excitation spectrum. Analogue plots of Fig. 2(b) and (c), are described in (d) and (e) respectively for 451 inclined cleat simulation. Fig. 3(a) and (b) represents the simulation trials for the same operating conditions, over straight and 451 inclined cleats. The 451 inclined cleat is chosen to have equal excitation in longitudinal and lateral direction of the rolling tyre. The rim is modelled by rigid element outer surface definition and road modelled as rigid surface. The focus of the current research work is to predict structure borne vehicle interior noise due to tyre road interaction. One of the main noise source for this noise is the low frequency (o500 Hz) belt vibrations that contribute to the typical wheel rim dynamics in this region that transfer road excitation to the spindle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002829_iros.2011.6094909-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002829_iros.2011.6094909-Figure4-1.png",
        "caption": "Fig. 4. Analytical Model of a section of a Continuum Arm",
        "texts": [],
        "surrounding_texts": [
            "This work is primarily intended to study the dynamics of general continuum robots. To ground the results on real hardware, the model herein is focused on the Octarm VI continuum robot [12], [23]. Hence, the parameters and constraints implemented in this model conform to that of Octarm VI. Octarm VI is a three section continuum robot. Each section is made up of three McKibben actuators tied together along their lengths. A section of the device extends when there are equal pressure levels in all three actuators and bends when there are different pressure levels in the actuators (noticing that there is no torsion along the length of the arm). Since each section bends in space to form a constant curvature section its analysis can be restricted to a plane during these movements (the orientation of the plane changes as the robot moves). Therefore, a planar model is effective for the case of a single continuum robot section, the subject of the analysis in this paper. The shape of a section of the continuum arm is parameterized by the variables, s - length of arc, \u03ba - curvature and \u03c6 \u2013 orientation. In the 2-D single-section case, orientation (\u03c6) can be neglected. Two actuators are sufficient to model planar operation of a single-section of a continuum arm. We model each actuator as a Mckibben actuator, as realized in the Octarm hardware. Each such pneumatic actuator has air-filled latex tubing enclosed in a braided sleeve. The inherent compliance and damping of the actuator will be represented by a linear spring and damper combination. Thus each module in the model has a pair of linear spring and damper struts. The actuators maintain a nearly constant diameter at all pressure levels and this is accounted for in the model by constraining the distance between the two spring and damper struts. The length of arc (s) of each module is the average length of the two actuators. Another parameter, \u03b8, is introduced to account for bending such that 1 s = \u03ba \u03b8 ."
        ]
    },
    {
        "image_filename": "designv10_10_0000720_cdc.1993.325331-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000720_cdc.1993.325331-Figure1-1.png",
        "caption": "Figure 1: Model of a car with n trailers.",
        "texts": [
            " 4 is the diatance from the wheels of trailer i to the wheels of trailer i - 1, where i E (2,. . . ,n). dl is then the distance from the wheels of trailer 1 to the wheels of the car. ~0 is the tangential velocity of the car and is an input to the aystem. The other input is the angular velocity of the car, w . We denote v = [UO,W]T The tangential velocity of trailer i , v i , is given by i vi = cm(ei,l - ej)vi-l = n c ~ ( e , - l - e,) u0 (3) j=1 where i E (1,. . . , n). An illustration of these definitions is presented in Figure 1. 3 Conversion into a Chained Form In this section, we present a theorem on the conversion of a class of nonholonomic systems into a chained form. The kinematic model (2) is then modified to belong to this class. This theorem will provide the transformation of the kinematic model of a car with n trailers into a chained form. First, denote A A 3 = tqi,.--gqmIT t(3-1) = [ f i ( % - , ) i . . . , f m ( ~ _ l ) I ~ Theorem 1 Let a driflless, two-input system be given bsv 9 1 = U1 (4) 9 2 = U 2 ( 5 ) 4i = f i (&- l )v l , i E { 3 , - * - , m } (6) where f i ( "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.26-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.26-1.png",
        "caption": "FIGURE 1.26 The automobile subjected to longitudinal forces and the resulting load transfer.",
        "texts": [
            " When the slip angles become larger, the forward speed u may no longer be considered as a constant quantity. Then, the system is described by a third-order set of equations. In the paper (Pacejka 1986), the solutions for the simple automobile model have been presented also for yaw angles > 90 . When the vehicle is subjected to longitudinal forces that may result from braking or driving actions possibly to compensate for longitudinal wind drag forces or down or upward slopes, fore-and-aft load transfer will arise (Figure 1.26). The resulting change in tire normal loads causes the cornering stiffnesses and the peak side forces of the front and rear axles to change. Since, as we assume here, the fore-and-aft position of the center of gravity is not affected (no relative car body motion), we may expect a change in handling behavior indicated by a rise or drop of the understeer gradient. In addition, the longitudinal driving or braking forces give rise to a state of combined slip, thereby affecting the side force in a way as shown in Figure 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-31-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-31-1.png",
        "caption": "Figure 12-31 shows a three-point hitch design of the early 1920s that resulted in limited success. This hitch (Patent I\\'o. 1,464,130), developed for the Fer guson-Sherman plow, did not result in any appreciable increase in the rear wheel reaction because the virtual hitch point, f', was too low. Note that the vector sum of c, the compression force in the upper link, and t, the tension force in the lower link, passes near to 0', the instant center of the wheel and soil. It is obvious that the increase in the rear-wheel reaction resulting from P),/L 1 (see chapter 10) is approximately zero because YI is very small.",
        "texts": [
            " It is often desirable to use a hitching system that allows the implement to be controlled more completely than is possible with a single-point drawbar hitch and at the same time provides for rapid hitching and unhitching of the tractor to the implement. Space considerations preclude a detailed discussion of all the systems that have been and are being used. Because the three-point hitch is used by almost every manufacturer of tractors in the world, it would seem advisable to devote most of the discussion to it. As the plow in figure 12-31 enters the soil, the virtual hitch point J' continues to rise until the plow reaches equilibrium. The three-point hitch was developed in 1935 by the late Harry Ferguson (Gray 1954). The dimensions of categories I, II, III, and IV three-point hitches have been standardized by ASAE and SAE. Figure 12-32 illustrates the stan dard three-point hitch. Details of the standard are shown in ASAE S217.1 0 (also SAEJ715 SEP83). Another standard, ASAE S320.1, describes the three point hitch standard for lawn and garden tractors having less than 15 kW of power"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001662_s00422-006-0117-1-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001662_s00422-006-0117-1-Figure1-1.png",
        "caption": "Fig. 1 Experimental setup for the biological experiments (left); force oscillations in the standing legs (right, both middle legs are standing): upper trace shows the movement of the walking hind left leg (L3), other traces show force oscillations in the standing middle legs (L2, R2); (figure after Cruse and Saxler 1980b)",
        "texts": [
            " For the insect, autotomy of a leg is a natural process and the effect of removing one or two legs seems to be little. The insects only reduce their velocity and the step pattern is adapted to result in a stable gait. Second, Cruse and Saxler (1980a,b) performed experiments where a stick insect walked on a treadwheel and one or more of the legs were standing on separate platforms equipped with force transducers. Standing on the fixed platform, the leg developed forces that usually oscillated in the rhythm of the other walking legs (see Fig. 1). In experiments with a diversity of configurations of standing legs the coactivation in the neighbouring legs was observed, resulting in an in-phase relation of the force oscillations in the standing legs in most of the cases. In this paper we want to describe the refinement of Walknet in order to describe these additional biological findings not covered by the earlier version: we introduce the analog-selector which incorporates position and load signals of the controlled leg. It is not a simple state switch as the selector net used in the earlier version, but is providing two analogous motor commands which can be used to drive the intensity of the motor output",
            " An additional coordination influence is needed to account for this data: a coordination influence similar to rule 1 was implemented between hind and the ipsilateral front leg (rule 1HF). With this additional influence the Walknet can also account for amputations of the middle legs. Cruse and Saxler (1980a,b) analysed forces in standing legs of walking stick insects. The insect walked on a treadwheel while one or more of the legs were standing on separate platforms. The forces of the legs were recorded using force transducers: the standing legs produced oscillating forces in the rhythm of the walking legs (see Fig. 1). Cruse and Saxler analysed this oscillations in a set of experiments with a diversity of configurations of standing legs: a coactivation in neighbouring legs was observed, which results in most cases in an inphase relation of the force oscillations in the standing legs. In some situations also out-of-phase oscillations or double frequency oscillations have been reported. Such force oscillations have also been found in lobsters (Cruse et al. 1983). The earlier Walknet could not simulate such a variation of the motor output"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure22-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure22-1.png",
        "caption": "Fig 22 OrcumferentiaEy grooved bearing (NEL/VEB study ease).\" (a) experimental /ournaI orbit (NEL ), (b ) predicted journal orbit {Glacier Metal), {c) oit flow versus feed pressure",
        "texts": [
            " exam- O = 1 8 0 \u00b0 I 58 June I983 Voi !8 No 3 pie of the experimental results obtained, a few of the results relating to the Ruston 6VEB-X Mk III simulated tests are reproduced here (Figs 22, 25 and 27). The shape of the load diagram applied to the NEL Engine Bearing Simulator rig for this engine was closer to that seen relative to the cylinder axis (Fig l(b)) than to that seen relative to the connecting rod (Fig l(a)). The test results for the simulated VEB bearing with a circumferential groove are shown in Fig 22. The experimental orbit is surprisingly similar in shape to that predicted by Glacier (short bearing theory) for the same operating conditions. Cooke infers in the NEL report that the orbit shape is quantitatively realistic although the positioning of the orbit within the clearance space may not be exact. The blunt point on the orbit at position A may be due to the inertia effect of the massive housing yoke in accordance with comments relating to the predictions from the University of Sussex (Fig 2(h)). Experimental oil flow results for the simulated VEB bearing with different feed pressures are shown in the lower part of Fig 22, together with feed pressure flow (Qp) predictions carried out by the author. The comparison with the NEL results is good, suggesting that the feed pressure flow predictions may, at least for a circumferentially grooved bearing, be adequate for design purposes. A more commonly used oil feed arrangement for big end connecting rod bearings is through a drilling in the shaft. The actual position of the drilling is very important, as this affects the oil flow and the resultant film pressures. One can get a direct appreciation of this effect by simply superimposing on the journal orbit relative to the shaft (eg, from load diagram as Fig 1 (c)) the lines for constant values of feed pressure flow, using the Martin/Lee equations s , see Fig 23",
            " . Load line - - - - - Region of increasin(] film thickness-A ~g 29 Predicted performance illustrating increas#~g film t,%iekness regions (NEL/ VEB dam) experimental journal centre orbits from NEL for this single oil feed s tudy did not have the same characteristic shape as the predicted orbits shown in Fig 27 (see typical results for hole posit ioned at 270 \u00b0 around the shaft). This result was rather surprising since the previous NEL experimental orbit for the circumferentially groove bearing (Fig 22) showed remarkably good correlation with the predicted orbit shape. The shape of the NEL orbits for the single h o b case are difficult to understand and shouid be interpreted with caution. ]'he NEL tests show that very large changes in oil flow results frorn different oil feed arrangements. This is pardcutarly so with the single oil feed in the shaft. However. ~\u00a3 one considers the best h o b position and uses that flow as a reference then Cooke found from the NEL Engine Bear\u00b0 mg Simulator that general"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000585_s0040-6090(99)00355-7-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000585_s0040-6090(99)00355-7-Figure1-1.png",
        "caption": "Fig. 1. Sketch of a shaft-loaded blister test, showing the geometry of a conic blister (solid line) and that of the average membrane stress approximation (dashed line).",
        "texts": [
            " The important ratio of shaft to blister radii and its effect upon the constitutive equations will be discussed based on linear elasticity. There are two existing elastic models available for a central point loaded blister test: (i) assuming a blister of conic geometry [3], and (ii) assuming a uniform membrane stress [4,5]. In this paper, we will modify both methods accordingly to accommodate for the blunt tip shaft and will discuss their shortcomings based on experimental results of a model interface. The loading con\u00aeguration is illustrated in Fig. 1. A thin \u00afexible \u00aelm of elastic modulus, E, Poisson ratio, n, and thickness, h, is adhered onto a rigid substrate with a blister radius a. To prevent delamination at the blister edge, the sample is arranged such that the coating faces the shaft with the substrate underneath. A transverse central load P is applied onto the \u00aelm via a steel ball of radius R, resulting in an inner contact circle (denoted by subscript c hereafter) of radius c and an outer non-contact annulus (denoted by subscript n) of width (a 2 c)",
            " Wan) d3w dr3 1 1 r d2w dr2 2 1 r2 dw dr 2 Nr D dw dr F D 1 d dr 72f 1 Eh 2r dw dr 2 0 2 where F is the load function with F Fc pr 2 for 0 # r # c, Fn P 2pr for c # r # a; f is the stress function with the radial stress Nr 1=r df =dr and tangential stress Nt d2f =dr2, and D is the \u00afexural rigidity with D Eh3=12 1 2 n2 . The exact solution of Eqs. (1) and (2) was discussed earlier [5]. In this paper, we will consider in detail a \u00afexible membrane under pure stretching with negligible D. The overall blister pro\u00aele can be separated into the contact and non-contact parts: w r wc r 1 wn r 3 In the contact region 0 # r # c , the blister geometry conforms to the spherical steel ball. The contact radius is shown by simple geometry to be equal to c Rsinu 4 where u is the half angle subtended from the ball (Fig. 1). In case of large R and small wc0 wc wc0 1 2 r2=c2 5 with wc0 R 1 2 cosu < c2=2R. Such a spherical geometry suggests that the deformation is caused by a uniform applied pressure, p. It was indeed shown in literature that Eq. (5) satis\u00aees both Eq. (1) and Eq. (2) in the limit of D! 0 [8]. Drawing an analogy to a liquid bubble with a radius of curvature, R, Hinkley [6] suggested a uniform membrane stress approximation, Nr Nt pR=2. For small membrane strain R pc4Eh 3P 1 2 n \" #1=3 6 which leads to a cubic constitutive equation P 8pEh 3c2 1 2 n w3 c0 7 In the non-contact region (c # r # a), since the membrane stress Nr(r) may take the form of a polynomial in r, Eq",
            " There are two possible ways leading to an analytical elastic solution: (i) by assuming a straight edge conic blister geometry [3] where Eq. (2) only is satis\u00aeed, the corresponding membrane stress is deduced; or (ii) by assuming an average membrane stress [5], Nr Nt N, where Eq. (1) is solved analytically, the blister geometry is deduced. It will be seen later in Sections 3 and 4 that these two complimentary approaches set the upper and lower bounds for actual measurements. If a conic geometry is assumed for the non-contact region (Fig. 1), the blister pro\u00aele becomes wn a 2 r tanu 8 The overall blister height is found by substituting both Eqs. (5) and (8) into Eq. (3) so that w0 wc0 1 wn0 a 1 2 z tanu 1 r 1 2 cosu 9 where wn0 w jr c a 2 c tanu, z c=a rrsinu and r R=a. For small u, wc0 < c2=2R and wn0 < az 1 2 z =r, therefore Eq. (3) gives w0 a2 2R ! z 2 2 z2 10 Now the membrane stress can be deduced by substituting Eq. (8) into Eq. (2), so that df dr 2 Eh tan2u 4 rlogr 1 C1r 1 C2 r 11 with constants C1 and C2 satisfying the two boundary conditions: (i) Nr jr c P=2pcsinu, which is the maximum stress, Nmax PR=2pa2 1=z2 and (ii) Nr jr a P=2pasinu, which is the minimum stress Nmin PR=2pa2 1=z ",
            " {The loading con\u00aeguration considered by Williams is equivalent to a shaft with \u00afat end pressing on the membrane. In this case, the contact area does not change with external load, i.e. z is a constant throughout the entire loading process}. It is interesting to note that (i) Nav is independent of r so that d Nr 1 Nt =dr 0 and Eq. (2) is violated, (ii) Nav does not possess the singularity at the blister center for r 0, and (iii) limit Nav ! 1 as r! 0. The blister pro\u00aele in the noncontact region is found by solving Eq. (1) exactly [4,5] to be wn r P 2pNav log a r 17 (see Fig. 1). Therefore, from Eqs. (4) and (14), wn0 P=2pNav log 1=z c2=R log 1=z . By substituting Eqs. (5) and (17) into Eq. (3), the overall blister height is equal to w0 a2 2R ! z2 2log 1=z 1 1 18 In the limiting case of R 0, z 0 and w0 is unde\u00aened at r 0 because of the logarithmic term in Eq. (18) and \u00aelm puncture becomes inevitable. Combining Eqs. (15) and (16), we get P pEha 1 2 n C2 z 19 where C2 z; r z6log 1=z r3 1 2 z2 By combining Eqs. (18) and (19), the constitutive equation becomes P pEh 4a2 1 2 n V2 z w3 0 20 where V2 z 32 log 1=z = 1 2 z2 2 log 1=z 1 1 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001800_j.jmatprotec.2006.11.149-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001800_j.jmatprotec.2006.11.149-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the forming process. (a) 3D reconstruction; (b) t",
        "texts": [
            " The application of sheet with square holes, on one and it is need which the human body organization can grow n it, on the other hand the forming performance of it can be mproved, the resistance to deformation can be reduced effecively in the forming process, and the wrinkle defects can also e suppressed effectively. . Brief introduction of the forming process In this paper, the 3D curved surface is formed in a high ccuracy MPF press with blank-holder device. It is realized by ollowing processes: 3D reconstruction of the absenting cranium ccording to the sufferer\u2019s primary cranium CT data (Fig. 1(a)), btaining the model data file of the absenting part, technologic omputation by MPF special-purpose CAD software (Fig. 1(b)), djusting the matrices of punches to curved surface by the shape easurement system based on the information generated by AD, acquiring the convex\u2013concave shape cavity (Fig. 1(c)), orming eligibly shaped 3D curved surface of prosthesis from itanium alloy retiary sheet in the MPF press. . Forming result prediction and control of forming efects Numerical simulation is an effective method to predict formng results, but the simulation of MPF process is much more omplicated than that of conventional pressing. Here LS-DYNA ith an explicit solver is introduced to simulate the MPF of itanium alloy cranial prosthesis, including the creation of FE d e s echnologic computation; (c) convex\u2013concave shape cavity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001127_rob.4620120903-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001127_rob.4620120903-Figure6-1.png",
        "caption": "Figure 6. (Cases A and B). Foot trajectories for a discontinuous crab gait",
        "texts": [
            "1. TPDC Gait with No Change in Initial Position The general formulation for the crab gait consists in computing the foot displacements needed to follow a specified crab angle trajectory. These new foot positions must be located inside the leg workspace. This means that if a displacement in the y-axis was trying to locate the foot outside its workspace, this displacement will be restricted to its maximum, given by R,/2, and the displacement along the x-axis will be related to the y displacement. Figure 6 illustrates two possible cases. The stroke, or increment in the foot position ( L x , L,,), may be defined as follows: Case A R 2 if IR, tan a ( 5 L, = R, L, = R, tan a Figure 5 shows a sequence of body postures. For the crab angle, a, shown in this figure, each leg moves (R.v, R, tan a) during a locomotion cycle, and the body moves (R,/2, (R,/2) tan a) in each phase. Figure 5 shows the diagonal that determines the stability margin for a crab gait (solid lines) and the diagonal for a non-crab body motion (dotted lines)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003227_s11071-014-1701-x-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003227_s11071-014-1701-x-Figure7-1.png",
        "caption": "Fig. 7 Simulation results of phase diagrams, Poincar\u00e9 maps, Lyapunov exponent and fractal dimension obtained for rotor center at s = 2.00 (l\u2217 = 0.3) in the horizontal direction (xr). a Phase diagram, b Poincar\u00e9 map, c Lyapunov exponent, d fractal dimension",
        "texts": [],
        "surrounding_texts": [
            "3.1 Analytical tools for observing nonlinear dynamics The analytical tools used for observing nonlinear dynamics of the gear-rotor\u2013bearing system with rubimpact effect in this study are dynamic trajectories, Poincar\u00e9 maps, bifurcation diagram, Lyapunov exponent and fractal dimension. We can check the dynamic trajectories and Poincar\u00e9 maps for each bifurcation parameters to clarify the more detailed dynamic behaviors. Then, a bifurcation diagram summarizes the essential dynamics of the system and is therefore a useful means of observing its nonlinear dynamic response at this step. Finally, maximum Lyapunov exponent and fractal dimension are used as the most useful tools to detect chaotic motions for nonlinear dynamical systems. The basic principles of each analytical tool are reviewed in the following subsections."
        ]
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure2-1.png",
        "caption": "Fig. 2 Screw.",
        "texts": [
            "org/ on 01/15/2018 Ter classification of the V-chains, especially the parallel V-chains, of 3-DOF motions is still an open issue. Three-DOF PMs can be named according to the types of their V-chains. The motion patterns of the 3-DOF PMs are thus clearly shown by their names. For example, in a PPR-PM, the moving platform can rotate about an axis which translates along a plane which is parallel to the directions of the two P joints. Planar PMs, spherical PMs and translational PMs can be alternatively called E-PMs, S-PMs, PPP-PMs and PPR-PMs. A (normalized) screw is defined by (See Fig. 2) $ =  [ s s\u00d7 r + hs ] if h is finite[ 0 s ] if h =\u221e (1) where s is a unit vector along the axis of the screw $, r is the vector directed from any point on the axis of the screw to the origin of the reference frame O-XYZ, and h is called the pitch. Two screws, $1 and $2, are said to be reciprocal if they satisfy the following condition: $1 \u25e6 $2 = [\u03a0$1]T $2 = 0 (2) where \u03a0 = [ 0 I3 I3 0 ] (3) Copyright  2004 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Down where I3 is the 3 \u00d7 3 identity matrix and 0 is the 3 \u00d7 3 zero matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001105_robot.2001.933160-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001105_robot.2001.933160-Figure8-1.png",
        "caption": "Figure 8: Multiconnection digraph representation the configurations shown in Figs. 7.a-b",
        "texts": [],
        "surrounding_texts": [
            "the n ports of another module, then there are n! ways in which the two modules can be connected, many of which might be topologically different.\nThe Conro module is a multiport module and thus, we cannot use a connectivity graph to uniquely identify a configuration. For example, the two configurations shown in Figs. 4.a-b have the same connectivity graph shown in Fig. 4.c (a module has been colored for visualization purposes). A way to distinguish between configurations of multiport modules is to use the labels of the ports in the representation. In this case a suitable representation of the module is that shown in Fig. 3.c, where tlie module is represented by its ports, i.e., a vertex represents a port while an edge indicates that two ports either belong to the same module or belong to two connected modules.\nOur goal is to find a graph-only representation of a robot that would allow us to distinguish between dif-\nferent configurations regardless of their labelings, i.e., the unlabeled version of the graph must be sufficient to identify the configuration. Unfortunately, the direct use of the labeled-graph representation of a robot with multiport modules leads to ambiguous unlabeled graphs. Figures. 5.a-b show the labeled graphs of the two configurations shown in Figs. 4.a-b. We can see that the unlabeled version of both graphs is the same.\nThe problem of how to make the \u201clabel\u201d itself a part of the graph can be solved in various ways. In our case, we mapped the labeled graph in Fig. 3.c to the digraph in Fig. 6.a by extending an edge from port fi to port f, for i < j , i.e., vertex fi has n - i edges leaving it or, equivalently, it has i - 1 edges arriving to it, where n is the number of ports of the module. This digraph unambiguously represents a multiport module because it is rigid, i.e., it has no automorphisms and thus, there is only one way to interpret it [ll]. Hence, we can now represent robots built with multiport modules without ambiguity. For example, the two configurations shown in Figs. 4.a-b have the digraph representations shown in Figs. 6.b-c, respectively. An inspection shows that the corresponding unlabeled digraphs, indeed, are not isomorphic. The graph representation of Fig. 3.c preserves the symmetries of the module while the digraph representation of Fig. 6.a destroys it; modules that have partial symmetries can be represented using a combination of both representations.",
            "The same approach used to distinguish configurations of multiport modules can be used to distinguish configurations of modules with multiconnection ports. A multiconnection port is one that allows two ports of two modules to be connected in different ways. For example, the Conro modules can be connected to each other while they are both lying on their \u201cbellies\u201d or we can turn one of them \u201cbelly-up\u201d and still have a legal physical connection. This situation is shown in Figs. 7.a-b where module A is attached to module B while both lying on its belly and after been turned upside-down. In this case, the multiport digraph representation of a module is insufficient to uniquely represent both configurations as both share the same such digraph, namely that of Fig. 6.b.\nIn the same way that we disambiguated multiport modules by representing the module as a set of ports, we can disambiguate multiconnection multiport modules by representing the ports as a set of connections, i.e., each possible connection in each port needs to be labeled. In the case of the Conro module, a given port of a module can be connected to a given port of another module in one of two relative orientations: belly-down or belly-up. Hence, each port has only two associated connections d l and d2 as shown in Fig. 3.a. The corresponding labeled graph of this module representation is that of Fig. 3.d. As before, the labeled graph of the module is replaced by a digraph to make the label itself a part of the graph. This multiconnection digraph is shown in Fig. 7.c. Using this representation of the module, the configurations in Figs. 7.a-b are represented by the graphs shown in Figs. 8.a-b. which have nonisomorphic unlabeled graphs.\nThe module representations described in this section are quite general and can be used to represent other homogeneous modular robots. The extension to heterogeneous modular robots is straightforward as different types of modules can be labeled by attaching to a given vertex of each digraph a tag that identifies the type of the module (e.g., [Ill, pg. 7).\nof\n4 Configuration discovery The configuration discovery process is used to obtain a representation of the robot configuration. In Section 3 we discussed three different module representations: the connectivity graph and the multiport and multiconnector digraphs. Since the Conro module is a multiport module, it is possible to have two configurations with the same topology (as shown in Figs. 4.a-b) and thus, we cannot use the connectivity graph to represent Conro robot configurations. On the other hand, although physically the Conro module is a multiconnector module, functionally it is not. Indeed, as shown in Figs. 7.a-b, a port can be connected to a module in either a \u201cbelly-up\u201d or \u201cbelly-down\u201d configuration. However, a working \u201cbelly-up\u201d Conro module cannot be connected to a \u201cbelly-down\u201d module because the modules would not be able to communicate, i.e., the infrared pairs will be paired emitterto-emitter and transmitter-to-transmitter. Hence, the multiport digraph representation is all that is needed to obtain an unambiguous representation of a working Conro robot.\nWe can represent a digraph using its adjacency list or its incidence or adjacency matrix. In this paper we will use the adjacency matrix representation because it will help us with the identification of the configuration. The adjacency matrix PA of the multiport digraph G(A) of the module A shown in Fig. 6.a is\nwhere P~(i,j) = 1 if there is an edge from the i-th vertex to the j - th vertex [12]. In the case of Conro, a module can be connected to another using one and only one of its ports. For example, the following matrix C represents a two-module configuration in which",
            "the port f3 of a module A is connected the port fl of a module .B (since the relation is symmetric, port f l of module B is connected to port f3 of module A):\nC = 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0\nThis matrix can be written as a block matrix as\nr o o 0 0 1 PA SAB 0 0 0 0 C = [ SA'R\n0 0 0 0 L\nwhere the Sij matrix indicates the connection between modules i and j. The general form of a configuration matrix of a N-module robot is\nSBTN . . .\nwhere SIJ = 0 if modules I and J are not adjacent. A matrix S I J such that S(u , w) = 1 is denoted as Su.u. Since Conro is a homogeneous robot, all its modules are identical and thus, P = Pi for all i .\nThe discovery of the configuration matrix has three stages: the determination of the adjacency list of each module, the collection of these lists and the construction of the configuration matrix using the multiport digraph representation of a module. Assuming that each module has a unique identification (ID), then these processes need only two commands: GETID() and GETADJLISTO. The command GETID() received by a module through its i-th port asks the module to transmit its ID to the module attached to the same port i . The command GETADJLIST(m-ID, s-ID) requests the module with ID s-ID (i.e., the slave) to send its adjacency list to the module with ID m-ID (i.e., the master). On power up, each module sends a GETID() command through each of its ports and thus, finds the IDS of all the modules to which it is connected. This provides cach module with a local adjacency list.\nThe second step of the configuration discovery, the collection of the adjacency lists of the modules, is done by the master. In order to put the process in a context, we will assume that the master is an external host computer that has communication with a module\nof the robot through one of its ports, as shown in Fig. 9. To the modules, the host computer looks like a module with I D = 0. Since the host does not know in advance how many modules are in the robot, we use a linked list of dynamically allocated structures called modules. If inod is a module then mod.ID is a field that contains the ID of the module, mod.port[i] is a field that contains a pointer to the module connected to the i-th port of module mod. ID and mod.idx is a field that contains the position of mod in the list of modules. Since there is a one-to-one correspondence between a module and its representation, we will refer\nlocal adjacency lists is done, in a depth-first search fashion, using the following pseudo-code.\nto both simply as the module. The collection of the\nBUILDADJLIST () 1 2 3 id t GETID () 4 if id f 0 then 5 6 7 8 9 return list masterMod t NEWMODULE ( 0, 0 ) list t APPEND ( A , masterMod ) adj t NEWMODULE ( id, 1 ) list t APPEND ( list, adj ) list t AUXADJLIST ( adj, list, 2 ) masterMod.port[ 1 ] t adj\nThe list is initialized with the module that represents the computer, the master module with I D = 0, in the 0-th position. In line 3, the master queries the serial port to see if it is attached to a robot. If there is a module adjacent to the master, a new module is created, initialized and appended to the list. The call in line 7 adds to the list all the modules attached.to this new module. Finally, in line 8, the new module is set as the module connected to the master through the first port."
        ]
    },
    {
        "image_filename": "designv10_10_0002180_ac50037a032-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002180_ac50037a032-Figure1-1.png",
        "caption": "Figure 1. Construction of electrodes. (a) redox electrode, (b) lactate enzyme electrode. A, Ag/AgCI electrode, B, Agar gel containing 3 M KCI, C, PVC tube, D, redox compound solution, E, PVC-Fc membrane, F, rubber ring, G, dialysis membrane, H, enzyme-gelatin gel layer",
        "texts": [],
        "surrounding_texts": [
            "National Chemical Laboratory for Industry, Hiratsuka Branch, Hiratsuka, Japan Naoki Kamo Faculty of Pharmaceutical Sciences, Hokkaido University, Sapporo, Japan A potentiometric enzyme electrode for lactate is developed. The enzyme electrode is constructed by coating the sensor membrane of the redox electrode with a film of enzyme-gelatin gel layer. The enzyme used is lactate dehydrogenase which catalyzes the oxidation of lactate by ferricyanide. The change in the concentration ratio of ferricyanide to ferrocyanide is monitored by the redox electrode which is a membrane electrode sensitive to redox potential of the solution. A plot of the potential of enzyme electrode vs. !og [lactate] gives an S-shaped curve which depends on enzyme quantity and ferricyanide concentration. A relation between the enzyme electrode poteniial and substrate concentration is derived semitheoretically. The equation explains the results successfully. Enzymes have been used widely in the field of analytical chemistry owing to their substrate specificity ( I ) . The enzyme electrode, one of many useful analytic a1 devices. is an electrochemical sensor made by combination of an enzyme reaction with an electrode. T h e enzymc electrode enables us to determine the concentration of a specific organic species continuously and easily. Many enzymc electrodes have been reported in the past decade. which are classified in two groups; (1) T h e change in concentration of a charged substance produced by an enzyme reaction is measured potentiometrically with use of the ion-selective electrode (2-6). (2) The amount of current caused by oxidation or reduction of a product or a reactant of t h e reaction is measured polarographically (7 -13). For enzymes catalvzing the oxidationreduction reaction. the polarographic method has mainly been employed (7-13). In the present paper. we report a new potentiometric enzyme electrode with use of the eii7yme catalyzing the I Present address, National Chemical I aboratory for Industry. Hiratsuka Branch. 1-3-4 Nishiyawata. Hira rqukashi, Kanagawaken, .Japan. Lactate oxidation-reduction reaction. For monitoring the progress of such reactions, a new membrane electrode sensitive to redox potential (redox electrode) was developed. The sensoimembrane of the redox electrode is a plasticized poly(vinylchloride) membrane containing dibutylferrocene (PVC-Fc membrane). I t responds to the redox potential of the solution. The enzyme electrode was constructed by coating the sensor membrane of the redox electrode with a film of enzymegelatin gel. The enzyme used is lactate dehydrogenase (cytochrome b2, EC 1.1.2.3) which catalyzes the oxidation of lactate in the presence of an electron acceptor such as ferricyanide; pyruvate + 2Fe(CN):- + 2H+ The change in the concentration ratio of ferricyanide to ferrocyanide in the enzyme gel layer caused by the enzyme reaction is detected by the redox electrode.. T h e equation relating the potential of the enzyme electrode to the substrate concentration is derived semitheoretically and it explains the results obtained successfully. EXPERIMENTAL Materials. Lactate dehydrogenase (cytochrome bp, EC 1.1.2.3; prepared from yeast) and catalase (EC 1.11.1.6) were purchased from Sigma Chemical Co. L-Lactate was purchased from Sigma Chemical Co. and used after neutralization with NaOH. Dibutylferrocene and dioctylphthalate were obtained from Tokyo Kasei Co. (Tokyo, Japan). Gelatin was obtained from Nippi Co. (Tokyo, Japan) and purified by electrodialysis a t room temperature for 30 h. Preparation of PVC-Fc Membrane and Redox Electrode. In 10 mL of tetrahydrofuran (THF) were dissolved 250 mg of poly(vinylch1oride) (PVC), 500 mg of dioctylphthalate (DOP), and 300 mg of dibutylferrocene (Fc). This solution was poured into a Petri dish (60 cm2 in area) and evaporated slowly a t room temperature to form a thin membrane (0.14.15 mm in thickness). A piece of the PVC-Fc membrane was peeled off and glued to a PVC tube with THF. An AglAgC1 electrode was used as the inner reference electrode which consisted of a silver wire mounted in a glass pipet filled with an agar gel containing 3 M KCI. The 1978 American Chemical Society 0003 '00/79~0351-0100$01 O O / G CC ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 101 inner reference solution consisted of 50 mM ferricyanide and 50 mM ferrocyanide. The redox electrode is schematically illustrated in Figure l (a) . Construction of Lactate Enzyme Electrode. An appropriate amount of lactate dehydrogenase and a small quantity of catalase were dissolved in 0.1 M phosphate buffer solution (pH 6.0) containing 0.1 mM EDTA, 0.1 mM MgSO,, and varying concentrations of K,Fe(CN), and K,Fe(CN)6. The concentration ratio of ferricyanide to ferrocyanide was kept constant a t 4:l (The reason is described in \"Results\".). This buffer solution was denoted by Fi-Fo solution, hereafter. To the enzyme solution. an equal volume of the Fi-Fo solution containing 5% gelatin was added and mixed. On the PVC-Fc membrane (0.25 cm2) of the redox electrode, 10 pL of the enzyme- gelatin mixture was placed dropwise and spread uniformly. After the mixture was gelated a t 4 \"C for 10 min, it was secured in place with a dialysis membrane and a rubber ring (see Figure l(b)). Enzyme Activity Measurement. The activity of lactate dehydrogenase was estimated by the initial rate of reduction of ferricyanide which was determined spectrophotometrically at 420 nm at 25 \"C (14). Except for experiments on determination of the optimum pH of activity, the reaction mixture contained 0.1 M Tris-C1 (pH 8.0), 0.1 mM EDTA, 0.1 mM MgSO,, 0.02 M L-lactate and 0.4 mM K,Fe(CN),. The reaction was initiated by addition of a small quantity of the enzyme. The buffers used for determination of optimum pH were 0.1 M Tris-C1 (pH 9.0-5.51, 0.1 M sodium phosphate (pH 7.5-6.01, and 0.1 M sodium acetate (pH 5.5-4.5). The stability of the enzyme at varying pH mas determined as the usual procedure. After the enzyme was incubated in an appropriate buffer for 2 h a t 25 \" C under the aerobical condition, the residual activity was measured as described above. The quantity of the enzyme entrapped in gelatin gel was expressed in \"units\". One unit is defined as the amount of the enzyme which catalyzes reduction of 1 pmol of ferricyanide in 1 min a t 25 \"C in the solution containing 0.1 M Tris-C1 (pH 8.01, 0.1 mM EDTA, 0.1 mM MgSO,, 0.02 M L-lactate and 0.4 mM K,Fe(CNI6. Potentiometric Measurements of the Redox Electrode and t h e Lactate Enzyme Electrode. The potential difference between the redox electrode and a reference electrode (Type N o 201 OA-05T, Hitachi-Horiba, Tokyo. Japan) was measured at 25 \"C with a vihrating reed electrometer (Model TR-8434, Takeda Riken. Tokyo, Japan) connected to a pen-writing recorder. The same apparatus was used for the lactate enzyme electrode. The enzyme electrode was immersed in 10 mL of Fi-Fo solution and the st,eady potential ( E ) was recorded. The solution was stirred magnetically and maintained at 20 \"C. When an aliquot of lactate solution was pipetted into the solution, the potential changed in negative direction and reached a steady value ( E 7 . The magnitude (absolute value) of the potential change, i.e. (E ~ E'I, is denoted by AE. hereafter. The enzyme electrode was stored in Fi-Fo snlrition a t 4 \"C. RESULTS Redox Electrode. When two solutions of different redox potential were separated hy the PVC-Fc membrane, the magnitude of the membrane potential generated depended on the redox potential difference across the membrane. In Figure 2, the potential of the redox electrode is plotted vs. log ([ferricyanide]/[ferrocyanide]). For the data points of the respective lines, the total concentration of ferricyanide and ferrocyanide was kept constant. The plots in Figure 2 gave a straight line with a slope of 52 niV per decade of [ferricyanide]/ [ferrocyanide] a t least in the range of [ferricyanide] / [ferrocyanide] between 0.01 and 4. T h e electrode must be used in this region. Therefore, the concentration ratio of ferricyanide to ferrocyanide in Fi-Fo solution was chosen as 4, because the enzyme reaction decreased this ratio. In the linear region, the electrode potential, E, can he expressed as: E = E o + 52 log ([ferricyanide] / [ferrocyanide]) (in mV) As the total concentration of ferricyanide and ferrocyanide in a test solution increased, E\" became larger in the positive direction. E\" also depended on the concentrations of electrolytes present in the test solution. The influence of pH on E\" was investigated by changing the pH of the solution containing 0.1 M KCI, 0.2 m M K,3Fe(CNR. and 0.2 m h l K,Fe(CN),. The pH of the solution was adjusted hy adding HC1 or NaOH. KC1 was added to eliminate the effect of change in ion concentration of E\". The pH of the solution had almost no effect on E\" except at low p H (less than 4) . Lactate Enzyme Electrode. Tt is reported that at constant lactate concentration the rate of rediiction of ferricyanide catalyzed by lactate dehydrogenase is nearly independent of acceptor concentration down to ahout 0.1 mM. Le., the reaction is of zeroth order with respect to acceptor concentration (1.5, 16). We obtained the same results. The optimum p H was found to he 8. This value was essentially the same as that reported by previous investigators (1.5). L,actate dehydrogenase, however, was unstable at optimum p H under the aerobical condition and it lost ahout 30%' of' its activity in 2 h at 25 \"C. In contrast. the enzyme retained almost all activit,y within 2 h at pH 6.0. Further storage a t p H 6.0 led to a decrease in activity. hut addition of a small quantity of catalase diminished inactivation of the enzyme. Taking these ohservations into account. lactate dehydrogenase was always used together with a small quantity of catalase and the pH of the enzyme gel was maintained at, 6.0. Figure 3(a) and (h) show plots of potential change of enzyme electrode (2) vs. concentration of lactate in logarithmic scale for various Fi-Fo solutions. Addition of lactate to Fi-Fo solution into which the enzyme electrode was immersed shifted 102 ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 a 1 1 r- I the electrode potential in the negative direction. This potential change indicates the decrease in the value of log ([ferricyanide] /[ferrocyanide]) due to the enzyme reaction, because the redox electrode did not respond to lactate or pyruvate in the range less than 10-1 M. The steady potential was found in 20-30 min after pipetting lactate. As described above, the absolute value of the potential deflection was denoted by AE. Plots of 1E vs. log [lactate] give an S-shaped curve, as shown in Figure 3, to which theoretical consideration is made in \"Discussion\". When ferricyanide concentration in Fi-Fo solution was increased under the condition tha t the enzyme quantity was kept constant, AE became smaller a t a given substrate concentration. Higher enzyme activities resulted in steeper slopes. Figure 4 shows the dependence of A E on the quantity of the enzyme. DISCUSSION Redox Electrode. Hinkle (17) has reported that addition of dibutylferrocene to the phospholipid membrane which separates oxidizing and reducing solutions generates membrane potential. Figure 2 reveals that the plasticized PVC membrane containing dibutylferrocene also generates the membrane potential corresponding to the difference of the redox potential. The mechanism of generation of membrane I - 1 - 2 -3 - L .cq (Lacrate M 1 Figure 4. Dependence of the enzyme electrode potential ( A \u20ac ) on enzyme quantity. The ordinate has the same meaning as in Figure 3. The concentration of ferricyanide in Fi-Fo solution is 20 mM. Enzyme quantity is: 0, 0.031 unit, A, 0.016 unit, 0, 0.006 unit potential in this system can be explained as follows. At the interface between the reducing solution (R phase) and the membrane (M phase), Fc is reduced to a neutral form, FC(,,d), while a t the interface between the oxidizing solution (0 phase) and M phase, Fc is oxidized to a cation, Fe+(oxl. If it is assumed tha t the PVC-Fc membrane is permeable predominantly to FC[,,d) and Fc+(,,), the accumulation of positive and negative charges is caused in R and 0 phases due to the redox reaction, respectively. The accumulation of charges supresses the redox reaction a t interfaces and apparent equilibrium is attained. The membrane potential in this stage is approximately equal to the redox potential difference between both sides of the membrane. As shown in Figure 2, the slope in the linear portion was 52 mV per decade of [ferricyanide] / [ferrocyanide] which was a little smaller than a Nernstian value of 59 mV. The reason for the deviation from the ideal value is not clear a t present, bu t the most possible explanation is tha t the membrane leaks inorganic ions slightly other than Fc+[,,). This leakage of the membrane may also explain the result that the value of Eo was affected by the presence of electrolytes. On this aspect, we are now performing further experiments. Lactate Enzyme Electrode. The change in the potential of the lactate enzyme electrode is due to the change in the value of [ferricyanide]/ [ferrocyanide] in the enzyme gel layer. When the electrode is immersed in a substrate solution, the fluxes of substrate, acceptor, and products are caused by diffusion and by the enzyme-catalyzed reaction. Then, the following equations are set up in accordance with the mass-conservation law; dS,\"/dt = U, + PL(S , - SIm) (i = 1, 2, 3) (I) where S,\", a,, P, and S, stand for the concentration of i in the enzyme gel layer, the production of i due to the enzyme reaction, the permeability coefficient of i in the dialysis-gelatin membrane and the concentration of i in the bulk solution, respectively. Subscripts 1, 2, and 3 represent lactate (substrate), ferricyanide (acceptor), and ferrocyanide (product), respectively. This set of equations is solved under the following assumptions ( 4 ) : (1) The enzyme reaction obeys Michaelis-Menten kinetics. (2) The rate of the enzyme reaction is independent of ferricyanide concentration as described above and the presence of ferrocyanide does not affect the reaction rate. (3) The concentrations of substrate, acceptor and products in the bulk solution are kept constant. According to the above assumptions and the stoichiometry of the reaction, u, is expressed as follows: a1 = -VS1\"/(K + S l m ) = 2a1 = -2VS,\"/(K + SI\") a3 = -2a1 = 2VS,rn/(K + S l m ) ( 2 4 (2b) (2c) ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 103 Substituting Equation 10 into Equations 8 and 9, we obtain (11) 2(V/K)PlSl P2[P1+ (V /K) I s z m = sz - ~ where V and K are the maximum rate and Michaelis constant, respectively. Substitution of Equation 2 into Equation 1 yields Equations 3, 4, and 5: dSl\"/dt = -VSlm/(K + S I m ) + Pl(S1 - SI\") dS,\"/dt = -2VSlm/(K + Si\") + P2(S, - S2\"') dS,\"/dt = 2VSI\"/(K + SI\") + PS(S3 - S g m ) (3) (4) ( 5 ) We confine the discussion only to the case of steady state and then, dS,\"/dt = 0 (i = 1, 2 , 3 ) (6) We consider the two cases where S1 << K and SI >> K. First, for the case where S, is dilute compared with K , i.e., S1 << K , Equations 3, 4, and 5 are reduced to the following set of equations with use of Equation 6 ( 7 ) (8) (9) -VS1\"/K + P,(S1 - S l m ) = 0 -2VS1\"/K + PZ(S2 - S 2 m ) = 0 2VSlm/K + P,(S3 - S 3 m ) = 0 Equation 7 is recast to give (10) Next, we consider the case where SI >> K , Equations 3, 4, and 5 are approximated as follows: -v + PI(s1- SIrn) = 0 (13) -2v + P& - S;!m) = 0 (14) 2v + P,(S, - Sp) = 0 (15) From Equations 14 and 15, we obtain (16) The electrode potential in the absence of lactate is given as Equation 18; E = E\" + 52 log ( S 2 / S 3 ) (18) When lactate is present in the bulk solution, the electrode potential is given as E ' = E\" + 52 log (Sgm/Sgm) (19) Then we obtain the following equations with use of Equations 11, 12, 16, 17, and 19 E' = RO + and 2v sz - - p2 2v s 3 + - p3 (SI >> K ) (21) E ' = E\" + 52 log Therefore, 1E ( = [ E - E l ) is expressed as follows; and 1E = 5 2 log S2(s3 + (S, >> K ) ( 2 3 ) S,(SZ - B ) where 2 ( V / K ) P i P3tP1 + (V/K)I a' = 2 ( V / K ) P , CY = P,[Pl + ( V / K ) I p = 2V/P2 p' = 2V/P3 The ratios of CY' to cy and B' to p are equal to P2/P3. Since P2/P3 is the ratio of the permeability coefficient of ferricyanide to ferrocyanide, it can be determined by the measurement of the permeation rates of ferricyanide and ferrocyanide through the three-layer membrane consisting of the dialysis-gelatin-dialysis membranes. The value of P2/P3 was found to be 1.5, and virtually independent of the concentrations of fer- 104 ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979 Table I. Values of 01 and p Calculated from Equation 24 As discussed above, the value of B changes from asl to @ with increasing the concentration of substrate, S,: 0 is proportional to S1 for such a region tha t SI << K and 0 increases to the constant value (3) with increase of S I . It seems as if 0 were a rate of enzyme reaction. Then we assume the following equation relating B to the substrate concentration; enzyme quantity 3 , units 0.006 0.016 0.031 ferri cyanide concn, mM 0.32 0.80 2.0 10.0 20.0 2.0 5.0 10.0 15.0 20.0 20.0 01 P 0.99 - 1.10 - 0.91 - 1.02 2.48 1.02 2.46 2.09 - 2.05 - 1.87 6.54 2.26 6.45 1.90 6.11 2.9 12.5 mean value 01 P 1.0 2.5 2.0 6.4 ricyanide and ferrocyanide. Introducing the value of P2/ P, into Equations 22 and 23, we obtain where 0 takes the following values 0 = ctS, (when S, << K ) and 0 = $ (when SI >> K ) . The values of cy and 9 are evaluated by the method of curve-fitting and are listed in Table I. These values are substantially independent of ferricyanide concentration in Fi-Fo solution a t a given enzyme quantity. The mean values of a and 9 for the respective enzyme 2uantities are also listed in Table I. Since the maximum rate of the reaction, V. is proportional to enzyme quantity, 3 must he proportional to enzyme quantity. The values of listed in Table I satisfy this relation. When the ferricyanide concentration in the enzyme gel layer, SZm, is less than 0.1 mM, assumption 2 used above becomes invalid. ( 2 5 ) With the use of this equation, we can formulate an empirical equation relating 1E to S,, which can simulate the experimental results in the whole range of substrate concentration. The solid lines in Figure 5(a) and (b) show the values calculated from Equation 24 together with Equation 25, revealing tha t Equation 25 is in good agreement with the observed values in the whole substrate concentration. In this comparison, the mean values of a and 13 listed in Table I are used. LITERATURE CITED (1) G. G. Guilbault, Anal. Chem , 40, 459R (1968). (2) G. G. Guilbault and G. Nagy, Anal. Chem., 45, 417 (1973). (3) G. G. Guilbault and E. Hrabankova, Anal. Chem., 42, 1779 (1970). (4) G. Nagy. L. H. Von Storp, and G. G. Guilbault, Anal. Chim. Acta, 6 6 , 443 (1973). (5) R . A. Llenado and G. A. Rechnitz, Anal. Chem., 43, 1457 (1971). (6) G. J. Papariello, A . K. Mukherji, and C. M. Shearer, Anal. Chem., 45, 790 (1973). (7) G. G. Guilbault and G. J. Lubrano, Anal. Chim. Acta, 64,-439 (1973). (8) W. J. Blaedel and C. L. Olson, US. Patent 3 367 849 (1968). (9) M. Nanjo and G. G. Guilbault. Anal. Chem., 46, 1769 (1974). (10) M. Nanjo and G. G. Guilbault, Anal. Chim. Acta, 7 5 , 169 (1975). (1 1) D. L. Williams, A. Doirg, and A. Korosi, Anal. Chem., 42, 118 (1970). (12) W. J. Blaedel and R. A. Jenkins, Anal. Chem., 48, 1240 (1976). (131 H. Durliat, M. Comtat, and A. Baudras, Clin. Chem. (Winston-Salem, N.C.), 22, 1802 (1976). (14) C. A. Appleby and R. K. Morton, Biochem. J . , 71, 492 (1959). (151 C. A . Aoolebv and R. K. Morton. Biochem. J . . 73. 539 11959). i16j R. K. Molton\u2019and J. M. Sturtevant, J . B i d Chem.\u2019, 239 \u2018(1964) (17) P . C. Hinkle. Fed. Proc.. 32, 1988 (1973). RECEIVED for review July 27, 1978. Accepted September 26, 1978. Studies of o-Tolidine Attachment to Pyrolytic Graphite Electrodes via Cyanuric Chloride Mino F. Dautartas,\u2019 John F. Evans,\u2019 and Theodore Kuwana\u201d Department of Chemistry, The Ohio State University, Columbus, Ohio 432 10 o-Tolidine, OT, which contains amino functional groups, was covalently attached to pyrolytic graphite electrodes via cyanuric chloride. These OT bound electrodes were examined by cyclic voltammetry and X-ray photoelectron spectroscopy, XPS. The cyclic voltammetric results for bound OT were similar to solution OT, although continual potential cycling produced changes in the XPS spectra which could be attributed to the presence and loss of some of the amine in the form of the hydrochloride salt. The bound OT was chemically stable to repeated potential scans from 0.0 to +0.8 V vs. SCE in acetonitrile solution. The surface coverages of OT from electrochemical and XPS data were estimated to be 2-5 X rnole/cm2. Present address: Department of Chemistry, University of Minnesota, 207 Pleasant St., S.E., Minneapolis, Minn. 55455. The area of chemically modified electrodes is presently one of great interest and activity. T o date, several modes of attachment of electroactive species to the surface of various electrode materials have been investigated. These modes have included the use of covalent modification (1-27), irreversible adsorption (28-34), and polymeric coatings (34-37). In the first category, the schemes have involved either the direct attachment of modifiers to electrode surface functional groups by amidization ( I , 11, 12, 15, 18, 19,21,22) or by esterification (38), and by the use of coupling agents such as silanes (2 9, 16, 17, 23-26) or a triazine (14, 20). The triazine, cyanuric chloride, has been recently shown to be an effective surface coupling agent, and hydroxyl-containing ferrocenes were utilized as examples of terminal reactants coupled to graphitic carbon, tin oxide, and indium oxide electrodes ( 1 4 , 20). In this paper, further study on the use of cyanuric chloride, CC, as a coupling agent is presented in which it is demon- 0003-2700/79/0351-0104$01 O O / O C 1978 American Chemical Society"
        ]
    },
    {
        "image_filename": "designv10_10_0003915_icuas.2014.6842287-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003915_icuas.2014.6842287-Figure2-1.png",
        "caption": "Figure 2. The geometric approximation of the propulsion system.",
        "texts": [
            " The load has an opposing torque To. The mechanical equation can be expressed as follows: \u03a9 \u03a9 0, (2) where: J - rotor and propeller inertia, B - viscous friction coefficient, km - torque constant. The motor shaft inertia is relatively small. In many cases it can be neglected. However, the inertia of the propeller is significantly large and is not easy to determine. Some geometrical simplifications can be made in order to estimate the plausible value of the inertia. For example the rod and the cuboid solids may be used (see Fig. 2). One of the main parameter of the propeller is stiffness which prevents fluttering, a kind of a propulsion vibration. Such vibrations can easily be transferred to the multiplatform frame and cause extra disturbances in measuring system. Amongst the other forces and torques acting on the rotor that we can distinguish as follows: bending which also depends on the propeller rigidity, centrifugal force \u2013 the effect of the rotating blade mass at high speeds. In the following considerations these forces are omitted, only main force such as thrust is discussed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000593_jsvi.2000.3412-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000593_jsvi.2000.3412-Figure5-1.png",
        "caption": "Figure 5. The inertia force and moment acted on the hub.",
        "texts": [
            " In expressions (36) and (37), we can \"nd that the forces due to the misalignment consist of two parts, one related to JZ i aX2/r2 b is clearly from the inertia force of the sleeve of a gear coupling, and the other related to c l aX is from the damping of the gear coupling; hence the amplitudes of the steady state vibration of the misaligned system are related to the misalignment, internal damping, the rotating speed, and the structural parameters of the gear coupling. The inertia force of the sleeve due to misalignment is equal to JZ i aX2/r2 b that coincides with the x-axis. Based on Newton's laws it reacted on the teeth of the hub along the engagement line, and equals F@ gi \"JZ i aX2 cos(Xt#b a )/r2 b shown in Figure 5. The force F@ gi can be equivalently replaced by a force and a moment. The former F gi acts on the center O e of the hub, and the later M gi acts on the hub in the torsional direction. Furthermore, the components of F gi in x and y directions are F gx \"!Jz i aX2 cos2 (Xt#b a )/r2 b \"!Jz i aX2[cos(2Xt#2b a )#1]/2r2 b , (38) F gy \"!Jz i aX2 cos2 (Xt#b a ) sin(Xt#b a )/r2 b \"!Jz i aX2 sin(2Xt#2b a )/2r2 b (39) and the moment is M gi \"Jz j aX2 cos (Xt#b a )/r b . (40) From equations (38)}(40), we can \"nd by supposing b a equal to constant, that equation (35) is linear, and the force components in x and y directions in its right terms become periodic functions of time in two integer multiple rotating speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-14-1.png",
        "caption": "FIGURE 13-14 Gear-tooth pressure angle.",
        "texts": [],
        "surrounding_texts": [
            "378 TRANSMISSIONS AND DRIVE TRAINS\ncan be used for higher gear reductions than the spiral bevel gear, but they have more sliding between the teeth and are therefore somewhat less efficient. Hypoid gears are often used in automotive-style axles because the hypoid pinion offset and small size allow more interior clearance.\nGear Design\nGear design is an iterative process involving adjustment of the shaft center distance, the number of teeth in both gears, gear width, pressure angle, helix or spiral angle, and other parameters to optimize the gear set. A gear set is normally considered optimized when both the tooth bending and surface compressive stresses are near the maximum allowable, although special con sideration may be given to noise control. Generally, the desired gear ratio is known so that when a nominal tooth size or module (pitch in English units) and center distance are selected, the basic gear size as represented by the",
            "GEAR DESIGN\n379\ntangential rolling diameters called the pitch diameters and the number of teeth can be determined. The pitch diameter of the pinion, or smaller gear, for spur and helical gears is\nwhere D CD\nD = 2(CD)/(1 + R)\nthe pitch diameter of the smaller gear the shaft center distance\nR the gear ratio greater than 1\n(8)\nIt follows that the pitch diameter of the larger gear can be calculated by",
            "380 TRANSMISSIONS AND DRIVE TRAINS\nsubtracting D from 2( CD) or setting R = llR. The relationship between the gear module, gear pitch diameter, and number of teeth is\nwhere m D N\nm = DIN\ntooth size, module nominal pitch diameter number of teeth\n(9)\nFor helical gears, m is the module in the transverse plane and is related to the normal or cutter module mn by\nm = mnlcos IjJ (10)\nwhere IjJ = the helix angle\nThe general range of tooth modules for various gears in the drive train is as follows:\n1. Transmission gears-4 to 5 2. Power shift planetary gears-2.5 to 3.5"
        ]
    },
    {
        "image_filename": "designv10_10_0002166_s11071-009-9504-1-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002166_s11071-009-9504-1-Figure6-1.png",
        "caption": "Fig. 6 Schematic of the nonredundant mechanism",
        "texts": [
            " It is known that for AX = B (Am\u00d7n,Bm\u00d71,Xn\u00d71, n > m), (31) X which minimizes \u2016X\u20162 = x2 1 + x2 2 + \u00b7 \u00b7 \u00b7 + x2 n, (32) subject to the constraint (31), is obtained from: X = AT ( AAT )\u22121 B. (33) This is known as the minimum norm solution. Using minimum norm method as above, \u03c4 can be found from (30) as \u03c4 = \u2212Jp ( J T p Jp )\u22121 ( \u0302Fp + \u2211 i J T i \u0302F i ) , (34) in which \u03c4 is as follows: \u03c4 = [\u03c41 \u03c42 \u03c43 \u03c44 f1 f2 f3 f4]T . (35) Detailed steps for determining \u03c4 from (35) can be found in [16, 17]. L. Beji et al. [17] introduced the nonredundant, 3-leg mechanism as in Fig. 6. This mechanism is similar to our proposed 4-legged mechanism, with the exception of one leg. In this section, we compare these two mechanisms in three different aspects and explain the positive effects of redundancy. 6.1 Reachable points Consider a 3- and a 4-legged mechanisms with g = 12 cm and h = 4 cm, respectively. Further assume the minimum length of the linear actuators (dmin) to be 35 cm. We assume a hypothetical cylindrical workspace 30 cm in height and 40 cm in diameter located 30 cm above the base platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002839_s10514-013-9343-2-Figure17-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002839_s10514-013-9343-2-Figure17-1.png",
        "caption": "Fig. 17 The robot is pushed by a forward force of 235 N for 100 ms. a The robot is taking a step and moving arms to perform Partial Inertia Shaping. b Safe fall occurs as a result of Take a Step and Partial Inertia Shaping strategies. The green line shows the unsafe fall direction if partial inertia shaping were not used",
        "texts": [
            " The humanoid falls on the single target without any control, which corresponds to a 0\u25e6 avoidance angle. Intelligent stepping improves this avoidance angle to 100\u25e6 and inertia shaping further improves to 180\u25e6. The oscillation of the avoidance angle is the result of the oscillation of the CoP, which is often caused by a rocking motion of the robot when it does not have a firm and stable contact with the ground Fig. 15 The robot is pushed with a backward force of 210 N, for a duration of 100 ms. The default fall direction is already safe. The No Action strategy is chosen in this case Figure 17 shows the safe fall behavior as a result of choosing Take a Step and Partial Inertia Shaping. As expected, we can see significant arm motions in this case, and the robot falls in the forward left direction. In Fig. 18 we consider a case with a stronger push force for which the stepping + PIS strategy was not successful, and the controller resorts to the use of whole body inertia shaping. In Fig. 19, we compare No Action, Take a Step and Partial Inertia Shaping strategies when the robot was pushed with a forward force of 235 N, for a duration of 100 ms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000722_1.2794209-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000722_1.2794209-Figure2-1.png",
        "caption": "Fig. 2 Initial conditions for periodic solution",
        "texts": [
            " The appro priate initial conditions will be the one's that will automatically guarantee that the Eqs. (3) and (4) are satisfied. These initial conditions can be obtained by using symmetry arguments. The vertical velocity at the end of the stance phase in Fig. 1 is negative of the vertical velocity at the beginning of the stance phase. Thus, the vertical velocity at the middle of the stance phase should be zero. Similarly, the point mass should be lo cated at the top of the foot in the middle of the stance phase. These conditions are shown in Fig. 2 and can be stated mathe matically as: Journal of Biomechanical Engineering NOVEMBER 1995, Vol. 1 1 7 / 4 6 7 Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use At the middle of the stance phase: x{t) = 0 y(t) = yi v{t) = 0 u(t) = Ui (5) These initial conditions and the parameter Kx^^ have certain bounds on them for a successful solution. The first condition is: ^ i e g ( 1 - -^ > 1 (6) If this condition is not satisfied then the initial acceleration in the y-direction is negative and the mass will never leave the ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003386_10402004.2014.968699-Figure26-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003386_10402004.2014.968699-Figure26-1.png",
        "caption": "Fig. 26\u2014Illustration of the view angles in (a) and (b) of Fig. 25, Fig. 27, and Fig. 28.",
        "texts": [
            " D ow nl oa de d by [ FU B er lin ] at 2 3: 04 0 2 M ay 2 01 5 Figure 25 illustrates the orientation of the ball body-fixed reference frame. Presented is the ball motion in a radial loaded bearing operating under the planar assumption for the inner race. Figure 25a illustrates the view normal to the OR from the perspective at the center of the bearing. The angle of the view rotates with the cage such that the view remains normal to the OR surface. Figure 25b is the view perpendicular to that of Fig. 25a. Further illustration of the view angles can be found in Fig. 26. The ball maintained motion along the centerline of the OR groove with rotation purely about the Xbf axis and no spin at the point of contact between the ball and OR. The results presented in Fig. 25 only occur with the planar assumption of the inner race. This is an unrealistic condition for any loading configuration of the rotor\u2013bearing system. For bearing 2 with interference, Fig. 27 depicts the orientation of the body-fixed reference frame of the ball, spin of the ball, and also the magnitude of slip between the ball and OR when considering all 6 degrees of reedom of the bearing components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001749_mmvip.2008.4749589-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001749_mmvip.2008.4749589-Figure9-1.png",
        "caption": "Figure 9. Step response of assisting pinch force",
        "texts": [
            " Considering the pinch force of the Pressure[kPa] general male is about 20N to 25N, this glove is Figure 8. Generated force of glove in pinch operation effective in assisting the pinch operation. A PI feedback control of assisting pinch force is of these operations, the power assist along the executed in the system shown in Fig.7. In the human body movement can be obtained. condition of that the human slightly pinches the object with thickness of 20mm, the step responses Rubber tube Rubber band are measured for the reference force from IN to 4N, _ _ _ __K_= __ as shown in Fig.9. Although the delay time of about s 4 Is appears, the response is enough fast to assist the humn oeraio. (a) Extension operationhuma operation. (c) Curve operation V. ELBOW POWER AS SIT WEAR Figure 10. Operation of sheet-like curved type muscle A sheet-like curved type pneumatic rubber artificial muscle is newly developed, and using this muscle, a power assist wear assisting the bending Rubber band Rubbertube Nylon band motion of the elbow is developed [5]. A. Sheet-like curved type artificial muscle ee It is com posed of the rubber tube sandw iched "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003051_1.3554919-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003051_1.3554919-Figure1-1.png",
        "caption": "Fig. 1 Rolling contact",
        "texts": [
            "1 The purpose of the study presenteu in this paper was to further analyze the influence of dissolved water by (a) determining its interaction with the structural anisotropy of rolling-element specimens, and (b) examining the surfaces of rolling-element specimens by light microscopy and profilometry. While the experimental details and results of the influence of water on rolling-element fatigue have been recently reported [I], they are partially restated to provide an integrated view. It is intended to show thereby the relationship between reduced fatigue life and the interaction of water with the bearing surface during rolling contact. Apparatus Fatigue experiments were conducted with an apparatus simu lating the performance of an angular-contact ball bearing. Fig. 1 is an exploded view of t he apparatus. A bearing ball is attached to the shaft which rotates at 1730 rpm. This ball is pyramided upon three lower balls which are positioned by a separator and are free to rotate in an angular-contact race. The upper and lower balL~ contact each other at an angle of 40 deg. The upper ball represents the inner ring, the lower balls t he rolling elements, and the angular-contact race the outer ring of ~ ball bearing. The stainless steel race holder encloses the rolling-element com- I Numbers in brackets designate References at end of paper. Contributed by the Lubrication Division of THE AMERICAN SOCIETY OF MECB.ANJCAL ENGINEERS and presented at the ASME ASLE Lubrication Conference, Atlantic City, N. J., October 8-10, 1968. Manuscript received at ASME Headquarters, July 10, 1968. Paper No. 68--Lub-ll. Journal of Lubrication Technology ponents and permits cCJlltinuolls lubricant fl ow as shown in Fig. 1. Axial load is applied fr.)m below by means of a lever a.rm arrangemen t . fatigue assembly APR ILl 96 9 / 301 Copyright \u00a9 1969 by ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jotre9/28551/ on 06/03/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Table 1 Chemical Analysis of Bearing Balls P/::Tcer,t b\" t\";ei.aht :'ot c 3i 'In S P I\"i Cr Ho 1 1 .02 0.3] O~33 0.009 0.017 0.11 1.55 0.006 ! 2 (J.97 0.27 0. ?Q 0.011 0.014 0.13 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-24-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-24-1.png",
        "caption": "FIGURE 5-24 Torsional vibration damper that attaches to front of crankshaft. (Courtesy Perkins Engine.)",
        "texts": [
            " However, secondary inertia forces exist in a vertical direction in the usual four-cylinder vertical engine, which was discussed previously. Torsional vibration of small farm tractor engines is not generally a prob lem because the crankshaft is relatively short. With a short crankshaft the BALANCE OF MULTICYLINDER ENGINES 109 natural frequency will be so high thai it will not be excited by the normal pulse from the ignition of each charge in the cylinder. Longer crankshafts (large engines) require torsional dampers that fit on the front of the crankshaft and keep the amplitude from becoming excessively large (fig. 5-24). It is convenient to cOIllbine the damper with the V -belt sheave attached to the front of the crankshaft. Torsional vibrations can never be eliminated COIll pletely from a piston-type engine, but proper design can reduce the magni tude to an acceptable level. Vibration analysis, isolation, and damping are very specialized and com plex subjects. For the student having Ihe necessary background, or having further interest in this subject, the suggested readings at the end of the chapter will be valuable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000896_j.1460-2687.2002.00094.x-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000896_j.1460-2687.2002.00094.x-Figure1-1.png",
        "caption": "Figure 1 Two-dimensional model, with muscle torque generators inserted at the spine, shoulder, and wrist, used in the simulation of the golfswing. The swing plane was assumed to be at an angle of 60\u00b0 to the ground.",
        "texts": [
            " The primary purpose of this paper was to re-examine the delayed release phenomenon in the golf swing using a three-segment model that incorporated the properties of human muscle into the simulation. A second objective of this paper was to identify the mechanical sources of power that are responsible for increasing clubhead speed. A representative mathematical model for a golfer was formulated using a three-segment, two-dimensional (2-D), linked system with the golfclub, arm, and torso segments moving in a plane tilted 60\u00b0 to the ground (Fig. 1) (Sprigings & Neal 2000). The assumption of planar movement of these segments during the downward swing is well supported in golf literature (Cochran & Stobbs 1968; Jorgensen 1994). The golfclub was modelled as a rigid segment which is consistent with the conclusion of Milne & Davis (1992) that, contrary to popular belief, shaft bending flexibility plays only a minor dynamic role in the golf swing. The arm segment was modelled as a rigid rod and reflects the inertial properties and mass of the left arm",
            " 1981) with variable step size was programmed and used to drive the simulation model. The simulation process commenced with the assumption that the golfer had just completed his back swing and was just about to initiate his down swing. It was assumed that at time zero the golfer\u2019s torso segment was rotated 90\u00b0 clockwise (top view) from the address position, with the arm and club segments positioned 60\u00b0 and 30\u00b0, respectively, above a horizontal line through their proximal end, which is a typical configuration for an elite golfer (Yun 1996) (Fig. 1). The acute 90\u00b0 of wrist-cock angle that corresponds to this starting configuration agrees with that observed for top players (e.g. Woods, Els) during the early stages of the downswing. The optimization scheme employed a single activation muscular control strategy where the onset of voluntary torque at each joint was controlled \u00d3 2002 Blackwell Science Ltd \u2022 Sports Engineering (2002) 5, 23\u201332 25 separately. The time of onset, as well as the length of time that the joint torques acted, provided six control variables for the optimization"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001081_s0022-460x(03)00072-5-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001081_s0022-460x(03)00072-5-Figure2-1.png",
        "caption": "Fig. 2. A 2-noded beam element with transverse uz parallel to the gear mesh line-of-action, bending rotation yx and torsion yy co-ordinates used to construct the input and output shaft models. The nodes are labelled as points 1 and 2.",
        "texts": [
            " The shafts are assumed flexible in the transverse and torsional directions. The longitudinal degree of freedom is neglected since no significant axial excitation is expected from the spur gears and to avoid unnecessary complexity in the analysis [11]. Moreover, the natural frequency associated with the longitudinal vibration is much higher than the frequency range of interest. Accordingly, each nodal point on the discretized shaft is only defined by three degrees of freedom (d.o.f.) that include transverse, bending rotation and torsion co-ordinates as shown in Fig. 2. The beam element stiffness matrix formulation can be shown to be Ke beam \u00bc 12K1 6K1L 0 12K1 6K1L 0 6K1L 4K1L2 0 6K1L 2K1L2 0 0 0 Ks 0 0 Ks 12K1 6K1L 0 12K1 6K1L 0 6K1L 2K1L2 0 6K1L 4K1L2 0 0 0 Ks 0 0 Ks 2 6666666664 3 7777777775 ; \u00f01\u00de where L is the element length, Ks \u00bc GJ=L; K1 \u00bc EI=L3; E is the modulus of elasticity, I and J are the area and polar moments of inertia, respectively, and G is the shear modulus. The corresponding mass matrix is Me beam \u00bc m 420 156 22L 0 54 13L 0 22L 4L2 0 13L 3L2 0 0 0 70R2 0 0 35R2 54 13L 0 156 22L 0 13L 3L2 0 22L 4L2 0 0 0 35R2 0 0 70R2 2 6666666664 3 7777777775 ; \u00f02\u00de where m is the element mass and R is the shaft radius. These matrices correspond to the coordinate vector fuz1; yx1; yy1; uz2; yx2; yy2g T; where the numeric subscript represents the corresponding node in Fig. 2. The gear mesh kinematics is modelled using a concept originally proposed by Tuplin [12], which has been widely used by many gear researchers [13\u201315]. The linear time-invariant model consists of an infinitesimal spring\u2013damper element positioned in series with the loaded static transmission error excitation e(t) at the mesh point as shown in Fig. 3. The mesh model couples the translational co-ordinates of the gear and pinion centroids along the tooth load line-of-action. Additionally, the bending rotation and torsion co-ordinates of the gears are considered, which match exactly to the corresponding shaft degrees of freedom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002230_s00170-010-2657-8-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002230_s00170-010-2657-8-Figure1-1.png",
        "caption": "Fig. 1 Working principle of the coaxial powder nozzle, \u03b1 is the angle between fed powder and the horizon, \u03b2 is the angle between shield gas and the horizon",
        "texts": [
            " A disperse phase model is adopted to conduct the numerical simulation of the powder flow field, including the distributing rules of the powder flow field and analysis of its gathering property, The gathering property of the powder flow field, the distributing rules of the flow field velocity, the rules of the flow field parameters (focus (f), focus radius (r), and powder concentration (CF)) are obtained by FLUENT, which can be referred in the design and optimization of the coaxial powder nozzle. In LMDM, the coaxial powder nozzle has the forming powder orbit of two coaxial cone ring gaps that are coaxial with laser beam, and then concentrate at the laser focus (see as Fig. 1). Lin has studied the gas\u2013solid two-phase flow in coaxial powder nozzle when the Reynolds number is 2,000 [13], and the result shows that the metal concentration will reach the maximum 0.315 kg/m3 when it is 5 mm under the bottom of the nozzle. Energy, momentum, and mass transmission process exist in coaxial powder feeding system, which directly determines the size, precision and performance of the part made by LMDM. Thus, it is necessary to conduct some research on its powder flow field, but until now, there is only limited relevant research on this subject [14, 15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003470_s12206-015-0901-8-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003470_s12206-015-0901-8-Figure3-1.png",
        "caption": "Fig. 3. Relationship of mesh force between a helical gear pair.",
        "texts": [
            " Kwx,px (Cwx,px) are the support stiffness (damping) of the wheel and pinion in x direction, respectively. Kwy,py (Cwy,py) are the bearing support stiffness (damping) of the wheel and pinion in y direction, respectively. Kwz,pz (Cwz,pz) are the bearing support stiffness (damping) of the wheel and pinion in z direction, respectively. Kwp (Cwp) represents the mesh stiffness (damping) of the wheel and pinion pair. ewp is static transmission error of the wheel-pinion pair. \u03b2wb represents the base helix angle of the 3rd transmission stage. The forces for the mesh of helical gears are shown in Fig. 3. Due to the existence of the helical angle, the normal meshing force on the tooth is decomposed into tangential component force, radial component force and axial component force in x direction, y direction and z direction. To synthesize the vibration displacement along the line of action, the base helix angle, position angle and pressure angle should be taken into consideration. On the basis of the relationship between the mesh forces of the helical gear pair as shown in Fig. 3, the equivalent displacement between the sun and the ith planet gear pair along the line of action can be represented by cos cos sin( )cos sin cos cos( )cos cos cos sin sin / cos spi pi pi b s s b s i sp b pi sp b s i sp b pi sp b s b pi b pi c c c b spi r r x u y v z w n n r e d q b q b j a b a b j a b a b b b q b = - - + + - - + + + - + + (1) where \u03b4spi is the equivalent vibration displacement between the sun and the ith planet gear pair along the line of action in the 1st stage transmission. rpi is the base radius of the ith planet gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002839_s10514-013-9343-2-Figure16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002839_s10514-013-9343-2-Figure16-1.png",
        "caption": "Fig. 16 The robot is pushed with a forward force of 210 N, for a duration of 100 ms, at the CoM of its trunk. The default fall direction is towards the object in the front. a The robot lifts the left leg to change fall direction; b this results in a safe fall at an empty space",
        "texts": [
            " 1994) from \u03c9d : R = exp(\u03a9d), (11) where \u03a9d is the skew-symmetric matrix corresponding to \u03c9d . To implement inertia shaping, we string out the 6 unique elements of the CRB inertia matrix in the form of a vector: I(3\u00d73) \u2192 s\u0302I(6\u00d71). Next, we obtain the CRB inertia Jacobian JI which maps changes in the robot joint angles into corresponding changes in s\u0302I, i.e., \u03b4s\u0302I = JI\u03b4\u03b8 . (12) To attain Id , the desired joint velocities are given by: \u03b8\u0307 = J# I (Id \u2212 I) (13) 4 Extension to a general case with multiple objects such as in Fig 16 is trivial once the desired fall direction is chosen. where J# I is the pseudo-inverse of J I . The humanoid can recruit all the joints to attain Id . The effect of inertia shaping might not always be big enough to obtain the desired CoM velocity VG , however, even a modest change is sometimes very useful. Equation 13 is used for whole body inertia shaping, which cannot be launched before stepping (foot placement) is completed, because the two actions may be in conflict. This can sometimes lead to the the loss of useful time during which the robot\u2019s upper body does not contribute to attaining a desired fall direction",
            " In this case, the robot\u2019s environment contains four objects as shown in Fig. 15. The robot is pushed at the CoM of its trunk with horizontal forces of different magnitudes and directions; and the performance of the safe fall controller for each case was analyzed. All forces are exerted for a duration of 100 ms. When the robot is pushed with a backward force of 210 N, the default fall is already safe. Our planning procedure successfully detects steady fall and chooses No Action as the best strategy, which results in a safe fall as shown in Fig. 15. Figure 16 shows the safe fall behavior as a result of choosing Lift a Leg strategy after identifying a steady fall when pushed with a forward force of 210 N. Fig. 14 Simulation plots of CoM trajectories (left) and avoidance angles (right) of a falling humanoid which was pushed during upright standing. The avoidance angle between the robot\u2019s fall direction and the direction of the nearest obstacle is computed using the lean line which extends from the CoP to the CoM. The humanoid falls on the single target without any control, which corresponds to a 0\u25e6 avoidance angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003515_tasc.2016.2602500-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003515_tasc.2016.2602500-Figure1-1.png",
        "caption": "Fig. 1. Structure and the cross section of the ironless BLDCM.",
        "texts": [
            " The authors are with the School of Electrical Engineering, Southeast University, Nanjin 210018, China (e-mail: kliu@seu.edu.cn; fuxinghe@seu.edu.cn; mylin@seu.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2016.2602500 Section IV presents an equivalent circuit model for circulating current losses calculation and three winding wires arrangements are compared. Section V gives the results and the conclusions. Fig. 1 shows the structure and the cross section of the ironless BLDCM and Table I gives the basic specifications. The BLDCM includes an iron-less armature (fixed in a fiber frame), an iron core and the permanent magnets. In this paper, the AC copper losses are carried out by using two-dimensional (2D) FE model. In order to consider the skin effect and proximity effect for the windings, the models with a large number of winding wires inside the slots are created, as shown in Fig. 2. To consider the effect of the winding wire diameter, several winding models with different wire diameter in parallel are created"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003040_00207721.2014.945984-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003040_00207721.2014.945984-Figure1-1.png",
        "caption": "Figure 1. A single-link robot system.",
        "texts": [
            " The aim of HOSMD is to make \u03b6 j approximate the differential term p(t)(j + 1) to arbitrary accuracy, i = 0, 1, . . . , n, j = 0, 1, . . . , n \u2212 1. To obtain the estimate of differential term \u03b1\u0307i\u22121, the order of HOSMD should be only 1 and p(t) = \u03b1i \u2212 1. In this section, simulation results of an example are given to illustrate the effectiveness of the proposed backstepping fault-tolerant control scheme for a non-linear system with unknown time-varying system fault and the dead-zone. In the simulation study, let us consider the single-link robot system which is shown in Figure 1. Its motion dynamics can be described as (Wang, Chai, & Zhangh, 2010) Mq\u0308 + 0.5m0gl sin(q) = \u03c4 + \u03b70(t) y = q, (53) where g = 9.8 m/s2 is the acceleration due to gravity, M is the inertia, q is the angle position, q\u0307 is the angle velocity, q\u0308 D ow nl oa de d by [ U ni ve rs ity o f V ic to ri a] a t 1 7: 06 2 5 A pr il 20 15 0 5 10 15 20 0 0.5 1 1.5 2 2.5 Time [s] y y d Figure 2. Tracking control result of case 1. is the angle acceleration, l is the length of the link, m0 is the mass of the link, \u03c4 is the control force, and \u03b70(t) denotes the actuator/component fault in the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure9-1.png",
        "caption": "Fig. 9 Different position relations between the face-gear tooth profile and the shaper tooth profile in the X-Y plane",
        "texts": [
            " During the processing, the planer tool with a long tool shank cannot rotate, and it will interfere with the shaper tooth profile at a moment, as shown in Fig. 8. However, it is proved that such interference cannot cause overcutting through derivation and verification of simulation machining (see section 5.1). Observed along the vertical direction of the X-Y plane in the moving coordinate system of the shaper Ss, there are different position relations between the face-gear tooth profile and the shaper tooth profile, as shown in Fig. 9. With the shaper rotating from a negative angle to a positive angle, the face-gear tooth profile L2 contacts the shaper tooth profile LS in different areas at each angle. It is certain that each side of the face-gear tooth profile is locally monotonic, that is to say, the normals of the left side of the face-gear tooth profile are all positive, while the normals of the right side are all negative. The normal of an arbitrary point of L2 coincides with the normal of the corresponding point of LS in the contact area based on the principle of the envelope, that is to say, the normal direction of contact point in the face-gear tooth profile can be considered either positive or negative at any instant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure4-1.png",
        "caption": "Fig. 4. Geometrical parameters definition of oblique cutting.",
        "texts": [
            " Based on the geometrical analysis of gear skiving, mechanical analysis of skiving is carried out, which is aimed at inves- tigating the mechanical performance of the tool in skiving with different commonly used feeding techniques. In order to investigate the cutting performance of the cutting edges more conveniently and accurately, the engaged cutting edges are decomposed into a set of cutting edge elements, and the edge elements are supposed to be perfectly sharp and the flank contacts are neglected. The normal section of the edge element at the cutting point \u201cC\u201d is shown in Fig. 4 . An orthonormal base coordinate system S n ( x n , y n , z n ) is associated to the cutting plane P s , S s ( x s , y s , z s ) is associated to the shear plane P , and S r ( x r , y r , z r ) is attached to rake face. sh The chip flow direction on the rake face and the shear force direction of the chip on the shear plane can be defined by the chip flow angle \u03b7c and the shearing direction angle \u03b7s , respectively [22] : tan \u03b7s = tan \u03bc sin \u03b7c cos ( \u03c6n \u2212 \u03b3n ) \u2212 tan \u03bc sin ( \u03c6n \u2212 \u03b3n ) cos \u03b7c (22) where, the angle \u03b7c can be calculated by the following implicit equation: cos ( \u03c6n \u2212 \u03b3n ) sin \u03c6n sin \u03b7c \u2212 tan \u03bbs cos 2 ( \u03c6n \u2212 \u03b3n ) cos \u03b7c + cos \u03b3n tan \u03bc sin \u03b7c cos \u03b7c \u2212 sin ( \u03c6n \u2212 \u03b3n ) sin \u03c6n tan \u03bc sin \u03b7c cos \u03b7c + tan \u03bc tan \u03bbs sin ( \u03c6n \u2212 \u03b3n ) cos ( \u03c6n \u2212 \u03b3n ) cos 2 \u03b7c = 0 (23) where, \u03bc is the mean friction angle at the tool-chip interface and n is the normal shear angle which can be determined by: \u03c6n = \u03c0 4 \u2212 \u03bc 2 + \u03b3n 2 (24) The inclination angle \u03bbs of the cutting edge at the cutting point can be obtained as the angle between the cutting velocity and the normal cutting velocity: \u03bbs = arccos v (2) cw \u00b7 v (2) n \u2223\u2223v (2) cw \u2223\u2223 \u00b7 \u2223\u2223v (2) n \u2223\u2223 (25) We suppose the material is incompressible when passing through the shear plane, so the chip flow speed can be ex- pressed as: v c = v cz cos \u03b7c = sin \u03c6n cos ( \u03c6n \u2212 \u03b3n ) cos \u03b7c \u00b7 v n (26) The shear stress distribution on the shear plane is considered as uniform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002752_j.ijnonlinmec.2013.01.016-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002752_j.ijnonlinmec.2013.01.016-Figure4-1.png",
        "caption": "Fig. 4. Scheme of the 5-bar linkage.",
        "texts": [
            " (10) and the time-update equations (11) and (12) are applied. If any sensor data are available, the measurement-update equations (24)\u2013(27) and (41) are applied. A 5-bar linkage has been employed to exemplify the implementation and the performances of all the aforementioned nonlinear observers. The mechanism parameters have been obtained from the experimental 5-bar linkage shown in Fig. 3 and the sensor characteristics from off-the-shelf sensors to reproduce a realistic simulation. A scheme of the mechanism is shown in Fig. 4 where the points A and E are fixed points. The mechanism has been modeled using mixed coordinates [20] with the vector of dependent Cartesian coordinates presented in the following equation: qT \u00bc \u00bdxB yB xC yC xD yD f1 f2 \u00f042\u00de As a first step in this research, the motion of the real mechanism has been simulated but the magnitudes that correspond to sensor data are passed to the observers with their respective noises and sample rates. After that, some known errors (lengths, mass, inertia measuring errors for example) have to be considered for the system nominal model of the filters, in order to allow the simulated real mechanism and the filter\u2019s model to have similar but different behavior"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure1-1.png",
        "caption": "Fig. 1 PPR V-chain.",
        "texts": [
            " For example, several kinematic chains, such as a chain composed of one E joint and a serial chain composed of three R joints with parallel axes, all correspond to a planar motion. The E chain is called the V-chain for the planar motion. The serial V-chains for the 3-DOF PMs proposed so far are: \u2022 E V-chain for planar PMs in which the moving platform undergoes a planar motion [1, 2]. \u2022 S V-chain for spherical PMs in which the moving platform can rotate about a fixed point [3]\u2013 [10]. \u2022 PPP V-chain for translational PMs in which the moving platform undergoes a spatial translation [11]\u2013 [30]. \u2022 PPR V-chain (Fig. 1) for PMs in which the moving platform can rotate about an axis which translates along a plane [27, 33]. In a PPR V-chain, the axis of the R joint is not perpendicular to the directions of the two P joints. For certain PMs [34], the motion pattern of the moving platform could not be represented with a serial V-chain. Further 1In [27, 33], different names were used for the PPR-PMs. 2 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/15/2018 Ter classification of the V-chains, especially the parallel V-chains, of 3-DOF motions is still an open issue",
            " To facilitate the type synthesis of PPR-PKCs, the conditions for a PKC to be a PPR-PKC can be described as: (1) Each leg of the PKC and a same V-chain constitute a 3-DOF single-loop kinematic chain. (2) The wrench system of the PKC is the same as that of the V-chain in any one general configuration. Condition (1) for PPR-PKCs guarantee that the moving platform can undergo PPR-motion, while Condition (2) for PPR-PKCs guarantee further that the DOF of the moving platform is 3. Thus, a 3-DOF PKC is a 3-DOF PPR-PKC if and only if it satisfy the above two conditions. For a PPR V-chain (Fig. 1), the wrench system is a 1-\u03b60-2-\u03b6\u221esystem, which is composed of (a) all the \u03b6\u221e whose axes are perpendicular to the axis of the R joint and (b) all the \u03b60 whose axes are perpendicular to the directions of the P joints and coplanar with the axis of the R joint, and (c) other \u03b6 which are linear combinations the above \u03b6\u221e and \u03b60. One set of basis wrenches of the 1-\u03b60-2-\u03b6\u221e-system is \u03b601, \u03b6\u221e2 and \u03b6\u221e3. For convenience, the axis of the R joint within the PPR V-chain is called a virtual axis, the plane which are parallel to the directions of the two P joints within the PPR V-chain is called a virtual plane. In any general configuration, the wrench system of a PPRPKC [Fig. 3(a)] is the same as that of its V-chain, i.e., a 1-\u03b602-\u03b6\u221e-system (Fig. 1). As the wrench system of a parallel kinematic chain is the union (linear combination) of those of all its legs in a general configuration [40], the wrench system of any leg in a PPR-PKC is a sub-system of its wrench system. Here and throughout this paper, the wrench system of a leg is called a leg-wrench system. In the type synthesis of PMs, one is only interested in the leg-wrench systems in which there is a set of basis Copyright  2004 by ASME rms of Use: http://www.asme.org/about-asme/terms-of-use Dow \u03b601 \u03b6\u221e2 \u03b6\u221e3 (a) 1-\u03b60-2-\u03b6\u221e-system",
            " According to the composition of these 3-DOF single-loop kinematic chains, they can be classified as follows: (a) Single-loop kinematic chains formed by a serial chain of class (b2) and a serial chain of class (b3) [Figs. 6(a) and 6(b)]. (b) Single-loop kinematic chains formed by one serial chain of class (b4) [Fig. 6(c)]. (c) Single-loop kinematic chains formed by a serial chain of class (b1) and a serial chain of class (b3) [Fig. 6(d)]. (d) Single-loop kinematic chains formed by two serial chain of class (b4) [Figs. 6(e) and 6(f)]. In the representation of the types of 3-DOF single-loop kinematic chains involving a V-chain (Fig. 1), PPR-PKCs, PPR-PMs and their legs, X denotes a P or an R joint, (PP)E denotes two successive P joints whose directions are parallel to the virtual plane. (XXX)E denotes three successive X joints in which the axes of all the R joints are perpendicular to the virtual plane and the directions of all the P joints are parallel to the virtual plane. (RR)S denotes two successive R joints whose axes intersect at the same point on the virtual axis, RC denotes an R joint whose axis is collinear with the virtual axis, RA denotes an R joint whose axis is parallel to the virtual axis, (XX)Y and (XXX)Y denote, respectively, two or three successive X joints in which there is at least one R joint and the axes of all the R joints are parallel within a 3-DOF single-loop kinematic chain or a leg for PPR-PKCs",
            " All the legs for PPR-PMs obtained are listed in Table 1. For legs with ci = 0, one are interested in legs with simple structures: RUS, PUS and UPS legs [1]. By assembling two or more legs for PPR-PKCs shown in Table 1, we obtain PMs in which the moving platform can undergo a PPR motion (Fig. 8). The geometric relation between different legs has also been shown in the notation of legs we proposed in Section 7. To guarantee that the DOF of the moving platform is three, the wrench system of the PKC must be a 1-\u03b60-2-\u03b6\u221esystem (Fig. 1). It is found that not arbitrary set of three legs can be used 6 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/15/2018 Term to construct a 3-legged PPR-PM since the wrench system of the PKC may be not a 1-\u03b60-2-\u03b6\u221e-system. For example, a set of three (RRR)ERC legs cannot be used since the wrench system of a 3-(RRR)ERC is a 1-\u03b60-1-\u03b6\u221e-system. Due to the large number of PPR-PKCs and space limitation, only the family of PPR-PKCs, which are denoted by the valid combination of sets of leg-wrench systems, are listed Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003404_ecc.2014.6862576-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003404_ecc.2014.6862576-Figure2-1.png",
        "caption": "Figure 2. Convergence of derivative estimations (a) and errors (b) with different initial conditions ofz, !(t) = 12 COSI, L(t) = 12 I cosll +81 + 15.",
        "texts": [
            "5L(t)II 2 I Z2 (tk) - v, (tk) 1'/ 2 sign(z2 (tk) - v, (tk)) - 2(Z2 (tk) -VI (tk)) + Z3 (tk), Z3 (tk+,) = Z3 (tk) - l.lL(t)sign(z3 (tk) - v2 (tk ))Tk -(Z3 (tk) - v2 (tk ))Tk\u00b7 The graph of the function L(t) is shown in Fig.l. It is easy to see that with large t the inequality I L / L I::; 2 holds. Parameters Ao = l.l, A, = 1.5, A2 = 2, A3 = 3,110 = I,ll, = 2, 112 = 3, 11 3 = 4 are chosen. Let the initial values be Zo = 10, z, = -10, z2 = 7, z3 = 12. Convergence of the outputs to the exact derivatives is shown in Fig. 2. The accuracies I Zo - J I::; 2.28.10-5, I Z, - j I::; 2.62 .10-3, I Z2 - j I::; 0.203 \u00b7 , I Z3 - j I::; 8.91 are kept with Tk = T = 0.01 on the time interval [8,10]. They change to I Zo - J I::; 2.27 .10-9 , I z, - j I::; 2.52 .10-6 , I Z2 - j I::; 1.96 .10-3, I Z3 - j I::; 0.894 with Tk = T = 0.001 . Let now the initial values be Zo = 1000, z, = -1000, Z2 = 1200, z3 = 10000. Convergence of the differentiation errors to 0 is shown in Fig. 3. The accuracies are the same as in the runs with other initial values"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002732_1.4025196-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002732_1.4025196-Figure11-1.png",
        "caption": "Fig. 11 Robust optimization of PPTE and pmax: Pareto-optimal tooth surface (total) modifications",
        "texts": [
            " The robust counterpart F \u00f0PPTE\u00de t (based on the triangular distribution) was used for PPTE, while F \u00f0pmax\u00de u (uniform distribution) was selected for pmax. As represented in Fig. 10, a total of five robust Pareto-optimal solutions were computed, namely, the two solutions corresponding to the extremes of the Pareto front, i.e., the individual minima of PPTE and pmax, plus three other solutions obtained from three reference points, arranged as illustrated in the same figure (and in Fig. 7). The optimal microgeometry solutions are shown in Fig. 11; it is interesting to highlight that all of them have nonzero bias, while lead slope modification is zero in all cases. The CPU time required to obtain all five solutions was about 2 h on a laptop equipped with a 2-GHz processor and 4 GB RAM. The time taken by LDP for a single tooth contact analysis was slightly less than 1 s. Neither a parallel architecture nor a parallel implementation was exploited. The optimized PPTE and pmax curves are plotted versus torque in Fig. 12, where they are compared with the two best designs obtained in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002695_6.2012-1733-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002695_6.2012-1733-Figure2-1.png",
        "caption": "Figure 2. Bidirectional scanning strategy.",
        "texts": [
            " To optimize the production time and the density of the SLM test specimens that were used for the fatigue experiments, the in-house SLM machine 12 was used to produce different cubical (5x5x5mm\u00b3) blocks using different values for the laser power P (100, 200, 250W), scan speed v (63-1600mm s -1 ), track distance h (53-145\u03bcm) and layer thickness t (30, 60, 90\u03bcm) while maintaining the same energy density E. This parameter gives an indication of the energy supply during SLM and can be calculated using the previous parameters, E = P/vht in J mm -3 . A bidirectional scanning strategy was used for all the specimens. After scanning the contour, the first layer is scanned in zigzag and each successive layer is rotated by 90\u00b0 as indicated in Figure 2. The relative density of the different blocks was measured using the Archimedes principle leading to a maximal value of 99.7% and a set of optimal scan parameters as indicated in Table 1. The relative density of the reference titanium was determined using the same principle leading to a value of 99,68%. Hence, the material density of the SLM parts equals the density of the VAR material. This will not only drastically improve the fatigue properties of the SLM-parts, it also eliminates the pores as driving force for fatigue failure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure19-1.png",
        "caption": "Fig. 19 Simulation result",
        "texts": [
            " The planer tool blade should be full fillet as it is convenient to calculate the tool path with this kind of blade. According to the design parameters in Table 1, the swing angle range and the feed range of the planer tool are calculated. The theoretical model of the face-gear (as shown in Fig. 18), the model of the face-gear blank and models of the planer machine are established using CATIA, and the model files and NC programs which are written based on the planing principle in this paper are imported into the Vericut software to simulate the processing. Finally, the result of the simulation is shown in Fig. 19. Firstly, the theoretical model (as shown in Fig. 18) and the simulation model (as shown in Fig. 19) are overlapped together, and the tooth surface error between the two models is analyzed in Vericut software. The results obtained from the analysis are shown in Fig. 20a. The whole regions, including the light regions and 3 4 5 6 7 8 9 -260 -255 -250 -245 -240 -235 -230 y 2 (mm) x 2 ) m m( 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Fig. 17 Error e2 the dark regions, represent the theoretical tooth surface of the spur face-gear, and the dark regions represent the surface with the error larger than 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003296_j.ymssp.2017.05.041-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003296_j.ymssp.2017.05.041-Figure8-1.png",
        "caption": "Fig. 8. 3-D involute contact model by FEM for a pair gear given in Table 3. (a) Gear contact model. (b) The local graph of the tooth root crack. (c) Nodes of the crack tip.",
        "texts": [
            " Aiming at the stress singularity at the crack tip, Barsoum et al. [33] pointed out that the intermediate nodes of the second-order element\u2019s near the crack tip moves to the 1/4 nodes along the crack tip, as shown in Fig. 7(b). It is clear that the point P\u00f0r; h\u00de is replaced by any 1/4 nodes which has the same radial location r and different orientation angles h for the crack tip. In order to raise its calculation efficiency and lower the cost, a 3-D involute gear contact model is generated using the parameters of gear listed in Table 3, as shown in Fig. 8(a), which only have five teeth and the rim length is 4m (m is modular). Besides, in order to meet the needs of the tooth root crack tip stress singularity, the meshing and elements around the crack tip are set as binomial singular elements whose intermediate node moves to the position which is at the 1/4 length of the crack tip. Therefore, the C3D10M 3D solid element is selected to cover the field near the crack tip, as shown in Fig. 8 (b) and (c). Furthermore, the material density is q \u00bc 7800 kg=m3, a Young\u2019s modulus E \u00bc 2:03 1011 Pa and a Poisson\u2019s ratio of 0.3. Impose constraints and loads on gear model and take the whole time of the gear contact as a gear rotation angle. The tooth root crack model has been generated for different crack depths which contain 0.5 mm, 1.0 mm, 1.5 mm, 2.0 mm. The stress distribution nephogram for mesh stiffness of the single-tooth contact and double-tooth contact with different crack levels are shown in Table 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-19-1.png",
        "caption": "FIGURE 11-19 Modes of vibration correspond ing to the (a) 2.21-Hz and (b) 3.38-Hz natural fre quencies of the tractor.",
        "texts": [
            " (Since the angular velocity, 9\" required to bring the tractor to the point of static instability is 1.46 rad/s, the tractor is in danger of overturning.) 9. Estimate the natural frequencies and illustrate the modes of vibration of the tractor considering it as a linear two-degree-of-freedom system. By linearizing the appropriate load-deflection curves, the spring rates for a single front and a single rear tire are estimated to be 287.41\\/mm and 337.7 N/mm respectively. (Natural frequencies are 2.21 and 3.38 Hz. The corresponding mode shapes are shown in fig. 11-19.) 10. (a) If the cornering stiffnesses of a single front and a single rear tire are 35.8 and 141.1 kN/radian, respectively, determine the understeer coefficient. (.076 radians) (b) Will the tractor tend to understeer or oversteer? (understeer) 11. The tractor is put into a steady-state turn such that the center of gravity of the 310 MECHANICS OF THE TRACTOR CHASSIS tractor traverses a circle of radius 7 m. The tractor is of the tricycle type and has a front wheel tread setting of 0.5 m and a rear wheel tread setting of 2 m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000841_a:1003285415420-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000841_a:1003285415420-Figure2-1.png",
        "caption": "Fig. 2. Apparatus for two-phase experiments. Fig. 3. Upper part of the channel.",
        "texts": [
            " The circuit was completed with an anode (8) arranged in an open tank and a PTFE-tube (9) \u00aelled with KOH solution. Diaphragms arranged between the tanks prevented mixing of dissolved gases. A catalytic layer of black platinum on the platinum wire was prepared with a solution of hexachloro-platinum acid. The volumetric void fraction of hydrogen and its distribution in forced convection \u00afow was determined by measuring the electrical resistance of the two-phase mixture \u00afowing up a vertical channel of rectangular cross section. The apparatus used in these experiments is shown in Fig. 2. It consists of two closed circuits, one for hydrogen and the other for oxygen. The gases were evolved on ten electrode pairs mounted in the upper section of the electrolyser. Cathodes and anodes were made of nickel, their size was 4 cm 2 cm. The channel was divided vertically by a diaphragm into two subchannels, and the electrolyte pumped through the electrolyser at velocities up to 1:0m s\u00ff1. At the end of the channel, the two separated two-phase \u00afows streamed into reservoirs where the liquids were purged from gases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003777_j.foodcont.2017.05.012-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003777_j.foodcont.2017.05.012-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the whole double-film visual screening card. (A) Outlook. (B) Decomposition diagram. (C) Longitudinal section.",
        "texts": [
            " We also optimized this system of card in sensitivity, stability, reproducibility, and used it in the detection of real food samples. AChE from Drosophila melanogaster was purchased from Beibei biotech. Co., Ltd. (Zhengzhou, China). Indoxyl acetate, acetylthiocholine chloride, 5,5\u2019-dithiobis-2-nitrobenzoic acid and other general chemicals were purchased from Sigma-Aldrich China (Shanghai, China). Polyesterfiber (PF), glassfiber (GF) and absorbent paper (AP) were purchased from Shanghai Kinbio Tech. Co., Ltd (Shanghai, China). Test cards were made of acrylonitrile butadiene styrene plastic and customized as Fig. 1. Ultra-pure water was preparedusing aMilli-Q reagentwater system(Millipore, Billerica,MA). Pesticide analytical standards were purchased from the National Information Center for Certified Reference Materials (Beijing, China). Individual pesticide stock solutions (100 mg/mL) were prepared in acetone and stored at 20 C in the darkness. To prepare working solutions, the sample solutions were spiked to the desired concentrations. Cabbage, lettuce and apple samples were purchased from a local supermarket (Zhengzhou, China), and were pre-checked with Ellman's method to confirm the absence of the target compound, and stored in the dark at < 4 C until required for analysis (Ellman, Courtney, Andres, & Featherstone, 1961)",
            " Photoshop software (Adobe, San Jose, CA) also was used to extract the color pixels from the images of color development results. A value of 100 was assigned to the blue-green color of the negative control without any inhibitor, and a value of zero was assigned to the faint color of the positive control without enzyme. Each experiment was run in duplicate. Data were analysed by using GraphPad Prism software (GraphPad Software, Inc., La Jolla, CA). The schematic diagram of the double-film visual screening card was shown in Fig. 1, which was composed of a card cover, a card base and test windows. The films containing the enzyme and substrate in the test windows were hydrophilic materials that were capable of adsorbing and releasing the full doze of enzyme or substrate. Bright blue-green color will show when indoxyl acetate is decomposed by AChE. The color developing speed is relatively slow, if compared with the speed of inhibition of AChE activity by pesticides. When a sample solution containing pesticides was dropped in the test window, the AChE would be efficiently and rapidly inhibited to a degree depending on the level of pesticide"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003597_s12555-017-0099-x-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003597_s12555-017-0099-x-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor structure.",
        "texts": [
            " The following assumptions applies; - Translation dynamics is expressed with respect to a fixed world coordinate frame, while the rotational dynamic is expressed with respect to body fixed frame for the purpose of simplicity. - Body frame origin and center of gravity are assumed to be coincident. - Air friction and drag moment together with external wind forces are considered. - Structure is assumed inflexible and symmetric. - Propellers are assumed to be rigid (no blade flapping). - The rotors are located at points O1, O2, O3, and O4, tilted with respect to the fixed rotor points as shown in Fig. 1. - These rotor frames are taken parallel to the body fixed reference frame at the center of gravity. - The translational and rotational dynamic equations are established according to Newton-Euler formation. Let RB ri represent the orientation rotor axis Oi with respect to the fixed rotor body frame. By denoting \u03b1i, the rotational angle about yi and \u03b2i, the rotational axes about zi as shown in above Fig. 1. Then the rotational matrix from the rotors-rotating frame to the fixed rotor frame is given by: RB ri =  c\u03b2 ic\u03b1i \u2212s\u03b2i c\u03b2is\u03b1i s\u03b2c\u03b1i c\u03b2i s\u03b2 is\u03b1i \u2212s\u03b1i 0 c\u03b1 i  , (1) where c denotes cosine and s denotes sine. The rotor thrust (Li) and moments (Td) at the center of gravity is proportional to square of the rotor speed (w). Typically, Li = bw2 i , Tdi = dw2 i , where b and d are the lift and drag constants respectively. For each rotor thrust, Fi is therefore given by: Fi =  c\u03b2 ic\u03b1i \u2212s\u03b2i c\u03b2is\u03b1i s\u03b2c\u03b1i c\u03b2i s\u03b2 is\u03b1i \u2212s\u03b1i 0 c\u03b1 i  0 0 bw2 i  "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002218_1559-0410.1134-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002218_1559-0410.1134-Figure2-1.png",
        "caption": "Figure 2: The defined hip and shoulder segments and the method used to calculate the hip and shoulder angles as viewed from the oblique frontal and transverse planes",
        "texts": [
            " Following the digitisation procedure and three-dimensional reconstruction, a quintic spline function (Woltring, 1985) was applied to the raw coordinates in order to smooth the data and calculate kinematic quantities. Digitisation of the video data within the Peak Motus 2000 software enabled a three-dimensional full body linked-segment model to be created, which was used to calculate two primary angles; the hip angle; and the shoulder angle. The hip angle was defined as the angle formed between the line joining the hip joint centres and a theoretical line parallel to the y-axis between the tee and the target, as viewed in the transverse plane (Figure 2). Similarly, the shoulder angle was 5 Brought to you by | Cambridge University Library Authenticated Download Date | 5/20/15 10:57 AM the angle that was formed between this theoretical line and the line between the shoulder joint centres (estimated using the shoulder markers). For both the hip and shoulder angles, a positive value was indicative of rotation from the neutral position away from the target (closed position), whilst rotation from the neutral position towards the target (open position) was represented by a negative value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001235_1.2826105-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001235_1.2826105-Figure2-1.png",
        "caption": "Fig. 2 Example cases: (a) eight-degree-of-freedom torsional model of an automotive transmission, and (b) generic four-degree-of-freedom geared system model with multiple clear ance non-linearity, given by Eqs. (9) and (10).",
        "texts": [
            " Such an analysis provides insight on the severity of the possible ill-conditioning which is then used to adjust the non-dimensionalizing parameters in order to reduce or avoid computational problems during the course of numerical inte gration. This is then followed by the selection of a suitable numerical algorithm to obtain actual solutions to the non-lin ear models and evaluating those solutions based on the criteria proposed. None of these issues have been addressed by prior gear rattle investigators. 3 Selection of System Dimension As an example consider a hypothetical, yet reasonable, eight degree-of-freedom (DOF) torsional model of an auto motive transmission with three gear pairs, a flywheel and a clutch as shown in Fig. 2(a). Initially all the torsional springs are assumed to be linear and the undamped system is solved for the natural frequencies w\u0302 and the corresponding modeshapes or eigenvectors tf/^ (r = 1, 2,. . ., 8). The to^ values in rad/s are 0 (0), 346 (346), 7412 (7937), 10134, 18526, 48442 (48091), 50869, 68632; the values in parenthesis ( ) are the w^ values of the reduced four DOF linear model of the same system, as shown in Fig. 2(b). The first two non-rigid body moves of the eight DOF model are given by tj/2 = [-0.01 0.98 1 1 1 1 1 I f and .//j = [0 1 0 0 -0.3 -0.3 -0.5 -0 .5 r respectively, where superscript T is the transpose. The exci tation for such a system is usually of the form T^(t) = HI^^T^j sin (jflj) and is due to rotating mass unbalances and/or prime mover torque pulsations. The important excitation frequencies typically lie in the low frequency range, say 25-75 Hz. For this range of excitation frequencies the linear system response is dominated by the first mode (22 Hz) with a much smaller participation of the second mode. In each mode of vibration however, it is observed that there is little or no relative motion between the gear pairs. Based on this information one can then lump the second and third gears on the countershaft onto their conjugate parts on the mainshaft. Further one can lump the final two gears on the mainshaft onto the first gear, thus reducing the original eight degreeof-freedom, Fig. 2(a), system into a four degree-of-freedom model. Fig. 2(b). The inertia I^ is replaced by I^ + I^ + Ij + If,(R^/R(,r + If,(Rj/Rg)^. At the end of this stage, the non linear model can be developed. 4 Development of a Non-linear Model The following non-linearities are introduced in the generic four degree-of-freedom model of Fig. 2(b): (i) a multi-staged clutch stiffness between the flywheel (/j) and clutch (/j) inertias, (ii) a clearance non-linearity between clutch (/j) and input gear (I^) inertias, and (Hi) a backlash between the gears (I^ and 74). The governing equations of motion are as 186/Vol. 117, MARCH 1995 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use follows hh + Tn + r,i = TliCO; hk - Tu + ",
            " The constraint torques Tjj, ^23, force F34 and drag torques T\u0302 ,- are defined, in terms of the stiffness ele ments Ki and damping elements C,, as ?i2 = ^i^(Si)5i + f i / ( s , ) ; 7\u030223 = ^2^(52)52+^2/(82) (5,6) 7\u030234 = C,g{~S,)S, + Kj{8,y, T, = D\u201e,^\u201e,. + Dj,, (7,8) where Sj = Oj - 62, 82 = dj- 6^, S^ = R^e^ - R^d^ - eQ) and e(?) js the transmission error. JThe excitadon terms are given by TJt) = T\u201e, + Tjt) with TJt) = E/\u201e. . sin (yfl,/). The rea/ life clearance type non-linear elements, as shown in Fig. 2(b), can be related to the clutch torque characteris tics or gear/spline backlash and are defined in terms of the following mathematical functions: |5 , . - ( l -a , ) fo , . , fo,<5,. 1.0, \\ < \\ g(S;)={ft , , -\\^l,<.b, (9,10) 1.0, S, < -6,. 5 Non-Dimensionalization The equations of motion can be written_in a non-dimen sional form by defining t = Ibt, 0, = 6i/ipci 'I'c \u2014 ^c/^c where tS, i/'\u0302 , x^, R^ represent characteristic frequency, angular displacement, length and radius, respectively. The purpose of this procedure is two-fold",
            " 4 The variation of r^ with the response amplitude S, for (a) singie-sided Impacts, and (b) double-sided impacts shows that at low stiffness contact ratios (associated with light mean loads and/or high alternating loads) the natural frequencies are much closer than at high stiffness contact ratios. Based on these results strong nonlinear behavior is anticipated at low loads, which is confirmed by actual time integration. 8 Example Cases and Algorithm Evaluation Criteria An analysis of numerical methods will be conducted using parameters from a generic automotive manual transmission (See Fig. 2). Baseline inertial and stiffness parameters are incorporated into the dimensionless format [refer to Eqs. (11)-(14)] and these are listed in Table 1. Typical values used to define the non-linearities will be given later. Three exam ple cases of differing complexity, from moderately non-linear (case 1) to extremely non-linear (case 3), are listed in Table 2. The extent of the stiffness non-linearity for each element is categorized as moderately non-linear (i.e. a < 0.01) and strongly non-linear (a < 0",
            " Hence, in order to determine the agreement of the solutions, only selected frequencies or bandwidths were used in the determi nation of K if), which is defined as \\{P^yif)Y\\/PM^PyyiD where P^^C/), Pyy(f) and P^yif) are the averaged auto, auto and cross power spectral densities (PSD), respectively. Typi cal signal processing includes 128 points per time window and four ensembles. The RK2 time domain results were used as a reference for comparison. 9 Results and Validation of Models Three selected case studies as identified in Table 2 are presented, covering a range of complexity regarding the number of non-linear elements and types of loading; also refer to Fig. 2. The typical excitation in each case consists of a mean load and five harmonics of sinusoidal load applied to the inertial element / j , a mean load applied to I^, and light drag loads applied to all elements. Additionally, cases 2 and 3 include transmission error excitation applied at the mesh frequency 20fl^jj where fl<,jj is the frequency of the main shaft rotation. Tables 3 and 4 show performance criteria for a system with two and three clearance type non-linearities with multiple excitations (case 1 and case 3, respectively)",
            " For case 3, the ratio of the mean to alternating load is set to 0.05 for the lightly loaded case and 0.5 for the moderately loaded case. An increase in the mean load on the system reduces the comput ing time for variable step algorithms by about 30 percent. The solution coherences are also better for such moderately loaded systems. In order to validate the proposed numerical techniques for non-linear systems, results were compared with available experimental data (Takemoto et al., 1992) from a four-degree-of-freedom system, as shown in Fig. 2(b). Comparisons between simulation and experimental angular accelerations (in rad/s^) are found to be excellent for three different cases, as evident from Table 5. These results and other comparisons (though not reported here because of industrial proprietary information involved) are very promising and indicate that the techniques presented in this study are indeed suitable. The choice of an algorithm is dictated by the type of physical system, including nonlinearities, under evaluation. For instance, higher order methods appear to become com putationally inefficient as evident from the excessive compu tational time and functional calls when the system becomes one or any combination of the following: lightly loaded, lightly damped, highly non-linear, or strongly stiff"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001390_j.mechmachtheory.2005.09.004-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001390_j.mechmachtheory.2005.09.004-Figure1-1.png",
        "caption": "Fig. 1. Worm grinding.",
        "texts": [
            " The tooth geometry for different types of cylindrical worm gears was developed, as are: the Archimedean, involute, convolute, thread-ground, and the new type of worm gear (the worm is ground by a grinding wheel whose axial profile consists of two circular arcs of different radii optimized [15]). Because of the limited length of the paper, only the geometry of the commonly used, thread-ground worm gear drive will be presented. The surface of the conical grinding wheel for worm grinding is defined by the following equation (Fig. 1) ~r \u00f0gw\u00de gw \u00f0u;u\u00de \u00bc u cos u u sin u zp \u00f0u tga0 pg\u00de 1 2 666664 3 777775 . \u00f01\u00de For the right flank of worm thread, AB, zp = 1, and for the left flank, CD, zp = 1. The ground worm surface points are defined by equations ~r \u00f0w\u00de w \u00bcMgww ~r\u00f0gw\u00de gw \u00bc 1 0 0 agw 0 cos sgw sin sgw 0 0 sin sgw cos sgw 0 0 0 0 1 2 66664 3 77775 ~r \u00f0gw\u00de gw ; ~n \u00f0gw\u00de gw ~v \u00f0gw;w\u00de gw \u00bc 0. \u00f02\u00de Matrix Mgww performs the coordinate transformation from the coordinate system Kgw (attached to the grinding wheel) into the system Kw (attached to the worm, Fig. 1). The setting angle of the grinding wheel axis, sgw, is equal to the worm lead angle, x0w. The second equation of Eqs. (2) defines the worm surface generation by the grinding wheel, where~n\u00f0gw\u00de gw is the normal vector of the grinding wheel surface and~v\u00f0gw;w\u00de gw is the relative velocity vector of the grinding wheel to the worm. Based on Eq. (1) and Fig. 1 it follows ~n \u00f0gw\u00de gw \u00bc cos u sin u zp cotga0 0 2 66664 3 77775; \u00f03\u00de ~v\u00f0gw\u00de gw \u00bc x\u00f0w\u00de zgw sin sgw ygw cos sgw \u00f0xgw \u00fe agw\u00de cos sgw \u00fe kw sin sgw \u00f0xgw \u00fe agw\u00de sin sgw \u00fe kw cos sgw 2 64 3 75. \u00f04\u00de The axial profile of the ground worm is defined by xwa \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 w \u00fe y2 w q ; zwa \u00bc zw kw tghwg; \u00f05\u00de where tghwg \u00bc yw xw . For the corresponding worm surface it follows ~r \u00f0w\u00de w \u00f0u; hw\u00de \u00bc xwa cos hw xwa sin hw zwa \u00fe kw hw 1 2 6664 3 7775; \u00f06\u00de where kw = r0w \u00c6 tgx0w. The gear teeth are generated by a hob (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002414_cdc.2009.5400463-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002414_cdc.2009.5400463-Figure1-1.png",
        "caption": "Fig. 1. Sketch map of quadrotor aircraft",
        "texts": [
            " In section 2, the mathematical model of the aircraft is given and the control problem is stated. In section 3, an integer-coefficient digital filter is proposed to restrain the effect of measurement disturbances. In sections 4 and 5, the attitude controller and position controller are given respectively. In section 6, the indoor flight experiment results are shown. And, the conclusions are given in section 7. The quadrotor aircraft under consideration consists of a rigid cross frame equipped with four rotors as shown in Fig. 1. The up (down) motion is achieved by increasing (decreasing) the total thrust while maintaining an equal individual thrust. The forward/backward, left/right and the yaw motions are achieved through a differential control strategy of the thrust generated by each rotor. In order to avoid the yaw drift due to the reactive torques, the quadrotor aircraft is configured such that the set of rotors (right-left) rotates clockwise and the set of rotors (front-end) rotates counterclockwise. There is no change in the direction of rotation of the rotors",
            " Hence, the yaw motion is then realized in the direction of the induced reactive torque. On the other hand, forward (backward) motion is achieved by pitching in the desired direction by increasing the end (front) rotor thrust and decreasing the front (end) rotor thrust to maintain the 978-1-4244-3872-3/09/$25.00 \u00a92009 IEEE 5213 total thrust. Finally, a sideways motion is achieved by rolling in the desired direction by increasing the left (right) rotor thrust and decreasing the right (left) rotor thrust to maintain the total thrust. In Fig.1, Sg denotes the inertial frame; Sb denotes the body frame; \u03be = [ x y z ]T \u2208 Sg and v = [ x\u0307 y\u0307 z\u0307 ]T denote the mass center position and the velocity of the aircraft in the inertial frame, respectively; The Fi lift generated by the rotor in the free air (expressed in Sb). The linear motion equations are given as follows: \u03be\u0307 = v v\u0307 = gez \u2212 THRe Z m where m denotes the aircraft mass; g denotes the acceleration due to the gravity; the vector ez = [ 0 0 1 ]T denotes the unit vector in the frame Sg; the orthogonal matrix R \u2208 <3\u00d73 depends on the pitch angle \u03d1, the yaw angle \u03c8 and the roll angle \u03c6, and is further expressed as R =   c\u03d1c\u03c8 c\u03c8s\u03d1s\u03c6\u2212 s\u03c8c\u03c6 c\u03c8s\u03d1c\u03c6 + s\u03c8s\u03c6 s\u03c8c\u03d1 s\u03c8s\u03d1s\u03c6 + c\u03c8c\u03c6 s\u03c8s\u03d1c\u03c6\u2212 c\u03c8s\u03c6 \u2212s\u03d1 c\u03d1s\u03c6 c\u03d1c\u03c6   (1) with c\u00b7 = cos(\u00b7), s\u00b7 = sin(\u00b7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001703_bfb0036159-Figure15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001703_bfb0036159-Figure15-1.png",
        "caption": "Figure 15: A hip actuator using Levered Isotonic Tendons for Human Emulation: LITHE. The pulleys maintain equal tensions in the two antagonistic tendons, while differential adjustment of their mechanical advantage determines the net torque about the crank. Elasticity in the tendons keeps the tension, and therefore the torque, constant over large swings in leg angle.",
        "texts": [
            " Moreover, it must be supple: when acting on a dangling leg, it should set the equilibrium position, but not affect the pendulum frequency or damping. The geared motors or fluidic actuators used on most mechanical bipeds do not satisfy this requirement; lift one of their legs, and it will hang catatonically or, at best, grind slowly to a halt at the bottom of its swing. With joints like these the physics of passive walking are reduced to so much background noise. To preserve dynamics we have developed the so-called LITHE actuator shown in figure 15. The mechanism has proved to be quite satisfactory in balandng a leg inverted, and we look forward to equally good performance in walking experiments. 7 The col lect ion of results The models that we have outlined are together capable of a strong repertoire of locomotion, including walking at a range of speeds, in two or three dimensions, up and down slopes steep and shallow, and over unevenly-spaced footholds. All of this repertoire is built upon the robust foundation of the elementary passive cycle, which leads to emcient performance and simple control methods for the design engineer (and, one might imagine, a forgiving feel for a child finding his feet)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.28-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.28-1.png",
        "caption": "FIGURE 1.28 The MTS Flat-Trac Roadway Simulator , Milliken (1995).",
        "texts": [
            " Another more practical solution would be to bring the vehicle in the desired attitude (b/ 8 ) by briefly inducing large brake or drive slip at the rear that lowers the cornering force and lets the car swing to the desired slip angle while at the same time the steering wheel is turned backward to even negative values. The MMM diagram, which is actually a Gough plot (for a single tire, cf. Figures 3.5 and 3.29) established for the whole car at different steer angles, may be assessed experimentally through either outdoor or indoor experiments. On the proving ground, a vehicle may be attached at the side of a heavy truck or railway vehicle and set at different slip angles while the force and moment are being measured (tethered testing), cf. Milliken (1995). Figure 1.28 depicts the remarkable laboratory MMM test machine. This MTS Flat-Trac Roadway Simulator uses four flat belts which can be steered and driven independently. The car is constrained in its center of gravity but is free to roll and pitch. In this section we will discuss the role of the tire in connection with the dynamic behavior of a car that tows a trailer. More specifically, we will study the possible unstable motions that may show up with such a combination. Linear differential equations are sufficient to analyze the stability of the straight-ahead motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002040_978-3-540-36119-0_18-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002040_978-3-540-36119-0_18-Figure3-1.png",
        "caption": "Fig. 3. Five strategies to avoid instability in an elastic three-segment leg: (A) nonlinear joint springs, (B) asymmetric leg segmentation and leg joint configuration, (C) biarticular elastic structures, (D) joint constraints, e.g. heel contact, and (E) operation in a bow configuration",
        "texts": [
            " To avoid this disastrous behavior, different measures can be introduced. One strategy is to steer the leg joint movements by a kinematic control approach, whereby the joint angle is constrained along a desired trajectory. This intervention may work at low energies through the use of a high-bandwidth controller to counteract the system dynamics. At faster leg movements however, a more systematic modification is required. Stability analysis of the three-segment leg reveals that different solutions exist to avoid this intrinsic instability (Fig. 3). Strategy A: The joint spring characteristics are slightly non-linear, e.g. the joint stiffness increases with joint flexion. If one joint flexes more than the other, the increased joint stiffness compensates for the mechanical disadvantage caused by the joint\u2019s increased flexion. The model predicts a higher nonlinearity in joints whose configuration at static equilibrium is characterized by greater extension (e.g. knee compared to ankle). This prediction is confirmed by experimental results. The required nonlinearity of the joint torque characteristics might be provided by the nonlinear stress-strain characteristics of tendons and aponeuroses connecting the muscle to the skeleton as found in human running or jumping [13, 21]",
            " All of these strategies guarantee parallel joint operation in a three segment leg and can be found in nature. It is important to realize that these measures are not exclusive and are often implemented in a highly redundant fashion. Similar to the air bags in our cars, the leg includes several design and control strategies to avoid mechanical instability potentially leading to serious damages of the musculo-skeletal system. Elastic joint behavior in itself does not guarantee stable leg operation during contact. However, for the identified leg design and control strategies (Fig. 3) the control of the highly nonlinear segmented leg could be simplified. The results demonstrate that spring-like leg operation can be a key for better understanding the architecture and function of biological legs. On the joint level, spring-like behavior (joint stiffness and nominal angle) can be adapted based on neuromuscular mechanisms [6], [10]. In turn, if all required measures are undertaken to guarantee stable leg operation, spring-like leg operation can result at various loading conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001554_j.enconman.2007.07.033-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001554_j.enconman.2007.07.033-Figure7-1.png",
        "caption": "Fig. 7. The measured temperature rise distribution in the induction cage machine TSg 100L-4B in nominal work conditions.",
        "texts": [
            " All the results are determined for the nominal load and the positive sequence voltage component equal to the rated value (an asymmetrically fed induction machine in the conditions of voltage and frequency deviations, often appearing in ship power systems, will be analyzed in separate papers). Figs. 5 and 6 show the measured and calculated additional end windings temperature rise (D#u) due to unbalance versus the CVUF angle Hv for VUF = 3%. The former figure corresponds to the delta connected motor TSg 100L-4B type and the latter to the wye connected motor Sg 132S-4. Additionally, in Figs. 7\u20139, there is a comparison of the measured temperature rise distribution for a nominally loaded machine TSg 100L-4B and various supply conditions. Fig. 7 corresponds to the nominal supply and Figs. 8 and 9 to a voltage unbalance with the VUF factor equal to 3% but with different values of the CVUF angle. Namely, the CVUF angle for the thermal test presented in Fig. 8 corresponds to the worst case (see Fig. 5) for phase winding V1-V2 (the hottest measured point in nominal work conditions is located in this winding), whereas Fig. 9 refers to the most favourable case. The presented results of the investigations show that D#u in each phase winding sinusoidally depends on the CVUF angle (superposition of a sinusoid component and a constant component)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003515_tasc.2016.2602500-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003515_tasc.2016.2602500-Figure12-1.png",
        "caption": "Fig. 12. 2-D and 3-D static FE model of the motor. (a) 3-D FE model. (b) 2-D FE model.",
        "texts": [
            " The impedances of the end part are taken into account. The equivalent circuit model includes the effective part and the end part. In the effective part, each wire is modelled as a series combination of a resistance, several inductances, and an induced voltage. And in the end part, each wire is modelled as a series combination of a resistance and several inductances. a) Inductance in the End Part: The inductance matrixes of the winding wires in the end part are carried out by using 2D static FE model and 3D static FE model, as shown in Fig. 12. For 2D FE analysis, the rotor position is varied from 0 to 90 degrees mechanical so that it goes over one complete electrical cycle while varying the current incrementally in 7 steps from 0 A to 30 A. For 3D FE analysis, the rotor position is varied from 0 to 90 degrees mechanical while varying the current incrementally in 2 steps from 15 A to 30 A. Fig. 13 shows the variation of the inductance of phase A with different rotor position and the phase current. Both variations of the inductances are less than 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002857_asjc.564-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002857_asjc.564-Figure1-1.png",
        "caption": "Fig. 1. Configuration of propulsive rocket engines (view from tail).",
        "texts": [
            " This brief paper is organized as follows: the model of LV and its input-output representation are briefly presented in Section II. Then in Section III the fault-tolerant controllers are derived, meanwhile the stability of the closed-loop system is considered. Simulation results are stated in Section IV, followed by the conclusions in Section V. 2.1 Modeling In this paper, we consider an LV with four strap-on rocket boosters (SRBs) and two central rocket engines (CREs), which are configured as in the illustration of Fig. 1. Irrespective of the influences of flex-mode and fuel sloshing, the rotational motion of a rigid LV [14\u201316] is governed by I I Dfault \u03c9 \u03c9 \u03c4 \u03c4= \u2212 + + +\u03a9 (1) where the inertia tensor I = diag(Ixx, Iyy, Izz) \u2208 R3\u00a53 of the axisymentrical structure of the LV, the angular rate vector w = [wx wy wz]T, the matrix W is given by \u03a9 = \u2212 \u2212 \u2212 \u23a1 \u23a3 \u23a2 \u23a2 \u23a2 \u23a4 \u23a6 \u23a5 \u23a5 \u23a5 0 0 0 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 \u03c9 z y z x y x (2) t is the control torque vector, tfault is an additive torque vector of actuator faults, and D = [Dx Dy Dz]T is the disturbance vector",
            " In this paper, we take the aerodynamic contributions account into a generalized disturbance vector D, and omit the expressions of aerodynamic moments in our model. Note that flexible dynamics and fuel sloshing of the LV can be regarded as mismodeling dynamics, and therefore treated as a kind of disturbance. The control torque t in (1) only includes contributions from the control input provided by the deflections of six engines, of which, the four SBRs make an one-axis motion, and the two CREs make a two-axis motion. The arrows attached to engines in Fig. 1 represent positive directions of movement. \u03b4 i c s, stand for the angle of each engine\u2019s deflection from its swinging center, here the subscript i represents the serial number of swinging directions, and the superscript c and s, respectively, represent CREs and SRBs. R = 3m and r = 1m are the distances from x-axis of the body frame to the center of the SRB and to the center of the CRE. Note here that SRB2 and SRB4 provide torques for pitch control, SRB1 and SRB3 for yaw control, and CRE1 and CRE2 provide torques for both pitch control and yaw control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000672_mhs.2000.903292-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000672_mhs.2000.903292-Figure2-1.png",
        "caption": "Figure 2: The spiral-type magnetic micromachine for running in a gel.",
        "texts": [
            " NdFeB magnet Figure 1: Schematic view of magnetic micro-machine for swiiiiiiiing in a high viscosity liquid 2000 INTERNATIONAL SYMPOSIUM ON MICROMECHATRONICS AND HUMAN SCIENCE 0-7803-6498-8/00/ $10.00 02000 IEEE. 65 blade (Tungsten wire: 0.15\" diameter). The magnet was magnetized to its radius direction. By applying a rotational magnetic field, the machine rotates synchronized to the external field. The rotation generates forward or backward thrust by the spiral blade to the rotational plane of the field. In the experiment that running in a gel, another type of the machine was used. The machine is shown in fig.2. This micro-machine was composed of a cylindrical NdFeB magnet (2.0 mm diameter, 7.5 mm long) and a brass tip with a spiral shape (2.1 mm diameter, 4 mm long, 1.0 mm pitch). In both experiment, the magnet used had the maximum energy product of 21.4MGOe and the residual magnetization of 9.85kG. 3. Results and discussion ' 3.1 Swimming in a high viscosity liquid The examination was carried out using silicone oils with kinematic viscosity of 500 - 5x105 mm2/s. By applying the rotational magnetic field of 40 - 100 Oe, the machine rotates and swam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000943_j.finel.2004.02.002-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000943_j.finel.2004.02.002-Figure1-1.png",
        "caption": "Fig. 1. Generating rack in a meshing position during the gear generation process.",
        "texts": [
            "elds such as computer graphics and robotics since they provide an e/ective way to unify the description of geometric transformations as matrix multiplications, and they were introduced to gearings by Litvin in Ref. [8]. Homogenous coordinates (x\u2032; y\u2032; z\u2032; t\u2032) of a point (x; y; z) in a three-dimensional space are any four numbers such that x\u2032=t\u2032 = x, y\u2032=t\u2032 = y and z\u2032=t\u2032 = z. With t\u2032 = 1, a point may be speci!ed by the homogenous coordinates (x; y; z; 1). See Refs. [7,9,10] for more information about homogenous coordinates. Interest in conical involute gears has been growing over the past few decades (see, for instance, [1,3,4,11\u201320]). Fig. 1 shows the generation of a conical involute gear with helix angle and cone angle by a generating rack (or tool). The operation is similar to that required to generate a helical gear, but instead of being parallel to the axis of the gear, the generating rack is inclined to the axis by the cone angle. The generating rack in Fig. 1 has pressure angle n in the normal plane and pressure angles t+ and t\u2212 in the transverse plane. According to Ref. [12], the relation between these angles is tan tj = tan n cos sec \u2212 j sin tan ; (1) where j is a variable that is equal to 1 or \u22121 (which is denoted with + or \u2212). As a consequence, the generated tooth is not symmetric. The base and pitch radii are de!ned as rbj = r cos tj; r = zm=2 cos : (2,3) Fig. 2 shows a part of the generating rack in Fig. 1. The normal coordinate system Sn is located and oriented such that the xn-axis coincides with the vertical symmetry plane of a space width of the rack, the yn-axis coincides with a normal plane of the rack and the zn-axis coincides with the datum plane. The position of the origin On along the width of the rack is arbitrary. A point on a straight Iank of the rack that will generate a point on an involute helicoid (or surface if the generated gear type is a spur gear) of the gear is located with the position vector rnIj, which is de",
            "ned as rnFj(uFj; vFj) = [ xn Fj yn Fj zn Fj 1 ]T =   \u2212e \u2212 sin uFj j[sr=2 + e tan n + (sec n \u2212 cos uFj)] vFj 1   ; (5) e = ha \u2212 : (6) The surface parameters uFj and %Fj are, respectively, the angle and distance that are de!ned in Fig. 2. A point on a rack root surface that will generate a point on a root surface of the gear is located with the position vector rnRj, which is de!ned as rnRj(uRj; vRj) = [ xn Rj yn Rj zn Rj 1 ]T =   \u2212ha juRj vRj 1   ; (7) where the surface parameters uRj and vRj are the distances that are de!ned in Fig. 2. The transverse coordinate system S t in Fig. 1 is oriented such that the yt-axis is parallel with a velocity vector of the rack and the zt-axis is parallel with the gear axis. The coordinate transformation from the normal coordinate system Sn to the transverse coordinate system S t involves two rotations and is represented by the matrix equation rt = [ xt yt zt 1 ]T =MtaManrn; (8) where Man =   1 0 0 0 0 cos sin 0 0 \u2212sin cos 0 0 0 0 1   ; Mta =   cos 0 sin 0 0 1 0 0 \u2212sin 0 cos 0 0 0 0 1   : (9) The parameters vIj, vFj or vRj represent normal sections of the rack",
            " Combining (4) and (8)\u2013(10) yields rtIj(uIj; w) =   uIj sec cos n + w tan \u2212juIj cos n tan tj sec + jsr sec =2 + w sec tan w 1   : (11) In a similar way, combining (5) and (8)\u2013(10) yields rtFj(uFj; w) =   \u2212( sin uFj + e) sec + w tan \u2212 sin tan sin uFj + j(cos uFj \u2212 sec n) cos + j ( e tan tj cos + sr 2 cos ) + w tan cos w 1   (12) and combining (7) and (8)\u2013(10) yields rtRj(uRj; w) =   \u2212ha sec + w tan juRj sec \u2212 ha tan tan + w tan sec w 1   : (13) Fig. 3 shows a transverse section of the generating rack and gear that are shown in Fig. 1 in a meshing position during the gear generation process. The pitch point P is located on the instantaneous axis of rotation, which is parallel with the gear axis. A global coordinate system Sq is located and oriented such that the xqyq-plane coincides with the xtyt-plane, the zq-axis coincides with the gear axis and the xq-axis is parallel with the xt-axis. The gear coordinate system Sg has rotated an angle \u2019 from the global coordinate system Sq. The rack coordinate system S t has moved a distance r\u2019 from Sq in a direction opposite to the yq-axis and the distance between Ot and Oq in the xq-axis direction is r + i, where i is the initial addendum modi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure10-4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure10-4-1.png",
        "caption": "FIGURE 10-4 Steady-state free-body diagram of draw bar pull and soil reactions on a tractor.",
        "texts": [
            " Motion resistance ratio (p) is defined as the rolling resistance force divided by the normal load on the traction device. The tractive ability is affected by the vertical soil reaction against the traction wheels. Weight transfer, from drawbar pull, decreases the soil reaction against the front wheels by an amount dRf and increases the reaction against the rear wheels by an amount dR\" thus adding to the maximum drawbar pull for a two-wheel-drive tractor. The symbols in the \"weight transfer\" equations are defined in figure 10-4. See chapter 11 for the derivation of these equations. dR=l!.11 r Ll (5) and dR - pYr f - Ll (6) Any means of increasing the rear wheel reaction will increase the traction of the rear wheel if the soil has sufficient strength and if sinkage does not limit the traction. Figure 10-5(a) illustrates one of several alternative methods of describing 244 TRACTION the forces acting on a wheel. The method illustrated in figure 10-5(a) and used in this book is condensed from a publication by Wismer and Luth (1974)",
            " Soil parameters are c = 14 kPa and <!> = 30\u00b0. 2. A tractor weighing 15.84 kN has the static weight divided so that 11.60 kN is on the rear wheels and 4.24 kN is on the front wheels. The rear tires are 11.25-36* (286- 914 mm) and the front tires are 5.00-16 (127-406 mm). Using equation 14 and figure 10-12, calculate the probable power to tow this tractor at 6.5 km/h on (a) silt loam at maize harvest and (b) concrete. 3. If the tractor of problem 2 is exerting a drawbar pull of 7.80 kN and if y! (fig. 10-4) equals 700 mm (also Yr) and L[ = 2160 mm, calculate (a) the true rear-tire load, and (b) the required coefficient of traction for the rear wheels. 4. Referring to equations 14 and 16, determine the maximum drawbar pull that the tractor of problem 2 is capable of exerting. Let Y! (fig. 10-4) be taken as 700 mm and Yr as 460 mm. Is the tractor in danger of tipping over backwards? Why? What is the drawbar pull required to lift the front wheels from the ground? 5. If the tractor of problem 2 has a maximum of 13.4-k W drawbar power on concrete, what speed would utilize the full tractor power on sandy loam (see fig. 10-12)? 6. Using dimensional analysis, find the dimensionless ratios (pi terms) listed in equa tion 13. 7. A series of soil tests is made with a plate as shown in figure 1 0-la, where l = b = 10 cm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002317_j.jbiosc.2008.09.009-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002317_j.jbiosc.2008.09.009-Figure2-1.png",
        "caption": "FIG. 2. Electrochemical cell for p",
        "texts": [
            " Alg-Na was first modified by introducing poly(oxyethylene)diamine. 1-Methy1\u2032-bromobutyl-4,4\u2032-bipyridinium iodide bromide (BrC4V) was attached to the amino groups of the modified Alg-Na, and the polymer so obtained is referred to here as Alg-V. Malic enzyme reaction for L-malic acid production with HCO3 \u2212 fixation with electrochemical coenzyme regeneration Electrochemical regeneration of coenzyme conjugated with the malic enzyme reverse reaction for HCO3 \u2212 fixation was performed using a two-compartment cell (Fig. 2), which was equipped with a threeelectrode system. The two compartments were separated by a semipermeable membrane (Cellophane) or a cation exchange membrane (Neosepta CMB; Tokuyama Soda, Tokyo) and filled with 25 ml of 55 mM HEPES\u2013KOH buffer (pH 7.4). The buffer solution in compartment I was composed of the desired amounts of methyl viologen (MV2+) or Alg-V and 0.1 mM NAD+, 0.1 M KHCO3, 0.5 M pyruvic acid, 2.0 U ml\u22121 LipDH, and 0.3 U ml\u22121of malic enzyme. The cells were immersed in a water bath and continuously purged with high-purity nitrogen gas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003669_j.mechmachtheory.2014.09.002-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003669_j.mechmachtheory.2014.09.002-Figure8-1.png",
        "caption": "Fig. 8. 3D gear model.",
        "texts": [
            " (72) and (73) into Eq. (20), vh(h, \u03d5c) can be calculated in Sb as vbh h;\u03d5c\u00f0 \u00de \u00bc dob g \u03d5c\u00f0 \u00de d\u03d5c \u00fe h dl b g \u03d5c\u00f0 \u00de d\u03d5c \u00bc dM14 d\u03d5c dM24 d\u03d5c dM34 d\u03d5c T \u00fe h dM13 d\u03d5c dM23 d\u03d5c dM33 d\u03d5c T \u00f074\u00de where dMi3/d\u03d5c and dMi4/d\u03d5c (i=1, 2, 3) are given in Eq. (A.3) in Appendix A. vh(\u03c6,\u03d5c) can be obtained by replacing h in Eq. (74)with h(\u03c6) in Eq. (70). By submitting Eqs. (72)\u2013(74) into Eq. (38), the closed-form representation of the tooth surface is obtained.Moreover, the 3D model is obtained in CATIA V5R20 as shown in Fig. 8. Curvature analysis is only conducted to the working part of the tooth surface. As stated in Section 6.2, the curvature analysis can be implemented with rh, r\u03d5, nh, and n\u03d5. According to Eqs. (43)\u2013(46), we have to calculate l, vh and their derivatives with respect to both h and \u03d5 to obtain rh, r\u03d5, nh, and n\u03d5. l and vh have been calculated in Eqs. (73) and (74), then we have dlbg \u03d5c\u00f0 \u00de dh \u00bc 0; dlbg \u03d5c\u00f0 \u00de d\u03d5c \u00bc dM13 d\u03d5c dM23 d\u03d5c dM33 d\u03d5c T \u00f075\u00de dvbh h;\u03d5c\u00f0 \u00de dh \u00bc dlbg \u03d5c\u00f0 \u00de d\u03d5c ; dvbh h;\u03d5c\u00f0 \u00de d\u03d5c \u00bc d2M14 d\u03d52 c d2M24 d\u03d52 c d2M34 d\u03d52 c \" #T \u00fe h d2M13 d\u03d52 c d2M23 d\u03d52 c d2M33 d\u03d52 c \" #T \u00f076\u00de where d2Mi3/d\u03d5c 2 and d2Mi4/d\u03d5c 2 (i = 1, 2, 3) are given in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure6-1.png",
        "caption": "Figure 6. Calculation of force and moment on interface node k.",
        "texts": [
            " The reactions on the interface nodes are calculated by linear interpolation of the roller loads, such that the roller load is gradually transferred from one interface node to the next as the roller passes between the interface nodes. This implies that a roller load calculated for a roller located exactly at an interface node is applied only to this interface node. The roller load for a roller located exactly in the middle between two interface nodes is split evenly on each interface node and so on. Referring to Figure 6, the loads on the interface node k (Fk and Mk) are calculated from the roller loads on rollers j and j\u00fe 1 (shown as grey). For each roller, j, the linear interpolation weighting factor, , for each interface node, k, is determined by jk \u00bc 0 if j4 k 1 k 1 j k 1 k if k 1 5 j 5 k k\u00fe1 j k\u00fe1 k if k4 j 5 k\u00fe1 0 if k\u00fe14 j 8>>>>>>>>>>< >>>>>>>>>>: \u00f025\u00de In the above interpolations, j must be limited to 04 j 5 2 . Furthermore, small modifications exist to handle the interpolation when crossing \u00bc 0= \u00bc 2 . Utilizing the interpolation weighting factor, the interface nodal loads are summarized as Fk \u00bc XZ j\u00bc1 jk Foj \u00f026\u00de Mk \u00bc XZ j\u00bc1 jk Moj \u00f027\u00de In models that do not only take into account the contact stiffness but also the stiffness of the supporting structure (FE models and the multi-dof model), the contact moments result in small local rotations of the bearing rings and supporting structure close to the contact zones, and these rotations reduce the total misalignment between the inner and outer raceways"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001370_elan.200603621-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001370_elan.200603621-Figure5-1.png",
        "caption": "Fig. 5. Microbial fuel cell (gas ports and external plumbing not shown).",
        "texts": [
            " The anodic half reaction for mixedMB and NR becomes: Glucose\u00fe 6H2O\u00fe 4ADP\u00fe 4Pi\u00fe 2 MB\u00fe 10NR! 4ATP\u00fe 2 MBH2\u00fe 10NRH2\u00fe 6CO2 In this case 2ATP are generated during glycolysis and 2ATP by the TCA cycle itself. When employing an oxygen cathode in the MFC, the 2MBH2\u00fe 10NRH2 represents a free energy of 2{46(0.82 \u2013 0.011)}\u00fe 10{46(0.82\u00fe 0.325)}\u00bc 601 kcal per mol of glucose or 87% energy efficiency. Electroanalysis 18, 2006, No. 19-20, 2001 \u2013 2007 www.electroanalysis.wiley-vch.de F 2006 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim Asmall desktop apparatuswas built, as shown inFigure 5, to test the hypothesis that a yeast-catalyzedMFCwill perform better undermixedmediation thanwhenmediators are used singly at the same overall concentration. Compartments: Annular virgin-grade PTFE (Teflon). End Plates: Square transparent Plexiglas Seals: Silicon rubber o-rings. Electrodes: Reticulated vitreous carbon (RVC), 100 pores per inch. Membrane: Nafion 115. Current Collector: Square carbon felt washer. Hardware: All Stainless Steel. Compartment Volumes: 32 mL each (both anode and cathode)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001523_j.optlastec.2005.08.012-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001523_j.optlastec.2005.08.012-Figure2-1.png",
        "caption": "Fig. 2. Schematic of LDF for thin wall.",
        "texts": [
            " In laser cladding formation, a thin wall is usually fabricated with laser scanning along a single row. To understand the formation of the thin wall by single-pass coaxial laser cladding, the effects of the process variables must be investigated. Since a thin metallic wall is fabricated by single-pass laser cladding, its thickness, d, is equal to the width of the ARTICLE IN PRESS J.C. Liu, L.J. Li / Optics & Laser Technology 39 (2007) 231\u2013236232 molten pool created in laser cladding. As shown in Fig. 2, a laser beam moves in the positive x-direction at velocity v. The origin is on the center line of the laser beam. The following assumptions can be made: 1. All thermophysical properties are considered to be temperature-independent. 2. Because the temperature of the melt pool is usually below 2000 1C (for ferrous alloys), the radiant heat flow and the convective heat flow from its surface to the surroundings are neglected. 3. The laser spot on the interaction area is small. The surface area of the melt pool is shaped as a disk"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000820_tmag.2003.816738-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000820_tmag.2003.816738-Figure2-1.png",
        "caption": "Fig. 2. Configuration of the motor-driving circuit.",
        "texts": [
            " of Electrical and Communication Engineering, Tohoku University, Aramaki, Aoba-ku, Sendai 980-8579, Japan (e-mail: ichinoku@ecei.tohoku.ac.jp). Digital Object Identifier 10.1109/TMAG.2003.816738 are 6 and 4, respectively. The stator has windings concentrated around each stator pole. The number of winding turns of each phase is 150. The rare-earth magnet \u201cNd-Fe-B\u201d is buried in the rotor iron. Residual magnetic flux density and coercive force of the permanent magnet are about 1.3 T and 1000 kA/m, respectively. Fig. 2 is the driving circuit of the IPM motor. In this paper, the rotor angle , where the rotor is in the position as shown in Fig. 2, is set to 0 . The IPM motor utilizes both magnet and reluctnace torques due to the variation of reluctance in the magnetic circuit. Therefore, it is understood that the magnetic circuit model of the IPM motor consists of reluctances and permanent magnet MMF sources. First, we obtain the reluctances of the magnetic circuit model. We assume that regions of permanent magnet burying in the rotor iron are the vacuum space. When a current flows through the U-phase windings under the assumption, the fluxes flow in the motor as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001545_0921-8890(91)90045-m-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001545_0921-8890(91)90045-m-Figure8-1.png",
        "caption": "Fig. 8. Geometry of mobile and object cell.",
        "texts": [
            " The common candidate with the best evaluation value gives the optimal structure for the given task. 4. Communication system 4.1. Communication in CEBOT the undocked state of The execution level of the previously described planning system (see Fig. 2) commands the mobile cells to build substructures of the manipulator. The mobile cells need communication to find object cells of the required type and their position. This is realized as a serial communication system, using infrared rotating sensor modules on top of the cells (see Fig. 8). The mobile cell detects the object and receives the object sensor module angle by communication. Light intensity leads to the approximate distance and the mobile cell sensor Step 4: The master adjusts and stops its sensor facing the selected object cell (master fine adjustment). angle is in its own database. Using distance and the two sensor orientations, the approach path is planned. A 12-bit, 1 start-bit and 2 stop-bits serial communication protocol (see Fig. 9) is used to transmit object cell type and attitude in a 6-step handshake sequence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002745_pime_proc_1966_181_036_02-Figure28-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002745_pime_proc_1966_181_036_02-Figure28-1.png",
        "caption": "Fig. 28. The general arrangement of the strain-gauge circuit",
        "texts": [
            " By adjusting the vertical and the base rings any orientation of the ball axis with respect to the track can be achieved. Both angles can be read directly from the vernier scales to within one-tenth of a degree. It was found necessary, however, to subdivide the vernier scale by means of a micrometer screw to 0.001 of a degree in order to have the degree of accuracy required. The rig when used for sliding experiments is not dissimilar to that used by Smith (33) and Misharin The extended octagonal ring D with eight strain gauges is mounted on the adjustable platform by means of two flexible cross-springs. Fig. 28 shows the different combinations of gauges with which the two force components, F, and F,, and the moment, M y can be measured. The selector and the monitor were designed to allow each output circuit to be balanced individually through potentiometers. The high gain of the bridge circuit with four active gauges permitted the use of a relatively stiff dynamometer ring. For example, at a total bridge current of 6 mA, ( 4 0 Vol18I Pr 1 No 16 at PENNSYLVANIA STATE UNIV on June 4, 2016pme.sagepub.comDownloaded from FRICTIONAL BEHAVIOUR OF LUBRICATED ROLLING-CONTACT ELEMENTS 365 Proc Instn Mech Emgrs 1966-67 Val 181 Pt 1 No 16 at PENNSYLVANIA STATE UNIV on June 4, 2016pme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001650_rob.4620010107-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001650_rob.4620010107-Figure8-1.png",
        "caption": "Figure 8. Transition in postural balance.",
        "texts": [
            " Digital computer simulations of this motion with the above reference signals are shown in Figure 6 . The needed control torques. computed from Eq. (15) are shown in Figure 7. Because of nonlinear feedback and decoupling all other angles remain zero. i.e, the right leg, the right thigh, and the trunk appear to form a stable platform for the rhythmic motion of the left leg and thigh. Hemami and Zheng: Dynamics and Control of Motion 111 The second movement is a transient study from a perturbed state: &I\", 6, to vertical stance +, hf (Fig. 8): m,= [O], d)f= [Ol; ~o=[o.l ,o. l .o. l .o. l .-o. l ,o,o,o,-o. l ,-o. l ] : Qo = [OI. For time delays of 7 2 10 ms and with no predictor, the digital computer simulations of this motion were unstable. For a time delay of 10 ms and a predictor as described before the system was stable and the transitions of the ten angles are shown in Figure 9. The transient duration is about 1 s, and is acceptable in view of the poles of the system all being at -5. 112 Journal of Robotic Systems-1 984 Hemami and Zheng: Dynamics and Control of Motion 113 VI"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003392_j.procir.2014.03.066-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003392_j.procir.2014.03.066-Figure2-1.png",
        "caption": "Figure 2: Milling operations",
        "texts": [
            " As turning can be done using standard tools, it makes sense to start from a pre-turned blank. Tooth trace form variation F\u03b2f 9 [\u03bcm] Run out Fr 24 [\u03bcm] Cumulative pitch error Fp 32 [\u03bcm] Single pitch error fp 7 [\u03bcm] Pitch to pitch error fu 9 [\u03bcm] Because of flexibility, only standard end and ball mills were used. Prototype gears were produced on a 5-axis milling machine (DMG Sauer 70-5). For the manufacturing of this gear, 4 tools have been used; the 4 machining steps are listed in Table 2 and illustrated in Figure 2. To know how much passes the tool should make per tooth to have a good surface quality it was necessary to perform a test, since the simulation of the scallop by the CAM system is not always that accurate for low roughness surfaces. Therefore a gear was machined using a different stepover per tooth. Afterwards these teeth have been investigated to check the scallop and surface roughness. Afterwards these teeth were investigated to check the scallop and surface roughness. Wire-EDM was used to cut the gear in segments to enable the roughness measurement of every tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001105_robot.2001.933160-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001105_robot.2001.933160-Figure3-1.png",
        "caption": "Figure 3: a) Ports and port orientations of Conro module and graphs that take into account b) connectivity, c) multiple ports and d) multiple-connection ports",
        "texts": [
            ", [2], [3]), a graph-only representation of the robot reduces the complexity of matching two robot configurations to exactly that of the isomorphism-complete class, i.e., there is no need to cycle permutations of labels. Furthermore, it can take into account multiport modules, multiconnector ports and loop structures. However, unlike the representation of Chen and Burdick, this representation is defined for static structures, i.e., extensions that address the kinematics or dynamics of the robot are not considered. The basic Conro module, shown in Fig. 3.a, has four ports. Any of the ports of the passive head can be connected to the port of the active connector of another module in any of two orientations, \u201cbelly-up\u201d or \u201cbelly-down\u201d. We denote the ports of the module as fi and the orientations of the port as d i . We want to find a graph representation of the module that can be used to identify, without ambiguities, any legal robot Configuration. In the connectivitygraph representation, a module is represented as a vertex (see Fig. 3.b) and a connection between modules, as an edge, as in the case shown in Fig. 2 . This graph describes the topology of a robot but cannot be used to uniquely identify configurations with modules that can be connected to each other using different ports, i.e., if a module with n ports can be connected to any of the n ports of another module, then there are n! ways in which the two modules can be connected, many of which might be topologically different. The Conro module is a multiport module and thus, we cannot use a connectivity graph to uniquely identify a configuration. For example, the two configurations shown in Figs. 4.a-b have the same connectivity graph shown in Fig. 4.c (a module has been colored for visualization purposes). A way to distinguish between configurations of multiport modules is to use the labels of the ports in the representation. In this case a suitable representation of the module is that shown in Fig. 3.c, where tlie module is represented by its ports, i.e., a vertex represents a port while an edge indicates that two ports either belong to the same module or belong to two connected modules. Our goal is to find a graph-only representation of a robot that would allow us to distinguish between dif- ferent configurations regardless of their labelings, i.e., the unlabeled version of the graph must be sufficient to identify the configuration. Unfortunately, the direct use of the labeled-graph representation of a robot with multiport modules leads to ambiguous unlabeled graphs. Figures. 5.a-b show the labeled graphs of the two configurations shown in Figs. 4.a-b. We can see that the unlabeled version of both graphs is the same. The problem of how to make the \u201clabel\u201d itself a part of the graph can be solved in various ways. In our case, we mapped the labeled graph in Fig. 3.c to the digraph in Fig. 6.a by extending an edge from port fi to port f, for i < j , i.e., vertex fi has n - i edges leaving it or, equivalently, it has i - 1 edges arriving to it, where n is the number of ports of the module. This digraph unambiguously represents a multiport module because it is rigid, i.e., it has no automorphisms and thus, there is only one way to interpret it [ll]. Hence, we can now represent robots built with multiport modules without ambiguity. For example, the two configurations shown in Figs. 4.a-b have the digraph representations shown in Figs. 6.b-c, respectively. An inspection shows that the corresponding unlabeled digraphs, indeed, are not isomorphic. The graph representation of Fig. 3.c preserves the symmetries of the module while the digraph representation of Fig. 6.a destroys it; modules that have partial symmetries can be represented using a combination of both representations. The same approach used to distinguish configurations of multiport modules can be used to distinguish configurations of modules with multiconnection ports. A multiconnection port is one that allows two ports of two modules to be connected in different ways. For example, the Conro modules can be connected to each other while they are both lying on their \u201cbellies\u201d or we can turn one of them \u201cbelly-up\u201d and still have a legal physical connection",
            " In the same way that we disambiguated multiport modules by representing the module as a set of ports, we can disambiguate multiconnection multiport modules by representing the ports as a set of connections, i.e., each possible connection in each port needs to be labeled. In the case of the Conro module, a given port of a module can be connected to a given port of another module in one of two relative orientations: belly-down or belly-up. Hence, each port has only two associated connections d l and d2 as shown in Fig. 3.a. The corresponding labeled graph of this module representation is that of Fig. 3.d. As before, the labeled graph of the module is replaced by a digraph to make the label itself a part of the graph. This multiconnection digraph is shown in Fig. 7.c. Using this representation of the module, the configurations in Figs. 7.a-b are represented by the graphs shown in Figs. 8.a-b. which have nonisomorphic unlabeled graphs. The module representations described in this section are quite general and can be used to represent other homogeneous modular robots. The extension to heterogeneous modular robots is straightforward as different types of modules can be labeled by attaching to a given vertex of each digraph a tag that identifies the type of the module (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001376_icca.2005.1528213-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001376_icca.2005.1528213-Figure9-1.png",
        "caption": "Fig. 9. Layout of the avionic system.",
        "texts": [
            " The original landing gear of the basic helicopter is plastic, which is too weak to undertake amount of bumping momentum when the UAV helicopter is landing on the ground in the automatic or manual mode. There is no enough room in the fuselage of the basic helicopter to install the designed avionic system (see Figure 1). Thus, we have designed and changed the material of the landing gear to aluminum alloy and make a larger room under the fuselage of the basic helicopter for the avionic system. The avionic system is packed in a carbon- ber box. The layout inside the box is shown in Figure 9, which is to set the IMU as close as possible to the center of gravity of the basic helicopter with the avionic system and the avonic system well-balanced. The layout is determined by major considerations of distribution of the weights of the basic helicopter and the avionic system in the horizontal plane as follows, 1) To measure the projected point of the center of gravity of the basic helicopter on the horizontal bottom plane of the carbon- ber box. 2) The IMU is placed as close as possible to the projected point of the center of gravity of the basic helicopter on the horizontal bottom plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003297_icra.2017.7989532-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003297_icra.2017.7989532-Figure3-1.png",
        "caption": "Fig. 3. Definition of the swing angle \u03b1 and \u03b2. \u03b1 is the angle between ze and taut tether in (ye \u2212 ze) plane, \u03b2 is the angle between the z\u2032e and taut tether in (ye \u2212 ze) plane.",
        "texts": [
            " In this section, we will develop the swing angle estimation technique with slung load generated axial disturbance forces. Therefore, we need to estimate the disturbance force in each xe, ye and ze axis independently. In the first subsection, we will define the swing angle of the slung load. After then, we will develop a disturbance force estimation method by using the acceleration-DOB[10] in the second subsection. In the last subsection, we will cover the swing angle estimation utilizing the estimated disturbance force. The swing angle is defined as follows. Two angles \u03b1 and \u03b2 are defined as Fig. 3 shows. \u03b1 is the angle between ze axis and the tether in (ye \u2212 ze) plane. \u03b2 is the angle between z\u2032e axis and the tether in (x\u2032e\u2212z\u2032e) plane, where the x\u2032ey \u2032 ez \u2032 e frame is the rotation of xeyeze in xe axis so that the direction of z\u2032e is same as the slung load in (ye \u2212 ze) plane. The DOB algorithm is originally developed for robust control of a system that is exposed to disturbance. The main idea of the DOB is to estimate the amount of disturbance and compensate it in the next step of control[7]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-34-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-34-1.png",
        "caption": "FIGURE 12-34 Method of force analysis on three-point hitch of a turning tractor. Forces shown are those imposed by tractor on hitch links 1,2, and 3. (F'rom A.W. Clyde, Agr. Engr., Feb. 1954.)",
        "texts": [
            " If it is desired to determine the vertical and transverse forces plus the longitudinal forces acting upon a three-point hitch, it will be necessary to equip each of the bottom links with strain gages that will independently mea sure tension and bending forces. The top link will need strain gages to sense only compression or tension. The design of three-point hitches provides for lateral motion of the entire hitch system. This allows the tractor to turn easily when pulling a load. If the lower links are designed to converge, the virtual center of the hitch system (as seen from a top view such as fig. 12-34) will be somewhere between the front wheels. It is apparent that the direction of the sum of all forces acting upon the three links of the hitch must be along the line B' - B\". The direction of the sum of all forces does not go through the point of intersection, f; of links 1 and 2 but must also consider the force in link 3. Thus the actual line of force in this case passes between the instant center of the lower links, J, and the center line of the tractor. Quick-Attaching Coupler for Three-Point Hitches The three-point hitch has many advantages, including extra weight transfer to the tractor for traction, ease of control and movement of the attached implement, and better control of the implement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002753_1.4024369-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002753_1.4024369-Figure1-1.png",
        "caption": "Fig. 1 Illustration of face gear transmission system: (a) Twodimensional schematic figure and (b) three-dimensional schematic figure",
        "texts": [],
        "surrounding_texts": [
            "Face gears have been used in power transmission applications for helicopters. A face gear transmission system is shown in Figs. 1(a) and 1(b). The advantages of such applications are the possibility of the split of the torque and the reduction of weight. This mechanism greatly reduces the size and cost compared with the conventional gear drives [1,2]. A design of face gear drives is based on the application of a conventional involute spur pinion being in contact with the conjugated face gear [3]. The teeth of the face gear pair can be helical or right and the shaft angle between the pinion and the face gear can be different from 90- deg. The teeth of face gear studied in this paper are right and the shaft angle is 90-deg. The noise, vibration and reliability performances of power transmission systems are the most important transmission quality factors. Because of the high sensitivity of the gear pair to its tooth profile errors and shaft misalignment, the vibratory response can be very complex and difficult to control. Therefore, it is essential to gain a thorough understanding of the dynamics of the face gear in the design and development of quieter and more durable geared rotor systems [4]. Extensive theoretical studies about the design and generation principle of the face gear pair have been carried out to achieve the desired tooth profiles and contact patterns that minimize transmission errors [5\u201311]. Litvin is one of the first persons to have defined the theoretical study of the face gear, and he has explored the computerized design, generation and simulation of the meshing of the orthogonal face gear drive with a spur involute pinion. Guingand et al. studied the quasi-static contact analysis of a face gear under torque [12]. Chen et al. [13] analyzed the tooth contact of face gear drives. Limited investigations are done on the dynamics of face gear pairs on account of the complexity of face gear nonlinear dynamics. The dynamics of gear transmission systems have been studied extensively in the past by Lim and Singh [14] and Chen et al. [15]. However, Only in recent years that the study of the dynamics of face gears has gained some attention. For instance, a multidegree-of-freedom, nonlinear time-varying lumped parameter dynamic model of the face gear pair with torsional and translational effects is formulated by Jin et al. [16] in Chinese. The model includes the elastic deformation of the bearings, the timevarying mesh stiffness and transmission error, but the definition of mesh stiffness is not included in their research. In this paper, different from the model of Jin et al. [16], a nonlinear six-dimension face gear dynamic model, considering backlash and mesh stiffness, is developed using the Lagrange\u2019s equation. The mesh stiffness is obtained based on the Tregold\u2019s approximation for the contact ratio mentioned in Ref. [17], and expressed in two forms: time-varying and time-invariant. The mesh stiffness is approximated contrasting to spur gear, and there are errors with it but the time-varying pattern is reasonable. The effect of mesh stiffness on the dynamic response of face gear transmission system is studied with the Runge-Kutta numerical integral method of self-adaptive varied steps. The nonlinear characteristics of face gear drive system like bifurcation, chaos and multijump are detected and analyzed."
        ]
    },
    {
        "image_filename": "designv10_10_0003862_j.intermet.2018.10.011-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003862_j.intermet.2018.10.011-Figure3-1.png",
        "caption": "Fig. 3. Finite element simulation (Eline =625 J/m): (a) top view, (b)cross-sectional view of the temperature field around molten pool; (c) cross-sectional view of the thermal stress (Pa) field around molten pool.",
        "texts": [
            " Interestingly, the micro-cracks in all samples initiated at micro-pores with relatively small size and located mainly at the edge between molten pool and heat affect zone (HAZ) (see the yellow-dash lines in Fig. 2(c\u2013f)). It is generally accepted that micro-cracks in 3D printed BMGs are mainly caused by thermal stress created by the steep temperature gradient around molten pools [16]. When thermal stress exceeds the fracture strength of a BMG, cracks may occur. As it is difficult to measure directly the thermal stress during SLM process, we, instead, performed FEM simulations to acquire instantaneous temperature field and thermal stress field around a molten pool at each laser scanning condition. Fig. 3(a), (b) and (c) show the simulated temperature fields (both top and cross-sectional views) and thermal stress field, respectively, under the line energy density of 625 J/m (corresponding to the experimental condition for Fig. 2(d)) as an example. Note that the others exhibit similar results, as shown in Fig. s2 in supplementary Materials. It can be seen that, in such a case, the width of molten pool is about 200 \u03bcm (see Fig. 3(a)), which is very close to value of 196 \u03bcm from experiment result, indicating the suitability of FEM model adopted in this work. As expected, the temperature field is quite inhomogeneous in the molten pool, where the center has a maximum temperature of approximately 2850 \u00b0C, and rapidly decreased to 1108 \u00b0C at the edge of molten pool (about 100 \u03bcm from the center), yielding a sharp temperature gradient of 17.42 \u00b0C \u03bcm/ around the molten pool. Based on the temperature field, the thermal stress field around the molten pool could be calculated (see Fig. 3(c)). Similarly, the distribution of thermal stress is also heterogeneous: The maximum thermal stress of 1.5 GPa appeared at the edge between molten pool and heat affect zone, but quickly reduced at regions away from the edge. For example, thermal stress decreased to 500MPa at the location about 30 \u03bcm from the edge (it is similar both inside and outside of the molten pool). Even though we take the maximum thermal stress of 1.5 GPa, it is still far below the fractural strength of the Fe-based BMG, which is roughly about 3",
            " It well known that thermal stress is mainly caused by huge temperature gradient due to rapid heating/ cooling in SLM process. To understand why thermal stress at edge of molten pool is higher than other regions (e.g. inside and outside of molten pool), we calculated the temperature gradients at different places. Taking Eline of 625 J/m (corresponding to laser power=250W, scanning speed= 400mm/s), the cooling rate at the edge of molten pool was calculated to be \u00d7 \u00b0C s4.37 10 /4 (The cooling rate was determined by the slope of the cooling curve, which was obtained from the temperature field shown in Fig. 3(a) and (b)). Similarly, the temperature gradient can be also calculated on the basis of the temperature field, which yields 30.73 \u00b0C \u03bcm/ at the edge of molten pool. This value is almost 3 times larger than other places. For example, temperature gradients are about 12.48 \u00b0C \u03bcm/ inside and 10.04 \u00b0C \u03bcm/ outside of molten pool (30 \u03bcm away from the edge), respectively. It is the steep temperature gradient at the edge of the molten pool that induces huge thermal stress and eventually causes the generation of micro-cracks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003983_j.mechmachtheory.2016.02.002-Figure2-1.png",
        "caption": "Fig. 2. Illustration of the involute worm surface SwI.",
        "texts": [
            " Thus, it is suitable as an example with no transmission errors. The K-worm gear drive is also widely used, but transmission errors occur when the oversized hob is used, as noted by Litvin [8]. Thus, it is suitable as an example with transmission errors. 2.1.1. Involute worm and hob surfaces The cylindrical worm surface SwI and hob surface ShI of the involute worm gear drives are involute helicoids. Here, subscript I indicates the involute type. An involute helicoid can be expressed by using an involute curve as a generator. In Fig. 2, the generator of SwI is represented in the coordinate system Cw\u2032[xw\u2032, yw\u2032, zw\u2032]. A position vector rwI ! of SwI can be represented in the coordinate system of the worm Cw[xw, yw, zw] as follows: rwI ! uw; \u03b8w\u00f0 \u00de \u00bc Owqw ! \u00bc cos \u03b8w \u2212 sin \u03b8w 0 0 sin \u03b8w cos \u03b8w 0 0 0 0 1 \u03bdw 0 0 0 1 2 664 3 775 \u2212uw sin invw\u00f0 \u00de uw cos invw\u00f0 \u00de 0 1 2 64 3 75; \u00f01\u00de where invw = tan \u03c1w \u2212 \u03c1w, \u03c1w = cos\u22121(rbw/uw) and \u03bdw \u00bc \u03b8wlw 2\u03c0 . rbw is the base radius of the worm; lw is the lead of the worm; Ow is the center of the worm; and zw is the axis of rotation of the worm, which overlaps zw\u2032"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002748_0954405413475961-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002748_0954405413475961-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of the deposition system used for the experiment. CNC: computer numerical control.",
        "texts": [
            " A Malvern Mastersizer 2000 laser diffraction system was used to determine the size distribution, and a Hitachi S-3400 scanning electron microscopy (SEM) was used to identify the morphology of particles within each batch. Ten particles from each batch were also selected at random for surface element analysis by energy-dispersive spectroscopy (EDS), which was performed using a Zeiss EVO60 SEM. A Laserline LDL160-1500 diode laser deposition system was used to prepare test samples. The system is shown schematically in Figure 1. The laser beam had a uniform, \u2018top-hat\u2019 intensity distribution and was focused to a spot of 1.7mm diameter at the substrate surface. The particles were conveyed from a SIMATIC OP3 disc powder feeder using a 5 L/min flow of argon. The feeder was tested and calibrated prior to the experiment by measuring the mass delivery rate at different disc rotation speeds, 40 times for each of the different batches of particle. It was found that the feeder provided a consistent mass flow rate that varied linearly with disc speed in all cases",
            " The values of laser power were chosen as those known from previous experience with GA powder to give continuous, good quality tracks. Fibre losses in this system have been previously measured as 30%21 so for this experiment the laser powers of 800 and 1000 W correspond to power densities of 247 and 308 W/mm2 and specific energies of 82.4 and 103 J/mm2 at the workpiece surface. Following laser deposition, samples were characterised for size, elemental composition, microstructure, hardness and corrosion resistance. Each sample was sliced in a perpendicular plane to the direction of laser travel (the yz plane in Figure 1) and approximately half way along the length of the track. The exposed faces were mounted in phenolic resin, ground and polished following standard metallographic procedure. The overall dimensions of the layer were measured with a Keyence VHX-500F optical microscope at 10\u2013203 magnification and elemental distribution on the face measured using a Philips XL30 FEG SEM fitted with a Rontec (now Bruker) EDS analytical system with silicon drift diode detector. The samples were then etched electrochemically using 10% oxalic acid, and images were taken using the same optical microscope"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003424_tie.2015.2426671-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003424_tie.2015.2426671-Figure1-1.png",
        "caption": "Fig. 1. Topologies of a SFPM. (a) Double-layer winding - all poles wound. (b) Single-layer winding - alternate poles wound.",
        "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. machine is asymmetric and non-sinusoidal, which can also be found in a lot of other type of PMSM machines including DSPM machines, and hence a high torque ripple may be caused by the back-EMF harmonic components. In this paper, the performances of sensorless control of SFPM with two different winding configurations being depicted in Fig. 1(a) and (b) are investigated, whose back-EMFs exhibit different waveform characteristics, such as sinusoidal, asymmetric and non-sinusoidal waves. The single-layer machine is found to exhibit asymmetric back-EMFs, due to which the performance of conventional flux-observer based sensorless control will deteriorate. In order to overcome this issue, a modified flux-linkage observer is developed and acts in synergy with a harmonic elimination technique, by which a higher accuracy of rotor position estimation is achieved. The performance of proposed sensorless control strategy is experimentally validated on a prototype SFPM machine, and the effectiveness of the proposed rotor position estimation will be demonstrated by comparing with that of a conventional flux-linkage observer based sensorless control under both steady and dynamic states. BACK-EMFS The SFPM machine with different stator topologies as shown in Fig. 1, i.e. all poles wound and alternate poles wound, are under investigation and exhibit the different back-EMF features. Both topologies have the same machine structure, very simple and robust rotor, and \u201cU-shaped\u201d laminated iron segments around magnetized PMs in the stator [14] [17]. In order to investigate the back-EMF characteristics, the three-phase back-EMFs can be represented as     1 1 1 sin sin 2 / 3 sin 2 / 3 N a ai mgi r i N b bi mgi r i N c ci mgi r i e e E e e E e e E                                   (1) where eai, ebi and eci are the ith-order harmonics of the three-phase harmonic back-EMFs. Emgi presents the magnitude of the ith-order harmonics of the phase back-EMF. Moreover, in order to investigate the influence of harmonics in different stator topologies, the original winding configuration (Fig. 1 (a)) is separated into two series-connected coils for each set which transforms the double-layer winding machine into a single-layer winding machine as the alternate poles wound machine (Fig 1 (b)), i.e. (coils A1* and A3*) is described as eA1*+A3*, and then the back EMF of phase A is given as * * * * * A1 +A 3 A1 A3ae e e e   (2) where * ae is the phase A back-EMF of alternate poles wound machine. *A1 e and *A3 e are the back-EMFs of coils A1* and A3*, respectively. Thus, the expression of back-EMF waveform of alternate poles wound machine can be re-written as     * * * * * * A1 Am Am 1 A3 Am Am 1 cos cos N i i i N i i i e e i t e e i t                       (3) where eAmi*, and \u03c6Ami* are the magnitudes and phase angles of ith-order back-EMF harmonic and i is the order number of harmonic component for coils A1* and A3*, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000856_s0956-5663(97)00138-3-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000856_s0956-5663(97)00138-3-Figure5-1.png",
        "caption": "Fig. 5. Cyclic voltammograms in pH7.2 phosphate buffer at a sweep rate of 2O mV s -I for a glassy carbon electrode modified with a film of (Fe(phendione)j)(PFr) e, containing (a) 0.0, (b) 0.062, (c) 0.124, (d) 0.187, and (e) 0.248 mM NADH. Inset: Plot of the",
        "texts": [
            "18 and - 0-92 V, respectively, which correspond to reductions of the quinone groups in the phen-dione ligands. In aqueous media (e.g. pH7.2 phosphate buffer) instead of two phen-dione-based one-electron reductions, as in AN, the complex exhibits one reversible reduction, which is assigned to the two-electron/two-proton reduction of the quinone moiety to the corresponding hydroquinone. Transition metal complexes of phen-dione adsorb strongly to GC electrodes at negative potentials ( - 0.20 V), and these modified electrodes retain their electroactivity in pure supporting electrolyte. Fig. 5(a) shows a cyclic voltammogram for a GC electrode modified with an electrodeposited film of the Fe-complex in a pH 7.2 phosphate buffer solution. This reversible voltammetric wave, with the shape anticipated for a surface immobilized redox couple, had a formal potential o f - 0.09 V. In addition, the peak current was directly proportional to the scan rate, as predicted by theory. In an analogous form, all of the other complexes (except for Ru(v-bpy)) could also be electrodeposited onto GC electrodes at negative potentials in aqueous media",
            " One of the objectives of these investigations was the development of modified electrodes capable of the electrocatalytic oxidation of NADH. This, in part, was responsible for the choice of DHB isomers and the transition metal complexes of phen-dione as modifying agents, since they have an o-quinone functionality. In order to test the potential electrocatalytic activity of electrodeposited films, their cyclic voltammetric responses were obtained in phosphate buffer in the absence and in the presence of NADH. As can be seen in Fig. 5 for the Fe-complex, in the absence of NADH [Fig. 5(a)], the response is that previously described for the modified electrode and is ascribed to the reversible two-electron/two-proton redox process of the hydroquinone/quinone groups. Upon the addition of NADH, the cyclic voltammogram exhibited a dramatic enhancement of the anodic peak current with a decrease in the cathodic peak current. Both of these observations demonstrate a strong electrocatalytic effect in the oxidation of NADH. The peak potentials (Ep) for NADH electrocatalysis for the different electrocatalysts employed are presented in Table 1. As can be ascertained from the table, these represent dramatic potential shifts when compared to the NADH oxidation at a bare GC electrode which takes place around + 0.7 V. In addition, the anodic peak current increased linearly with NADH concentration (Fig. 5, inset). Cyclic voltammetry and rotated disk electrode (rde) techniques were employed to study the kinetics of the reaction between the various modified electrodes and NADH. In the first case, rate constants can be obtained according to the theory of Andrieux & Savrant (1978) from the catalytic current at a given NADH concentration as a function of sweep rate. In the case of rde, the analysis is based on the dependence of the limiting current on the rate of rotation and the use of the Koutecky-Levich equation (Murray, 1984)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-37-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-37-1.png",
        "caption": "FIGURE 5-37 Cross-sectional view of a turbocharger. (Courtesy Mitsubishi Heavy Industries, Ltd.) Key: 1. Compressor cover 2. Compressor wheel 3. Piston rings 4. Thrust bearing 5. Bearings 9. Waste gate actuator 6. Bearing housing 10. Waste gate valve",
        "texts": [
            " 120 ENGINE DESIGN Turbochargers\u00b7 The most efficient method of increasing the power of an engine is the addition of a turbocharger. A turbocharger, by definition, is an engine supercharger *There are many methods of supercharging or increasing the flow of air into an engine. The use of a turbocharger is the most cost-effective method of supercharging. TURBOCHARGERS 121 7. Pressure regulator 8. Governor 9. Governor weights 10. Metering valve II. Discharge fitting driven by an exhaust gas turbine. Figure 5-37 shows a typical turbocharger. Exhaust gases from the engine enter the turbine housing radially and drive the turbine wheel, which drives the compressor wheel, both being mounted on the same shaft. Turbocharging increases the density of air delivered to engine cylinders above that available in natural aspiration and thereby allows an engine to burn more fuel and, in turn, develop more power. A turbocharged engine operates with lower cylinder temperatures and reduces fuel consumption for the power produced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001252_21.478451-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001252_21.478451-Figure8-1.png",
        "caption": "Fig. 8. Two robots carrying an object in a circular arc path.",
        "texts": [
            " In our next simulation, constraint on the magnitude of the internal force is employed. The maximum values of XI and A 1 are set to be 1.5(N) and 0.5(N), respectively. The graphs in Fig. 7(a)-(c) show the results in this case. Note that only one joint torque is saturated when both XI and A2 are saturated from s = 0.979 s = 1.294. Traveling time is found to be 8.288 seconds, which are increased by 4.9% due to the internal force constraint. As an example for showing the existence of the islands in the multirobot case, we provide here the results for an another path. Fig. 8 shows the system configuration. Robot 1 stays at (1, 1) and robot 2 moves from (2, 1) along a circular arc until 6 becomes rI/3 radian. Joint displacements of each robot and the Cartesian position of the object are described using the parameter 6 as n 61 = - 4 r1 =.Jz 1 - cos6 II O2 = tan-' ( l - s i n o ) + Y ~ 7-2 = J( 1 - cos 8)2 + (I - sin 6 ) 2 2 = 1 + fr cos8 y = I - ;sin6 ff =-6 n @ = O m - 3 The relation between the forces applied by the robots and the total force at the center of the object is described by L and the dimension of the internal force X is mn - p = 2 x 2 - 3 = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002069_0025-5416(80)90124-x-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002069_0025-5416(80)90124-x-Figure7-1.png",
        "caption": "Fig. 7. A schematic diagram showing the formation of the depression beneath the beam and liquid flow to form (a), (b) surface ripples and (c), (d), (e) a continuous central ridge and side troughs.",
        "texts": [
            " The melting isotherm for r = 3 X 10 -2 s clearly shows the onset of the \"deep penetration mode\", as discussed later. As already discussed, several workers have considered moving point source and line source heat flow models [7, 9, 12]. However, the pertinent hydrodynamics involved have received less attention and consequently we now consider this highly important aspect. Some fluid mechanics considerations giving rise to ripples of high amplitude and low frequency and the central ridge-side trough topography (Fig. 7(e)) are summarized in Fig. 7. This both combines and extends previous concepts and observations [6, 13]. The critical feature, leading to all subsequent phenomena, is the depression beneath the incident beam; contributory causes of this are (i) the progressive increase in the surface tension between the center and edge of the molten pool [5] and (ii) the \"keyhole\" due to the actual beam penetration into the material. Motion of the material, relative to the beam, results in formation of a liquid bulge ahead of the beam which, as shown in Fig. 7(a), causes liquid flow beneath the beam. This then results in liquid overflow at the trailing edge, as shown in Fig. 7(b). The formation rate of liquid in the bulge ahead of the beam is determined by the velocity and beam power density. For instance, with a low power incident beam it takes a short time before a sufficient liquid bulge forms for liquid flow to the trailing edge to occur. Overflow at the trailing edge is thus periodic and results in ripple formation. However, with a high power incident beam the excess liquid ahead of the beam forms at a sufficient rate that there is cont inuous liquid f low beneath the beam (Fig. 7(c)). This results in the formation of a central ridge with accompanying side troughs [13] , as shown in Fig. 7(e). In the plan view in Fig. 7(d) the arrows show the major flow direction of molten material within and around the beam depression. In practical applications, surface smoothness is of overriding importance and obviously the type of profile in Fig. 7(e) is highly undesirable. Fortunately the present experiments show that this effect can be reduced until it is almost negligible; this is attained by the selection of appropriate processing parameters. The cross-sectional micrographs in Fig. 3 clearly show that the t rough-cres t effect is minimal at the three velocities selected in the range 1.7 - 97.5 cm s -1 for a beam power of 375 W. By increasing the power to 550 W the effect is readily apparent (Fig. 8) and very pronounced when the beam power is 750 W"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002304_j.cap.2010.08.010-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002304_j.cap.2010.08.010-Figure1-1.png",
        "caption": "Fig. 1. Synthesis of the Poly(GMA-co-MTM).",
        "texts": [
            " Epoxide is a three-membered cyclic ether and very reactive due to the large strain energy (about 25 kcal mol 1) associated with the threemembered ring. Therefore, it can be employed into a large number of chemical reactions by ring opening, thus offering the opportunity for chemical modification of the pendant copolymers for various applications such as immobilization of enzymes, DNA, catalysts, and biomolecules. In this study, random copolymer of electroactive 3-methylthienyl methacrylate (MTM) and side chain epoxy group containing glycidyl methacrylate (GMA) monomers was prepared via free radical polymerization (Fig. 1) to use as a part of a compositematrix of the biosensor for the first time. The whole composite matrix was a composite of Polypyrrolle (PPy) and Poly(GMA-co-MTM) including carboxylated carbon nanotubes (CNTs). Since the novel composite film carried the side chain epoxy and carboxyl functional groups, enzyme was stably immobilized onto the working electrode. The response dependences and amperometric characteristics including sensitivity, linear range, detection limit, response time and stability of the Poly(GMA-co-MTM)/PPy/CNT/HRP composite film electrode in the detection of eighteen phenol derivatives have been investigated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002546_c0cp02420a-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002546_c0cp02420a-Figure1-1.png",
        "caption": "Fig. 1 (A) Scheme of the setup used for the electrochemical measurements: 1-Ag/AgCl reference electrode, 2-salt bridge (KCl saturated 1% agar), 3-Pt wire as a counter electrode, 4-magnetic stirrer, 5-O-ring, 6-boron doped diamond or glassy carbon substrate, 7-connection to the potentiostat; (B) the Randles\u2019 model used for fitting the electrochemical impedance spectroscopy data, where Re is the solution resistance, Rct is the charge transfer resistance, Cdl is the double layer capacitance and W is the Warburg impedance.",
        "texts": [
            " The second scan was used for analysis. Furthermore, after 10 CV scans in PBS with albumin, another SEM picture was obtained to investigate albumin adsorption on the substrates. The 3 electrode setup was completed with a Pt wire as the counter electrode and an Ag|AgCl, saturated KCl reference electrode connected to the cell through a saline bridge (1% agar saturated with KCl). A piece of the BDD substrate was clamped under a teflon electrochemical cell, and the electrode area was defined with an O-ring (area E 0.2 cm2) as shown in Fig. 1A. CV were performed using a CHI 800 potentiostat (CHI Instruments, Austin, Texas, USA). The scan rate was 50 mV s 1 for all the experiments. Electrochemical impedance spectroscopies (EIS) was performed using an Ivium Compactstat Pu bl is he d on 0 7 M ar ch 2 01 1. D ow nl oa de d by S ta te U ni ve rs ity o f N ew Y or k at S to ny B ro ok o n 23 /1 0/ 20 14 2 3: 45 :1 5. 5424 Phys. Chem. Chem. Phys., 2011, 13, 5422\u20135429 This journal is c the Owner Societies 2011 (Ivium Technologies, Netherlands)",
            " The CV data were analyzed by measuring the mid-peak potential E1/2, the cathodic current density jox, the peak separation DEp. Results from the second cycles were used for this analysis. Only the anodic wave was considered to avoid oxygen interferences in the case of the ruthenium III/II hexaammine couple (Ru(II) - Ru(III)). The second CV cycle was used, as albumin can be oxidised on BDD substrates.15,16 However, this signal appears on the first cycle only. For the EIS, the resulting graphs were fitted using the Randles model17 presented in Fig. 1B implemented in the Ivium software to obtain the solution resistance Re, the charge transfer resistance Rct and the double layer capacitance Cdl. The experimental results were compared using a two-tailed Student\u2019s t test. For the sake of clarity, only the changes considered as significant (p o 0.05), in comparison to the control case without albumin, are reported here. All the potentials reported are measured vs. Ag|AgCl, 3 M KCl. First, we compare the results for different substrates, and in particular their resistance to chemical fouling (dopamine)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001900_978-1-4020-8829-2_11-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001900_978-1-4020-8829-2_11-Figure1-1.png",
        "caption": "Fig. 1. Product of dual vectors: nomenclature",
        "texts": [
            " The necessary and sufficient conditions in order F to be analytic are [10] \u2202f \u2202xo = 0 , \u2202f \u2202x = \u2202g \u2202xo . (2) Therefore, the following equality must hold (see also Table 1) f (x\u0302) = f (x + \u03b5xo) = f(x) + \u03b5xo \u2202f \u2202x . (3) A line vector is a vector bound to a definite line L in space. The dual vector V\u0302 = v + \u03b5vo (4) is combination of two vectors which specifies the position of L with respect to an arbitrary origin O. The primary part is a vector v parallel to L and the dual part is vo = \u2212\u2212\u2192 OP \u00d7 v, where P is an arbitrary point on L. With reference to Fig. 1, A\u0302 = a + \u03b5 (r1 \u00d7 a) , B\u0302 = b + \u03b5 (r2 \u00d7 b) , be two dual vectors representing two distinct line vectors and let s\u2217 the direction versor of the minimum distance between these line vectors directed from a to b. as a variable required to characterize the relative position and orientation of line vectors A\u0302 and B\u0302. The angle \u03b8 is measured counterclockwise about s\u2217. The scalar and cross products of two dual vectors are respectively defined as follows [10]: A\u0302 \u00b7 B\u0302 = a \u00b7 b + \u03b5 [a \u00b7 (r2 \u00d7 b) + b \u00b7 (r1 \u00d7 a)] , = a \u00b7 b + \u03b5 [(r1 \u2212 r2) \u00b7 (a \u00d7 b)] , = ab cos \u03b8 \u2212 \u03b5 [(ss ) \u00b7 (ab sin \u03b8s )] , = ab [cos \u03b8 \u2212 \u03b5s sin \u03b8] = ab cos \u03b8\u0302 , (6) A\u0302 \u00d7 B\u0302 = a \u00d7 b + \u03b5 [a \u00d7 (r2 \u00d7 b) + (r1 \u00d7 a) \u00d7 b] , = a \u00d7 b + \u03b5 [(a \u00b7 b) (r2 \u2212 r1) + r1 \u00d7 (a \u00d7 b)] , = ab {s sin \u03b8 + \u03b5 [s cos \u03b8s + sin \u03b8 (r1 \u00d7 s )]} , = abS\u0302 (sin \u03b8 + \u03b5s cos \u03b8) = abS\u0302 sin \u03b8\u0302 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003010_imece2014-36661-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003010_imece2014-36661-Figure5-1.png",
        "caption": "Figure 5. CAD model used in EBAM fabrications and temperature measurements.",
        "texts": [
            " Post-processing data of NIR images was analyzed to quantify the maximum temperatures and melt pool sizes. EXPERIMENTAL DETAIL \u00a0 An Arcam S12 EBAM system, shown in Figure 4, at NASA\u2019s Marshall Space Flight Center (Huntsville, AL) was used to fabricate parts of a designed model in conjunction with temperature measurement experiments. Ti-6Al-4V powder from Arcam was used. The part designed for was a simple block: 50 mm long, 25 mm wide and 30 mm tall (x\u00d7y\u00d7z), with notches on the edge along the build direction, shown in Figure 5.\u00a0 The EBAM primary settings used were default values typically employed for Ti-6Al-4V powders. The layer thickness was 0.07 mm. A set of parameters called a build theme are suggested to dynamically control the electron beam speed and current as well as the raster spacing during the part fabrication process. These parameters are known as the speed functions and the purpose is to achieve and maintain the desired melt pool size. Additionally, the focus offset current is an influential parameter that controls the electron beam diameter [6]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure6-1.png",
        "caption": "Fig. 6 Some three-DOF single-loop kinematic chains involving a PPR V-chain.",
        "texts": [
            "org/ on 01/15/2018 Te is always parallel to a line, one can obtain 3-DOF single-loop kinematic chains composed of a PPR V-chain and a leg with a 1-\u03b6\u221e-system. The 3-DOF single-loop kinematic chains we obtained are respectively composed of two serial kinematic chain of classes (b4) [see Figs. 6(e) and 6(f)]. The axes of the R joints in each of the 3-DOF single-loop kinematic chains are always parallel to two different lines which further determine one plane. The 3-DOF single-loop kinematic chains we obtained are listed in Table 1. Several of the 3-DOF single-loop kinematic chains are also shown in Fig. 6. According to the composition of these 3-DOF single-loop kinematic chains, they can be classified as follows: (a) Single-loop kinematic chains formed by a serial chain of class (b2) and a serial chain of class (b3) [Figs. 6(a) and 6(b)]. (b) Single-loop kinematic chains formed by one serial chain of class (b4) [Fig. 6(c)]. (c) Single-loop kinematic chains formed by a serial chain of class (b1) and a serial chain of class (b3) [Fig. 6(d)]. (d) Single-loop kinematic chains formed by two serial chain of class (b4) [Figs. 6(e) and 6(f)]. In the representation of the types of 3-DOF single-loop kinematic chains involving a V-chain (Fig. 1), PPR-PKCs, PPR-PMs and their legs, X denotes a P or an R joint, (PP)E denotes two successive P joints whose directions are parallel to the virtual plane. (XXX)E denotes three successive X joints in which the axes of all the R joints are perpendicular to the virtual plane and the directions of all the P joints are parallel to the virtual plane",
            "2 ci = 0 Theoretically, any six R and P joints the twists of which are linearly independent together with a PPR Vchain constitute a 3-DOF single-loop kinematic chain. The type of a leg for PPR-PKCs can be represented by a chain of characters representing the type of joints from the base to the moving platform in sequence. By removing the V-chain in a 3-DOF single-loop kinematic chain involving a V-chain, one leg for PPR-PMs can be obtained. For example, by removing the V-chain in an (RRR)E(RR)SV Copyright  2004 by ASME rms of Use: http://www.asme.org/about-asme/terms-of-use Down kinematic chain [Fig. 6(d)], an (RRR)E(RR)S leg [Fig. 7(d)] can be obtained. Figure 7 shows some legs for PPR-PKCs and their leg-wrench systems. The leg-wrench system of the (RRR)ERC leg [Fig. 7(b)] is a 1-\u03b60-1-\u03b6\u221e-system. Its basis can be represented by a \u03b6\u221e whose axis is perpendicular to the axes of all the R joints within a same leg and a \u03b60 whose axis intersects the axes of the RC joint and is parallel to the axes of the R joints within (RRR)E . The leg-wrench systems of the RA(RRR)Y RA leg [Fig. 7(e)] and the (RR)Y (RRR)Y A leg [Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure11-1.png",
        "caption": "Fig. 11 Selection of actuated joints for some PPRPKCs.",
        "texts": [
            " For practical reasons, the selection of actuated joints for m- Copyright  2004 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Down legged PPR-PMs 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. For example, the possible 3-legged PPR-PM corresponding to the 2-(RRR)ERC-RA(RRR)Y RA PPR-PKC [Fig. 8(b)] is the 2-(RRR)ERC-RA(RRR)Y RA PPR-PM [Fig. 11(a)]. The actuation wrenches of all the actuated joints are shown in Figs. 10(a) and 10(c). Following the procedure for the validity detection of the actuated joints, it can be proved that the set of actuated joints is valid. The possible 3-legged PPR-PM corresponding to the 2-(RRR)ERC-(RR)Y (RRR)Y APPR-PKC (Fig. 9) is the 2- (RRR)ERC-(RR)Y (RRR)Y A PPR-PM [Fig. 11(b)]. The actuation wrenches of all the actuated joints are shown in Figs. 10(b) and 10(c). Following the procedure for the validity detection of actuated joints, it can be proved that the set of actuated joints is invalid. The possible 2-(RRR)ERC-(RR)Y (RRR)Y A PPR-PM is thus discarded. Based on the above validity condition of PPR-PMs, a number PPR-PMs have been identified. It is also found that there are no 3-DOF PPR-PMs with identical types of legs. Due to the large amount of PPR-PMs and space limitation, only several PPR-PMs are presented (Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003864_rpj-04-2017-0058-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003864_rpj-04-2017-0058-Figure6-1.png",
        "caption": "Figure 6 Schematic of three Ra components of surface roughness for AM parts",
        "texts": [
            " A 3D mesoscopic powder model is usually required to consider physical characteristics of powder-based AM processes, but those computational models are extremely numerically inefficient. Therefore, physics-based modeling of areal roughness Sa is very challenging. Current approaches to simulate surface roughness are based on theoretical models or regression analysis, and limited to the simulation of onedimension roughnessRa. The value of roughnessRa is dependent on themeasurement direction, and it can be classified into three aspects in AM parts. As shown in Figure 6, roughness Ra in the three directions (x: scan direction; y: transverse direction; z: along Figure 4 Melt pool geometry at different scanning path in SLM (Cheng and Chou, 2015) Metallic part qualification Jingfu Liu et al. Rapid Prototyping Journal D ow nl oa de d by R M IT U ni ve rs ity L ib ra ry A t 0 7: 28 2 3 O ct ob er 2 01 8 (P T ) the inclined wall) have different formation mechanisms, and therefore need to be calculated differently. Ra(x) modeling: Roughness in the scan direction is mainly formed due to the melt pool flow during the building process, and a physics-based model is necessary to account for the fluid dynamics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002925_j.triboint.2013.06.008-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002925_j.triboint.2013.06.008-Figure2-1.png",
        "caption": "Fig. 2. Developed simulated model: (a) whole simulated model, (b) crack initiation definition, (c) crack tips location.",
        "texts": [
            " A plane sketch of the geometric model used for the RCF analysis is presented in Fig. 1. The material defect is modeled as a quadrate pore located at a depth (0.5 mm) below the raceway surface and its size is assumed to be 0.5 mm. The symbol \u03b8 indicates the rotation angle of the inner ring. The rotation angle is defined to be negative when the contact position is to the left of the pore. The moment M is exerted on the inner ring in the anticlockwise direction. The numerical model was developed as shown in Fig. 2. The material used in this study was AISI 52100 steel, and the main parameters are: Young's modulus E\u00bc2.10 105 MPa, Poisson's ratio \u03bd\u00bc0.3 and material density \u03c1\u2032\u00bc7.85 103 kg/m3. The inner ring was meshed with 20-noded quadratic hexahedron elements. To get accurate stress and strain, the refined mesh was created around the pore. The element size near the pore was an approximately 0.1-mm cube, as shown in Fig. 2(b). The refined meshes above the pore were 10 layers and they were increased with increasing the depth of the pore. The other part of the inner ring was roughly meshed for reducing the computer calculation time. To study the effect of the pore on the crack initiation, it was necessary to define the crack front, crack tip and crack extension direction [18], as shown in Fig. 2(b). The surface of the pore was defined as the crack front, the edge was defined as the crack tip, and the direction parallel to the crack front was assumed as the crack extension direction. To improve the accuracy of the stress intensity factors, the singularity parameter is defined to be 0.25 due to this linear elastic model. Using this method, four crack tips were defined due to the radial load applying to the inner ring, as shown in Fig. 2(c). Tip 1 and 2 were located on the upper crack front, and tip 3 and 4 were located on the lower crack front. The steel ball was defined as a rigid body and its displacement degrees of freedom were constrained. A radial force Fr in the radial direction and a moment M in the circumferential direction were exerted on the inner ring. The surface friction coefficient was 0.15, and the crack face friction coefficient was assumed to be 0. In a real contact between the steel ball and the inner ring, the pressure distribution is often complex and highly dependent on the exact profiles of the steel ball and inner ring as well as their relative positions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003386_10402004.2014.968699-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003386_10402004.2014.968699-Figure2-1.png",
        "caption": "Fig. 2\u2014Radii of two bodies coming in contact and the resulting contact ellipse.",
        "texts": [
            " (30), given as K = \u03c0keEeff 3/2 ( 2\u03b6R 9 )1/2 . [3] The effective modulus of elasticity is given by Eeff = 2[( 1\u2212\u03c52 1 E1 ) + ( 1\u2212\u03c52 2 E2 )] , [4] where E1, \u03c51 and E2, \u03c52 are the moduli of elasticity and Poisson\u2019s ratios of bodies 1 and 2, respectively. R is a curvature sum of the two contacting bodies given by 1 R = 1 Rx + 1 Ry , [5] where Rx and Ry are given by 1 Rx = 1 R1x + 1 R2x [6] 1 Ry = 1 R1y + 1 R2y . [7] The definition of the radii of the original bodies for the example of the contact between the ball and outer race is shown in Fig. 2. Convex surfaces are considered as having positive radii of curvature, whereas concave surfaces are considered as having negative radii of curvature. The variables a and b in Fig. 2 are the contact ellipse major and minor axes. ke, , and \u03b6 can be calculated using iterative methods, but for this study, the approximations given by Hamrock, et al. (30) were used: ke = \u03b12/\u03c0 r [8] = \u03c0 2 + qa ln \u03b1r [9] \u03b6 = 1 + qa \u03b1r , [10] where \u03b1r and qa are given by \u03b1r = Ry Rx [11] qa = \u03c0 2 \u2212 1. [12] Along with the normal force, a tangential force at the point of contact exists due to frictional forces. This tangential force is determined using the relative tangential velocity and the normal force within a contact ellipse. An example of a contact ellipse can be seen in Fig. 2. In DBM, translational and rotational velocities of each bearing component are monitored in inertial and body-fixed reference frames, respectively. To reduce the calculation of relative tangential velocities within the contact, the relative translational and rotational velocities are transformed to a contact reference frame whose origin is located at the center of the contact ellipse, as shown in Fig. 3. The relative slip varies according to location within the contact area. In this study, the length of the minor axis is considered sufficiently narrow such that the variation in relative velocity along the minor axis is negligible as described by Gupta (31), (32)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001107_1.1564064-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001107_1.1564064-Figure1-1.png",
        "caption": "Fig. 1 Illustrations of \u201ea\u2026 hypoid gear setup, \u201eb\u2026 contact cells and three coordinate systems denoted by S0 , S1 and S2 , and \u201ec\u2026 load distributions on the tooth surface for a specific gear angular position",
        "texts": [
            " The program combines the finite element method and surface integral, and employs a Simplex type algorithm to simulate the elastic gear tooth contact engagement problem. The mesh point, stiffness, line-of-action, loaded transmission error, and normal and friction load distributions at discrete angular positions over one mesh cycle are computed. For a specific gear angular position, the contact areas of the gear teeth are discretized into groups of finite cells with uniform properties, as shown in Fig. 1. The local compliance between a pair of finite cells i and j, denoted by ci j , is a function of the spatial dimensions, gear tooth meshing position and applied mean torque. The position vector of each contact cell i in the coordinate system Sl represented by Xl , Y l and Zl axes, l51 ~pinion! or 2 ~gear!, is ri (l)5$xi (l) yi (l) zi (l)%T, while the unit normal vector is given by ni (l)5$nix (l) ,niy (l) ,niz (l)%T. The projection of the unit normal vector into the tangential direction of the gear rotational motion relative to Sl can be expressed as l ix ~ l ",
            "zi ~ l !2n ix ~ l !xi ~ l ! , t iy ~ l !5n ix ~ l !zi ~ l !2n ix ~ l !xi ~ l ! . (2) Here, tiu (l) relates to the tangential friction force component at contact point i per unit friction force in the sliding direction n i (l) . The loaded transmission error is typically the net result of both tooth profile errors, and tooth deflections due to base rotation, bending, shearing and contact deformation. Suppose the pinion and gear contact regions are divided into Nc number of finite cells as depicted in Fig. 1~b!, which is directly dependent on transmitted load and angular position. Since the instantaneous rotations of all simultaneously contacting cells are the same under load due to load sharing compatibility @27\u201330#, the following expression for the equilibrium state of gear relative rotation, which is identical to the LTE of the pinion assuming stationary gear, can be derived as DuL5 T12~$L1%2m$T1%!@Cd#21$E0% T ~$L1%2m$T1%!@Cd#21$L1% T , (3) where T1 is the mean torque applied to the pinion, m is the friction coefficient, $T1%5$t1y (l) ,t2y (l) , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000709_s1350-6307(01)00002-4-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000709_s1350-6307(01)00002-4-Figure1-1.png",
        "caption": "Fig. 1. Schematic drawing of gears, with the applied loads.",
        "texts": [
            " The gearwheels in this study are parts of an oleodynamic plant and are of carburized and hardened steel 16CrNi4 (according to Italian code UNI 7846) (UTS=1050 MPa, yield stress=850 MPa), with a surface hardness of about 63 HRC and a core of 35 HRC. The gears have spur teeth with a modified involute profile; the module is 2.65 mm, there are 12 teeth with a pitch diameter of 32.8 mm. The pressure angle is 20 and the standard pitch is 7.72 mm. Gears of the same dimensions create both the pinion and the driven gear. The loading conditions require the transmission of the torque Mt and the application of inter-axial forces Fx and Fy, directed along axes X and Y, as shown in Fig. 1. Such forces make the load on the tooth heavier, particularly as far as contact pressure and stress in the contact area are concerned. Besides, the presence of these loads alters the contact conditions, since it causes, at least partially during the cycle, a contact on both flanks of the tooth. These forces are responsible for the early damage of carburized and hardened toothflanks. To solve this problem, shot-peening was applied, since it induces inside the surface layers of the material a compressive residual stress field, able to stop, or at least to delay, the damage process, caused by the repetition of contact cycles",
            " Starting from the hypothesis that shot-peening has a beneficial effect in stopping microcrack growth but not in preventing initiation [12], the models considered cracked gears, including residual stress profiles caused by different treatment conditions. Fig. 10 shows the computation model, with the dark band indicating the site of the crack and the residual stress field. The elements employed are of \u2018\u2018plane strain\u2019\u2019 type with four nodes and first order shape functions. The total number of elements is 10,224 with 11,226 nodes. The contact was modelled by using the elements provided by the computing program library. The loads of the model are those required by the project, with a torque Mt and inter-axial forces of Fx and Fy (see Fig. 1). The analysis investigated the whole meshing cycle; this allowed one to evaluate the distribution of the forces between the teeth in moving contact. The crack modelled considers the maximum depth before which the crack changes its path: the crack under study thus has an inclination of 30 relative to the surface and is 0.03 mm long. Element dimensions in the microcrack area do not exceed 1/40 of the crack length. The literature considers hydrostatic pressure of crack lubricant to be the main cause of propagation of surface cracks caused by contact fatigue"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-4-1.png",
        "caption": "FIGURE 11-4 Kinematics associated with planar motion of the tractor. The dashed outline shows the position of the tractor after an angular displacement e.",
        "texts": [],
        "surrounding_texts": [
            "EQlJA TIOI\\S OF MOTIOI\\\nH, - We sin 13 - TFf - P cos ex\nWe cos 13 + P sin ex - V, - R j\n275\n(5)\n(6)\nLetting Inc be the moment of inertia of the chassis about the J or lateral axis passing through its center of gravity and summing moments about the chassis center of gravity,\n1\",8 = T, + H,h l , sin (8 1, + 8) - V,h l ! cos (8 1, + 8)\n+ P sin ex [h] sin <P + hIe cos (8 1, + 8)l\nP cos ex [hi cos <P + hlc sin (81c + 8)l TFj [h2' sin (8~, - 8) + rjl\n+ Rr [h2c cos (82 ,. - 8) + etl (7)\nEquation 7 may be simplified, since the traction mechanics of the unpowered front wheels assumes that er = (TFtIRtlrf.\nEquations 1, 2, and 4 are the differential equations of motion governing the three degrees of freedom that the rear wheels possess for general planar motion. Equations 5, 6, and 7 are the corresponding equations for the chassis. However, the constraint that the rear wheels arc attached to the chassis implies that the corresponding 6 degrees of freedom (xv., Zv., <Pw, Xc> Z\" 8) are not independent. Referring to figure 11-2, the following two equations express the con straint relation:\nZ,\nXu + hIe cos (8 1e + 8)\nZv\u00b7 - hI, sin (8 1, + 8)\n(8)\n(9)\nThe two constraint equations reduce the number of degrees of freedom of the system from 6 to 4 and thus imply that the rear wheel-chassis system (the total tractor) can also be described by four independent differential equa tions. These four equations can be derived from equations 1, 2, 3, 5, 6, and 7 by eliminating the internal reactions H\" V\" and T\" using constraint equa tions 8 and 9, and considering the relations between the locations of the centers of gravity of the rear wheels, chassis, and tractor. After some algebraic ma nipulation, the equations of motion for the tractor as a whole may be found. The free-body and kinematic diagrams associated with these equations are shown in figures 11-3 and 11-4.",
            "276 MECHANICS OF THE TRACTOR CHASSIS\nm/Xt = Fr - Wt sin ~ - TFf - TFT - P cos ex\nmtit = Wt cos ~ + P sin ex - Rr - Rf\nIyytS = Iyyw4>w + (Fr - TFr)[h lt sin (e lt + e) + rr] TFf [h2t sin (e 2t - e) + rf]\n+ Rf [h2t cos (e 2t - e) + ef] - Rr [hit cos (e lt + e) - er] + P sin ex [h3 sin <I> + hit cos (e lt + e)] - P cos ex [h3 cos <I> + hIt sin (e lt + e)]\n(10)\n\\ 11)\n(12)",
            "EQCA TIOl'\\S OF MOTION 277\nml is the mass of the tractor (ml = me + mw), and XI and ZI are the translational accelerations of the tractor center of gravity in the X and Z directions. 1\"1 is the moment of inertia of the entire tractor about the y or lateral axis passing through the center of gravity of that body. The right-hand sides of equations 10 and 11 represent force summations in the X and Z directions, respectively, whereas the right-hand side of equation 12 is a summation of moments about the center of gravity of the tractor. Thus, equations 10 and 11 are simply the translational equations of motion that can be derived more directly from the free-body diagram of figure 11- 3. Similarly, with the exception of the term In\", <bu, equation 12 can be derived directly from a summation of moments about the center of gravity of the tractor. Equations 10, 11, and 12 in combination with equation 4 form the four independent differential equations of motion discussed previously. Equation 10 governs the forward translational motion of the tractor. The gross tractive force F, is seen to be the only force acting to propel the tractor forward. This force must exceed the sum of the rolling resistance forces acting at the wheels, the portion of the tractor weight acting parallel to the ground surface, and the drawbar pull in order for the tractor to accelerate forward. If the rear wheels are braked instead of driven, F, changes direction and acts to decrease the forward speed of the tractor. As discussed in the section Traction Performance Equations in chapter 10, F, may be considered to be equal to the product of the coefficient of gross traction J-lg and the soil reaction R,. The coefficient of gross traction is, in turn, a function of the slippage S of the rear wheels as well as of tire and soil surface parameters. V sing equation 7 in chapter 10 and the kinematics illus trated in figure 11-2,\n(13)\nEquations 11 and 12 govern the vertical translation and rotation of the tractor. These equations are particularly important for describing tractor rear ward overturning and vibration. Equation 12 may be simplified by using the relations er = (TF,IR,)rr and ef = (TFflRf)rf\u00b7 If we consider that the power delivered to the rear axle is equal to the power output of the engine multiplied by an overall efficiency 11, we can write\nwhere Tp is the engine torque produced at engin.e speed <!:>r. Letting N be the ratio of engine speed to axle speed (N = 4>,/<!:>\",),"
        ]
    },
    {
        "image_filename": "designv10_10_0002539_1077546311399947-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002539_1077546311399947-Figure6-1.png",
        "caption": "Figure 6. Dynamic model of gear frame combination.",
        "texts": [
            " Equations (1) to (5) show that the tooth stiffness kt is directly proportional to the tooth width F, hence to measure the change in stiffness for simulated faults a piece of gear tooth has been removed width-wise as shown in Figure 5. The combination of gear frame assembly structure could be assumed to have two degrees of freedom with associated translational and rotational rigid body modes, these being solely dependent upon the mass and inertia properties of the system. The gear frame assembly is considered as rigid bodies having lumped masses and inertias located at their mass centers of gravity, as shown in Figure 6. The bodies can be considered to be connected to each other by four springs k1, k2, kS and ktor where k1, k2 represent the equivalent translational spring effect of the two points of suspension. kS represents the equivalent stiffness of the pre-load fixing screw. k tor represents the torsional spring effect of the pre-load screw during the relative rotational motion of the bodies. The equation of motion of the system can be expressed in terms of the relative displacement, X\u00f0t\u00de \u00bc Xf \u00f0t\u00de Xg\u00f0t\u00de and relative rotation \u00f0t\u00de \u00bc f \u00f0t\u00de g\u00f0t\u00de between the rigid bodies, where Xf and f are the displacement and rotations of the frame and Xg and g are the displacements and rotations of the gear By considering the force equilibrium in the direction of relative displacement Mg \u20acXg \u00fe k1 \u00fe k2 \u00fe kS\u00f0 \u00de Xg Xf \u00fe k2 k1\u00f0 \u00dea \u00bc 0 \u00f06\u00de Mf \u20acXf \u00fe k1 \u00fe k2 \u00fe ks\u00f0 \u00de Xf Xg \u00fe k1 k2\u00f0 \u00dea \u00bc 0 \u00f07\u00de Multiply (6) by Mf and (7) by Mg MfMg \u20acXg \u00feMf k1 \u00fe k2 \u00fe ks\u00f0 \u00de Xg Xf \u00feMf k2 k1\u00f0 \u00dea \u00bc 0 \u00f08\u00de MgMf \u20acXf \u00feMg k1 \u00fe k2 \u00fe ks\u00f0 \u00de Xf Xg \u00feMg k1 k2\u00f0 \u00dea \u00bc 0 \u00f09\u00de at UNIV OF CHICAGO LIBRARY on March 3, 2013jvc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001535_j.mechmachtheory.2006.11.002-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001535_j.mechmachtheory.2006.11.002-Figure3-1.png",
        "caption": "Fig. 3. The reachable workspace of the 3SPU + UPR parallel manipulator. (a) A family of similar surfaces cascaded from a lower boundary surface Sl to an upper boundary surface Su; (b) the isometric view; (c) the top of view; (d) the side view; (e) the front view.",
        "texts": [
            " Reachable workspace A reachable workspace W of a parallel manipulator is defined as all the positions that can be reached by the central point of the platform. When given the maximum extension rmax and the minimum extension rmin of active legs ri(i = 1,2,3), W of the 3SPU+UPR parallel manipulator can be constructed by using its simulation mechanism or some relative analytic formulae. In fact, W is formed by a family of similar spatial surfaces cascaded from a lower boundary surfaceSl to an upper boundary surface Su (see Fig. 3a). Each of the similar spatial surfaces is formed by a family of spatial curves cj (j = 0,1, . . . ,n1 1) by using the loft command. Since the 3SPU + UPR parallel manipulator has a symmetric plane of O-YZ in structure, its W must be of plane symmetry of O-YZ. Therefore, only an upper-right boundary surface Sur and a lower-left boundary surface Sll are constructed. The construction procedures are explained as follows: Step 1. Set Li = L = 100, li = l = 60, rmax = 200, rmin = 150, dr = 5 cm, n1 = (rmax rmin)dr",
            " Using similar the construction procedures of Sur2, construct the second left-lower boundary surface Sll2 except that set r2 = r3 = rmin, r1 = rmin + jdr(j = 0,1, . . . ,n1 1). Step 11. Construct Sur from Sur1 and Sur2 because one edge of Sur1 coincides with one edge of Sur2. Construct Sll from Sll1 and Sll2 because one edge of Sll1 coincides with one edge of Sll2. Step 12. Construct Su from Sur by using the mirror command vs. plane YZ. Construct Sl from Sll by using the mirror command vs. plane YZ (see Fig. 3b and c). Step 13. Construct W from Sl to Su by the loft command. Step 14. Verify all positions of the central point of platform m in a workspace which is under Su and above Sl. The results show that W of the 3SPU + UPR parallel manipulator has following characteristics: (1) W is formed by the outline of a family of similar surfaces, which are cascaded from Sl to Su. (2) W is symmetric about the O-YZ plane. (3) When point o of m is close to the side surface Ss which is lofted from Sl to Su, the orientation parameters (a, b, k) of m are increased obviously"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001092_s0092-8240(05)80069-2-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001092_s0092-8240(05)80069-2-Figure2-1.png",
        "caption": "Figure 2. The motion of the organism and the Frenet trihedron. (a) The motion of the organism ijk. The trajectory is traced by the organism's center of mass, which is the origin of ijk. The trajectory is determined by the organism's translational velocity V and rotational velocity ~. (b) The motion of the Frenet trihedron TNB. The origin of the Frenet trihedron also traces the trajectory, so the origin of TNB also is the organism's center of mass. The unit tangent vector T is always tangent to the trajectory, so it points in the direction ofV. TNB rotates with rotational velocity d (the Darboux vector).",
        "texts": [
            "t)I + r sin(Tt)J + (pTt'] K \\ 2 re ] (1) where IJK is a reference frame fixed to the helix such that K is the axis of the helix; p is the pitch; r is the radius; and 7 is the angular frequency (radians/time) (Fig. 1).* a round the cylinder. The organism is considered a rigid body represented by an orthogonal reference frame ijk. The organism moves in three-dimensional space with translational (linear) velocity V and rotational (angular) velocity to. As the organism moves, the origin ofijk describes a curve in space (Fig. 2a). The Frenet trihedron TNB also follows this curve such that the origin of TNB * For le\u2022hand helical motion the sine and cosine terms are interchanged. This analysis uses the equation for a right-hand helix, but the results also apply to left-hand helices. 200 H. C. C R E N S H A W a and ijk are the same point (Fig. 2b). Consequently, ijk and T NB translate and rotate with respect to XYZ and to each other. The first step in this analysis is to describe the unit vectors of the Frenet trihedron and the curvature and torsion of the trajectory in terms of V and ~. This will permit description of the parameters of helical mot ion in terms of V and ~. I begin with the conventional arrangements of V and ~ being described relative to the body of the organism, ijk (subscript b), and the unit vectors of the Frenet trihedron being described relative to space, XYZ (subscript s)",
            " Furthermore, the translational velocity of the Frenet trihedron is by definition: V s = VT~ (2) KINEMATICS OF HELICAL M O T I O N 201 i.e. the speed of the Frenet t r ihedron equals that of the organism, and the Frenet t r ihedron translates in the direction of T s . The rotat ional velocity of the Frenet t r ihedron is given by a vector known as the Darboux vector d~, which is given by Goetz (1970, pp. 63-64) as: d, = ' rT s + IcB~ (3) where z and t\u00a2 are the torsion and curvature, respectively, of the trajectory (Fig. 2b). The unit vectors of the Frenet t r ihedron are described in space as follows: Vs T~ = ~ (4) dTJds N s - i d T 2 d s ] (S) \u00d7Vs Bs = [;i x,gs I (6) where the dots indicate derivatives with respect to time (see Gillett, 1984, pp. 693-696). It is now possible to describe these unit vectors relative to ijk. T is parallel to Vb (7) %--V\" v ~ = v ~ + ~ , \u00d7 v~ (8) (see Symon, 1971, p. 278). The reader will notice that some of the vectors in equat ion (8) are described with respect to space and some with respect to the body of the organism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002331_2010-01-0703-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002331_2010-01-0703-Figure2-1.png",
        "caption": "Figure 2. Vector diagrams for different rotor position: a) \u03b1 = 240\u00b0; b) \u03b1 = 300\u00b0; c) \u03b1 = 0\u00b0; d) \u03b1 = 60\u00b0; e) \u03b1 = 120\u00b0; f) \u03b1 = 180\u00b0",
        "texts": [
            " The entrance circuits of the converter are connected to an ac source through stator windings of the motor. The rotor winding of the motor is connected to direct current side of the three phase thyristor bridge. The thyristor control is done in such manner, that the magneto - motive force, created by a stator winding currents, always produce a rotating torque in the motor. As the bridge thyristors are switched, the currents in the stator windings create a discrete rotating field with a step 60 degrees (Figure. 2). The thyristors are switched, when the orientation of vectors magneto-motive forces of stator and rotor windings corresponds to the motor torque. The entrance circuits of the converter are connected to an ac source through stator windings of the motor. The rotor winding of the motor is connected to direct current side of the three phase thyristor bridge. The thyristor control is done in such manner, that the magneto - motive force, created by a stator winding currents, always produce a rotating torque in the motor. As the bridge thyristors are switched, the currents in the stator windings create a discrete rotating field with a step 60 degrees (Figure 2). The thyristors are switched, when the orientation of vectors magneto-motive forces of stator and rotor windings corresponds to the motor torque. Let's make mathematical model of the electric drive. Here are taken some assumptions: a magnetic flux in the electric motor gap is not taken into account, thiristors are the ideal switchers, the mutual inductances between stator and rotor phases change under the sinusoidal law, Let's consider an interval of time, when the current passes through the series connected windings: phases A, rotor R and phase B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003575_j.ymssp.2017.11.011-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003575_j.ymssp.2017.11.011-Figure11-1.png",
        "caption": "Fig. 11. Test equipment.",
        "texts": [
            " Since HFD estimates the exit of the rolling element using the decay of the response to rattling, the lack of the transfer function simulation causes an erroneous recognition of the exit. The presented algorithms are developed relying on analytical derivations and numerical simulations. The establishment of the algorithms required an extensive verification with experimental data. This section presents the verification test setup, which was used for extraction of the experimental data and the algorithm implementation results. The experimental system includes two subsystems: a generic test rig (Fig. 11a) and a measurement unit. The generic test rig includes an AC motor, one shaft with two flywheels that load the bearings, mounted on two bearings. The measurement unit includes a data acquisition system that is connected to an optic sensor and accelerometers. The optic sensor measures the rotating speed of the shaft and the accelerometer, which is placed on the tested bearing housing (the right bearing housing in Fig. 11a) and measures the vibration signal in the vertical direction. The shaft speed was measured using a Keyence optic sensor and vibrations were measured using two accelerometers, Endevco 2250A-10 (location B in Fig. 11c) and Dytran 3053B2 (location A in Fig. 11c). The data was acquired for 60 s with a sample rate of 25 kSamples Sec h i . The monitored bearing (SKF 6208 ETN9) was installed with an implanted fault in the centre of the loading zone. The fault (Fig. 11b) is generated by an electrical discharge machining process. Fifteen different bearings were monitored, one healthy and fourteen with seven different fault widths (two bearings for each spall width: 0.39 mm, 0.61 mm, 0.78 mm, 1.12 mm, 1.61 mm, 2.13 mm and 2.61 mm). The acceleration signal is presented as a function of the shaft cycles (one cycle represents one shaft revolution). Fig. 12 presents an example of intermediate results of the algorithms implemented on the signal measured at location B (Fig. 11c). The original signal is filtered by the BP and HP filters. The entrance event (black line) is isolated by the BP signal and detected in a similar way by both algorithms. Both algorithms use the HP signal to isolate the events related to the exit of the rolling element from the spall. Each algorithm detects a different event to estimate the shaft angle of the exit event. HFD detects the beginning of the decay of the high-frequency acceleration (red line) and FI detects the first impact (green line). Fig. 13 presents the relative estimation error of the algorithms for the signals measured at location B (Fig. 11c). Corresponding to the lower-bound of a recognizable spall width, which is defined in Section 4.3 and demonstrated in Section 5, the errors for spalls smaller than 1.1 mm are not presented here. The measured acceleration signal is influenced by the signal-to-noise ratio and the transfer function between the bearing and the sensor. Four signals were measured by an additional sensor, which was placed in location A (Fig. 11c). The errors HFD and FI produced using these signals (Table 2) are of the same order as that produced using the measurements performed in location B (Fig. 11c). Evaluation of the damage severity in a mechanical system is required for the assessment of its remaining useful life. In rotating machines, bearings are crucial components. Hence, accurate estimation of the width of spalls that have developed in bearings is important for performing prognostics of the remaining useful life. Two new algorithms, FI and HFD, are proposed for estimating the width of a spall located on the outer raceway of a radial rolling element bearing using vibration analysis. For the first time, previously derived expressions for spall width based on the rolling element-spall interaction analysis were implemented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001165_0954406021525331-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001165_0954406021525331-Figure7-1.png",
        "caption": "Fig. 7 A corresponding metamorphic mechanism",
        "texts": [
            " A carton can now be presented in a new class of mechanism which changes its mobility during motion. The folding sequence of a carton can hence be obtained from the analysis of the equivalent mechanism and its Proc Instn Mech Engrs Vol 216 Part C: J Mechanical Engineering Science C17101 # IMechE 2002 motion. They are governed by actuating elements. In this particular case, the folding is governed by guiding elements and the sequence of a decomposed mechanism. Looking at the equivalent mechanism in Fig. 7, joints (3,4), (6,7), (9,10) and (12,13) are essential in actuating the four loops in the graph in F ig. 8. A single loop consisting of link 1 to link 5 in F igs 7 and 8 is a ve-bar spherical metamorphic mechanism which centres at O1. The mechanism transforms itself to a new structure during motion as a four-bar spherical mechanism when links 4 and 5 are attached. The mobility is then reduced from 2 to 1 in the loop. When link 3 and link 4 are joined with the relative joint angle of joint axis (3,4) at 1808, the mechanism becomes a structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001299_j.ijimpeng.2006.04.006-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001299_j.ijimpeng.2006.04.006-Figure4-1.png",
        "caption": "Fig. 4. (a) Deformed configuration of inflated, thin-walled spherical shell and (b) velocity components and forces acting on spherical shell during impact.",
        "texts": [
            " Hence, the pressure\u2013volume relation for a perfect gas and (3) give the ratio of internal pressure to atmospheric pressure pa outside the shell as pg pa \u00bc F\u00f0d\u00de F0 g \u00bc pg\u00f00\u00de pa 1 1 4 d2 R2 3 d R g , (4) where air has a ratio of specific heats, g \u00bc 1:4 and total initial internal pressure in the ball, p0 pg\u00f00\u00de. The flattened sphere has undergone a change in configuration, which moves its center of mass G a distance l away from the center of the sphere, l=R \u00bc d2=4R2. Consequently, there is distance rG between the center of the flattened cap and the center of mass G(d) of the flattened spherical shell as shown in Fig 4. rG R \u00bc 1 d 2R 2 . (5) The initial mass M0 of a thin-walled spherical shell is M0 \u00bc 4prR2h where r is material density and h is the wall thickness. A thin-walled spherical shell has mass distributed uniformly across the diameter so the part of the initial mass in the flattened cap Mc is given by Mc M0 \u00bc d 2R . (6) The mass of gas inside the ball is insignificant in comparison with the mass of the spherical shell [14]. The spherical segment of shell and flattened cap have a moment of inertia IG about the center of mass G(d) where it is assumed that the flattened segment of sphere can translate tangentially but not rotate (i",
            " basketballs, soccer balls, volleyballs, etc striking the surface of a court. For impact of an inflated thin-walled sphere, the velocity field can be approximated as a flattened cap that has no normal component of velocity relative to the stationary contact surface and the remainder of the sphere, not in touch with the contact surface. The velocity of each point on the spherical segment of shell is the sum of the translational velocity of the center plus the vector cross product of the angular velocity and the radial position relative to the centers shown in Fig. 4b. As material flows across the interface into the deformed cap during approach or compression, at the contact surface a momentum flux force decelerates the in-flowing material from an incoming velocity equal to that of the shell, to the velocity of the cap. This dynamic force results from transfer and subsequent deceleration of momentum from the moving spherical segment of the shell into the flattened cap (see Appendix A). The analysis of momentum flux depends upon whether at the perimeter of the contact circle, material is moving into or out of the flattened cap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001491_1.1876437-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001491_1.1876437-Figure2-1.png",
        "caption": "Fig. 2 Generating method of a curvilinear-tooth gear cut by hob cutters",
        "texts": [
            " Figure 1 depicts a schematic drawing of a 6-axis CNC hobbing machine, where axes X, Z, and Y represent the functions of the radial feed, axial feed and hob shift of the hob cutter, respectively; Axes A, B, and C are the hob\u2019s swivel axis, hob\u2019s spindle axis and worktable axis, respectively. Some axes of the CNC hobbing machine are fixed while some axes rotate with a specific relationship during the manufacturing process. For example, in the manufacturing of helical and spur gears, axes X and A are fixed and in the manufacturing of worm gears, axes A, X, and Z are fixed. Figure 2 illustrates the generating method of a curvilinear-tooth gear cut by hob cutters. Axes Zh and Zf are the rotation axis of hob cutter and work piece, respectively. Point Of is located on the middle section of a work piece width. Oh denotes the rotational center of the hob\u2019s swivel. Circular-arc MN\u0302 stands for the tooth traces of the curvilinear-tooth gear, Oe indicates the center of cir- cular arc MN\u0302, and R represents the nominal radius of circular tooth trace. In addition to a rotation motion about axis Zh for the hob\u2019s spindle, the rotation center of the hob\u2019s swivel Oh translates along axis Zf and the swivel axis rotates about point Oh",
            "org/about-asme/terms-of-use Downloaded F The hob and work piece perform related rotation with respect to their own axes. The relationship of rotational angles between the work piece and hob can be represented as follows: 2 = T1 T2 B + 2. 3 where 2 and B denote rotational angles of the work piece and the spindle of hob cutter. T1 and T2 are the number of threads of the hob cutter and the number of teeth of the generated gear, respectively. 2 represents an additional angle of work piece rotation due to feed motion of the hob. According to Fig. 2, the additional angle for cutting curvilinear-tooth gears can be represented by: 2 = R 1 \u2212 cos A + r2 , 4 where r2 indicates the radius of operating pitch cylinder of the work piece. Differentiating Eq. 3 with respect to time, then the relationship of angular velocity among A, B and 2 can be obtained as follows: 2 = T1 T2 B + R sin A + r2 A. 5 Equation 5 represents the work piece rotation 2 in terms of two independent variables A and B. To generate the curvilineartooth gears by a hob cutter, axes A, B, C, and Z of a hobbing machine must be controllable in the process of gear generation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002539_1077546311399947-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002539_1077546311399947-Figure3-1.png",
        "caption": "Figure 3. Translational model of spur gear tooth.",
        "texts": [
            " In such a model, the tooth is assumed to be an element which accumulates and releases potential energy during mesh. 2. A torsional model that is used when the factors affecting operational performance (i.e. torsional stiffness, tooth deformation, gear tooth spacing and profile errors, etc.) are considered. The tooth stiffness of a spur gear in the direction of the predominant (tangential) component of the transmitted load W can be calculated by considering the translational model (Yesilyurt, 1997; Yesilyurt et al., 2003) shown in Figure 3. The various notations used have been discussed in the nomenclature. The contribution of \u2018Wr\u2019, the radial component, is very small to the tooth deflection in the tangential direction; on the other hand the tangential component \u2018Wt\u2019 strives to bend and shear the tooth. If ytotal denotes the total deflection at the tip in the direction of the tangential load, then the overall stiffness of the gear tooth kt1 can be expressed as kt1 \u00bc Wt ytotal \u00f01\u00de ytotal is divided into a finite number of elements",
            " Therefore reduction in tooth stiffness or changes in vibration characteristics due to localized or distributed faults are revealed by vibration characteristics. Static and dynamic properties of a single tooth or a complete geared system can be predicted by considering a translational or rotational modal. The factors affecting operational performance, such as torsional stiffness, geared tooth spacing, profile errors etc. are analyzed using a torsional stiffness model. The translational model as shown in Figure 3 can be used in the analysis of problems related to vibration properties of a single tooth or for determining the gear tooth stiffness (Lin and McFadden, 1997; O\u0308zgu\u0308ven and Houser, 1998; Tavakoli and Houser, 1986). A defect severity can be assessed by reduction of stiffness in gear teeth. For the modal testing setup, the test pinion is clamped with a specially designed frame in which a pair of diametrically opposite teeth is machined to accommodate the test pinion. As the teeth suspended in the frame are excited by an instrument, the hammer, the frame assembly vibrates in a direction perpendicular to the plane passing through the pinion body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002827_bf02992786-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002827_bf02992786-Figure3-1.png",
        "caption": "Fig. 3 a Fig. 3 b",
        "texts": [
            " Using (ii), 2 (iii), and the definitions of ai, b~ in 2 (vii) and 2 (viii), these are given by : - - 5.1. ~ ~* : a~ -> a{l' a~ --> ai (1 < i < n) [ ~ . : a o -->a~l~ ~, bo -->a~lb61ao, ai -->a~, b~-->bi (1 < i < n ) . To induce the automorphism Pol in 3 (10), we construct a homeomorphism of T~, which arises from interchanging the handles T~ ( : T), T(T), and leaving the others fixed, - - after the manner in which a cowboy uses a cow's horns to twist its head. A precise description follows. On the surface of the ball 2: of Fig. 2, shown again in Fig. 3, let C1, C2 be parallel circles, so that C1 goes through p and cuts off a cap containing C~ and the surfaces of T, ~(T) only. Let C2 divide the are u (see Fig. 2) into portions ~, y, and let it divide a into ~, ~/(with induced orientations). C2 separates T , into parts A, B, of which A contai , s T and v(T). Let ~ denote the rotation of A through :~ radians, about the axis perpendicular to H0 and through the centre of C~, and in the sense that T comes \"up\" out of the page. Then ~ has an extension, still de- noted by v 2, to the whole of T , , which is the identity on the portion B' of B on that side of the plane through C~, remote from A. Thus W is an automorphism of T , , interchanging T and ~ (T), which is the identity on the remaining handles, and which leaves p fixed. We now compute the effect ofw on ~I(T,) and ~I(~T~). In fact, we assert : - - 6.1. ~ ( a ~ - arl/c111' ~(b~ ~ a'l-lb~lal [v2(al) ~_ k ,a~ lk~ lkT 1, y~(bl) ~_ ]cla~lb~laok.r 1 rel p on T~. the 2-holed cap D of 2: which we see as in Fig. 3a when the handles N ~J T, ~ (/V ~) T) are removed; the outer boundary of D is CI, and the two holes in D are bounded by the curves hi, h 2. We have represented the effect of ~ on D in Fig. 3a, 3b, in order respectively to calculate the effect (shown dotted) on ao, bo, and on al, b~; and the effect of ~ is to interchange hi, h 2 and rotate C2 through s radians anti-clockwise. I t is then apparent from the diagram that rel O on D, (and with fixed ends), (i) ~(z0) ~(Y0) -~ (Y1~1) -1 (v(y0) -1 kl.ly where kl is the commuta to r described in 2 (ix). Now ao ---- a, al = z (a) with a as in 2 (i), so ao = ~oYoO~oYo~o, (x o = vw2\"2(vi~; therefore b y (i), we have (rel p on ~T~) : - - B y 2 (i) again, we can write bo = Ho Yo ~o/30 (~o Yo ~o) -I where ~o = vw2, flo = fl,fl-1. Hence b y (i), ~(bo)---- (yl~l)-l~rlflrl~l~/1~l rel p on ~ T , , where fll = \"r(flo), ~1 = (21~bxvl) -1- Thus v/(bo) - [ (~l~/ l~1)- l~/-~]~f l r~- l [~l~/~] (7 = ~1Y1~1) so b y 2 (i) W(bo) - arlb~Xal, rel p on OT, . Turning to Fig. 3b , we see tha t (rel p on D) with fixed e n d s : - - (ii) { ~(glYl) -- ]gl(~toko) -1 ~(~]1~1) --~ (goYo)-l~olki -1. With the above notat ion, then, r(al) = r ( ~ l y l ~ l y a ~ ) _~ kl (Yo~o)-~a~ ~ (~o Yo) -~ k~ ~ k? ~ (by (ii)) ]cla~lk~l]ffi-ll rel p on ~ T , . ~o (bs) -~ ~ (ul Yl ~1]31 (~r Yl ~s) -1) _~ ks(y)o~o)-S~o-S/3~S~oYo~ok~ 1 (by (ii)) ~ kla~SuoYo~ofl~l(uoYo~o)-Saokf 1 = kla~lb~Saokr 1 re lp on ~gT~. By 2 (x) and 6.1, v 2 therefore induces an automorphism ~, : ~s(T~) ~1 (T~) such that ao -> ai -s, al ---> ao -s, ai --> a~ (1 < i < n)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001814_pime_proc_1983_197_102_02-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001814_pime_proc_1983_197_102_02-Figure3-1.png",
        "caption": "Fig. 3 The preload measuring ring",
        "texts": [
            " Minute errors in the displacement would account for large variations in the preload force. The simplest method or measuring the force would be to mount strain gauges in the housing in a position between the bearings. However this was unsatisfactory as it necessitated introducing a high degree of flexibility into the housirdg and so would no longer simulate a constant displacement preload method. As a result a load ring was manufactured to measure the amount of preload placed on the bearings during assembly. The preload ring (Fig. 3) was designed to measure the axial load on a ceniral annular bush when the outer annular Range was rigidly held. The central bush and the outer fldnge were connected by a thin annular disc (1.4 mm thick) which could be considered as a ffexihle annular piate with encastrk supports at the inner and outer diameter. Since both concave and convex bending would occur on one side of the disc surface, eight strain gauges were connected to form a completely active wheatstone bridge. This typc of wiring Q lMechE December I983 at CORNELL UNIV on June 24, 2015pic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000618_s0013-4686(00)00373-x-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000618_s0013-4686(00)00373-x-Figure3-1.png",
        "caption": "Fig. 3. Calibration graph for phosphoric acid using the PyOxbased electrode.",
        "texts": [
            " TPP, the activators of PyOx, is known to contain phosphoric acid as an impurity even after the purification by using ion-exchanging resin [42], which would be responsible for the large background current. On the other hand, the addition of phosphoric acid brought about further increase in the electrode current. A steady-state current response was obtained within 20 s, and was proportional to the phosphate concentration up to 0.4 mM (current response/phosphate concentration=51.0 mA cm\u22122 mM\u22121, i.e. almost the same sensitivity as the case of pyruvic acid; see Fig. 3). The detection limit was ca. 0.2 mM; the lower sensitivity than the case of pyruvate determination was caused by an increase in the noise level, which was followed by that in the background current. The relative standard hydrogen peroxide with L-ascorbic acid has been reported to proceed on enzyme electrodes after the addition of the substrate/L-ascorbic acid-mixture, which brought about anomalous current responses [48,49]. However, the reaction rate was too low to give a discernible effect within the measuring time of the present enzyme electrode [49]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000892_robot.1993.291971-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000892_robot.1993.291971-Figure2-1.png",
        "caption": "Figure 2: Motion of mobile plate",
        "texts": [
            " I t consists of two plates that are connected by six legs BjMi(i = 1,. . . , 6 ) acting in- lem for p ! anar closed-chain mechanisms. Hypotheti- ics of genera 1 form of in-parallel mechanisms. Free- parallel. One of the plates, defined as the mobile plate, has six degrees of freedom relative to the other plate which is the base plate. A leg in a typical Stewart platform has a spherical joint a t one end, a universal joint at the other end, and a prismatic joint in between which is actuated to change the length of the leg. Figure 2 shows one of the legs, &Mi. In order to effectively control a Stewart platform, formulations that are s ecific to Stewart platform have been studied. Fichter {] assumed that the effect of leg inertia is negligible and obtained a simple formula for calculating the driving forces for Stewart platforms. This assumption is valid in many applications, because the effect of leg inertia is negligible compared with the inertia of the load carried by the mobile plate. There are, however, other applications where load is not acting in the form of mass but in the form of force and moment on the mobile plate",
            " By computing these two components separately, comparison can be made for determining whether the inertia effect of legs is negligible. When the effect is not trivial, the method can also be used in runtime to combine both components for control the Stewart platform. Additionally, this method can also be used for dynamic simulation during application development. 2 Computation of actuating force The motion of the mobile plate can be described by a rotation matrix R(2) and a translation vector d i of the attached frame {M} expressed in frame {L] attached to the fixed base plate, as shown in Figure 2. This motion is resulted from the action of the force exerted by the legs flag = [egMEg]T and the external force fezt = [ezt MTZ,lT. Therefore, this motion is governed by the following equation: fleg + fezt + f' = 0 (1) where f' = [(3')T (M*)T]T is the inertia force of the mobile plate. Because of the type of joints used, only pure force fi can act between leg i and the mobile plate a t joint Mi. Therefore the resultant force Tieg and moment Mleg applied by the legs to the mobile plate are We need to find fi ( i = 1 , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-16-1.png",
        "caption": "FIGURE 5-16 Typical cam outline.",
        "texts": [
            " If the minimum diameter is Db and the slant height is s, then the valve opening area, A 3 , is sInce and then s = h cos a D2 = D J + 2h cos a sin a 1T A3 = - (DJ + DJ + 2h cos a sin a)h cos a 2 A3 = 1T (DJ + h cos a sin a)h cos a CAMS 93 cos a 0.707, sin a = 0.707 TI(D[ + 0.707 X 0.707 h )0. 707 h (1) If the lifts are high, the line 5 will fall outside the point 4, in which event the line 1-4 becomes the slant height, from which the valve-opening area is determined. The valve port area is commonly designed to produce a maximum gas velocity of 71 m/s in the exhaust port and 56 m/s in the intake valve port. Cams Valves are usually lifted by cams similar to that shown in figure 5-16. The cam contour is formed by two arcs joined by two flanks which may be either arcs or straight lines tangent to the arcs. The cam may be symmetrical or the leading flank may vary from the following flank. In a four-stroke-cycle engine the camshaft rotates at one-half the crankshaft speed and, therefore, the cam 94 ENGINE DESIGN angle for the valve opening will be one-half the valve range of operation, the latter being 'expressed in degrees of crankshaft rotation. One of the means used to increase the maximum power of an engine is to increase its volumetric efficiency",
            " The maximum piston speed in meters per second for this engine is approximately 1.04 times the velocity of the crankpin. You may assume (approximately true) that the valve is open the maximum distance at this point. 2. Construct a valve-timing diagram similar to thal shown in figure 5-4 for a tractor engine with the following specifications: intake valve opens 5\u00b0 after hdc; intake valve closes 40\u00b0 after cdc; exhaust valve opens 45\u00b0 before cdc; exhaust valve closes 10\u00b0 after hdc. 3. Construct (to three times actual size) a cam similar to that shown in figure 5-16 to give the inlet valve timing shown in problem 2. Let the radius of the base circle be 20.3 mm. Let the flanks be straight lines, and determine the nose radius necessary to give a maximum lift of 5.1 mm. Neglect the tappet clearance and ramp on the cam. Determine graphically the lift for each 5\u00b0 of cam rotation, and plot the results on cross-section paper. 4. For an assigned tractor engine, determine the average and maximum gas velocity through the intake and exhaust valve ports. Data needed are stroke, bore, piston rod length, valve lift and timing, and the diameters of the valve stem and valve face"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.1-1.png",
        "caption": "FIGURE 1.1 Characteristic shape factors (indicated by points and shaded areas) of tire or axle characteristics that may influence vehicle handling and stability properties. Slip angle and force and moment positive directions, cf. App. 1.",
        "texts": [
            " The Moment Method 51 1.3.6. The Car-Trailer Combination 53 1.3.7. Vehicle Dynamics at More Complex Tire Slip Conditions 57 .00001-2 rights reserved. 1 This chapter is meant to serve as an introduction to vehicle dynamics with emphasis on the influence of tire properties. Steady-state cornering behavior of simple automobile models and the transient motion after small and large steering inputs and other disturbances will be discussed. The effects of various shape factors of tire characteristics (cf. Figure 1.1) on vehicle handling properties will be analyzed. The slope of the side force Fy vs slip angle a near the origin (the cornering or side slip stiffness) is the determining parameter for the basic linear handling and stability behavior of automobiles. The possible offset of the tire characteristics with respect to their origins may be responsible for the occurrence of the so-called tire-pull phenomenon. The further nonlinear shape of the side (or cornering) force characteristic governs the handling and stability properties of the vehicle at higher lateral accelerations",
            " When the wheel moves in a way that the condition of zero slip is no longer fulfilled, wheel slip occurs that is accompanied by a buildup of additional tire deformation and possibly partial sliding in the contact patch. As a result, (additional) horizontal forces and the aligning torque are generated. The mechanism responsible for this is treated in detail in the subsequent chapters. For now, we will suffice with some important experimental observations and define the various slip quantities that serve as inputs into the tire system and the moment and forces that are the output quantities (positive directions according to Figure 1.1). Several alternative definitions are in use as well. In Appendix 1, various sign conventions of slip, camber, and output forces and moments together with relevant characteristics have been presented. For the freely rolling wheel, the forward speed Vx (longitudinal component of the total velocity vector V of the wheel center) and the angular speed of revolution Uo can be taken from measurements. By dividing these two quantities, the so-called effective rolling radius re is obtained: re \u00bc Vx Uo (1",
            " During braking, the fore-and-aft slip becomes negative. At wheel lock, obviously, k \u00bc 1. At driving on slippery roads, k may attain very large values. To limit the longitudinal slip K to a maximum equal to one, in some texts the longitudinal slip is defined differently in the driving range of slip: in the denominator of (1.2),Uo is replaced by U. This will not be done in the present text. Lateral wheel slip is defined as the ratio of the lateral and the forward velocity of the wheel. This corresponds to minus the tangent of the slip angle a (Figure 1.1). Again, the sign of a has been chosen such that the side force becomes positive at positive slip angle. tana \u00bc Vy Vx (1.3) The third and last slip quantity is the so-called spin which is due to rotation of the wheel about an axis normal to the road. Both the yaw rate resulting in path curvature when a remains zero and the wheel camber or inclination angle g of the wheel plane about the x axis contribute to the spin. The camber angle is defined to be positive when, if looking from behind the wheel, the wheel is tilted to the right",
            " In Chapter 2, more precise definitions of the three components of wheel slip will be given. The forces Fx and Fy and the aligning torque Mz are results of the input slip. They are functions of the slip components and the wheel load. For steady-state rectilinear motions, we have, in general, The vertical load Fz may be considered as a given quantity that results from the normal deflection of the tire. The functions can be obtained from measurements for a given speed of travel and road and environmental conditions. Figure 1.1 shows the adopted system of axes (x, y, z) with associated positive directions of velocities and forces and moments. The exception is the vertical force Fz acting from road to tire. For practical reasons, this force is defined to be positive in the upward direction and thus equal to the normal load of the tire. Also, U (not provided with a y subscript) is defined positive with respect to the negative y-axis. Note that the axes system is in accordance with SAE standards (SAE J670e 1976). The sign of the slip angle, however, is chosen opposite with respect to the SAE definition, cf",
            " The diagrams include the situation when the brake slip ratio has finally attained the value of 100% (k \u00bc 1) which corresponds to wheel lock. The slopes of the pure slip curves at vanishing slip are defined as the longitudinal and lateral slip stiffnesses, respectively. The longitudinal slip stiffness is designated as CFk. The lateral slip or cornering stiffness of the tire, denoted by CFa, is one of the most important property parameters of the tire and is crucial for the vehicle\u2019s handling and stability performance. The slope of minus the aligning torque versus slip angle curve (Figure 1.1) at zero slip angle is termed as the aligning stiffness and is denoted by CMa. The ratio of minus the aligning torque and the side force is the pneumatic trail t (if we neglect the socalled residual torque to be dealt with in Chapter 4). This length is the distance behind the contact center (projection of wheel center onto the ground in wheel plane direction) to the point where the resulting lateral force acts. The linearized force and moment characteristics (valid at small levels of slip) can be represented by the following expressions in which the effect of camber has been included: Fx \u00bc CFk k Fy \u00bc CFa a\u00fe CFgg Mz \u00bc CMa a\u00fe CMgg (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-35-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-35-1.png",
        "caption": "FIGURE 12-35 Standard quick-attaching coupler for three-point hitch on agricultural tractors. (From SAE 1909 [Apr. 1980]. Also, ASAE S278.6.)",
        "texts": [
            " Quick-Attaching Coupler for Three-Point Hitches The three-point hitch has many advantages, including extra weight transfer to the tractor for traction, ease of control and movement of the attached implement, and better control of the implement. When the original (Category 356 HYDRAULIC SYSTEMS AND CONTROLS I) hitch was developed, the implements being attached were generally small enough so that the operator could manually move them if the tractor was not in the correct location. With the advent of larger hitches and larger imple ments, it became much more difficult for the operator to align the implement and the tractor. The quick-attaching coupler is an attachment to the three point hitch (see fig. 12-35) that allows easier and safer hitching and unhitching, especially with the large tractors. The quick-attaching coupler moves the im plement rearwards approximately 10 cm. PROBLEMS PROBLEMS 357 1. A rubber-tired tractor is pulling a plow at 6.5 km/h on level ground when the plow hooks a large boulder. causing the unit to stop suddenly. The coefficient of traction is 0.60, the maximum possible drawbar power is 18 kW, the rear wheels weigh 14,7001\\, and the front wheels weigh 7350 K (a) Compute the kinetic energy to be absorbed in stopping the tractor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001079_004-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001079_004-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of laser cladding process.",
        "texts": [
            " In this paper, an analytical model is presented for computing the attenuation of the laser energy by a powder stream, based on classic physical optics theories, and to compute the heating of the powder particles by the radiation of the laser beam according to the heat equilibrium principle. The effects of powder feeding rate and powder feeding angle on the temperature distribution and the laser intensity distribution are studied for a practical case under a given stream spread and speed of powder particles. Figure 1 shows the laser cladding process studied in this paper. The origin of coordinates, O, is fixed at the laser spot centre, the nozzle has an obliquity, \u03c6, with the horizontal surface, and the half spreading angle of the powder stream is \u03b8 . O\u2032 is a virtual feeding origin for the convenience of computing, which is at distances of S and H from the origin, O, in the horizontal and vertical directions, respectively. The nozzle can be adjusted to give different feeding angles. To develop a model of interaction between the laser beam and powder stream, the following assumptions are made: (1) The laser beam has no divergence or convergence in the interaction region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002208_tie.2009.2031190-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002208_tie.2009.2031190-Figure5-1.png",
        "caption": "Fig. 5. Instantaneous magnet loss due to tooth-ripple fields.",
        "texts": [
            " The effect can be virtually eliminated if the air-gap length can be increased to approach the slot-opening width. For the Zephyr motor design, the slot-opening width could not be reduced below 2.0 mm without making the winding process very cumbersome. The air-gap length was increased to 1.0 mm. This, in turn, necessitated relatively deep magnets in order to maintain the air-gap flux density but was not enough to eliminate tooth-ripple losses. A 2-D time-stepping finiteelement solution was therefore employed to evaluate magnet losses due to these tooth-ripple fields. Fig. 5 shows the instantaneous loss-density distribution in a portion of the rotor. Regions shaded have the highest loss density. Note that when a magnet is over a tooth, it has a uniform flux density and, therefore, no eddy-current flow. Peak losses occur when a magnet is centered over a slot. The portion over the slot has a lower flux density and, therefore, less induced voltage than the magnet sides. Consequently, eddy currents flow down the center of the magnet and return at the circumferential ends"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003556_rnc.3868-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003556_rnc.3868-Figure1-1.png",
        "caption": "FIGURE 1 The sector of h(\ud835\udf021)",
        "texts": [
            " (33) By choosing L > max { 1, \ud835\udf0f2h\u0303 + di,1 + di,5 + di,2+di,6 1\u2212\ud835\udefe d\u0303i , \ud835\udf0f2h\u0303 + dj,3 + dj,7 + dj,4+dj,8 1\u2212\ud835\udefe b\u0303n,j } , (34) there is a positive constant \ud835\udf1a3 and class  function \ud835\udefc3 such that T \u2a7d \u2212\ud835\udf1a3 ( n\u2211 i=1 \ud835\udf092 i + n\u2211 j=2 e2 j ) \u2a7d \u2212\ud835\udefc3(|(s)|). (35) It is obvious that v in Equation 15 is 1, by which and the fact that fi and gi are 1, the locally Lipschitz condition of the closed-loop system 4, Equation 14 and 15 can be guaranteed. By Equation 26, 35 and Lemma 1, the systems 4, 14, and 15 are globally asymptotically stable in probability. Since Equations 3 and 28 are equivalent transformations, the closed-loop system constituting of Equations 1 and 29 has the same properties as the systems 4, 14, and 15. Remark 2. We use Figure 1 to clearly show the sector \u0394. For all the known or unknown 1 functions with bounded first derivative in the shadow region [1 \u2212 ?\u0304? + \ud835\udf00, 1 + ?\u0304? \u2212 \ud835\udf00](\ud835\udf00 \u2208 (0, ?\u0304?)) included in \u0394 = (1 \u2212 ?\u0304?, 1 + ?\u0304?) in Figure 1, an output feedback controller relying on h(\u00b7) can be designed to guarantee the globally asymptotical stability in probability. \u25a1 Remark 3. Because of the existence of \ud835\udf0f2(t), we explain why the existing transformation in13 xi(t) = \ud835\udf02i(t) Li\u22121 , i = 1, \u00b7 \u00b7 \u00b7 , n, v(t) = u(t) Ln , (36) with 0 < L \u2a7d 1 being a gain to be determined is inapplicable to system 1. By Equation 36, Equation 1 becomes dxi(t) = (Lxi+1(t) + fi(t, x(t), u(t), x(t \u2212 \ud835\udf0f1(t)), u(t \u2212 \ud835\udf0f1(t))))dt + g\u22a4i (t, x(t), u(t), x(t \u2212 \ud835\udf0f1(t)), u(t \u2212 \ud835\udf0f1(t)))d\ud835\udf14(t), \u03b6 = 1, \u00b7 \u00b7 \u00b7 , n \u2212 1, dxn(t) = Lv(t \u2212 \ud835\udf0f2(t))dt, y(t) = h(x1(t)), and Assumption 1 is reinterpreted as | fi| \u2228 |gi| \u2a7d cL2 n\u2211 j=i+2 (|xj(t)| + |xj(t \u2212 \ud835\udf0f1(t))| + |v(t)| + |v(t \u2212 \ud835\udf0f1(t))|), where fi = \ud835\udf19i Li\u22121 , gi = \ud835\udf13i Li\u22121 , i = 1, \u00b7 \u00b7 \u00b7 , n \u2212 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002533_j.ymssp.2011.07.002-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002533_j.ymssp.2011.07.002-Figure7-1.png",
        "caption": "Fig. 7. Wavelet-based integrated feature using the same integration bandwidth B as for the WB feature: the unpitted (left) and pitted (right) cases.",
        "texts": [
            " As for the WB integrated feature, the WT energy distribution (scalogram) of the residual signal may be integrated over a specific frequency bandwidth in order to derive a time dependent energy-based feature, as performed in [24]. It was also shown in [4] that the mean value of a WT crosssection could be used for crack detection in gears. Using frequency instead of scale the proposed WT integrated energy feature is defined as EW \u00f0t\u00de \u00bc Z B 9W\u00f0t,f \u00de92 df : \u00f011\u00de The selection of the integration bandwidth B was the same as for the WB-based feature (200\u2013400 orders). Also, the signals were previously normalized in amplitude by the standard deviation of the raw vibration signal. Fig. 7 shows the WT energy-based features for all realizations in the unpitted (left) and pitted (right) cases. Some peaks emerge in the pitted case corresponding to the pitting positions. However, contrary to the WB-based feature, the WT-based feature also exhibits some strong peaks in the unpitted case, especially around angle 1001. As for the WB-based feature, a threshold was experimentally set in order not to trigger any false alarm for the unpitted case WT-based integrated feature. This threshold (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003915_icuas.2014.6842287-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003915_icuas.2014.6842287-Figure3-1.png",
        "caption": "Figure 3. I-th rotor geometric configuration with the Earth, body and motor frames.",
        "texts": [
            " Forces and torques generated by a drive unit act on the flying platform frame and their impact is depended on the geometrical distribution of the propulsion systems. From the mechanical point of view the multirotor vehicle is a multi-body system which consists of the N+1 rigid bodies, where N is a number of the actuators. Let us consider the i-th propulsion system. The { }e w w w w F : O ;,X ,Y ,Z is an Earth inertial frame and { }b b b b b F : O ;,X ,Y ,Z is a frame attached to the multirotor body in the COG. For the i-th actuator the { }s s s s s F : O ;,X ,Y ,Z frame is established (see Fig. 3). The rotation matrices can be specified for orientations between each frame. Let us denote e bR as an orientation of body frame in the earth one. Whereas b sR is an orientation of the motor drive unit with respect to the body frame. Using the notation of the elemental rotation matrices in the following form: for the rotation around x-axis about \u03c6 angle ( )x R \u03d5 , around y-axis ( )y R \u03d5 and around z-axis ( )z R \u03d5 we can denote that motors orientation in the body frame is as follows (for the uniform distribution of the actuator): ( )( )b si z R R 2 i 1 N , i 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001491_1.1876437-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001491_1.1876437-Figure3-1.png",
        "caption": "Fig. 3 Geometry of the straight-edged cutting blade and worm-type hob cutter",
        "texts": [
            " Therefore, the ZA worm-type or ZN worm-type hobs are chosen instead of the ZI worm-type hob for generation of involute gears. The ZN worm-type hob cutter is widely used in the gear manufacturing. A right-hand ZN worm-type hob cutter is used to simulate the manufacture of curvilinear-tooth gears in this study. The surfaces of the hob cutter can be generated by a blade with the straight lined shape, performing a screw motion with respect to the hob cutter\u2019s axis. The cutting blade is installed on the groove normal section of the ZN-type worm, as shown in Fig. 3 a . Parameter designates the lead angle of the worm. The generating lines can be represented by a coordinate system Sc Xc ,Yc ,Zc that is rigidly connected to the blade, as shown in Fig. 3 b , expressed by: Rc B = rt + l1 cos n 0 \u00b1l1 sin n 1 , 6 where symbol l1 is one of the design parameters of the straightlined cutting blade surface which represents the distance measured from the initial point Mo, moving along the straight line MoM1, to any point M1 on Xc\u2013Zc section of the cutting blade surface. Design parameter n symbolizes the half-apex blade angle formed by the straight-lined blade and Xc-axis, as illustrated in Fig. 3 b . In Eq. 6 , the upper sign represents the left-side cutting blade while the lower sign indicates the right-side cutting blade. In Fig. 3 c , the symbols ro, r1, and rf represent the outside radius, pitch ra- dius, and root radius of the ZN type-worm hob cutter, respec- SEPTEMBER 2005, Vol. 127 / 983 hx?url=/data/journals/jmdedb/27813/ on 03/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F tively. The cutting blade width bn equals the normal groove width of the hob cutter. Then, the design parameter rt can be obtained from Figs. 3 c and 3 d as follows: rt = r1 2 \u2212 bn 2 4 sin2 \u2212 bn 2 tan n . 7 Figure 4 shows the relations among coordinate systems Sc Xc ,Yc ,Zc , S1 X1 ,Y1 ,Z1 , and Sf Xf ,Y f ,Zf , where coordinate system Sc is the blade coordinate system, coordinate system S1 is rigidly connected to the hob cutter\u2019s surface, and coordinate system Sf is the reference coordinate system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003749_j.ymssp.2016.11.005-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003749_j.ymssp.2016.11.005-Figure2-1.png",
        "caption": "Fig. 2. Schematic design of the test stand and measuring track.",
        "texts": [
            " The mounting distances between the gears can be adjusted by the application of different thickness shims. Fig. 1 shows the schematic design of this gear. Additional information about this type of gearbox with respect to contact pattern and spectra can be found in [3,17]. The test stand was powered by an electric motor. Given the high angular velocity of the tested gear, it was necessary to use a multiplier with spur gears. Load torque was applied by a water brake and verified using a torque transducer (Fig. 2). The test stand was used to control and calculate vibrations, temperature, load torque and the angular velocity of gears. Vibrations were measured using two three-axis acceleration sensors, Br\u00fcel & Kjaer type 4321, equipped with B& K Nexus signal conditioners as well as the National Instruments PXI-1044 measurement PC provided with the NI PXI-4472B measuring card and LabView software. The sampling frequency of the vibrations signal was set to 40 kHz. The tests were performed with the gear angular velocity set to 6196 rev/min and at three loads: 34"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002829_iros.2011.6094909-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002829_iros.2011.6094909-Figure3-1.png",
        "caption": "Fig. 3. Parameters in spatial and planar configurations (originally appeared in [23])",
        "texts": [],
        "surrounding_texts": [
            "This work is primarily intended to study the dynamics of general continuum robots. To ground the results on real hardware, the model herein is focused on the Octarm VI continuum robot [12], [23]. Hence, the parameters and constraints implemented in this model conform to that of Octarm VI. Octarm VI is a three section continuum robot. Each section is made up of three McKibben actuators tied together along their lengths. A section of the device extends when there are equal pressure levels in all three actuators and bends when there are different pressure levels in the actuators (noticing that there is no torsion along the length of the arm). Since each section bends in space to form a constant curvature section its analysis can be restricted to a plane during these movements (the orientation of the plane changes as the robot moves). Therefore, a planar model is effective for the case of a single continuum robot section, the subject of the analysis in this paper. The shape of a section of the continuum arm is parameterized by the variables, s - length of arc, \u03ba - curvature and \u03c6 \u2013 orientation. In the 2-D single-section case, orientation (\u03c6) can be neglected. Two actuators are sufficient to model planar operation of a single-section of a continuum arm. We model each actuator as a Mckibben actuator, as realized in the Octarm hardware. Each such pneumatic actuator has air-filled latex tubing enclosed in a braided sleeve. The inherent compliance and damping of the actuator will be represented by a linear spring and damper combination. Thus each module in the model has a pair of linear spring and damper struts. The actuators maintain a nearly constant diameter at all pressure levels and this is accounted for in the model by constraining the distance between the two spring and damper struts. The length of arc (s) of each module is the average length of the two actuators. Another parameter, \u03b8, is introduced to account for bending such that 1 s = \u03ba \u03b8 ."
        ]
    },
    {
        "image_filename": "designv10_10_0003916_1.4914594-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003916_1.4914594-Figure7-1.png",
        "caption": "FIGURE 7. MSFC computed tomography images of Pogo-Z baffles, RS-25/J2-X nozzles, injectors, and valve bodies made by a direct metal laser sintering process",
        "texts": [
            " This limitation places greater emphasis on developing ASTM Guides, which are educational, and Practices, which provide \u201chow-to\u201d NDE instruction, so that experience gained allows refinement of qualitative NDE procedures into high TRL Test Methods, which generate numerical NDE results that can be used in procurement, for accept-reject, and as a basis for qualification and certification of AM parts. Computed tomography scans of an additively manufactured Ti-6-4 ASTRO-H adiabatic refrigerator component (Fig. 6), and Pogo-Z baffles, RS-25/J2-X nozzles, injectors, and valve bodies (Fig. 7) demonstrate the ability of CT to detect simulated internal flaws and inaccessible internal features. Computed tomography has also demonstrated utility to confirm closure of porosity by hot isostatic pressing (HIP) post-processing and to detect high density inclusions in as-manufactured Ti-6-4 specimens subjected to HIP (Fig. 8). This demonstrates the value of CT to 1) detect deep or embedded defects; 2) interrogate inaccessible features; 3) confirm the effectiveness of post-process treatments often required to make usable AM parts; and 4) characterize and qualify as-manufactured AM parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000834_978-94-017-0657-5-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000834_978-94-017-0657-5-Figure10-1.png",
        "caption": "Figure 10. V AF along the isotropy continuum locus",
        "texts": [
            " Example manipulator dimensions Figure 9 schematically represent three B'-B\" type insensitivity positions. It is easily observable that the complexity of IPC determination reduces to that of six simple crank- rocker mechanisms, that can be easily determined numerically or using 2D graphical techniques. Mechanism at three B'\" type lPCs is depicted in Fig. lO. Positions are much more difficult to compute and to design for as demonstrated by Zabalza et al., 1999, and can be considered less interesting in the context of the modified manipulator. 298 Figure 9. B' and B\" type IPCs \u2022\u2022 .. ~ \u2022 Figure 10. B'\" type IPCs It should be noted that the figures presented in this example do not consider any variability in the crank, coupler and fixed link lengths nor in the angles that the fixed link of any of the 6 crank- rocker mechanism can sustain with the fixed platform. A simplistic case study is presented in this section. A 6- RKS parallel manipulator of the type shown in Fig. 6 is designed so that the manipulator achieves the following two IPC positions: 1 The position obtained after turning the moving platform 5 degrees around an axis parallel to the Y axis that passes through its gravity centre, starting from a horizontal position with gravity centre coor dinates (0, 0, 0",
            " The 2-DOF Orthoglide mechanism, extended to three DOF in Wenger and Chablat, 2000, was designed to have an isotropic configuration for which the VAF are unitary. But this mechanism also provides an isotropy continuum which is a straight line (Fig. 9). Figure 9. 2-DOF Orthoglide isotropy continuum locus The two VAF are equal along the continuum, but not constant, Angeles, 1997. It means that 11,1 = 11,2, and therefore cond(J) = 1. The variation of the VAF along the isotropy continuum is limited (Fig. 10), which is interesting as it shows that isotropy brings homogeneousness to kinetostatic performances, which is prefered for this application. The Biglide isotropy continuum is not studied here because it has few consequences on the VAF homogeneousness inside the u-workspace. See section 4.1 for more details on its location. The 2-DOF Orthoglide u-workspace is first arbitrarily centered on the point S where the VAF are equal to 1 (Fig. 11). Changing the u workspace center position will be discussed in section 4",
            " When the singularity is reached a minimum speed is obligatory. If the minimum speed could not be obtained, the friction forces in the joints are higher then the inertia forces of the masses moved and the singularity will not be crossed. Immediately when reaching the singularity the drive has to decelerate to prevent an oscillation about the singularity. If the active drive is decelerated too late an oscillation about the singularity can move the manipulator back into the initial assembly mode. Figure 10. Path through the complete workspace envelope whether the crossover was successful. As step five, the kinematic equations are adjusted in the control software. In the sixth step, the disabled drives are enabled. This is done by increasing the proportional parameter of the drive controller from zero to its optimal value with an exponential function. In step seven, the manipulator is moved in articulated coordinates to the target pose. In the last step, the crossover is reported successful, and the manipulator controller continues with its prior program. A sample path through the workspace is shown in Fig. 10. Figure 11. Prototype on both sides of a singularity 356 First experiments with the prototype show that the method is very reliable. Mter the minimum speed and the deceleration parameters for the active drive had been determined by experiments, the crossover itself has not once been unsuccessful. The time that is required for the crossover is mainly determined by the power up time of the disabled drives. The main difference to moving in only one workspace is that not any path is possible. But this is no restriction for handling tasks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000774_978-94-011-4120-8_24-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000774_978-94-011-4120-8_24-Figure6-1.png",
        "caption": "Figure 6. D-H Frames for Spatial Case",
        "texts": [
            " We use the minimum norm solution for simplicity, but other redundancy resolution techniques could be applied, see Nenchev (1989). 236 A linear desired end point trajectory is shown in Fig. 5 a). Fig. 5 b) shows the self motion, :i; = 0, of the robot using the null space projection as given by (25) As noted earlier, one section of a spatial continuum robot can be viewed as a planar curve rotated out of the plane. We can apply the same techniques as the planar case with only the addition of an angle of rotation about the tangent. A possible way to set up the frames for a spatial curve is given in Fig. 6. As with the planar curve, the frames were chosen so that frames 0 and 4 would have a direct relationship to the orientation of the tangents, and the out of plane rotation would be about the tangent vector. Using the D-H technique as before, we can use the same technique as used in the planar case to generate the kinematics for spatial continuum robots. Note that since /'i, can take on both positive and negative values, 4> need only take on the values in a range of 7r to uniquely describe the curve in space. An example using a two section spatial robot is presented. 237 The frames for a two section continuum robot can be setup as a combination of two sections, where each section's frames are setup as in Fig. 6. The transformation matrix Ag E !R4x4 is omitted for compactness. The velocity kinematics can be again written as Eq. (24), where x = [x iJ i ]Tand it = [;PI f;;1 ;P2 f;;2] T. The elements of the Jacobian are omitted for compactness. Using the minimum norm solution for the inverse of J, the curvatures needed for a desired end effector position can be determined. Fig. 7 shows a linear end effector trajectory in !R3. We have presented a novel approach for deriving the kinematics of finitely actuated continuum robots that incorporates not only the bending of a sec tion, but also the coupling between adjacent sections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000764_s0094-114x(97)00022-0-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000764_s0094-114x(97)00022-0-Figure1-1.png",
        "caption": "Fig. 1. Orthogonal offset face-gear drive.",
        "texts": [
            " The solution to the problem of teeth pointing is based on the application of the concept of axes of meshing developed in [2] and [4]. (ii) Design of face-gear drives with improved conditions for the localization and stabilization of bearing contact due to application of an involute pinion with a crowned surface. The developed theory was tested by computerized simulation of meshing and contact of pinion and face-gear tooth surfaces. Numerical examples are provided. 2. GENERATION OF FACE-GEAR DRIVES WITH LOCALIZED BEARING CONTACT The pinion is a conventional involute spur one (Fig. 1). A face gear may be generated by an involute spur shaper. The process of generation is based on the simulation of shaping as meshing Meshing of orthogonal offset face-gear drive 89 of the pinion and the face gear of the drive represented in Fig. 2. The shaper and the face gear form an offset drive that is similar to the face-gear drive to be designed, and perform rotational motions about the same axes as in the face-gear drive (Fig. 2). Misalignment of the face gear may cause separation of the pinion-gear tooth surfaces and edge contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001617_cdc.2005.1582539-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001617_cdc.2005.1582539-Figure1-1.png",
        "caption": "Fig. 1. The four rotor rotorcraft",
        "texts": [
            " INTRODUCTION In the past few years, many researches have been attracted to the area of automatic control of flying machines. Generally, the control strategies are based on simplified models. These reduced models should however retain the main features of the aerial vehicle. In this paper, we are interested in the design of a relatively simple trajectory tracking algorithm to perform hover and tracking of desired trajectories. Particularly, we are interesting in controlling a mini rotorcraft having four rotors (Fig. 1). In this type of helicopters, the throttle input is the sum of the thrusts of each motor. Pitch movement is obtained by increasing (reducing) the speed of the rear motor while reducing (increasing) the speed of the front motor. The roll movement is obtained similarly using the lateral motors. The yaw movement is obtained by increasing (decreasing) the speed of the front and rear motors while decreasing (increasing) the speed of the lateral motors. This should be done while keeping the total thrust constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003033_s00170-012-4406-7-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003033_s00170-012-4406-7-Figure14-1.png",
        "caption": "Fig. 14 Virtual machine simulation results for AC type table-tilting",
        "texts": [
            " In the verification test, a machining scenario is built where the bottom of the blank workpiece is located at the machine rotary zero position. Work offset (programmed zero) is located at the rotary zero of the machine, therefore workpiece offset distance is set to W \u00bc 0i\u00fe 0j\u00fe 0k mm. Selected tool is a 12-mm diameter ball-end mill and the tool offset length is 150 mm from the tooltip of the cutter to the spindle. The distance from the machine home position to the workpiece zero is \u2212315i+0j\u2212605k mm. Screenshots of virtual machine simulation module and close-ups are shown in Fig. 14 while the simulation is running. The results of the second simulation demonstrate that generated NC data matches with the CL data (toolpath) for machine tool with AC type table-tiltingmachine configuration as well. In this paper, a postprocessor for table-tilting/rotating type five-axis machine tool based on generalized kinematics and a virtual machine simulation module are presented. The approach developed based on this model is modular. Therefore, machine tools with different kinematic configuration can be incorporated into the model very easily"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure3-1.png",
        "caption": "Fig. 3. The pressure distribution and streamline in bearing radius plane.",
        "texts": [
            " Around the negative pressure zone, a high pressure zone is Table 2 Calculation parameters of angular contact ball bearing B7008C. Bearing parameters Value (K) Bearing parameters Value Outer raceway temperature 323 Air density 1.23 103 kg/m3 Inner raceway temperature 333 Oil density 8.76 103 kg/m3 Cage temperature 335 Air viscosity 1.79 10 5 kg/m s 1 Ball temperature 338 Oil viscosity 5.8 10 2 kg/m s 1 Oil\u2013air inlet temperature 303 Oil type 32# turbine formed, and the pressure is higher at the zone along the rotating direction. Fig. 3 shows air velocity contour and stream line on radial plane of bearing at rotation speed 2.0 104 r/min and 3.0 104 r/min. Air flow inward bearing cavity along the inner ring surface because of its highest rotating speed. For lower rotating speed, single vortex forms in each side (A, B) of bearing cavity by the comprehensive effect of bearing subassemblies motions. With the increase of rotating speed, the vortex center of the A side moves inward and separates, and a stable vortex near the contact area forms, which blocks the lubrication and heat dissipation performance",
            " Since the Type II lubrication device is prior, so the following work was conducted to optimize the Type II lubrication device for the specific angular contact ball bearing B7008C/ZYS. According to the installation of bearing B7008C in machine tool spindle and tool holder system, the spacer and lubrication device are arranged in A side, while B side is sealed up. Single nozzle (at 0 plane) and double nozzles (at 0 and 180 plane) were compared and the internal flow at 40 and 160 plane were monitored. As mentioned above, vortex flow occurs in cylindrical cage pocket (seen in Fig. 3), so here the spherical pocket was employed, seen in Fig. 10. Compared to the above analysis, air flow inside bearing cavity with spacer structure is better. According to the turbulence intensity and vortexes number, the inside air flowwith double nozzles is superior to single nozzle structure. A further field synergy analysis shows that, the field synergy angles of double nozzles structure are smaller, which indicates the air flow performance is improved. As seen in Fig. 9(b), the four key structural parameters of the Type II lubrication device are the pipe inclined angle, the inner surface inclined angle, the nozzle outlet structure and the distance between the outlet and the inner surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure35-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure35-1.png",
        "caption": "Fig 35 Feed groove geometry",
        "texts": [
            " 9 8 3 Vo l 16 No 3 Appendix Feed-pressure f low The predicted feed pressure flow s's~ averaged over the load cycle appears to give a good guide to actual flows from engine bearings. This is substantiated by the experimental results on the NEL Engine Bearing Simulator ~ and from experiments on the 1.8 litre engine 6 . Apart from the full circumferential grooved bearing case these equations are all newly developed, superceding those of Cameron s\u00b0'S1 and are given here for easy access. For rectangular grooves The general comprehensive equation considering any groove extent (up to 270\u00b0), any groove aspect ratio, groove position (see notation defined in Fig 35) and any journal position is given below: Qp r? _ 1.25 - 0.25a/L [ D/L ] C3r e f 6(L/a - 1) 0.333 \" f l + 6(1 - a l L ) \" f2 where f l = (1 + e Cos01) s + (1 + e Cos02) 3 and f2 = [0 + 3 e Sin0 + e 2 (1.50 + 0.75 Sin 20) + e 3 (Sin0 -0 .333 Sin30)] \u00b02 (4) u1 For a small circular hole (Qp~)/(C3rPf) = 0.675 (hg/Cr) 3 (dh/L + 0.4) ''Ts (5) where d h = diameter of oil hole For a complete (360 \u00b0) circumferential groove (Qp~)/(C3r p f ) = 7rD (1 + 1.5e2)/(3(L - a)) (6) where L is the overall length of bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003033_s00170-012-4406-7-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003033_s00170-012-4406-7-Figure2-1.png",
        "caption": "Fig. 2 Definition of coordinate frames",
        "texts": [
            " In order to define five-axis motion three coordinate frames will be introduced as: XT\u2013YT\u2013ZT: The fixed coordinate frame attached to the tooltip of the cutter. XR\u2013YR\u2013ZR: The center of rotation of two rotary axes intersects at a point where machine rotary zero and the rotary zero coordinate frame are located. XW\u2013YW\u2013ZW: Workpiece coordinate frame attached to the blank workpiece mounted on the machine. In practical use, it is also called work offset or fixture offset. Detailed illustration of the coordinate frames is shown in Fig. 2. The vector W in Fig. 2 represents the offset distance from the workpiece coordinate frame to the rotary zero coordinate frames and denoted as W \u00bc Wxi\u00feWyj\u00feWzk. As it is stated before, the position and the orientation of the cutting tool relative to workpiece coordinate frame can be obtained using homogenous transformations sequentially. First, workpiece coordinate frame is translated by the offset vector W. Then, two consecutive rotations for C and B axis of the machine around ZR and YR coordinate frame axes are applied respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002238_iros.2010.5653006-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002238_iros.2010.5653006-Figure5-1.png",
        "caption": "Fig. 5 Cylindrical tube",
        "texts": [],
        "surrounding_texts": [
            "A. Performance Evaluation Parameters The prototype is shown in Fig. 6, and its specifications are shown in Table 1. In this study, we define the closing area and volume exclusion rates as performance evaluation parameters of the unit. Fig. 7 shows the schematic diagram of the closing area and volume exclusion rates. The closing area rate Ca is defined using the percentage as where S0 is the unit-opening space viewed from the axial direction at the initial state, and S is the unit-opening space viewed from the axial direction at the time of pressurization. The closing area rate shows the performance of the unit as a valve. The volume exclusion rate E is defined using the percentage as where V0 is the internal volume of the unit at the initial state, and V is the internal volume of the unit at the time of pressurization. The volume exclusion rate becomes an index of the transportation efficiency of the peristaltic pump. B. Performance Evaluation Fig. 8 shows the relationship between pressure and closing area rate, and Fig. 9 shows the relationship between pressure and volume exclusion rate. From these figures, it is confirmed that both the closing area and the volume exclusion rates are close to 100 %. Moreover, sufficient performance was demonstrated at a low pressure of about 0.03 MPa. In addition, when the thickness of cylindrical tube is changed, both the closing area and the volume exclusion rates have not changed. Fig. 10 shows the relationship between rise time and closing area rate, and Fig. 11 shows the relationship between fall time and closing area rate. From these figures, it is confirmed that the rise time is 1 second and the fall time is 3 second. We think that the difference of this response time was observed because the drive of a unit depends only on elastic power of the cylindrical tube at the time of fall time. Moreover, when the rubber thickness of the cylindrical tube is changed, it is confirmed that the rise becomes late and the fall becomes early as the rubber thickness becomes high. We think that it is because the rigidity of the cylindrical tube becomes high and the elastic force becomes high at the time of the unit returning as the rubber thickness becomes high. Therefore, we think that a pump using the suggested mechanism can demonstrate sufficient performance. ,100 0 0 \u00d7 \u2212 = S SSCa (5) ,100 0 0 \u00d7 \u2212 = V VVE (6) Fig.10 Relationship between rise time and closing area rate 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 Rise time [s] d C lo sin g ar ea ra te [% ] d Thickness of cylindrical tube 1.0 [mm] Thickness of cylindrical tube 1.5 [mm] Thickness of cylindrical tube 2.0 [mm] Fig.11 Relationship between fall time and closing area rate 0 20 40 60 80 100 0 0.5 1 1.5 2 2.5 3 Fall time [s] f C lo sin g ar ea ra te [% ] d Thick of cylindrical tube 1.0 [mm] Thick of cylindrical tube 1.5 [mm] Thick of cylindrical tube 2.0 [mm] Fig.9 Relationship between pressure and volume exclusion rate 0 20 40 60 80 100 0 0.01 0.02 0.03 0.04 Pressure [MPa] f V ol um e ex cl us io n ra te [% ] g"
        ]
    },
    {
        "image_filename": "designv10_10_0000694_0094-114x(96)84593-9-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000694_0094-114x(96)84593-9-Figure4-1.png",
        "caption": "Fig. 4. 3-RPS mechanism. (a) Mechanism sketch; (b) RPS branch; (c) SPR branch.",
        "texts": [
            " related; only two translations in the plane are constrained. The body has four degrees of freedom. The possible motions are the translation along the normal line and the three-dimensional rotations, the axes of which pass through the intersecting point. When three line vectors have a common point in space, there exist three rotations which are not independent rotations; their axes must pass through the common point. 4. 3 - R P S P A R A L L E L M E C H A N I S M W I T H T A N G E N T I A L A X E S Figure 4a shows a typical 3 DOF parallel mechanism, all its three branches are formed by revolute joint R, prismatic pair P and spherical pair S (RPS) kinematic chains. The axes of the revolute joints are tangential to the circumcircle of the triangle platform. The RPS branch is formed by connecting the kinematic pairs in series, as shown in Fig. 4b. Generally, the axis of the revolute pair and the axis of the prismatic pair are not orthogonal. A spherical joint is equivalent to three revolute pairs. The kinematic pairs can be represented using unit line vectors. If OA = 1, we have, $ , = ( 1 0 0;0 0 O) $ 2 = ( 0 0 0;~ 0 ~) ~ 2 + ~ 2 = 1 $ 3 = ( ~ 0 ~ ;0 0 o) $ , = ( 0 1 0 ; - /~ o ~) $5=(/~ o - ~ ; o 1 o) If the reciprocal screw Sr = (a b c; d e f), from equation (1) we have, td = f = b = 0 ~ta + tic = 0 e - fla + ac = 0 Solving the above equations, the reciprocal screw can be obtained, Since gr . g~ = 0, the reciprocal screw is a force line vector. To the SPR branch shown in Fig. 4c, we have, $1=(1 0 0;0 0 0) $ : = ( 0 1 0;0 0 O) $ 3 = ( 0 0 1;0 0 0) $~=(o 0 o;o 0 1) $5=(~ o /~;o i o) Therefore, the reciprocal line vector becomes, $r= 0 0 0;0 0 0) The above two reciprocal screws are all force line vectors, which pass through spherical centres in the direction perpendicular to the prismatic pair and which are co-planar with the revolute pair, respectively. If the revolute joint axis is normal to the prismatic pair axis, the force line vector will pass through the spherical centre and lie parallel to the revolute pair axis. The mechanism shown in Fig. 4a has three RPS branches. The upper platform subjects to three force line vectors which pass through a, b and c points and parallel with the axes of the A, B and C kinematic pairs, respectively. Initially, the upper and lower platforms are parallel, three forces line vectors do not intersect at a common point. The translations of the platform in the X and Y directions and the rotation around the Z axis are restricted. The possible motions of the platform are translation in the Z direction and rotations around the axis in the moving plane parallel to the X or Y axis or any axis in that platform plane",
            " It can be seen from a particular example that, if the platform is in the incline position and Aa = Bb, the line ab on the platform is parallel to $r and intersects with all three force line vectors, therefore the line ab can be a rotational axis. Furthermore, any lines parallel to ab and having the same Z coordinate as that of ab can be the rotational axes. If we make the mechanism upside down, let the platform that has three spherical pairs be the fixed frame. The mechanism is changed into a 3-SPR mechanism. Three branches are all SPR kinematic chains, as shown in Fig. 4c. Three reciprocal screw force line vectors pass through the spherical centres and parallel with each rotational axis, respectively. Initially, the upper and lower platforms are parallel with each other, three force line vectors are in a common plane on the lower platform. The X and Y axes in the fixed coordinate system can be the rotating axes, and any lines in the lower platform plane can be the rotating axis as well. The moving platform will rotate around the axis on the lower platform plane. When the upper platform is inclined, the situation will be more complicated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure14-14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure14-14-1.png",
        "caption": "FIGURE 14-14 Fuel flow meter. (Courtesy Fisher-Porter Co.)",
        "texts": [
            " If the number of cycles re quested is greater than one, the pressure values of the successive cycles sat Isfying the test are accumulated to build up an ensemble-averaged pressure cycle. The processing stage is automatically initiated at the end of the data acquisition. First, some checks on the acquired data are performed. Next, the number of cycles tested to satisfy the selection criteria is given, as are the mean and standard deviation values. Finally, the IMEP (indicated mean ef fective pressure) is calculated and the results printed out. Fuel Flow Meter The variable-area type of flow meter (fig. 14-14) provides rapid and instan taneous readings on the rate of flow of liquids or gases. An annular aperture or orifice exists between the head of the float and the inside of the wall of the tapered tube in which the float travels. The upward and downward forces acting on the float are in equilibrium so that the float assumes a definite elevation at a given flow rate. Since the net weight of the float is the same at all elevations, the pressure drop across the float must also be constant. There fore, increasing flow rate causes the float to move to a higher position with a correspondingly greater flow area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure13-1.png",
        "caption": "Fig. 13 \u2013 Discreet model \u2013 floor reinforcement beneath the seats.",
        "texts": [],
        "surrounding_texts": [
            "The object of study was a bus structure based on Volkswagen LT vans type: 2DX0AZ model LT produced by Automet in Sanok, Poland (Fig. 9). The basic technical specifications of the vehicle are presented in Table 2. The body of the bus was made of steel characterized by the following properties (Table 3): yield limit, Re_min = 198 MPa, tensile strength, Rm_min = 364 MPa, elongation, A5 = 22% Table 3 \u2013 Tensile characteristics for the material of the body. Strain [ ] Stress (MPa) 0.005 210.3 0.01 222.5 0.02 245.2 0.04 277.5 0.06 299.8 0.08 316.6 0.10 328.8 0.12 341.0 0.14 347.8 0.16 353.1 0.18 357.5 0.20 361.1 0.22 363.7 According to the manufacturer (VW) the frame of the vehicle was made of steel St 12.03 and St 37-2, whose strength properties are listed in table: St 12.03 yield limit, Re_min = 210 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% St 37-2 yield limit, Re_min = 235 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% Taking into account the quantitative changes in the material, i.e. the strain rate, the material model based on the assumed viscoplasticity of the material was obtained. A broad review of this characteristic is included in works [10,11]. The hardening velocity \u00c7 e equals elastic hardening velocity \u00c7 eel and viscoplastic hardening velocity, \u00c7 ev p \u00c7 e \u00bc\u00c7 eel \u00fe \u00c7 ev p; whereas the value of stress equals: s \u00bc E \u00c7 e \u00c7 ev p ; where E is the elasticity module. The finite element method uses the models of hardening at deformation velocity based on the abovementioned model, e. g. Cowper\u2013Symonds model [12]: s \u00bc\u00c5 s0 1 \u00fe \u00c7 e D 0 @ 1 A 1= p2 64 3 75; where \u00c5 s0 is the static yield limit, p, D are material constants, equalled to 5 and 40 s 1 respectively. The bodywork is supported by a frame on wheels (twin wheels in the rear). The bodywork was furnished with basic elements of bus interior, i.e. seats, seats frame, reinforcement of side wall, reinforcement of back wall, reinforcement of roof with a support structure for the emergency compartment, shelves and ventilation shaft and the air-conditioning system. It also includes glass panes which are glued to the reinforced body structure. All these elements constitute a load to the bodywork structure but do not alter its original shape. The first stage was to prepare the geometric model of the external shape of the structure. The strength calculations [13] were conducted using specialized software which implements an explicit algorithm for computing simultaneous differential equations [14]. The geometric model served as a basis for a discreet model of the bus bodywork, which was used for calculations using the finite element method. The body and frame were modelled using shell elements. These are rectangular four-node shell elements with 6 degrees of freedom in the node. The average size of the finite element is approximately 20 mm. Due to the fact that during a strength test the material may be subject to partial plastification (material nonlinearity) and large hinges may cause the configuration to change significantly (geometric nonlinearity), all finite elements are adapted to calculations with both types of nonlinearity [15]. The geometric model of the bus is shown in Figs. 10 and 11. The discrete model with division into finite elements is presented in Figs. 12 and 13. In total the discreet model comprises 105 151 finite elements on 102 879 nodes. The complete model has approximately 617 000 degrees of freedom. Since there are two rows of seats on the left side of the bus, the centre of gravity is somewhat moved leftwards relative to the axis of the vehicle. Its coordinates relative to the system, whose beginning is on the tilting edge above the rear wheel, are presented in Table 4. By tilting the bus on its right side the worst case was analysed (greater kinetic energy). From the law of conservation of energy: Ep \u00bc Ek; Table 4 \u2013 Moments of inertia relative to the edge of tilt (the Z axis along the tilting edge) (kg T m2). Ixx Iyy Izz 28130 28840 7226 Ixy Iyz Izx 2586 4036 6493 where Ep is the potential energy, Ek is the kinetic energy of rotational motion. Thus, in accordance with point the Regulations Ep \u00bc M g h1 \u00bc M g 0:8 \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 0 \u00fe B t\u00f0 \u00de2 q where M = Mk is the unladen kerb mass of the vehicle type if there are no occupant restraints, or Mt is the total effective vehicle mass when occupant restraints are fitted, and, Mt = Mk + k*Mm, where k = 0.5. h0 is the height (in metres) of the vehicle centre of gravity for the value of mass (M) chosen, t is the perpendicular distance (in metres) of the vehicle centre of gravity from its longitudinal vertical central plane, B is the perpendicular distance (in metres) of the vehicle's longitudinal vertical central plane to the axis of rotation in the rollover test, g is the gravitational constant, h1 is the height (in metres) of the vehicle centre of gravity in its starting, unstable position related to the horizontal lower plane of impact. Ek \u00bc I v2 2 where I is the moment of inertia relative to the temporary axis of rotation (Table 4), v is the angular velocity relative to the temporary axis of rotation. Therefore v \u00bc 2:558 rad=s Fig. 14 depicts main initial conditions of the analysis. An additional initial condition was the influence of gravity and the contact phenomena occurring on the contact points of the bus bodywork and the tilt plane as well as in the structural elements of the superstructure. Method of performing the strength test of the bus is shown in Fig. 14 while Fig. 15 presents the location of the seats inside the vehicle and the definition of residual space [16]."
        ]
    },
    {
        "image_filename": "designv10_10_0000886_1350650011541774-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000886_1350650011541774-Figure1-1.png",
        "caption": "Fig. 1 The experimental set-up",
        "texts": [
            " The present paper describes a quantitative study of the evolution of a separating film of lubricant in a ball-on-flat contact experiencing very rapid acceleration from rest. To measure EHD film thickness, this study used ultra-thin film interferometry in combination with a high-speed video camera. This enables lubricant film thickness to be determined at up to 1000 measurements per second. The technique has been fully detailed in reference [25]. The experimental set-up consists of a steel ball (Young\u2019s modulus E \u02c6 210 GPa and Poisson\u2019s ratio \u00ee \u02c6 0:3) loaded against the spacer layer-coated surface of a disc (E \u02c6 75 GPa and \u00ee \u02c6 0:25), as shown in Fig. 1. White light is shone through a microscope into the contact area, where division of amplitude on reflection produces an interferometric fringe pattern which is dependent on lubricant film thickness. The interfered light from the contact is directed to the entrance slit of a spectrometer where it is dispersed by wavelength and then captured by a black-and-white video camera. Both the disc and the ball can be independently driven by electric motors through their shafts. The speeds of the disc and ball are both recorded at the same rate as the sampling speed of the camera"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001907_physreve.78.061701-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001907_physreve.78.061701-Figure11-1.png",
        "caption": "FIG. 11. The helical director distribution for a simple cholesteric left . Initial directors are in the plane perpendicular to x, the helix axis. Directors are induced to rotate out of the transverse plane towards the helix axis, remaining in the n 0-x plane. A shear displacement u in the n 0 direction varies with x right .",
        "texts": [
            " Being distrib- uted with weight sin 0d 0, the majority of the n\u03020 and thus the rods associated with the domains are in the equatorial region. The dye units are accordingly most susceptible to the E vectors of the unpolarized light, rather than formerly where the E vector was uniquely along the polar axis of the distribution of directors. We now turn to an even more extreme case of directors initially localized to an equatorial region. C. Unpolarized light incident on a cholesteric photoelastomer Consider a planar distribution of directors, all of which are in the yz plane, Fig. 11 left . This is essentially the 2D equivalent of a standard polydomain. Practically, such a distribution could be realized using a cholesteric LCE with the helix axis parallel to the propagation direction of the incident unpolarized light. If the sample is thick compared with the pitch, one can adopt a coarse graining procedure. Variations over the length of the pitch can be integrated over and one is left with an effectively planar distribution of directors that would be uniformly illuminated by unpolarized light",
            " For our model thus far to be applicable one must be careful to make sure that while the sample is thick compared with the pitch of the cholesteric, it is thin compared with the absorption length of the film, which can be tuned by reducing the concentration of dye in the film, or illuminating with light that is not quite on resonance for the trans\u2192cis isomerization. Since all domains are oriented initially in plane i.e., 0= /2 for all domains we no longer need to integrate over the initial orientation of domains. Figure 11 right shows how the director can rotate towards the helix axis, moving in the plane of the original director and this axis. The plane in which n\u0302 rotates itself rotates with advancing x. There are now more strain possibilities than before. The deformation gradient tensor = k , Eq. 18 , can be augmented by zx and yx shears associated with the displacements u in the transverse plane shown in the figure. Such a shear is advantageous since there is elongation along the diagonal of the n\u03020-x plane section of the sample which accommodates the rotating director and its associated elongation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000615_20.573842-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000615_20.573842-Figure1-1.png",
        "caption": "Fig. 1. Model for the representation of a skewed rotor (only one quarter of rotor is shown): (a) a skewed rotor and (b) a multislice rotor.",
        "texts": [
            " The test current waveforms of two 11 kW skewed cage induction motors are used to verify the computed current waveforms. The following assumptions are made. 1) There are no leakage fluxes in the outer surface of the stator core and in the inner surface of the rotor core. 2) Because the iron cores are laminated, the eddy currents in the iron cores are neglected in the mathematical model. 3) The end effects are considered by coupling the electrical circuits into the FEM equations. 4) The motor in the axial direction is considered as composing of multislices as shown in Fig. 1. In each slice, the magnetic vector potential has an axial component only. The magnetic field is present in planes normal to the machine axis. Hence, the characteristics of the electromagnetic field of each slice are 2-D. The relationship between slices is based on the principles that the current flowing in the bars of one slice is the same as that which flows in the same bars of every other slice. According to the stated assumptions, the Maxwell\u2019s equations applied to all domains under investigation will give rise to the following equation: (1) where is the axial component of the magnetic vector potential, is the reluctivity of the material, and is the total current density"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001179_s0263574701004039-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001179_s0263574701004039-Figure2-1.png",
        "caption": "Fig. 2. Coordinate system of parallel manipulator.",
        "texts": [
            " The proposed planar manipulator is categorized as a PRR type, because one closed chain consists of the prismatic joint and two consecutive revolute joints. In contrast to well-known RPR type parallel manipulators, the actuator hardware of the proposed PRR configuration remains stationary, resulting in low inertia of moving parts. With appropriately selected kinematic parameters, listed in Table I, the reachable workspace of the manipulator is approximately 400 mm * 400 mm. Generalized coordinates for dynamic formulation of the manipulator are shown in Figure 2. The position and orientation of the platform at its mass center is written with respect to the fixed X-Y coordinate system as X\u0304P =[xP yP ]T (1) The origin of the fixed coordinate system is located on the point where imaginary extended lines of three actuators intersect. The distances of sliders from Ai, which correspond to solutions to an inverse kinematic problem, are expressed as \u0304=[ 1 2 3] T (2) Three linkages including associated coordinates are numbered with a subscript starting from the right linkage, in a counterclockwise direction. i is defined as the angle between the X-axis of the fixed frame and the ith intermediate link and i is the constant angle between the Xaxis of the fixed coordinate frame and the ith linear actuator. From the geometry of Figure 2, coordinates of point Ci are written as xci =xai + i cos i + l cos i wi(l ) sin i (3) yci =yai + i sin i + l sin i +wi(l ) cos i (4) where xai and yai are coordinates of point Ai and l is length of the linkage. wi(l ) is defined as a lateral deformation at the end of the linkage, Ci, due to flexibility of the linkage. Since length of the linkage is long compared with the thickness of the linkage, the linkage can be treated as an Euler-Bernoulli beam. The coordinates of point Ci can be formulated using the platform coordinates as xci =xp +x ci cos y ci sin (5) yci =yp +x ci sin +y ci cos (6) x ci and y ci are constant coordinates measured from mass center of the platform when is zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001321_j.snb.2005.06.013-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001321_j.snb.2005.06.013-Figure3-1.png",
        "caption": "Fig. 3. Cyclic voltammograms of a CMCPE at 20 mV s\u22121 in 0.1 M phosphate buffer (pH 7.0). (a) In the absence and (b) in the presence of 0.4 mM NADH; (c) as (a) and (d) as (b) for a unmodified carbon paste electrode.",
        "texts": [
            " There is also a change in the slope for pH values above 9.0, which can be ascribed to the deprotonation of the coumestan. The slope \u221228.8 mV/pH was obtained for pH values greater than 9.7, which is close to the Nernstian value of \u221229.5 mV for a two-electron, oneproton process. The pH relative to the intersection of two l o 3 m w I c b a t c a F e inear segments (pH 9.7) should therefore correspond to pKa1 f coumestan. .2. Catalytic oxidation of NADH at the coumestan odified carbon paste electrode Fig. 3, curve b, shows a cyclic voltammogram obtained ith a CMCPE in a solution which was 0.4 mM in NADH. t can be seen that there is a great increase in the anodic urrent compared to the cyclic voltammogram recorded in a uffer solution without NADH (curve a). The reason is that long with the anodic sweep of potential, NADH diffuses oward the electrode surface and reduces the coumestan(ox) to oumestan(red) while, the simultaneous oxidation of regenerted coumestan(red) causes an increase in the anodic current. or the same reason, the cathodic current of the modified lectrode is smaller in the presence of NADH, indicating that coumestan(ox) is consumed during a chemical step. The process could be expressed as follows: coumestan(red) ks\u2212\u2192coumestan(ox) + 2H+ + 2e (1) coumestan(ox) + NADH k\u2032 \u2212\u2192coumestan(red) + NAD+ (2) The catalytic effect can be seen directly when curve b is compared with curve d in Fig. 3. Curve d is obtained with an unmodified CPE. The decrease in overvoltage is about 240 mV at pH 7.0. The calibration plots of NADH catalytic oxidation at CMCPE at various solution pH (not shown) indicate that for pH values lower or higher than about 7, a decrease in the sensitivity (slope) observed. These results suggest a more effective interaction of the NADH with o-quinone groups of the coumestan at neutral pH with respect to acidic or basic pH. The calibration plots (not shown) illustrate that the peak current was proportional to the NADH concentration in the range from 40"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001516_acs.940-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001516_acs.940-Figure1-1.png",
        "caption": "Figure 1. Four-rotor aircraft configuration.",
        "texts": [
            " A four-rotor craft is controlled by varying the angular speed of each one of the rotors. The force fi produced by motor i is proportional to the square of the angular speed, that is fi \u00bc ko2 i : Copyright # 2007 John Wiley & Sons, Ltd. Int. J. Adapt. Control Signal Process. 2007; 21:189\u2013204 DOI: 10.1002/acs 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 f3; while the roll torque is a function of f2 f4; and the yaw torque is the sum tM1 \u00fe tM2 \u00fe tM3 \u00fe tM4 ; where tMi is the reaction torque of motor i due to shaft acceleration and the blade\u2019s drag. Ge \u00bc f#ie; #; e; #keg and Gb \u00bc f#ib; #; b; #kbg denote the inertial and the fixed-body frames, respectively, and qe \u00bc \u00bdxe ye ze c y f T \u00bc \u00bdn g T is the generalized coordinates which describe the vehicle\u2019s position and orientation. n 2 R3 denotes the position of the vehicle\u2019s centre of mass relative to the inertial frame, and g 2 R3 are the three Euler angles \u00f0c y f\u00de yaw, pitch and roll, which represent the aircraft\u2019s orientation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure19-1.png",
        "caption": "Fig. 19 \u2013 Residual space not infringed in a deformed bus body.",
        "texts": [
            " A crucial function in limiting displacements was performed by the rear wall. The body of the bus was additionally reinforced and stiffened by such elements as: frame in the rear wall in the position of the door, reinforcing profiles for the roof frame, reinforcing profiles for the sidewalls, platform under the seats and seat frames. To sum up, the bodywork of the Automet 2DX0AZ bus satisfies the requirements established in Regulation No. 66 of UN/ECE in such a way that none of the deformed parts of the vehicle encroach on the residual space (Fig. 19). In the case of buses, manufacturers prefer the equivalent method of rollover test using body sections [17]. This is due to significantly lower costs of such tests. However, in the case of buses based on van structures such tests are impossible to perform because it is difficult to choose a representative section. In the case of vans, the strength of their structure during rollover determined by the frame of rear door and the driver's cabin which is often stiffened from the back by reinforcements to the whole superstructure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001891_tro.2008.926863-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001891_tro.2008.926863-Figure1-1.png",
        "caption": "Fig. 1. 3PRR mechanism\u2014kinematical structure.",
        "texts": [
            " A new method of AM changing is possible by encircling an \u03b1-curve in the joint space, as is shown in Section IV, for 3PRR and 3RPR mechanisms. In addition, clearance in the 1552-3098/$25.00 \u00a9 2008 IEEE joints, which is relevant especially to micromechanisms, may cause AM changing, and is shortly treated in Section V. The mathematic tool for analyzing these three ways of AM changing is given in the next section. As an example of AM changing, we utilize the 3PRR planar mechanism kinematical structure shown in Fig. 1. The mechanism consists of an equilateral triangle platform, whose center is the point P . The platform pose is determined by x- and y-coordinates of point P and by the platform orientation \u03b8. Points P1 , P2 , and P3 are located on the platform in an equal distance r from the platform center P . The length of each of the links that connect the actuators with the platform is l, and the angles between those links and x-axis are \u03b8i (i = 1, 2, 3). The linear actuators determine the position of the points Mi ",
            " The geometric condition for this case, which was developed for 3RPR mechanism [4] and for 3RRR mechanism [11], is also valid for 3PRR mechanism, and can simply be written as (M2x \u2212 M1x) sin(\u03b82) sin(\u03b83 \u2212 \u03b81) + [(M3x \u2212M1x) sin(\u03b83)\u2212M3y cos(\u03b83)] sin(\u03b81 \u2212 \u03b82) = 0 (2) where Mix and Miy are the x- and y-coordinates of the ith actuator. The singularity map shows all the combinations of the actuator locations in which direct kinematic singularities occur. The singularities occur on a 2-D manifold in the joint space, where DKSs coincide. In the case of a 3RPR mechanism, Zein et al. [4] presented 2-D sections of the 3-D singularity map, for a specific length of one of the actuators. In contrast, for a 3PRR mechanism having parallel actuators, as in Fig. 1, a 1-D curve of (M3x \u2212 M1x ) vs. (M2x \u2212 M1x ) is sufficient to show the whole picture. For simplicity, and without loss of generality, assume that M1x = 0. The singularity map for the mechanism of Fig. 1 is described in Fig. 2, followed by its derivation in the next section. The dashed curves represent actuator combinations where at least two DKSs coincide. We denote them as direct kinematic singularity curves [8], since the geometric condition (2) of intersection between the links MiPi is satisfied, meaning that the mechanism is singular. Note that not all the DKSs coincide on the singularity curves (e.g., two coincide and four do not); consequently, nonsingular solutions may exist even on these curves",
            " In this case, the actuators cannot pass to the adjacent gray area, and the mechanism can only stay in its original AM or switch to the other AM that is singular on that curve. This is a singular AM changing that should be avoided. On the other hand, if the mechanism AM is not one of these two, the mechanism can pass to the adjacent area smoothly, while staying in its original AM, as if the singularity curve does not exist. The singularity map can be calculated using (2), along with the following intuitive geometric equations that relates between the actuators\u2019 locations (see Fig. 1): l cos (\u03b81) + r \u221a 3 cos (\u03b8 \u2212 30\u25e6) = M2x + l cos (\u03b82) l sin (\u03b81) + r \u221a 3 sin (\u03b8 \u2212 30\u25e6) = l sin (\u03b82) l cos (\u03b81) + r \u221a 3 cos (\u03b8 + 30\u25e6) = M3x + l cos (\u03b83) l sin (\u03b81) + r \u221a 3 sin (\u03b8 + 30\u25e6) = M3y + l sin (\u03b83) . (3) This problem can be solved numerically, by running, e.g., the platform orientation angle \u03b8 from 0\u25e6 to 360\u25e6, yielding five equations, (2) and (3), in five unknowns \u03b81 , \u03b82 , \u03b83 , M2x , and M3x . Solving these equations yields some discrete points in the joint space M2x \u2212 M3x , which are part of the singularity curve",
            " This technological process requires maintaining relatively large gaps between links in order to maintain the mechanism\u2019s motion. These gaps result in clearances between moving parts that can be as large as the same order of magnitude as the typical dimensions of the mechanism itself. These were the reasons in traditional machinery during the eighteen century that caused inaccuracy of the mechanism, shocks, vibrations, noise, and wear at the joints, whereas the high-precision manufacturing achievable in the macroworld today diminishes these effects. As shown in Fig. 1, the physical length of the links, which are near the actuators, is l, meaning that under zero clearance, this would be the distance between each actuator and the corresponding point on the platform. It is likely that when micromechanisms are considered such as manufactured by MEMS techniques, large clearances are introduced into the revolute joints. The clearance is expressed by an offset between the axes of the bearing and the journal. Therefore, these axes are not coincident, but may be distant from each other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure8-1.png",
        "caption": "Fig. 8 (a) 2-(RRR)ERC-RA(RRR)Y RA PPR-PKC with a PPR V-chain added; (b) 2-(RRR)ERCRA(RRR)Y RA PPR-PKC.",
        "texts": [
            " The leg-wrench systems of the RA(RRR)Y RA leg [Fig. 7(e)] and the (RR)Y (RRR)Y A leg [Fig. 7(f)] are both a 1-\u03b6\u221e-system. The axis of the basis wrench \u03b6\u221e is perpendicular to the axes of all the R joints within a same leg. All the legs for PPR-PMs obtained are listed in Table 1. For legs with ci = 0, one are interested in legs with simple structures: RUS, PUS and UPS legs [1]. By assembling two or more legs for PPR-PKCs shown in Table 1, we obtain PMs in which the moving platform can undergo a PPR motion (Fig. 8). The geometric relation between different legs has also been shown in the notation of legs we proposed in Section 7. To guarantee that the DOF of the moving platform is three, the wrench system of the PKC must be a 1-\u03b60-2-\u03b6\u221esystem (Fig. 1). It is found that not arbitrary set of three legs can be used 6 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/15/2018 Term to construct a 3-legged PPR-PM since the wrench system of the PKC may be not a 1-\u03b60-2-\u03b6\u221e-system. For example, a set of three (RRR)ERC legs cannot be used since the wrench system of a 3-(RRR)ERC is a 1-\u03b60-1-\u03b6\u221e-system",
            " Due to the large number of PPR-PKCs and space limitation, only the family of PPR-PKCs, which are denoted by the valid combination of sets of leg-wrench systems, are listed Table 2. Using Tables 1 and 2, PPR-PKCs of different families can be obtained. Let us take PPR-PKCs of family 3 (Table 1) as an example. A PPR-PKC of family 3 has two legs with a 1-\u03b60-1-\u03b6\u221e-system and one leg with a 1-\u03b6\u221e-system. These required legs can be selected from Table 1. By assembling these legs, we obtain PPR-PKCs of family 3. For example, a set of two (RRR)ERC legs with a 1-\u03b60-1-\u03b6\u221e-system and one RA(RRR)Y RA leg with a 1-\u03b6\u221e-system can be used to construct a 2-(RRR)ERC-RA(RRR)Y RA PPR-PKC [Fig. 8(b)]. A set of two (RRR)ERC legs with 1-\u03b60-1-\u03b6\u221e-system and one (RR)Y (RRR)Y A legs with a 1-\u03b6\u221e-system can be used to construct a 2-(RRR)ERC-(RR)Y (RRR)Y A PPR-PKC (Fig. 9). Copyright  2004 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http://p Table 2 Combination of sets of leg-wrench systems. ci leg-wrench system Family 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3 1-\u03b60-2-\u03b6\u221e m1 2 1-\u03b60-1-\u03b6\u221e m2 2 2 1 1 1 1 1 2-\u03b6\u221e m3 1 1 1 1 2 1 1 1 1 1-\u03b60 m4 1 1 1 2 1 1 2 1 1-\u03b6\u221e m5 1 1 1 1 1 1 2 0 omitted m6 1 1 1 Here, \u22116 i=1 mi = 3, m1 > 0 Base Moving platform Fig",
            " The detailed discussions are omitted here due to the space limitation. For practical reasons, the selection of actuated joints for m- Copyright  2004 by ASME ms of Use: http://www.asme.org/about-asme/terms-of-use Down legged PPR-PMs 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. For example, the possible 3-legged PPR-PM corresponding to the 2-(RRR)ERC-RA(RRR)Y RA PPR-PKC [Fig. 8(b)] is the 2-(RRR)ERC-RA(RRR)Y RA PPR-PM [Fig. 11(a)]. The actuation wrenches of all the actuated joints are shown in Figs. 10(a) and 10(c). Following the procedure for the validity detection of the actuated joints, it can be proved that the set of actuated joints is valid. The possible 3-legged PPR-PM corresponding to the 2-(RRR)ERC-(RR)Y (RRR)Y APPR-PKC (Fig. 9) is the 2- (RRR)ERC-(RR)Y (RRR)Y A PPR-PM [Fig. 11(b)]. The actuation wrenches of all the actuated joints are shown in Figs. 10(b) and 10(c)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002208_tie.2009.2031190-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002208_tie.2009.2031190-Figure4-1.png",
        "caption": "Fig. 4. 3-D Finite-element analysis of demonstrator machine showing fluxdensity shading plot.",
        "texts": [
            " All important harmonics other than the fundamental are very significantly attenuated, predominantly due to the distribution factor of the phase windings. Fifth and seventh harmonics are reduced to 8.7% and 13.4%, respectively, while 11th and 13th harmonics are almost completely eliminated. The choice of magnet pole is also made to give very low fifth-harmonic flux harmonics; therefore, the overall arrangement should give a high-quality sine-wave back electromotive force (EMF). Figs. 3 and 4 show 2-D and 3-D finite-element models of the machine on no load: The narrow core-back depths are apparent. Fig. 4 shows how peak flux densities in the teeth and rotor core back are virtually equal. Magnet loss can be a further source of inefficiency. Losses due to asynchronous stator-winding fields are negligible in machines of low magnetic loading\u2014this is the case at the lightly loaded night-time condition. Tooth-ripple harmonics reflected back into the magnets are more problematical, since they are load independent. The reluctance perturbation seen from the rotor, due to slotting of the stator, can be greatly reduced by combining a small slot opening with a large airgap length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000608_60.815019-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000608_60.815019-Figure2-1.png",
        "caption": "Fig. 2 (a) Cross section with equal stator and rotor number of slots. 'pl is the angle of a slot pitch. (b) Motor corresponds to the half-stator slot pitch. 5 and care the unit vectors normal to the corresponding surfaces",
        "texts": [
            " In most cases, in this type of machine, the winding temperature in space No. 1 of Fig. 1 is approximately a few degrees lower than the winding temperature in the core, while the winding temperature in space No2 is a few degrees higher. Therefore, the axial heat that flows from the end winding in space No. 2 to the actual radial dimensions of the rotor are kept constant, while the tangential dimensions are modified in proportion to the ratio NI/N2. Because of the symmetry, only the section which corresponds to the half stator slot pitch is dealt with in Fig. 2. 1- 998 111. LOSSES Due to the above assumptions, the copper losses of the windings in the core and the iron losses, are taken into account. In the transient condition, the resistance of the windings and the winding currents are 'calculated as described later in Section V. For the calculation of the iron losses it is assumed that the magnetic flux density in the yoke is predominantly circumferential and the magnetic flux density in the teeth is predominantly radial [I. Both of them have a sinusoidal distribution on the circumference but are constant on the radial direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000764_s0094-114x(97)00022-0-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000764_s0094-114x(97)00022-0-Figure6-1.png",
        "caption": "Fig. 6. Intersection of shaper tooth surface and axis of meshing i-1 by planes FI, and FI:.",
        "texts": [
            " 3) Er-- instantaneous value of the shortest center distance between the pinion and the grinding disk (Fig. 3) l~d i sp l acemen t of the grinding disk in the direction of the pinion axis (Fig. 3) a~--parabola coefficient of the parabolic function Si--coordinate system u~0k~--surface parameters of the shaper 0o~--angular width of the space of the shaper on the base circle (Fig. 5) r ,~posi t ion vector in system S,(i = s, 1, 2) rh~--radius of the base circle of the shaper (Fig. 5) ~o--pressure angle [Fig. 6 (b)] ~--proflle angle for determination of pointing (Fig. 7) n,, N~--unit normal and normal (Fig. 5) to the shaper surface Mj~--matrix of coordinate transformation from system S~ to system S, E,--shaper (i = s), pinion (i = 1) or gear (i --- 2) tooth surface ~,--angle of rotation of the shaper (i = s) or face gear (i = 2) (Fig. 2) v,m~--~relative velocity vector ~c~-'~--relative angular velocity vector E--shortes t center distance between the shaper and the face gear (Fig. 2) X,, Y,, Z,---coordinates of the axis of meshing m.,,--gear ratio R,--inner (i = 1) and outer (i = 2) radii of face gear free of undercutting and pointing (Fig. 8) Pj---diametral pitch A/, Aq--segments for the determination of pointing [Fig. 6 (a)] vd~---velocity of contact point that moves over the tooth surface of the shaper L,----limiting line on the shaper tooth surface (i = s) (Fig. 9), or face-gear tooth surface (i = g) L--fillet line (Fig. 10) 87 88 F.L. Litvin et al. 0k,.--shaper parameter at the addendum cylinder r~,~--radius of the addendum cylinder of the shaper L,--limiting length of the shaper for avoidance of undercutting (Fig. 8) 7 shaft angle 05/ angles of rotation of pinion (i = l), and face gear (i = 2) being in mesh A~--transmission errors [Figs 14 (a), (b), (c)] v~(s)--velocity vector of the shaper in S~ v;2--velocity vector of the face gear in S~ o,'\"--angular velocity vector of the face gear in S~ p--screw parameter 1",
            " Both approaches have been applied by the authors; the results are compared but only the second one, the simpler one, is presented in this paper. This approach is based on the following considerations: (1) Drawings of Fig. 5 show that xs = 0 is the plane of symmetry of the shaper space. At a position of the shaper when \u00a2~ = 0, coordinate system & coincides with Sh (Fig. 2) and the axis of meshing I-I belongs to the plane x~ = 0. (2) It is evident that cross-sections of the shaper tooth surface, produced by planes that are parallel to xs axis, represent the same involute curves. Two such planes, H~ and I-I_,, are shown in Fig. 6(a). Plane Hi which is perpendicular to zs (it is parallel to x0 intersects the axis of meshing I-I at a point P~ that belongs to the axis of symmetry of the cross-section of the space of the shaper. Figures 6(b) and 7 show points P~ and P2 of the intersection of the axis of meshing I-I planes HI and I-I2, respectively. (3) A normal to the shaper tooth surface is perpendicular to the z~ - axis and therefore it lies in plane 1-I,. In accordance to the definition of the axes of meshing the common normal to the surfaces of the shaper and the face-gear passes through the axis of meshing",
            " 7) of the intersection of the tangents to the profiles is the point of intersection of the real cross-section profiles of the face gear. (5) Using the consideration discussed above, we are able now to derive the equations for the determination of the outer radius R2 of the face gear for the zone of pointing. Step I: Vector equation (Fig. 7) yields that [4]: O~A + ANI + N t K = OsK - t a n ~ - - w h e r e 0o~ is represented by equation (4). (13) 2Pdrm _ 0o~ (14) N~ Meshing of orthogonal offset face-gear drive 95 Step 2: We consider that point P~ belongs to the pitch cylinder of the shaper [Fig. 6(a)], and the location of P2 with respect to P~ is determined with segments AI and Aq [fig. 6(a)]. Drawings of Figs 6(a), 6(b) and 7 yield Aq = O~P: - O~P, = rb~ rb~ _ N~ / c o s a zo _-- cos ~'] (15) cos~ cos~0 2 / '~ \\ cos~ / AI= Aq (16) tan y~ Step 3: The location of plane H2 is determined with parameter L2 [Fig. 6(a)], where L2 = rp + Aq = Nscos ~o (17) tan 7s 2PdCOS ~ tan y~ where tan 7~ = 1/m2s. The outer radius R2 of the face gear (Fig. 8) is represented as R: =,j-k-;+ L~ (18) M M T 33/I-2 D 96 F.L. Litvin et al. Undercutting can be avoided if the face-gear tooth surface is free of singularities. This can be achieved by limiting of the inner radius of the face gear. An effective approach for the determination of singularities of the generated surface is proposed in [2] and [4]. The approach is based on application of the following equations \u00a5~s ) + \u00a5~s2) = 0 (19) 0fdu 0f 00ks 0fd4,s OUs dt + dOks dt t- 0dpl d t = 0 (20) Vectors of equation (19) are represented in coordinate system Ss; v~ ~ is the velocity of a contact point that moves over the tooth surface of the shaper; v~ ~21 is the relative velocity of a shaper point with respect to the face gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.2-1.png",
        "caption": "Figure 6.2 the z axis. Current element I de symmetrically located at the origin 0 and oriented along",
        "texts": [
            " A short conducting linear wire element carrying harmonically oscillating current is one of the fundamental sources of radiation in antenna theory. A Hertzian dipole consisting of two harmonically oscillating electric charges also behaves like an equivalent short current element. In antenna literature, the terms short current element, Hertzian dipole, and simply the electric dipole are often used interchangeably to represent a basic source of radiation. Consider a current element of moment I de (where I is a phasor current) oriented along the z axis and placed symmetrically at the origin of a special coordinate system shown in Figure 6.2. The medium is assumed to be linear, homogeneous, isotropic, lossless, and of infinite extent. We wish to determine RADIATION FROM A SHORT CURRENT ELEMENT 201 the fields produced by the current element at any field point P(r, 6,4). Note that with a similarly oriented Hertzian dipole of moment q de, q being the electric charge, the desired fields can be obtained from the current element fields by replacing I by jwq. At first, we will use (6.20) to obtain A due to the current element. With reference to Figure 6.1 and equation (6.20), it can be seen that for the linear current element oriented along the z axis as in Figure 6.2, we have J dv\u2019 = I de = I (z\u2019) dz\u2019 2, (6.22) where dependence of current on the source point location is explicitly indicated. In the present case we can write R = Ir - r\u20191 2 r = r. (6.23) Thus for the present case the vector potential at the field point P is from (6.20) is (6.24) 202 ANTENNAS AND RADIATION We will assume I ( z \u2019 ) = I , meaning the current amplitude is constant along the element and for sufficiently small dl. So we approximate (6.23) by (6.25) Using the relationship of 2 = i cos 0 - 6 sin 0, we obtain the spherical components of A at P given by A, = A, cos 0 AQ = -A, sin 0 A#, = 0, (6",
            " In contrast to the plane electromagnetic waves in free space, the power carried by the spherical waves varies inversely as 1/r2, which implies that the total power carried by the wave is finite, and hence spherical waves are amenable to generation in unbounded space. Power considerations will be taken up in a later section. 6.3.3 Near Zone and Far Zone Fields Examination of the total field amplitudes versus distance from the source in a given direction can be used to characterize the behavior of the near zone and far zone fields. For this purpose we choose the broad side direction 8 = 90\" (Figure 6.2) in which the field components EQ and H4 are maximum and E, = 0. RADIATION FROM A SHORT CURRENT ELEMENT 207 where EQ and H@ are obtained from (6.28) and (6.27), respectively. The transition distance (pr = 1) at which the nature of the field variation changes is clearly evident in Figure 6.3, which indicates that in the reactive near field region (also called the inductionjeld region), (Eel decays off as l / r 3 (or 60 dB/decade of distance) and decays off as l/r2 (or 4.0 dB/decade of distance). In the far field region (pr > 1) both ]Eel and IH4I fall off as 1 / ~ (or 20 dB per decade of distance)",
            " carrying sinusoidal current of peak value 10 cos (q cos 6 ) - cos (q ) K=-- 1 (6.192~) 27r sin 6 where ,B = 27r/X, X is the wavelength in the medium, and q = is the intrinsic impedance ofthe medium. Note that for free space 7 = 70 = 1207r R. We will apply the theory described in the previous section to a two-element antenna array. The array consists of two z-directed half-wave dipoles separated by a distance a and placed symmetrically with respect to the z axis and along the TC axis of a coordinate system shown in Figure 6.2 1. As shown, the dipoles 1 and 2 are excited by currents 10.42 and I o h , respectively. As shown in Figure 6.2 1, we have U 1111 = 10, a1 = 0, U l = -- 2 From (6.185) we have COS $1 = sin cos 4, cos $2 = - sin 6 cos 4, where (O,$) specify the far field point direction. 260 ANTENNAS AND RADIATION With the parameters above we obtain the un-normalized array factors from (6.190) as (6.193) The complete expression for the far field produced by the antennas array is now obtained by using (6.188) and (6.189) as sin Q cos ($ainHcoso- - \") 2 . (6.194) cos (5 cos 6 ) X ANTENNA ARRAYS 261 Note that in (6.194) the normalized element and array factors field patterns for the antenna array are cos (5 cos 8 ) f (8) = (6",
            " Although we consider wires of circular cross sections, the results can be applied to linear sections PCB traces with rectangular cross section provided that we identify a conductive strip of width W = 4a [l]. We will consider the emissions from a current element of length t, small compared with a wavelength and which carries a current Iejut with w = 27rf. The complete electric fields radiated by a small current element have been discussed in Section 6.3. We shall use the same geometry shown in Figure 6.2. except that for convenience we use the z-directed current element as I!? instead of I d t2 . The far zone electric field produced by the element is given by (6.35a). We can write the amplitude of the maximum electric field, produced in the broad side direction 6 = 7r/2, as EMISSIONS FROM LINEAR ELEMENTS 337 where all the parameters are as defined earlier. Assuming free space, we obtain 7 1 4 E,,,,, = 27r x 10- - f ; T which gives the maximum electric field amplitude produced by a short current element (i",
            " Basic electric and magnetic sources of radiation are the electric (Hertzian) dipole or a small current element and magnetic dipole or the small loop of current, respectively. The complete fields produced by the sources above, SHIELDING EFFECTIVENESS: NEAR FIELD ILLUMINATION 359 and the behavior of the fields in various regions of space were described in Sections 6.3 and 6.4. The far zone fields produced by an electric dipole in free space and located at the origin of a spherical coordinate system, as shown in Figure 6.2, can be written as (9.16) where q) = d-lo/to = intrinsic impedance of free space, and Ef) is given by (6.35a). Generally, the wave impedance of the far zone wave given by (9.16) is defined by (9.17) where the superscript \u201ce\u201d indicates it applies to the electric dipole fields. It is clear from (9.17) that in the far zone, the wave impedance for the electric dipole equals the intrinsic impedance ofthe medium, Z;k = 110. 360 ELECTROMAGNETIC SHIELDING Similarly the far zone fields produced by a magnetic dipole (or small current loop) in free space and located at the origin of a spherical coordinate system, as shown in Figure 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002026_tmag.2009.2012785-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002026_tmag.2009.2012785-Figure2-1.png",
        "caption": "Fig. 2. Analyzed model (1/2 region).",
        "texts": [],
        "surrounding_texts": [
            "Here, the distribution of flux density vectors and the losses of the SCIM with the 4/3 slot pitch skewed rotor and that with rotor without skew are calculated. The calculated losses are compared with measured ones to clarify the validity of the 3-D analysis. Further more, the bar-current and the torque are calculated. Fig. 4 shows the distributions of flux density vectors of SCIM with the 4/3 slot pitch skewed rotor. The flux density vectors of the upper section are larger than those of the lower section. The imbalance of the magnetic flux distributions makes the loss distributions imbalanced in the SCIM with skewed rotor. Fig. 5 shows the contours of eddy current loss. The eddy current loss in the tip of teeth and the surface of the rotor is especially large. From Fig. 5(b), the eddy current loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 6 shows the contours of hysteresis loss. The hysteresis loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 7 shows the loss of the SCIM. The iron loss of the SCIM is decreased by the skewed rotor. The calculated total losses agree well with the measured ones. Fig. 8 shows the waveforms of bar-current. The ripple of the bar-current of the motor with the 4/3 slot pitch skewed rotor is smaller than that of the motor with the rotor without skew. Fig. 9 shows the torque waveforms. The average torque of the motor with the 4/3 slot pitch skewed rotor is larger than that of the motor with the rotor without skew, and the torque ripple of the SCIM is decreased by the skewed rotor. B. Effects of Skew Angle of Rotor on Motor\u2019s Characteristics Here, it is numerically clarified that the effects of the skew angle of the rotor of the SCIM on the secondary current, torque, loss and efficiency characteristics. Fig. 10 shows the waveforms of bar-current. The ripple of the bar-current becomes small as the rotor skew angle increases. rotor skew angle increases. The average torque once increases and then decreases as the rotor skew angle increases. Fig. 13 shows the loss characteristics. The iron loss becomes small as the rotor skew angle increases. Fig. 14 shows the efficiency characteristics. In this calculation, the efficiency approaches to the maximum value when the skew angle is 4/3 slot pitch. Table II shows the discretization data and CPU time. V. CONCLUSION In this paper, the influence that the skew angle of the squirrelcage induction motor exerted on the secondary current, torque, loss and efficiency characteristics was clarified by using a threedimensional finite element method. As a result, it has been understood that torque ripple and iron loss decreases as the rotor skew angle increases in this model. Moreover, it has been understood that the average torque once increases, then decreases as the rotor skew angle increases. The efficiency is the best when the rotor is skewed 4/3 slot pitch rotor angle. REFERENCES [1] T. Yamaguchi, Y. Kawase, and S. Sano, \u201c3-D finite-element analysis of skewed squirrel-cage induction motor,\u201d IEEE Trans. Magn., vol. 40, no. 2/2, pp. 969\u2013972, Mar. 2004. [2] S. Ito and Y. Kawase, Computer Aided Engineering of Electric and Electronic Apparatus Using Finite Element Method. Japan: Morikita, 2000. [3] K. Yamazaki, \u201cLoss calculation of induction motors considering harmonic electromagnetic field in stator and rotor,\u201d IEEJ Trans. IA, vol. 123, no. 4, pp. 392\u2013400, 2003. [4] Y. Kawase, T. Yamaguchi, M. Watanabe, and H. Shiota, \u201cNovel mesh modification method using Lapace equation for 3-D dynamic finite element analysis,\u201d in Conf. Record 16th Conf. Comput. Electromagn. Fields, 2007, vol. PB7-15. [5] Y. Kawase, T. Yamaguchi, M. Watanabe, N. Toida, Z. Tu, and N. Minoshima, \u201c3-D finite element analysis of skewed squirrel-cage induction motor using novel mesh modification method,\u201d in Int. Symp. Electromagn. Fields in Mechatron., Elect. Electron. Eng., 2007, pp. 269\u2013270."
        ]
    },
    {
        "image_filename": "designv10_10_0003715_1464419314522372-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003715_1464419314522372-Figure2-1.png",
        "caption": "Figure 2. Schematic diagram of ball bearing vibration system. (a) Vibration transmission process, and (b) schematic diagram of a ball bearing.",
        "texts": [
            " , n \u00f08\u00de Balls continuously contact on the surfaces at different points during rotation. The radial displacement of any angular position for the ith ball is expressed as rbi \u00bc xbi cos i \u00fe ybi sin i \u00f09\u00de Bearing surface damage determines the spectrum of excitation force; simultaneously, the vibration transmission is determined by dynamic contact relationship. Hence, the final vibration spectrum characteristics are determined by these two factors. Ball bearings vibration transmission process caused by external load is a complex nonlinear dynamical system. As shown in Figure 2, vibration in the form of an elastic wave propagates outward through the overall process of inner race\u2013balls\u2013outer race\u2013pedestal, as it is usually to be measured on the pedestal by an accelerometer. xi, yi\u00f0 \u00de, xo, yo\u00f0 \u00de, xb, yb\u00f0 \u00de and xp, yp are, respectively, the motion coordinate of the inner at WEST VIRGINA UNIV on July 9, 2015pik.sagepub.comDownloaded from and outer race, ball and pedestal, as shown in Figure 2(a). Figure 3 shows the contact relationship and coordinate distribution of the ball bearing components. Having obtained the radial displacement of the ith ball in its contact direction, therefore, the contact deflections of the ith ball are provided geometrical considerations by the following expression (refer to Figures 2 to 3) inneri \u00bc xi xbi\u00f0 \u00de cos i \u00fe yi ybi\u00f0 \u00de sin i \u00f010\u00de outeri \u00bc xbi xo\u00f0 \u00de cos i \u00fe ybi xo\u00f0 \u00de sin i \u00f011\u00de It is clear that the nonlinear contact deformation is equal to the sum of the vertical components of the contact reactions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002676_1.4006791-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002676_1.4006791-Figure3-1.png",
        "caption": "Fig. 3 The kinematic quantities of the DFTV (a) and SHTV (b)",
        "texts": [
            " The radial coordinates r1 and r3 of the roller disks contact points change and so does the geometric ratio srID defined as srID \u00bc r1 r3 (1) The radii of curvature of the disks at the roller\u2013disks contacts can be expressed in a dimensionless form as a function of the cone angle h and the tilting angle c (see Fig. 2) as ~r11 \u00bc ~r1 cos\u00f0h\u00fe c\u00de (2) ~r33 \u00bc ~r3 cos\u00f0h c\u00de (3) where, the dimensionless wrapping radii ~r1 and ~r3 of the input and output disks are simply written as ~r1 \u00bc r1 r0 \u00bc 1\u00fe k cos\u00f0h\u00fe c\u00de (4) ~r3 \u00bc r3 r0 \u00bc 1\u00fe k cos\u00f0h c\u00de (5) The expression of the roller rolling radius r2 is r2\u00bc r0 sin h in the case of the single-roller variator, whereas, using the condition of zero spin at unit speed ratio the rolling radius for the DFTV is r2\u00bc (r0\u00fe e)sin(a/2). 2.2 Kinematic Quantities. Figure 3 shows the angular velocities triangles for the DFTV (see Fig. 3(a)) and for the SHTV variator (see Fig. 3(b)), respectively. The real speed ratio is defined as the ratio between the output disk angular velocity jx3j and the input disk angular velocity jx1j sr \u00bc x3j j x1j j (6) Beside this quantity, also the creep and slip coefficients are utilized in the scientific literature related to traction drives to take into account the percentage difference of the velocities of the sliding contact pairs. In the most general case of double roller toroidal drive, we define the input and output creep coefficients, respectively, Crin and Crout , as 071005-2 / Vol",
            " Spin is a parasitic effect caused by the geometry of the roller and toroidal cavity and should be reduced as much as possible, as it causes significant energy dissipation and reduces the traction performance: at any given torque, the amount of creep needed to transmit the torque increases in presence of spin. Of course spin depends on the speed ratio and, for particular toroidal geometries and speed ratio values, it may even disappear. So let us now consider a single-roller toroidal variator at geometric ratio srID \u00bc 1. Figure 3(b) shows that the point H, which represents the point of intersection of the tangents to the toroidal circular cross section about the roller\u2013disk contact points, does not always coincide with the point X, defined as the intersection point of the roller and disk rotation axes. The angular velocity vectors of the roller relative to the input and output disks x21\u00bcx2 x1 and x23\u00bcx2 x3, respectively, have, in general, nonzero-spin components x21spin and x23spin (the reader is referred to Ref. [7] for a more detailed explanation of the kinematics of the half- and full-toroidal variators) x21spin \u00bc x1 sin\u00f0h\u00fe c\u00de x2 cos h (10) x23spin \u00bc x3 sin\u00f0h c\u00de x2 cos h (11) We define the spin coefficients as a function of the tilting angle c and the creep coefficients as r21 \u00bc x21spin x1 \u00bc sin\u00f0h\u00fe c\u00de \u00f01 Crin \u00de 1\u00fe k cos\u00f0h\u00fe c\u00de tan h (12) r23 \u00bc x23spin x3 \u00bc sin\u00f0h c\u00de 1 \u00f01 Crout \u00de 1\u00fe k cos\u00f0h c\u00de tan h (13) We observe that in the case of SHTV the zero-spin condition is obtained only for two values of the geometric ratios (see Fig. 4(b)), whereas, in the case of the full-toroidal drive, the spin motion never vanishes [7]. The kinematics of the DFTV variator is slightly different if compared to the single-roller geometries. Again, spin motion occurs at the roller\u2013disk contact points, whilst only slip is present between the two rollers in contact (see Fig. 3(a)). For each ith roller of the roller pair, we can define points Hi and Xi. The spin velocities can be inward or outward directed, depending on the considered geometric ratio. A proper choice during the design stage of the cone incidence angle a allows the DFTV variator to present almost zero-spin velocities at srID \u00bc 1 (see Fig. 4(a)). By following the same argument traced Journal of Mechanical Design JULY 2012, Vol. 134 / 071005-3 Downloaded From: http://mechanicaldesign.asmedigitalcollection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure7-1.png",
        "caption": "Fig. 7 Planer tool modeling the shaper",
        "texts": [
            " Geometrically, the motor direction of the planer tool is parallel with the axis of the shaper cutter, and then the planer tool copies the section profile of the shaper cutter in the axial direction. According to the meshing principle, the spur face-gear gullet needs to be obtained through numerous continuous envelopes of the tool. However, with the consideration of the practical efficiency, the copying profile and the rotation of the tool are reasonably discretized to obtain the qualified tooth surface in the highest efficiency. A group of cutter location points, derived after the discretization of the copying profile, are named as the basic cutter location group, as shown in Fig. 7. In the process of the spur face-gear planing, the planer tool makes a series of movements like feeding and retracting along the basic cutter location group. After the manufacturing of one Basic cutter location group is finished, the workpiece and the basic cutter location group will rotate through an angle around the respective axis according to the design parameters and, then, undergo the planing of the next group of points. This process will go on until the manufacturing of a single tooth is finished"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003378_s1560354714010055-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003378_s1560354714010055-Figure1-1.png",
        "caption": "Fig. 1. Examples of Painleve\u0301\u2019s paradox and dynamic jamming \u2014 (a) The sliding rigid rod model. (b) Inverted pendulum on a slider (IPOS); Examples of passive dynamic walking \u2014 (c) The compass biped model. (d) The rimless wheel model.",
        "texts": [
            " MSC2010 numbers: 70E18, 70E55, 70F35 DOI: 10.1134/S1560354714010055 Keywords: multibody dynamics, rigid body contact, dry friction, Painleve\u0301 paradox, passive dynamic walking Painleve\u0301\u2019s paradox occurs in rigid-body mechanics of contact with dry friction, where the instantaneous solution of the contact dynamics becomes either inconsistent or indeterminate in certain configurations [31, 43]. This paradox has been demonstrated mathematically in simple models of a rigid rod or rectangular block sliding on a rough plane [27, 43] (Fig. 1a), as well as more complicated models of multibody mechanisms with a single frictional contact [42]. In order to resolve Painleve\u0301\u2019s paradox, one approach proposes regularization of the bodies\u2019 rigidity into an elastic contact interaction, followed by rigorous examination of the limit of infinite stiffness [25, 45, 48]. This approach works well for resolving cases of solution indeterminacy [39]. In configurations of inconsistency where no finite-force solution exists that satisfies the rigid-body assumptions along with Coulomb\u2019s friction law, it has been shown that there exists a consistent solution under impulsive contact forces [49], which is termed tangential impact [56], or impact without collision [4]",
            " Another phenomenon which is related to Painleve\u0301\u2019s paradox is dynamic jamming [10, 42], where *E-mail: izi@tx.technion.ac.il 64 a rigid body or a multibody mechanism begins with consistent slippage and the dynamic solution reaches an inconsistent configuration in finite time, where the contact force grows unbounded. This scenario has been analyzed theoretically by Ge\u0301not and Brogliato [14] for the rigid rod. Another mechanism of an inverted pendulum on a slider (IPOS) was proposed in [10, 42], see Fig. 1b, and its dynamic jamming solutions were analyzed. An early attempt to experimentally demonstrate dynamic jamming in an IPOS-like mechanism was made in [34], with only partial success. The main reason for the difficulties in experimental realization of Painleve\u0301\u2019s paradox and dynamic jamming is the fact that the conditions for their occurrence require extreme (and rare) values of physical parameters, and a narrow range of initial conditions. The goal of this paper is to demonstrate that Painleve\u0301\u2019s paradox and dynamic jamming phenomena can also occur, at least theoretically, in another related and widely studied area \u2014 passive dynamic walking. The principle of passive dynamic walking was exploited a long time ago for bipedal toys walking down an inclined plane powered solely by gravity, without motors and actuation. The pioneering work of McGeer [32] was the first one to theoretically study passive dynamic walking and analyze orbital stability of its solutions. McGeer has studied a very simple model of a passive robotic walker that consists of two rigid links connected by a passive rotary joint (Fig. 1c), which was later dubbed \u201ccompass biped\u201d in [16]. He also identified in [32] that the passive dynamics of a biped is also very similar to the intermittent rolling motion of a rimless spoked wheel down an inclined plane, see Fig. 1d. Unlike the compass biped model, the low dimensionality of the rimless wheel model enables explicit analysis of its dynamics, as thoroughly studied by Coleman and Ruina in [6, 7]. Later on, the study of bipedal passive walking was extended to account for knees [33], three-dimensional passive walker [9] and stabilization of lateral rocking [26]. More importantly, several works studied these simple walking models with added actuation [53, 58]. It was found that controlled actuation which is based on passive dynamics can significantly improve the energetic efficiency of powered walking [8]",
            " Within this portion of the periodic solution, any small perturbation which involves forward slippage x\u0307 > 0 will result in the onset of Painleve\u0301\u2019s paradox, where no finite-force solution is consistent. We now demonstrate that the scenario of dynamic jamming can also occur in the RW model, under perturbation of slippage. Dynamic jamming is associated with a solution under initial conditions of consistent slippage, which tends towards the inconsistency region. The conditions for dynamic jamming are thoroughly studied in [14] for the uniform rod, and in [42] for the IPOS mechanism (Fig. 1b). The continuous-time dynamics of the rimless wheel model in (3.3) is equivalent to a degenerate case of the IPOS model, with m1 \u2192 0. Thus, the analysis of dynamic jamming in [42] also applies to the RW model, as briefly summarized below. Dynamic jamming solutions should start at the region R1 of consistent slippage and evolve towards the inconsistency region R4. The arrows in Fig. 3a show (qualitatively) the direction of the tangent vector (\u03b8\u0307, \u03b8\u0308) of solutions in the region R1. Similar to [42], the directions of these arrows indicate that the only way in which a forward slippage solution can reach the region R4 is from its left side, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-5-1.png",
        "caption": "FIGURE 13-5 Constant mesh gears with shifter col lar. (Courtesy ZahnradLlbrik Passau GmbH.)",
        "texts": [
            " This type of transmission is very efficient, but practical applications are limited to small tractors because large gears are hard to move, the large teeth pro vide too much engagement interference, and the teeth can be damaged dur ing shifting. In the constant mesh transmission the gears are mounted so that they are always in mesh with at least one of the meshing gears free to rotate on the shaft. Splined couplings of various types, usually called shifter collars, are used to engage the gears. Figure 13-5 shows a typical arrangement. Again, it is necessary to disengage the traction clutch and advisable to stop the tractor when shifting. This type of transmission is slightly less efficient than the sliding gear type as a result of the friction between the rotating gears and shafts, but it is used when helical gears are selected to control noise or when it is desired to reduce the shifting effort that would be created by moving large gears. Most tractor transmissions are, at least partially, of the constant mesh type",
            " Although the maximum rate will occur at initial engagement at full pressure when the slip velocity is the highest, the average rate for the engagement generally should be used. The energy rate can be calculated from BEVEL GEARS where F, T\" N\" A F, = T\"N,/(9.5493 A) the energy rate, W/mm2 the average torque, N . m the average slip, rpm the total facing area, mm2 Spur and Helical Gears 377 (7) Most transmission and drive train gears transmit power between parallel shafts and are spur or helical (see fig. 13-5). Spur gears have teeth that are parallel to the axis of rotation of the gear, whereas the teeth of helical gears are at an angle to the axis of rotation. Spur gears are somewhat less expen sive to manufacture than helical gears and often can be supported in the transmission much more simply and inexpensively because there is no axial thrust force as there is with helical gears. However, helical gears gradually transfer the tooth loads from one tooth to the next and generally generate much less noise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000579_s0094-114x(98)00043-3-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000579_s0094-114x(98)00043-3-Figure5-1.png",
        "caption": "Fig. 5. De\u00aenitions of the coordinate system and the position vectors.",
        "texts": [
            " 4, in the triangle ARB, because the line OrR is perpendicular to the line AB, according to the Pythagorean theorem, one can derive the following expressions: r1 L2 A L2 1 \u00ff L2 2 =2LA; r2 LA \u00ff r1; mr L2 1 \u00ff r21 1=2: 1a Similar procedures could also be applied in the triangles BSC and CTA, and one can lead to the expressions: s1 L2 B L2 6 \u00ff L2 5 =2LB; s2 LB \u00ff s1; ms L2 6 \u00ff s21 1=2; 1b t1 L2 C L2 4 \u00ff L2 3 =2LC; t2 LC \u00ff t1; mt L2 4 \u00ff t21 1=2: 1c Next, it is necessary for us to de\u00aene the position vectors of the revolute joints of Or, Os and Ot. These position vectors are denoted as POr , POs and POt , respectively. To this end, let us place a \u00aexed coordinate system, say X\u00b1Y\u00b1Z, on the base platform with the X\u00b1Y plane lying on the base platform and the origin of this coordinate system being arbitrarily chosen. Then, as referred to Fig. 5, the position vector POr can be expressed as: POr PB r1 PA \u00ff PB =LA: 2a Similarly, the position vectors POs and POt are expressed as: POs PC s1 PB \u00ff PC =LB; 2b POt PA t1 PC \u00ff PA =LC; 2c in which PA, PB and PC are the position vectors of points A, B and C. The angle made by the line perpendicular to AB with the X-axis (from Fig. 5) is denoted as br and is given as: br cos\u00ff1hf PA \u00ff PB k ig=j PA \u00ff PB kji: 3a Similarly, the angles made by the lines perpendicular to BC and AC with the X-axis are denoted as bs and bt, respectively. They are expressed as: bs cos\u00ff1hf PB \u00ff PC k ig=j PB \u00ff PC kji; 3b bt cos\u00ff1hf PC \u00ff PA k ig=j PC \u00ff PA kji; 3c where i and k are the unit vectors of the X- and Z-axis of the X\u00b1Y\u00b1Z coordinate system, and the symbols `` '' and `` '' indicate the cross product and inner product. In addition, the unit vectors along the lines OrR, OsS and OtT are denoted as wr, ws and wt, respectively, and as referred to in Figs 3 and 5, they are expressed as: wr cos br cosfri sin br cosfrj sinfrk; 4a ws cos bs cosfsi sin bs cosfsj sinfsk; 4b wt cos bt cosfti sin bt cosftj sinftk; 4c in which j is the unit vector of the Y-axis of the X\u00b1Y\u00b1Z coordinate system; fr, fs and ft are the inclination angles made by the lines OrR, OsS and OtT with the base platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002122_s0263574708004256-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002122_s0263574708004256-Figure1-1.png",
        "caption": "Fig. 1. 3-RPRR planar 6-ADOF kinematically redundant parallel manipulator (if \u03b8is were fixed, the manipulator would be a 3-PRR).",
        "texts": [
            " A 3-RPRR mechanism indicates that the end-effector is connected to the base by three serial kinematic chains (limbs), each consisting of two active (and therefore underlined) joints, one revolute joint (R), connected to the base and one prismatic joint (P), respectively, followed by two passive revolute joints, the second of which connects the limb to the end-effector. http://journals.cambridge.org Downloaded: 02 Feb 2015 IP address: 128.59.222.12 The proposed kinematically redundant 3-RPRR parallel manipulator (Fig. 1) originates from the non-redundant 3- PRR planar parallel manipulator proposed in.17 Considering Fig. 1, if each limb of the illustrated manipulator has basejoint angles \u03b8i fixed, the resulting manipulator would be a 3-PRR. That is, the 3-PRR would have a prismatic actuator at point Ai , followed by two passive revolute joints at points Di and Bi . The addition of the active revolute joint at Ai turns the manipulator into the depicted 3-RPRR redundant planar manipulator. Note that throughout the present work, the solid circles in the figures represent active revolute joints whereas empty ones represent passive joints",
            " Figure 2 shows a planar parallel manipulator which has 1-DOKR in its first limb. Considering limb A1D1, point D1 can be anywhere on the hatched circle centred at point A1 with radius \u03c1max given by the maximum displacement of the prismatic actuator. For a given position and orientation of the end-effector, link B1D1 can fully rotate \u00b6 Note the difference in the order of the first two active joints. around point B1. Therefore, the locus of IDP solutions for branch 1 is the arc \u0302RD1S. Based on quantities shown in Fig. 1, the vector loop equation for branch i can be written as: DiBi = DiAi + AiO + OP + PBi (1) li 2 = (\u2212\u03c1ic\u03b8i \u2212 xAi + xp + ric(\u03c6+\u03c8i ) )2 + (\u2212\u03c1is\u03b8i \u2212 yAi + yp + ris(\u03c6+\u03c8i ) )2 (2) li 2 = xli 2 + yli 2 = ( lic\u03b1i )2 + ( lis\u03b1i )2 (3) where c and s represent cos( ) and sin( ), respectively. Jacobian matrices transform the velocity vector of the active joints in the velocity vector of the end-effector and vice-versa. The expression combining them all is: Jxx\u0307 = Jqq\u0307 (4) where q\u0307 is the velocity vector of the associated active joints and x\u0307 is the velocity vector associated to the end-effector",
            " Since each point of the dexterous workspace must be able to rotate from 0 to 2\u03c0 , the radius of the circle at all positions must be li \u2212 ri .19 This creates an oval shape for each leg. Their intersection constitutes the dexterous workspace as shown in Fig. 5(a). For the 3-RPRR, since branch i can also rotate around point Ai , the dexterous workspace is obtained by rotating the oval shapes for branch i around points Ai when the latter are located at a zero length prismatic stroke, as shown in Fig. 5(b). The geometric parameters of the 3-PRR and the 3-RPRR manipulators based on Fig. 1 are: A1A2 =A2A3 = A3A1 = 1.0 m, B1B2 = B2B3 = B3B1 = 0.10 m, ri = 0.0577 m, li = 0.25 m, \u03c81 = 7\u03c0 6 , \u03c82 = 11\u03c0 6 , \u03c83 = \u03c0 2 , \u03c1maxi = 0.577 m and \u03c1mini = 0 m. Based on Figs. 5(a) and 5(b), the 3-PRR nonredundant manipulator dexterous workspace is 0.196 m2 and the redundant 3-RPRR manipulator dexterous workspace is 0.261 m2, an increase of more than 33%. The increase in the area of the dexterous workspace of the redundant versus http://journals.cambridge.org Downloaded: 02 Feb 2015 IP address: 128"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003148_j.protcy.2014.08.041-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003148_j.protcy.2014.08.041-Figure4-1.png",
        "caption": "Fig. 4 Two defects on inner race",
        "texts": [
            " 1 Three defects on outer race (a) def1< & def 2 < (b) def1 < & def 2 > (c) def1 < & def 2 = (d) def1> & def 2 > def1 def2 a b c d B def1 A 1 2 C def2 def2 C def1 A B 1 2 A B 1 2 C A B 1 2 C Inner race rotates with shaft speed as it is rigidly mounted on the shaft. Therefore, the defects on the inner race also rotate at shaft speed as opposed to outer race defects. Because of the rotation of the defects, the same ball does not strike the next defect but the successive ball strikes the next defect. From Fig. 4 it is observed that ball number 1 strikes defect \u2018A\u2019 at time \u2018t1\u2019 and ball number 2 strikes the defect \u2018B\u2019 at time \u2018t2\u2019. In case of inner race defects the generalised equation for time delay between two strikes is expressed as follows: n = tn+1 \u2013 tn = in (7) Where, \u2018 \u2019 is angle difference between defect, and nearest ball in direction of rotation of inner race, \u2018 fin\u2019 is ball pass frequency of inner race and \u2018n\u2019 is an integer. For the shaft rotational speed of 1500 rpm, the ball pass frequency of inner race (BPFI, fin) is 122"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003844_tia.2018.2859310-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003844_tia.2018.2859310-Figure2-1.png",
        "caption": "Fig. 2. Winding connections and DC current configurations of 12-statorslot DC-biased VRMs. (a) Model 1: 8-rotor-slots, Pf=3, Pa=5. (b) Model 2: 10-rotor-slots, Pf=3, Pa=7. (c) Model 3: 10-rotor-slots, Pf=6, Pa=4. (d) Model 4: 14-rotor-slots, Pf=6, Pa=8. (e) Model 5: 11-rotor-slots, Pf=6, Pa=5. (f) Model 6: 13-rotor-slots, Pf=6, Pa=7.",
        "texts": [
            " Average torque will be produced if the following relationships are satisfied: a f rP P N  (1) (2 ) 60 e r r r n N N    (2) where Pa is the pole pair number of the MMF by AC component, Pf is the fundamental pole pair number of the MMF by DC component, Nr is the number of rotor slots, and \u03c9e, \u03c9r are the electrical and mechanical rotating velocity. In order to enrich the alternative slot/pole combinations and explore the scheme with better performance, the possible slot/pole combinations are investigated, and some practical combinations of 12-stator-slots machines are shown in Fig. 2. It can be seen from Fig. 2 (a)-(b) that for 12-stator-slot machines, Pf is 3 if the direction of the injected DC currents changes alternately every two stator slots. Meanwhile, seen from Fig. 2 (c)-(f), Pf is 6 if the direction of the injected DC currents changes alternately every one stator slot. Besides, the concentrated windings can be either single layer (Fig. 2 (a)-(b)), or double layer (Fig. 2 (c)-(f)). Another interesting phenomenon is that except the phase sequence, the stator winding connections and the current configurations for machines in Fig. 2 (a) and (b) are nearly the same. This is also valid for Fig. 2 (c) and (d), and Fig. 2 (e) and (f). (a) (b) For Model 1 and 2 in Fig. 2 (a) and (b), the phase currents are: 2 sin( ) 2 sin( 2\u03c0 3) 2 sin( 2\u03c0 3) A dc ac e B dc ac e C dc ac e i I I t i I I t i I I t                  (3) While for Model 3-6 in Fig. 2 (c)-(f), the phase currents are: - 2 sin( ) 2 sin( ) 2 sin( 2\u03c0 3) 2 sin( 2\u03c0 3) 2 sin( 2\u03c0 3) 2 sin( 2\u03c0 3) A ac e dc A ac e dc B ac e dc B ac e dc C ac e dc C ac e dc i I t I i I t I i I t I i I t I i I t I i I t I                                        (4) where Idc the DC component, Iac the AC component, and a is the phase A current angle, respectively. The corresponding winding factors of the slot/pole combinations in Fig. 2 are listed in Table I. The winding MMF harmonics vary in diverse slot/pole combinations. The one phase winding MMF harmonics are compared in Fig. 3 when only the AC currents of 1 A are injected. Considering Model 1 and 2 have the same winding connections except the phase sequence, their harmonic components and amplitudes are exactly the same, as are the cases in Model 3 and 4, Model 5 and 6. As shown, although the pole pair number of Model 1 and 5 are the same, the 1st harmonic in Model 1 is obviously higher than that in Model 0093-9994 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 5 due to the higher winding factor. As shown in Fig. 2, for Model 1 and 2, the injected DC components in one phase winding flow in unidirectional direction, while in the other models, the DC currents in the coils of one phase winding have two flowing directions. Therefore, two main drive circuits in Fig. 4 can be applied for these machines, and vector control method can be adopted [15], [22]. Compared with the regular three phase synchronous machine, although the number of the power electronic devices increases, total cost for the control system is not increasing too much considering the cost of power electronic device is decreasing. To investigate the influence of slot/pole combinations on the machine performance, machines in Fig. 2 are designed, and their main parameters are listed in Table II. The stator/rotor tooth arc are optimized to obtain maximum torque, while the other parameters are kept identical for a fair comparison. A. Inductance Characteristic Taking Phase A as an example, the self-inductance can be calculated according to the winding function theory: 2 2 0 0 ( ) ( ) ( , ) cos( )aa g eff a s s s aa aaj r r j L t r l N t d L L jN w t          (5) where rg is the air gap radius, leff is the effective stack length, j are the inductance harmonic numbers, Na is the winding function of phase A, ( , )s t is the air gap permeance",
            " Then the total flux linkage of Phase A in Model 3-6 are: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) a a a a a a a b a c dc a a a b a c dc a a a a b a c dc a a a b a c dc t t t t L M M I M M M I t M M M I L M M I                                                (9) where the subscripts + and \u2013 imply the DC current direction in the armature windings. Then the fundamental back-EMF is: 1 ( ) ( ) sin( )a a r r aa dc r r d t e t N L I N t dt     (10) When only DC current is injected to the windings as the specified direction in Fig. 2, an exciting field will be produced in the air gap. The no load flux distributions with a DC current of 13.44 A are compared in Fig. 8, and the radial air gap flux densities are shown in Fig. 9. The asymmetric flux of Models 5 and 6 is mainly due to an odd number of rotor slots while the number of stator slots is even. Assuming that on one side, the stator tooth aligns with the rotor tooth and the magnetic flux is maximal. Then in the opposite position, the stator tooth must align with the rotor slot and the magnetic flux is minimal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003354_icra.2014.6907498-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003354_icra.2014.6907498-Figure7-1.png",
        "caption": "Fig. 7. The catheter tip coordinates x t , y t are visually tracked with a blob tracker. The intersection points between the targeted circular path and a circle around the anchor point with radius l t are derived. Target point x j ,y j is chosen from the two solutions with a flag defining the side of the circle. The desired a j is calculated from the kinematics model.",
        "texts": [
            " Model based closed loop control of the catheter tip orientation is triggered when the currently tracked tip position reaches the targeted circular path with center C = (x C ,y C ), defined by (x j x C )2 + (y j y C )2 = R 2. The desired deflection of the catheter tip is dependent on the tracked length l t = p x 2 t + y 2 t of the catheter. A circle with radius l t is described around the anchor point A = (x A ,y A ) for each l t as (x t x A )2 +(y t y A )2 = l 2 t . The intersection point of the two circles defines the targeted point (x j ,y j ) and therefore allows to derive the desired deflection angle a j from the kinematics model, as illustrated in Figure 7. The targeted point on the circle (x j ,y j ) is chosen from two solutions by evaluating a flag that specifies the side of the targeted circular path. The error between the tracked angle a t and the desired angle a j is ea = a j a t which is used to compute a scalable gain factor that adapts the angle of the magnetic field to guide the catheter tip along the circular segment with radius l t towards the desired point on the targeted circular path with radius R. The maximum torque that can be applied by the catheter tip in the OctoMag workspace is directly obtained from the knowledge of the maximum magnetic field strength (40 mT) and the total magnetization of the three magnets inside the magnetic tool to be 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000991_s0022112003005147-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000991_s0022112003005147-Figure1-1.png",
        "caption": "Figure 1. Definition of orientation e \u2261 (\u03b8, \u03c6) of an axisymmetric cell suspended in simple shear flow and subject to an external field acting in the direction F\u0302 \u2261 (\u03b8f , \u03c6f ).",
        "texts": [
            " Asymptotic calculations of the requisite fields are outlined in the Appendix. In a dilute monodisperse suspension, we focus on the motion of a single \u2018tracer\u2019 micro-organism. This, in turn, is modelled as a rigid Brownian axisymmetriccentrosymmetric particle\u2020 possessing a permanent embedded dipole (aligned with the axis of symmetry). The instantaneous geometrical configuration of the cell is thus completely specified by R, its physical-space position vector and its orientation represented by the unit vector e attached to the dipolar axis (see figure 1). Orientation space may effectively be represented in the present problem by S2, the unit sphere. We consider a steady homogeneous shear flow defined by a prescribed constant and uniform ambient velocity gradient dyadic G (see \u00a7 5). The present transport problem is thereby decoupled from the dynamic problem. No a priori restrictions are imposed on the magnitude of shear rate (represented by G, an appropriate norm of G). According to Pedley & Kessler (1990), this is a prerequisite for the discussion of transport phenomena in fully developed bioconvection",
            "2) of the original problem. We have focused in the following on the simple shear flow V = i\u03022Gx, (2.17) wherein (i\u03021, i\u03022, i\u03023) is a right-handed triad of orthonormal space-fixed unit vectors in the directions of the (x, y, z) axes. Parameterizing e = (\u03b8, \u03c6) and F\u0302 = (\u03b8f , \u03c6f ) in terms of the spherical polar and azimuthal angles, the orientation-space gradient operator is \u2207e \u2261 \u2202 \u2202e = i\u0302 \u03b8 \u2202 \u2202\u03b8 + i\u0302\u03c6 1 sin \u03b8 \u2202 \u2202\u03c6 , (2.18) in which (e, i\u0302 \u03b8 , i\u0302\u03c6) is a right-handed triad of particle-fixed unit vectors (figure 1) and e\u0307 = i\u0302 \u03b8 \u03b8\u0307 + i\u0302\u03c6\u03c6\u0307 sin \u03b8 . Making use of these in (2.4), (2.13) and (2.15) we obtain for P \u221e 0 and bi(i = 1, 2, 3), the scalar components of P \u221e 0 B, LP \u221e 0 = 0, \u222b \u03c0 0 \u222b 2\u03c0 0 P \u221e 0 sin \u03b8 d\u03c6 d\u03b8 = 1, (2.19a, b) Lbi \u2212 Pe b1\u03b4i2 = P \u221e 0 (ei \u2212 e\u0304i), \u222b \u03c0 0 \u222b 2\u03c0 0 bi sin \u03b8 d\u03c6 d\u03b8 = 0, (2.20a, b) \u2020 From the definitions of P \u221e 0 and B in terms of long-time limits of expressions involving the statistical moments of P , we can attribute to these fields the following kinematic significance: P \u221e 0 is the steady orientation distribution; B represents the long-time limit of the displacement of the centroid of the sub-population of micro-organisms instantaneously swimming in the direction e relative to the physical-space position of the centroid of the entire population (cf"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-9-1.png",
        "caption": "Figure 11-9 illustrates a simplified model that can be used to describe tractor transient handling. The wheels on the front and rear axles have been replaced by an equivalent single wheel at each axle having lateral force properties equivalent to the total of the wheels on that axle.",
        "texts": [
            " The forward velocity, u, of the center of gravity is assumed 290 MECHANICS OF THE TRACTOR CHASSIS to be constant, whereas the steer angle, of' of the front wheels is assumed to be a known function of time. A pneumatic tire can be considered to develop a lateral force whenever the direction in which the tire is headed differs from the direction of the plane of the wheel itself. This difference in directions, called the tire slip angle, is expressed in terms of the velocities of the wheel in the vehicle co ordinate system. Figure 11-9 illustrates the slip angles of the front, asf, and rear, asn wheels. From that figure, asf = tan- 1 ((v + xfwr)/u) - of a sr = tan- 1 ((v - Xcgr)/u) The lateral force developed by a tire at a given vertical load takes the form shown in figure 11-10. The lateral force varies nearly linearly with slip angle at small slip angles and reaches a maximum value asymptotically. The slope of the curve at the origin is termed the cornering stiffness, Ca. Thus, for small slip angles, L = - Caas; i.e., a positive slip angle produces a negative lateral force. If the lateral force versus slip angle relation is nondimension alized by dividing the lateral force by the normal force on the tire, the resulting ratio, JoLl, is termed the cornering coefficient. TRAKSIEKT A?\\D STEADY-STATE HA!\\,DU!\\'G 291 The equations of motion for the tractor in figure 11-9 are most easily expressed in terms of the vehicle coordinate system. In such a system, the lateral acceleration of the center of gravity is v + ur. Thus, (50) Letting I zzt be the moment of inertia of the tractor about the vertical (or z) axis through its center of gravity, (51 ) In transport situations, the steer and slip angles will be small so that the preceding equations can be linearized yielding mt (v + ur) = [v + xfur Of] [v - Xcgr] (52) -Cal - Cm u u I zzt r = [v + Xfur ] - C'f u - Of Xf\" + Ca, [v-Xcgr ] u Xcg (53) T\\ote that Caf and Ca , represent the total cornering stiffness at the front and rear axles, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001572_ichr.2007.4813852-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001572_ichr.2007.4813852-Figure7-1.png",
        "caption": "Fig. 7. Strategies linking in order to realize a paint task while keeping balance, especially during disturbance. (Dynamic simulation environment \u201cArboris\u201d developped by CEA/LIST-ISIR in Matlab, 2006)",
        "texts": [
            " 5 illustrates our global architecture control. First of all, HR has an inexact perception of the physical simulation. For example, HR does not know disturbance force. Then, it analyses its state and chooses a strategy. We consider two global strategies: reaction to disturbance and task. In the first strategy, HR can have different reactions (simple/complex subsection V-B.1). Thanks to stability criteria, HR uses complex reaction to disturbance if necessary. In task mode, HR can realize task sequences (Fig. 7). Finally, thanks to subsection IV-C, we can formulate and solve two QP (Static and Dynamic) in order to compute the HR articular torque. 1) Towards Multi-Phase Balance Control: In these examples (Fig. 6), HR contacts are activated/deactivated as the simulation carries on. It is a more high-level control. We implement a two phase balance control. At the beginning of the scene, the HR is upright and its hand contacts are deactivated. On account of a disturbance force applied on its back, its CoM moves away from itsgoal position \u2016xgoal G \u2212xG\u2016> dist (dist is an arbitrary distance)",
            " 6(a)), hand contacts are activated and try to come in touch with the environment. Thanks to its hands, the HR can maintain its balance. Finally, its hand contacts are deactivated in order to meet up with its starting posture. We note that it is a non-coplanar multi contact problem and the Static QP of our algorithm allows us to stabilize the motion. The HR converges to a stable CoM and posture. In the second case (Fig. 6(b)), contact accelerations of the right feet have a new goal so that HR makes one step forward. 2) Strategies Linking: In this example (Fig. 7), HR must grasp a brush and realize the task of painting the wall. In order for its hand to reach the brush, we use the previously evoked joint limit control (Eq. 17). When HR is close enough, we activate the damped spring in the simulation (Fig. 7(b)). A disturbance hits the floor, at an unpredicted time. Though it does not qualitatively know the nature of the disturbance, it knows that one was applied. It stops in its task (Fig. 7(e)) and goes back to its initial posture, to possibly make use of complex reaction (Subsection V-B.1). Once the disturbance is over and it has recovered its balance, the HR fulfills its task. We introduced a global architecture to control HR with multiple grasps and non coplanar frictional contacts. Thanks to this architecture, we solve simultaneously the problem of tasks involving grasping and balance control after a disturbance. Thanks to constraints optimization algorithm (QP), the HR can be controlled in a large range of situations and is consistent with the same set of parameters (control gain, weighing)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002287_1.42574-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002287_1.42574-Figure1-1.png",
        "caption": "Fig. 1 Coordinate reference frames.",
        "texts": [
            " To describe time delays in the response of actuators such as, for example, thrusters, an expansion of the general actuatormodel is suggested. In this paper, reference coordinate frames are denoted by F , and we denote by !cb;a the angular velocity of F a relative to F b, referenced in F c. Matrices representing coordinate transformation between F a and F b are denoted by Rb a. When the context is sufficiently explicit, we may omit function arguments. To form the basis of our spacecraft attitude model, we use the standard definition of the Earth-centered inertial frame F i (cf. Fig. 1), with the z axis toward celestial north, normal to the equatorial plane. The spacecraft is assumed to travel in a general elliptic Earth orbit, and we employ a standard local vertical/local horizontal definition of the spacecraft orbit reference frame F o, with unit vectors x o yo zo; yo h=h and zo rc=rc (1) where h rc _rc is the angular momentum vector of the orbit, and h jhj. We also define a spacecraft body frameF b with an origin in the spacecraft center of mass and the axes fixed to the spacecraft body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001561_bf00610585-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001561_bf00610585-Figure2-1.png",
        "caption": "Fig. 2. Silhouette of the animal and field of view (shaded) of the specialized ventral part of the eye during foward flight (a) and while the body is raised in the plunge reaction (b). Arrow: direction of the Brewster angle",
        "texts": [
            " It is conceivable that the animals carry out this maneuver because it is a necessary preliminary, for aerodynamic reasons, to the downward tilting and closing of the wings (or in order to gain time for the wing closing; Walton 1935). But it may also be that the raising phase serves to assist vision; in the compound eye of Notonecta a ventral region is specialized for the detection of polarized UV light with horizontal e-vector, owing to the particular arrangement of the microvilli in the UV retinula cells (Schwind 1983, 1984; Schwind et al. 1984). In rapid flight straight forward the angle between the long axis of the body and the horizontal is only ca. 15 ~ (Fig. 2, Schwind 1983). With the body in this position the ommatidia in the ventral part of the eye do not look in the direction from which the water surface reflects light with the highest degree of polarization; the degree of polarization d of the light incident in the ventral region of the eye is only about 30% (values for d as a function of direction of view are given by Chen and Rao 1968). But when the body axis is raised to an angle of >33 ~ , as in the plunge reaction, ommatidia in the ventral part of the eye look in the direction of the Brewster angle (Fig. 2, arrow). Light reflected in this direction is maximally polarized, with d = 80% for UV light (according to Chen and Rao). The sudden incidence of strongly polarized light in the ventral part of the eye could contribute to the immediate elicitation of the following R. Schwind : The plunge reaction of Notonecta 32l phases of the plunge reaction. This hypothesis is supported by the observation that the duration of the phase of flying with the body raised, before the actual plunge, is longer in the laboratory, over polarizing film than outdoors over water"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003507_j.cirp.2016.04.013-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003507_j.cirp.2016.04.013-Figure10-1.png",
        "caption": "Fig. 10. Results of FEA: (a) temperature, (b) pressure, (c) sliding velocity, (d) map, and (e) die design.",
        "texts": [
            " The wear resistance of the specimen with the Type 2 design of the TL is compared to that of the SKD61 specimen, as shown in Table 1. The worn volume of the Type 2 specimen is smaller than that of the SKD61 specimen by nearly 76.9%. Softening of the worn region takes place for the case of the SKD61 specimen, unlike the Type 2 specimen. These results reveal that the proposed technology with the TL can improve the wear resistance of hot forging dies. Archard\u2019s wear model is used to estimate the wear map [10]. wear coefficient of SKD61 is cited from reference 10. Fig. 10 shows the estimated wear map of the hot forging die for the a shaft. Top and interface regions are predicted as excessively w regions. The maximum wear appears in the vicinity of the region. In terms of a local bonding mechanism of wear, possibility of the wear augments when the pressure and temperature increase. Hence, the deposited region of the di determined as the top region of the die, as shown in Fig. 10(e Fig. 11 shows the design and fabrication procedures of the forging die. Using the results of wear experiments and numer analyses, a hot forging die with the deposited layer and the T designed, as shown in Fig. 11(a). In order to consider p processing of the deposited die, the offset geometry is created fr the reference geometry of the die. The offset is applied to application region of the DED process. The offset distance is ne 1.0 mm. Considering the distance from the external surface of deposited layer to that of the TL, the TL design with a trapezo shape is contrived",
            " substrate of the die is created by machining of SKD61. deposited layer and the TL are deposited by the DED process shown in Fig. 11(b). Two hoppers are used to selectively supply Stellite21 powder and the mixed powder with Stellite21 of 50 w and SKD61 of 50 wt.%. After creation of the deposited regio vacuum heat treatment is performed to harden the depos region and the substrate together. Finally, post-processing performed to obtain the final shape and the desired sur roughness of the die, as shown in Fig. 11(b). Fig. 10 shows the results of FEA for a hot forging process of the axle shaft. Temperature, pressure and sliding velocity distributions are estimated to create the wear map of the die, as shown in Figs. 10(a)\u2013(c). The maximum temperature and the maximum pressure appear in the vicinity of the top region of the die. The sliding velocity of the top region is smaller than the remaining region of the die. The maximum pressure and the maximum sliding velocity are nearly 791 MPa and 734 mm/s, respectively. The 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003349_tmag.2015.2437194-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003349_tmag.2015.2437194-Figure2-1.png",
        "caption": "Fig. 2. Illustration of structure parameters.",
        "texts": [
            " Each phase consists of alternately stacked cores and separators. The separators are made from aluminum and they are only used to fix the position of each mover core, which is the same as backplate. Three long coils construct the three-phase winding. The three pieces of PMs shown in Fig. 1 are all magnetized in one direction. In fact, PMs in opposite polarities are arranged alternately in moving direction for each phase. For the sake of further clarity, a small segment with marked structure parameters is plotted in Fig. 2. The parameter values are listed in Table I. In this paper, each phase consists of six segments. A 0018-9464 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. machine, the z-x plane view is adopted, as shown in Fig. 3. Based on Fig. 3, the operation principle of this machine can be clearly explained. When the mover is located in the positive d-axis position, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003535_acs.2759-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003535_acs.2759-Figure2-1.png",
        "caption": "FIGURE 2 Forces and moments on the quad tilt-wing unmanned aerial vehicle",
        "texts": [
            " Equations of motion for the quad tilt-wing UAV are briefly presented in this section. A more detailed analysis can be found in 1 study.37 Overall dynamic equations of the system are given as[ mI3\u00d73 03\u00d73 03\u00d73 Ib ] [ V\u0307w \u03a9\u0307b ] + [ 0 \u03a9b \u00d7 (Ib\u03a9b) ] = [ Ft Mt ] , (1) where m and Ib represent the mass and the diagonal inertia matrix in the body frame and Vw and \u03a9b represent the linear and the angular velocities of the vehicle in the world and body frames, respectively. The net force and the moment applied on the vehicle are represented by Ft and Mt, respectively (see Figure 2). It should be noted that for tilt-wing quadrotors, these forces and moments are functions of the rotor trusts and wing angles. Using vector-matrix notation, Equation 1 can be rewritten as follows: M?\u0307? + C(\ud835\udf01)\ud835\udf01 = G + O(\ud835\udf01, \ud835\udf14i) + E(\ud835\udf09, \ud835\udf142 i ) + W(\ud835\udf09), (2) where, \ud835\udf01 = [X\u0307, Y\u0307 ,Z, p, q, r]T , (3) and \ud835\udf09 = [X,Y ,Z,\u03a6,\u0398,\u03a8]T , (4) where X, Y , and Z are the coordinates of the center of mass with respect to the world frame, p, q, and r are the angular velocities in the body frame, \u03a6, \u0398, and \u03a8 are the roll, pitch, and yaw angles of the vehicle expressed in the world frame, and \ud835\udf14i, i = 1, 2, 3, 4 represents the rotor rotational speeds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003049_j.phpro.2014.08.102-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003049_j.phpro.2014.08.102-Figure6-1.png",
        "caption": "Fig. 6. (a) machined tensile testing geometry; (b) schedule of machined tensile testing geometry; (c) tensile testing geometry at different building directions with support structure after LBM.",
        "texts": [
            " The most important values for qualifying additive manufactures components are the yield strength YS, the ultimate tensile strength UTS and the elongation at break E. All three parameters can be identified by standardized uniaxial tensile testing according to DIN EN ISO 6892-1 [2]. Thereby, cylindrical bars are manufactured with a height of 70.0 mm and a diameter of \u00d8 8.0 mm applying process parameters described within chapter 3. Afterwards the finale tensile testing geometry is produced with a grinding process. According to DIN 50125 [3] the testing geometry is manufactured as scheduled in Fig. 6 (b), while a picture of the actual geometry is given in Fig. 6 (a). For testing an evaluation length of 8.0 mm with a diameter of \u00d8 4.0 mm is utilized. With a clamp length of 28.0 mm in combination with hydraulic clamping equipment slipping of the high strength material is avoided. Comparable testing geometries have been used for mechanical characterization of LBM aluminum specimens within different research projects [4]. As described in chapter 2 the LBM is a layer by layer process. Consequently, different elastic-plastic and failure behavior can be expected for different testing orientations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003296_j.ymssp.2017.05.041-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003296_j.ymssp.2017.05.041-Figure4-1.png",
        "caption": "Fig. 4. Modeling of tooth root crack. (a) Schematic graph of a crack. (b) Modeling of a tooth root crack as a non-uniform cantilever beam.",
        "texts": [
            " It indicates that LOD decomposition results are more close to the simulation signal x\u00f0t\u00de. Therefore, for simulation signal shown in Eq. (11), the method of LOD is superior to the EMD in the accuracy of components and their comparison parameters. Hence, in this paper LOD is employed to preprocess the gear vibration signal. The deflections of a spur gear tooth can be determined by considering it as a non-uniform cantilever beam with an effective length Le which is separated into n portions as shown in Fig. 4(a). Here, the crack is assumed to go through the whole tooth width W with a constant depth q0 and a crack with inclination angle ac as shown in Fig. 4(b). Based on literature [27], the bending stiffness, shear stiffness and Hertzian contact stiffness in a meshing gear tooth can be obtained as follows: 1 Kb \u00bc cos2 am Xn i\u00bc1 ei di ei di \u00fe 1 3 e 2 i Ee Ii \u00fe 1 Sh G Ai \u00fe tan2 am Ai Ee \u00f012\u00de 1 Kh \u00bc 4\u00f01 m2\u00de p E W \u00f013\u00de where E is the Young\u2019s modulus, G represents the shear modulus, Sh is a shear factor, Ee is the equivalent Young\u2019s modulus, m is the Poisson ratio, W is the tooth width. Ee \u00bc E \u00f01 m\u00de \u00f01\u00fe m\u00de \u00f01 2m\u00de ; G \u00bc E 2\u00f01 m\u00de \u00f014\u00de Ii represents area moment of inertia and Ai is area of the tooth cross section where the distance between the section and acting point of the applied force is Si: Ii \u00bc 1 12 \u00f02 hi\u00de3 W; i P le 1 12 \u00f0hq \u00fe hi\u00de3 W; le P i P lt 1 12 \u00f02 hi\u00de3 W; lt P i P 0 8>>< >: \u00f015\u00de Ai \u00bc \u00f02 hi\u00de W; i P le \u00f0hq \u00fe hi\u00de W; le P i P lt \u00f02 hi\u00de W; lt P i P 0 8>< >: \u00f016\u00de hi, hq, ei, di, le, lt , h, am are given in Fig. 4. hq represents the reduce dimension of the tooth thickness when the crack depth q and crack angle ac is changed. Next, the effect of fillet-foundation deflection on the gear mesh stiffness is considered. The fillet-foundation deflection of the gear is based on theory of Muskhelishvili [28] which derives an analytical formula for deflection by assuming linear and contact stress variations at root circle. Calculation expression is given by the equation: 1 Kf \u00bc cos2 am W E L uf sf 2 \u00feM uf sf \u00fe P \u00f01\u00fe Q tan2 am\u00de ( ) \u00f017\u00de where uf and sf are the lengths between the root circle and position of the contact force, and root circle with single tooth arclength, respectively",
            " Therefore, in this section, the SIF is introduced to the calculation of tooth crack mesh stiffness. Firstly, the mapping relation between the deformation of the position in the gear mesh line and the SIF was constructed, then the stress intensity factor of the cracked tooth model is calculated by three-dimensional finite element model. Finally, the mesh stiffness of the cracked gear obtained by the assist-SIF replaces the stiffness value of the cracked tooth in the analytical model, which is Kc in Eq. (20). Considering a gear system with width of teeth \u2018\u2018W\u201d and crack of depth \u2018\u2018q\u201d, see Fig. 4(b), the total deformation of tooth surface dc under the action of the force can be determined. Then the mesh stiffness of gear tooth crack can be written as: kc \u00bc F dc \u00f021\u00de The definition of the tooth crack depth of \u2018\u2018q\u201d will cause change of elastic potential energy in the cracked gear. And the change in elastic potential energy dU can be calculated as: dU \u00bc Z q 0 @U @q dq \u00f022\u00de Next, the strain energy release rate G can be expressed as a function of type-1 and type-2 stress intensity factor composite crack model: G \u00bc 1 W @U @q \u00bc 1 E K2 I \u00fe K2 II \u00f023\u00de where K I and K II represent type-1 and type-2 SIF respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001352_s00707-005-0307-2-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001352_s00707-005-0307-2-Figure1-1.png",
        "caption": "Fig. 1. An annular plate subjected to uniform displacement fields on its boundaries. In this case the pre-buckling orthoradial stress field rhh changes from compressive, near the inner boundary, to tensile, in the complementary region",
        "texts": [
            " Finite element investigations for various such problems (mostly, rectangular plates) have been presented in [11]\u2013[13], which contain additional pointers to similar works. A special mention must be made to the original contribution of Gilabert at al. [14], who established numerically and experimentally the existence of complex spatial patterns around defects such as holes or cracks in a thin stretched plate. The \u2018\u2018Maltese cross\u2019\u2019 buckling pattern reported in that reference is triggered by a local compressive stress induced by the presence of the defect, and is strongly dependent on the thickness of the plate, a situation similar to that described in Fig. 1. The mechanics of wrinkle formation has found novel applications in cell biomechanics [15], [16], as it provides insight into living cell locomotion. Roughly speaking, the quantitative analysis of wrinkled patterns produced by cells crawling on elastic membranes gives an indication of the force applied by the cell cytoskeleton. Ge\u0301minard et al. [17] have provided an experimental and numerical study of a model that mimics this situation. They employed the Donnell-von Ka\u0301rma\u0301n equations involving nonlinear kinematics, and used a linear pre-buckling state for a pre-stressed annular plate subjected to a uniform displacement field along its inner boundary (see Fig. 1). The particular type of loading adopted yields an orthoradial stress distribution that is compressive in a concentric region adjacent to the inner edge, while in the remaining part of the plate it is tensile. This leads to a wrinkling pattern localized near the inner edge, and, as we are going to see in the next Sections, several features of this problem can be understood by looking at the linearized bifurcation equation. The wrinkling we have in mind in this work is a typical buckling instability for thin plates rather than membranes (i",
            " The outcome of this approximate analysis is a second-order eigenvalue problem that provides a qualitative and quantitative description of the original wrinkling phenomenon; it also shows that the localized instability experienced by the stretched annular film is intimately linked to the presence of a turning point in this reduced model. The paper concludes with a discussion about the limitations of the WKB approach, and a few remarks on several issues to be tackled in the near future. We consider an annular plate of inner radius R1, outer radius R2, and thickness h \u00f0h=R2 1\u00de, corresponding to the situation shown in Fig. 1. As usually, a cylindrical system of coordinates \u00f0r; h; z\u00de is used to define various quantities of interest associated to this problem. Displacement components in the r; h, and z directions, respectively, are denoted by ur, uh, and w. Assuming that the plate is initially in a state of plane strain, the internal strains are defined according to err \u00bc @ur @r ; ehh \u00bc 1 r @uh @h \u00fe ur ; erh \u00bc 1 2 1 r @ur @h \u00fe @uh @r uh r ; \u00f01\u00de and the corresponding stresses are assumed to obey the classical Hooke\u2019s Law rij \u00bc 2leij \u00fe k\u00f0err \u00fe ehh\u00dedij; i; j 2 fr; hg; \u00f02\u00de where l and k are the Lame\u0301 constants, and dij is the usual Kronecker delta"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001130_j.jmatprotec.2005.05.020-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001130_j.jmatprotec.2005.05.020-Figure5-1.png",
        "caption": "Fig. 5. Geometry between the cutter and the rotor blank.",
        "texts": [
            " Tooth machining and cutter trajectory The novel rotor has been proved to have longer exhaust time and less rate change. However, the proposed tooth cross section and profile present a challenge to tooth machining. To machine the rotor tooth profile, it is required to character- ize the contact between a milling cutter and the rotor blank and produce the trajectory of the cutter along the blank. This section is to analyze the cutter trajectory and propose the analytical cutter mounting angle and centre distance in tooth machining. The machining of the arc\u2013cycloidal helical rotor can be illustrated in Fig. 5. In Fig. 5, coordinate system S0(x0, y0, z0) represents the disc-milling cutter and coordinate frame S1(x1, y1, z1) represents the rotor blank,\u00b5 is the mounting angle of a disc-milling cutter and a0 is the center distance between the disc-milling cutter and the work piece. 5.1. Cutter trajectory The cutter coordinate system S0 is fixed at the centre of a fi c  a (\u03be) =   \u03c9L(r2 a \u2212 a2 \u2212 (r \u2212 \u221a a2 + b2 \u2212 2ab cos \u03be) 2 ), \u03c9L ( r2 a \u2212 a2 \u2212 ( r \u2212 \u221a a2 + b2 \u2212 2ab cos ( \u03be \u2212 here \u03c9 is the angular speed of the rotor, L the length of otor, ra the radius of the addendum circle of the rotor, b the istance between the centre point F2 and o1 and b = ra \u2212 rr",
            " The coordinate transformation from oordinate S1 to S0 is given by, x0 = a0 \u2212 x1 y0 = \u2212y1 cos\u00b5\u2212 z1 sin\u00b5 z0 = \u2212y1 sin\u00b5+ z1 cos\u00b5 (6) In machining, the milling cutter rotates about axis z0 at ngular velocity \u03c90 and the work piece fulfills the helical movement along the axis z1 at angular velocity\u03c91 with helical parameter p. Similar to the gear meshing, the contacting curve of the cutter path and the work piece path must obey the following: (1) the contact point on the contacting curve must be the common point on both paths; (2) two paths are tangent at all contacting points; (3) the common normal at the contact point of two paths must be normal to any of the two paths at the contacting point. Suppose point M in Fig. 5 is the contact point of a rotor blank and a milling cutter, it can be expressed in the cutter coordinate system S0 at the centre of the cutter as, r0 = O0M = x0i0 + y0j0 + z0k0, (7) and in the reference coordinate system S1 at the centre of the rotor blank as, r1 = O1M = x1i1 + y1j1 + z1k1. (8) Hence, the velocity of the cutter at point M represented in the cutter coordinate frame is, v0 = \u03c90(k0 \u00d7 r0) (9) The velocity of the rotor blank at point M is, v1 = \u03c91(k1 \u00d7 r1 + pk1). (10) r v \u03c9 where n is the normal vector of the helical tooth profile as in Appendix A",
            " (17)\u2013(19) into (20), the cutter center distance can be expressed as, a0 = \u2212p 2\u03b8 y1 = \u2212 p2\u03b8 rc1 sin(\u03b1c1 + \u03b8) (21) Finally, the relationship between the cutter centre distance and the mounting angle can be expressed as, a0 = \u2212 rc1\u03b8 tan2 \u00b5 cos2(\u03b1c1 + \u03b8) sin(\u03b1c1 + \u03b8) (22) This equation gives the relationship between the cutter centre distance and the cutter mounting angle. By adjusting the cutter mounting angle and the centre distance, machining the helical tooth profile can avoid the undercut and over-cut at the connecting points. 6 T e m s r a he plane o1y1z1 in Fig. 5, the cutter mounting angle can be btained as, an\u00b5 = tx1 ty1 = p x1 = p rc1 cos(\u03b1c1 + \u03b8) (19) Thus, the cutter mounting angle \u00b5 can be determined by electing parameters of the screw pitch p, radius of the conecting point rc1 , angle \u03b1c1 between o1c1 and x1 axis and . The machining Hence, the above analysis generates the cutter trajectory. his can be obtained from the above four steps, by considring the cutter centre distance a0, the disc-milling cutter ounting angle \u00b5 and the helical angle \u03b8. The trajectory is imulated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003860_j.mechmachtheory.2018.09.013-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003860_j.mechmachtheory.2018.09.013-Figure6-1.png",
        "caption": "Fig. 6. Kinematic diagram of a standard PRS with respect to the test bench (left) and the planet carrier (right).",
        "texts": [
            " Finally, once the dimensions of the contact ellipse are known, the maximum Hertzian and average pressures can also be calculated: P h = 3 N 2 \u03c0ab P m = N \u03c0ab (44) From a kinematic point of view, roller screws work similarly to planetary gear trains, with the addition of axial movement and some inherent slip. In this section, we study the stationary regime of an idealized mechanism, i.e. all speeds are assumed constant and there is no geometrical error due to machining, wear or deformation that would prevent roller-nut or roller-screw thread contacts from being identical between themselves. Rollers are assumed to be identical, such that their rotation axis and geometrical axis coincide at all times. In these conditions, we can draw the kinematic diagram of a roller screw as shown in Fig. 6 . Let us assume that ( O, x, y, z ) is a Galilean frame fixed to the test bench on which the mechanism operates. The screw S pivots with respect to this frame, such that only a rotation around z is permitted. The nut N , on the other hand, can only translate in this direction. Although in reality there are actually two planet carriers, it is assumed that the rollers pivot in between with axes parallel to the z direction, such that the two sides of the carrier P exhibit an identical movement at all times. Furthermore, this movement is assumed to be a pure rotation around the same z axis as the screw and nut. Note that the figure was drawn for a standards PRS and therefore there is no contact between the carrier and the screw. For an inverted PRS, P would pivot around S instead of N . Let c be the radial distance between the screw/nut/carrier and roller axes during the stationary regime. As shown on the right side of Fig. 6 and mentioned in [5,14] , the contact points I between the screw and a given roller are usually not included in the plane formed by the axes of the two objects for a standard PRS. This is due to the difference in helix angles. The same is true for the contact points J between the nut and a roller in the case of an inverted PRS. Let us now consider a reference frame ( O p , x p , y p , z ) attached to P such that x p points towards the center of one of the rollers. If the carrier is fixed as a reference, the relative motion of the other 3 components in the x p y p plane corresponds to pure rotations around z , which means that the geometrical x p and y p coordinates of the contact points remain constant in this frame. This simplifies equations a lot, because instead of deducing the contact points location during motion, we can use purely geometrical formulas like the ones published by the authors in Ref. [1] . In the stationary regime, the mechanism\u2019s kinematics can be entirely defined by four variables, one for each component ( S,R,N and P ). This is because all links on the left side of Fig. 6 only have one degree of freedom. Three of these variables are chosen to represent relative rotation speeds around z with respect to the planet carrier ( \u03c9 s / p , \u03c9 r / p , \u03c9 n / p ), while the fourth variable quantifies the axial translation speed along z of the nut assembly with respect to the screw ( \u0307 zn/s ) . In the following paragraphs, we show how it is possible to reduce the number of kinematic variables from four to one, for both standard and inverted PRS. We thus obtain a kinematic model of the roller screw with only one degree of freedom in the form of a non-dimensional slip ratio \u03b5, which could afterwards be adjusted according to the forces, materials and lubricants present in the mechanism",
            " In all cases, the kinematic model developed earlier predicts a certain allowed interval for this slip ratio, as well as an ideal value \u03b5\u2217, which should be approached to reduce the amount of sliding in the mechanism. These conditions are summarized below: standard PRS: \u03b5 \u2208 [0, \u03b5\u2217] where \u03b5\u2217 defined by Eq. (60) inverted PRS: \u03b5 \u2208 [ \u03b5\u2217, 1] where \u03b5\u2217 defined by Eq. (61) . As shown in the previous sections, the amount of sliding which occurs in a given roller screw can be characterized by the slip ratio \u03b5. For the current paper, \u03b5 was measured using the setup presented in Fig. 9 . The experimental device uses a standard PRS and follows the same kinematic diagram as the one shown in Fig. 6 , where the screw is powered by a motor to rotate with respect to the test bench, while the nut assembly can only translate. When the screw turns, it pushes the nut assembly towards the right. The motor is placed on the left side and is not shown in Fig. 9 . Two thermocouples used to monitor temperature are also present on the apparatus, although we don\u2019t discuss thermal effects on \u03b5 in the current paper. All the experiments were conducted at a room temperature of 20 \u00b0C. The motor can be controlled such that we are able to specify a target speed for the screw"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.1-1.png",
        "caption": "Fig. 1.1. Aircraft coordinate system",
        "texts": [
            " This chapter aims at offering the reader a clear understanding of the control application and its requirements. Before discussing the physics governing the dynamics of the aircraft on the ground, we will give the notations, the conventions and the main coordinate systems used in this chapter. D. Bates et al. (Eds.): Nonlin. Anal. & Syn. Tech. for Aircraft Ctrl., LNCIS 365, pp. 3\u201324, 2007. springerlink.com c\u00a9 Springer-Verlag Berlin Heidelberg 2007 4 M. Jeanneau This coordinate system, also called the \u201daircraft coordinate system\u201d , is a mobile coordinate system (c.g.; XAC, YAC, ZAC), see Fig. 1.1. Its origin is the centre of gravity of the aircraft and its three longitudinal, lateral and vertical axes correspond respectively to the three longitudinal, lateral and vertical axes associated with the aircraft symmetry characteristics. The translations and rotations of this coordinate system are therefore directly linked to the motion of the aircraft. This coordinate system (O; XE , YE , ZE ) is a Galilean coordinate system where the origin is a fixed random reference point in space. In general, this point is taken as being equal to the initial position of the centre of gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003985_cjece.2015.2465160-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003985_cjece.2015.2465160-Figure1-1.png",
        "caption": "Fig. 1. 8/6 double-sided AFSRM.",
        "texts": [
            " Associate Editor managing this paper\u2019s review: Hilmi Turanli. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/CJECE.2015.2465160 research has been done on the torque ripple reduction in the radial flux SRM [5]\u2013[9]. Due to the importance of this matter, a new structure is introduced here for the double-sided AFSRM in which the torque ripple is smaller. The geometrical model of an 8/6 double-sided AFSRM is shown in Fig. 1. The motor has two stators and each stator is considered as a disk-shaped core with eight poles on 0840-8688 \u00a9 2016 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. one side. The rotor is a disk-shaped aluminum core with six embedded rotor poles on each side. Since there are two paths for stator pole flux in the stator core, the stator core thickness should be selected to correspond with the stator pole area. In order to minimize the eddy current losses, both poles and stator back-iron must be made of the laminated steel plate as it has already been manufactured for the prototype machine in [3]. To form the phase winding, the coils of the pair of stator poles placed on each stator are connected in series and the corresponding phase windings on the two stators are then connected in parallel. As a result, the 8/6 double-sided AFSRM is a four-phase motor. For the 8/6 double-sided AFSRM shown in Fig. 1, the rotor poles are located symmetrically in both the sides of a rotor core. In other words, the rotor poles in the two halves of the rotor are completely aligned. In the case that the rotor poles are displaced by \u00b1\u03b1\u00b0, a new topology is obtained which is shown in Fig. 2. Due to this displacement, the phase inductance profile of the motor changes as explained hereafter using an analytical method. When the rotor poles in the two halves of the rotor are aligned (Fig. 1), the phase inductance of the 8/6 doublesided AFSRM can be modeled using the Fourier series as follows [10]: L(i, \u03b8) = L0(i) + L1(i) cos(Pr\u03b8) + L2(i) cos(2Pr\u03b8) (1) where \u03b8 is the rotor position, i is the phase current, Pr is the number of rotor poles, and L0(i) = 1 2 [ 1 2 (La + Lu) + Lm ] (2) L1(i) = 1 2 (La \u2212 Lu) (3) L2(i) = 1 2 [ 1 2 (La + Lu) \u2212 Lm ] (4) where La and Lu are the inductance values at the aligned and unaligned positions and Lm is the inductance at the midway between the unaligned and aligned positions",
            " In the case that the rotor poles are displaced by \u00b1\u03b1\u00b0, as shown in Fig. 2, the inductance related to one side of the rotor can be rewritten as Lx (\u03b8, \u03b1)= 1 2 [L0 + L1 cos(Pr (\u03b8\u2212\u03b1)) + L2 cos(2Pr (\u03b8 \u2212 \u03b1))]. (5) And for the other side L y(\u03b8, \u03b1)= 1 2 [L0 + L1 cos(Pr (\u03b8+ \u03b1)) + L2 cos(2Pr (\u03b8+ \u03b1))]. (6) For the 8/6 double-sided AFSRM, when the rotor poles are displaced, the inductance profiles obtained from (5) and (6) and the phase inductance profile are shown in Fig. 3. For the motor without the displacement (Fig. 1), the phase inductance profile calculated using (1) is also shown in this figure. Due to the displacement, the phase inductance profile varies as shown in Fig. 3. The rotor poles displacement certainly results in changing the instantaneous torque waveform because of its dependence on the inductance profile. For the changed instantaneous torque waveform, the torque ripple is reduced, as shown in Section III, using the simulation results derived from 3-D finite-element (FE) method. An 8/6 double-sided AFSRM with the specifications given in Table I is considered here, the simulation results are presented when the 3-D FE transient analysis of the motor is carried out using the MAXWELL FE package for the operating point: phase voltage = 93 V, speed = 1500 RPM, TON = 10\u00b0, and TOFF = 25\u00b0, and the package is in singlepulse control mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003860_j.mechmachtheory.2018.09.013-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003860_j.mechmachtheory.2018.09.013-Figure9-1.png",
        "caption": "Fig. 9. Experimental apparatus for measuring \u03b5.",
        "texts": [
            " In all cases, the kinematic model developed earlier predicts a certain allowed interval for this slip ratio, as well as an ideal value \u03b5\u2217, which should be approached to reduce the amount of sliding in the mechanism. These conditions are summarized below: standard PRS: \u03b5 \u2208 [0, \u03b5\u2217] where \u03b5\u2217 defined by Eq. (60) inverted PRS: \u03b5 \u2208 [ \u03b5\u2217, 1] where \u03b5\u2217 defined by Eq. (61) . As shown in the previous sections, the amount of sliding which occurs in a given roller screw can be characterized by the slip ratio \u03b5. For the current paper, \u03b5 was measured using the setup presented in Fig. 9 . The experimental device uses a standard PRS and follows the same kinematic diagram as the one shown in Fig. 6 , where the screw is powered by a motor to rotate with respect to the test bench, while the nut assembly can only translate. When the screw turns, it pushes the nut assembly towards the right. The motor is placed on the left side and is not shown in Fig. 9 . Two thermocouples used to monitor temperature are also present on the apparatus, although we don\u2019t discuss thermal effects on \u03b5 in the current paper. All the experiments were conducted at a room temperature of 20 \u00b0C. The motor can be controlled such that we are able to specify a target speed for the screw. As the screw starts turning, the nut assembly translates along its track with increasing speed. The stationary regime, which corresponds to approximately constant velocities, begins when the target screw speed is reached. It lasts long enough for us to gather sufficient data points, then ends when the end of the track is reached and the mechanism stops. The roller screw is loaded using a system of two parallel hydraulic cylinders, not shown in Fig. 9 . These cylinders apply a constant resistive force on the nut assembly, directed towards the left. Its magnitude is adjustable and can be measured with a sensor based on deformable elements. A more precise value of the screw speed can be obtained from a Hall effect sensor, placed close to an encoder wheel fixed to the shaft. The wheel has grooves machined into it, which can be counted to determine the angle traveled by the screw in a certain amount of time. A similar setup is used to measure the angular speed of the planet carrier",
            " The first method consisted in plotting \u03b5 as the point-by-point ratio of the carrier and screw speeds, then calculating the average of the obtained signal when the mechanism was at steady-state. This method proved to be very inaccurate with regard to the expected behavior and was discarded. In the second method, we calculated the averages of the two speed signals first, then computed \u03b5 as the ratio of the obtained averages. Better tendencies were observed and the method was retained. A total of 15 experiments have been performed using a standard PRS with dimensions and lubricant mentioned in the table in Fig. 9 . The rectified screw diameter was approximately 30 mm. Each experiment was conducted for different values of the resistive force on the nut and input speed on the screw, in order to sweep the entire range available on the test bench. The tested domain with the obtained values for \u03b5 are presented in Fig. 10 . For each experiment, the number of discrete points forming the speed and force signals was different. However, a minimum of 30 0 0 points on the speeds and 600 points on the force has been assured for calculating the averages shown in Fig",
            " For the hypotheses made in the current paper, where all roller-screw contacts I are identical and all roller-nut contacts J are also identical, we have: W PRS = N R N C (W I + W J ) + W 0 , (74) where W I and W J are obtained numerically, using Eq. (73 ). N R represents the number of rollers and N C the number of rollerscrew (R/S) or roller-nut (R/N) contacts per roller. W 0 corresponds to all the other power dissipation sources, including the planet carrier and gears. In the current work we consider sufficient play in the carrier pivots, such that W 0 becomes negligible. For the PRS dimensions mentioned in Fig. 9 , where the sliding velocity field has been traced in Fig. 13 , the total dissipated power calculation yields W PRS = 130 . 1 Watts. This is the reference value ref considered in the following analysis, which has a corresponding optimality of 99.72%. In Fig. 14 , we show the influence of optimality (or the slip ratio \u03b5) on the dissipated power. Calculations were performed for different optimality values, while keeping the rest of the parameters constant. The left side of Fig. 14 was traced for coarse variations in optimality, while the right side considers finer values near the reference case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001206_bit.260310607-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001206_bit.260310607-Figure1-1.png",
        "caption": "Figure 1. Schematic view of the reactor. Cross-sectional area of the working electrode is 2.5 X 1 cm and the length (L) is 6 cm. The electrical section area is 6 X 2.5 cm.",
        "texts": [
            " 10 cm2 and optimization of the catalytic current was performed in the case of a batch operation, but the preparative potentiality of this method could not be demonstrated with so low currents (0.5 mA gave a gluconic acid production of ca. 2 mg/h). The purpose of this report is to scale up this process ca. lo00 times in order to reach the laboratory preparative scale and to investigate new specific methods and modeling adapted for catalytic enzyme electrodes of large areas. CCC 0006-3592/88/060553-06$04.00 We utilized a fixed-bed reactor with a parallelepipedic electrode of a total volume of 14 cm3 (Fig. 1). This electrode is a carbon felt (RVG 4000 from Carbone Lorraine) and individual fibers of the felt have an average diameter of 10 pm. The volumic area (a) is 350 cm2/cm3 which gives a total effective area of 5000 cm2 for the electrode. Auxiliary electrode and working electrode collector are both made of vitreous carbon. The working and auxiliary compartments are separated by an anion exchange membrane (Selemion A M V from Asahi). This electrochemical reactor may be used in a three-electrode configuration (with a saturated KCl calomel reference electrode: SCE) or if necessary as a twoelectrode system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002454_melcon.2010.5476026-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002454_melcon.2010.5476026-Figure3-1.png",
        "caption": "Fig. 3. Tracking response of the \u03c6 Euler angle",
        "texts": [],
        "surrounding_texts": [
            "From equation (15) and for a given U \u2217 1 a discrete time system that computes the desired values for roll and pitch \u03c6d,\u03b8d using the referenced values for position control xd,yd can be formulated. By discretizing (4) it is obtained: xp d(k) \u2212 2xp d(k \u2212 1) + xp d(k \u2212 2) = \u2212T2 s m \u03b8d(k)U\u2217 1 yp d(k) \u2212 2yp d(k \u2212 1) + yp d(k \u2212 2) = T2 s m \u03d5d(k)U\u2217 1 (19) where Ts is the sampling period used in the CFTO\u2013controller. Solving for \u03c6d, \u03b8d the expression for desired roll and pitch as a function of the reference position signals is derived: \u03b8d(k) = \u2212mxp(k)\u22122xp(k\u22121)+xp(k\u22122) U\u2217 1 T2 s \u03d5d(k) = m yp(k)\u22122yp(k\u22121)+yp(k\u22122) U\u2217 1 T2 s \u03b8d(1) = \u03b8d(2) = \u03d5d(1) = \u03d5d(2) = 0 These reference signals are produced from the planning module and are utilized as the reference input to the CFTO attitude controller. By the integration of this two\u2013phase approach the trajectory tracking is achieved for planar and smooth motion of the UqH."
        ]
    },
    {
        "image_filename": "designv10_10_0003796_j.prostr.2017.07.166-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003796_j.prostr.2017.07.166-Figure1-1.png",
        "caption": "Fig. 1: Original (left) and optimized (right) shape of the analyzed bracket.",
        "texts": [
            " The case study herein analyzed is a structural bracket for aerospace application, made of Ti-6Al-4V alloy through the AM techniques. The shape of bracket was defined by a topological optimization, aimed at reducing mass, limiting displacement and stress, and controlling the natural frequencies to satisfy some design requirements of the main system where the bracket will be assembled. It is worthy noticing that the optimization process reduced the mass of the original configuration to the 80% of its initial value. The shape was conformingly changed as shown in Fig.1. The new brackets were then produced by SLM and EBM. The research activity was aimed at assessing a design process to define the optimized shape of the bracket which could fit some customer needs. A key issue in modelling the mechanical component for design purpose concerns the material behavior. The presence of internal defects makes the material inhomogeneous, but inhomogeneities are randomly distributed within the volume of the mechanical component. A preliminary estimation of the mechanical behavior of material was therefore performed by assuming a homogeneous constitution of material, with average values of mechanical properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001794_ac00226a030-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001794_ac00226a030-Figure2-1.png",
        "caption": "Figure 2. Effect of pH on the response of the tissue-based adenostne electrode for adenosine (0) and AMP (A) (four electrodes tested).",
        "texts": [
            " From Figure 1 it can be seen that each of the adenosine-containing nucleotides studied severly interferes with the adenosine response of the electrode system. In order to enhance the selectivity of the tissue-based adenosine electrode, it is desirable to optimize the adenosine deaminating activity and to repress the nucleotide deaminating activity. The optimum pH for the system is determined by measuring the relative activity from potential vs. time data (see procedures) with respect to changes in pH to optimize the adenosine deaminating activity of the biocatalytic layer. Figure 2 shows the percent maximum activity of the adenosine and AMP deaminating activities with respect to pH. This indicates that a pH range of 9.0-9.4 is optimum for the adenosine deaminating activity. A pH of 9.0 is used for all further studies in order to take advantage of the maximum adenosine deamination, the decrease in the AMP deamination, and the larger buffering capacity of the Tris-HC1 buffer system. The most effective method of repressing the interfering activity is dependent upon the metabolic pathway responsible for this activity",
            " The effect of L-phenylalanine on the response for AMP of the tissue-based adenosine electrode is shown in Figure 4. It can be seen that at a concentration of 0.1 M L-phenylalanine, inhibition of the AMP deaminating activity is realized and virtually no response for AMP is detectable by the electrode system. The reported pH optima for the enzymes under consideration are approximately 6.5 for AMP deaminase (9) and from 7.0 to 9.0 for alkaline phosphatase (1 7). The pH optimum for the AMP deaminating activity of the mouse small intestinal mucosal cells is 8.2 (See Figure 2) which is within the optimum pH range of alkaline phosphatase. High activity of AMP deaminase is commonly found in muscle tissues (9); whereas, alkaline phosphatase is found at maximum activity levels in intestinal mucosal cells of various animal species (1 7). Previously reported distribution patterns of these enzymes and the results presented above, including the inhibitory effects of glycerophosphate, phosphate, and L-phenylalanine, the lack of activation by potassium ions, and the pH optimum of the interfering activity, provide strong evidence that the coupling of alkaline phosphatase and adenosine deaminase is principally responsible for the interfering activity of the mucosal cell biocatalytic layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002124_3.7566-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002124_3.7566-Figure1-1.png",
        "caption": "Fig. 1 Magnus and normal forces on a spinning projectile.",
        "texts": [
            " Recent Army interest in achieving increased range and greater payload capacity in artillery projectiles has led to designs with long, slender ogives, increased projectile length, and boattailed afterbodies. These designs have resulted in decreased drag with a resulting increase in range; however, the gyroscopic stability of these shapes is less than that of more conventional designs. This means that these new shapes are more susceptible to a Magnus-induced instability. The Magnus force is small (Fig. 1), typically 1/10 to 1/100 of the normal force; however, its effect is important because the Magnus moment can be of sufficient magnitude to cause the projectile to become dynamically unstable. Thus, it is desirable to minimize the Magnus moment in order for the projectile to fly at a small average angle of attack and achieve the greatest range capability. D ow nl oa de d by U N IV E R SI T Y O F M A R Y L A N D o n O ct ob er 1 5, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .7 56 6 688 W"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure12-1.png",
        "caption": "Figure 12. A double-slider spatial linkage, showing how two rotational freedoms in both the G-pairs are inactive, and how the output-input relationship is the same as that of the projected planar linkage.",
        "texts": [
            " There are a few other minor variations on this theme, such as revolute pairs whose axes intersect, but these are not now pursued. . Miscellaneous Linkages w i th Prismatic Pairs 6.1. Besides all the linkages listed so far, there are many single loops containing one or two prismatic pairs that behave fully as expected from equation (I) with b = 6 . Since this paper concentrates on 'special' linkages, these are not detailed. But there is one linkages, the spatial double slider, that appears in various forms, one being that shown in Fig. 12. There is here an additional freedom (rotation of member 3 about its own longitudinal axis) that does not affect the conversion of one translation along P~ 2 into another along P+t. The fact that the two guides on member 1 do not physically intersect, and do not physically pass through the centres of the G-pairs, is immaterial f rom the kinematic point of view. The transmission of movement from one slide to the other is identical in a linkage obtained by projecting the original one on a plane defined by the . directions of Ptz and P41, namely in a planar linkage of the elliptic trammel type as shown in Fig. 12. Even with the guides offset, as in the original linkage, two of the three rotational freedoms available in, each G-pair can always remain inactive, and both G-pairs can be replaced by appropriately aligned parallel R-pairs. Closure 7.1. The survey in this paper does not claim to be complete. In fact one is led to believe that there may be several other classes of 2P--4S single-loop linkages with M = 1 that are not covered in Table 4. Dimentberg [I0], [1 I] proves the existence of a special 2C-2R linkage that could be regarded as deriving from the more general 2P--4S linkage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure2-1.png",
        "caption": "Fig. 2. Illustrative diagram of coordinate transformation of honing stone dressing process.",
        "texts": [
            " In a normal generating honing process, the dressing tool profile is given, the profile of honing stone is shaped by a dressing tool using a generating dressing process, and the work gear profile is generated by the honing stone using a generating honing process. Fig. 1 shows that the honing stone is dressed by a standard involute diamond dressing gear mounted on the C2 axis. The dressing process is completed by A, X, C1, and C2 axis of the internal gear honing machine. CNC axes X, C1, and C2 are the simultaneously controlled axis for the dressing motion, while A is the machine setting, which is kept constant during the dressing process. The coordinate systems for the honing stone dressing process are shown in Fig. 2 , in which coordinate systems S d ( O d \u2212 x d , y d , z d ) and S h ( O h \u2212 x h , y h , z h ) are rigidly connected to the dressing tool and honing stone, respectively. The coordinate systems S 1 ( O 1 \u2212 x 1 , y 1 , z 1 ) and S 2 ( O 2 \u2212 x 2 , y 2 , z 2 ) are the auxiliary coordinate systems for the dressing process. On a CNC internal gear honing machine, there are two dressing movements: a rotation of the dressing tool \u03c6 (the C2-axis movement in Fig. 1 ) and a rotary motion of the honing stone \u03c6 (the C1 axis motion in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003005_s12046-014-0275-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003005_s12046-014-0275-0-Figure2-1.png",
        "caption": "Figure 2. Mechatronic system of UAV engine with ETCS.",
        "texts": [
            " (11) The flight path angle is denoted by \u03b3 = tan\u22121 (w/u) = tan\u22121 (V sin \u03b1/V cos \u03b1), where V =\u221a u2 + w2 and \u03b1 = (\u03b8 \u2212 \u03b3 ) (Akmeliawati & Mareels 2010; Hull 2009). The pitching moment M is written as (Wang & Stengel 2000; Hull 2009) M = 1 2 \u03c1V 2Sc ( CM0 + CM\u03b1\u03b1 + CMq cq 2V + CM\u03b4e \u03b4e ) , (12) where CM0 , CM\u03b1 , CMq and CM\u03b4e are pitching moment control derivative of the UAV model. After applying trim condition on (12), yield (13) \u03b1 = \u2212(CM0 + CM\u03b4e \u03b4e)/CM\u03b1 . (13) Equations (9) to (13) give the complete model of nonlinear UAV. The Mechatronic system of UAV engine that provides thrust force, with electronic throttle control system (ETCS) is shown in figure 2. In figure 2 the throttle position is shown with \u03b4T and if \u03b4T is controlled the kinetic energy given by Ek = (1/2)mV 2 may be controlled using (9). In figure 2 the ETCS consists of DC servo motor to rotate the throttle plate. Here the DC servo motor is controlled by the applied motor voltage Ea (Yadav & Gaur 2014; Vasak et al 2007). dia dt = ( 1 La )( \u2212Raia \u2212 Kb d\u03b8m dt + Ea ) , (14) where ia is armature current (A), \u03b8m is armature angular position (rad). The back EMF Eb due to the motor rotation is Kb(d\u03b8m/dt). The meaning of symbols used in equations is given in table 1. The motor and rotational dynamics of throttle is as follows: d2\u03b8m dt2 = ( 1 Jm )( \u2212Bm ( d\u03b8m dt ) \u2212 TL + Tm ) , (15) d2\u03b4T dt2 = ( 1 Jg )( \u2212Tsp \u2212 Bt ( d\u03b4T dt ) \u2212 Ta + Tg ) , (16) where N is the gear ratio which governs the engine speed that is defined as N = \u03b8m/\u03b4T = Tg/TL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003811_j.mechmachtheory.2017.11.024-Figure5-1.png",
        "caption": "Fig. 5. Illustrative diagram of coordinate transformation of honing process.",
        "texts": [
            " Mathematical model of gear generating honing The CNC axes on an internal gear honing machine and the corresponding coordinate systems for gear generating honing are shown in Figs. 1 and 2 , respectively. The motion control diagram for the gear honing machine is shown in Fig. 4 , in which the tangent circle icon defines a constant gear ratio applied to fulfill a specific relative motion between the work gear and honing stone in a standard gear generating process. The curve table icon represents a modified function added onto the corresponding standard constant gear ratio to modify the work gear\u2019s tooth surface topology. Fig. 5 shows that the coordinate systems S h ( O h \u2212 x h , y h , z h ) and S g ( O g \u2212 x g , y g , z g ) are rigidly connected to the honing stone and work gear, respectively, while coordinate systems S 3 ( O 3 \u2212 x 3 , y 3 , z 3 ) , S 4 ( O 4 \u2212 x 4 , y 4 , z 4 ) , and S 5 ( O 5 \u2212 x 5 , y 5 , z 5 ) are auxiliary coordinate systems for simplicity of coordinate transformation during the gear honing process. The honing stone has three movements: axial feed F z1 along the axis of gear z g , the swivel rotation \u03c6A of honing stone head A for axis crossing angle, and the swivel rotation \u03c6B of honing stone head B for longitudinal crowning and tapering"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-18-1.png",
        "caption": "FIGURE 12-18 Elementarv hydraulic position control. (From W. S. Hockey, The Institution of Mechanical Engineers, Nov. 1961.)",
        "texts": [
            " The relative positions of the hand lever and of the hydraulic cylinder are always identical. Within the limit of the relief valve controlling the maximum pressure, the hydraulic cylinder will automatically move the implement to its predetermined position and maintain it there, regardless of any leakage in the system. The position-control system is normally associated with a three-point hitch system. It is not used with a remote cylinder. The most elementary form of a position control system is shown in figure 12-18. Automatic Draft-Control System These systems will automatically raise or lower an implement as the draft or resistance of the attached implement increases or decreases. The sensing device, which tells the hydraulic system to lower or raise the hitch system, is located on either the lower links or the upper link, depending on the size of the tractor. The position of the hand-control lever, in effect, establishes the draft to be maintained. For example, a draft-control system on a tractor pulling a plow will raise and lower the plow to maintain a constant force on the sensing device",
            " 332 HYDRAULIC SYSTEMS AND CONTROLS The overall transfer function, o/i, is o/i (15) Until now we have not discussed the physical meaning of G j , G2 , and F (the blocks). G j can be a valve whose output is the flow rate (measured in volume/time) and the input is the motion of the spool. Thus, G j is the output! input ratio (or flow gain) with the units of (L/s)/mm. G2 includes the dynamic behavior of the system (the cylinder plus the hydraulic oil plus the masses attached to the cylinder). F is the feedback loop, which might be either a mechanical linkage at tached to an \"error bar\" (see fig. 12-18) or a pressure line to sense the load on, or the position of, the output of the cylinder, as in hydrostatic power steering. Further information on automatic control theory can be obtained from the references at the end of the chapter. A concise and yet complete treatise on automatic hydraulic, or fluid power, control systems is provided by Merritt ( 1967). The method of automatically controlling a three-point hitch can be vis ually grasped by a thorough study of figure 12-22. This illustration shows the hydraulic system controlling the three-point hitch on a series of large tractors by a major manufacturer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.33-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.33-1.png",
        "caption": "Figure 6.33 material. (Source: From [2], p. 349.) Finite biconical antenna with boundary sphere replaced by shell of magnetic",
        "texts": [],
        "surrounding_texts": [
            "1. E. C. Jordan and K. G. Balmain, Electromagnetic Waves and Radiating Systems, Prentice- 2. J. D. Kraus, Antennas, 2nd ed., McGraw-Hill, New York, 1988. 3. S. A. Schelkunoff and H. T. Friis, Antennas; Theory and Practice, Wiley, New York, Hall, Inc., Englewood Cliffs, NJ, 1968. 1952. 4. S. Silver, ed., Microwave Antenna Theory andDesign, M.I.T. Radiation Laboratory Series, McGraw-Hill, New York, 1949. 5 . W. L. Stutzman and G. A. Thiel, Antennu Theory and Design, 2nd ed., Wiley, New York, 1998. 6. C. A. Balanis, Antenna Theory; Analysis and Design, 2nd ed., Wiley, New York, 1997. 7. R. E. Collin, Antennas andRadio M'ave Propagation, McGraw-Hill, New York, 1985 8. D. H. Staelin, A. W. Morgenthaler and J. A. Kong, Electromagnetic Waves, Prentice-Hall, Englewood Cliffs, NJ, 1994. PROBLEMS 281 9. S. Ramo, J. R. Whinnery and T. Van Duzer, Fie1d.v and Wnves in Comnnmrcution Electronics, 3rd ed., New York, 1994. 10. A. A. Smith Jr., Radio Frequency Principles and Applications, IEEE Press/ Chapman & Hall, New York, 1998. 1 I . C. R. Paul, Introduction to Electromagnetic Compatihilih, Wiley, Inc., New York, 1992. 12. IEEE, IEEE Standard 100- 1972, IEEE Standard Dictionaiy of Electrical and Electronics Terms, Wiley-Interscience, New York, 1972. 13. IEEE, 1983 version of 12 14. G. Sinclair, \u201cThe Transmission and Reception of Elliptically Polarized Waves,\u201d Proc. IRE, 38 (February 1950): 148-1.51. 15. E. J. Jahnke and F. Emde, Tables of\u2019Functions,4th ed., Dover, New York, 1945. 16. M. Abramowitz and I. A. Stegun, Handbook of Muthematical Functions, Applied Mathematics Series 5 5 , National Bureau of Standards, Washington, DC, June 1969."
        ]
    },
    {
        "image_filename": "designv10_10_0003231_s00332-013-9174-5-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003231_s00332-013-9174-5-Figure2-1.png",
        "caption": "Fig. 2 Comparison between trajectories of a single dipole in an unbounded plane and in a doubly periodic domain for \u03c91 = 0.2, \u03c92 = 0.2i, and \u03b1(0) = \u03c0/3. Black color denotes the path taken by the dipole in a doubly periodic domain, while gray color denotes the path taken by the dipole in the unbounded plane. In both cases, the orientation \u03b1 remains constant for all time, but in the doubly periodic domain, the slope of the trajectory traced by the dipole center is not equal to \u03b1",
        "texts": [
            " (13) Note that the second term on the right-hand side of the first equation is identically zero in a square domain. This equation can be integrated in closed form, z = \u0393 2\u03c0 i [ \u03b6 (\u2212i ei\u03b1) \u2212 ( \u03c0\u03c91 \u0394\u03c91 \u2212 \u03b71 \u03c91 ) i ei\u03b1 \u2212 \u03c0 \u0394 i e\u2212i\u03b1 ] t + z(0), \u03b1 = \u03b1(0). (14) Here, z(0) and \u03b1(0) are the initial position and orientation of the dipole, respectively; that is, a single dipole always moves in a straight line with its orientation angle \u03b1 unchanged. However, the slope of the linear trajectory of the dipole center is not in the direction of the orientation angle \u03b1 (see Fig. 2), except for special initial conditions such as \u03b1(0) = k\u03c0/2, k arbitrary integer. The reason for this discrepancy between the slope of the dipole trajectory and its orientation is due to the periodic effect brought by the dipole images included in the \u03b6 -function. A single dipole affords two distinct types of dynamical behavior: aperiodic and periodic. For the former type, the single dipole traces out a path which fills up the whole domain, as depicted in Fig. 3(a). Here, the dipole never returns to the same location it visited, thus the term aperiodic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure12-1.png",
        "caption": "Fig. 12 \u2013 Discreet model of bus frame \u2013 top front part.",
        "texts": [],
        "surrounding_texts": [
            "The object of study was a bus structure based on Volkswagen LT vans type: 2DX0AZ model LT produced by Automet in Sanok, Poland (Fig. 9). The basic technical specifications of the vehicle are presented in Table 2. The body of the bus was made of steel characterized by the following properties (Table 3): yield limit, Re_min = 198 MPa, tensile strength, Rm_min = 364 MPa, elongation, A5 = 22% Table 3 \u2013 Tensile characteristics for the material of the body. Strain [ ] Stress (MPa) 0.005 210.3 0.01 222.5 0.02 245.2 0.04 277.5 0.06 299.8 0.08 316.6 0.10 328.8 0.12 341.0 0.14 347.8 0.16 353.1 0.18 357.5 0.20 361.1 0.22 363.7 According to the manufacturer (VW) the frame of the vehicle was made of steel St 12.03 and St 37-2, whose strength properties are listed in table: St 12.03 yield limit, Re_min = 210 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% St 37-2 yield limit, Re_min = 235 MPa, tensile strength, Rm_min = 360 MPa, elongation, A5 = 19% Taking into account the quantitative changes in the material, i.e. the strain rate, the material model based on the assumed viscoplasticity of the material was obtained. A broad review of this characteristic is included in works [10,11]. The hardening velocity \u00c7 e equals elastic hardening velocity \u00c7 eel and viscoplastic hardening velocity, \u00c7 ev p \u00c7 e \u00bc\u00c7 eel \u00fe \u00c7 ev p; whereas the value of stress equals: s \u00bc E \u00c7 e \u00c7 ev p ; where E is the elasticity module. The finite element method uses the models of hardening at deformation velocity based on the abovementioned model, e. g. Cowper\u2013Symonds model [12]: s \u00bc\u00c5 s0 1 \u00fe \u00c7 e D 0 @ 1 A 1= p2 64 3 75; where \u00c5 s0 is the static yield limit, p, D are material constants, equalled to 5 and 40 s 1 respectively. The bodywork is supported by a frame on wheels (twin wheels in the rear). The bodywork was furnished with basic elements of bus interior, i.e. seats, seats frame, reinforcement of side wall, reinforcement of back wall, reinforcement of roof with a support structure for the emergency compartment, shelves and ventilation shaft and the air-conditioning system. It also includes glass panes which are glued to the reinforced body structure. All these elements constitute a load to the bodywork structure but do not alter its original shape. The first stage was to prepare the geometric model of the external shape of the structure. The strength calculations [13] were conducted using specialized software which implements an explicit algorithm for computing simultaneous differential equations [14]. The geometric model served as a basis for a discreet model of the bus bodywork, which was used for calculations using the finite element method. The body and frame were modelled using shell elements. These are rectangular four-node shell elements with 6 degrees of freedom in the node. The average size of the finite element is approximately 20 mm. Due to the fact that during a strength test the material may be subject to partial plastification (material nonlinearity) and large hinges may cause the configuration to change significantly (geometric nonlinearity), all finite elements are adapted to calculations with both types of nonlinearity [15]. The geometric model of the bus is shown in Figs. 10 and 11. The discrete model with division into finite elements is presented in Figs. 12 and 13. In total the discreet model comprises 105 151 finite elements on 102 879 nodes. The complete model has approximately 617 000 degrees of freedom. Since there are two rows of seats on the left side of the bus, the centre of gravity is somewhat moved leftwards relative to the axis of the vehicle. Its coordinates relative to the system, whose beginning is on the tilting edge above the rear wheel, are presented in Table 4. By tilting the bus on its right side the worst case was analysed (greater kinetic energy). From the law of conservation of energy: Ep \u00bc Ek; Table 4 \u2013 Moments of inertia relative to the edge of tilt (the Z axis along the tilting edge) (kg T m2). Ixx Iyy Izz 28130 28840 7226 Ixy Iyz Izx 2586 4036 6493 where Ep is the potential energy, Ek is the kinetic energy of rotational motion. Thus, in accordance with point the Regulations Ep \u00bc M g h1 \u00bc M g 0:8 \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h2 0 \u00fe B t\u00f0 \u00de2 q where M = Mk is the unladen kerb mass of the vehicle type if there are no occupant restraints, or Mt is the total effective vehicle mass when occupant restraints are fitted, and, Mt = Mk + k*Mm, where k = 0.5. h0 is the height (in metres) of the vehicle centre of gravity for the value of mass (M) chosen, t is the perpendicular distance (in metres) of the vehicle centre of gravity from its longitudinal vertical central plane, B is the perpendicular distance (in metres) of the vehicle's longitudinal vertical central plane to the axis of rotation in the rollover test, g is the gravitational constant, h1 is the height (in metres) of the vehicle centre of gravity in its starting, unstable position related to the horizontal lower plane of impact. Ek \u00bc I v2 2 where I is the moment of inertia relative to the temporary axis of rotation (Table 4), v is the angular velocity relative to the temporary axis of rotation. Therefore v \u00bc 2:558 rad=s Fig. 14 depicts main initial conditions of the analysis. An additional initial condition was the influence of gravity and the contact phenomena occurring on the contact points of the bus bodywork and the tilt plane as well as in the structural elements of the superstructure. Method of performing the strength test of the bus is shown in Fig. 14 while Fig. 15 presents the location of the seats inside the vehicle and the definition of residual space [16]."
        ]
    },
    {
        "image_filename": "designv10_10_0000834_978-94-017-0657-5-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000834_978-94-017-0657-5-Figure12-1.png",
        "caption": "Figure 12. Orientation ofthe Biglide u-workspace",
        "texts": [
            " 325 Furthermore in the case of orientation A, singular configurations may appear inside the C-workspace, which is not acceptable. Indeed, the u workspace is used for the machining task, but the C-workspace can be used for changing the tool position between two machining operations. Singularities are then strictly prohibited. Thus orientation B is selected for the 2-DOF Orthoglide. Same comments about compactness and singularities avoidance can be made for the Biglide, thus orientation B is chosen (Fig. 12). This section explains how the u-workspace is designed: first the best workspace center locus is found by computing the VAF along the u workspace sides. Then the u-workspace is sized so that the VAF are inside the boundaries defined in section 3.1. 326 To find the best u-workspace center locus, we shift the u-workspace perpendicularly to (L1) and along (L1) (Fig. 13) and the VAF are computed for each configuration. In each case, VAF extrema are located along the sides PiPj: they start from 1 at point S, then they vary until they reach prescribed boundaries on VAF (Fig. 15, section 4.2). Computing the VAF (which analytical expressions Ai (XP,Yp) have been obtained with Maple) along the 4 sides of the square takes only 5 sec. with a Pentium II class PC. orthogonal to (L1) (Fig. 12), VAF are constant along these lines. Consequently, the workspace position will only be discussed along (11). This corresponds to the u-workspace sizing process described in section 4.2. in section 4.1 then the u-workspace is grown until the VAF meet their limits (Fig. 14). It appears that the VAF limits are met at points PI and P3 (Fig. 15). For the 2-DOF Orthoglide, the initial u-workspace center is point S. It appears that the first limit met is the upper one (Ai < 3), and that it is met by 11,2, simultaneously at points PI and P3, therefore point S remains the final u-workspace center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002670_imac4s.2013.6526493-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002670_imac4s.2013.6526493-Figure1-1.png",
        "caption": "Fig. 1. Twin Rotor MIMO System [4]",
        "texts": [
            " In the sliding mode, the system is completely insensitive to the parameter variations and external disturbances. In [2], the sliding mode controllers are proposed for the Twin Rotor MIMO System (TRMS). In [3], the sliding mode controllers are developed based on fuzzy inference for nonlinear systems. II. MODEL DESCRIPTION OF TWIN ROTOR MIMO SYSTEM TRMS is a laboratory prototype of a flight control system [4], [5]. It is a multi-input-multi-output (MIMO) nonlinear system, with significant cross coupling between main rotor and tail rotor as shown in Figure 1. The main rotor produces a lifting force allowing the beam to rise vertically (pitch angle), while the tail rotor is used to control the beam to turn left or right (yaw angle). Both motors produce aerodynamic forces through the blades. TRMS consists of two propellers which are perpendicular to each other and joined by a beam pivoted on its base in such a way that it can rotate freely in both horizontal and vertical planes. Also, a counterbalance arm with a weight at its end is fixed to the beam at the pivot to make the TRMS stabilizable",
            " Next, the derivative of \u03c3h can be written as: \u03c3\u0307h = Ch1(Ah11eh1 +Ah12eh2) + Ch2(Ah21eh1 +Ah22eh2) +Ch2Bh2uh (39) and using constant proportional reaching law: \u03c3\u0307h = \u2212\u03c11h\u03c3h \u2212 \u03c12hsign(\u03c3h) (40) From (39) and (40), it can be rewritten as: \u2212\u03c11h\u03c3h \u2212 \u03c12hsign(\u03c3h) = Ch1(Ah11eh1 +Ah12eh2) + Ch2(Ah21eh1 +Ah22eh2) +Ch2Bh2uh (41) The output of SMC uh = \u2212(Ch2Bh2) \u22121(Ch1(Ah11eh1 +Ah12eh2) +Ch2(Ah21eh1 +Ah22eh2) + \u03c11h\u03c3h + \u03c12hsign(\u03c3h)) (42) B. Design of Integral Sliding Mode Controller for a Vertical Subsystem From Figure 1, it can be seen that the TRMS weighs asymmetrically, where the main propeller is heavier than the tail propeller, i.e., the pitch angle would not stay under the uncontrolled situation. In this case, it is not easy to control the VS of the TRMS to achieve zero position error for the pitch angle by simple SMC. In order to eliminate the effect of the asymmetrical weight at ev1 = 0, an integral sliding mode controller (ISMC) is designed in this section. Let the scalar sliding function for the TRMS\u2013VS be \u03c3v = Cv1ev1 + Cv2ev2 + Cv3 \u222b ev1dt (43) where Cv1 = [Cv11 Cv12] \u03b5R 2, Cv11, Cv12 > 0, and Cv2 \u03b5R, Cv2 > 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003441_2.099309jes-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003441_2.099309jes-Figure3-1.png",
        "caption": "Figure 3. 3D and 2D models representing the fluid in the biofuel cell. The left model proved to be unnecessary, because the 2D version on the right had a very similar fluid velocity profile.",
        "texts": [
            " The results from the anode model were combined with experimental cathode half-cell results to approximate the performance of the biofuel cell. COMSOL Multiphysics 4.3a was used to solve the governing equations for fluid flow and species concentration. Geometry.\u2014The fluid in the biofuel cell was originally modeled as a 3-D solid. It was abandoned in favor of a simplified 2D version when it was found that the fluid velocity profile at the anode was only 10% different in the 2D version compared to the 3D one. Figure 3 shows the original 3D fluid model and the simplified 2D version. Note that only half of the anode was modeled since that portion of the device is plane-symmetric, which made the simulation run more efficiently. Fluid flow.\u2014In all regions except inside the anode, fluid flow was described by the equations for conservation of mass and momentum, Equations 2 and 3, respectively. The flow inside the porous anode was modeled using the Brinkman equation (Equation 4), which is an extension of Darcy\u2019s Law"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure2-1.png",
        "caption": "Fig. 2. Kinematic schematic of test bench. 1 \u2014 reducer with test gears, 2 \u2014 locking reducer, 3 \u2014 planetary gear, 4 \u2014 hydraulic jack, 5 \u2014 auxiliary reducer, 6 \u2014 motor.",
        "texts": [
            " The tooth gearing parameters necessary for the calculation of the lubricant film thickness and the results of the calculations from Eqs. (20) and (21) are presented in Table 2. As seen from Table 2, \u03bb \u226a 1. Therefore, in the zone of tooth contact of the gearing, a boundary lubrication regime exists, while a partial-EHL and hydrodynamic lubrication regime are not possible. 5. Test bench for experimental investigation on scuffing gears For the testswith natural gears, a special test bench6was constructed (Fig. 2). This test benchwas designed to solve two problems: the determination of scuffing load and the examination of gear efficiency during the wear tests. The test bench includes four gear reducers and a motor. A single-stage reducer 1 comprises experimental gears and together with the locking reducer 2 and planetary reducer 3 (operating in the regime of increasing angular velocity) forms a closed kinematic contour with circulating power. The product of the gear ratios of reducers 1, 2 and 3 is equal to i1i2i3 = 1",
            " As for the test gear cases, the mining machine cases were used. The main parameters of the test gear are shown in Table 1. The test gear wheels, which would be similar to those used in operation, were cut into the sameworkpieces. To increase the specific load on the teeth of the test gears, and to maximize the efficiency of a single pair of wheels in the design of the ring gears, the following changes were introduced: the teeth were made to be narrow, with a length of 2.5 times the module gear and with two rows of teeth set on one ring gear (Fig. 2, reducer 1). This design allows for four tests to be conducted by one pair of gears (because of the permutations of the wheels along the shaft and the reversal of the rotation direction). Gear lubrication was carried out by plunging the gears into an oil bath. The presence of a special cover that could be removed quickly provides easy access for teeth inspection and wear measurements. In gearminingmachines,\u0426-24machine piston oil is recommendedwithA\u041a-15motor car or tractor oil as a substitute. However, in practice, \u0418-45 industrial oil is often used",
            " 3, the change in frequency of torque Ti is in the range of frequencies for the variation of resistance torque for mining machines. Thus, using gear parameters and manufacturing technology, the characteristics and level of loading and lubrication of the test bench correspond to the range of operating conditions of mining machine gears. The device shown schematically in Fig. 4 is overlaidwith a specialized apparatus formeasuring toothwear atfixed points along the involute profile of the irreversible gear [28]. In Fig. 5, a general view of the instrument for measuring the tooth wear of the pinion (reducer 1 in Fig. 2) is shown. The apparatus consists of two parts, namely a base I and a lever II. Lever II is set in slide conic bearings of base I, and can be rotated around the axisOk, the position ofwhich is chosen such that the circular arc of the radius Rk passes through the primaryH, secondary P (usually pitch point), and the ending E points of the active part of the involute tooth profile. Base I ismade in the formof a framewith thewidth equal to the facewidth of the ring, embracing the ends of the gear. The left side of the frame ismolded into themolding of cavity 1 between the teeth,made of a fusiblemetal alloywith a low coefficient of shrinkage",
            " In each subsequent step (if scuffing did not occur), the contact stress was increased by 200 MPa. The working time at each step was equal to 0.25 h. The change is load was applied without stopping the motor. The initiation of scuffing was accompanied by a sharp increase in temperature of the pinion tooth, an increase in torque Te on the output shaft of the auxiliary reducer (which indicates an increase in friction between the teeth of the test wheels), a change in the character of noise, and a rapid release of oil vapor from reducer 1 (Fig. 2). An examination of the working surfaces of the teeth made after removal of the load and stopping the test bench showed growths, damage and cut-away metal on the friction surfaces. Every 30 min, if scuffing was not observed, the test bench was unloaded and the state of the working surfaces of the teeth was checked. A checking of the zero setting and a verification of the amplifier were also undertaken. The transition (after stopping) to the next load step was made only after the pinion tooth temperature became the same as that before stopping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003069_12.2042170-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003069_12.2042170-Figure3-1.png",
        "caption": "Figure 3. Morphology of the molten/solidified tracks.",
        "texts": [],
        "surrounding_texts": [
            "PROCESS"
        ]
    },
    {
        "image_filename": "designv10_10_0001596_dia.2006.8.296-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001596_dia.2006.8.296-Figure2-1.png",
        "caption": "FIG. 2. Interrogation techniques and microphotography of sensors for evaluating the acute and chronic performance. (A) The acute and chronic response of an entirely implanted hollow fiber sensor bundle was interrogated through skin with a fiber optic bundle containing six peripherally located optical fibers (diameter 0.2 mm) for fluorescence excitation and one centrally located optical fiber (diameter 0.4 mm) for fluorescence detection. (B) The fiber-coupled sensor was used to study the acute sensor response. It consisted of a hollow fiber sensor attached to the tip of optical fiber (diameter 150 m). The distal end was inserted into subcutaneous skin tissue with the help of a hypodermic needle, which was then retracted. The proximal end of the fiber was split into two optical fibers (diameter 105 m) to allow light from the laser light-emitting diode (650 nm, 4.5 mW) to enter the fiber lumen and to measure emitted fluorescence with a USB spectrometer. (C) Photomicrograph of the two-fiber sensor bundle. (D) Photomicrograph of the fiber-coupled sensor.",
        "texts": [
            " The introducer was then attached to a 200- L plastic tip filled with 100 L of suspension and connected to an automatic pipette. By slowly turning the plunger knob, the suspension was pushed down into the introducer tip and inside the hollow fiber. Short segments (length 0.5\u20131 cm) of the hollow fiber that were homogeneously filled with the blue-colored suspension were cut with scissors and sealed at the ends with cyanoacrylate. To increase the absolute fluorescence signal, up to two or three active sensor fibers were assembled into a bundle by gluing the ends of fibers with cyanoacrylate (Fig. 2C). Sensors were stored in PBS at 4\u00b0C until use. Manufacturing of fiber-coupled sensor One end of a 150- m-diameter multimode silica optical fiber was mechanically spliced with the distal ends of two 105- m-diameter optical fibers. The proximal ends of the two smaller fibers were terminated with SMA-905 connectors. One of the fibers was attached to the light source (collimated laser diode) at 650 nm (Thorlabs, Newton, NJ), and the other was attached to a miniature spectrometer (USB2000, Ocean Optics, Dunedin, FL). An individual hollow fiber sensor (diameter 220 m, length 5 mm) was carefully pushed onto the end of the 150- m fiber (length 1 mm). The hollow fiber was then filled with sensing suspen- sion and sealed with cyanoacrylate (Loctite) at both ends. The entire fiber-sensor assembly was then placed inside of a 20-gauge hypodermic needle to ensure protection during insertion into skin tissue (Fig. 2D). Through-skin fluorescence measurements of sensor response with simulated physiological glucose concentrations Prior to in vivo experiments, fluorescence of sensors was investigated with a specially made flow chamber inserted in skin tissue at different depths. The flow chamber was made of a thin Teflon\u00ae (Dupont, Wilmington, DE) tubing (o.d. 1.3 mm) containing a triple hollow fiber sensor assembly, which was then inserted through the subcutaneous tissue of a healthy anesthetized rat (Fig. 3A). Buffered saline solutions with various glucose concentrations (0, 2",
            " Hairless rats were used because the optical properties of their skin are similar to those of humans. Prior to the in vivo testing, rats were anesthetized with isoflurane by inhalation. Before implantation, sensors were rinsed with 50% ethanol and copious amounts of sterile saline solution. The sites of sensor implantation were on the ventral side of the lower abdomen. Fiber-coupled sensors were implanted by inserting a hypodermic needle (with the hollow fiber sensor attached to the optical fiber inside) into subcutaneous skin tissue at a 10\u201320\u00b0 angle to a length of approximately 1 cm (Fig. 2B and D). The needle was then retracted, and the optical fiber was carefully fixed to the skin with tape. Hollow fiber sensor bundles (consisting of two individual fibers) were placed in a small skin pocket prepared by inserting an 18-gauge intravenous catheter 0.5\u20131 cm into dermal skin tissue. Briefly, before implantation the sensor were rinsed in 50% ethanol followed by rinsing with copious amounts of sterile saline. The sensor bundle was then carefully pushed through the catheter, while slowly retracting the catheter, leaving the sensor inside the skin pocket"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003732_physrevfluids.1.032101-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003732_physrevfluids.1.032101-Figure1-1.png",
        "caption": "FIG. 1. Schematic of the problem.",
        "texts": [
            " For convenience, we consider a stationary particle, focusing upon the hydrodynamic force it experiences. Once this \u201cphoretic force\u201d is determined, the velocity of a force-free freely suspended particle is readily obtained using the well-known resistance coefficients for particle motion perpendicular to a solid wall [15]. It is convenient to normalize all length variables by a and define \u03bb = a/L. We employ cylindrical coordinates (\u03c1,\u03c6,z) with the plane z = 0 coinciding with the wall and the z axis passing through O, where z = 1/\u03bb (see Fig. 1). The corresponding unit vectors are (e\u0302\u03c1,e\u0302\u03c6,e\u0302z); the azimuthal angle \u03c6 is degenerate in the present axisymmetric problem. Towards using a dimensionless notation it is convenient to employ the flux scale j = Kc\u221e. The excess-solute concentration c is normalized by aj/D, D being the solute diffusivity. Neglecting advection, it is governed by Laplace\u2019s equation in the fluid domain, the no-flux condition on the inert wall, \u2202c \u2202z = 0 at z = 0; (1) far-field decay, c \u2192 0 as |x| \u2192 \u221e, in which x = e\u0302\u03c1\u03c1 + e\u0302zz is the position vector; and the chemicalreaction condition on the particle boundary, \u2202c \u2202n = 1 + Da c, (2) wherein \u2202/\u2202n is the normal derivative in the direction pointing into the fluid and Da = aK/D is the Damko\u0308hler number, representing the relative importance of solute absorption and diffusion",
            " The first is that of a particle that is remote from the wall, where \u03bb 1. The second is where the particle is nearly touching the wall, for which \u03bb is close to unity, When the particle is remote from the wall the solute-transport problem may be solved iteratively using successive reflections [16]. In the absence of the wall it is readily found that the excess concentration that satisfies (2) is a solute sink positioned at x = \u03bb\u22121e\u0302z, c(0) = \u2212 1 (1 + Da)r ; (4) here r = |r|, r = x \u2212 \u03bb\u22121e\u0302z being a position vector measured from O (see Fig. 1). As this spherically symmetric distribution does not animate any fluid flow, we need to consider the first reflection from the wall. Given (1), this is simply an image sink, positioned at x = \u2212\u03bb\u22121e\u0302z: c(1) = \u2212 1 (1 + Da)|x + \u03bb\u22121e\u0302z| . (5) Taylor expansion of c(1) about O yields an asymptotic series in \u03bb, namely, c(1) = 1 1 + Da ( \u22121 2 \u03bb + 1 4 \u03bb2e\u0302z \u00b7 r + \u00b7 \u00b7 \u00b7 ) . (6) The harmonic reflection from the particle is a comparable asymptotic expansion, expressed in terms of spherical harmonics that decay at large r: c(2) = \u03bb \u03b1 r + \u03bb2 \u03b1 \u00b7 r r3 + \u00b7 \u00b7 \u00b7 ",
            " The engendered O(\u03bb2) flow may be calculated using Hankel transforms [18]; evaluation at O gives there the axial velocity \u2212\u03bb2\u03b3 /2(1 + Da) (see the Supplemental Material [19]). The leading-order force on the particle fW \u2248 \u22123\u03c0\u03b3 (1 + Da)\u22121\u03bb2 is readily obtained from Faxe\u0301n\u2019s law. Both contributions are accordingly of the same asymptotic order. The total force f \u2248 \u2212 3\u03c0\u03bb2 1 + Da ( 1 2 + Da + \u03b3 ) (9) can be either positive or negative, depending upon the value of \u03b3 . For b > 0, these respectively correspond to repulsion and attraction. When the sphere is in close proximity to the wall, it is convenient to use the separation distance \u03b4 = 1/\u03bb \u2212 1 (see Fig. 1) instead of \u03bb. The limit \u03b4 1 is addressed by conceptually decomposing the fluid domain into an \u201cinner\u201d region, namely, the narrow gap between the particle and the wall, and the remaining \u201couter\u201d region. We consider first the inner region, employing the gap-scale stretched cylindrical coordinates [20] R = \u03c1/\u03b41/2, Z = z/\u03b4, (10) with the particle boundary given by Z = H (R) + O(\u03b4), in which H (R) = 1 + R2/2. The excess concentration c satisfies Laplace\u2019s equation \u22022c \u2202Z2 + \u03b4 R \u2202 \u2202R ( R \u2202c \u2202R ) = 0, (11) the no-flux condition on the wall \u2202c \u2202Z = 0 at Z = 0, (12) and the reactive condition on the particle( \u2212 \u2202c \u2202Z + \u03b4R \u2202c \u2202R ) [1 + O(\u03b4)] = \u03b4(1 + Da c) at Z = H (R) + O(\u03b4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure1-9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure1-9-1.png",
        "caption": "FIGURE 1-9 Four-wheel drive tractor with smaller steering wheels in front. Power ranges from 7 to 120 k W. (Courtesy Fiat Trattori. Also see fig. I-I I.)",
        "texts": [
            " The tree skidder is a combination of an agricultural and an industrial tractor. The skid-steer tractor (fig. 1-8) was designed especially for industrial use, but it is often used in agriculture when turning room is restricted, such as in a dairy or a fruit storage building. The name \"skid-steer\" comes from the TRACTOR TYPES 7 method of turning, which is exactly like that of a crawler. The wheels on one side are braked or reversed, causing the tractor to skid in order to turn. A four-wheel-drive tractor with smaller front wheels (fig. 1-9) is simply a stan dard or a row-crop tractor with the front wheels also being driven. In regard to price and traction, this type of tractor falls between the standard and the four-wheel-drive tractor with equal-sized wheels (fig. 1-10). This tractor has become particularly popular in Japan because of its excellent steering and traction characteristics in soft, wet rice fields. Four-wheel-drive, or simply 4WD, tractors have been developed so as to be able to produce more drawbar power. The size of 4WD tractors varies in the United States and Canada from 100 kW to more than 300 kW"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002261_icece.2010.178-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002261_icece.2010.178-Figure2-1.png",
        "caption": "Figure 2. Isolation force analysis Figure 3. Isolation force of the car analysis of the rod",
        "texts": [],
        "surrounding_texts": [
            "Keywords-inverted pendulum; system performance; LQR controller; simulation\nI. INTRODUCTION Inverted pendulum system is a typical model of multivariable, nonlinear, essentially unsteady system, which is perfect experiment equipment not only for pedagogy but for research because many abstract concepts of control theory can be demonstrated by the system-based experiments. The research on such a complex system involves many important theory problems about system control, such as nonlinear problems, robustness, ability and tracking problems. Therefore, as an ideal example of the study, the inverted pendulum system in the control system has been universal attention. And it has been recognized as control theory, especially the typical modern control theory research and test equipment. So it is not only the best experimental tool but also an ideal experimental platform. The research of inverted pendulum has profound meaning in theory and methodology, and has valued by various countries' scientists [1].\nLinear quadratic optimal control theory( LQR) is the most important and the most comprehensive of a class of optimization-based synthesis problem, obtain the performance index function for the quadratic function of the points system, not only taking into account both performance requirements, but also taking into account the control energy requirements.\nII. MATHEMATICAL MODEL First, confirm that you have the correct template for your paper size. This template has been tailored for output on the A4 As a linear inverted pendulum system, the mathematical mode will be established by the method of mechanical analysis as follows. The Schematic diagram of the inverted pendulum is shown in Figure 1.\nIsolation force analysis of the car as shown in Figue 2, and isolation force analysis of the rod as shown in Figure 3.\nAnalysis the horizontal direction force of the car via the Newton's law, we can get the following equation:\nMx F bx N= \u2212 \u2212 Similarly, from the analysis of the pendulum which suffered the horizontal force ,we can get the following equation:\n2\n2 ( sin )dN m x l dt \u2032 = + \u03a6\nBecause:\n\u03b8 \u03c0\u03a6 = \u2212 \uff0c N N\u2032 = \u2212 So:\n2008 experimental teaching technology research projects of CUG Item Number: SJ-200804\n\uff0aCorresponding author, e-mail:donghb@cug.edu.cn\n978-0-7695-4031-3/10 $26.00 \u00a9 2010 IEEE\nDOI 10.1109/iCECE.2010.178\n699",
            "2\n2 ( sin( ))dN m x l dt \u03b8 \u03c0\u2032 = + \u2212 = 2 2 ( sin )dm x l dt \u03b8\u2212 That is:\n2cos sinN mx ml ml\u03b8 \u03b8 \u03b8 \u03b8\u2032 = \u2212 + (1)\nSubstituting this equation into the equation, we can get the\nsystem equations of motion. 2( ) cos sinM m x bx ml ml F\u03b8 \u03b8 \u03b8 \u03b8+ + \u2212 + = (2)\nSimilarly, from the analysis of the pendulum which suffered the vertical force ,we can get the following equation:\n2sin cosP mg ml ml\u03b8 \u03b8 \u03b8 \u03b8\u2212 = \u2212 \u2212 (3)\nSuppose\u03b8 \u03c0= + \u03a6 ,and make u to represent the controlled object with the input force F, the latter two linear equations of motion are as follows:\n( )2\n( )\nl ml mgl mlx\nM m x bx ml u\n\u23a7 + \u03a6 \u2212 \u03a6 =\u23aa \u23a8\n+ + \u2212 \u03a6 =\u23aa\u23a9 (4)\nTake the equations(4)with Laplace transform, to be:\n( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2( ) l ml s s mgl s mlX s s M m X s s bX s s ml s s U s \u23a7 + \u03a6 \u2212 \u03a6 =\u23aa \u23a8\n+ + \u2212 \u03a6 =\u23aa\u23a9\nNote: the transfer function is derived assuming the initial condition is 0,as the output angle is \u03a6 ,solving the equations ,we can get:\n( ) ( ) ( ) 2 2 2 s mls X s I ml s mgl \u03a6 = + \u2212\n( ) ( ) ( ) ( ) 2 2\n2 2( ) I ml I mlg gM m s s b s s ml s ml s \u23a1 \u23a4 \u23a1 \u23a4+ + \u23a2 \u23a5 \u23a2 \u23a5+ \u2212 \u03a6 + \u2212 \u03a6 \u23a2 \u23a5 \u23a2 \u23a5\u23a3 \u23a6 \u23a3 \u23a6\n( ) ( )2ml s s U s\u2212 \u03a6 = After finishing, obtain the transfer function:\n( ) ( ) ( ) ( )\n2\n2 4 3 2 ml ss q U s b I ml M m mgl bmgls s s s\nq q q\n\u03a6 =\n+ + + \u2212 \u2212\nMeanwhile\uff1a\n( ) ( ) ( )2 2q M m I ml ml\u23a1 \u23a4= + + \u2212\u23a3 \u23a6\nBy the principles of modern control theory, and then substituted the inverted pendulum system parameters which is designed by ourselves into the state space equation[2 ~ 4]:\n0 1 0 0 0 0 0.098 0.629 0 0.883 0 0 0 1 0 0 0.237 26.853 0 2.356 x x x x u \u23a1 \u23a4 \u23a1 \u23a4\u23a1 \u23a4 \u23a1 \u23a4 \u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u2212\u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5= +\u23a2 \u23a5 \u23a2 \u23a5\u03a6\u23a2 \u23a5 \u23a2 \u23a5\u03a6 \u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u2212 \u03a6\u03a6\u23a2 \u23a5 \u23a3 \u23a6 \u23a3 \u23a6\u23a3 \u23a6\u23a3 \u23a6\n1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 x x x x y u \u23a1 \u23a4 \u23a1 \u23a4\u23a1 \u23a4 \u23a1 \u23a4 \u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5= = + \u23a2 \u23a5 \u23a2 \u23a5\u03a6 \u03a6\u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5 \u23a2 \u23a5\u23a2 \u23a5 \u23a2 \u23a5\u03a6 \u03a6\u23a3 \u23a6 \u23a3 \u23a6\u23a3 \u23a6 \u23a3 \u23a6\nIII. CHARACTERISTIC ANALYSIS OF SYSTEM After obtaining the mathematical model of the system features, we need to analyze the stability, controllability and observability of system's in order to further understand the characteristics of the system [5~7].\nA. Stability Analysis If the closed-loop poles are all located in the left \u201cs\u201d plane,\nthe system must be stable, otherwise the system instability. In MATLAB, to strike a linear time-invariant system, the characteristic roots can be run by eig (a,b) function. According to the sufficient and necessary conditions for stability of the system, we can see the inverted pendulum system is unstable.\nLinear time-invariant controllablility systems necessary and sufficient condition is:\n1nrank B AB A B n\u2212\u23a1 \u23a4 =\u23a3 \u23a6 . The dimension of the matrix A is n.\nIn MATLAB, the function ctrb (a,b) is used to test the controllability of matrix ,through the calculation we can see that the system is status controllable.\nLinear time-invariant observability systems necessary and sufficient condition is:\n1 Tnrank C CA CA n\u2212\u23a1 \u23a4 =\u23a3 \u23a6 . In MATLAB, the function obsv(a,b) is used to test the observability of matrix ,through the calculation we can see that the system is status considerable.\nIV. DESIGN AND SIMULATION OF LQR CONTROLLER\nLQR control theory, is an important tool in modern control theory. It provides an effective analysis method multi-variable for feedback system design, adapt to time-varying systems"
        ]
    },
    {
        "image_filename": "designv10_10_0000828_robot.1997.620041-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000828_robot.1997.620041-Figure3-1.png",
        "caption": "Fig. 3 Design of Biped Locomotion Robot [mm]",
        "texts": [
            " In this research, we regard a matrix which is weight of joins in recurrent neural networks as one chromosome, and we operate GAS which have selfadaptive mutation for the recurrent neural networks. We search the optimal weight matrix of the recurrent neural networks. We apply the strategy of the elite as a selection. As the crossover, we use replacement at a part of the weight matrices of parents and replacement at a part of the parent\u2019s weight matrices with a internal ratio. And we apply the mutation as follows. Here, \u201c 6\u201d is Gaussiun noise. ( aij ) - > ( a i j + 6 ) mutation 6 = N (0, a; * f i tness + b ) dimensional mechanism. The main scales of biped locomotion robot are shown in Fig.3. The weight of this biped robot is 24 [kg]. For the reduction of weight, the body is made of aluminum materials. The inclinometers and force sensors are mounted in waist plate and foot plate respectively. Each joint is driven by the actuator which consists of a DC servo motor and a reduction spiral gear. And each of the actuators and gears are mounted in t8he link struct,ure. This structure is strong against falling down of the robot and it looks smart and more similar to human. 4 Conditions for Continuous Walking In this section, we consider the conditions for stable walking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002860_s12239-013-0077-0-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002860_s12239-013-0077-0-Figure6-1.png",
        "caption": "Figure 6. Free body diagram of elliptical contact surface.",
        "texts": [
            " Therefore, if linear velocity of contact point affect power transmission efficiency. There are some limitations which constrain the objective function. Optimized parameters must satisfy these constraints. One of the constraints is the maximum stress exerted over the contact surface duo to the limitation of disks and roller\u2019s strength. Von misses equivalent stresses of critical points are calculated as a function of dynamic parameters. Contact surface has an elliptical (Tanaka and Machida, 1996; Attia et al., 2003). Figure 6 shows the free body diagram of elliptical contact surface between disks and roller. Hertzian stress produced by normal force (FN) and shear stresses duo to traction force (F \u03c4 ) and spin momentum are shown in the figure. The values of a and b can be obtained using geometry of bodies, normal force at contact point, elastic modulus, E and Poisson\u2019s ratio, \u03c5 of disks and roller (Carbone et al., 2004). Hertzian stress is much more than stress duo to spin momentum and traction force. Maximum Hertzian stress occurs at point A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002428_s13272-011-0005-9-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002428_s13272-011-0005-9-Figure9-1.png",
        "caption": "Fig. 9 Proposal of mechanical HHC system [17]",
        "texts": [
            " power required, but applies 2 and 3/rev control, he indeed did not apply HHC, but IBC for the reasons explained in Sect. 3. He concluded that 2/rev feathering could increase the speed by approximately 25% and adding 3/rev by further 5%. But these figures need to be taken with some care. His models were rather simple. It is not clear, why CT of the ideal thrust distribution at w = 270 shows larger values than CT of the conventional rotor. Finally, Arcidiacono proposed a mechanical HHC system as shown in Fig. 9. His design featured a curved track cut into the stationary part of the swashplate. Rotating control arms ride in this track and move the push rods vertically. Surely, this design would suffer from fatigue and wear. However, largest drawbacks would be the preshaping of the curved track and its impossibility to adapt HHC amplitude and phase to the flight state as well as the fact, that the generated HHC input cannot be switched off, e.g. in hover. While first investigations focussed on the enhancement of helicopter maximum speed, first flight tests focussed on the effect of 2/rev HHC on vibrations, oscillatory rotor loads and stall [18]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003591_s12206-018-0240-7-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003591_s12206-018-0240-7-Figure2-1.png",
        "caption": "Fig. 2. A modularized 7-DOF redundant manipulator.",
        "texts": [
            " (37), ( )b d e c l L g b\u00c5 + + \u00d1 \u00ae 0&J x E JJ \u03c8 J G- , the joint angular velocity may be able to increase in the opposite direction due to the action of the repulsive potential field - cg J \u03c8 . In the worst cases, the joint angular velocity may violate the corresponding limit, but b\u00d1G , using the property of redundancy, decreases the joint velocity reversely and strictly imposes the joint motion in the joint angular velocity limit, while - cg J \u03c8 pushes the manipulator away from the singularity. To verify the validity of the proposed ICWN method, we took a modularized 7-DOF redundant manipulator as shown in Fig. 2. The D-H parameters of the manipulator with permit regions of joint angular positions and joint angular velocities are shown in Table 1, where 2 297.5,m = 3 355.5,m = 1 450,l = 4 293,m = 2 400,l = 5 255,m = 6 197,m = 7 104.m = Comparison simulations with the original CWLN method were performed to show the superiority of avoiding joint angular velocity limits of the proposed ICWLN method. Meanwhile, the GPM [29] and WLN [13] methods based on Eqs. (15)-(18) for the closed-loop inverse kinematics resolution with simultaneously optimizing multiple criteria defined by Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003692_iros.2015.7354157-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003692_iros.2015.7354157-Figure1-1.png",
        "caption": "Fig. 1. Illustration of stiffness-based path correction for a machining operation. Picture courtesy of Fraunhofer IPK.",
        "texts": [
            " Deflections of industrial arms when used in contact applications have several causes: i) compliance of the links, ii) compliance of joint bearings and gears and iii) compliance of the position control loops which are typically influenced by the individual axis controller gains in the controller software. One possible approach to increase the accuracy of robotic machining is to adjust the off-line generated CAD/CAM-based toolpaths based on estimates of the robot\u2019s joint stiffnesses and estimated or measured forces from the machining operations. The main contribution in this paper is the developed off-line path correction based on the combined joint stiffness and process force estimation for a machining operation which is shown in Fig. 1. *The research leading to these results has received funding from the European Union\u2019s Seventh Framework Programme (FP7/2007-2013) under grant agreement no 314739 (Hephestos). 1 Authors are with the Faculty of Engineering and Science, University of Agder, N-4898, Grimstad, Norway. ilya.tyapin/geir.hovland@uia.no In order to make such adjustments, accurate estimates of the robot\u2019s combined joint stiffnesses are key parameters in addition to the process model, see for example [1]. In [1] a similar method for identifying the joint stiffness of sixrevolute industrial serial robots was presented",
            " Feed direction pull (down milling or climb milling) is when the direction of the cutting velocity opposes the feed direction of the tool, see Fig. 5. Note that in the figure the material is stationary and the feedrate describes the linear motion of the robot moving the tool. Fig. 6 shows an example of the measured forces in the x\u2212,y\u2212,z\u2212 directions for aluminum (push direction, depth of 1.5mm, width of 8mm). Note that these forces have mean values of about \u221234, 20, 91N , respectively. In addition there are large high-frequency variations in the range 100- 200N. With off-line compensated toolpaths, as illustrated in Fig. 1, it is not possible to compensate for the highfrequency oscillations. Hence, only the mean values of the machining forces are modeled and estimated in this paper. Due to the relatively large inertia of the robot arms, it is assumed that the mean value of a force contributes more to the arm deflection than the high-frequency component. The evolutionary optimization approach is used to estimate both thrust and cutting forces. The optimization problem is defined as follows. min : N\u2211 i=1 ( (\u00b5 [Fe(K,\u03b1, \u03b2, \u03b3)]\u2212 \u00b5 [Fm(K,\u03b1, \u03b2, \u03b3)]\u2211n i=1 \u00b5 [Fm(K,\u03b1, \u03b2, \u03b3)] ) (12) Subject to : 0 \u2264 \u03b1 \u2264 1 0 \u2264 \u03b2 \u2264 1 0 \u2264 \u03b2 \u2264 1 0 \u2264 K \u2264 100 where the objective function (12) is minimized by the Complex Search algorithm and defined as the normalized mean (\u00b5) difference between the estimated force Fe and measured force Fm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003375_j.triboint.2014.10.007-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003375_j.triboint.2014.10.007-Figure9-1.png",
        "caption": "Fig. 9. (A) The six measurement points are shown in black. The stencil was extended by 3 points, marked in blue, accounting for symmetry across the EGM (marked in dotted line). (B) Experimentally calculated \u00f0hGap;Rlv=hRef \u00de for the operating condition of n\u00bc2000 rpm, \u00f0p=pRef \u00de \u00bc 0:8 are shown along with interpolated \u00f0hGap;Rlv=hRef \u00de field. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            "1 \u03bcm accounting for the accuracy for the CMM measurements of the EGM casing: 0.01 mm, and the accuracy of measurement of the capacitive sensors: 0.09 \u03bcm which was 0.08% of the full scale (110 \u03bcm). The inaccuracies in the measurement of the gears and bushing thicknesses can be lumped into the unknown offset \u03b4 (Eq. (30) and therefore does not affect the relative film thickness. In addition, an assumption of film thickness symmetry as regards the driver and the driven/slave gear sides (i.e. across the line of symmetry marked in Fig. 9) of the EGM was made, which allowed the measurements from the asymmetrically placed measurement points on the driver and the driven side of the EGM to be used for their mirror images. This is illustrated in Fig. 9 with the six measurement points in black extended to a further 3 points in blue and using point numbers with the postscript \u201cm\u201d, so as to extend the total stencil of points to 9. The assumption of symmetry is motivated by the consideration that the geometry of the EGM is symmetric in a time-averaged sense as regards the driver and the driven gear sides of the EGM, with the main asymmetry existing between the HP and LP sides of the EGM. In order to verify the assumption of symmetry made, two measurement points were mirror images of each other: points 1 and 2, and measurements made at these points were observed in order to check the validity of this assumption. Further, the measurements were also used to create a spatially interpolated hGap;Rlv field over the entire lateral gap domain. The spatial interpolation was performed using thin-plate splines, which are commonly used two-dimensional cubic splines [35\u201337]. An example of a typical measurement, in this case performed for n\u00bc2000 rpm,\u00f0p=pRef \u00de \u00bc 0:8, is shown in Fig. 9. In order to respect confidentiality agreements with the sponsor of the present work, the relative film thickness is normalized using hRef which was O (5 \u03bcm). It must be reiterated at this point that since hGap;Rlv is a relative film thickness, a result of 0 \u03bcm simply means that the point at which this is reported had the lowest film thickness. The film-thickness calculated by the experimental method was the time averaged film thickness when the EGM is operating at steady-state. This result can be compared against the final steady state film thickness result provided by the FSI\u2013thermal coupled model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002624_j.bios.2013.10.053-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002624_j.bios.2013.10.053-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagrams of (a) GSG electrode for frequency based measurement. (b) The optical microscope image of detection area and (c) probing area. (d) The cross-sectional view of glucose detection region and (e) the equivalent circuit involving R, L, G and C in between two ports after glucose solution was dropped.",
        "texts": [
            " Thus, this is possible to read out complex composition. In the future, this method will develop for data-collected based verification collected from various measurements and speed up opening the in-situ multi-variables sensing. In order to minimize the signal loss, Silicon (Si)/silicon oxide (SiO2, 500 nm) substrate was prepared first for glucose sensing device, and then Ground-Signal-Ground (GSG) pattern was deposited by the standard photolithography using titanium (Ti, 10 nm)/ gold (Au, 500 nm), as shown in Fig. 1(a). This GSG pattern is consists of two kinds of electrodes. One is a pair of transmission electrodes (S), which shapes V-notch to minimize signal loss on transmission line (Fig. 1(b)), and the other is a pair of ground electrodes (G), the symmetrical shape to each other (Fig. 1(c)). Fig. 1(d) is a magnified view at the center of the signal electrodes, and the mechanism about detecting glucose molecules between two ports is schematically presented with S-parameter and its decomposed parameters, the resistance (R), the inductance (L), the conductance (G), and the capacitance (C). S-parameter was measured by GSG probing with a network analyzer (E5071C). S-parameter, \u201cSij\u201d can be defined as the ratio between the incident voltage to port \u2018j\u2019 and the voltage measured at port \u2018i\u2019, providing four components, S11, S21, S12, and S22. Because this mechanism is based on a symmetric two port network (S11\u00bcS22 and S21\u00bcS12), all the data of S-parameter can completely be analyzed by plotting the reflected signal (S11) and transmitted signal (S21). Because of the linear electrical network of S-parameter, it can be also separated into various components, RLGC. As shown in Fig. 1(e), these components can be expressed using the equivalent circuit. More specifically, R and L are closely related to the transmission line on the sensing chip, and G and C are indirectly affected by sensing property through the effects of dielectric on target material. Glucose solution was analyzed by three kinds of measurements. First, in order to get the structural information of glucose molecule, glucose solution (1 mM) was dropped and dried on Si wafer, and then measured by X-ray diffraction (XRD)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001590_j.jbiomech.2006.12.012-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001590_j.jbiomech.2006.12.012-Figure2-1.png",
        "caption": "Fig. 2. Retro-reflective markers used for the UWA model on the mechanical arm.",
        "texts": [
            " This study aimed to determine the inherent error of opto-reflective (Vicon-612) and video-based (Peak Motus) systems, with respect to the measurement of elbow flexion\u2013extension, over the relevant section of a bowling delivery. It also aimed to identify error that may be attributable to the modelling method employed by comparing an elbow angle often calculated in field-based markerless conditions, with a \u2018gold standard\u2019 3D laboratory-based calculation. The error associated with occluding relevant landmarks during manual digitising using the video-based system was also investigated by covering the arm with a shirt during the field condition. A mechanical arm (Fig. 2), representing the upper limb constructed with one DOF at the \u2018shoulder\u2019 (flexion\u2013extension) and two DOF at the \u2018\u2018elbow\u2019\u2019 (flexion\u2013extension and abduction) was used for all testing (Table 1). The arm was attached to a servo-motor and driven by a custom designed program that allowed for representative planar rotation of the shoulder. Movements of upper arm external and internal rotation (ER/IR) were achieved via manual manipulation of the arm through the ICC specified arc (Fig. 3). A Vicon MX motion analysis system with 12 near infrared cameras (ViconPeak, Oxford Metrics, Oxford, UK) operating at 250Hz was used for laboratory testing. Vicon\u2019s generic static and dynamic calibration procedure was used to calibrate the volume and to linearise all 12 cameras. The UWA model consisted of two marker sets. The static calibration marker set and the bowling marker set, a subset of the static set (Fig. 2). The 16 static markers were as follows: one marker each on the anterior (ASH) and posterior (PSH) surfaces of the shoulder, overlying the glenohumeral joint with a third marker positioned over the acromion process (ACR); three markers (UA1, UA2, UA3) mounted on a lightweight frame, called the upper arm cluster, placed distally on the upper arm; one marker each B.C. Elliott et al. / Journal of Biomechanics 40 (2007) 2679\u20132685 2681 on the lateral (LEP) and medial (MEP) epicondyles of the elbow; three markers (FA1, FA2, FA3) mounted on a lightweight frame, called the forearm cluster, located distally on the forearm, slightly superior to the wrist flexion extension axis; one marker each on the medial (MWR) and lateral (LWR) aspects of the wrist; and three markers (H1, H2, H3) secured to the dorsal surface of the hand"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003024_cjme.2014.0519.098-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003024_cjme.2014.0519.098-Figure4-1.png",
        "caption": "Fig. 4. Local coordinate frames of deployable structure",
        "texts": [
            " 2, the length of connecting link and link is li and l respectively, the radius vector between center of mass of connecting link and origin of coordinates is respectively 1 0 0 , 2 cosl \u03b2           r 2 1 0 2 2 sin , 2 cos l l l \u03b2 \u03b2           r 3 1 0 2 2 sin , 0 l l \u03b2           r 1 4 1 (2 2 sin )sin( / 3) (2 2 sin )cos( / 3) , 2 cos l l l l l \u03b2 \u03b2 \u03b2 \u03c0 \u03c0            r 1 5 1 (2 2 sin )sin( / 3) (2 2 sin )cos( / 3) . 0 l l l l \u03b2 \u03b2 \u03c0 \u03c0            r Therefore, the location of each connecting link in the inertial coordinate frame is pi=(\u03d5i ri)T, i=1, 2, 3, 4, 5. Based on the motion characteristic of this deployable structure, three SLEs (6B7, 8P9, and 10W11) move in their respective planes, with local coordinate frames x o y   and x o y   as shown in Fig. 4. From the above, this deployable structure motion in space will be seen as three SLEs motion in their respective planes. As shown in Fig. 4, two local coordinate frames can be obtained by rotation by an angle \u03d5, with transformation matrix given as cos sin 0 sin cos 0 . 0 0 1 \u03c6 \u03c6 \u03c6 \u03c6            R Assume that the rotation angle of each link is \u03d5i ( i=6, 7,  , 11) with respect to the local coordinate frame, the rotation angle in the global coordinate frame is given as .i i\u03c6 R\u03c6 The radius vector of each link is ri (i=6, 7,  , 11), then the location of each link in the inertial coordinate frame is given as: pi=(\u03d5i ri)T, i=6, 7,  , 11. Therefore, the location of each component may be combined to give  T ,i i ip \u03c6 r 1, 2, , 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003763_s10846-017-0545-2-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003763_s10846-017-0545-2-Figure3-1.png",
        "caption": "Fig. 3 The figure shows the gimbal testbed coordinate frames. Note that for the gimbal case L0 and LCoG coincide. Therefore, we introduced the coordinate frame Lb attached to the quadrotor rigid body CoG. For the free-flight quadrotor Lb and L0 coincide (see Fig. 2)",
        "texts": [
            " For the horizontal motion, we expect that the rotor drag forces, which are proportional to horizontal velocity and rotor speed [16, 17], would produce some influence on attitude dynamics, particularly if the rotors are significantly displaced from the CoG (zr >> 0). We will address the model and influence of these forces in our future work. In this paper we address the controller design in discrete domain. To that end, we give the discrete transfer function of (38) using the parameters from Table 1 and ZOH transformation: \u03c9y(z) u\u03b8 (z) = \u22120.03377z2 + 0.06832z \u2212 0.03379 z3 \u2212 2.724z2 + 2.473z \u2212 0.749 . (39) 2.3 Linearized Dynamical Model of an Experimental Testbed In order to test the proposed algorithm we developed a 2 DOF laboratory testbed shown in Fig. 3. The full scale UAV that we have recently developed is fixed to a gimbal which is free to rotate around a center point of rotation (roll and pitch angle). Although the ICE engines and rotors are mounted on the vehicle, in this experimental testbed we do not used them to produce forces and torques. Furthermore, since the gimbal is constrained to rotate around a fixed point, there are some substantial differences between the gimbal model and free-flight quadrotor model. Therefore in this section, we derive the model of the testbed from the afore disseminated free-flight quadrotor model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure5-15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure5-15-1.png",
        "caption": "FIGURE 5-15 Poppet valve partly open.",
        "texts": [
            " This allows the valve to seat on the combustion chamber side and to minimize the accumulation of combustion products between the valve and the valve seat. Figure 5-14 also shows a valve seat insert of extra hard material. Such inserts are commonly used on exhaust valve seats and some times on the intake valve seat. Valves that are seated into the cast iron head of the cylinder block are only satisfactory for light-duty engines. Hard alloy materials are used for inserts. The insert must fit very tightly to ensure proper heat flow. Valve-Opening Area The port area (see fig. 5-15) is equal to where DJ is the diameter of the port and d is the diameter of the valve stem. 92 ENGINE DESIGN The beveled poppet valve is almost universally used since it presents a conical seating surface that makes it self-centering. If the minimum diameter is Db and the slant height is s, then the valve opening area, A 3 , is sInce and then s = h cos a D2 = D J + 2h cos a sin a 1T A3 = - (DJ + DJ + 2h cos a sin a)h cos a 2 A3 = 1T (DJ + h cos a sin a)h cos a CAMS 93 cos a 0.707, sin a = 0.707 TI(D[ + 0",
            " Total enclosure, 15-20 dB (A) From figure 5-40 and the list of source treatments is should be clear that the sources of sound in most cases are radiating surfaces. The techniques used serve to: 1. Modify stiffness and mass distribution 2. Add shielding 3. Add damping 4. Provide isolation PROBLEMS 131 PROBLEMS 1. A three-cylinder tractor engine has a gO-mm bore, a gO-mm stroke, and a governed speed of 2400 rpm. It develops 24 kW on the pto at maximum load. The intake valve face angle is 30\u00b0, and the exhaust valve face angle is 45\u00b0. The specified valve seat width is 1.6 mm. The maximum valve head diameter G (fig. 5-15) is 35.3 mm for the intake and 30.6 mm for the exhaust. Assume that the dimension 1-2 (fig. 5-15) is 6.4 mm and that the valve seat rests against the middle of surface 1-2 when the valve is closed. The cam lift for both intake and exhaust valves is 7.11 mm. The valve stem is 9.5 mm for both intake and exhaust. Assume the valve port diameter to be the distance mea sured across the lower edges of the valve seat. (a) Compute the valve-opening area for the intake valves. Note the possibility that the line 1-5 (fig. 5-15) mayor may not fall outside the point 4 and that the line 1-4 may become the minimum slant height for computing the valve-opening area. (b) Compute the valve-opening area for the exhaust valves. (c) What would be the.effect on the valve-opening area for the exhaust valves if the valve seats were ground so that the seats were 4.7 mm wide? Assume the valve port diameter remains the same. (d) Compute the maximum instantaneous velocity through the intake valve in meters per second. The maximum piston speed in meters per second for this engine is approximately 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000954_s1359-6454(04)00390-8-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000954_s1359-6454(04)00390-8-Figure2-1.png",
        "caption": "Fig. 2. Schematic representation of the angular relationships between the solidification interface normal \u00f0n~\u00de and the x\u2013y\u2013z reference system and between the normal \u00f0n~\u00de and the [hk l] dendrite growing direction \u00f0V~\u00de.",
        "texts": [
            " In the case of dendritic growth, due to the effects of preferred crystallographic direction, the dendrite growth velocity is not always equal to the velocity of the solid\u2013liquid interface (Vn). A relationship between the growth velocity (Vhk l) of the dendrite tip along a specific crystallographic direction [hk l] and the heat source travel speed (Vb) was derived by Rappaz et al. [6], as given by V~h k l \u00bc V~b cos h cosWh k l ; \u00f07\u00de where Wh k l is the angle between the normal \u00f0n~\u00de to the melt-pool interface and the [hk l] direction (Fig. 2). For the face-centered cubic (fcc) nickel-base superalloys studied in present work, the six \u00c6100\u00e6 directions are the preferred directions of growth. At a given location of the melt-pool interface, it is assumed that the dendrite trunk which is selected from among the six possible \u00c6100\u00e6 variants is the one that is the closest in orientation to the direction of maximum temperature gradient (i.e., the direction of the normal to the melt-pool interface). In other words, the minimum value of the angle-Wh k l determines the orientation [hk l] (where [hk l] is one of the six \u00c6100\u00e6 directions) of the dendrite trunk that is selected at a given location of the melt-pool interface [6]",
            " The minimum growth velocity also leads to a minimum undercooling of the dendrite tip since the undercooling increases with increasing growth velocity over the dendritic stability range, as indicated by Rappaz et al. [7]. In order to calculate the angle-Wh k l and subsequently the growth velocity (Vhk l), one needs to determine the angles h and / that are used to specify the direction of the normal \u00f0n~\u00de to the melt-pool interface (where / is the angle between the y-axis and the projection of n~ on the y\u2013z plane). Based on Fig. 2, the components of the unit vector of the normal \u00f0n~\u00de to the melt pool interface are given in the x\u2013y\u2013z reference system by n~\u00bc \u00f0cos h sin h cos/ sin h sin/\u00de: \u00f08\u00de By comparing Eq. (8) with Eq. (5), one can obtain h and / in the following expressions: h \u00bc arctan of =oy\u00f0 \u00de2 \u00fe of =oz\u00f0 \u00de2 0:5 ; \u00f09\u00de / \u00bc arctan of =oz of =oy ; \u00f010\u00de (see Appendix B for details of calculations of h and /). The unit vector describing the [hk l] crystallographic direction in the x\u2013y\u2013z reference system can be expressed with its components ux, uy and uz as u~h k l \u00bc ux uy uz : \u00f011\u00de Thus, after determining the values of h and /, the angleWh k l characterizing the orientation of a specific \u00c6100\u00e6 variant with respect to the normal \u00f0n~\u00de can be obtained through Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-20-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-20-1.png",
        "caption": "FIGURE 13-20 Differential with hydraulic lock. (Courtesy White Farm Equip ment.)",
        "texts": [
            " Thus, the output gears can rotate at any speed as required for turning but will deliver equal torque to both wheels. Note that when turning occurs, the power delivered to the wheels will not be equal. When one wheel is locked by braking, all of the power is delivered to the opposite wheel. Since the torque on both output gears must be the same, the torque is limited by the wheel having the least tractive capability. Thus most tractor differentials can be locked to deliver as much torque as possible to each wheel (fig. 13-20). The need for the differential is readily apparent, however, when steering is attempted with the differential lock engaged. Differentials are really a special type of planetary gear system where bevel gears are used instead of spur or helical gears. Differentials can (and are) constructed from systems such as those in figure 13-17( b) and 13-17 (c). Thus the kinematic relationships given for planetary systems can also be applied to differentials. Transmission Drive Shafts Transmission drive shafts are used to transmit gear loads to the bearings and to transmit power from one component to another"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002650_tec.2012.2200898-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002650_tec.2012.2200898-Figure5-1.png",
        "caption": "Fig. 5. PHESF machine. (a) Cross section. (b) Configuration.",
        "texts": [
            " The amplitude-frequency and phase-frequency characteristics as well as the dc gain of the improved estimation method are shown in Table I. For comparison, Table I also gives the It can be found that the improved estimation method is suitable for use in high-performance AC motor drives. The DTC and the DTLC schemes are such cases that need stator flux estimation method with high accuracy; thus, the DTC and the DTLC schemes using the improved stator flux estimation method will be developed in Section III. GENERATOR DC POWER SYSTEM A PHESF generator is shown in Fig. 5; this parallel topology can avoid PM magnetic short circuit and demagnetization. Furthermore, the electrical excitation part has a wide iron flux bridge that will increase the utilization ratio of the excitation current and reduce excitation loss. It can be found that the PHESF generator is suitable for use in dc power systems that require wide flux-weakening range, high reliability (without PM demagnetization), and relatively high torque density (without PM magnetic short-circuit). Fig. 6 gives the DTC scheme for the PHESF generator dc power system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000902_3516.847091-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000902_3516.847091-Figure9-1.png",
        "caption": "Fig. 9. Changes of the dislocation of the swimming direction by the desired bending angle (swimming speed: about 1.5 mm/s).",
        "texts": [
            " This correction angle is investigated by a manual operation experiment. The experimental method is as follows. 1) First, a paramecium is controlled to the center of the pool by electrical field. 2) If the paramecium arrives at the pool center, the direction of the electrical field is changed to the setting angle. 3) The paramecium\u2019s swimming course is recorded by video. 4) Difference angle between the direction of the electrical field and the paramecium\u2019s swimming course is calculated by video image processing. Fig. 9 summarizes the approximation of the difference angle. The above-mentioned experimental results show the difficulty of speed control by the gradient of electrical fields. In this study, therefore, speed control is not included in the control program; direction control is only included. If the paramecium always swims straight to the negative electrode, direction control is very easy. The above-mentioned manual control experiments, however, show that the turning angle of the paramecium is smaller than the direction of the gradient of the electrical field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure11-1.png",
        "caption": "Figure 11. A 3P-S-G linkage showing one possible order for the pairs, and indicating that the only active freedom of the G-pair is a rotation about the axis parallel to that of the screw pair.",
        "texts": [
            " The rules relating numbers of joints and numbers of members in multiple-loop M = I spatial P-pair linkages comply exactly with those for planar linkages as described, for instance, by Davies and Crossley [9]. A single-loop 4P linkage is shown in Fig. 10. 5.2. Some other ways of closing a single M = 1 loop containing three P-pairs are given in Table 3(e). If, however, the loop were closed to form a 3P-1S-1G (or 3P-1R-1G) linkage (taking the pairs in any order), the mobility would still be I, but two of the three rotational freedoms possessed by the spherical joint (G-pair) would be inactive, the relative movement in the G-pair always being a rotation about an axis parallel to the S-pair (Fig. 11). In general, however, a 3P-..4S (or 3P--4R) linkage (taking the pairs in any order) will have a mobility of 1 provided that the axes of all the S-pairs, and of course of the P-pairs, are randomly orientated; it is only when there are as many as four randomly orientated S-pairs (or R-pairs) that the vector sum of four relative angular velocities about their four axes can always (uniquely) be made equal to zero, and this is a necessary condition for M = 1 in this context, as would indeed be expected from equation (1) taking b =6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001604_iros.2005.1545594-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001604_iros.2005.1545594-Figure2-1.png",
        "caption": "Fig. 2. Perception of geometries by IR beam. (a),(b) Example of indiscernible distance; (c) Active perception of the robot; (d) Recognition of geometries.",
        "texts": [
            " Based on them the robot can perform first the individual surface recognition, that can later be expanded on collective perception of large objects. In the distance measurement the following parameters are the most important: max. measuring distance Rmax, optimal recognition distance Rrec, opening angle of radiation/reflection ray \u03b1 on Rrec, degradation of the IR radiation outsize opening angle Din dist/Dout dist, object and geometry resolution Ores, Dres in Rrec, dependency of reflection on color/slope of an object, as shown in Fig. 2. We expect that distances are provided, at least, within Rc and a section of the IR radiation cone is less than the size of robot\u2019s body. The general problem of distance and proximity sensing is so-called indiscernible distance (Fig. 2(a,b)). The sensor cannot differentiate whether the object is on the central line but in a large distance, or the real distance is smaller but the object is displaced from the central line. This problem still remains open (can be solve when a robot undertakes several measurements in different directions). Finally, robots should have some touch sensor, that is required for transporting operations. Sensors, that can perceive a color of objects, are also useful in many scenarios. We collect the required IR devices in Table I",
            " We are going to use the same receiver for distance measurement and communication, therefore we prefer sensors wide opening angle, e.g. TEFT4300, TEST2600 (\u03b1 = 60), in the \u201dcontrol group\u201d we have SFH3100F with \u03b1 = 30. Some distance measurements are shown in Fig. 5(a). V o lt ag e, V In the Fig. 5(b) we plot for some tested pairs the degradation of Vo in dependance on a deviation from the central line in the distance 100 mm. We see that in fact all values disappear only at the angle 30-35 grad. For 30o radiation ray, the geometrical resolution Gres from Fig. 2(d) is 25-30 mm for the distance of 100 mm. The slope of degradation corves is too small to provide \u201dabrupt boundary\u201d of the radiation ray, needed for a good object resolution. Ambiguity in 5-10o leads to the minimal resolution of 15-20 mm in 100 mm distance. The geometrical resolution depends also on the accuracy of robot\u2019s rotation. The minimal recognizable distance is about 5 - 10 mm and depends on a construction of the sensor and optical isolation. Generally, a detection of the touch (contact with an object) is not possible with reflective IR sensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure18-1.png",
        "caption": "Fig. 18 Theoretical model of the spur face-gear",
        "texts": [
            " Finally, from Eq. (24), E\u2264e1max+e2max, that is, E\u22640.193. The 4-axis CNC planer mentioned above (as shown in Fig. 5) is adopted to run the manufacturing simulation of the spur face-gear planing studied in this paper. The planer tool blade should be full fillet as it is convenient to calculate the tool path with this kind of blade. According to the design parameters in Table 1, the swing angle range and the feed range of the planer tool are calculated. The theoretical model of the face-gear (as shown in Fig. 18), the model of the face-gear blank and models of the planer machine are established using CATIA, and the model files and NC programs which are written based on the planing principle in this paper are imported into the Vericut software to simulate the processing. Finally, the result of the simulation is shown in Fig. 19. Firstly, the theoretical model (as shown in Fig. 18) and the simulation model (as shown in Fig. 19) are overlapped together, and the tooth surface error between the two models is analyzed in Vericut software. The results obtained from the analysis are shown in Fig. 20a. The whole regions, including the light regions and 3 4 5 6 7 8 9 -260 -255 -250 -245 -240 -235 -230 y 2 (mm) x 2 ) m m( 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Fig. 17 Error e2 the dark regions, represent the theoretical tooth surface of the spur face-gear, and the dark regions represent the surface with the error larger than 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-8-1.png",
        "caption": "FIGURE 11-8 Method of illustrating a mode shape.",
        "texts": [
            " The two amplitudes may then be combined with a scaled drawing of the tractor to indicate the mode of vibration as shown in figure II-S. In figure II-S, the mode of vibration is represented by what might be described as a TRANSIE!\\'T AND STEADY-STATE HANDLING 289 double-exposure photograph. The solid line drawing of the tractor represents one extreme position of the mode of vibration (sin wt = 1), and the dashed line drawing illustrates the other extreme (sin wt = -1). Of course, the amplitude of the motion indicated by a mode shape draw ing such as figure 11-8 has no relation to the am plitude of motion that would result if that mode were excited experimentally or in the field. However, the mode shape drawing does provide a valuable insight into the type of motion associated with each of the natural frequencies of the system. The model has 2 degrees of freedom, the lateral translational velocity, v, of the center of gravity and the yaw angular velocity, r, of the tractor about its center of gravity. The forward velocity, u, of the center of gravity is assumed 290 MECHANICS OF THE TRACTOR CHASSIS to be constant, whereas the steer angle, of' of the front wheels is assumed to be a known function of time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003876_j.mechmachtheory.2018.12.019-Figure9-1.png",
        "caption": "Fig. 9. Three-dimensional contact finite element model for the wide-faced spur geared rotor system.",
        "texts": [
            " When the output torque is 20 0 0N \u2022 m, the power inputs from the left side of input shaft and outputs from the left side of output shaft, quasi-static and dynamic behaviors of the wide-faced spur/helical geared rotor system under four types of supporting layouts are investigated in this section. In order to validate the effectiveness of the quasi-static contact analysis model for the wide-faced cylindrical geared rotor system, three-dimensional contact finite element model of a wide-faced spur geared rotor system is developed, as shown in Fig. 9 . All of degrees of freedom of the nodes on external surfaces of the four shaft segments supported by rolling bearings except for the degree of freedom around shaft axis are constrained. All of the nodes on external surface of the shaft segment where power inputs are coupled into a lumped node, and the input torque is applied on the rotational degree of freedom around shaft axis. Similarly, all of the nodes on external surface of the shaft segment where power outputs are coupled into a lumped node, and all of the degrees of freedom are constrained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000831_1.533552-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000831_1.533552-Figure3-1.png",
        "caption": "Fig. 3 Palloid bevel-worm-shaped hobbing method",
        "texts": [
            " The imaginary generating gear consists of a roll circle that rolls with the ground circle @19#. The cutter blade is attached to the roll circle while the ground circle is attached to the imaginary generating gear. The trajectory of the cutting blades mounted on the roll circle ~head cutter! is an epicyloid curves. Therefore, the cutting blades of face-hobbing cutter are divided into several groups and blades of each group are aligned with the epicycloid curves. As shown in rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/20 Fig. 3, the bevel-worm-shaped hobbing cutter is similar to the hob of the cylindrical gear. The cutting edges of bevel-worm-shaped hob perform an involute curve on the imaginary generating plane. In this paper, the mathematical models of the above-mentioned cutters are assumed to be given and the position and unit normal vectors of the cutter are denoted as rt and nt , respectively. rt~a ,b!5@xt ,yt ,zt,1#T (1) nt~a ,b!5@ntx ,nty ,ntz# T5 ]rt ]a 3 ]rt ]b U]rt ]a 3 ]rt ]bU Based on the mathematical model developed by Litvin @6#, a modified mathematical model for universal hypoid generator with supplemental flank correction motions is proposed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000786_1.1518501-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000786_1.1518501-Figure2-1.png",
        "caption": "Fig. 2 Relation between input axis of rotation $i , output axis of rotation $o , instantaneous screw axis $isa , and contact normal $l",
        "texts": [
            " The theorem of three axes is very useful in the analysis and synthesis of spatial gearing ~see Ball @23#, Beggs @24#, along with Phillips and Hunt @25#!. Its significance to gearing is presented by Dooner and Seireg @22# as follows1: v i$ i1v is$is2vo$o50 (2) where v i \u2014 angular speed of input gear v is \u2014 angular speed of output gear relative to input gear vo \u2014 angular speed of output gear $ i \u2014 homogeneous screw coordinates of input axis of rota- tion $is \u2014 homogeneous screw coordinates of IS ~Instantaneous Screw! $o \u2014 homogeneous screw coordinates of output axis of ro- tation. Depicted in Fig. 2 are the input axis of rotation $ i , the output axis of rotation $o , and the corresponding ISA $isa along with the tooth contact normal $ l . Invoking the reciprocity condition between the line of action $ l5(SI l ;SI ol) and the vector loop equation above yields $ l(~dn i$ i1dn is$is2dno$o!50. (3) Provided that the screw dot product between the line of action $ l and the instantaneous twist $is is zero ~i.e., dn is$is($ l50), the above relationship is rearranged to 1This notation deviates from established literature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002346_tee.20393-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002346_tee.20393-Figure2-1.png",
        "caption": "Fig. 2 Experimental setup",
        "texts": [
            " Under the background above, this paper presents a novel precise modeling methodology for the angular transmission error to improve the static positioning accuracy [10], where the nonlinear elastic component in micro-displacement region is mathematically modeled by applying a modeling framework for the rolling friction with hysteresis attributes [11,12], as well as the conventional modeling for the synchronous component by spectrum analyses for rotation angle [4]. This transmission error model is then adopted to the positioning system as a modelbased feedforward compensation manner, in order to improve the settling accuracy. The proposed modeling and compensation have been verified by a series of numerical simulations and experiments using a laboratory prototype. 2. Configuration of Experimental Setup Figure 2 shows a schematic configuration of the laboratory prototype as an experimental positioning device, which is comprised of an actuator (AC motor) with an encoder, a harmonic drive gearing, an inertial load, and a load side encoder. Specifications of the prototype are listed in Table I. This positioning device is controlled in a typical semi-closed control manner by an angular feedback with an encoder mounted on the motor shaft, while the load side encoder measures and evaluates the load angle, i.e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure6\u00b718-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure6\u00b718-1.png",
        "caption": "FIGURE 6\u00b718 Spark-plug construction.",
        "texts": [],
        "surrounding_texts": [
            "150\nELECTRICAL SYSTEMS\nFarber (1982) also points out that the operator is not always a predictable control element because he or she has a variety of skills; may not always be alert; may be diverted by other functions; may be hampered by vision ob structions; and may be largely isolated from sound signals because of the tractor cab. Farber notes that variables that must be considered in making choices are difficult to process and combine except by electronics. Basic sensors are:\n1. Pressure 2. Temperature 3. Torque (fig. 6-19) 4. Force 5. Flow 6. Position 7. Velocity 8. Voltage\nCombinations that give additional information can supplement this list. For example, tire slip can be determined by making two velocity measurements (vehicle velocity and tire surface velocity), or S = 1 - VvlVt \u2022\nIn the following list, G. R. Mueller (1985) provides some of the operational",
            "SENSORS\n151\ninformation that can be obtained from sensors. The sensor plus the read-out device is often called a monitor.\n1. Low engine oil pressure 2. Air filter restriction 3. Coolant level 4. Alternator not charging 5. Park brake engaged 6. Transmission oil temperature 7. Transmission oil pressure 8. Transmission oil filter restriction",
            "152 ELECTRICAL SYSTEMS\nPrinciple stress lines of:\n9. Coolant temperature 10. Exhaust temperature 11. Fuel level 12. Voltage level 13. \"Systems Normal\" indicator\nOne common sensor for measuring torque is shown in figure 6-19. This sensor uses electrical resistance strain gages to measure the torque or moment on any shaft that needs to be monitored. For example, automatic control of a three-point hitch must measure the force on the lower links. This can be done by attaching the lower links of the three-point hitch to offsets on two shafts that are fixed on one end.\nEnvironmental Problems\nElectrical and electronic components on a tractor must be designed and tested to withstand a variety of environmental conditions. The reliability of each component must be determined through methods that are briefly discussed"
        ]
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure8-1.png",
        "caption": "Fig. 8 \u2013 Dimensions for the anthropomorphic ballast used for tests [3].",
        "texts": [
            " which may be substituted with safer equivalents. In the case where occupant restraint devices (safety-belts\u2013 coaches) are part of the vehicle type, a mass should be attached to each seat fitted with an occupant restraint following one of these two methods, at the choice of the manufacturer: mass constitutes 50% of the individual occupant mass of 68 kg and should be fixed rigidly and securely, or mass constitutes an anthropomorphic ballast with a mass of 68 kg and should be restrained with a 2-point safety-belt (Fig. 8). The platform on which the vehicle is situated should be tilted with a constant velocity not exceeding 0.087 rad/s (58/s) until the bus or tested section loses stability. According to the Regulation, the impact area on which the bus is tilted should have a dry and smooth concrete surface. This is essential as the friction coefficient on dry concrete and steel may vary significantly depending on the humidity. According to PN-82/ B-02003 \u2018\u2018Actions on building structures \u2013 variable actions during exploitation and assembling\u2019\u2019 the value of the static friction coefficient for steel and concrete with smooth surface equals 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001764_ichr.2008.4755950-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001764_ichr.2008.4755950-Figure5-1.png",
        "caption": "Fig. 5. Model of a humanoid robot to generate the shock-reducing motion. p: position of ZMP, Pc: position of the COG, f: floor reaction force.",
        "texts": [
            " Using the method of reference [21], the target terminal position and velocity to achieve this condition can be calculated. Because the optimal shock-reducing motion depends on the initial conditions, it must be generated online. To mitigate the damage to the humanoid robot, it is necessary to reduce the velocity enough when colliding with ground. These require ments are not met by the previous techniques as described in section I. Thus, in this research, we propose a method to generate the shock-reducing motion using the Dynamical 3D Symmetrization method[16]. This dynamic model is shown as Fig. 5. The equations of motion of the humanoid robot are written as follows: (6) (8) (5) (4) Tp -2\u00a2 m==-==--- dt 2 ddt G(s) == -- + {3; 2 S - PI S2 + 2( n S + n Next, m is obtained. (3) is written by the following transfer function of continuous-time system. Kalman filter by (2), and the predicted ZMP computed by multiplying Am by this estimate value like (4): where d == 1 - (2 n. Therefore, the next expressions are written. where tan \u00a2 == ~. As above, the first extremal value of y 1 (2 y(t) is written as ~ == dTp+\u00a2, where Tp is the peak time, and dt is the sampling time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003948_0954406214544311-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003948_0954406214544311-Figure2-1.png",
        "caption": "Figure 2. 3-DOF PUMA560 robot manipulator.",
        "texts": [
            " In order to verify the effectiveness of the proposed controller scheme, its overall procedure is simulated for a PUMA560 robot in which the first three joints are used. The PUMA560 robot is a well-known industrial robot that is widely used in industrial applications and robotic research.22 Its explicit dynamic model and the parameter values necessary to control it are given in Armstrong et al.27 The three degree of freedom (3-DOF) PUMA560 robot is considered with the last three joints locked. Figure 2 shows its kinematic description. The uncertainties used in this simulation are given as follows F\u00f0 _q\u00de \u00bc 0:8 _q1 \u00fe 0:8 sin\u00f03q1\u00de 2:5 _q2 \u00fe 2:7 sin\u00f02q2\u00de 1:1 _q3 \u00fe 1:15 sin\u00f0q3\u00de 2 6664 3 7775 \u00f054\u00de and d \u00bc 1:2 sin\u00f0 _q1\u00de 1:8 sin\u00f0 _q2\u00de 1:15 sin\u00f0 _q3\u00de 2 64 3 75 \u00f055\u00de Matlab/Simulink is used to perform all simulations; the sampling time was set to 10 3 s. An actuator fault is considered in the simulations because it represents one of the most serious failures and usually occurs in robotic systems. In a robotic system, damage to the actuators can be caused by damage to an internal actuator, power supply systems, or wirings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000948_2.5084-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000948_2.5084-Figure8-1.png",
        "caption": "Fig. 8 ICE vehicle.",
        "texts": [
            " 10)The frequencydomain characteristicsof the open-and closedloop SMC system with observer, boundary layer, and reference model are examined to ensure that stability of the linear system is in evidence. ICE Vehicle The ICE aircraft model has been developedby Lockheed-Martin, Fort Worth, Texas, under a U.S. Air Force Research Laboratories (AFRL) sponsoredprogram30 and is the vehicle of choice for many controls applications in the current literature.1;2;11;23;31\u00a136 It is a single-engine, multirole, supersonic, tailless ghter aircraft with a 65-deg sweep delta wing (Fig. 8). The conventional control effectors include elevons, symmetric pitch aps, and outboard leadingedge aps. The innovative control effectors include pitch and yaw thrust vectoring,all-movingtips, and spoiler slot de ectors. The allmoving tips and spoiler slot de ectors have zero lower de ection limits. The static aerodynamic force and moment data were collected by NASA Langley Research Center and AFRL using wind-tunnel tests with a 1/18th scale model. Additional wind-tunnel tests during phase 2 of the ICE program provide updated data for simulation models"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000851_1.1415739-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000851_1.1415739-Figure4-1.png",
        "caption": "Fig. 4 First four lateral-torsional coupled mode shapes of geared rotor system",
        "texts": [
            " Table 2 lists the natural frequencies and the physical descriptions of the corresponding mode shapes for the system having a gear mesh with constant stiffness coefficient K\u0304g51.03108 N/m, and undamped isotropic bearings with stiffness coefficients Kyy5Kzz51.0 3109 N/m @5#. Results of Kahraman, et al. are also listed in Table 2 for comparison. It is observed that these two sets of results are in reasonably good agreement except for higher modes, modes 10 to 13, and that the present results are slightly lower than the corresponding ones obtained by Kahraman, et al. @5# The first four lateral-torsional coupled modes are shown in Fig. 4. The Campbell diagrams for the two-shaft system with and without the gear mesh are shown in Fig. 5 with bearing stiffnesses Kyy5Kzz 51.03107 N/m. It is observed that the 1st and 3rd lateral modes in the Z-direction of both shafts in the non-geared system are replaced by the coupled lateral-torsional modes in the geared system. For steady-state response analysis of the system, damped orthotropic bearings are used with stiffness coefficients Kyy ,151.0 3109 N/m, Kzz ,151.03107 N/m, Kyy ,25Kzz ,251"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002098_j.mechatronics.2008.11.013-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002098_j.mechatronics.2008.11.013-Figure6-1.png",
        "caption": "Fig. 6. Novel redundantly actuated interface. (a) Same directions and (b) opposite directions. (1) Bearing, (2) nut, (3) self-turning rod, (4) lead screw and (5) moving platform.",
        "texts": [
            " The prototype of the 6-dof parallel seismic simulator is developed by Shanghai Jiao Tong University as shown in Fig. 4. In the building of prototype, the following schemes are considered. A novel redundantly actuated interface module with force self-turning mechanism is used to the prototype [19\u201320]. The spherical joint is replaced by the combination of the Hooke joint and rotational joint. The novel redundantly actuated interface is shown in Fig. 5. It is consist of bearing, nut, self-turning rod, lead screw, moving platform and frame work. There are two cases shown in Fig. 6. One is that the directions of the two lead screws are same. The other is that the directions of the two lead screws are opposite. There is no significant difference in the two conditions. The later one is adopted to the prototype as shown in Figs. 5(b) and 6(b). The two lead screws are driven by two servomotors which are controlled synchronously. They are master\u2013slave system which means that the input signal of one motor is the encoder signal of the other motor. The motors employed for the prototype is SANYO DENKI: P60B2211KBCS00 whose power rating is 11 kW"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001623_iros.2004.1389998-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001623_iros.2004.1389998-Figure5-1.png",
        "caption": "Fig. 5. The movemen1 made hy cach moue",
        "texts": [
            " In our case, the two mice are associated to arcs under the same angle, which corresponds to the change in the orientation made by the robot, i.e. AB (see Figure 3). It follows that: y = la1 - 4. If we substitute Equations 6 and 7 into Equation 5 , we can obtain the following expression for the orientation variation: 1: + 1: - 2cos(y)l&, ' sign(V, - V I ) (8) U AB= !/ The movement along the z and y axes can be derived by considering the new positions reached by the mice (w.r.t. the reference system centered in the old robot position) and then computing the coordinates of their mid-point (see Figure 5). The mouse on the left stans from the point of coordinates (-f:Oj, while the mouse on the right stam from (4;O). The formulas for computing their coordinates at the end of the sampling period are the following: D T( (sin (a, + A@) - sin (a,)) sign(A0) + - 2 D T< (sin (ai +A@) - sin (mi)) sign(4B) - - 2 x: y: = rY (cos (a-) - cos (n? +A@)) sign(Afl) xi y; = q ( c m ( a i ) -cos(ai +A@))sign(A@). = = From the mice positions, we can compute the movement executed by the robot during the sampling time with respect to the reference system centered in the old pose using the following formulas: (9) (10) x: + x; Ax = ~ Y: + Y; Ay = - 2 2 ' "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002596_we.447-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002596_we.447-Figure7-1.png",
        "caption": "Figure 7. RomaxWind Model of GRC gearbox.",
        "texts": [
            " Thus the effect of the whole system behavior on contact elements is captured. Designers use these models for achieving good alignment of the system under the loads, calculating gear and bearing contact stress and life, optimizing the microgeometry of the gears for increased life and transmission error and predicting the gear vibration magnitudes, as well as for many other purposes. The gearbox model is used in this paper in various forms to illustrate technology and design approaches important to improving wind turbine gearbox reliability, and Figure 7 provides one arrangement where the gearbox is modeled as installed in the NREL dynamometer test cell (Figure 8) Figure 9 provides a model for the purpose of simulating the GRC gearbox as installed in the wind turbine. The load case shown with the fi gure includes a signifi cant off-axis moment as well as loading from rotor mass (wind turbine blades and hub). Large off-axis moments are common in wind turbines, under conditions such as wind direction change, yaw error Wind Energ. 2011; 14:637\u2013651 \u00a9 2011 John Wiley & Sons, Ltd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003385_12.2010577-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003385_12.2010577-Figure10-1.png",
        "caption": "Figure 10. Measured items for mechanical assembly.",
        "texts": [
            " This seems to suggest that a further improvement of support definition is required in order to avoid shape distortion on the airfoil. Furthermore, the airfoil could be thickened to obtain good accuracy via finishing operations. Proc. of SPIE Vol. 8677 86771H-7 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/07/2013 Terms of Use: http://spiedl.org/terms Additional checks have been carried out on the side hole and platform rails on specific items which are critical for mechanical assembly. Measured entities are shown in Figure 10, corresponding mismatches are listed in Table 4. Roundness mismatches of 0.086 and 0.103 mm have been measured for \u03a6int and \u03a6ext respectively. The higher errors t2 and t7 refer to the same area on the sample and are due to delamination phenomena between piece and support structure which cause inadequate recoating on sintered layers. Improvement in support structures would also be effective to avoid these mismatches. Table 4. Mismatches of measured items for mechanical assembly. Item Mismatch[mm] \u03a6int -0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001875_s00707-008-0037-3-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001875_s00707-008-0037-3-Figure6-1.png",
        "caption": "Fig. 6 Cross section along diameter of circular membrane in adhesive punch pull-off test",
        "texts": [
            " It was found that the values are slightly higher for the R and GR theories, but the differences are insignificant. 4.2 Adhesive punch pull-off test on circular blister This type of analysis is relevant to an adhesive pull-off test in which a rigid, vertical, circular cylindrical punch is in adhesive contact axisymmetrically with a horizontal, circular (not annular) membrane whose edge is fixed. The cylinder is pulled upward and the membrane slowly debonds from the cylinder, with decreasing contact radius, until the membrane suddenly separates from the punch at a finite contact radius. Fig. 6 depicts the cross section along a diameter, in nondimensional terms. This problem has been analyzed in [37\u201342]. The analysis in the last five of these papers considered a cylindrical radius just smaller than the membrane radius, and applied approximate solutions, mostly assuming (i) that nr and n\u03b8 are equal and independent of r , or sometimes assuming (ii) that w(r) is linear. As an example, the closed-form solution in Eqs. (30) is considered, with the FvK theory and \u03bd = 1/3. In nondimensional terms, the circular membrane is fixed at r = 1, and a flat punch is adhered to the membrane for 0 \u2264 r \u2264 a. The punch is displaced upward with deflectionw1(< 0) and total force f (Fig. 6). The adhesion energy (or critical strain energy release rate) is denoted (\u2206\u03b3 )N . The quantities f and (\u2206\u03b3 )N are related to the dimensional upward force F and adhesion energy (\u2206\u03b3 )D by f = F/(Eh B), (\u2206\u03b3 )N = (\u2206\u03b3 )D/(Eh). (31) Vertical equilibrium of the bottom of the punch gives, with the use of Eqs. (30), f = 2\u03c0anr (a)w \u2032(a) = \u2212(\u03c0/3)w3 1(1 \u2212 a2/3)\u22123. (32) Following [39], the nondimensional net input energy is UT = f |w1| \u2212 \u03c0a2(\u2206\u03b3 )N \u2212 (\u03c0/12)w4 1(1 \u2212 a2/3)\u22123, (33) where the first term represents the work done by the punch, the second term represents the surface energy of adhesion, and the last term is the negative of the membrane strain energy [43] computed with w and u given in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001505_bf01320814-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001505_bf01320814-Figure3-1.png",
        "caption": "Fig. 3. Ciliary beat pattern, a The cycle of movement of a cilium composed of the effective stroke E and the recovery stroke R. b In the effective stroke an element L moves at velocity V N and exerts a force F N on the water, c In the recovery stroke an element L moves at a velocity VT and exerts a force F T on the water; this is less than F N because CN = 2 C r and VN > VT",
        "texts": [
            " Because CN is about twice CT, the lengths of flagellum between wave crests exert substantial forces in the direction of the waves, but near the wave crests, where there is no normal motion but only axial motion, drag forces opposing the flow will dominate. The resultant in two rows in the plane of beat Cr/CN = 1.8 (Holwill and Sleigh 1967), so that reverse propulsion of water is much more effective with mastigonemes in the latter configuration. The presence of slender flexible hairs, or scales, on flagella is likely to produce small increases in both CN and Ca- and probably somewhat enhances propulsion by a helical flagellum (Lighthill 1976). During a cilium-type beat (Fig. 3 a) the motion of the organelle is very different during the two active phases of the beat, and consequently the motion of the surrounding water is also different. During the effective stroke the cilium swings around its basal anchorage (Fig. 3 b) and, because it remains nearly straight, all elements of its length remain approximately perpendicular to the direction of movement. During the recovery stroke the cilium \"unrolls\" as a bend travels towards the tip, drawing the distal part longitudinally through the water (Fig. 3 c). In the effective stroke the dominant forces are normal to the axis of the smoothsurfaced organelle and only the larger CN is important, whereas in the recovery stroke the dominant forces are tangential to the axis and only the smaller CT is important. There is also a difference in velocity in the two strokes. Typically the velocity in the effective stroke is higher than thai in the recovery stroke, but in the Mytilus abfrontal cilium (Baba and Hiramoto 1970) and in walking hypotrichs (Machemer and Sugino 1986) beat patterns have been described in which the \"recovery\" stroke is of much shorter duration than the \"effective\" stroke"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure31-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure31-1.png",
        "caption": "Fig 31 Optimum bearing shape study oscillating /ournal: the effect of surface ellipticity (Cornell University)",
        "texts": [
            " The author, in an associated discussion to Ref 3 has shown that this particular 'optimum' bearing shape is almost identical to a 'fitted arc' bearing, where the local bearing radius (in the loaded region) is equal to the journal radius over an arc of 90 \u00b0 . Such bearings are common in crosshead applications, although the fitted arc then usually extends over 120 \u00b0. When the journal bearing surfaces in a 'fitted arc\" bearing are separated, the film profile has a 'crescent moon' shape. This is ideal for oscillating motion, with imposed converging films together with the small local clearances at the ends of the functional arc which help to maintain pressure during squeezing action. From Fig 31 it can be seen that the improvement gained by the elliptical bearing (for the particular case studied) is not confined to the optimum design. There is indeed a large range of bearing types where the film thickness is more than twenty times that for the conventional bearing (however some of these have the complication of requiring an elliptically shaped shaft). More work on similar lines should be encouraged, to consider different bearing arrangements and different criteria (eg, minimum power loss)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure3.16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure3.16-1.png",
        "caption": "Figure 3.16 for perpendicular polarization. Incident reflected and refracted rays and the orientation of the E and H fields",
        "texts": [
            " It should be noted that although the E-field vector is in the plane of incidence, it is 102 FUNDAMENTALS OF FIELDS AND WAVES not necessarily in the vertical direction with respect to the horizontally oriented interface. We will consider the two cases separately. The reflection and transmission coefficients for plane waves discussed here are commonly known as Fresnel coefficients in the physics community, in honor of Fresnel who originally derived them for optical waves. Perpendicular or Horizontal Polarization The orientation of the electric and magnetic field vectors along the incident, reflected and refracted rays are sketched in Figure 3.16. There it can be seen that all the electric vectors are perpendicular to the plane of the paper (which is the plane of incidence) and are chosen to be directed toward the reader. The magnetic vectors in the plane of incidence are then as shown so that the energy flow for each ray is in its respective direction. REFLECTION AND REFRACTION (TRANSMISSION) OF PLANE WAVES 103 Explicit expressions for the E and H vectors along the various rays can be obtained by using (3.204a), (3.204b) in Section 3.6",
            "280) where nl, n 2 are the refractive indexes of medium 1 and medium 2, respectively. Equation (3.279) indicates that for incidence from the rare medium to a dense medium, the angle of refraction is less than the angle of incidence, and vice versa. It should be noted that (3.279) was originally introduced by Maxwell [ 1 11, and it is often referred to as Maxwell\u2019s relation. 106 FUNDAMENTALS OF FIELDS AND WAVES Angle, critical We consider the case when the wave is incident from a dense medium to a rare medium, meaning when \u20ac1 > \u20ac2 (or 721 > 712) in Figure 3.16. We see from (3.280) 8i > Ot in this case and also that as 8i increases, 8t also increases. It is clear from Figure 3.16 that the maximum value for the angle y refraction can be 7r/2. The angle of incidence Bi = 8, for which the maximum angle of refraction occurs is called the critical angle. The critical angle is obtained from (3.280) as sin 8, = - - &; = :1 (3.281) when n1 > 722, so the incidence is from the more dense medium side. It can be seen from (3.277a) and (3.280) that for Bi = $, I\u2018l = 1, that is the wave is totally reflected. Thus for 8i 2 8, there is total reflection and there is no power transmitted in the z direction through the interface into the less dense medium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003631_jmr.2015.110-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003631_jmr.2015.110-Figure2-1.png",
        "caption": "FIG. 2. (a) Schematic diagram of the SLM system and (b) scanning strategy applied in SLM experiments.",
        "texts": [
            " In the current study, the argon atomized (rapidly solidified), pre-alloyed AA8009 aluminum alloy powder with a nominal composition of Al\u20138.5Fe\u20131.3V\u20131.7Si (wt%) was utilized. Figure 1 illustrates the morphology and cumulative particle size distribution of the precursor powder, exhibiting a spherical shape [Fig. 1(a)] and particle size between 6 and 60 lm in diameter [Fig. 1(b)]. The powder was processed in an in-house developed SLM system. This SLM machine is equipped with an IPG YLR-500 Yb:YAG fiber laser, which projects a laser beam with a wave length of 1060 nm and can reach a maximum power of 500 W in a continuous mode. Figure 2 shows the SLM apparatus schematically and the scanning strategy deployed in this work. In this SLM system, the AA8009 alloy precursor powder [(4) in Fig. 2(a)] is contained in an automated powder tank indicated at (6), which feeds it onto the building part (5) on a build platform (7) (AA8009 alloy, 65 mm 65 mm 15 mm dimensions), where it is raked (3) into layers with a thickness of 50 lm. The laser beam (9) generated in a fiber laser source (1) is scanned across the powder layer by a CAD-driven X-Y scanner (2). Each layer was scanned twice with the same processing parameters (laser power: 350 W, scan speed: 1000 mm/s, hatching space: 0.1 mm, and layer thickness: 0.05 mm) but rotated over 90\u00b0, as depicted in Fig. 2(b). After the melting of a layer, the building platform (7) is lowered down and a new layer is raked (3). These two basic processes, power spreading and melting, are repeated, preparing an additivelayered 3D part. Excess powder is collected at (8) and recycled. To avoid alloy oxidation, the building chamber is first evacuated and then filled with an inert argon atmosphere, keeping the residual oxygen level below 0.1%. In this investigation, rectangular samples with a width, length, and height of 10, 10, and 15 mm, respectively, were produced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002238_iros.2010.5653006-Figure15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002238_iros.2010.5653006-Figure15-1.png",
        "caption": "Fig. 15 Schematic diagram of the experimental arrangement",
        "texts": [
            " This system controls the air pressure through voltage signals. The pressure supplied to each unit is independently controlled using six electromagnetic proportional valves. The conveyance of the inclusion is enabled by supplying a controlled pressure to the peristaltic pump according to a specified regular motion pattern. In transportation experiment, the supply pressure was unified by 0.04 MPa. When the static pressure is measured, a pressure gauge is attached in the outlet of pump. B. Experimental Arrangement Fig. 15 shows a schematic diagram of the experimental arrangement. As shown in this figure, one end of the peristaltic pump is put into a tank containing conveyed fluid, and the fluid is transported upward \u03b8 degrees. We performed the transportation experiment with both one and two units immersed in fluid. The fluid flowing from the upper side of the pump accumulates in the reservoir, and the flow rate of the pump is measured using the scales. In this experiment, \u03b8 is 90 degrees. C. Motion Pattern Fig. 16 shows the schematic diagram of the motion pattern used in the transportation experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003842_1.g003441-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003842_1.g003441-Figure4-1.png",
        "caption": "Fig. 4 Schematic drawing of deficient actuation system.",
        "texts": [
            " Each actuator is driven with a normalized PWM signal \u03b4i \u2208 0; 1 , which maps directly to lift of magnitude cf\u03b4i along the respective propeller axis. The proposed model neglects actuation dynamics as fast electric drive units and low-inertia propellers are assumed.Based on the blade element theory, proportionality applies between the propeller thrust and the aerodynamic resistance [33]. Given the propeller drag coefficient c\u03c4 > 0, the torque produced by the aerodynamic drag acting on each propeller thus reads c\u03c4\u03b4i. Figure 4 provides a sketch of the force and torque components, where the bent arrows next to c\u03c4\u03b4i indicate the direction of the propeller drag acting on the vehicle. D ow nl oa de d by T U FT S U N IV E R SI T Y o n Ju ly 2 , 2 01 8 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .G 00 34 41 Note that the sense of rotation for each actuator cannot be reversed. The lower PWM bound \u03b4i \u2265 0 corresponds to the engine running idle, whereas the upper bound \u03b4i \u2264 1 relates to a power restriction. The actuation torque in body-fixed coordinates reads \u03c4a l m n T , where l is the roll torque,m is the pitch torque, and n is the yaw torque. Given a symmetric configuration with respect to the CoG, a linear mapping from PWMsignals \u03b4i to \u03c4a and the total thrust f\u03a3 is defined as0 BBBB@ l t m t n t f\u03a3 t 1 CCCCA cf 0 BBBB@ \u2212\u03bbsin \u03ba \u03bbsin \u03ba \u2212\u03bbcos \u03ba \u03bbcos \u03ba \u03bbcos \u03ba \u2212\u03bbcos \u03ba \u2212\u03bbsin \u03ba \u03bbsin \u03ba c\u03c4\u2215cf c\u03c4\u2215cf \u2212c\u03c4\u2215cf \u2212c\u03c4\u2215cf 1 1 1 1 1 CCCCA 0 BBBB@ \u03b41 t \u03b42 t \u03b43 t \u03b44 t 1 CCCCA (5) where \u03bb > 0 represents the distance of the propeller shaft to the vehicle\u2019s CoG and \u03ba \u2208 \u2212\u03c0; \u03c0 is a configuration angle (see Fig. 4). Exploiting the bijectivity of the actuation map, the vast majority of control schemes for nominal quadrotor operation found in the literature (e.g., Refs. [34\u201336]) rely on the actuation torque \u03c4a and total thrust f\u03a3 as pseudo controls, which are then converted to PWM signals \u03b4i via inversion of Eq. (5). Without loss of generality the fourth actuator is assumed inoperable such that0 BBBB@ l t m t n t f\u03a3 t 1 CCCCA cf 0 BBBB@ \u2212\u03bb sin \u03ba \u03bb sin \u03ba \u2212\u03bb cos \u03ba \u03bb cos \u03ba \u2212\u03bb cos \u03ba \u2212\u03bb sin \u03ba c\u03c4\u2215cf c\u03c4\u2215cf \u2212c\u03c4\u2215cf 1 1 1 1 CCCCA\u03b4 t (6) where \u03b4 \u03b41 \u03b42 \u03b43 T is a reduced PWM signal for the remaining three actuators"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002650_tec.2012.2200898-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002650_tec.2012.2200898-Figure8-1.png",
        "caption": "Fig. 8. Calculation process of stator flux vector difference in the DTLC scheme.",
        "texts": [
            " As can be seen from (19), Te is strictly linear related to sin\u03b4; hence, based on this relationship, an DTLC scheme is investigated in this paper, where closed-loop control of the voltage based on PI controller is developed and the output of PI controller is defined as the sine value of the given torque angle, viz., sin \u03b4\u2217. The torque loop is omitted and the torque can be controlled directly and linearly by the output of the voltage loop. The DTLC scheme for the PHESF generator dc power system is shown in Fig. 7. Fig. 8 shows the calculation diagram of the stator flux vector difference. In Fig. 8, \u03b8s(k) is the angle of the stator flux-linkage vector of period k ( \u21c0 \u03c8s(k)), and \u03b8r(k) is the angle of the excitation flux- linkage vector of period k ( \u21c0 \u03c8e(k)). Since the mechanical time constant is greater than the electrical time constant during an interrupt period, \u03c9r can be taken as constant; thus, the change of the excitation flux-linkage vector angle is \u03c9rT . Then, the excitation flux-linkage vector of period k + 1 can be achieved, viz., \u21c0 \u03c8e(k+1) . According to \u03b4\u2217, the stator flux-linkage vector angle of period k + 1 can be obtained, viz., \u03b8r(k) + \u03c9rT + \u03b4\u2217. The magnitude of \u21c0 \u03c8s(k+1) is \u03c8\u2217 s . It should be noted that \u03b4\u2217 is a negative value, indicating generating mode and the phase angle of \u21c0 \u03c8s(k+1) lags behind that of \u21c0 \u03c8e(k+1) . In Fig. 8, the DTLC scheme employs SVPWM to achieve smooth and direct regulation of the instantaneous torque, which substitutes the hysteresis control of the DTC scheme. As can be seen, both the DTC and DTLC need the instantaneous torque information. To verify the improved estimation method, experimental tests have been carried out on a PHESF generator dc power system. Fig. 9 shows the prototype machine and the machine dimensions and parameters are shown in Table II. The phase currents ia , ib , ic are obtained by current sensors LA28-NP and phase voltages ua , ub , uc are acquired as follows [14]: ua = udc 3 (2DA \u2212 DB \u2212 DC ) ub = udc 3 (2DB \u2212 DA \u2212 DC ) uc = udc 3 (2DC \u2212 DA \u2212 DB ) (20) where DA , DB , and DC are the duty ratios of leg A, leg B, and leg C, respectively, and the dc bus voltage udc is acquired by a voltage sensor LV28-P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001165_0954406021525331-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001165_0954406021525331-Figure3-1.png",
        "caption": "Fig. 3 An equivalent mechanism",
        "texts": [
            " This mechanism has a characteristic that changes its link number and consequently changes its mobility during motion. When endlink 5 in the gure is attached to link 1, equivalent to at 5 being attached to panel 1, the mechanism changes its structure and mobility and forms a new con guration state (F ig. 3). This presents a metamorphic mechanism [9] that allows a mechanism representation of a carton. It can be seen that, during motion, the main part of the mechanism changes from a ve-bar serial kinematic chain in F ig. 2 to a four-bar closed-loop kinematic chain in Fig. 3. This facilitates the study of folding motion of artefacts, fancy gift packs and paper folds. The nature of the changeable mobility of a metamorphic mechanism represents the con guration changes of artefacts and foldable cartons during carton folding. The mobility of an equivalent metamorphic mechanism can be derived from a Kutzbach\u2013Grubler criterion [14], which is dependent on the type of pairs and constraints as follows: m mc mo b n \u00a1 g \u00a1 1 g go 1 where mc is the mobility in closed loops, mo is the mobility in open loops and is equal to number of joints, go, in open loops, b the order of the screw system formed by joint axes of a closed loop, n the number of links in a closed loop and g the number of joints in a closed loop"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001382_bf02460302-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001382_bf02460302-Figure1-1.png",
        "caption": "Figure 1. A right-hand helix. The axis of the helix K is the axis of the circular cylinder wrapped by the helix. The radius r is the radius of the cylinder's cross-section. The pitch p of the helix is the distance travelled in the direction of K for every revolution",
        "texts": [
            " This discussion also uses the Frenet trihedron, which is a reference frame conventionally used to describe the geometry of three-dimensional curves. The Frenet trihedron is represented by TNB where T is the unit tangent vector, N is the unit normal vector, and B is the unit binormal vector (see Gillett, 1984, Ch. 16, for an introduction). A right-hand helical trajectory is given by: H(t) = r cos(Tt)I + r sin(Tt)J + \\ 2nJ K (1) where IJK is a reference frame fixed to the helix such that K is the axis of the helix; p is the pitch; r is the radius; and 7 is the angular frequency (radians/time) (Fig. 1).* around the cylinder. The organism is considered a rigid body represented by an orthogonal reference frame ijk. The organism moves in three-dimensional space with translational (linear) velocity V and rotational (angular) velocity o~. As the organism moves, the origin of ijk describes a curve in space (Fig. 2a). The Frenet trihedron TNB also follows this curve such that the origin of TNB * For left-hand helical motion the sine and cosine terms are interchanged. This analysis uses the equation for a right-hand helix, but the results also apply to left-hand helices"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001050_robot.1990.126272-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001050_robot.1990.126272-Figure2-1.png",
        "caption": "Figure 2",
        "texts": [
            " S t e p B: At time t i , take q(t;)(q(O) = qo) as the initial configuration, and plan a desired path s f ( t ) whose lift connects q(t;) to q f . (Hope this can be done in zero time.) Step C: During the time interval [tj,ti+l], execute the path s f ( t ) . R e m a r k 3.2 In step B, i f the current configuration q(t;) agrees with the expected value (i.e., the lift of sf-l(t;)), then, s f ( t ) remains the same as sf-,(t). Otherwise, correction terms will be incorporated into the new trajectory, s f ( t ) . 0 4 Holonomy and Optimal Control Consider again Figure 2 and assume that p = 0. Let s( t ) , t E [O,T], be a closed path in the shape space, i.e., s(0) = s(T), and lift it to a path q(t) in the configuration space. From our early discussions we know that, (1) q(t) is horizontal, and (2), q(t) is in general not closed, i.e., q(0) # q(T). This follows from the constraint being nonholonomic. Since q(T) and q(0) project to the same point, they must differ by a constant. That is, if q(0) = ( 6 b ( O ) , 6l(O), U ( O ) ) ~ , then q(T) = ( 6 b ( O ) + a, 6,(0) + a, U ( O ) ) ~ , where a is expressed in radians"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure12-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure12-1.png",
        "caption": "Fig. 12. Comparison of rough-cut geometry of the gear tooth surfaces with regard to the objective geometry for the 20th valid geometry on (a) the concave side and (b) the convex side.",
        "texts": [
            " As depicted, the maximum stock for the finishing operation is concentrated on the central dedendum area of both concave and convex active surfaces of the rough-cut geometries, whereas the minimum stock is located on the addendum area of concave active surfaces and on the heel and toe areas of convex active surfaces. More concretely, the magnitude of the aforementioned raw material surplus is very limited, being about 360 \u03bcm for the concave side, whereas a minimum stock of 103.8 \u03bcm is obtained at the concave side, which meets the requirement of 100 \u03bcm stock allowance for the rough-cut geometry. Additionally, Fig. 12 shows the results of comparison of the rough-cut geometry and the objective geometry for the 20th valid geometry and Fig. 13 shows the corresponding results for the 40th and final valid geometry before the COBYLA algorithm returns after 500 iterations. In Figs. 11\u201313 , the rough-cut geometry is represented as solid body and the objective geometry as a wireframe model. Comparison of normal distances corresponding to the three reached roughcut geometry reveals, firstly, similar tendencies, and secondly, negligible differences among them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000827_robot.2001.933264-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000827_robot.2001.933264-Figure3-1.png",
        "caption": "Figure 3: A 6-DOF model of the environment (elastic pads and the ground contact)",
        "texts": [
            " robots are equipped with some kinds of shock-absorbing elastic pads at their soles [6] [7]. Such pads, however, allow small movements of the feet, and might cause unstable locomotion. Park and Chung [7] proposed a 3-DOF environment model of pads in their simulation of motions of a 6-DOF biped robot in the sagittal plane. This paper expanded the environment model to a 6-DOF model, which allows twisting of the foot on the ground. Again, the pads are modeled as compliant contact models with linear and nonlinear springs and dampers Figure 3 describes a foot of the biped robot with an elastic pad along with its environment and the ground. The pad of the robot is approximated as the model which consists of a nonlinear damper and a linear spring in order to simulate the motion of the biped robot. Each elastic pad is assumed to be composed of four vertical units of a nonlinear damper and a linear spring at the corners, two horizontal units of a nonlinear damper and a linear spring at the heel and the toe, aligned along the lateral direction, and two horizontal units of a nonlinear damper and a linear spring at the toe, one at the inside and the other at the outside of the foot, aligned along the walking direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002153_j.rcim.2010.05.007-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002153_j.rcim.2010.05.007-Figure3-1.png",
        "caption": "Fig. 3. Hexaglide parallel robot with notation.",
        "texts": [
            " With the calibration method proposed above, we would like to calibrate a Hexaglide parallel robot. The first Hexaglide parallel robot has been developed at ETH Zurich [22]. As shown in Fig. 2, Hexaglide is composed of a moving platform that is connected to the six legs through universal joints and these legs are connected to six linear actuators or sliders through spherical joints. These sliders that are distributed on three parallel rails are actuated by ball screws and servo motors. Movements of the sliders or the spherical joints guide the platform in 6 DOF. As shown in Fig. 3, two coordinate systems are used for modeling of this robot. Global coordinate system is fixed to the base frame and local coordinate system is fixed to the moving platform whereas its origin is the end-effector center point. The geometric parameter vector of this robot can be defined as [20] d\u00bc BT 1 BT 2 . . . BT 6 ST 1 ST 2 . . . ST 6 l1 l2 . . . l6 h i \u00f014\u00de where Bi is the universal joint position vector defined in the local coordinate system, Si is the spherical joint position vector defined in the global coordinate system when the corresponding joint variable, qi, is zero and li is length of the ith leg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003024_cjme.2014.0519.098-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003024_cjme.2014.0519.098-Figure1-1.png",
        "caption": "Fig. 1. Three deployable structures",
        "texts": [
            " Screw theory has been applied to the development of traditional dynamic modeling approaches, such as Newton-Euler method[14\u201315], Lagrange\u2019s equations[14, 16\u201317], principle of virtual work[7, 18] and Kane\u2019s equations[19]. Recently, the kinematics and dynamics of deployable structures has been the focus of great interest by researchers[20\u201321], however, there are still fewer papers which present kinematics and dynamics of these deployable structures based on screw theory. As the basic building unit for a deployable structure, the SLE is one of the most widely used units found in deployable structures[22\u201323]. As shown in Fig. 1, the SLE SUN Yuantao, et al: Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory \u00b7656\u00b7 mechanism consists of two bars with a middle hinge, and there are different deployable structures because of the different combination of SLE. The deployable structures, which incorporate the SLE as its basic building unit, have a common characteristic in that they have a single degree of freedom. In contrast, the deployable structure assembled from three SLEs is the research focus of this paper, and is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure12-19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure12-19-1.png",
        "caption": "FIGURE 12-19 Elementary hydraulic draft control. (From W. S. Hockey, The Institution of Mechanical Engineers, Nov. 1961.)",
        "texts": [
            " Automatic Draft-Control System These systems will automatically raise or lower an implement as the draft or resistance of the attached implement increases or decreases. The sensing device, which tells the hydraulic system to lower or raise the hitch system, is located on either the lower links or the upper link, depending on the size of the tractor. The position of the hand-control lever, in effect, establishes the draft to be maintained. For example, a draft-control system on a tractor pulling a plow will raise and lower the plow to maintain a constant force on the sensing device. A simple form of a draft-control system is shown in figure 12-19. Draft Sensing When the draft-control system was first developed by the late Harry Ferguson, the draft-sensing device was located on the upper link and responded to a compressive force. For a close-coupled implement-for example, a two-bot- 330 HYDRAULIC SYSTEMS AND CONTROLS tom plow-the upper link will normally be in compression, and as the draft increases, the compressive force will increase. It can be shown that the com pressive force in the upper link becomes smaller as the size of an integrally mounted plow increases, and will often be a tension force for mounted plows of four or five bottoms and larger"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003702_s11071-016-2669-5-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003702_s11071-016-2669-5-Figure1-1.png",
        "caption": "Fig. 1 Planar interception geometry",
        "texts": [
            " Since the guidance process occurs in a short time, the finite-time stabilization of state variables is required. Furthermore, the target maneuver is an external disturbance which can lead the guidance loop to instability. So, in order to hit the target, designing a robust guidance law which can reject the target maneuver is mandatory. For these reasons, the proposed law in this paper is a suitable tool to design a robust finite-time convergent guidance law based on partial stability. 4.1 Formulation of interceptor\u2013target engagement and guidance law design The geometry of planar interception is shown in Fig. 1. According to the principle of the kinematics, the corresponding equations of motion between the target and the interceptor can be described by [26]: R\u0308 = \u03bb\u03072R + aT R \u2212 aMR (22) \u03bb\u0308 = \u22122R\u0307 R \u03bb\u0307 + aT\u03bb R \u2212 aM\u03bb R (23) where R denotes relative distance between the target and the interceptor; \u03bb\u0307 represents the line-of-sight (LOS) angular rate; aT R and aMR denote the target and the interceptor acceleration along the LOS, respectively; andaT\u03bb andaM\u03bb represent the target and the interceptor acceleration normal to the LOS, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure1-1.png",
        "caption": "Fig. 1. Definitions of skiving coordinate systems.",
        "texts": [
            " Secondly, mathematical model of cutting force in gear skiving is presented, and the mechanical performances of the tool in skiving with different commonly used feeding techniques are investigated. Finally, an improvement of the multiple-side-feeds technique is proposed for wear reducing of the top-recess nose of the skiving tool tooth. The working rake and relief angles and the cutting thickness of skiving tool are discussed in geometrical analyses of gear skiving, which is based on the methodical model of skiving. In gear skiving, the tool and the workpiece rotate around their own axis, and the workpiece feeds along its rotation axis at the same time. As shown in Fig. 1 , tool setting parameters , a and L are used to define the shaft angle, the center distance and the offset distance between the tool and the workpiece, respectively. S 1 ( x 1 , y 1 , z 1 ) is the fixed coordinate system of workpiece that rotates around and moves along the axis of z 1 . S w ( x w , y w , z w ) is rigidly attached to the workpiece, and its original position is identical with S 1 . S 2 ( x 2 , y 2 , z 2 ) is the fixed coordinate system of the tool that rotates around axis of z 2 ",
            " R is the position vector of the tool which can be expressed in coordinate system S 1 as R = [ a \u2212 L \u00b7 sin 0 ] T (1) If the angular speed of the tool is \u03c9 c and the axial feed speed of the workpiece along z 1 axis is f , the angular speed of the workpiece \u03c9 w can be described as \u03c9 w = Z c Z w \u03c9 c + f p (2) where, Z c and Z w are the numbers of teeth of the tool and the workpiece, respectively, and p is the helix parameter which can be expressed as p = p z 2 \u03c0 (3) where, P z is the helix lead on the reference cylinder of workpiece. The cutting edges of a skiving tool tooth can be defined as the approach edge \u201cA\u201d which is the earliest side edge that approaches the workpiece, the recess edge \u201cR\u201d which is the last side edge that separates from the workpiece and the top edge \u201cT\u201d, as shown in the Chip view of Fig. 1 . There are lots of different design methodologies of skiving tool. As recommended in the Ref. [15] , the side cutting edges of the skiving tool are curves on the rake face conjugated with the tooth flanks of the workpiece. Based on the recommended skiving tool design method, the position vector and the tangent vector of the point on the cutting edge of the skiving tool can be obtained and expressed in S c as: r c = [ x c y c z c 1 ]T (4) t c = [ t x t y t z ]T (5) If the rotation angle of the tool around axis Z 2 is \u03d5c , the position vector of the cutting point and the tangent vector can be expressed in S 2 as: r ( 2 ) c ( \u03d5 c ) = M 2 c \u00b7 r c (6) t ( 2 ) c ( \u03d5 c ) = L 2 c \u00b7 t c (7) where, M 2 c is the transfer-matrix from S c to S 2 , whose upper-left 3 \u00d7 3 submatrix is L 2 c "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure8-13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure8-13-1.png",
        "caption": "FIGURE 8-13 Lubrication flow schematic on a modern diesel engine. (Courtesy Cummins Engine Co., Inc.) Key: 1. Oil Pump 7. Full Flow Filter 2. Pressure Regulator Valve 8. Oil Cooler 3. Oil Return to Pan 9. Bypass Filter 4. High Pressure Relief Valve 10. Bypass Filtered Oil Return 5. Oil Return to Pan 11. Accessory Drivel Air Compressor 6. Full Flow Filter Bypass Valve 12. Idler Gears",
        "texts": [
            " Filters offering high 200 PROBLEMS 201 resistance to flow are practically useless in winter for short periods of operation when the oil seldom reaches a normal crankcase temperature. Figure 8-12 shows a cross-sectional view of an oil filter made of pleated resin-impregnated paper. The surface area of the filter has been increased many times by pleating the paper. This type of filter is not reusable but is replaced after a predetermined number of hours of tractor engine use. Lubricating Oil Systems Tractor engines are equipped with an internal pressurized system of lubri cation (fig. 8-13). A pump takes the oil from the sump and delivers it to a distributor duct that connects with all the main bearings. The crankshaft is drilled to provide an oil passage to the connecting rod, which is drilled to provide an oil passage to the piston pin. A pressure-regulating valve controls the pressure of the oil at the desired level. The system shown in figure 8-13 is a \"full-flow\" type. In other words, this system continually filters the entire stream of oil being pumped to the lubricated parts. PROBLEMS 1. Calculate the kinematic viscosity of an SAE 50 oil at 60\u00b0C. How does your answer compare with the value read from figure 8-6? 2. An engine operating at 2000 rpm has a main bearing 57.2 mm long and 36.3 mm in diameter, carrying an estimated load of 1335 N. The engine crankcase is filled with SAE 30 oil at a temperature of 121\u00b0C. Assuming that the bearing follows the curves of figure 8-10 and that the oil has a specific gravity of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002837_j.mechmachtheory.2013.10.001-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002837_j.mechmachtheory.2013.10.001-Figure4-1.png",
        "caption": "Fig. 4. Bearing terminology.",
        "texts": [
            " Needle rollers are difficult to guide and rollers get rubbed against each other. NRB is illustrated in Fig. 1. In NRBs, flanges that are integral to the outer raceway retain rollers. Fig. 2 shows the inner ring that is used with the needle and cage assembly. It is used when the shaft cannot be hardened and grounded to a suitable raceway tolerance. The inner ring is hardened and grounded, and is provided with a chamfer on both sides for assembly. Fig. 3 shows the needle roller which is relieved at ends to prevent edge stresses. Fig. 4 shows the terminology for NRBs. The figure shows different components of the bearing like (1) outer ring, (2) lubrication hole, (3) raceway, (4) needle roller and cage assembly, and (5) open end. Flaking is a phenomenon where the scaly particles get separated from the bearing material which is due to the metal fatigue that occurs between the raceways and rolling elements. Bearing fatigue life is nothing but the number of revolutions after which the flaking starts due to the stresses [21]. Thus, the bearing life is an important factor in the bearing design and thus the design has been chosen so that the life can be maximized"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002740_iet-cta.2010.0232-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002740_iet-cta.2010.0232-Figure8-1.png",
        "caption": "Fig. 8 Model of the aluminium plate",
        "texts": [
            " The apparatus has roughly two parts connected by LAN: computer PC1 as a controller and the controlled process which is composed of a Peltier-actuated process for cooling the aluminium plate and the serial communication (RS232C) for communication interface between computer PC2 and the micro-computer. The photo of the apparatus is shown in Fig. 7. Peltier device and sensor are installed on both sides of the aluminium plate, respectively. On the heat radiation side of the Peltier device, a heat sink is installed to prevent it from having heat too much. Thus, the model of the aluminium plate can be drawn as Fig. 8, where S3 is a Peltier element, and on the opposite side of it, there exists is a sensor for measuring temperature of the aluminium plate. The parameters of the model are given in Table 1. According to Fourier\u2019s law concerning thermal conduction, Newton\u2019s law of cooling, equation on the variation of heat capacities, Electrothermal amount by Peltier effect, thermal conduction by temperature gradient and Joule exothermic heat by current, a differential equation with regard to heat IET Control Theory Appl"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002221_00220345740530061201-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002221_00220345740530061201-Figure1-1.png",
        "caption": "FIG 1.-Lef t, butt solder joint being pulled in uniaxial tension along longitudinal axis; right, applied axial stress results in radial stresses along solder-parent metal interface.",
        "texts": [
            " Soldering provides a convenient means of assembling structures, such as dental bridgework, and can provide an excellent bond while adding bulk. This investigation was designed to study some of the factors which determine the strength of butt solder joints in an effort to suggest ways of optimizing the strength characteristics. Those factors examined were solder joint size (that is, radius-tothickness ratio), rate of deformation, and perfection of the solder-parent metal interface. THEORETICAL CONSIDERATION.-Triaxiality.Figure 1, left shows schematically a butt soldered joint being pulled in uniaxial tension. The assumption is made that the solder material is softer than the parent metal which it joins. During deformation the adhesion and the penetration of solder into surface irregularities tend to hold the solder in place at the solder-parent metal interfaces. Thus, while the applied force produces an axial tensile stress, the interfacial bonding produces shearing stresses in an outward radial direction acting at the solder-parent metal interface (Fig 1, right). As detailed in Appendix A, these orthogonal stresses (called triaxial since stress components are present along the x, y, and z axes) produce a conical region of complex stress within the solder at and slightly above the interface (Fig 2). Figure 2, a to b, shows the effect of decreasing the thickness, h, of the solder. The Received for publication September 24, 1973. stronger complex stress regions occupy a relatively greater portion of the solder joint as the joint becomes thinner. A detailed calculation (see Appendix A) of UP, the theoretical yield stress of a solder joint under tension, gives the following: 3 h( (1) where o-O is a constant which becomes the shear strength of the solder as perfect adhesion is achieved at the interfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002906_j.mechmachtheory.2013.01.010-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002906_j.mechmachtheory.2013.01.010-Figure1-1.png",
        "caption": "Fig. 1. Typical application of an eight-point double row ball bearing.",
        "texts": [
            " Shortcomings of standardized calculation procedures become especially noticeable in case of special bearings, such as large slewing rolling bearings. These are commonly used in transport devices (cranes, transporters, turning tables, etc.), large vehicles, wind turbines etc. They can accommodate axial and radial forces and tilting moments, which can act either singly or in combination and in any direction. Typical configuration of an eight-point double row ball bearing, which is a common type of slewing bearing in wind turbine applications, is shown in Fig. 1. Thus, this paper will focus on problems with the calculation of contact load distribution over the rolling elements and static capacity of such bearings. It has to be noted that throughout the paper the term static capacity refers only to the capacity of the raceway, hence the capacity of bolts is not a subject of this paper. Most notable things, which are not taken into consideration in standards ISO 76 and ISO 281 are [3]: \u2022 non-parallel displacement of rings (as a result of tilting moment for example), \u2022 clearance of the bearing, \u2022 rotational speed and consequently centrifugal forces, \u2022 incorrect ring geometry, etc",
            " 3): OOo \u00bc oo;r \u00fe \u0394o;r \u03c8; oo;a \u00fe \u0394o;a \u03c8 : \u00f05\u00de In terms of vectors the positions of Oi and Oo in coordinate system xyz are defined by vectors ri and ro as: ri \u00bc cos\u03c8 d 2 \u00fe D 2 cos\u03b10 1 S \u22121 \u00fe \u0394i;r j\u03c8 sin\u03c8 d 2 \u00fe D 2 cos\u03b10 1 S \u22121 \u00fe \u0394i;r j\u03c8 D 2 sin\u03b10 1 S \u22121 \u00fe \u0394i;aj\u03c8 1 2 666666664 3 777777775 \u00f06\u00de and ro \u00bc cos\u03c8 d 2 \u2212D 2 cos\u03b10 1 S \u22121 \u00fe \u0394o;r j\u03c8 sin\u03c8 d 2 \u2212D 2 cos\u03b10 1 S \u22121 \u00fe \u0394o;rj\u03c8 \u2212D 2 sin\u03b10 1 S \u22121 \u00fe \u0394o;aj\u03c8 1 2 666666664 3 777777775 : \u00f07\u00de Due to later multiplication with the transformation matrix as described in next section vectors have been extended by the fourth component, i.e. scalar 1. In case of multiple row bearing, for example in case of a four-point double row ball bearing as shown in Fig. 1, similar relations can be written for any raceway. Furthermore, every parameter in Eqs. (6) and (7) can be parametrized as a function of an angle\u03a8, which makes it possible to specify virtually any reasonable bearing geometry. Contact forces transmit external loads from one ring to another as schematically shown in Fig. 4 (for one rolling element). The magnitude of a given contact force depends on the contact deformation between the raceways and rolling element in contact. Hence, in order to calculate the contact force the exact relative approach of the tow opposite raceways has to be known",
            " The algorithm does not require to know the derivatives of the function, since they are calculated by finite difference approximation. However, initial values for the unknown variables u, v, w, \u03c6x and \u03c6y have to be chosen sensibly, so that the computation successfully converges. In most cases these are the values, which result in some reasonable contact load distribution. The convergence is determined by testing the residual values of the functions against some absolute error bound. The algorithm presented above has been tested on a double row slewing ball bearing with eight contact points as shown in Fig. 1. This means that each ball can be loaded by two pairs of contact forces, i.e. four contact points per ball. The algorithm has been used to analyse the influence of different geometrical parameters on the static capacity of the bearing. The computational example was done for a bearing with the following \u201cinitial\u201d geometry (same for both rows): d=2010 mm, D=45 mm, S=0.97 mm, \u03b10=45\u00b0, and Z=123. In order to examine the influence of the clearance the calculations were done for the following clearances (in axial and radial direction): 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003928_j.mechmachtheory.2014.08.016-Figure4-1.png",
        "caption": "Fig. 4. Schematic of apparatus for measuring tooth wear.",
        "texts": [
            " Because of the misalignment of shafts, small (z = 5) number of teeth couplings, and casual arrangement of vectors of additional load in three couplings, the torque inside the contour is variable. As can be seen from Fig. 3, the change in frequency of torque Ti is in the range of frequencies for the variation of resistance torque for mining machines. Thus, using gear parameters and manufacturing technology, the characteristics and level of loading and lubrication of the test bench correspond to the range of operating conditions of mining machine gears. The device shown schematically in Fig. 4 is overlaidwith a specialized apparatus formeasuring toothwear atfixed points along the involute profile of the irreversible gear [28]. In Fig. 5, a general view of the instrument for measuring the tooth wear of the pinion (reducer 1 in Fig. 2) is shown. The apparatus consists of two parts, namely a base I and a lever II. Lever II is set in slide conic bearings of base I, and can be rotated around the axisOk, the position ofwhich is chosen such that the circular arc of the radius Rk passes through the primaryH, secondary P (usually pitch point), and the ending E points of the active part of the involute tooth profile",
            " By comparing them with the base readings for the value of wear at the corresponding points of the tooth, the following can be determined: Ii \u00bc abi\u2212ai; 0\u2264 i\u2264nz; \u00f023\u00de where abi and ai are the base and current readings of the indicator, respectively, at the point with number i and nz is the number of measurement points. Theminimumnumber of points, atwhich one can reliably describe the profile of theworn teeth, is taken to be equal to nz min=10. The maximum number of points must be no more, than nz max = 20, so with increasing nz max, the requirements for accuracy of the angular step of the ratchet mechanism are increased. When measuring the gear wear of the wheel with the other parameters it is necessary to smelt the molding 1 (Fig. 4) and the apparatus must be based on the new gear to fill a tooth cavity. This apparatus records the wear in the function of curvilinear coordinate L (length of involute), which is defined for an arbitrary point as follows: Li \u00bc LE\u2212\u0394L nz\u2212i\u00f0 \u00de\u2212\u03b4L \u00bc Rb 2 tan\u03b1E\u00f0 \u00de2\u22122\u03c0 zs Rk nz\u2212i\u00f0 \u00de\u2212\u03b4L \u00f024\u00de where LE is the length of the involute from the base circle of radius Rb to the top of the tooth, \u03b1E is the involute angle at the top of the tooth, \u0394L is the movement step of the probe along the profile of the tooth and zs is the total number of teeth of the ratchet sector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001077_s0045-7825(02)00351-1-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001077_s0045-7825(02)00351-1-Figure2-1.png",
        "caption": "Fig. 2. Model of a gear drive consisting of gear and pinion.",
        "texts": [
            " Thus the reduced function attains a local extremum at the origin if w w determines a tooth flank point. Moreover in [18] it is shown, that conversely the point x w \u00bc Fw\u00f0w w \u00de considered belongs to the local range boundary of Fw if the reduced function is extremal at the origin, independently of the direction rw chosen. Without loss of generality, we throughout require that the reduced function k attains a maximum, that is g0 w \u00f0w w \u00devw\u00f0w w \u00de < 0 8w w 2 Sw: \u00f04\u00de This can be achieved by choosing the direction rw to \u2018point out\u2019 of the range of Fw as in Fig. 1. As depicted in Fig. 2, a hypoid gear drive consists of a pair of separately generated gear wheels, the larger one is called the gear\u2013\u2013the smaller one the pinion. The gear and pinion are installed in a structural housing typically referred to as gear box. In order to model the meshing of the gear and pinion both gear wheels have to be represented in one common coordinate system R preferably fixed with respect to the gear box. In [17] for each of the meshing gear wheels the coordinate transformation from its wheel system Rw to the common gear box system R \u00bc eRw is determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003615_978-3-319-27149-1-Figure21-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003615_978-3-319-27149-1-Figure21-1.png",
        "caption": "Fig. 21 The Microsurgery worm.",
        "texts": [
            " Due to the nature of this surgical technique, the forces applied by the tools are low; hence small motors with encoders are suitable for the intervention. Another characteristic of this robot is the end effector, which has been designed to hold standard tools currently used in conventional surgery. They are substantially cheaper than those articulated, or even those motorized robotic tools. Moreover, these tools can be easily replaced by a fast plug-and-play system. The purpose is to reduce the intervention times, whether for the setup preparation or in tool changes during the operation. The general design of the microsurgery robot is shown in fig. 21. In working conditions, its dimensions are 30 cm height and the extended arm reaches a distance of 60 cm, approximately. The Microsurgery worm has been validated through simulation. The prototype is pending for construction to verify its viability and suitability for this kind of surgery. Challenges in the Design of Laparoscopic Tools 475 References 1. Mettlere, L.: Historical Profile of Kurt Karl Stephan Semm, Born March 23, 1927 in Munich, Germany, Resident of Tucson, Arizona, USA Since 1996. JSLS 7(3), 185\u2013188 (2003) 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002696_e2013-02067-x-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002696_e2013-02067-x-Figure1-1.png",
        "caption": "Fig. 1. Schematic sketch of the experimental setup. Standard video microscopy is used to observe the system. Tilting of the entire experimental setup by the angle \u03b1 leads to an external driving force Fdrive = m \u2217g sin\u03b1, with the effective mass m\u2217 of the particle. In this case, the particles will flow down from the upper reservoir through the channel into the lower reservoir. Due to their weight, the particles settle down to the surface and form a quasi two-dimensional system inside the channel.",
        "texts": [
            " Due to their high density, the particles settle down to the channel surface and buoyancy leads to an effective mass of m\u2217 = V \u03c1particle \u2212 V \u03c1water = 2, 3850(8) \u00d7 14\u221214 kg where V denotes the volume of the particle. In this case, height fluctuations of the colloids can be neglected and the motion of the particles inside the channel is limited to two dimensions. Two large reservoirs are placed at each end of the channel acting as source and drain for flowing particles. The entire setup can be tilted by an angle \u03b1 causing the particles to flow along the channel (for illustration see Fig. 1). In our case, this mechanism is used for the generation of a constant driving force as well as for the manipulation of the particle density inside the channel. The interaction between two particles i, j at distance rij is of repulsive nature and can be described by a dipole potential [17] Vij(rij) = \u03bc0 4\u03c0 M2 r3ij \u00b7 (1) Here, \u03bc0 is the magnetic constant and the magnetic dipole momentM of the particles is given by M = \u03c7effBext, where Bext represents an external applied magnetic field. Thus, the magnetic interaction strength in the system can be adjusted by variation of the external field. The value of \u03c7eff can be determined with simple methods [18] and leads in our case to a value of \u03c7eff = 7.88(8)\u00d7 10\u221211Am2/T. All experiments in the following sections were done by means of a standard video microscopy setup (see Fig. 1). To track the position of each particle, particle tracking software is used which is able to locate the particles with sub-micron accuracy [19]. At the beginning of the measurement, the sample is aligned horizontally in the video setup to ensure that the particles undergo only Brownian motion (\u03b1 = 0 to avoid additional driving forces inside the channel). After that, the system is equilibrated for at least 5 h before the measurement is started at afinite value of \u03b1. All particle trajectories contain at least 20000 data points with a time resolution of one frame per second"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000851_1.1415739-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000851_1.1415739-Figure3-1.png",
        "caption": "Fig. 3 Section view of a meshing pair of spur gears",
        "texts": [
            " The state vector of coupled lateral-torsional motion is set up as: $S%5^Y c,uz c ,M z c ,Vy c ,Y s,uz s ,M z s ,Vz s ,Zc,uy c , M y c ,Vz c ,Zs,uy s ,M y s ,Vz s ,fc,Tc,fs,Ts&T The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set along the pressure line and the transmission error is simulated by a displacement excitation at the mesh. The transmission error arises from several sources, such as tooth profile error, deformation of tooth during engagement, manufacturing errors, etc. A section view at the gear location is shown in Fig. 3. The tooth flexibility and damping are represented, respectively, by a spring and a damper which connect two gears in mesh along the pressure line with an angle fh relative to the Y-axis. Each gear is modeled as a rigid disk carried by a rotating shaft. For simplicity, rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/14/201 the spur gear pair is assumed to be heavily loaded with zero backlash and the teeth spacing is assumed to be uniform. The coupling force along the pressure line in the Y -Z plane can be written as @3# P52Kg~ t "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure13-1.png",
        "caption": "Fig. 13 Equation of profiling curve",
        "texts": [
            " With the consideration of planer tool performance, only vertical shank is adopted, and the blade should be arc or right angle. The copying coordinate system of the planer tool is established, as shown in Fig. 12.: the moving coordinate system of the shaper Ss (xs,ys,zs) is fixed to the shaper so that they can rotate together; St0 is the fixed coordinate system of the planer tool; the moving coordinate system of the planer St is a copy of Ss; and they completely coincide. Initially, St0 coincides with St. \u03b8t is the rotation angle of the basic cutter location group. As shown in Fig. 13, P is an arbitrary point on the tooth profiling curve, Ot is the corresponding point on the profiling curve after compensation, and Ot is also the original point of St, PQ with the length of the sum of the allowance and the radius of the tool corner is the normal of the tooth profile, and QOt is the horizontal segment with the length of H/2. The angle between PQ and x axis can be calculated according to the unit normal of the shaper ns * , then Q can be calculated. Finally, Ot can be calculated according to the length of QOt"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003024_cjme.2014.0519.098-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003024_cjme.2014.0519.098-Figure2-1.png",
        "caption": "Fig. 2. Cartesian coordinate system, motion pairs, connecting links and links",
        "texts": [
            " 1, the SLE SUN Yuantao, et al: Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory \u00b7656\u00b7 mechanism consists of two bars with a middle hinge, and there are different deployable structures because of the different combination of SLE. The deployable structures, which incorporate the SLE as its basic building unit, have a common characteristic in that they have a single degree of freedom. In contrast, the deployable structure assembled from three SLEs is the research focus of this paper, and is shown in Fig. 2. As shown in Fig. 2, the elements numbered 0\u20135 and 6\u201311 represent connecting links and links respectively. Because the forces are seen to act the component center of mass, the relationship between input forces or torques and all forces or torques of center of mass need to be determined according to the principle of virtual work. Therefore, before deriving the equations of motion, the Jacobian matrix of center of mass is derived firstly. This paper is organized as follows. Utilizing a screw theory formulation, the kinematic equations of a deployable structure are first derived",
            " In this derivation, the deployable structure kinematic equation is assembled from three individual SLEs, in which the structure is sub-divided into three independent closed-loops. The constraint topology graph, shown in Fig. 3, combined with the closed-loop motion equations and the constraints amongst three closed-loops, permits the kinematic equations to be derived. The dynamics of the deployable structure is then derived. The component twists are computed and the dynamics equations are then derived based on the principle of virtual work. To simplify the following development, the origin of the reference is defined in the point O of connecting link 0 as shown in Fig. 2, and kinematic pairs are identified with Roman letters. The angular velocity \u03c9A of revolute joint A is assumed to be given. The constraint topology graph is shown in Fig. 3, with circles and lines used to represent links and revolute joints respectively. From Fig. 3, it is seen that there are three kinematic closed-loops, denoted as closed-loop I, II and III. A common revolute joint is shared amongst every pair of closed-loops. Every closed-loop is composed of n=6 links and g=6 revolute joints. If fi and v is the number of the degree of freedom(DOF) of ith revolute joint and over-constraint separately, based on the modified formula[24\u201325] of degree of freedom m=6(n\u2013g\u20131)+ \u03a3 fi+v=1, each closed-loop has one DOF",
            " Therefore, there is one independent input amongst the previous three closed-loop inputs, and the motion of the remaining links can be determined through the solution of the closed-loops within the deployable structure. Here, the connecting link 0 of closed-loop I is chosen as the fixed frame, hence the kinematic equations of closed-loop II and III may be derived from the moving platform. In addition, the kinematic equations, which describe paths shown by dotted and dot-dashed line in Fig. 3, not only express the relationship between the closed-loop, but also lead to the solution of the kinematics of the moving platforms. These are represented by connecting link 3 and connecting link 5, shown in Fig. 2. In the following, the velocity and acceleration kinematic equations are first derived for the deployable structure, and then discussed subsequently. First, the kinematic equation of closed-loop I, a parallel mechanism with two branches is developed. Since connecting link 0 is the fixed frame, it follows that connecting link 1 is located on the moving platform. Assuming that the velocity of connecting link 1 is 1v , based on screw theory, it follows that 1,A A B B C C\u03c9 \u03c9 \u03c9  \u03be \u03be \u03be v (1) CHINESE JOURNAL OF MECHANICAL ENGINEERING \u00b7657\u00b7 1",
            " Since the angular velocity \u03c9i is obtained through solution of the above equations, the velocity is \u03c9i\u03bei and its coordinate component may be expressed as  ,i i i\u03c9 \u03c9\u03c9 \u03be (11) where \u03c9() is a matrix representing the first three screw velocities. Since these screw velocities in the above represent angular velocity, we may now write the linear velocity of the motion joint i as     ,i i i iv \u03c9 \u03c9 \u03c9  v \u03be \u03be \u03c1 (12) where v() is a vector representing the last three elements of the velocity, \u03c1 is a radius vector from the point to the basis point. Based on the previous analysis, we note that the key aspect of this approach is to solve the relevant component velocity for the linear velocity component. From Fig. 2, it can be seen that closed-loop I has a fixed frames, while closed-loops II and III do not have a fixed frame. Therefore, the approach utilizing the velocity is discussed separately. As seen in closed-loop I, there is a fixed reference frame and the linear velocity of connecting link 1 is computed below as an example. Beginning with frame 0, connecting link 1 will move due to the revolute joint A, B and C or revolute joint E, W and H. Therefore, its velocity and linear velocity can be obtained as 1,A A B B C C\u03c9 \u03c9 \u03c9  \u03be \u03be \u03be v (13)    1 1 1 1.v \u03c9  v v v \u03c1 (14) Linear velocities of the left hand side components of closed-loop I will be solved similarly. However, the SLE consisted of components 8 and 9 are treated somewhat differently. To solve its linear velocity, the reference body, such as connecting link 3 or 5, shown in Fig.2 must first be chosen. Without loss of generality, the linear velocity of revolute joint P in closed-loop II is derived below, with connecting link 3 regarded as a reference body. The velocity of connecting link 3 is 3.A A B B K K\u03c9 \u03c9 \u03c9  \u03be \u03be \u03be v (15) And based on the vector of velocity of relative motion, the velocity of revolute joint P is given as 3 ,Q P v v v (16) where vQ is velocity of revolute joint. Based on Eq. (12), the linear velocity of revolute joint P is obtained as     .P P P Pv \u03c9  v v v \u03c1 (17) SUN Yuantao, et al: Kinematics and Dynamics of Deployable Structures with Scissor-Like-Elements Based on Screw Theory \u00b7658\u00b7 Since the derivation of the remaining linear velocity terms is identical, these derivations are omitted. In this paper, vectors \u03b5, a and scalar \u03b1 represent the relevant acceleration, linear acceleration and angular acceleration respectively. In the following, j\u03b5i is defined as the screw acceleration of component i relative to component j. Analyzing closed-loop I, shown in Fig. 2, the screw acceleration is obtained as 1 Lie 0 1,A A B B C C\u03b1 \u03b1 \u03b1   \u03be \u03be \u03be S \u03b5 (18) 2 Lie 0 1,E E W W H H\u03b1 \u03b1 \u03b1   \u03be \u03be \u03be S \u03b5 (19) 1 2 Lie Lie ,A A B B C C E E W W H H\u03b1 \u03b1 \u03b1 \u03b1 \u03b1 \u03b1      \u03be \u03be \u03be S \u03be \u03be \u03be S (20) where    1 Lie ,A A B B C C B B C C\u03c9 \u03c9 \u03c9 \u03c9 \u03c9  S \u03be \u03be \u03be \u03be \u03be    2 Lie .E E W W H H W W H H\u03c9 \u03c9 \u03c9 \u03c9 \u03c9  S \u03be \u03be \u03be \u03be \u03be The notation \u201c[ ]\u201d represents the Lie bracket operation in this paper. Since neither closed-loop II nor III is attached to a fixed frame, closed-loop II or III may be represented as a parallel mechanism without a fix reference body relative to closed-loop I",
            " To derive the dynamic equations of motion of this deployable structure, the Jacobian matrix at the center of mass of each link is first developed in this section. Since there are two types of components in this deployable structure, namely a connecting link and link, here we develop the relevant Jacobian matrices based on their characteristics in the motion process. Since not all connecting links rotate during the folding and unfolding process, the attitude angle of the CHINESE JOURNAL OF MECHANICAL ENGINEERING \u00b7659\u00b7 connecting links are given by \u03d5i=(0 0 0)T, i=1, 2, 3, 4, 5. Assuming that the angle between link 7 and the z-axis is \u03b2 as shown in Fig. 2, the length of connecting link and link is li and l respectively, the radius vector between center of mass of connecting link and origin of coordinates is respectively 1 0 0 , 2 cosl \u03b2           r 2 1 0 2 2 sin , 2 cos l l l \u03b2 \u03b2           r 3 1 0 2 2 sin , 0 l l \u03b2           r 1 4 1 (2 2 sin )sin( / 3) (2 2 sin )cos( / 3) , 2 cos l l l l l \u03b2 \u03b2 \u03b2 \u03c0 \u03c0            r 1 5 1 (2 2 sin )sin( / 3) (2 2 sin )cos( / 3) . 0 l l l l \u03b2 \u03b2 \u03c0 \u03c0            r Therefore, the location of each connecting link in the inertial coordinate frame is pi=(\u03d5i ri)T, i=1, 2, 3, 4, 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003759_s11432-016-0604-6-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003759_s11432-016-0604-6-Figure3-1.png",
        "caption": "Figure 3 Structure of 2-DOF manipulators.",
        "texts": [
            " Theoretical analysis indicates that as long as the disturbance is bounded and the derivative of the disturbance is bounded, the disturbance observer based method can be applied to guarantee the tracking performance shown in Theorem 2. In simulation, we employ sine disturbance as example to show the performance. 0 2 4 6 8 10 12 14 16 18 \u22122 \u22121 0 1 2 3 4 Time (s) (a) Jo in t an g le o f li n k 1 ( ra d ) Reference signal Error learning Composite learning 0 2 4 6 8 10 12 14 16 18 \u22120.05 0 0.05 0.10 0.15 Time (s) (b) Jo in t an g le e rr o r o f li n k 1 ( ra d ) Error learning Composite learning Figure 4 (Color online) Tracking response of link1. The structure of the 2-DOF flexible-link manipulator is shown in Figure 3. In order to verify the effectiveness of the control strategy, the simulation is performed in MATLAB software. The desired joint angle is set as yr1 = \u2212 cos(2\u03c0t), yr2 = \u2212 cos(2\u03c0t). The length and the mass for each link are set as 0.5 m and 0.5 kg respectively while the constant flexural rigidity is set as 10 Nm2. For more model information, please refer to [24]. The sampling period of the input-output subsystem Ts = 0.01 s, \u03b1 = [0.9, 0.81]T. For internal dynamics, we select k\u03b4 = [ 0.1 0.1 0 0 0 0 10 10 ] , k\u03b4\u0307 = [ 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001349_s00707-006-0329-4-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001349_s00707-006-0329-4-Figure4-1.png",
        "caption": "Fig. 4. 2D approximation of Goldak heat source",
        "texts": [
            " The spatial heat distribution in a moving frame of reference can be calculated using qf \u00bc 6 ffiffiffi 3 p gQ ff p ffiffiffi p p afbc e h 3 x2 a2 f \u00fey2 b2\u00fez2 c2 i ; \u00f01\u00de qr \u00bc 6 ffiffiffi 3 p gQfr p ffiffiffi p p arbc e h 3 x2 a2 r \u00fey2 b2\u00fez2 c2 i ; \u00f02\u00de where, Q \u00bc VI and ff \u00fe fr \u00bc 2. The origin of the coordinate system is located at the center of the moving arc. A user subroutine is used to calculate the centroidal distance of elements from the moving arc center corresponding to the arc position at any instant. The heat source for two-dimensional axisymmetrical models as shown in Fig. 4 is modeled as volumetric heat density cloud entering into the section and moving across it with welding torch speed. Power density is calculated at the intersection of the plane representing the model geometry and the ellipsoidal model. The power density of the source and thus the temperature increases till the arc center reaches themodeled section, after which it keeps on decreasing and the arc vanishes when the tail of the heat source leaves the section. The calculated power density distribution is projected throughout the thickness of the finite element mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002157_00423117308968441-Figure21-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002157_00423117308968441-Figure21-1.png",
        "caption": "Fig. 21 Equilibrium of forces.",
        "texts": [
            " Since in a steady turn equilibrium between the cornering forces, front and rear, and the centrifigal force must exist, also the maximum possible centrifugal force K will be reduced at the same rate. The effect of rear wheel drive (or bralung at the rear wheels only) on the handling curve is illustrated in Fig. 20. We note that irrespective of the handling character of the car at free rolling, the curve will always end with a positive slope when propulsion forces are applied at the rear. A steady-state motion requires equilibrium also in longitudinal direction. Considering Fig. 21, we obtain the following equation (angles small, aerodynamic forces disregarded): Fig. 19 Idealized characteristics of front and rear tyre pairs. Rear-wheel drive. D ow nl oa de d by [ U ni ve rs ity o f B ri st ol ] at 0 5: 25 2 6 Ja nu ar y 20 15 We also derive: which becomes after elimination of 0: By comparison with the relation we finally obtain: The same expression holds for a driving force, F,1, applied at the front wheels. The important result is, that apparently the driving force required to maintain a steady turn is independent of the steer angle 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.10-1.png",
        "caption": "FIGURE 1.10 The steer angle versus lateral acceleration at constant path curvature (left graph). The difference in slip angle versus lateral acceleration and the required steer angle at a given path curvature (right graph). The understeer gradient h.",
        "texts": [
            " For our model, this quantity is defined as h \u00bc mg l aC1 bC2 C1C2 \u00bc s l mgC C1C2 (1.54) with g denoting the acceleration due to gravity. After having defined the lateral acceleration which in the present linear analysis equals the centripetal acceleration, ay \u00bc Vr \u00bc V2 R (1.55) Equation (1.53) can be written in the more convenient form: d \u00bc l R 1\u00fe h V2 gl \u00bc l R \u00fe h ay g (1.56) The meaning of understeer versus oversteer becomes clear when the steer angle is plotted against the centripetal acceleration while the radius R is kept constant. In Figure 1.10 (left-hand diagram) this is done for three types of vehicles showing understeer, neutral steer, and oversteer. Apparently, for an understeered vehicle, the steer angle needs to be increased when the vehicle is going to run at a higher speed. At neutral steer the steer angle can be kept constant, while at oversteer a reduction in steer angle is needed when the speed of travel is increased and at the same time a constant turning radius is maintained. According to Eqn (1.56), the steer angle changes sign when, for an oversteered car, the speed increases beyond the critical speed that is expressed by Vcrit \u00bc ffiffiffiffiffiffiffi gl h s \u00f0h < 0\u00de (1",
            " Consequently, as one might expect when the centrifugal force is considered as the external force, a vehicle acts oversteered when the neutral steer point lies in front of the center of gravity and understeered when S lies behind the c.g. As we will see later on, the actual nonlinear vehicle may change its steering character when the lateral acceleration increases. It appears then that the difference in slip angle is no longer directly related to the understeer gradient. Considering Eqn (1.56) reveals that on the left-hand graph of Figure 1.10, the difference in slip angle can be measured along the ordinate starting from the value l/R. It is of interest to convert the diagram into the graph shown on the right-hand side of Figure 1.10 with ordinate equal to the difference in slip angle. In that way, the diagram becomes more flexible because the value of the curvature l/R may be selected afterward. The horizontal dotted line is then shifted vertically according to the value of the relative curvature l/R considered. The distance to the handling line represents the magnitude of the steer angle. Figure 1.11 depicts the resulting steady-state cornering motion. The vehicle side slip angle b has been indicated. It is of interest to note that at low speed this angle is negative for right-hand turns",
            " It can easily be observed from this diagram that relation (1.81) holds approximately when the angles are small. The ratio of the side force and vertical load as shown in (1.80) plotted as a function of the slip angle may be termed as the normalized tire or axle characteristic. These characteristics subtracted horizontally from each other produce the \u2018handling curve\u2019. Considering the equalities (1.80), the ordinate may be replaced by ay/g. The resulting diagram with abscissa a1 a2 is the nonlinear version of the right-hand diagram of Figure 1.10 (rotated 90 anticlockwise). The diagram may be completed by attaching the graph that shows, for a series of speeds V, the relationship between lateral acceleration (in g units) ay /g and the relative path curvature l/R according to Eqn (1.55). Figure 1.17 shows the normalized axle characteristics and the completed handling diagram. The handling curve consists of a main branch and two side lobes. The different portions of the curves have been coded to indicate the corresponding parts of the original normalized axle characteristics they originate from. Near the origin, the system may be approximated by a linear model. Consequently, the slope of the handling curve in the origin with respect to the vertical axis is equal to the understeer coefficient h. In contrast to the straight handling line of the linear system (Figure 1.10), the nonlinear system shows a curved line. The slope changes along the curve which means that the degree of understeer changes with increasing lateral acceleration. The diagram of Figure 1.17 shows that the vehicle considered changes from understeer to oversteer. We define understeer if: vd vV R > 0 oversteer if: vd vV R < 0 (1.82) The family of straight lines represents the relationship between acceleration and curvature at different levels of speed. The speed line belonging to V \u00bc 50 km/h has been indicated (wheel base l \u00bc 3 m)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003340_978-3-319-06698-1_23-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003340_978-3-319-06698-1_23-Figure1-1.png",
        "caption": "Fig. 1 Example of an output pulley mounted on a vertical axis revolute joint",
        "texts": [
            "eywords Cable-driven parallel robots \u00b7Kinematics \u00b7Static \u00b7Hefty cable modeling The mobile platform of a cable-driven parallel robot is driven by a number of cables. The cable lengths are generally modified by means of winches. Each cable is wound around a winch drum and is routed to the mobile platform by means of a set of pulleys. This chapter focuses on the output pulley, i.e., the \u201clast\u201d pulley from which the cable extends to the mobile platform. As shown in Fig. 1, this pulley should be mounted on a revolute joint whose (vertical) axis is coincident with the cable segment exiting the pulley toward the winch. The revolute joint allows the pulley to align with the cable segment which exits the pulley toward the mobile platform. Such output pulley M. Gouttefarde (B) \u00b7 D. Q. Nguyen LIRMM, CNRS - University Montpellier 2, Montpellier, France e-mail: marc.gouttefarde@lirmm.fr D. Q. Nguyen e-mail: dinhquan.nguyen@lirmm.fr C. Baradat Tecnalia France, Montpellier, France e-mail: cedric"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003698_j.triboint.2016.01.044-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003698_j.triboint.2016.01.044-Figure1-1.png",
        "caption": "Fig. 1. Diagram of the optical interference technique used in the EHD2 equipment.",
        "texts": [
            " In order to improve the resolution and to avoid the melting of the polymer thickener given the high energy of the beam, all samples were covered with a very thin carbon film. With this process, an electron beam of higher energy can be used, highly improving the image quality. The EHD2 is an equipment produced by PCS Instruments which allows the measurement of the lubricant film thickness in ball-ondisc or roller-on-disc configuration, over different ranges of temperature, speed, load and slide-to-roll ratio (SRR). The device uses the space layer interferometry method which allows the measurement of thin-films using the setup shown in Fig. 1. Light is shone into the contact between the ball and the disc. Part of this light is reflected from the underside of the glass disc and some passes through any lubricant film and is then reflected back from the steel ball. Since the two beams of light have travelled different distances they interfere, resulting in an interference image from which the central film thickness can be computed. Please cite this article as: Gon\u00e7alves D, et al. Film thickness and fric International (2016), http://dx.doi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000786_1.1518501-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000786_1.1518501-Figure3-1.png",
        "caption": "Fig. 3 Two systems of cylindroidal coordinates that share a common cylindroid \u201enote tangency between pitch surfaces\u2026",
        "texts": [
            "org/about-asme/terms-of-use Downloaded From: http://mechani Dooner and Seireg introduced a system of curvilinear coordinates to parameterize the kinematic geometry of motion transmission between skew axes. These curvilinear coordinates are based upon the cylindroid determined by the two axes of rotation $ i and $o and are referred to as cylindroidal coordinates. Cylindroidal coordinates consist of families of pitch, transverse, and axial surfaces as formulated using a cylindroid ~a special ruled surface!. Cylindroidal coordinates can facilitate the specification of gear teeth or surfaces in direct contact necessary to produce any desired transmission function. Depicted in Fig. 3 are two systems of anical Design caldesign.asmedigitalcollection.asme.org/ on 01/29/20 cylindroidal coordinates that share a common cylindroid. Hyperboloidal or spatial gearing differs from cylindrical or planar gearing in that the axodes and the pitch surfaces are, in general, not the same. This difference results from the non-zero pitch of the instantaneous screw $is . Further, the two hyperboloidal pitch surfaces are always tangent to one another. At the instant two hyperboloidal pitch surfaces are tangent to one another, there are two generators common to the two ruled surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002026_tmag.2009.2012785-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002026_tmag.2009.2012785-Figure1-1.png",
        "caption": "Fig. 1. Mesh modification process by solving Laplace equation (a) initial mesh, (b) distribution of potential , (c) skewed mesh.",
        "texts": [
            " Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2009.2012785 The hysteresis loss taking into account the major and minor loops of the hysteresis loop is estimated using waveform of the calculated flux density [3]. C. Mesh Modification Method for Motors With Skewed Rotor [4],[5] The procedure of the novel mesh modification method for motors with the skewed rotor is briefly described as follows (see Fig. 1). i) The initial mesh without skew is prepared by building up the 2-D mesh as shown in Fig. 1(a). ii) The potential ( is the skew angle of the rotor) is given to nodes in the top of the rotor, and the potential is given to nodes in the bottom of the rotor. iii) Under the above condition, the distribution of potential of the rotor is calculated by solving the following Laplace equation [see Fig. 1(b)]: (2) In the same way, the potential in the air gap region is calculated under conditions that the potential obtained by step (iii) is given to nodes in the rotor region and the potential zero is given to nodes in the stator region. iv) The coordinates of nodes in the rotor region [see Fig. 1(c)] and the air gap region is skewed according to the each potential . 0018-9464/$25.00 \u00a9 2009 IEEE Here, the distribution of flux density vectors and the losses of the SCIM with the 4/3 slot pitch skewed rotor and that with rotor without skew are calculated. The calculated losses are compared with measured ones to clarify the validity of the 3-D analysis. Further more, the bar-current and the torque are calculated. Fig. 4 shows the distributions of flux density vectors of SCIM with the 4/3 slot pitch skewed rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001938_0020-7403(76)90006-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001938_0020-7403(76)90006-0-Figure2-1.png",
        "caption": "FIG. 2. Elevation and plan views of a partially submerged sphere, defining the angles ~b, 4'o, tbw and 4'.",
        "texts": [
            " This is clearly only an approximation to the complex pressure distribution acting on a partially submerged projectile, but it will be argued below that equation (2) gives a better representation of the true forces than Birkhoff's equation. Figure 1 shows the wetted area of a sphere at various depths of immersion during oblique impact on water; these diagrams were taken from those of Richardson. 4 From Fig. 1 it appears that the water pressure must act over a considerably greater area than that assumed by Birkhoff et al.; 3 in this work it is proposed that ~b~, the angular extent of the wetted area, over which the pressure acts, is equal to 2~b0 for 0~<~b0~<Tr/2 and ~bw = ~r for 4)o > 7r/2, as showh in Fig. 2. 3. SPHERICAL PROJECTILE WITH NO SPIN The ricochet of a projectile is caused by the vertical component of the pressure distribution resulting from its *Morpurgo 2 shows a photograph of an oblate spherical bomb. However, this was clearly an experimental version, since his text and other references ~'6 indicate that the bombs dropped in the raid on the dams (project Downwood) were in fact cylindrical. A photograph showing a definitely cylindrical bomb in its mounting beneath a Lancaster bomber has been published. 6 Another smaller bomb (codenamed Highball) developed for naval use in the Mosquito aircraft and employing exactly the same principles of ricochet assisted by backspin was an oblate sphere. 7 motion, partially submerged, through the water. We shall here calculate the lift force on a sphere of radius a whose centre is at a height y above the undisturbed water surface (Fig. 2). From the assumptions of the previous section, the pressure will act over the whole wetted area shown in Fig. 2. The water velocity normal to the element of the sphere's surface dA will be v sin ~ cos 0. The pressure p acting on dA is therefore ~r s in ~b c o s P = 4 ~7 g ~ i ~ s \u00a2, p~\" (3) The ricochet of spheres and cylinders from the surface of water 245 This expression may be rendered more tractable by making an approximation. The pressure will be integrated over the wetted surface; 4~ will vary between 0 and a maximum of w, ~ between - w / 2 and w/2. The denominator in equation (3) will therefore vary between 4.0 and 7.1; no great inaccuracy will be introduced by replacing it by the intermediate value of 5.0. The lift force on the area dA is therefore 7g 2 \u2022 dL = \"ff pv sm 4' cos tk cos 4~ dA. (4) Since dA -- a 2 sin ~b d$ d~b, the total lift on the sphere shown in Fig. 2 is 2 d'w ~ 1 2 L=-SPv2a fo f~12 s i n 2 ~ b c \u00b0 s ~ b c \u00b0 s S d S d * 2rr ~ . ~ = - ~ p v a sm $~. (5) Ignoring gravitational forces on the sphere, its equation of motion vertically is d 2 y _ m ~ - L (6) where m is the mass of the sphere. Assuming that the impact and rebound angles are small the velocity, v=(dx/dt) , of the sphere may be assumed constant throughout the impact. So d2y dx d (dy d~) zd2Y at ---'5 - d-~\" d--x dxx\" = v dx------ 5. (7) Substituting in equation (6) for L and the mass of the sphere (density p ' ) and using equation (7), d2y_ 1 P \u2022 3 ~-~ - ~ ~ sm 4,-",
            ", agrees well with the empirical relationship (equation (1)) and with the relationship deduced by Johnson and Reid 1 from Birkhoff's pressure law (0~ = 17'5/V'0r) deg.). A small error in the numerical value of the constant in equation (13) would undoubtedly be revealed by an accurate numerical treatment, in which the denominator in equation (3) is not assumed constant. The forces acting on a cylindrical projectile, possessing back-spin about its axis with angular velocity oJ and moving in a plane perpendicular to its axis, will now be considered. The velocity of the water relative to an element of surface dA, v ' , may be deduced from Fig. 3 in Fig. 2. which shows the direction of spin. The angles ~b, ~bo and ~bw are as shown in Fig. 2. The lift force acting on the element is where and 7r s i n a dL 4 + ~ sina PV'~COs~b dA (14) v'2=(v+acocos~b)2+(aoJsin~b)2 (15) s i n a = sin ~b cos 3' - c o s ~b sin 3'. (16) We assume that ato .~ v and neglect terms in a2toz/v 2. The angle 3' is therefore small, and v '2 ~ v 2 + 2atov cos ~b (17) a t o . sin y = 3' = '~ ' - sm ~b (18) sin a = sin d' - - ~ sin cb cos d'. (19) For a cylinder of length 1, dA = al d~b, and making the approximation that the denominator in equation (14) is equal to 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001065_20.179706-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001065_20.179706-Figure1-1.png",
        "caption": "Fig. 1. Basic structure of a LSM.",
        "texts": [
            " This paper deals with the magnetic circuit analysis using finite element method (FEM), and investigates the static thrust and normal force characteristics from the aspects of analysis as well as experiment. The effect of the size of permanent magnets on the static thrust is investigated using FEM, and a prototype machine is fabricated on the basis of its results. The measured values of static thrust and normal force of the prototype machine are compared with the calculated values obtained by using FEM. 11. STRUCTURE OF A LSM Fig. 1 shows the basic structure of a LSM. A three-phase winding is rolled, in distribution, on the iron core of the armature. The armature is laminated with electromagnetic steel sheets sewed as the mover of the LSM, forming a sixpole structure. A permanent magnet is affixed to the yoke of the stator such that the face opposite to the mover becomes the N and S poles alternately. Table I lists the parameters of the LSM. The authors are investigating the basic wave and high harmonic wave components of static thrust in the event that the magnet width W has been varied from 28 to 40 mm ( W/T = 0",
            " 3 shows harmonic wave components of the generated thrust versus the ratio of magnet width between the pole pitch ( W / t). These values are calculated by using (4) with the DC current f, = 5 A. As the value of W i t decreases, both the components of the fundamental wave as well as those of higher harmonics decrease, and at W / t = 0.73, the third order harmonics become zero, and at W i z = 0.84, the 5th order harmonics become zero. Based on these calculation results, the prototype machine was built with a magnet width of W / z = 0.85 which decreases the 5th order harmonics. Fig. 1 shows a speed electromotive force which has been measured to confirm the accuracy of the magnetic f l u x analysis. The calculated value of phase voltage was obtained using (2). Further, the calculated value of line voltage is obtained as the total vol tage of the two phases. The calculated values show conformity with the measured values, 150 7 ?z i 100 3029 1 =-8.8 [AI and the calculation error proves to be within 10 %. Fig. 5 shows the static thrust characteristics in the case that the three-phase sinusoidal current has flown to each of the phases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-11-1.png",
        "caption": "FIGURE 13-11 Cross section of a dry clutch. (Courtesy International Harvester.)",
        "texts": [
            " Mechanical front-wheel-drive clutch Brakes and clutches can be designed to operate wet (oil cooled) or dry (air cooled) and can be of single- or multiple-disk, caliper, cone, band, or drum configuration. The particular choice depends on the torque capacity and durability required, on the space available, and on whether the element will be manually or power operated. The disk type of clutch provides generally high capacity and durability and is often used in tractor drive trains. For tractors below about 80 kW, a dry, single-disk traction and pto clutch of the type shown in figure 13-11 is otten used because It IS low cost, can be manually operated, has good torque FRICTION BRAKES AND CLUTCHES 373 capacity, and facilitates shifting as a result of having relatively low inertia. Higher power tractors require oil-cooled traction clutches for good durability (fig. 13-12). These are usually operated with hydraulic power. Wet disk clutches and brakes have also been used for all of the other drive train functions listed previously. Multiple disks often are used in wet clutches and brakes to obtain the required torque capacity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001623_iros.2004.1389998-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001623_iros.2004.1389998-Figure4-1.png",
        "caption": "Fig. 4. Thc triangle ma& up of ,he joining lines and the two radii",
        "texts": [
            " In particular, if we place the mice as in Figure 3, we have that the x values measured by the two mice should he always equal ZL = 3%. In this way, we can compute how much the robot pose has changed in terms of Ax, Ay, and As. In order to compute the orientation variation we apply Pig. 3. otieniuion of thc mhot lhc angle arc of each mouse i s equal to ihc change in the the theorem of Camot to the triangle made by the joining line between the two mice and the two radii between the mice and the center of their arcs (see Figure 4): DZ = r: + r: - 2 Cos(y)rvri, (5 ) where rI and r( are the radii related to the arc of circumferencec described respectively by the mouse on the right and the mouse on the left, while y is the angle between rr and rl. It is easy to show that y can be computed by the absolute value of the difference between a1 and ar (which can be obtained by the mouse measures using Equation 3): The radius r of an arc of circumference can be computed by the ratio between the arc length 1 and the arc angle 8. In our case, the two mice are associated to arcs under the same angle, which corresponds to the change in the orientation made by the robot, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure14-1.png",
        "caption": "Fig. 14. Temperature distribution of the stator-end copper winding when the relative magnetic permeability of the press plate is 50.",
        "texts": [
            " 13 that the temperature of the press plate when the relative magnetic permeability of press plate is 1 is higher than when relative magnetic permeability of press plate is 50 at the same location. When the relative magnetic permeability of press plate is 1, the temperature of the press plate is relatively high and the highest temperature appears in the outer diameter of the press plate. When the relative magnetic permeability of press plate is either 1 or 50, the temperature of the inner diameter of the press plate is relatively low. The temperature of the press plate gradually increases along the radial direction. Fig. 14 shows the temperature distribution of the stator-end copper winding when the relative magnetic permeability of press plate is 50. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 8 It can be seen from Fig. 14 that the temperature of the stator-end copper winding which contacts the stator end core is relatively high (about 52.6 \u00b0C). However, the temperature of the stator-end copper winding nose is relatively low (about 44.3 \u00b0C). When the relative magnetic permeability of the press plate is 50, the highest temperature and average temperature of stator-end copper winding are 54 \u00b0C and 52.1 \u00b0C, respectively. Fig. 15 shows the temperature distribution of the finger plate when the relative magnetic permeability of the press plate is 50"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000943_j.finel.2004.02.002-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000943_j.finel.2004.02.002-Figure3-1.png",
        "caption": "Fig. 3. A transverse section of the generating rack and gear that are shown in Fig. 1 in a meshing position during the gear generation process.",
        "texts": [
            " Since the geometry of the gear is most easily built up from a number of transverse sections, the following relation is used: rtk = zt = w; (10) where k is the unit vector of the zt-axis and w is a parameter that de!nes a transverse section of the rack. Combining (4) and (8)\u2013(10) yields rtIj(uIj; w) =   uIj sec cos n + w tan \u2212juIj cos n tan tj sec + jsr sec =2 + w sec tan w 1   : (11) In a similar way, combining (5) and (8)\u2013(10) yields rtFj(uFj; w) =   \u2212( sin uFj + e) sec + w tan \u2212 sin tan sin uFj + j(cos uFj \u2212 sec n) cos + j ( e tan tj cos + sr 2 cos ) + w tan cos w 1   (12) and combining (7) and (8)\u2013(10) yields rtRj(uRj; w) =   \u2212ha sec + w tan juRj sec \u2212 ha tan tan + w tan sec w 1   : (13) Fig. 3 shows a transverse section of the generating rack and gear that are shown in Fig. 1 in a meshing position during the gear generation process. The pitch point P is located on the instantaneous axis of rotation, which is parallel with the gear axis. A global coordinate system Sq is located and oriented such that the xqyq-plane coincides with the xtyt-plane, the zq-axis coincides with the gear axis and the xq-axis is parallel with the xt-axis. The gear coordinate system Sg has rotated an angle \u2019 from the global coordinate system Sq",
            " The rack coordinate system S t has moved a distance r\u2019 from Sq in a direction opposite to the yq-axis and the distance between Ot and Oq in the xq-axis direction is r + i, where i is the initial addendum modi!cation. According to the fundamental theorem of conjugate gear-tooth surfaces, the common normals to the transverse rack and gear-tooth pro!les at all points of contact must pass through the pitch point (for uniform transmission of motion). Therefore, by multiplying the unit normal vector to the transverse rack pro!le n\u0302t t with a scalar with an appropriate length, we obtain from Fig. 3 n\u0302t t = OtPt \u2212 rtt = [ \u2212 i r\u2019 ]T \u2212 [ xt yt ]T; (14) where OtPt and rtt are, respectively, the projections of the vectors OtP and rt on a transverse plane. Multiplication of this expression with a tangent vector ttt to the rack pro!le gives us 0 = ttt \u00b7 [ \u2212xt \u2212 i r\u2019 \u2212 yt ]T = \u2212ttx(x t + i) + tty(r\u2019 \u2212 yt): (15) By di/erentiating (11\u201313) with respect to the surface parameter u, we get [ ttIjx ttIjy ]T = [ 9xt Ij=9uIj 9yt Ij=9uIj ]T = [ cos n sec \u2212j cos n tan tj sec ]T; [ ttFjx ttFjy ]T = [ 9xt Fj=9uFj 9yt Fj=9uFj ]T = [ \u2212 cos uFj sec j cos uFj tan utFj sec ]T; [ ttRjx ttRjy ]T = [ 9xt Rj=9uRj 9yt Rj=9uRj ]T = [ 0 j sec ]T; (16) where tan utFj = tan uFj cos sec \u2212 j sin tan (17) The angle utFj is the representation of the angle uFj in a transverse plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001567_tim.2007.895674-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001567_tim.2007.895674-Figure6-1.png",
        "caption": "Fig. 6. Single-link flexible robotic manipulator model.",
        "texts": [
            " Due to this, if the RBFNN controller gets stuck in the local minima, the adaptation process in the MRAC helps to pull the error function out of these steadystate minimum values. Thus, the error asymptotically reaches zero. As indicated before, since the node growth is controlled and as the input vector is sequentially fed at a constant rate, the dimension space that is required for the RBFNN is always within the limits. The proposed approach is applied to a manipulator for tracking the angular position based on the desired trajectory. Fig. 6 shows a single-link flexible manipulator, which was modeled using actual physical parameters. The dynamic model, as discussed in the Appendix, is utilized to track the command signal that is applied for 8 s, and the tip load is varied arbitrarily at different time instants. The variation in the tip load contributes to the mode swings. The robotic arm has position zero, with the x-axis and y-axis denoted as x0 and y0, respectively. At each time instant, depending on the angular movement and based on the required trajectory, there will be a deflection that causes the arm to settle to new axes that are denoted as x1 and y1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002122_s0263574708004256-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002122_s0263574708004256-Figure2-1.png",
        "caption": "Fig. 2. 4-ADOF kinematically redundant planar parallel manipulator and its locus of solutions (branch 1) for the inverse displacement problem shown as arc \u0302RD1S.",
        "texts": [
            " Having the actuators at the base of the manipulator has the advantage of lessening the dynamic effects. Kinematic redundancy in parallel manipulators results in increasing the number of solutions for the IDP. More particularly, for a given pose of the end-effector inside the workspace, there is an infinite number of solutions. That is, the IDP in kinematically redundant parallel manipulators results in a locus of solutions for each limb as opposed to a finite number of solutions in non-redundant parallel manipulators. As shown in Fig. 2, each of the two non-redundant branches has only two possible inverse displacement solutions. Figure 2 shows a planar parallel manipulator which has 1-DOKR in its first limb. Considering limb A1D1, point D1 can be anywhere on the hatched circle centred at point A1 with radius \u03c1max given by the maximum displacement of the prismatic actuator. For a given position and orientation of the end-effector, link B1D1 can fully rotate \u00b6 Note the difference in the order of the first two active joints. around point B1. Therefore, the locus of IDP solutions for branch 1 is the arc \u0302RD1S. Based on quantities shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002802_0022-2569(67)90042-0-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002802_0022-2569(67)90042-0-Figure6-1.png",
        "caption": "Figure 6. The C-S-S-S linkage showing the instantaneous h-value h13 that applies to the C-pair for the configuration shown.",
        "texts": [
            " a mobility with all freedoms in all pairs active) will still hold with as many as three S-pairs with h=0, i.e. with as many as three R-pairs, even if the remaining two S-pairs have the same h-value. If there are two R-pairs, the remaining three may have the same finite (non-zero) h-value, and M = 1 still. 3.3. If one of the S-pairs (say S~2) has h = oo (i,e. if it becomes a P-pair parallel to the original S-pair) it may be shifted sideways (see 1.4. above) to coincide with one of the adjacent S-pairs (say $23) and thus become a C-pair (see 2.6. (a) above). This is illustrated in Fig. 6. For a particular configuration there is a unique, but not time- invariant, h-value now instantaneously associated with this resultant pair C13 that must be compatible (by the ladder construction shown) with the prescribed h-values for. $34, $45 and $5~. If, however, h34=h45=hs~, the instantaneous h-value for the C13-pair remains constant and equal to the others throughout the gross motion, i.e. one freedom of the C-pair is inactive. For h34=h45=hst---O the linkage behaves as a planar mechanism and the C~3-pair may be replaced by an R-pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.16-1.png",
        "caption": "Figure A.16 included angle O A B . Geometrical interpretation of the vector product of two vectors A and B with",
        "texts": [],
        "surrounding_texts": [
            "PRODUCT OF VECTORS 429\nSolution\nFrom Figure A. 15, C = A + B .\n:. c 2 = C . C = ( A + B ) . ( A + B )\n= A . A + B . B + 2 A . B\n1 /AI2 + IBl2 + 21AllBI C O S Q A B\n= u2 + b2 + 2ubcos(-ir - a )\n= a2 + b2 - 2abcos a.\n0 Dot Product as Projection of a Vector, Geometric Representation\nThe dot product is frequently used to determine the component of a vector in a given direction. For example,\nOP = B . i = scalar component of B in the direction ofti\n(B .ii) = vector component o f B in the direction of&\nA.5.2 The Cross Product of Two Vectors\nThe cross (or vector) product of two given vectors A and B is denoted by A x B (read as \u201c A cross B\u201d) and is a vector quantity defined as\nA x B = .izlAllB[ sinOAB, (A.29)\nwhere ii denotes a unit vector perpendicular to both and B, and is pointed to the right-hand screw advance direction where we turn from A (the first-named vector) to B through the smaller included angle HAB between the two vectors, as in Figure A. 16. By definition,\n_ _ 12 x Bl = area of the parallelogram having adjacent sides A, B.\n= 2 x area of the triangle OPQ.\nNote that from the definition it follows that\nThis means that the cross product does not obey commutative law, or in other words, the order in which the product is carried out is significant.\nThe following properties hold for the vector product:",
            "430 VECTORS AND VECTOR ANALYSIS\n1. B x A # A x B, not commutative\n2. A x (B x C ) # (A x B) x C, not associative\n3. A x (B x C) = A x B i- A x C, is distributive.\nA x B = 0 if OAB = 0, i.e., when A 1 1 B\nA x B = AAB if ~ \u2018 A B = - 2\nUsing the above, it can be shown that for rectangular systems of coordinates\n2 x 2 = i j x i j = 2 x 2 G 0. (A.30)\n2 x j j 1 2 : 0 x 2 = 2 : 2 x 2 = j j . (A.3 1)\njj,.) as a right-handed triad of orthogonal unit vectors serving as the base vectors of the coordinate system. Using the distributive law plus (A.30) and (A.3 l), it can be shown that\n7r i.e., when A I B.\nEquation (A.3 1) defines\nA x B = (A,2 + A,ij + Az2) x (B,2 + B,ij + Bz2)\n= ( A y B z - AzB,)2 i- (AZB, - A,Bz)ij + ( A X B Y ~ A,B,)2\nY = A, A, A, . (A.32) 1 i. By :z 1\nIn cylindrical and spherical Coordinate systems it can be shown that\na 4 0 A x B = I .\u201d, 134 : = I iT A6 A\u201d+ 1. (A.33)\nB p 134 B z BT B,9 B,",
            "PRODUCT OF VECTORS 431\n2. Force on a charge Q moving with velocity v in a B field, as shown in\n(A. 34 b) Figure A. 17b, is FQ = Q(v x B).\nA 5 3 Product of Three Vectors\n1. A x B x C must necessarily be defined as (A x B) x C or A x (B x C ) ;\n2. ( A . B) C is nothing more than the product (scalar) of (A . B) times C , that is, a vector in the direction of C with appropriate magnitude.\nno new definition needed, and one can proceed as before."
        ]
    },
    {
        "image_filename": "designv10_10_0001907_physreve.78.061701-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001907_physreve.78.061701-Figure2-1.png",
        "caption": "FIG. 2. a trans and cis bent forms of a dye rod with a central azo unit. Parallel ordering of the remaining rods is hindered by the bent species. b A polydomain elastomer illuminated by light polarized along the E direction c a test rod, direction u\u0302, in a region with director currently along n\u0302",
        "texts": [
            " The contractions can be huge 10,11 , up to a factor of 4 or more: heating reduces the orientational order and hence the shape anisotropy of the distribution of the polymer chains making up the elastomeric network. Macroscopic strain then follows the network chains\u2019 shape change. In Sec. II C we sketch the derivation of such shape change. Schematically, Fig. 1 a shows this shape change in response to order change. Light can also reduce the order parameter in nematics when dye molecules chromophores, for example, containing azo-benzene are present. Chromophores are often rodlike in their ground trans state. Photon excitation yields a bent cis state, see Fig. 2 a , and nematic order is reduced, analogously to the thermal case, as the dye is converted. In a nematic network, a mechanical strain then follows 1 . In the dark, the order parameter recovers its original value as bent molecules decay back to their straight trans conformation and hence the strain is reversed. Another route to recovery is the stimulation, by light of another color, of the cis to trans transition which offers even greater speed and control. We shall also consider another important mechanism for photomechanical distortion, that of director rotation rather than order change",
            " As well as dealing here with several polarization and polydomain types, we also extend our modeling to strongly crosslinked elastomers which offer certain qualitative distinctions from our earlier analysis. The nonmonotonicity of the response with intensity could even lead to a reversal of the sign of cantilever curvature. When the incident light intensity is high enough that the photostrain at the upper surface vanishes, but where there is contraction lower down, then the beam will curve away from rather than towards the light. The situation we first model is shown in Fig. 2. Plane polarized light propagating in the k direction is incident normally on a thin polydomain liquid crystal elastomer LCE . A region with current director n\u0302 is shown; we neither discuss the origin of domains, nor require their length scale typically microns , in what follows. We model an elastomer with initially random directions for domains. At each point the extent of photoreactions depend on the angle between the local director and the electric field. The strain, however, we will take to be global, as we discuss below",
            " Finally we consider the photomechanical response of cholesteric elastomers to unpolarized light propagating along the helix axis. A. Intensity and angular dependence of isomer concentrations The rodlike character of molecules is responsible for the orientational order of the nematic state. To examine the stability of the nematic state, we therefore first determine how their number changes as a result of irradiation. Consider a total number density nn of nematogenic rods, of which a number density np are photoresponsive nematogens giving a fraction A=np /nn . In the domain shown in Fig. 2 b a photorod is described by a unit vector u\u0302 along its long axis. In the simple case of chromophores also with u\u0302 as the direction of their active bonds, the probability of photon absorption by a rod depends on the intensity along its axis E \u00b7 u\u0302 2. The rate per unit volume of photoinduced trans-cis reactions is hence E \u00b7 u\u0302 2 nt t , where is a constant and nt t is the current number density of trans nematogens at time t. The local thermodynamic average \u00af is taken over photorods in the 061701-2 region with n\u0302 ",
            " It is the eventual bleaching of all regions that causes the polydomain system to lose overall mechanical response when light is intense: if all domains have the same , their mechanical fate must be the same. The lack of a preferred direction implies zero strain for a polydomain system, just as one obtains no strain on heating such a system to another state of order. A mean-field theory for nematics was first proposed by Maier and Saupe 24 . The simplest Hamiltonian to describe uniaxial nematic ordering arises after azimuthal averaging about n\u0302 the free angle in Fig. 2 b : H = \u2212 1 2 i j JijP2 cos i P2 cos j , 6 where i is the angle of the long axis of the ith nematogen with respect to the director n\u0302 , Jij represents the interaction potential between the ith and jth rod and the sum is taken over all pairs of nematogens. Maier and Saupe MS assumed that the interacting potential arose from anisotropic van der Waals forces, but the precise form of Jij is not important here. We follow the MS approach, but with vital modifications to deal with populations of rods changing on illumination by amounts dependent upon the mean order",
            " There is still a narrow band of domains close to /2 and the order parameters of domains within this band remain somewhat larger. The second kink in Fig. 6 occurs when back rotation is complete, and beyond this point one has 0 for all domains. This is the case by I\u0303=12. The order parameter for domains is now small for all 0, the system is essentially isotropic, there is no preferred direction, and the elastomer returns to =1. B. Incident unpolarized light We now consider unpolarized light incident normally upon a sample, that is we consider light traveling along the beam direction k shown in Fig. 2, the electric field vectors being uniformly distributed in the plane perpendicular to k . The average E \u00b7u 2 =Tr E E E u u u must now be recalculated, we have E E E= E2 2 z z +y y = E2 2 = \u2212x x , while u u u =Sn\u0302n\u0302 + 1\u2212S 3 = , and thus E \u00b7 u 2 = E2 3 1 \u2212 SP2 cos , 20 where cos =n\u0302 \u00b7x , i.e., the angle is now that between the director n\u0302 and the x direction. The fraction of cis nematogens is therefore S, , I\u0303 = A I\u0303 1 \u2212 SP2 cos 3 + I\u0303 1 \u2212 SP2 cos . 21 We once again take the Taylor limit, that is we assume each domain suffers the same uniaxial deformation. The unique direction is now the beam direction, thus we adopt the second of the deformation gradient tensors in Eq. 18 . The step length tensors l=0 and l=\u22121 are given by Eqs. 13 \u2013 17 . Since the deformation gradient is isotropic within the yz plane domains which make the same polar angle with respect to the direction k but have different azimuthal angles within the yz plane are mechanically equivalent. Our model predicts uniaxial extensions along the beam direction k , Fig. 2, and corresponding contractions in the plane of the film. Now the regions with director in the plane of the sample rotate away from the yz plane causing elongations along the beam direction in complete analogy with the effects described above. Such distortions turn out to be large in our model, i.e., comparable to those suffered by cooling monodomains. Figure 9 shows the equilibrium deformation gradient as a function of I\u0303 for the strongly cross-linked case \u0303=1 /10. Figure 10 shows the result for the weakly cross-linked case \u0303=1 /50"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003715_1464419314522372-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003715_1464419314522372-Figure5-1.png",
        "caption": "Figure 5. Surface fault model.",
        "texts": [
            " mLo \u20acxLo \u00fe co \u00fe cp _xLo \u00fe ko \u00fe kp xLo cp _xLp kpxLp Pn i\u00bc1 KL outer outer L 1:5 cos i \u00bc 0 mLo \u20acyLo \u00fe co \u00fe cp _yLo \u00fe ko \u00fe kp yLo cp _yLp kpyLp Pn i\u00bc1 KL outer outer L 1:5 sin i \u00bc 0 mp \u20acxLp \u00fe cp _xLp \u00fe kp xLp xLo \u00bc 0 mp \u20acyLp \u00fe cp _yLp \u00fe kp yLp yLo \u00bc mpg 8>>>>>>< >>>>>>: \u00f018\u00de mbR1 \u20acxbR1 KR inner inner 1 1:5 cos i \u00fe KR outer outer 1 1:5 cos i \u00bc 0 mbR1 \u20acybR1 KR inner inner 1 1:5 sin i \u00fe KR outer outer 1 1:5 sin i \u00bc mbR1g mbR2 \u20acxbR2 KR inner inner 2 1:5 cos i \u00fe KR outer outer 2 1:5 cos i \u00bc 0 mbR2 \u20acybR2 KR inner inner 2 1:5 sin i \u00fe KR outer outer 2 1:5 sin i \u00bc mbR2g mbRn \u20acxbRn KR inner inner n 1:5 cos i \u00fe KR outer outer n 1:5 cos i \u00bc 0 mbRn \u20acybRn KR inner inner n 1:5 sin i \u00fe KR outer outer n 1:5 sin i \u00bc mbRng 8>>>>>>>>>>>>>>>>>>< >>>>>>>>>>>>>>>>>>: \u00f023\u00de mRo \u20acxRo \u00fe co \u00fe cp _xRo \u00fe ko \u00fe kp xRo cp _xRp kpxRp Pn i\u00bc1 KR outer outer R 1:5 cos i \u00bc 0 mRo \u20acyRo \u00fe co \u00fe cp _yRo \u00fe ko \u00fe kp yRo cp _yRp kpyRp Pn i\u00bc1 KR outer outer R 1:5 sin i \u00bc 0 mp \u20acxRp \u00fe cp _xRp \u00fe kp xRp xRo \u00bc 0 mp \u20acyRp \u00fe cp _yRp \u00fe kp yRp yRo \u00bc mpg 8>>>>>>>>>< >>>>>>>>>: \u00f024\u00de at WEST VIRGINA UNIV on July 9, 2015pik.sagepub.comDownloaded from Defect model on races has been shown in Figure 5 for better illustration. For each fault, the width l in the surface coordinate system is also defined in the figure. When the balls run to the defect area, the clearance will increase by h. It can be de described as follows \u00bc \u00fe h \u00f025\u00de In the defective area, the clearance increases suddenly, and the variance of the contact force grows consequently. Consequently, mathematical simulation of local defects in outer race, inner race and ball can be, respectively, established. The defect on the running surface is shown in Figure 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001450_detc2006-99628-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001450_detc2006-99628-Figure1-1.png",
        "caption": "Fig. 1 Some legs for parallel mechanisms with both spherical and translational modes.",
        "texts": [
            "\u201d Since the R\u030cR\u030c(RRR)E , (RRR)ER\u030cR\u030c, R\u030cR\u030c(RRR)S , R\u030c(RRR)SR\u030c, (RRR)SR\u030cR\u030c legs for spherical parallel mechanisms cannot reach a configuration in which they satisfy the above condition, there are no legs for parallel mechanisms with both spherical and translational modes that are associated with the above five types of legs. An R\u030c(RRR)ER\u030c leg for spherical parallel mechanisms will be a leg for parallel mechanisms with both spherical and translational modes if it can reach a transitional configuration in which the axes of the two R\u030c joints are coaxial. In this configuration, the leg is denoted by R\u030b(RRR)ER\u030b [see Fig. 1(a)]. Similarly, from the legs for spherical parallel mechanisms composed of three R\u030c joints and two inactive R joints, we can obtain the following types of legs for parallel mechanisms with both spherical and translational modes in their transitional configuration: R\u030bR\u030cR\u0300R\u0300R\u030b, R\u030bR\u0300R\u030cR\u0300R\u030b, R\u030bR\u0300R\u0300R\u030cR\u030b, R\u030bR\u0301R\u030cR\u0300R\u030b, R\u030bR\u0301R\u0300R\u030cR\u030b [see Fig. 1(b)], R\u0301R\u030bR\u030cR\u0300R\u030b, R\u0301R\u030bR\u0300R\u030cR\u030b, R\u030bR\u030cR\u0300R\u0301R\u030b, R\u030bR\u0300R\u030cR\u0301R\u030b, R\u030bR\u030cR\u0300R\u030bR\u0301, and R\u030bR\u0300R\u030cR\u030bR\u0301. It is noted that the R\u030b(RRR)ER\u030b leg is different from the R\u030bR\u030cR\u0300R\u0300R\u030b, R\u030bR\u0300R\u030cR\u0300R\u030b and R\u030bR\u0300R\u0300R\u030cR\u030b legs. If a parallel mechanism with both spherical and translational modes involving an R\u030bR\u030cR\u0300R\u0300R\u030b, R\u030bR\u0300R\u030cR\u0300R\u030b, or R\u030bR\u0300R\u0300R\u030cR\u030b leg works in the spherical mode, the R\u0300 joints are inactive. If a parallel mechanism with both spherical and translational modes involving an R\u030b(RRR)ER\u030b leg works in the spherical mode, no joints in the leg are inactive",
            " Forty-three types of legs with a 1-wrench-system have been obtained for parallel mechanisms with both spherical and translational modes (Table 4). These legs are composed of R and P joints. Their variations, which involve U (universal), C (cylindrical), S (spherical) joints and parallelograms, can be obtained using the techniques summarized in [29]. It is also noted that a leg for parallel mechanisms with both spherical and translational modes is always singular at its transitional configuration since the axes of its two R\u030b joints are coaxial (Fig. 1). The wrench system of a leg, which is a 1-wrench-system in a regular configuration, becomes a 2-wrench-system in a transitional configuration. In the previous section, we have obtained the types of legs for parallel mechanisms with both spherical and translational modes. In this section, we will discuss how to obtain parallel mechanisms with both spherical and translational modes by assembling these legs. In assembling a 3-DOF parallel mechanism with both spherical and translational modes, it should satisfy both the assembly conditions for the spherical parallel mechanisms that guarantee the moving platform can undergo at least the spherical motion [8] and the assembly conditions for the translational parallel mechanisms [19] that guarantee the moving platform can undergo at least the translational motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002839_s10514-013-9343-2-Figure24-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002839_s10514-013-9343-2-Figure24-1.png",
        "caption": "Fig. 24 Coordinates of the body and the anchor foot. C is the foot/ground contact point. T0 c is a global frame of the contact point. and T0 b is the global body frame. Note that the transformation from the foot to C with respect to the foot is constant",
        "texts": [
            " Kalman filters (Welch and Bishop 1995) have been implemented for robust estimation of the roll and pitch angles. Given these estimated orientations, the position of the body is still missing. In order to estimate it, we use the relative pose between the contact point and the body given the assumptions of no slip, no movement of contact point and a polygonal foot geometry. If the robot does not experience any slip and maintain the contact point during the fall, the contact point can be referenced for global position. Figure 24 shows an example of the falling robot. The point is that we can obtain the estimated orientation of the body frame (i.e., body rotation matrix R0 b in the global body transformation T0 b) and the estimated location of the foot contact point (i.e., position column P0 c in the global contact point transformation T0 c). Combining them results in the full posture of the body frame. The following equation describes the relative posture between the contact point and the body frame: T0 cTc b = T0 b, (21) which is equivalent to the following: [ R0 c P0 c 0 1 ] Tc b = [ R0 b P0 b 0 1 ] , (22) where T is the transformation matrix and R and P are the rotation matrix and the position vector, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure13-6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure13-6-1.png",
        "caption": "FIGURE 13-6 Synchronizer assembly. (Courtesy Zahnradfabrik Passau GmbH.)",
        "texts": [
            " Again, it is necessary to disengage the traction clutch and advisable to stop the tractor when shifting. This type of transmission is slightly less efficient than the sliding gear type as a result of the friction between the rotating gears and shafts, but it is used when helical gears are selected to control noise or when it is desired to reduce the shifting effort that would be created by moving large gears. Most tractor transmissions are, at least partially, of the constant mesh type. A synchronized or synchromesh transmission has small friction clutches (fig. 13-6), usually cone type, that engage when a shift is initiated. The resulting frictional torque is used to prevent engagement of the shifter collar until the rotational speed of the collar and gear are nearly the same, i.e., synchronized. When synchronization occurs, the frictional torque reduces and the shifter collar can then be engaged with the gear to complete the shift. The advantage of a synchronized transmission is that gear changes can be made easily without damaging the transmission, even when the vehicle is moving"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001967_0094-114x(78)90041-1-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001967_0094-114x(78)90041-1-Figure7-1.png",
        "caption": "Figure 7. Paper feed mechanism.",
        "texts": [
            " This assumes that these intermediate loops do not contain more than one prismatic joint. These properties of a loop can be used to advantage. To begin with, the loop is an ideal means of checking whether a linkage can be force balanced as a result of it containing more than one prismatic joint. Simply, to balance the linkage it must be observed that each prismatic joint is contained in its own separate loop. The loop can also be used to identify which links in a linkage may be left uncounterweighted. The linkage mechanism of Fig. 7 is used for feeding paper in a duplicating machine. Link AD rotates at constant speed and the paper is fed by link FG. The balance conditions for the mechanism will now be determined. There are two loops which can contain a separate dependent link. For convenience, these are taken as the internal loops. However, one loop, loop AGFECDA, includes a prismatic joint.Hence the link to be left uncounterweighted must be one of the two links this joint connects. One of these links, link AG, is the frame, and so the link to be left uncounterweighted must be link 5, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003306_tmag.2017.2665639-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003306_tmag.2017.2665639-Figure1-1.png",
        "caption": "Fig. 1. Three-phase stator winding of an IM with ITSC in the phase \u201ca\u201d.",
        "texts": [
            " Therefore, the two first cases are the ones worth investigate. Thus, in this article two studies are presented. The first one is based on finite element analysis (FEA), to approach the following question: Do the location of an ITSC with fixed fault severity factor affects the damaged IM parameters?. In the second part, an improved general model for the leakage inductance calculation of a winding under ITSC fault is investigated. A squirrel-cage three-phase IM with stator winding ITSC in one phase, phase \u201ca\u201d, is shown in the Fig. 1(a) where represents the short-circuited turns and is the total number of winding turns. The fault severity factor is S This work was partially supported by grants for the Office of Naval Research. The authors are with the Energy Systems Research Laboratory, Department of Electrical and Computer Engineering, Florida International University, Miami, FL 33174 (e-mail: mohammed@fiu.edu). 0018-9464 (c) 2016 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. > FOR CONFERENCE-RELATED PAPERS, REPLACE THIS LINE WITH YOUR SESSION NUMBER, E.G., AB-02 (DOUBLE-CLICK HERE) < 2 defined as . Fig. 1(b) presents a circuit diagram of a three-phase IM stator. It is assumed that is the fault impedance that will determine the faulty leakage current ( magnitude in the short-circuit path, and are the stator winding current and voltage for the phase x where x = {a,b,c}. From [4], [5] the voltage and torque equations in complexvector notation are shown in (1) where: , , , , , are the complex vectors for the stator and rotor, and are the selfinductance for the stator and rotor respectively, is the mechanical speed and is the magnetizing inductance, is the resistance of the phase winding, is the leakage inductance of stator, is the leakage inductance of the rotor and the symbol is the derivative operator",
            " 5(b) is the one that have more instantaneous difference, however, in average all of them are close to zero (in steady state). The reason for this discrepancy is due to the MMF shape difference in the 4 cases. Distinct locations of the fault will create different MMFs with different harmonic components, but same general behavior. From the zoom of Fig. 5(b) a double-line frequency oscillation can be noticed. This torque variation comes from the fact that when the ITSC happens the current in the fault winding ( from Fig. 1(a)) reverses its direction (opposite to ) producing a counter rotating magnetic field (negative sequence) deforming the shape of the original MMF and introducing a negative sequence component. Fig. 6(b) and 7(b) shows the steady state currents in the fault and in the winding. Notice a small peak difference among all of them. From Fig. 8(a), notice the 2D distribution for one case of study ( ). The other 3 cases are quite similar which match with the previous results. It can be concluded, from these results, that the fault location impact on the IM electrical parameters, of the mathematical modeling, can be neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001217_70.240203-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001217_70.240203-Figure2-1.png",
        "caption": "Fig. 2. Two-DOF planar robot handling a nonpoint-massload.",
        "texts": [
            " bnIT with Matrix W2(q,q) defined by (29) becomes a 3 x 3 matrix with B ( d ) E R3x3 given by B ( d ) = diag(;RJ,i) (54) that is, the 3 x 3 diagonal matrix with bRJyQ as entries along its main diagonal. Matrix Yl becomes where and YZ E RnX3 is given by (42) with B(d) given by (54). For ' p , , = [0 O p Z l T , a simplified formula can also be established that is almost identical to (52H59) except that p.1 there should be replaced by ;rs-the third column of YR. C. Example Consider the 2-DOF planar arm shown in Fig. 2, where the length of link i is denoted by I , . It is assumed that the links are of pointmass type, with each mass center at the origin of its link frame. The robot handles a rectangular bar with uniform material density. The parameters of the load include mass m3. mass center 3pc3, and inertia tensor \"Ic3 , where 3p, , = [PI 0 01 and ' 1 3 = diag(Izz,Iyy,Izz) . For comparison, the manipulator regressor will be evaluated using the conventional approach described in Section I and the approach proposed in Section III"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002658_j.jsv.2012.12.025-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002658_j.jsv.2012.12.025-Figure8-1.png",
        "caption": "Fig. 8. (a) Laboratory test rig, (b) schematic diagram of test tig.",
        "texts": [
            " The results from KSMEA are compared with DE and other two well know intelligent algorithm without Kriging, Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), the control parameters for these optimization algorithms are shown in Table 5. Table 6 lists the compared results and it indicates that the Kriging surrogate model uses less computational time but achieves better identification results. Since the calculation of unbalance responses of rotor-bearing system is substituted by the Kriging surrogate model, it reduces the computational burden and saves the computational time. The test rig shown in Fig. 8 is a RK-4 rotor system by BENTLY NEVADA. A controllable DC motor is connected to one side of the shaft. The disk is installed in the middle of the shaft and each side of the rotor system has a ball bearing which is simplified two springs and two dampers. The shaft vibration in the vertical and horizontal directions is measured by two sensors, and the measured signals are processed by the ME\u2019scope 4.0 software. The parameters of the Rotor-Kit system are listed in Table 7 and the equivalent FE model is given in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002389_j.jsv.2010.03.014-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002389_j.jsv.2010.03.014-Figure2-1.png",
        "caption": "Fig. 2. A schematic of the simple model for gear rattle.",
        "texts": [
            " In [14] it was observed that at the same amplitude of displacement excitation forcing, large variations in the magnitude of any contact losses between the gears (which we term \u2018disconnections\u2019 for brevity) were possible, the variations being dependent on the phase of the displacement excitation relative to the angular positions of the gears. In a geared system with no profile errors, changing the phase of the input would have no effect. However, in a real system, the inevitable profile errors meant that the total forcing transmitted between the gears would be a superposition of the external displacement excitation and the internal forcing due to the STE. Changing the phase of the input changed the magnitude of this superposition. Fig. 2 shows a schematic diagram of the gear pair model, an impacting model in which it is assumed that there is no compliance as the driven gear is not loaded. Subscript 1 denotes the drive gear which moves with a defined displacement, and subscript 2 denotes the driven gear. By resolving the moments acting upon the driven gear the equation of motion is obtained I \u20acy2\u00fec _y2 \u00bc b\u00f0y1,y2,2b,epos,eneg\u00de, (2) where I is the moment of inertia of the gear, c is the viscous linear friction coefficient, and y is the angular displacement of each gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002696_e2013-02067-x-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002696_e2013-02067-x-Figure13-1.png",
        "caption": "Fig. 13. Preparation of the particles used in the experiment. Top: silica (\u03c3 = 4.8\u03bcm) spheres are floated on top of a glass slide, leading to a dense monolayer. Thin metal layers are evaporated onto the colloid monolayer, resulting in metallic half caps on top of the particles which act as catalytic layers. Afterwards, the particles are redispersed into the solvent and used inside the channel geometry. Bottom: by use of an underlying [Co/Pt] multilayer stack in the cap the particles obtain a permanent magnetic momentm perpendicular to the particle surface. In this case, the direction of movement of the catalytically driven particle can be controlled by means of an external magnetic in-plane field B\u2016 by orienting m and therefore suppressing the rotational diffusion of the particle.",
        "texts": [
            " This can be explained with stable sliding modes along the channel walls where the rotation of the particle is strongly suppressed. This leads to a directed motion of the particle increasing DL drastically. Here, we present a colloidal model system based on catalytically driven Janus particles [48\u201351] to model the system used in [37]. To fabricate the Janus particles used in the experiment, colloidal spheres with metallic caps (Ni, Pd, Pt) are prepared by evaporating the metal onto the dry particles. Then, the capped spheres are redispersed in water and used in the experimental setup (Fig. 13). When H2O2 is added (between 3% to 7%), the particles are propelled by the products of the catalytic reaction of H2O2 with the metal layer [52\u201354] leading to a strongly enhanced diffusion coefficient DL [51,55]. Furthermore, by using silica particles with underlying magnetic multilayers, we are able to control the direction of the particle by an external magnetic field [51,56,57]. The particles are placed in channels made from PDMS (same as described in section 1.2) and polycarbonate. All experiments are performed in a sealed sample cell to prevent a distortion of the system due to evaporation of the solvent as well as suppress the generation of air bubbles due to the catalytic reaction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002664_s10999-012-9181-y-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002664_s10999-012-9181-y-Figure2-1.png",
        "caption": "Fig. 2 One link of parallel mechanism",
        "texts": [
            " According to principle of Kane, the calculation of acceleration and partial acceleration, the partial velocities of mass centers, and partial angular velocities of all links are required. The mechanism studied in this paper is a 6-DOF parallel mechanism, which is shown in Fig. 1, herein referred to as a 6-SPS (spherical-prismatic-spherical) parallel mechanism. This parallel mechanism consists of a moving platform which is manipulated by six actuated links. Each link is connected with fixed platform and moving platform through spherical hinge. Since six links are identical, one link is choosed to derive dynamic equation. As shown in Fig. 2, it illustrates a link of parallel mechanism. Coordinate frames Cum-XumYumZum and Cbm-XbmYbmZbm are two moving coordinate frames that are located in up link and bottom link respectively. The origin of Cum is located the in mass centre of up extensible link. The origin of Cbm is located in the mass centre of bottom extensible link. Axis Xum and axis Xbm along with link AiBi (i = 1, 2,\u2026,6). Axis Yum and axis Ybm are perpendicular to plane OAiBi (i = 1, 2,\u2026,6). Axis Zum and axis Zbm comply with right hand rule",
            " q = [x, y, z, a, b, c]T is defined as generalized coordinate vector of the system. x, y and z denote orientation vector of the origin of the moving coordinate frame O1-X1Y1Z1 in inertial coordinate frame O-XYZ, and a, b and c denote three Euler angles of moving coordinate frame O1-X1Y1Z1 in inertial coordinate frame O-XYZ. Thus, generalized velocity of the moving platform could be written as q \u00bc x; y; z; a; b; c : h iT \u00bc v; x\u00bd T in inertial coordinate frame O-XYZ. v and x denote line velocity and angular velocity of the moving platform respectively. According to Fig. 2, vector equation of link AiBi could be written as follows. S \u00bc P\u00fe Rbi Ai \u00f0i \u00bc 1; 2; . . .; 6\u00de \u00f02\u00de where R\u00bc cbcc cbsc sb sasbcc\u00fe casc cacc sasbsc sacb sasc casbcc casbsc\u00fe sacc cacb 2 4 3 5; s denotes sine function and c denotes cosine function. In Eq. 2 S denotes the vector of link AiBi in inertial coordinate frame O-XYZ; P denotes orientation vectors of the origin of the moving coordinate frame O1-X1 Y1Z1 in inertial coordinate frame O-XYZ; bi denotes the orientation vector of point Bi in moving coordinate frame O1-X1Y1Z1; Ai denotes the orientation vector of point Ai in inertial coordinate frame O-XYZ; R denotes transformation matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003579_1.4038528-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003579_1.4038528-Figure3-1.png",
        "caption": "Fig. 3. Underconstrained 7R linkage in the rank 3 singularity q0.",
        "texts": [
            " Because CK q0 L3 \u2282 CK q0 L4, the tangent cone CK q L4 is the union of the tangent spaces to the six 1-dim manifolds L1 4 = { q = (0,0,0,s,0,\u2212s) } , L2 4 = { q = (0,0,s,0,\u2212s,0) } L3 4 = { q = (0,s,0,0,0,\u2212s) } , L4 4 = { q = (0,s,0,\u2212s,0,0) } L5 4 = { q = (s,0,\u2212s,0,0,0) } , L6 4 = { q = (s,0,0,0,\u2212s,0) } of singularities of rank 3. Due to CK q0 L3 = {0} the set of configurations of rank less than 3 is locally the 0-dim manifold L3 \u2229U (q0) = {q0}. Thus, starting from q0, the linkage can perform 1-dim finite singular motions with rank 3. A representative configuration in L1 4 is shown in Fig. 2. The linkage is overconstrained since CK q0 L6 =CK q0 V and dmax = 6. 1 5 3 6 2 4 Fig. 2. 6R linkage in a rank 4 singularity belonging to L1 4. Fig. 3 shows a 7R linkage in the reference configuration q0 where r = rank J(q0) = 3 so that q0 \u2208 L4,L5,L6. The joint screw coordinates in this configuration are Y1 = Y3 = (0,1,0,0,0,0)T ,Y2 = Y4 = (1,0,0,0,0,0)T Y5 = (1,0,0,0,0,\u22121/3)T ,Y6 = (1,0,0,0,0,\u22122/3)T Y7 = (1,0,0,0,0,\u22121)T . Tangent cone to L6 and V : For all 7 minors of order 6, it is di dt i mab (q)|q=q0 = 0, i \u2265 0. Consequently CK q0 L6 = CK q0 V , and the c-space is locally identical to the variety of configurations of rank less than 6. Since dmax = 6 the linkage is overconstrained",
            " Cq0 L5 is the union of the tangent spaces to the three 3-dim manifolds of rank 4 singularities, since Cq0 L4 \u2282Cq0 L5. The manipulator exhibits rank 4 singularities as long as either joints 2,3,4, joints 2,4,5, or the joints 4,5,6 remain in their reference configuration and all other joints variables attain generic values. Cq0 L4 is the 2-dim manifold of rank 3 singularities. This happens as long as joints 2, . . . ,6 remain locked. The motion of the first and last joint have no effect on the rank, as it is well-known [39, 45]. The rank 4 singularity q0 = 0 of the spatial 6R manipulator in Fig. 3 of [39] is investigated. Again J = J. The screw coordinate vectors in the reference configuration q0 are given in [39] sec. 7.1. Since rank J(q0) = rank (Y1, . . . ,Y6) = 4, it is q0 \u2208 L5,L6. Tangent Cone to L6 It is K 6,1 q0 = R6. The tangent cone is Cq0 L6 = K 6,2 q0 = K 6,3 q0 = . . . with K 6,2 q0 = K 6,2\u2032 q0 \u222aK 6,2\u2032\u2032 q0 where K 6,2\u2032 q0 = V ( x3,x4 ) K 6,2\u2032\u2032 q0 = V ( x3,2x2\u2212 x4 ) K 6,2\u2032\u2032\u2032 q0 = V ( x2 3 +2x2x4\u2212 x2 4\u2212 x3x5 ) . Tangent Cone to L5 It is Cq0 L5 = V ( x2,x3,x4,x5 ) . This is the tangent space to the set of points of rank 4, which is thus locally the 2-dim manifold where joints 2-5 do not move",
            ", Springer, Berlin, 2007 16 Mu\u0308ller Final manuscript of JMR-16-1390 Acc pt ed M an us cr ip t N t C op ye di te d Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 11/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use List of figure captions Fig. 1: Decision tree for classifying a point q \u2208V as regular or singular, where r = rankJ(q). It is presumed that the zero set of the loop constraints is real at q. Fig. 2: 6R linkage in a rank 4 singularity belonging to L1 4. Fig. 3: Underconstrained 7R linkage in the rank 3 singularity q0. Fig. 4: a) Planar linkage in the reference configuration where its c-space has a cusp singularity. Bodies are numbered with I, . . . ,V III and joints with 1, . . . ,10. b) Topological graph and the \u03b3 = 3 FCs. Fig. 5: Redundant serial 7R manipulator (KUKA LWR) in the singular configuration q0 with rank 3. 17 Mu\u0308ller Final manuscript of JMR-16-1390 Acc ep te d Man us cr ip t N ot C op ye di te d Downloaded From: http://mechanismsrobotics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-3-1.png",
        "caption": "FIGURE 11-3 Free-body diagram of a rear-wheel-driven tractor.",
        "texts": [
            " However, much useful information, particularly for evaluating tractor field performance, can be obtained from a static equilibrium analysis. For the static equilibrium situation, it = 0 and equation 11 becomes (15) Similarly, for static equilibrium, e = ~w = 0, and equation 12 could be used to represent the moment equilibrium of the tractor. However, since the sum of moments about any transverse axis must be zero for the tractor to be in static equilibrium, the location of the axis may be chosen to help simplify the resulting moment summation. A convenient axis to use passes through point C of figure 11-3. This axis has the advantage that the resulting moment arms of forces F\" TF\" Rn and TFf all become zero. Then, summing moments about point C, taking counterclockwise moments as positive, and assuming e o when the tractor is in static equilibrium, Rf (hit cos elt + h2t cos e2t + ef - er) + Wt sin ~ (rr + hIt sin elt) - Wt cos ~ (hit cos elt - er) + P cos a (rr - h3 cos <1\u00bb + P sin a (h3 sin <I> + er) = 0 (16) Solving equation 16 for Rf , Rf = {W, [(hIt cos elt - er) cos ~ - (rr + hit sin elt) sin ~] - P [(rr - h3 cos <1\u00bb cos a + (h3 sin <I> + er) sin an I{h lt cos elt + h2t cos e2t + ef - eJ (17) Although equation 17 is useful for computation, its complexity tends to STATIC EQCILIBRICM ANALYSIS-FORCE ANALYSIS 279 obscure its physical meaning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure14-1.png",
        "caption": "Figure 14. Bearing load distributions for moment load and l \u00bc 90 , except for (e) where l 2 \u00bd0, 180 . (a) Front bearing, (b) rear bearing, (c) time-domain simulation model with force visualization for I46, (d) pressure profile for the highest loaded roller for each model and (e) bearing fatigue life vs. moment axis.",
        "texts": [
            " While the comparison in Figure 13(a) to (d) only includes a single load case/time step, Figure 13(e) shows the bearing fatigue life calculated for a full azimuthal revolution of the radial force. Due to symmetry, only the angles from 0 to 180 are shown. In this study, a full revolution of a moment of 10 MNm is applied at the load node. Referring to the coordinate system in Figure 12(d), the applied loads are Fx \u00bc Fy \u00bc 0 \u00f043\u00de mx\u00f0 l \u00de \u00bc sin\u00f0 l \u00de 10MNm, l 2 \u00bd0, 360 \u00f044\u00de my\u00f0 l \u00de \u00bc cos\u00f0 l \u00de 10MNm, l 2 \u00bd0, 360 \u00f045\u00de A detailed load distribution and relative raceway misalignment comparison for l \u00bc 90 is shown in Figure 14(a) and (b). The small deviation between at Eindhoven Univ of Technology on June 17, 2014pik.sagepub.comDownloaded from the results of the I46 and the FE model can easily be explained by the model differences discussed previously. Figure 14(c) shows the time-domain simulation model and Figure 14(d) shows the interpolated pressures for the highest loaded roller. While the comparison in Figure 14(a) and (d) only includes a single load case/time step, Figure 14(e) shows the bearing fatigue life calculated for a full azimuthal revolution of the moment. Due to symmetry, only the angles from 0 to 180 are shown. The studies show that for a single bearing ring, the precision is improved by increasing the number of interface nodes from 10 to 46, but even at 16 interface nodes, a reasonable agreement is seen and the difference between 23 and 46 is generally marginal. The number of interface nodes is a balance between precision, as demonstrated previously, and computational performance since each interface node introduces six additional dof to the model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.9-1.png",
        "caption": "Fig. 1.9. Projection of gravitational force onto aircraft coordinate system",
        "texts": [],
        "surrounding_texts": [
            "The weight of the aircraft is considered to be applied at its centre of gravity along the vertical axis. When the attitude of the aircraft is not null, it induces longitudinal and lateral forces due to the projection onto aircraft-axis: FxG = \u2212sin\u03b8 \u00b7m \u00b7g FyG = cos\u03b8sin \u03d5 \u00b7m \u00b7g FzG = cos\u03b8cos\u03d5 \u00b7m \u00b7g (1.10)"
        ]
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure6-19-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure6-19-1.png",
        "caption": "FIGURE 6-19 Torque sensor. Arrangement of strain gages on a shaft to measure torque.",
        "texts": [
            " 150 ELECTRICAL SYSTEMS Farber (1982) also points out that the operator is not always a predictable control element because he or she has a variety of skills; may not always be alert; may be diverted by other functions; may be hampered by vision ob structions; and may be largely isolated from sound signals because of the tractor cab. Farber notes that variables that must be considered in making choices are difficult to process and combine except by electronics. Basic sensors are: 1. Pressure 2. Temperature 3. Torque (fig. 6-19) 4. Force 5. Flow 6. Position 7. Velocity 8. Voltage Combinations that give additional information can supplement this list. For example, tire slip can be determined by making two velocity measurements (vehicle velocity and tire surface velocity), or S = 1 - VvlVt \u2022 In the following list, G. R. Mueller (1985) provides some of the operational SENSORS 151 information that can be obtained from sensors. The sensor plus the read-out device is often called a monitor. 1. Low engine oil pressure 2. Air filter restriction 3. Coolant level 4. Alternator not charging 5. Park brake engaged 6. Transmission oil temperature 7. Transmission oil pressure 8. Transmission oil filter restriction 152 ELECTRICAL SYSTEMS Principle stress lines of: 9. Coolant temperature 10. Exhaust temperature 11. Fuel level 12. Voltage level 13. \"Systems Normal\" indicator One common sensor for measuring torque is shown in figure 6-19. This sensor uses electrical resistance strain gages to measure the torque or moment on any shaft that needs to be monitored. For example, automatic control of a three-point hitch must measure the force on the lower links. This can be done by attaching the lower links of the three-point hitch to offsets on two shafts that are fixed on one end. Environmental Problems Electrical and electronic components on a tractor must be designed and tested to withstand a variety of environmental conditions. The reliability of each component must be determined through methods that are briefly discussed ENVIRONMENT AL PROBLEMS 153 in chapter 14 \"Tractor Tests and Performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000830_s0736-5845(96)00023-3-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000830_s0736-5845(96)00023-3-Figure9-1.png",
        "caption": "Fig. 9. A three-revolute manipulator.",
        "texts": [
            " In method II, singular surfaces inside the workspace are intersected to form subsurfaces that may Determination of boundaries to manipulator workspaces \u2022 K. ABDEL-MALEK et al. 69 exist inside or on the boundary to the workspace. Once those surface patches are determined, the perturbation method presented above is used to identify whether the subsurface (surface patch) is on the boundary. However, a difficulty may arise m partitioning a singular surface to subsurfaces due to the nature of the parametric equation of singular surfaces. To illustrate, consider the three-degrees-offreedom manipulator shown in Fig. 9. The position vector can be written as 10 cos ql cos q2 cos q3 - 10 sin ql x = K2(q) = 10 sin ql cos q2 cos q3 + 10 cos ql 10 sin q2 cos q3 + subject to the following joint limits: 7r< <_~ , n < q 2 < _ q 3 _ < Z - ql _ ~ _ _ ~, and 0 < 2n. Singular sets were determined by Abdel-Malek and Yeh. 2 Substituting these singularities into Eq. (33) yields parametric equation of singular surfaces that intersect in the workspace. For example, in order to parti t ion the singular surface lq 3 into subsurfaces, it is necessary to determine all intersections of lq 3 with all other singular surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.31-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.31-1.png",
        "caption": "FIGURE 1.31 On the stability of a trailer (Exercise 1.4).",
        "texts": [
            " Another effect of this reduction of the average cornering stiffness is that when the vehicle moves at a speed lower than the critical speed, the originally stable straight-ahead motion may become unstable if, through the action of an external disturbance (side wind gust), the slip angle of the caravan axle becomes too large (surpassing of the associated unstable limit cycle). This is an unfortunate, possibly dangerous situation! We refer to Troger and Zeman (1984) for further details. Exercise 1.4 Stability of a Trailer Consider the trailer of Figure 1.31 that is towed by a heavy steadily moving vehicle at a forward speed V along a straight line. The trailer is connected to the vehicle by means of a hinge. The attachment point shows a lateral flexibility that is represented by the lateral spring with stiffness cy. Furthermore, a yaw torsional spring and damper are provided with coefficients c4 and k4. Derive the equations of motion of this system with generalized coordinates y and 4. Assume small displacements so that the equations can be kept linear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003939_j.jelechem.2014.08.021-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003939_j.jelechem.2014.08.021-Figure3-1.png",
        "caption": "Fig. 3. Schematic representation for Ab detection by ALP-based signal amplification combined with AA-triggered \u2018\u2018outer-sphere to inner-sphere\u2019\u2019 ECC redox cycling on a SAMcovered gold electrode.",
        "texts": [
            " In conventional competitivetype immunoassays, antibodies are immobilized on a solid support surface for the capture of antigens. The disadvantages of the format are that the random orientation of antibodies decreases their immunoaffinity capacity and the instability of antibodies limits the regeneration and long-time storage of the sensing electrode. Thus, the competitive immunoassays used in this work were carried out by immobilizing Ab peptides (antigen) on the electrode surface. The schematic representation of the method is illustrated in Fig. 3. Ab(1\u201316) peptide appended with a cysteine residue (Ab(1\u201316)Cys) was immobilized on a gold electrode through the formation of the Au\u2013S bond. The ALP-conjugated mAb(1\u201316) (mAb(1\u201316)\u2013ALP) specific to the amino acids 3\u20138 of Ab can be captured by the electrode through the strong and specific antibody\u2013Ab interaction (Sample I). After the addition of the AAP substrate, the enzymatic reaction from AAP to AA proceeds. The produced AA will trigger the ECC redox cycling. If the mAb(1\u201316)\u2013ALP bound to the native Ab in the samples (Sample II), it would be incapable of anchoring onto the electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003985_cjece.2015.2465160-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003985_cjece.2015.2465160-Figure7-1.png",
        "caption": "Fig. 7. Modified topology for the rotor poles displacement.",
        "texts": [
            " In order to see the impact of the displacement on axial force, the instantaneous axial force waveform is predicted for the motor with the optimal displacement angle and it is compared with that for the motor without the displacement in Fig. 6. As it is obvious in this figure, the amplitude of average axial force is negligible for the motor without the displacement. However, there is a small average axial force for the motor with the displacement because of the unbalance in the rotor system. To minimize this small axial force, another topology shown in Fig. 7 is suggested in which the poles are alternatively displaced by \u00b1\u03b1\u00b0. Carrying out the 3-D FE transient analysis for the considered operating point when the optimal displacement angle is selected, the instantaneous torque of this modified topology is predicted and compared with that for the motor with simple displacement in Fig. 8. They are very similar and the values of the average torque are almost the same for them. The instantaneous axial force predicted for this modified structure is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000981_978-3-540-32256-6_25-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000981_978-3-540-32256-6_25-Figure2-1.png",
        "caption": "Fig. 2. Principle of treating legs as wheels [9]. Walking a) forwards, b) sideways. c) Turning. d) Turning while walking forward",
        "texts": [],
        "surrounding_texts": [
            "Since gaits using the typical PWalk-style originally introduced by the team from the University of New South Wales [2] are state of the art, such a kind of walk is also used for the work presented in this paper (cf. Fig. 3). This is important, because with this kind of walk, only the contact sensors of the hind legs touch the ground, and therefore, only these two sensors can be used for calculating the motion of the robot. The current position of such a ground contact sensor can easily be determined based on the measurements of the angles of the three joints the Aibo has in each leg using forward kinematics. These angles are automatically determined by the Aibo every 8 ms. The three-dimensional positions (cf. Fig. 1b) for the left and right hind feet change over time with the motion of the legs and can be computed relative to some origin in the body of the robot. However, for odometry, only their lengthwise and sideward components are required. Therefore, pleft t and pright t are only two-dimensional vectors. The overall offset a hind leg h has walked during a period of time ta . . . tb can be determined by summing up all the 2-D offsets between successive positions at which the foot had contact to the ground: dh ta,tb = ( dxh ta,tb dyh ta,tb ) = tb\u2211 t=ta+1 { ph t \u2212 ph t\u22121 , if gh t \u2227 gh t\u22121 0, , otherwise (1) g just states whether the ground contact sensor of leg h was active at time t or not. Since each leg has sometimes contact to the ground and sometimes not while walking, it is important to always determine the distance with ground contact for a complete step phase. Otherwise, the distances measured by the left and the right feet are not comparable. For quadruped walking, the three requested motion speeds xr, yr, and \u03b8r are overlaid to result in the actual xh and yh amplitudes of the legs. The walking engine of the GermanTeam [9] uses the following equations for the two hind legs. Please note that the feet move always in the opposite direction of the robot\u2019s body, so everything is negated (r is the radius to the body center): xleft = \u2212xr + r\u03b8r (2) yleft = \u2212yr + r\u03b8r (3) xright = \u2212xr \u2212 r\u03b8r (4) yright = \u2212yr + r\u03b8r (5) For odometry, everything is the other way round. The foot motion is known, and the speed components have to be calculated. By transforming the motion equations, the measured walking speeds xm, ym, and \u03b8m can be calculated from the measured ground contact distances dleft and dright. Please note that dx and dy measure only half of a step phase (while the corresponding foot touches the ground), so everything measured is multiplied by 2, i. e. all divisions by 2 are missing: xm ta,tb = \u2212dxright ta,tb + dxleft ta,tb tb \u2212 ta (6) ym ta,tb = \u2212dyright ta,tb + dyleft ta,tb + dxright ta,tb \u2212 dxleft ta,tb tb \u2212 ta (7) \u03b8m ta,tb = \u2212dxright ta,tb \u2212 dxleft ta,tb r(tb \u2212 ta) (8)"
        ]
    },
    {
        "image_filename": "designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003693_j.ijheatmasstransfer.2015.12.036-Figure10-1.png",
        "caption": "Fig. 10. Oil flow analysis inside lubrication devices with different nozzle number.",
        "texts": [
            " Since the Type II lubrication device is prior, so the following work was conducted to optimize the Type II lubrication device for the specific angular contact ball bearing B7008C/ZYS. According to the installation of bearing B7008C in machine tool spindle and tool holder system, the spacer and lubrication device are arranged in A side, while B side is sealed up. Single nozzle (at 0 plane) and double nozzles (at 0 and 180 plane) were compared and the internal flow at 40 and 160 plane were monitored. As mentioned above, vortex flow occurs in cylindrical cage pocket (seen in Fig. 3), so here the spherical pocket was employed, seen in Fig. 10. Compared to the above analysis, air flow inside bearing cavity with spacer structure is better. According to the turbulence intensity and vortexes number, the inside air flowwith double nozzles is superior to single nozzle structure. A further field synergy analysis shows that, the field synergy angles of double nozzles structure are smaller, which indicates the air flow performance is improved. As seen in Fig. 9(b), the four key structural parameters of the Type II lubrication device are the pipe inclined angle, the inner surface inclined angle, the nozzle outlet structure and the distance between the outlet and the inner surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001721_tac.2007.900825-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001721_tac.2007.900825-Figure1-1.png",
        "caption": "Fig. 1. Kinematic car model.",
        "texts": [
            " Though the convergence is destroyed with large noises, simulation shows that the sampling law (15) might be a better strategy, for it can provide for better accuracy with relatively large noises (see the simulation results, Table I). It is especially useful if assumption (3) only locally holds. Note that Theorems 3, 5, 6 provide for the best possible asymptotic accuracy in the absence of noises [17]. Consider a simple kinematic model of car control where and are Cartesian coordinates of the rear-axle middle point, is the orientation angle, is the longitudinal velocity, is the length between the two axles and is the steering angle (Fig. 1). The task is to steer the car from a given initial position to the trajectory , while and are assumed to be measured in real time. Let , , , at . Define . The relative degree of the system is 3 and the 3-sliding homogeneous quasi-continuous controller [23] can be applied here with . Substituting estimations , , of , , , respectively, obtain (16) Consider two possibilities (17) with a constant measurement step [from (9)] and (18) with the variable step (12), and (from (14)). The control was applied only from providing some time for the calculation of the finite differences"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002040_978-3-540-36119-0_18-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002040_978-3-540-36119-0_18-Figure8-1.png",
        "caption": "Fig. 8. (A) Dependency of hopping direction on control parameters (oscillation frequency f, offset angle O) of the servo motor. (B) With no hip actuation the leg force FLEG merely depends on joint torque M and leg geometry. (C) Leg force is enhanced compared to (B) if the hip retracts actively (hip extension torque). The opposite is true if leg retraction is pointing to the left, in which case the leg force is reduced",
        "texts": [
            " To investigate the influence of an enforced leg retraction after touch-down, we implemented a higher torque motor using very stiff coupling of the motor to the hip joint. As a result the boom keeping the upper body upright broke. Consequently, a more compliant coupling was inserted between the motor and the hip joint, imitating the biological function of tendons in hip muscles. The robot demonstrates a variety of behaviors depending on the selected oscillator frequency f and offset angle O. Surprisingly, at low oscillation frequencies, the hopping direction is not as expected, namely opposite to the leg joint (Fig. 8A). This movement could well be compared to that of a hopping bird. This behavior is not very sensitive to changes in the control parameters. At higher frequencies (above 6 Hz) a more human-like movement is observed. Then, the leg joint points forward (similar to a human knee). At an intermediate region hopping in place is observed with no substantial horizontal movement. Why does the robot change its movement direction depending on the selected control frequency? To approach this question the effect of active limb retraction on the leg dynamics is considered in Figs. 8B and 8C. For simplicity, we focus on a static approach neglecting all dynamic effects, i.e. due to segmental accelerations, joint damping, or torques at the foot point. With no retraction (zero hip torque), leg force is directly dependent on limb configuration. This is a consequence of the rotational spring which relates joint torque to joint angle. If the hip is actively contributing to limb retraction (Fig. 8C), leg force is increased or decreased depending on the geometrical relation between leg joint torque and hip torque. In bird-like hopping, leg force is reduced whereas in human-like hopping the force is increased. As a consequence of this increased (or decreased) leg force, the natural frequency of the hopping system is changed, i.e. an increased leg force to some extent imitates a stronger (stiffer) leg associated with a higher step frequency. This is a well known dependency for the spring-mass model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003574_j.mechmachtheory.2017.08.004-Figure2-1.png",
        "caption": "Fig. 2. Definition of cutting edge element.",
        "texts": [
            " In gear skiving, the cutting thickness and the working rake, relief and inclination angles of the tool are changing continuously, which indicates the cutting performance of the skiving tool. For each cut of a cutter tooth, a layer of material will be removed from the tooth space of the workpiece. The cutting edge starts to cut in when it crosses the meshing line on the tooth flank of the workpiece until it moves out of the tooth space. In the cutting process, the cutting thickness of the cutter tooth increases gradually, especially for the top edge and the up-recess edge as shown in Fig. 2 (a). In order to investigate the cutting condition of the cutting edges more conveniently and accurately, the cutting edges are decomposed into a set of cutting edge elements, and each edge element is treated as an oblique cutting edge as shown in Fig. 2 (b). For the spur cylindrical skiving tool, the rake face is a conical surface whose axis is set on the axis of the tool and coneapex angle is the complementary angle of the cutter rake angle \u03b3 p . The normal vector of the rake face at the cutting point \u201cC\u201d can be expressed as: n r = [ \u2212 sin \u03b3p cos \u03c8 \u2212 sin \u03b3p sin \u03c8 \u2212 cos \u03b3p ]T (15) where, is the tooth thickness half angle of the cutting point \u201cC\u201d as shown in Fig. 2 (a), which is used for describing the angle between the line O c C and the axis x c .. The tangent vector of the tooth flank helix of the spur cylindrical skiving tool at the cutting point can be expressed in S 2 and S c as: t (2) r = t r = [ 0 0 1 ]T (16) The normal vector of the rake face can be transformed to S 2 as: n (2) r = L 2 c \u00b7 n r = [ \u2212 sin \u03b3p cos \u03c8 cos \u03d5 c + sin \u03b3p sin \u03c8 sin \u03d5 c \u2212 sin \u03b3p cos \u03c8 sin \u03d5 c \u2212 sin \u03b3p sin \u03c8 cos \u03d5 c \u2212 cos \u03b3p ] (17) The normal cutting velocity of the cutting point is parallel to the cross product of the normal vector n c and the tangent vector t c , and can be expressed in S 2 as: v (2) n = n (2) c \u00d7 t (2) c \u00b7 \u2223\u2223v ( 2 ) cw + v (2) s \u2223\u2223\u2223\u2223n (2) c \u00d7 t (2) c \u2223\u2223 (18) So the normal working rake angle of the cutting point can be obtained as the angle between the normal vector of the rake face and the normal cutting velocity: \u03b3n = arccos n (2) r \u00b7 v (2) n \u2223\u2223n (2) r \u2223\u2223 \u00b7 \u2223\u2223v (2) n \u2223\u2223 (19) The normal vector of the flank at the cutting point can be determined by the cross product of the tangent vector t c of the cutting edge and the tangent vector t r of the tooth flank helix in S 2 as: n (2) f = t (2) c \u00d7 t (2) r (20) So the normal working relief angle of the cutting point can be obtained as the angle between the normal vector of the flank and the normal vector of the cutting plane: \u03b1n = arccos n (2) f \u00b7 n (2) c \u2223\u2223n (2) f \u2223\u2223 \u00b7 \u2223\u2223n (2) c \u2223\u2223 (21) A numerical example of work rake and relief angles calculation is carried out, which is aimed at investigating the geometrical performance of the cutter tooth in gear skiving",
            " sh The chip flow direction on the rake face and the shear force direction of the chip on the shear plane can be defined by the chip flow angle \u03b7c and the shearing direction angle \u03b7s , respectively [22] : tan \u03b7s = tan \u03bc sin \u03b7c cos ( \u03c6n \u2212 \u03b3n ) \u2212 tan \u03bc sin ( \u03c6n \u2212 \u03b3n ) cos \u03b7c (22) where, the angle \u03b7c can be calculated by the following implicit equation: cos ( \u03c6n \u2212 \u03b3n ) sin \u03c6n sin \u03b7c \u2212 tan \u03bbs cos 2 ( \u03c6n \u2212 \u03b3n ) cos \u03b7c + cos \u03b3n tan \u03bc sin \u03b7c cos \u03b7c \u2212 sin ( \u03c6n \u2212 \u03b3n ) sin \u03c6n tan \u03bc sin \u03b7c cos \u03b7c + tan \u03bc tan \u03bbs sin ( \u03c6n \u2212 \u03b3n ) cos ( \u03c6n \u2212 \u03b3n ) cos 2 \u03b7c = 0 (23) where, \u03bc is the mean friction angle at the tool-chip interface and n is the normal shear angle which can be determined by: \u03c6n = \u03c0 4 \u2212 \u03bc 2 + \u03b3n 2 (24) The inclination angle \u03bbs of the cutting edge at the cutting point can be obtained as the angle between the cutting velocity and the normal cutting velocity: \u03bbs = arccos v (2) cw \u00b7 v (2) n \u2223\u2223v (2) cw \u2223\u2223 \u00b7 \u2223\u2223v (2) n \u2223\u2223 (25) We suppose the material is incompressible when passing through the shear plane, so the chip flow speed can be ex- pressed as: v c = v cz cos \u03b7c = sin \u03c6n cos ( \u03c6n \u2212 \u03b3n ) cos \u03b7c \u00b7 v n (26) The shear stress distribution on the shear plane is considered as uniform. Then the shear force can be expressed as: F s = \u03c4 \u00b7 A c cos \u03c6n (27) where, \u03c4 is the shear strength of the material of the workpiece and A c is area of the chip section of the cutting edge element as shown in Fig. 2 (a). The forces F cs and F cr , exerted on the chip from the shear plane of the workpiece and the rake face of the tool, can be expressed respectively in S s and S r as: F cs = [ \u2212F s cos \u03b7s F s sin \u03b7s N s ]T (28) F cr = [ N c \u2212F r sin \u03b7c \u2212F r cos \u03b7c ]T (29) Transformed to the base S n , the forces F cs and F cr can be expressed respectively as: F (n ) cs = M ns \u00b7 F cs = \u23a1 \u23a3 F (n ) cs _ x F (n ) cs _ y F (n ) cs _ z \u23a4 \u23a6 = [ \u2212F s cos \u03b7s cos \u03c6n \u2212 N s sin \u03c6n F s sin \u03b7s \u2212F s cos \u03b7s sin \u03c6n + N s cos \u03c6n ] (30) F (n ) cr = M nr \u00b7 F cr = \u23a1 \u23a3 F (n ) cr _ x F (n ) cr _ y F (n ) cr _ z \u23a4 \u23a6 = [ N r cos \u03b3n + F r cos \u03b7c sin \u03b3n \u2212F r sin \u03b7c N r sin \u03b3n \u2212 F r cos \u03b7c cos \u03b3n ] (31) where, M ns is the transfer-matrix from S s to S n and M nr is the transfer-matrix from S r to S n M ns = [ cos \u03c6n 0 \u2212 sin \u03c6n 0 1 0 sin \u03c6n 0 cos \u03c6n ] (32) M nr = [ cos \u03b3n 0 \u2212 sin \u03b3n 0 1 0 sin \u03b3n 0 cos \u03b3n ] (33) The equilibrium of the forces applied to the chip in a stationary process can be expressed in S n as: F (n ) cs + F (n ) cr = 0 (34) Thus the normal forces N s , N r and the friction force F r , exerted on the chip from the shear plane of the workpiece and the rake face of the tool, can be expressed in S n as: F r = F s \u00b7 sin \u03b7s sin \u03b7c (35) N s = F s \u00b7 cos \u03b7s sin ( \u03c6n \u2212 \u03b3n ) + F s \u00b7 sin \u03b7s cot \u03b7c cos ( \u03c6n \u2212 \u03b3n ) (36) N r = \u2212F s \u00b7 cos \u03b7s cos \u03c6n + N s \u00b7 sin \u03c6n + F r \u00b7 cos \u03b7c sin \u03b3n cos \u03b3n (37) The cutting graph in gear skiving with single-feed technique is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002792_36007-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002792_36007-Figure1-1.png",
        "caption": "Fig. 1: (Colour on-line) (a) A solid nematic cylindrical shell alters its length and radius to accommodate in a stress-free way changes when the director field aligned along these directions. (b) If the director field is tilted by \u03b8 to the azimuthal (\u03c6) direction, the shell must change its topology, here for example by tearing itself along the length (z) direction, in order to find a stress-free configuration.",
        "texts": [
            "edu We analyse here shells of non-trivial topology \u2014cylinders, tori and spheres\u2014 adorned with in-plane director fields that are either simple or defected, depending in part on the topology of the underlying surface. Global topology will play an essential role, giving rise to elastic stresses even if there is local elastic compatibility everywhere. There are similarities with the intervention of topology in crystallography on the surface of a sphere [4]. Cylinders and tori. \u2013 Consider a cylindrical nematic solid shell with n\u0302 azimuthal, see fig. 1(a). Cooling elongates a circumference by \u03bb and hence equally the cylinder\u2019s radius. The length contracts by \u03bb\u2212\u03bd . There is no energy cost to these stretches/contractions, just a modified bending energy which we continue to neglect. However when n\u0302 is at an intermediate angle \u03b8 to the circumference, see fig. 1(b) where \u03b8= \u03c0/4, then the director and its perpendicular are along spirals of opposite chirality (and of equal pitch when \u03b8= \u03c0/4). Any change of the cylinder\u2019s radius or length to accommodate, say, \u03bb ruins that needed for \u03bb\u2212\u03bd in the other spiral and the cylinder will suffer internal stresses from its failure to attain the natural deformation. Specifically the in-plane deformation gradient would like to be \u03bb= ( \u03bb\u03c6\u03c6 \u03bb\u03c6z \u03bbz\u03c6 \u03bbzz ) = ( \u03bbc2+\u03bb\u2212\u03bds2 (\u03bb\u2212\u03bb\u2212\u03bd)sc (\u03bb\u2212\u03bb\u2212\u03bd)sc \u03bbs2+\u03bb\u2212\u03bdc2 ) , (2) where s= sin \u03b8 and c= cos \u03b8. However for non-zero shear \u03bbz\u03c6 the z displacement increases with increasing distance along the reference spatial direction given by \u03c6. After one 36007-p1 turn, the z displacement advances by 2\u03c0r0\u03bbz\u03c6 and fails by this much to match its starting z value at \u03c6= 0 \u2014an elastic incompatibility. This incompatibility can only be relieved by the cylinder changing its topology; it must be cut from top to bottom. An example of such a cut is in fig. 1(b), namely along the length of the deformed cylinder. Note that, because of the accompanying torsional shear \u03bb\u03c6z, this cut seen back in the reference state would be along a spiral. One can estimate the stress when there is no cut: an inverse shear of \u03bb\u2032z\u03c6 \u2212(\u03bb\u2212\u03bb\u2212\u03bd)sc must be applied to the relaxed state, the opened fig. 1(b), to restore it to the closed form, incurring thereby a stress \u03c3z\u03c6 = \u00b5\u03bb \u2032 z\u03c6, where \u00b5 is a shear modulus. The shear \u03bb\u2032z\u03c6 is correct only at linear order in \u03bb\u2212 1 due to non-linear geometrical effects in \u03bb\u22121 and there being partially compensating further relaxations in the other \u03bbij when \u03bb \u2032 z\u03c6 needs to be imposed. While still a cylinder, the shell will therefore only elongate or contract (\u03bbzz), change its girth (\u03bb\u03c6\u03c6) and suffer torsion (\u03bb\u03c6z) with changing \u03bb until the stored stress energy surpasses the cost of elastic failure and the cylinder tears itself apart, acting as a physical \u201cstress fuse\u201d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000600_02783640122067543-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000600_02783640122067543-Figure2-1.png",
        "caption": "Fig. 2. A roller wheel that allows free motion along its axis of rotation.",
        "texts": [],
        "surrounding_texts": [
            "We built a prototype MDMS in which each cell consists of a pair of orthogonally mounted motorized roller wheels (Figs. 2 and 3). These wheels are capable of producing a force perpendicular to their axes while allowing free motion parallel to their axes. The combined action of the two roller wheels effects force in any planar direction to an object resting on top of the array. Each of these cells is connected to a large breadboard-style base (Fig. 4) to create a regular array of manipulators. Currently, we have 18 cells that can be arranged at UCSF LIBRARY & CKM on April 19, 2015ijr.sagepub.comDownloaded from arbitrarily in a two-dimensional grid. A photograph of the prototype MDMS is shown in Figure 5 (see Extension 11). Each cell is controlled by an inexpensive single-board computer based on the MC68HC11 microcontroller. We are exploring the use of distributed control on the MDMS because we believe that it would become impractical or impossible for a single centralized controller to control hundreds or possibly thousands of cells. Each cell communicates with its four neighboring cells, allowing messages to be passed along the array. In addition, each cell contains one (or more) binary sensors to detect the presence of an object. Figure 6 shows this control architecture. 1. Please see the Index to Multimedia Extensions at the end of this article. at UCSF LIBRARY & CKM on April 19, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_10_0003402_j.ymssp.2015.04.006-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003402_j.ymssp.2015.04.006-Figure6-1.png",
        "caption": "Fig. 6. Modal model geometry for Operational Modal Analysis.",
        "texts": [
            " In the frequency range of interest (o500 Hz), in order to get higher circumferential mode number, a total of 300 points in five circles around the circumference of the tyre are considered for acceleration response measurements (60 nodes on each circle of the tyre). These output responses in x, y and z direction result in 900 signals. They are considered for further signal processing. Secondly, these output responses are communicated to LMS Test Lab software, as if they have been acquired from 300 triaxial accelerometers through a data acquisition system. Fig. 6 shows the modal model geometry used for modal extractionwhere all these 900 signals are mapped to this model. As the energy content of the travelling wave is more in the leading edge than the trailing edge, three sets of reference signals are chosen at the leading edge node point RTD60074; Table 1 represents the correlation of these reference signals with the response signals at the top of the tyre (CTD9041) and it is observed that vertical and longitudinal acceleration responses have good correlation with other measurement points and hence the point (RTD60074) responses are considered to be reference signals for crosspower sum calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001787_0094-114x(87)90010-3-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001787_0094-114x(87)90010-3-Figure1-1.png",
        "caption": "Fig. 1. A manipulator with m revolute joints.",
        "texts": [
            " The above oo 3 surfaces may sweep the entire volume in the positional space; thus, these may not exist in dextrous region. For certain special cases, such as the last three orthogonal revolute axes intersecting at a point, the oo 3 surfaces reduce to only one surface, since in equation (6) ~, fl and r are decoupled from X, Y and Z. The Jacobians for various mappings are given in the Appendix. 4. BOUNDARY SURFACES OF THE WRIST CENTER Let us consider a manipulator with m revolute joints, as shown in Fig. 1. Let the rigid body space consist of three coordinates of the origin of the last link (wrist center). Let us use the necessary condition from Theorem 2. The (3 \u00d7 m) Jacobian matrix of the mapping is of a rank less than 3 at the boundary. We consider the location of the wrist center in a cartesian frame attached to the base. Since the three rows of the Jacobian matrix are dependent, it is obious that for these sets of 0 the instantaneous motion of the wrist center could not occur in all its immediate neighborhoods"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003477_978-3-319-18997-0_37-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003477_978-3-319-18997-0_37-Figure5-1.png",
        "caption": "Fig. 5 Sketch of the proposed tangent overlapping model (TOM)",
        "texts": [
            " While the requirements for the control of arc welding processes, including parameters such as metal transfer mode, welding current and arc voltage, have been discussed [12], the literatures concerning the method for determining the welding parameters that directly affect deposition shape, such as welding speed, wire feed-rate, and overlapping distance in WAAM, are relatively few. The geometry of a single weld bead as well as the multi-bead overlapping process is important for achieving high surface quality and dimensional accuracy on the fabricated parts. In order to accurately predict the shape of weld beads that are deposited adjacently, the cross sections of two neighboring beads are modeled using a Tangent Overlapping Model (TOM), shown in Fig. 5. The detailed TOM is introduced in our recent publication [27]. The overlapping center distance d is equal to the line space of the tool path. In addition, for a given weld bead, the overlapping center distance is correlated to the overlapping model. Let a single bead have a height h and width w; and the adjacent beads have a center distance d. The shape of the bead is modeled as an inverted parabola. The area of valley and overlapping area in adjacent beads are depicted in Fig. 5. The top of the valley is modeled as a straight line that is tangential to bead 2. The center distance d between adjacent beads will determine the surface quality and smoothness. When the center distance d is greater than the single bead width w, there is no overlap between the two adjacent beads. So the valley, overlapping area and tangent do not exist. As the center distance is decreased, the overlapping area in Fig. 5 increases, and the area of the valley decreases. As the center distance d decreases to a certain value d*, the overlapping area becomes equal to the area of the valley and the overlapped surface will become a tangent line. This condition produces maximum surface smoothness because there is no valley between adjacent beads. The bead height h is effectively the WAAM layer thickness. With a further decreasing of d, excessive overlapping area leads to an increased thickness of the deposited layer and decreased surface smoothness",
            " In model development experiments conducted as part of this study, combinations of 5 m/min wire feeding rate and 8 different travel speeds were conducted. Based on the experimental data shown in Fig. 7, when the wire-feed rate is fixed at 5 m/min, a second order polynomial model was generated for bead width w as a function of welding speed Vw as, W \u00bc 10:15V2 w 21:863Vw \u00fe 16:162 \u00f00:2 Vw 1\u00de \u00f02\u00de For certain wire-feed rate Vf and overlapping distance d, Vw could be solved by combining Eqs. (1) and (2). Layer thickness h, or bead height in Fig. 5, is expressed as h \u00bc Abead d \u00bc pVfD2 w 4Vwd : \u00f03\u00de where, Dw is the diameter of the wire electrode, and A is the cross-sectional area of a single weld bead. Through using the procedures described in this section, the welding parameters that are required for each layer of the WAAM component can be readily determined. From specifying the wire-feed rate and welding speed that are needed to meet the user-specified line space and simultaneously optimize the surface smoothness of each layer, the layer thickness can be determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003919_tac.2015.2398880-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003919_tac.2015.2398880-Figure1-1.png",
        "caption": "Figure 1. Accelerated twisting controller",
        "texts": [
            " Without that condition the problem is unsolvable by controls bounded in a vicinity of the manifold \u03c3 = \u03c3\u0307 = 0. In the following we do not consider such real-life phenomena as actuator saturation effects, which would exclude any significant convergence acceleration. Meantime, until Section VI \u03c3, \u03c3\u0307 are assumed to be available in real time. B. Exact problem formulation and structure of its solution Consider the twisting controller [13] of the form u = \u2212\u00b5\u03b1 sign \u03c3 if \u03c3\u03c3\u0307 \u2264 0, \u2212\u03b1 sign \u03c3 if \u03c3\u03c3\u0307 > 0, (4) where \u00b5 < 1 is some fixed number. Its trajectory in the plane \u03c3, \u03c3\u0307 is qualitatively shown in Fig. 1a. With \u03b1 > C/(\u00b5Km) the function \u03c3(t) oscillates [13], and the trajectories rotate around the origin. The trajectory starts at the point (\u03c30, \u03c3\u03070) at the moment t0. The intersections \u03c3k, k = 1, 2, ..., of the trajectory with the \u03c3-axis correspond to local extrema of \u03c3 at the time instants tk. The respective intersections of the trajectory with the \u03c3\u0307-axis in the time range (tk, tk+1) are denoted \u03c3\u0307k (Fig. 1a). Note that with k > 0 the values \u03c3k and \u03c3\u0307k correspond to different time instants. Describe the prescribed convergence rate by a positivedefinite strictly growing convergence-rate function T (s) \u2265 0, T (0) = 0, determining an upper bound of the convergence time to \u03c3 = \u03c3\u0307 = 0 from the moment when |\u03c3| = s, \u03c3\u0307 = 0 (Fig. 1b). Let T0 = lim s\u2192\u221e T (s). Allow the value T0 = \u221e to include the case of finite-time, but not fixed-time convergence. The inequality 0 < T0 < Tmax is assumed, if the fixedtime convergence in time not exceeding Tmax is required. For example, one can use the function T (s) = T0 ( 1\u2212 1 s+1 ) . The problem is to provide for the needed convergence rate by properly changing the coefficient \u03b1 at each intersection \u03c3k of the trajectory with the \u03c3-axis at the times tk, k = 1, 2, .... The transient is divided into three stages: the preliminary one, when \u03c3\u0307 is steered to zero for the first time; the twistingacceleration stage, when \u03b1 is regulated providing for the needed convergence rate; and the final stage from the moment, when a threshold condition |\u03c3| \u2264 \u03c3th, \u03c3\u0307 = 0 is detected for the first time",
            " The parameter \u03c3th > 0 is assigned in advance. At the final stage the standard twisting controller is applied to complete the task, if the predefined convergence rate T (s) requires unfeasibly large or infinite control, as \u03c3 approaches 0. The following stage description is relevant for the three-stage and two-stage algorithms of Sections III and IV, where the corresponding formulas are proved. 1) The preliminary stage: The trajectory of the system starts with the initial conditions \u03c30 = \u03c3(t0), \u03c3\u03070 = \u03c3\u0307(t0) (Fig. 1a). The control u = \u2212\u03b10 sign \u03c3\u0307, t \u2208 [t0, t1), \u03b10 > 0, (5) forces the trajectory to reach the axis \u03c3\u0307 = 0 at some point \u03c31 = \u03c3(t1) in the time \u2206t0 = t1 \u2212 t0, which can be made as Preprint submitted to IEEE Transactions on Automatic Control. Received: January 28, 2015 13:53:37 PST 0018-9286 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. small as needed by a proper choice of \u03b10. 2) The main stage. Twisting acceleration: The control takes the form u = { \u2212\u00b5\u03b1k sign\u03c3 if\u03c3\u03c3\u0307 6 0, t \u2208 [tk, tk+1) \u2212\u03b1k sign\u03c3 if\u03c3\u03c3\u0307 > 0, k = 1, 2, ... (6) Choose the parameter \u00b5, define a function \u03c9\u2217, 0 < \u00b5 < Km/KM , \u03c9\u2217(\u03b1) = \u00b5\u03b1KM + C \u03b1Km \u2212 C , (7) and fix some \u03b1\u2217, such that \u03c9\u0303 = \u03c9\u2217(\u03b1\u2217) < 1, \u03b1\u2217 > C \u00b5Km . (8) Define the function \u2206T (s) = T (s)\u2212 T (\u03c9\u0303s), s > 0, (9) to provide upper estimates of the time periods tk+1 \u2212 tk with tk+1 = s. The value \u03b1k > \u03b1\u2217 is assigned at the moment tk (Fig. 1b) so as to ensure that tk+1 \u2212 tk \u2264 \u2206T (|\u03c3k|), which results in \u03b1k = max{\u03b1\u2217, 2Q2|\u03c3k|\u2206\u22122 T (|\u03c3k|) with |\u03c3k| > \u03c3th, Q = \u221a \u00b5KM+ C \u03b1\u2217( \u00b5Km\u2212 C \u03b1\u2217 ) + \u221a \u00b5KM+ C \u03b1\u2217( Km\u2212 C \u03b1\u2217 ) . (10) 3) Final stage. Standard twisting: The standard twisting controller (4) with constant \u03b1 = \u03b1th \u2265 \u03b1\u2217 is applied, if the main stage yields unfeasible control magnitudes, as the trajectory approaches the origin. This stage starts at the moment tkth , when the condition |\u03c3k| \u2264 \u03c3th is detected for the first time. It is further shown that Tth = \u221a 2(\u03b1thKM+C)\u03c3th (1\u2212 \u221a \u03c9\u0303) ( 1 (\u00b5\u03b1thKm\u2212C) + 1 (\u03b1thKm\u2212C) ) (11) is a corresponding upper estimation of the residual convergence time",
            " The inequalities |\u03c3k+1| \u2264 \u03c9\u0303|\u03c3k|, tk+1 \u2212 tk \u2264 \u2206T (|\u03c3k|) are ensured for all k = 1, 2, ..., kth. As the result, \u03c42 \u2264 T (|\u03c31|) \u2264 T0 holds. Proof: It is proved in [13] that |\u03c3k+1/\u03c3k| \u2264 \u03c9\u2217(\u03b1k). Thus (7) and (8) imply |\u03c3k+1/\u03c3k| \u2264 \u03c9\u0303 < const < 1 and so the algorithm convergence. Furthermore, tk+1 \u2212 tk can be estimated [13] as tk+1 \u2212 tk \u2264 \u221a 2(\u00b5KM\u03b1k+C)|\u03c3k| (\u00b5Km\u03b1k\u2212C) + \u221a 2(\u00b5KM\u03b1k+C)|\u03c3k| (Km\u03b1k\u2212C) . (15) Calculations show that (15), (10) imply \u2206T (|\u03c3k|)\u221a 2|\u03c3k| \u2265 Q 1\u221a \u03b1k , which in its turn implies tk+1\u2212tk \u2264 \u2206T (|\u03c3k|). Thus (10) and monotonicity of T (s) ( Fig. 1b) imply \u03c42 \u2264 \u2211 k \u2206T (|\u03c3k|) = T (|\u03c31|) \u2264 T0. Lemma 2. The final-stage time duration \u03c43 satisfies \u03c43 \u2264 Tth. Proof: Obviously \u03c43 \u2264 \u2211( |\u03c3\u0307kth+j | \u00b5\u03b1thKm\u2212C + |\u03c3\u0307kth+j | \u03b1thKm\u2212C ) , Preprint submitted to IEEE Transactions on Automatic Control. Received: January 28, 2015 13:53:37 PST 0018-9286 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. j = 0, 1, .",
            " Obviously, similarly to Sections III, IV, one can find values of \u00b5 and \u03c1 so as to satisfy an explicit time restriction. Let now only the sampled values \u03c3\u0302(t) = \u03c3(t) + \u03b7(t) be available. The noise \u03b7(t) is assumed bounded and Lebesguemeasurable, |\u03b7(t)| \u2264 \u03b5. The time instants tk, k > 0, are detected as the moments, when the \u03c3 increment between successive samplings changes sign. The corresponding detection errors do not destroy the robust algorithm performance, for \u03b1 is locally bounded and the rotation motion persists (Fig. 1a). Due to a piece-wise constant upper bound on |\u03c3\u0308|, a fixedtime differentiator [7] can be applied, theoretically providing for the global possibly-fixed-time stable output-feedback controller. Unfortunately, its discrete-sampling version is not feasible for large initial errors [15]. In the following we construct a robust output-feedback controller. Preprint submitted to IEEE Transactions on Automatic Control. Received: January 28, 2015 13:53:37 PST 0018-9286 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000593_jsvi.2000.3412-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000593_jsvi.2000.3412-Figure1-1.png",
        "caption": "Figure 1. Engagement relations of gear coupling.",
        "texts": [
            " Regarding the vibration problems of a multirotor system connected by a coupling, Xu and Maranfoni [11] developed a theoretical model of a motor-#exible coupling-rotor system recently; the universal joint e!ects were included in the model to take the misalignment e!ects into account. In this paper, the non-linear dynamic model for a rotor-bearing-gear coupling system is developed based on the engagement conditions of gear coupling, and the phenomena of lateral}torsional vibration of the system under the improper aligning are presented. 2. CONSTRAINT EQUATION FOR A GEAR COUPLING Figure 1 shows an involute tooth pro\"le and the engagement relations between the hub and the sleeve of a gear coupling. O i m i g i f i is the moving co-ordinate system, \"xed with the sleeve. Omgf is the rotating co-ordinate system, f-axis coincides with the axis of the rotor in a static equilibrium state. The co-ordinate transformations of the two systems may be expressed as m\"m i cos(c#h i )!g i sin(c#h i )#m ji , g\"m i sin(c#h i )#g i cos(c#h i )#g ji . (1) Let O e m e g e f e denote the moving co-ordinate system, \"xed with the hub of the gear coupling: m\"m e cos(c#h e )",
            " (11) Substituting equations (6) and (8) into the second condition (V p !V p{ ) ) n i \"0, it reads as (mQ p !mQ p{ ) [r b c i sin(h i #c i #c)]#(gR p !gR p{ )[!r b c i cos(h i #c i #c)]\"0 (12) Using equation (11), equation (12) then becomes r b (hQ ji !hQ je )!(mQ ji !mQ je ) sin(h i #c i #c)#(gR ji !gR je ) cos(h i #c i #c)\"0. (13) Since the radii of base circles of the hub and the sleeve are equal, the tangent line of the two base circles (or engagement line) should be parallel to the line of centers of the base circles as shown in Figure 1, we can obtain b#n/2\"h i #c i #c\"h i #b i #a#c. (14) Thus, sin(h i #c i #c)\"cosb\"(m ji !m je )/J(m ji !m je )2#(g ji !g je )2, cos(h i #c i #c)\"!sinb\"!(g ji !g je )/J(m ji !m je )2#(g ji !g je )2, (15) where b is the angle between the line of centers and m direction. Substituting equation (15) into equation (13), it can be expressed as r b (hQ ji !hQ je )\" (m ji !m je ) J(m ji !m je )2#(g ji !g je )2 (mQ ji !mQ je )# (g ji !g je ) J(m ji !m je )2#(g ji !g je )2 (gR ji !gR je ). (17) Integrating the above equation, \"nally we can obtain r2 b (h ji "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000722_1.2794209-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000722_1.2794209-Figure9-1.png",
        "caption": "Fig. 9 Initial conditions for a periodic solution for quadruped bound",
        "texts": [
            " The body pitch will now become zero at the middle of the phase and then decrease to a negative value at the end of the aerial phase. At the beginning of the second stance phase, the angular velocity of the body will be negative. The front legs will apply a positive moment on the body. Thus at the end of that stance phase, the angular velocity will be positive, the pitch angle will be negative and the above cycle will be repeated. The above discussion gives the conditions at the middle of the stance phase. The configuration of the quadruped at the middle of the stance phase is shown in Fig. 9. The rear legs are compressed and the body is given some initial horizontal veloc- 470 / Vol. 117, NOVEMBER 1995 Transactions of the ASME Downloaded From: http://biomechanical.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ity. The angular velocity of the body is set to zero, and the body is given some inclination. There are three unknown initial conditions. These are the compression in the spring, the speed in the ;c-direction and the angle of the body with the j;-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002486_1.4004225-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002486_1.4004225-Figure2-1.png",
        "caption": "Fig. 2 The 6R double-centered overconstrained mechanism with arbitrary axis intersection angle",
        "texts": [
            " Applying the homogeneous transformation [40], a closed-loop equation can be obtained as H1 H2 H3 H4 H5 H6 \u00bc I (1) Equation (1) can be rearranged as follows: H1 H2 H3 \u00bc H 1 6 H 1 5 H 1 4 (2) Since the focus is on the 6R double-centered mechanism, it is assumed that axes z3, z4, and z5 intersect at a point to form one center and the axes z6, z1, and z2 intersect at another point to form the second center. This arrangement assigns zero to the axis perpendicular-link parameters a1, a3, a4, and a6 and the axial link parameters d1 and d4 as a6 \u00bc d1 \u00bc a1 \u00bc 0; a3 \u00bc d4 \u00bc a4 \u00bc 0 (3) and leads to forming the 6R double-centered overconstrained mechanisms in Fig. 2, with two remaining axis perpendicular-link parameters a2 and a5, four axial link parameters d2, d3, d5, and d6, and axis intersection-angles d1 to d6. In this arrangement, instead of orthogonal intersection of adjacent axes in the current available 6R overconstrained mechanisms, the intersection angels di can be of any value. Substituting the parameters of the double-centered mechanisms in Eq. (3) to Eq. (2) yields 031004-2 / Vol. 3, AUGUST 2011 Transactions of the ASME Downloaded From: http://mechanismsrobotics",
            " This gives the determinant as 4 1\u00fe x2 3 2 K4x4 3 \u00fe K3x3 3 \u00fe K2x2 3 \u00fe K1x3 \u00fe K0 \u00bc 0 (43) where K0 to K4 are functions of the obtained motion parameters h1, h2, and h6 with given input angle h2. The equation hence gives the motion parameter h3. Substituting the obtained motion parameters h1, h3, and h6 to Eq. (38) yields the angle h5. The last motion parameter h4 can further be obtained by substituting the above obtained motion parameters into Eq. (10). Hence, the closed-form solutions of angles h1 and h3 to h6 are obtained in terms of h2. This gives the joint-space solution. A numerical example is given to confirm the mobility of a general double-spherical linkage in Fig. 2. Set the link and axis 031004-6 / Vol. 3, AUGUST 2011 Transactions of the ASME Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use parameters of the 6R double-spherical overconstrained mechanism with nonorthogonal axis intersection-angles as a1 \u00bc 0; a2 \u00bc 40; a3 \u00bc 0; a4 \u00bc 0; a5 \u00bc 20:3263; a6 \u00bc 0 d1 \u00bc 7p=8; d2 \u00bc 3p=8; d3 \u00bc 2p=8; d4 \u00bc 6p=8; d5 \u00bc 2p=8; d6 \u00bc p=8 d1 \u00bc 0; d2 \u00bc 70; d3 \u00bc 30; d4 \u00bc 0; d5 \u00bc 60; d6 \u00bc 40 The above parameters satisfy the category 3 Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003268_9783527697489.ch12-Figure12.3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003268_9783527697489.ch12-Figure12.3-1.png",
        "caption": "Figure 12.3 The basic elements of a multilayered electrode.",
        "texts": [
            " Of course, lower volume percentages of inert binder can be used if some of the dead volume is packed with smaller particles of the conducting material (fines). Indeed, if the fines are equally sized among themselves, then the revised dead volume falls to 13% (i.e., 36% of 36%) and the volume percentage of inert binder that is needed to create a functioning porous electrode falls to 6.5%. At the other extreme, a volume percentage of binder higher than 18% could conceivably be used, but this would also increase the electrical resistance of the electrode. 12.16 The basic elements of a multilayered electrode are shown in Figure 12.3. Each part has its own design specification, depending on end use. First, electrode materials have to withstand both oxidizing and reducing conditions. Second, total electrode resistance should be below 10\u03a9 to minimize errors associated with IR drop. Third, electrodes must have electroactive areas which are reproducible within 5% coefficient of variation. Fourth, during manufacture, all materials must withstand repetitive thermal cycling to T > 110 \u2218C. Fifth, all the electrode materials must be mutually adhesive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001641_jb.171.6.3560-3563.1989-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001641_jb.171.6.3560-3563.1989-Figure2-1.png",
        "caption": "FIG. 2. Construction of microscopic chambers. s, Glass microscopy slide; p, bent Pasteur pipette tip; f, plastic frame; V, general view, when assembled and sealed.",
        "texts": [
            " majus became evident after several weeks. Samples from the raw enrichments were pipetted and placed in filter-sterilized seawater, where swarms of cells swam from the pieces of veil and congregated in certain areas. There, they were repipetted and transferred to the experimental vessels. Glass vials (3-ml capacity) or spectrophotometric cuvettes (with sulfide-agar plugs, when gradients were to be created) were used to reproduce and study bioconvective patterns. Microscopic chambers, as depicted in Fig. 2, were constructed for video microscopy of the cells and patterns. The chamber was filled with seawater, and a bubble of H2S gas was created at the bottom by carefully injecting the gas through the pipette with a syringe. After inoculation and monitoring of cell behavior, movement of the cells could be microscopically recorded. Cell velocities were calculated in recordings of preparations not undergoing bioconvection by tracing trajectories of single cells on the television screen, monitoring them frame by frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000618_s0013-4686(00)00373-x-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000618_s0013-4686(00)00373-x-Figure2-1.png",
        "caption": "Fig. 2. Current-time curves for the PyOx-based electrode by addition of different activities of GPT. GPT activities are given in U l\u22121.",
        "texts": [
            "7 mA cm\u22122 mM\u22121 in the concentration range). The detection limit was 50 nM (signal-to-noise ratio, 3). The relative standard deviation for ten successive measurements of 50 mM pyruvic acid was 2.0%. When 1 U l\u22121 GPT was added into the test solution containing L-alanine and 2-oxoglutaric acid, pyruvic acid was produced with a rate of 1 mM min\u22121. From the performance characteristics of the enzyme electrode for pyruvic acid, we can expect that the addition of 1 U l\u22121 brings about a current increase with a slope of 51.7 nA cm\u22122 min\u22121. Fig. 2 shows the enzyme electrode response upon the addition of 0.5\u20135 U l\u22121 GPT. The electrode current increased linearly with time from 30 s, and the current-increasing rate was proportional to the activity. The value of current-increasing rate/enzyme activity obtained from the experimental results was 51.0 nA cm\u22122 min\u22121 U\u22121 l, which was very close to the value expected from the pyruvate response. This means that, for determining GPT activities, only a calibration for pyruvic acid is needed and that for GPT itself can be omitted: this would be useful in practice"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001390_j.mechmachtheory.2005.09.004-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001390_j.mechmachtheory.2005.09.004-Figure3-1.png",
        "caption": "Fig. 3. Coordinate systems for worm gear mesh.",
        "texts": [
            " The instantaneous contact line on the gear tooth surface, for a prescribed value of the rotational angle of the worm, ww, is defined by ~r \u00f0g\u00de g \u00bcMg M0 Mw r\u00f0w\u00dew \u00bcMwg ~r\u00f0w\u00dew ; ~n \u00f0w\u00de w ~v \u00f0w;g\u00de w \u00bc 0; \u00f013\u00de where matrix Mwg transforms the coordinates from system Kw (attached to the worm) into the system Kg (attached to the gear),~n\u00f0w\u00dew is the normal vector of the worm surface, and~v\u00f0w;g\u00dew is the relative velocity vector of the worm to the gear. The equations for vectors~n\u00f0w\u00dew and~v\u00f0w;g\u00dew are similar to Eqs. (11) and (12), only the elements of vector~r\u00f0w\u00dew and its derivative should be substituted instead of vector~r\u00f0h\u00deh and its derivative. Matrices, Mg, M0 and Mw are defined by the following equations (based on Fig. 3) Mg \u00bc cos wg 0 sin wg 0 0 1 0 0 sin wg 0 cos wg 0 0 0 0 1 2 6664 3 7775; \u00f014\u00de M0 \u00bc cos ev 0 sin ev a sin ev sin eh cos eh cos ev sin eh Dy sin ev cos eh sin eh cos ev cos eh 0 0 0 0 1 2 6664 3 7775; \u00f015\u00de Mw \u00bc cos ww sin ww 0 0 sin ww cos ww 0 0 0 0 1 0 0 0 0 1 2 6664 3 7775; \u00f016\u00de where wg \u00bc Nw Ng ww. As it was mentioned before, in mismatched (modified) worm gears point contact of the meshing worm thread and gear tooth surfaces appears. In the instantaneous contact point the common normal vector of the contacting surfaces exists, and the generation equations of the worm surface by the grinding wheel and of the gear tooth surface by the hob are satisfied",
            " 6\u20138 show the pressure distributions for 21 instantaneous positions of rotating members through a mesh cycle, with three tooth pairs ct pressure. instantaneously in contact in all these 21 mating positions, for a worm gear with fully conjugated tooth surfaces (Fig. 6) and for worm gear pairs with 20 lm (Fig. 7) and +20 lm (Fig. 8) tooth spacing errors. In the case of fully conjugated gear teeth the influence of the angular worm shaft misalignment, ev, in the vertical plane (i.e. in the middle plane of the gear, see Fig. 3) on maximal tooth contact pressure is moderate (Fig. 9, Dd = 0), but for mismatched worm gear pairs (due to Dd = 2%, 5% hob oversizes) the pressures are considerably effected by this angular shaft misalignment. The transmission errors are slightly reduced by hob oversize for negative values of angle ev (Fig. 10), but for its positive values the hob oversize increases the angular displacement of the gear member, i.e. the transmission error. By the comparison of pressure distributions in fully conjugated worm gears for different values of shaft misalignment angle, ev, (Figs. 6, 11 and 12), it can be noted that its influence on pressures is negligible. In the case of positive values of angular worm shaft misalignments in the horizontal plane, that means in the plane passing through the worm axis and parallel to the gear axis (eh in Fig. 3), the maximal tooth contact pressure and the transmission errors can be considerable reduced by the modification of gear tooth surface introduced by the use of an oversized hob (Figs. 13 and 14). Also it can be seen that for negative values of angle eh the influence of gear tooth modifications is negligible. Figs. 15 and 16 show the tooth contact pressure distributions for fully conjugated worm gears in the case of angular misalignments in the horizontal plane of eh = 0.1 and eh = 0.1 , respectively. In Figs. 17\u201320 it can be seen that the worm gears are very sensitive to the axial offset (Dy in Fig. 3) of the wheel. In the case of positive values of the offset the maximal tooth contact pressure and the transmission errors can be considerably reduced by gear tooth surface modifications introduced by the use of an oversized hob, but for negative values of offset Dy the modifications have a slight counter-effect. Even for small values of the offset (Dy = \u00b10.1 mm) edge contact occurs with very inconvenient, unbalanced pressure distributions (Figs. 19 and 20). Because of that the axial adjustment of the gear should be made very carefully"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003033_s00170-012-4406-7-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003033_s00170-012-4406-7-Figure4-1.png",
        "caption": "Fig. 4 Tool movement and vectors",
        "texts": [
            " Any difference in the CL data and the corresponding NC data will directly affect engagement boundaries of the tool with the workpiece and the resulting cutting force. Most of the existing interpolation methods [5, 6] are linear and interpolation of tool orientation vectors is not accurate in these approaches. Here a spherical interpolation scheme for more accurate interpolation of the tool axis vectors is introduced. In five-axis machining, the tool can rotate as well as translate as shown in Fig. 4. Therefore, during translation tool axis rotates from Ti ! toTi\u00fe1 ! around an arbitrary axis ki ! an amount of \u0394\u03b8 where rotation axis is both orthogonal to Ti ! and Ti\u00fe1 ! . Rotation axis ki ! and rotation angle \u0394\u03b8 are calculated as, ki !\u00bc kx ky kz 8< : 9= ; \u00bc Ti ! T ! i\u00fe1 T ! i T ! i\u00fe1 \u0394\u03b8 \u00bc atan2 T ! i T ! i\u00fe1 Ti ! T ! i\u00fe1 0 @ 1 A \u00f015\u00de Considering the translation and rotation in the tool axis, cutter location points are interpolated linearly and the orientation vectors are interpolated spherically where m changes from 0 to 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001630_robot.1987.1087758-Figure1.1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001630_robot.1987.1087758-Figure1.1-1.png",
        "caption": "Figure 1.1. Finding the mounting position of a camera by solving a homogeneous transform equation of the form AX=XB, where A is the robot motion, B is the resulting camera motion, and X is the cam-",
        "texts": [],
        "surrounding_texts": [
            "sensor. This yields a homogeneous transform equation of the moving the robot and observing the resulting motion of the form AX=XB, where A is the change in T, due to the a rm movement, B is the resulting sensor displacement, and X is the sensor position relative t o T,. A and B are known, since A can be computed from the encoder values and B can be found by the sensor system. The solution to an equation of this form has one degree of rotational freedom and one degree of translational freedom. In order t o solve for X (the sensor position) uniquely, it is necessary t o make two arm moveA,X=XB, and A,X=XB,. A closed-form solution to this sysments and form a system of two equations of the form: tem of equations is presented. The necessary condition for a unique solution is that the axes of rotation of A, and A, are neither parallel or antiparallel to one another. The theory is supported by simulation results.\n1. Introduction\ntransform equation of the form A X = X B, where A are B are The investigation into the solution of the homogeneous known and X is unknown, is motivated by a need t o solve for the position between a wrist-mounted sensor and the manipulator wrist center (T,).\nMuch research has been done on using a sensor t o locate an object. The three-dimensional position and orientation of an ob'ect can be found by monocular vision, stereo vision, denselsparse range sensing, or tactile sensing. Monocular vision locates an object using a single view, and the object dimensions are assumed to be known aprlori [2,6,8,10,13,22,29,31,32]. Stereo vision uses two views instead of one so that the range information of feature points can.be found [1,6,12,14,20,24,32]. A dense range sensor scans a reglon of the world and there are as many sensed points as i ts resolution allows [3,7,17,25]. A sparse range sensor scans only a few points, and If the sensed points are not sufficient to locate the object, additional points will be sensed [5,15,16]. Tactile sensing is similar to sparse range sensing In that i t obtains the same information: range and surface normal of the sensed points [4,15,16].\nA sensing system refers to object positions with respect t o a coordinate frame attached to the sensor, but robot the sensor information for a robot task, the relative position motions are specified by the wrist positions. In order t o use between the sensor and the wrist must be known.\nobstacles to obstruct the measurement path, the points of Direct measurements are difficult because there may be interests may be inside a solid and unreachable, and the coordinate frames may differ in their orientations. The measurement path can be obstructed by the geometry of the sensor or frames that are unreachable includes T, and the camera the robot, the sensor mount, wires, etc. The coordinate frame: T, is unreachable because it is the intersection of three link axes, the camera frame is unreachable because its\nCH2413-3/87/0000/1666$01.00 0 1987 IEEE\norigin is at the focal point, inside the camera. Instead of direct measurement, we can compute the camera position by displacing the robot and observing the changes in the sensor frame using the sensor system. This method works for any sensors capable of finding the three-dimensional position and orientation of an object. Figures 1.1 and 1.2 show the cases of sors. In both examples, a homogeneous transform equation of a monocular vision system and a robot hand with tactile senthe form A X=X B is formed, where A is the movement of the robot, B is the resulting displacement of the sensor, and X is the unknown transform between the sensor and the robot wrist. Let T,] and Te2 be the robot wrist positions before and after the motion, respectively. Since T,I and TB2 can be calculated by the robot controller from the joint encoder values, A can be calculated by A=T,]-lT,? Similarly, if OBJ, and OBJ, are the object positions wlth respect ot the sensor before and after the motion, the displacement of the sensor can be calculated by B=OBJ,OBJ,-l.\nera mounting position.\nAX=XB. A is the robot motion, B is the resulting motion of the hand coordinate frame, and X is the mounting position of the hand.\n1666",
            "Matrix equations of the form A X = X B have been discussed in linear algebra [ll]; however, no known work has been done for homogeneous transform equations, in which case the matrices are much more restricted and a geometric interpretation is desired. Using Gantmacher\u2019s method, the solution to the 3x3 rotational part of X (R,) is any linear combination of n linearly independent matrices: R,=k,M,+ * * . +k,Mn, where n is determined by properties of eigenvalues of RA and R, (rotational parts of A and B), k,, . . . ,kn are arbitrary constants, and M,, . . . M, are linearly independent matrices. Gantmacher\u2019s solution IS for general matrices; the given solution may not be a homogeneous transform. To restrict the solution to homogeneous transforms, we must impose the conditions that the 3x3 rotational part of the solution be orthonormal and that the righthanded screw rule is satisfied. These restrictions will result in non-linear equations in terms of k , . . . k,. There are many disadvantages using this method: (1) Only iterative solutions are possible, since non-linear equations are involved. (2) Iterasolutions. Different initial estimates will converge to different tive solutions are not useful when there are infinite number of solutions, and it is not possible to generalize the solutions. (3) The solution cannot be expressed symbolically. (4 Geometric interpretation of the solution is not possible an d the conditions for uniqueness cannot be specified in geometrical terms.\nArbitrary Axis 2. Homogeneous T r a n s f o r m s and Rotation about an\nHomogeneous transforms [28 can be viewed as the relative position and orientation o i a coordinate frame with respect to another coordinate frame. The lements of a homogeneous transform T\nLo 0 0 1 1 We also denote [nX,ny,nzlT as a, [ o ~ , o ~ , o , ] ~ as 0, and [aX,ay,a,lT as a. n, 0, and a can be interpretated as unit vectors which indicate the x, y , and z directions of coordinate frame T; p can be viewed as the origin of T. The vectors n, 0, a and p are referenced with respect t o a frame represented by a transform to which T is post-multiplied. If there is no frame to the left of T, then n, 0 , a, and p will be vectors relative to the world or absolute frame.\nWe will refer to the upper-left 3x3 submatrix of T as the\norientation of the coordinate frame. A rotational submatrix rotational submatrix since it contains information about the can be expressed as a rotation around an arbitrary axis. From [28], the matrix representing a right-hand-rule rotation of 0 around an axis [kX,ky,k,lT is :\n1 kxkxvers8+cos8 kykxversO-k,sinO k,k,vers0+kysin8\nRot(k,B)= kxkyversO+k,sinO kykyversO+cos8 k,kyversO-kxsinO\nkxk,vers8-k,sin0 k,k,versO+k,sinO k,k,versO+cosO\nwhere verso = (1-cos0). (2.2)\nIn this paper, we will follow the convention tha t O<S<r. From Paul\u2019s text [28], we have the following two equations:\ncos0 = -(nx+oy+a,-l) 1 2 (2.3)\nand\nSince 0<8<7r, we only take the positive sign of Equation 2.4. Thus, we have only one solution for 8:\n0 = atan2(~(o,-a~~+(ax-n~+(ny-o~~,nx+oy+a,-l). (2.5) We can now find k using 0 computed by Equation 2.5. The set of equations used depends on whether n,, oy, or a, is most\npositive. Prom Paul\u2019s text, if nx is most positive,\n(2.6a)\nk =A k=& 2kxvers6\u2019 \u2019 2kxvers0 \u2019\na +n (2.6b,c)\nwhere sgn(e)=+l if e20 and sgn e)=-1 if e<O. (Note that our definition of sgn(e) is different I rom that in Paul\u2019s text. We will discuss this further on.) If oy is the most positive,\nFinally, if a, is the most positive,\n(2.7a)\n(2.7b,c)\nverso (2.8a)\nk =A a +n 0, +a, k =- x 2k,versO\u2019 2k,versO.\n(2.8b,c)\nFrom a geometric point of view, when O=X, there are two solutions to k, one opposite to the other. Also, when O=n, we can see from Equation 2.2 tha t 0,-a 4, a,-n,=O, and ny-ox=O. In this case, we can use either sgn(O)=+l or sgn(O)=-1 for Equation 2.6a, Equation 2.7a, and Equation 2.8a; we have two solutions for k. However, i t is desirable to use some convention so t h a t we can solve for k uniquely even when O=T. To do this, we can modify Paul\u2019s definition for the sgn function. In Paul\u2019s text, sgn(0) can be either +1 or -1. We define sgn(O)=+l, so t h a t we have unique 0 and k for each rotational matrix.\nA general rotational matrix can be represented as the exponent of a skew-symmetric matrix [26,23]:\nY\n0 -k, k,\nRot(k,O) = eKa, where K = (2.9)\nnot equal to identity are 1, d e , and e-J\u2019. Let ejs and e-\u2019\u2019 be Lemma 1: The eigenvalues of a general rotation matrix denoted by X and X. Then 0 can be calculated by:\nmatrix. See [33], or both [21] and [28f Proof: This is a well known roperty of a rotational\n0\nLemma 2: For a general rotation matrix not equal to identity, the eigenvector corresponding to the eigenvalue 1 can be expressed as a vector with real components and is either parallel or antiparallel to the axis of rotation. The other two eigenvectors cannot be expressed as real vectors.\nProof: Follows from Lemma 1 and Fisher\u2019s thesis [9]. More details can be found in a technical report [33]. 0\ntat ive if and only if their axes of rotation are parallel or Lemma 3: Non-identity rotational matrices are commuantiparallel to one another. Proof: Follows from Lemmas 1 and 2. See [33] for more details.\n3. Solut ion to the E q u a t i o n A X = X B\nand translational components, A X = X 8 becomes Dividing a homogeneous transform into its rotational"
        ]
    },
    {
        "image_filename": "designv10_10_0000634_978-1-4471-0853-5_9-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000634_978-1-4471-0853-5_9-Figure1-1.png",
        "caption": "Fig. 1 Two link robotic arm.",
        "texts": [],
        "surrounding_texts": [
            "original DAE in (x, u) is five. If actuator dynamics were included the index would be six [17]. Two stabilized differentiations will be done to make the DAE index three. The dynamic model of the system is given by -lq~I\u00b7T2 + F2q~ -IB'lxl + FIB' ][~ 1 [ B - q1 1 o (32a) q1 - B (32b) (32c) The last two equations model dry friction [10]. Control variables are the torques {Tl' T2}. State variables are {QI, Q2, B, Xl> X2}' The outputs are q1, Q2. Values of physical parameters are from [10]. We use DPC to impose the reference trajectories qdi (t) on the outputs qi. Thus H(q,t) = [ ql ~ qd, ] q2 ~ qd2 Following [43], we take W(s) = S-lp(S)J where pes) = s3 + 3as2 + 3a2 s +a3 \u2022 The integrator is added to avoid the reconstruction of the third derivative of qi. Due to the factor l/s we have to add the following integrator equations, (33) so that the stabilized error equations become o = (q~' ~ q~,) + 3ai(q~ ~ q~,) + 3a;(qi ~ qd.) + Wi, i = 1,2 (34) A linear analysis of the DAE is impossible since (32) contains non differ entiable (dry friction) terms. As proposed in [10], in order to eliminate the dry friction torques Xi we add the nonlinear observer (35) where VI = () and V2 = q2. Using the observed dry friction torque Xi we can precompensate the effect of dry friction by Ti = 'f\\ + X Ii' i = 1,2. Linearizations of the dry friction compensated plant were examined. Nu merical evaluation of the eigenvalues of A4 for linearizations around different nominal points shows that the eigenvalues stay close to 2.63 \u00b1 j29.58. As a consequence DPC as implemented in [43] yields an unstable closed loop system for small prediction horizon based on our linear analysis. This is con sistent with the experimental results in [43]. By applying the preliminary linear feedback where K = (q1 ~ qdJ (q2 ~ qd2) (81 ~ qdJ (q~ ~ q~J (q~ ~ q~2) (8' ~ q~,) + [ ~~ 1 [ 102.3 ~0.07 ~ 103.0 15.97 ~0.1O ~ 17 ] 16.17 ~0.01 ~16.3 2.55 ~0.02 ~2.71 (36) (obtained by standard LQ techniques) the eigenvalues of A4 are moved to ~2.61 \u00b1 j29.58. V = (f\\, T2)T is the new control input. The application of DPC to this new system then yields a stable control for all h < hmax , hmax = 0.3 sec. Numerical implementation The DAE we use to compute DPC is com posed of (32),(33),(34), the inputs TI and T2 are replaced by the controls defined in (36) (friction is considered to be precompensated, that is, the DAE does not include the friction model in {Xl, :r2}). In the following simulations we have taken as controller parameters Ctl = Ct2 = 2, k = 12 and m = 8. Furthermore, the sizes of the sampling period and the prediction horizon are identical, that is, h = E. We take the same reference trajectory as in [43]. For sampling periods E = h ~ 0.04, DPC works without preliminary feedback and preliminary feedback yields no major performance improvement. For smaller h, DPC without preliminary feedback destabilizes the controlled system and the use of preliminary feedback is necessary. DPC without preliminary feedback For given values of E and h, the closed loop system can be determined to be stable for 0.04 :s: h :s: 0.12. If we a<;sume infinitesimal E, we can determine lower and upper bounds for h, hmin = 0.053 and hmax = 0.158. The mot locus in Figure 2 shows the root which determines stability of the the characteristic equation of the delay differential system (29) as a function of h. Note that the root has positive real part on several h intervals of physical interest. DPC with preliminary feedback If preliminary feedback is applied we see in Figure 3 one root of the characteristic equation of the delay differ ential system. The root is stable for all h. However, the closed loop system is unstable for h > h*, since other roots, introduced by the delay, shift to the right hand side of the complex plane. The discrete linear closed loop system is stable for 0 < h < 0.24. Preliminary feedback does not improve tracking. However, the error de creases gradually 8..<; hand E becomes small. The application of DPC to the nonlinear system with and without pre liminary feedback gives the tracking errors in the first and second links as shown in Figures 4 and 5. The results support the linear analysis."
        ]
    },
    {
        "image_filename": "designv10_10_0001695_s0022112005008013-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001695_s0022112005008013-Figure1-1.png",
        "caption": "Figure 1. Cross-section of two parallel, horizontal cylinders lying at an interface with a non-dimensional centre\u2013centre separation of 2\u2206.",
        "texts": [
            " Here we consider the effects of these interactions via a series of model calculations that shed light on the physical and mathematical concepts that are at work in such situations. For simplicity, the calculations presented here are purely two-dimensional, though the same physical ideas apply to three-dimensional problems. Perhaps the most natural way to characterize the effects of interaction is to ask how the maximum vertical load that can be supported by two floating cylinders varies as the distance between them is altered. We thus consider two cylinders of infinite length lying horizontally at the interface between two fluids of densities \u03c1A < \u03c1B , as shown in figure 1. We assume that these cylinders are non-wetting so that the contact angle \u03b8 , a property of the three phases that meet at the contact line, satisfies \u03b8 > \u03c0/2. We non-dimensionalize forces per unit length by the surface tension coefficient, \u03b3AB , and lengths by the capillary length, c \u2261 (\u03b3AB/(\u03c1B \u2212\u03c1A)g)1/2, and use non-dimensional variables henceforth. We wish to determine the maximum weight per unit length, W , that can be supported by each of two identical cylinders with radius R and centre\u2013centre separation 2\u2206. To remain afloat each individual cylinder must satisfy a condition of vertical force balance: their weight (or other load) must be balanced by the vertical contributions of surface tension and the hydrostatic pressure acting on the wetted surface of the cylinder. We assume that an external horizontal force is applied to maintain the separation of the cylinders and so do not consider the balance of horizontal forces explicitly. Using the notation of figure 1, the vertical force balance condition may be written W = U1 + U2 where Ui \u2261 \u2212 sin(\u03b8 + \u03c8i) \u2212 H0R sin \u03c8i + 1 2 R2(\u03c8i + sin \u03c8i cos \u03c8i) (i = 1, 2) (2.1) are the contributions to the vertical upthrust provided by the deformation on each half of the cylinder separately, and H0 is the height of the cylinders\u2019 centres above the undeformed free surface. Physically, the first term on the right-hand side of (2.1) is the vertical component of surface tension, and the second and third terms quantify the resultant of hydrostatic pressure acting on the wetted perimeter of the cylinder. The latter is given by the weight of water that would fill the dashed area in figure 1 (see Keller 1998). The angles \u03c81 and \u03c82 are determined by the interfacial shape, which is governed by the balance between hydrostatic pressure and the pressure jump across the interface associated with interfacial tension. This balance is expressed mathematically by the Laplace\u2013Young equation. In two dimensions this is HXX = H ( 1 + H 2 X )3/2 , (2.2) where H (X) is the deflection of the interface (again measured positive upwards) from the horizontal, and subscripts denote differentiation. Since the exterior meniscus extends to infinity, the first integral of (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure11-1.png",
        "caption": "Fig. 11. Temperature distribution of the copper screen when the relative magnetic permeability of the press plate is 50.",
        "texts": [
            " When the relative magnetic permeability of the press plate is 50, the highest and average temperatures of the copper screen are 63.6 \u00b0C and 59.8 \u00b0C. The highest temperature of the copper screen (when the relative magnetic permeability of press plate is 50) is 3.4 K higher than that of the copper screen (when the relative magnetic permeability of the press plate is 1). 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 7 Fig. 11 shows the temperature distribution of the copper screen when the relative magnetic permeability of the press plate is 50. It can be seen from Fig. 11 that the highest temperature of the copper screen is 63.6 \u00b0C and appears in the copper screen inner circle zone. The highest temperatures of the copper screen inner circle zone, copper screen transitional circle zone, and copper screen external circle zone are 63.6 \u00b0C, 54.1 \u00b0C, and 44.5 \u00b0C, respectively. The average temperatures of the copper screen inner circle zone, copper screen transitional circle zone, and copper screen external circle zone are 59.8 \u00b0C, 47.6 \u00b0C, and 44.2 \u00b0C, respectively. Since the loss of the copper screen inner circle zone is high, the temperature of the copper screen inner circle zone is much higher than the temperature of the copper screen transitional circle zone and copper screen external circle zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003763_s10846-017-0545-2-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003763_s10846-017-0545-2-Figure6-1.png",
        "caption": "Fig. 6 CAD designs of the UAV arm and moving mass mechanism",
        "texts": [
            " (57) The arm length of the vehicle presented in Section 6 is almost identical to the optimal value computed in this Section. The biggest difference between the analyzed system and designed vehicle is the length of the moving mass path. In this analysis we assumed that the moving mass path length is equal to the arm length. However, due to the physical dimensions of the designed moving masses and central UAV body, the actual path length is limited to 50 cm. The final CAD designs of the UAV arm and moving mechanism are shown in Fig. 6a. 4.2 Moving Mass Dynamics Design In this analysis we aim to determine the required speed-torque curve for the servo system driving a moving mass. The determined curve plays a crucial role for choosing the appropriate servo drive. Our approach is to determine the required dynamics for the moving mass which stabilizes the vehicle and achieves desired robust performance. Given the determined dynamics, we compute accelerations and velocities exhibited by the moving mass given a step setpoint on its position. To transform these linear quantities to their angular counterparts exhibited by the motor, a transmission mechanism, which translates the angular motion of the motor to the linear motion of the moving mass, is required. We have chosen a rack and pinion mechanism where the motor, mounted on a linear guide, acts as the moving mass (see Fig. 6). For this design, the radius of the gear determines the relation between linear and angular velocities/accelerations. First, we analyze the influence of the moving mass dynamics to system stability and robustness. In particular, we compute gain margin, phase margin and crossover frequency of the transfer function (38) as a function of the moving mass natural frequency \u03c9mm. From these characteristics we determine natural frequency required to achieve desired robustness and speed of the closed loop response [19]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002837_j.mechmachtheory.2013.10.001-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002837_j.mechmachtheory.2013.10.001-Figure2-1.png",
        "caption": "Fig. 2. Needle roller bearing inner ring.",
        "texts": [
            " Because of higher sliding these bearings have higher coefficient of friction. They are used to take pure radial load. They differ than other bearings in aspects like they have considerably greater length-to-diameter ratio (2.5Dr b le b 10Dr), needle rollers are difficult to manufacture accurately as compared to cylindrical rollers. Needle rollers are difficult to guide and rollers get rubbed against each other. NRB is illustrated in Fig. 1. In NRBs, flanges that are integral to the outer raceway retain rollers. Fig. 2 shows the inner ring that is used with the needle and cage assembly. It is used when the shaft cannot be hardened and grounded to a suitable raceway tolerance. The inner ring is hardened and grounded, and is provided with a chamfer on both sides for assembly. Fig. 3 shows the needle roller which is relieved at ends to prevent edge stresses. Fig. 4 shows the terminology for NRBs. The figure shows different components of the bearing like (1) outer ring, (2) lubrication hole, (3) raceway, (4) needle roller and cage assembly, and (5) open end"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure5-1.png",
        "caption": "Fig. 5 Diagram of the 4-axis CNC planer",
        "texts": [
            " The former planer tool repeats movement with workpiece feeding during every intermittence, and the latter workpiece repeats movement with planer tool feeding during every intermittence. Considering the processing technology and the design parameters of the face-gear, a planer machine is needed with the following functions and characteristics: 1. The squaring machine meets the demand of size, since the diameter of the face-gear is less than 1 m. 2. The B axis should be added in the planer machine, as the rotation of the face-gear blank around the face-gear axis is needed when the face-gear is processed, as shown in Fig. 5. 3. The 4-axis CNC planer is needed, for the location of planing should be precise, and the positioning should be rapid in the process of planing. As the spur gear matched with the spur face-gear can be regarded as a stretched body, the stretched body can be obtained through enveloping by the straight line. Hence, the planing method proposed in this paper is based on the straight line motion of the planer tool, which simulates the generating motion of a single tooth of the shaper cutter (as shown in Fig",
            " Prior to this, the pitch swing angle is chosen to be studied as the theoretical analysis and verification of the simulation machining. According to the design parameters in Table 1, the theoretical error of the tooth face of the face-gear is calculated. First, through calculating, the range of the radius of the shaper cutter is 5.110<Rc<34.747. From Eq. (26), e1max=max{e1}=0.025. Then, according to Eq. (27), e2(v, w) can be obtained with MATLAB, as shown in Fig. 17. Accordingly, e2max=max{e2(v, w)}=0.168. Finally, from Eq. (24), E\u2264e1max+e2max, that is, E\u22640.193. The 4-axis CNC planer mentioned above (as shown in Fig. 5) is adopted to run the manufacturing simulation of the spur face-gear planing studied in this paper. The planer tool blade should be full fillet as it is convenient to calculate the tool path with this kind of blade. According to the design parameters in Table 1, the swing angle range and the feed range of the planer tool are calculated. The theoretical model of the face-gear (as shown in Fig. 18), the model of the face-gear blank and models of the planer machine are established using CATIA, and the model files and NC programs which are written based on the planing principle in this paper are imported into the Vericut software to simulate the processing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003385_12.2010577-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003385_12.2010577-Figure5-1.png",
        "caption": "Figure 5. Prototype positioning and support structures.",
        "texts": [
            " Supports are in light grey while the prototype is in dark grey. In the first case (left), the airfoil is fully hidden being it completely embedded within the support, which is needed to build the platform and would hamper a proper removal; it also results in a longer processing time due to the fact that additional powder has to be sintered to create the support itself. In the second case (right), a support would be necessary inside and along the airfoil so affecting a key surface of the element. Figure 5 shows the definitive positioning of the prototype examined in this study with its corresponding support structures. This positioning does not require any support on the airfoil which is the functional part of the turbine blade and has therefore to be preserved. It is noteworthy that regardless of the suggested supports for the desired geometry, one Proc. of SPIE Vol. 8677 86771H-5 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/07/2013 Terms of Use: http://spiedl.org/terms may further improve them with refined scanning meshes in the critical areas of the part where risk of break between support and prototype is in place; these areas are those ones where the part lays along a thin but long support"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001252_21.478451-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001252_21.478451-Figure1-1.png",
        "caption": "Fig. 1. A cooperating multiple robot system.",
        "texts": [
            " When multiple robots carry an object cooperatively, the relation between the forces applied by each robot and the total force at the center of mass of the object is described by a linear transformation ] w1 : w, : . . . : w, \"\"f Ob? [ W F (4) where ObgI(I is the p x 1 vector of total force at the center of mass of the object expressed in the object coordinate frame, \"fi is the n x 1 vector of force/moment applied at the zth contact point expressed in the zth contact frame, and Wi defines a mapping from to the resultant force at the center of mass of the object. Refer to Fig. 1 for the definition of coordinate frames. Since F satisfying (4) is redundant for given Ob3+, how to find F from Ob'$ has been the main subject of the load distribution problem [1]-[5]. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 25, NO. 12, DECEMBER 1995 1651 Constant Description Moment of inertia of 8 The general solution to (4) is given by \"\"f $+ N l - ~ i - o b ~ where W+ E R m n X p is the pseudoinverse of W defined by W+ = WT(WWT)- . ' , N E RmnXp consists of the basis vectors of the null space of W produced by orthogonalizing and normalizing the linearly independent column vectors of ( I - W+ W ) , and X E Rmn--p is an arbitrary vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000772_s0094-114x(99)00068-3-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000772_s0094-114x(99)00068-3-Figure3-1.png",
        "caption": "Fig. 3. Balancing elastic system with cam rotating follower I.",
        "texts": [
            " The balancing helical spring 4 is joined with its A end to the follower 2. The parametrical equations of the directrix curves of the cam active surfaces are: x1 XC3 R dOC=dj sin j XC Q , y1 YC2 R dOC=dj cos j\u00ff YC Q , where XC OC cos j; YC OC sin j; Q dXC=dj 2 dYC=dj 2 q : The distance OC and its derivative dOC=dj are calculated by integrating the following di erential equation: Fs YB OC AC cos j AB \u00ff R02OC cos j\u00ff a \u00ff g \u00ff m1OG1 m4A OC AC m2 OC CG2 cos j 0, 2 where: R02 g m2 m4A \u00ff Fscos j\u00ff y cos j\u00ff a ; a arctan dOC=dj OC : Fig. 3 shows another possibility for the balancing of the weight force of the link 1 \u00d0 the industrial robot arm, for example \u00d0 which rotates around a horizontal \u00aexed axis O. The balancing helical spring is joined on the link 1 at point A and on the cam 2 at point B. The cam is articulated to frame in point C and is driven by the link 1 through roll 3. The angle c, which de\u00aenes the position of the moving axes system x2Cy2 attached to the cam 2 I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b113111302 with respect to the stationary co-ordinate axes system XOY, is calculated as a solution of the following di erential equation: Fs YB \u00ff YC cos y\u00ff XB \u00ff XC sin y \u00ff g m2XG2 m4BBC cos c x2Esin F \u00ff y2Ecos F g m1OG1cos j m4AXA Fs YAcos y\u00ff XAsin y y1Ecos c\u00ff F\u00ff j \u00ff x1Esin c\u00ff F\u00ff j 0, 3 where: y arctan YB \u00ff YA XB \u00ff XA ; F arctan \u00ff T dc=dj U V dc=dj W ; T XCsin c\u00ff YCcos c\u00ffU; U x1Esin c\u00ff j \u00ff y1Ecos c\u00ff j ; V XCcos c YCsinc\u00ffW; W x1Ecos c\u00ff j y1Esin c\u00ff j ; x2E x1Ecos c\u00ff j y1Esin c\u00ff j \u00ff XCcos c\u00ff YCsin c; y2E y1Ecos c\u00ff j \u00ff x1Esin c\u00ff j XCsin c\u00ff YCcos c; XB XC BC cos c; YB YC BC sin c; XG2 XC x2G2 cos c\u00ff y2G2 sin c; YG2 YC x2G2 sin c y2G2 cos c; Fs F0 k AB\u00ff l0 : The initial conditions, which are necessary to solve the di erential equation (3), are considered in a convenient mode, adequate to a known equilibrium position",
            " The mechanical work used for acting the robot arm 1 of mass m1 which move around a horizontal \u00aexed axis has the value [1]: Mm1 m1 8><>:OG1 g cos j1 OG1 d2j1 dt2 mOrO 1 dj1=dt 8<:OG 2 1 \" dj1 dt 4 d2j1 dt2 2 # g2 \u00ff 2gOG1 \" dj1 dt 2 sin j1 \u00ff d2j1 dt2 cos j1 #9=; 1=2 9>=>; IG1 d2j1 dt2 , 6 where: mO represents the friction coe cient from joint O; rO represents the radius of the rotating joint O; IG1 represents the moment of inertia with respect to the horizontal axis parallel to the movement axis of the joint O and which pass through the centre of mass G1: I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b113111306 4.1. The e caciousness of the four-bar linkage for discrete static balancing There are many discrete static balancing systems. In the proposed scheme (see [4], Fig. 3), for studying the e caciousness, the helical spring 4 is joined with one of its ends to arm 1 at the point A and with the other one to link 2 at the point B. The link 2 rotates around a \u00aexed axis C. The acting of the four-bar linkage is made by arm 1 through the link 3. In this case, the mechanical work used for acting all the mechanism bodies has the value: Mm2 Mm1 1 dj=dt ( 1 2 m4 \" g dYA dt dYB dt BC dc dt d2c dt2 OA dj dt d2j dt2 AB2 12 dy dt d2y dt2 # IG2 dc dt d2c dt2 m2 g dYG2 dt CG2 dc dt d2c dt2 IG3 dx dt d2x dt2 m3 g d2YG3 dt2 dYG3 dt dXG3 dt d2XG3 dt2 djdt \u00ff dy dt MfA dcdt \u00ff dy dt MfB dcdt MfC dcdt \u00ff dx dt MfD djdt \u00ff dx dt MfE ) , 7 where Mm1 has the expression (6) and: MfA mArA ( Fscos y m4A d2XA dt2 2 Fssin y m4A g d2YA dt2 2)1=2 8 represents the friction moment from joint A; MfB mBrB ( Fscos y\u00ffm4B d2XB dt2 2 Fssin y\u00ffm4B g d2YB dt2 2)1=2 9 represents the friction moment from joint B; MfC mCrC R2 02X R2 02Y q 10 represents the friction moment from joint C; MfD mDrD R2 32X R2 32Y q represents the friction moment from joint D; MfE mErE R2 13X R2 13Y q represents the friction moment from joint E, where rA, rB, rC, rD and rE represent the bearing radii from joints A, B, C, D and E, I",
            " Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b11311 1307 respectively, and the resultant forces from joints C, D and E are calculated by solving the following equations: R13X \u00ff R32X \u00ffm3 d2XG3 dt2 0; R13Y \u00ff R32Y \u00ffm3 g d2YG3 dt2 0; R32X YD \u00ff YE \u00ff R32Y XD \u00ff XE \u00ff IG3 d2x dt2 m3 d2XG3 dt2 \u00ff YG3 \u00ff YE \u00ff g d2YG3 dt2 \u00ff XG3 \u00ff XE MfD MfE 0; R02X R32X Fscos y\u00ffm4B d2XB dt2 \u00ffm2 d2XG2 dt2 0; R02Y R32Y Fssin y\u00ffm4B g d2YB dt2 \u00ffm2 g d2YG2 dt2 0; R32Y XD \u00ff XC \u00ff R32X YD \u00ff YC \u00ff IG2 d2c dt2 Fs XB \u00ff XC sin y\u00ff YB \u00ff YC cos y m4B d2XB dt2 YB \u00ff YC \u00ff g d2YB dt2 XB \u00ff XC m2 d2XG2 dt2 \u00ff YG2 \u00ff YC \u00ff g d2YG2 dt2 \u00ff XG2 \u00ff XC MfB MfC MfD 0: 4.2. The e caciousness of the cam mechanism for continuous static balancing In the same manner as the discrete balancing, in order to realise a continuous balancing of the weight force of an industrial robot arm by the elastic force of a helical spring, it is necessary that the spring be joined with one of its ends to a link which moves with respect to the frame or with respect to the arm [4]. In the kinematics scheme depicted in Fig. 3, the balancing helical spring 4 is joined on the link 1 at point A and on the cam 2 at point B. The cam is articulated to frame in point C and is driven by the link 1 through roll 3. The mechanical work used for rotating the robot arm and for moving the bodies of the cam mechanism are calculated the following formula: I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b113111308 Mm2 Mm1 1 dj=dt ( 1 2 m4 \" g dYA dt dYB dt BC dc dt d2c dt2 OA dj dt d2j dt2 AB2 12 dy dt d2y dt2 # IG2 dc dt d2c dt2 m2 g dYG2 dt CG2 dc dt d2c dt2 djdt \u00ff dy dt MfA dcdt \u00ff dy dt MfB dcdt MfC djdt \u00ff dx dt MfE ) , 11 where Mm1 , MfA, MfB and MfC has the relations (6), (8)\u00b1(10), respectively, and MfE mrER23, where rF represents the radius of bearing from the joint F",
            " The resultant forces from joints C and E are calculated by solving the following equations: R02X R42X m2 d2XG3 dt2 R23sin j a ; R02Y R42Y m2 g d2YG2 dt2 \u00ff R23cos j a ; R23 1 OE cos a\u00ff mERE g \u00ff m1OG1cos j1 m4AXA \u00ff Fs YAcos y\u00ff XAsin y \u00ffm1OG 2 1 m4AOA2 d2j dt2 MfA , where MfA has the relation (8) and: R42X m4B d2XB dt2 \u00ff Fscos y, R42Y m4B g d2YB dt2 \u00ff Fssin y; a arctan OD OC sin b 1\u00ff dj dt 1 dc=dt 1 tan b , b j\u00ff arctan YC XC ; dx dt 1 YD \u00ff YE \" R dj dt sinj CD sin c arctan y3D x3D dc dt # 1 XD \u00ff XE \" R dj dt cos j1 CD cos c arctan y3D x3D dc dt # : 4.2.1. Example 1 For the discrete balancing of a robot arm with mass m1 10 kg and OG1 1 m, the four- I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b11311 1309 bar linkage shown in [4] Fig. 3 is used. The work \u00aeeld is de\u00aened by angles j1min \u00ffp=4 and j1max p=4: The helical spring 2 has the mass m2 3 kg and the characteristics: l0 0:5 m, F0 0:00870632 N/m and k 3520:80 N/m. The link 3 has the dimensions: BC 0:158576 m, CD 0:1857 m, b 1:41038 and it is joined at the point C of co-ordinates: XC 0:00572993 m, YC 0:0957131 m. The link 4 has the length BC 0:101095 m. In joint O, the value of friction coe cient is mO 0:06, and in the other joints, the values of friction coe cients are mA mB mC mD mE 0:03: For the arm position angle j1 j1min \u00ffp=4, the unbalanced moment has the maximum value 0",
            " The unbalanced moment diagram with respect to arm rotation angle j1 is shown in Fig. 5. The e caciousness coe cient diagram with respect to arm angular speed _j1 is shown in Fig. 6. Note that the magnitude of the e caciousness coe cient is very large for small value of arm angular speed. This magnitude becomes less than one when the maximum angular speed of arm 1 is greater than _j1lim 4:318397 s\u00ff1. I. Simionescu, L. Ciupitu /Mechanism and Machine Theory 35 (2000) 1299\u00b113111310 4.2.2. Example 2 The balancing of the body that rotates around a horizontal \u00aexed axis (Fig. 3) has been taken as an example to illustrate the usefulness of the methods proposed in this paper. The masses of the component elements have the values: m1 22 kg, m2 1 kg, m4 5 kg. The length at the unextended balancing helical spring is l0 0:72 m and the sti ness coe cient of the spring is k 10650 N/m. The following values were considered for the dimensions of the elements, the co-ordinates of the \u00aexed points and the positions of the mass centres: BC 0:08 m, XC 0 m, YC 0:135 m, x1A 1:0 m, y1A 0m, x1E 0:085 m, y1E 0 m, R 0:0125 m, OG1 0:6 m, x2G2 0:015 m, y2G2 0 m, m4A m4B: The co-ordinates of the points which de\u00aene one directrix curve of the active surface of the cam have been calculated. The results are presented in Table 1. Since the work \u00aeeld has been considered symmetrical with respect to the vertical axis, jmin p=4, jmax 3p=4), the directrix is symmetrical with respect to the moving axis Cx2 (Fig. 3). The magnitude of the calculated unbalanced moment is con\u00aened between \u00ff0.05566 and 0.07171 Nm. [1] P. Appell, Traite\u00c2 de me\u00c2 canique rationnelle, Gauthier Villars, Paris, 1928. [2] K. Hain, in: N.D. Chironis (Ed.), Spring Mechanisms \u00b1 Continuous Balancing, Spring Design and Application, McGraw-Hill, New York, 1961, pp. 268\u00b1275. [3] F. Leistner, J. Ba\u00c8 tge, E.P. Soldatkin, W. Novikov, Machinenbautechnik 5 (Berlin) 37 (1988) 196\u00b1198. [4] Simionescu I, Ciupitu L. The static balancing of the industrial robot arms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002389_j.jsv.2010.03.014-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002389_j.jsv.2010.03.014-Figure1-1.png",
        "caption": "Fig. 1. Experimental rig. (i) Electronic brushless servo motor; (ii) drive side encoder, both encoders are Hengstler RI76-TD Series hollow shaft incremental encoders, with 10,000 pulses per revolution (giving a resolution of 1.57 10 4 rad by detecting each pulse edge); (iii) drive gear, both gears are module 6, 108 mm pitch circle diameter, mild steel spur gears precision ground to BS436 Grade 6 (equivalent to ISO 1328-2) standard; (iv) inertial mass; (v) base plate, bolted to a table of large mass to eliminate the possibility of any undesirable vibrational modes; (vi) driven side encoder; (vii) driven gear; (viii) bearing housings; (ix) single row radial ball bearings, shaft diameter is 30 mm.",
        "texts": [
            " Thus we incorporate a meshing damping term, describing the frictional losses incurred as the gear teeth rub against one another. The approximate value of this parameter is obtained experimentally via a run-down test. Using a combination of numerical and analytical methods we calculate trajectories of relative gear motion which we are able to compare directly with experimental findings. We draw conclusions as to the effect of STE on gear rattle from cases where we obtain good agreement and offer suggestions for future work to enhance the accuracy of the model. The experimental rig, shown in Fig. 1 (and described in detail in [14]) consisted of gear pair, with each gear attached to a high accuracy optical encoder. A servomotor was used to drive one of the gears (the drive gear). The second gear was unloaded and represents the idling or driven gear. Since the idling gear is unloaded it is assumed that it does not affect the motion of the driven gear, hence the servomotor was controlled in angular displacement (using a proportional plus derivative feedback controller). The 1:1 ratio gears employed were of high module and the shaft diameters were large, allowing the system to be considered rigid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002397_j.apsusc.2010.02.060-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002397_j.apsusc.2010.02.060-Figure5-1.png",
        "caption": "Fig. 5. Sketch of the real-time tracking monitoring of the pool temperature during LSF process.",
        "texts": [
            " During double-color measurement, since the intensities at two operating wavelengths are compared in the pyrometer, the changes in the target emissivity have little effect on the obtained temperature. In addition, the thermometer allows the credible temperature measurements for the deposition layer when the molten pool is partly obliterated by the feeding powders. So the double-color infrared measuring temperature technique is suitable under a worse environment during LSF. Two kinds of methods on temperature measurement: real-time tracking (illustrated in Fig. 5 in which the sensor moves together with the laser head and aims at the molten pool) and fixed-point J. Yu et al. / Applied Surface Science 256 (2010) 4612\u20134620 4617 F p m m o A p 2 l F w r p s p F m the temperature will tend to be stable, which causes the pool size ig. 6. Sketch of the fixed-point monitoring of the pool temperature during LSF rocess. onitoring (illustrated in Fig. 6 in which the sensor aims at the idpoint of the track without moving), are performed during LSF f AISI-304 metal powders"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003534_j.mechmachtheory.2017.01.010-Figure5-1.png",
        "caption": "Fig. 5. Coordinate systems applied for face-milled spiral bevel gear generation: (a) Right-hand (RH) gears; (b) Left-hand (LH) gears.",
        "texts": [
            " r (P) t (s, \u03b8 ) = M ts (\u03b8 ) r (P) s (s ) (10) r (P) (\u03bb, \u03b8 ) = M ts (\u03b8 ) r (P) s (\u03bb) (11) t Finally, introducing Eqs. (9) , (8) and (4) in Eqs. (10) and (11) , the face-milling cutter generating surfaces are obtained and represented in coordinate system S t ( x t , y t , z t ), which are given by r (P) t (s, \u03b8 ) = \u23a1 \u23a2 \u23a3 cos \u03b8 ( R \u2213 s sin \u03b1) sin \u03b8 ( R \u2213 s sin \u03b1) \u2212s cos \u03b1 1 \u23a4 \u23a5 \u23a6 (12) r (P) t (\u03bb, \u03b8 ) = \u23a1 \u23a2 \u23a2 \u23a3 cos \u03b8 [ R \u00b1 \u03c1 (( 1 \u2212sin \u03b1 cos \u03b1 ) \u2212 cos \u03bb )] sin \u03b8 [ R \u00b1 \u03c1 (( 1 \u2212sin \u03b1 cos \u03b1 ) \u2212 cos \u03bb )] \u03c1( sin \u03bb \u2212 1 ) 1 \u23a4 \u23a5 \u23a5 \u23a6 (13) 2.3. Family of head-cutter surfaces Auxiliary coordinate systems shown in Fig. 5 are used to take into account the generating machine-tool settings and motions listed in Table 1 . A description of each coordinate system is given below. \u2022 S m ( x m , y m , z m ). This is the fixed coordinate system and it is rigidly attached to the gear generator. \u2022 S c ( x c , y c , z c ). This movable coordinate system is rigidly connected to the cradle. Its axis z c is directed along the cradle rotation axis and its origin coincides with the origin O m . It takes into account the cradle angular position \u03c6c regarding the fixed coordinate system S m "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003375_j.triboint.2014.10.007-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003375_j.triboint.2014.10.007-Figure7-1.png",
        "caption": "Fig. 7. (A) Sensor placement in the casing was performed using a profilometer. The probe travel path is marked in red. (B) Sensor offset measurement. The sensors and the casing profiles are shown along with the probe travel. The measured sensor offset is also shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            "5 \u03bcm) using high accuracy coordinate measuring machines to be used for the calculation of hGap;Rlv according to Eqs. (28) and (33). The capacitive sensors selected had to be placed with great accuracy inside the EGM casing. The sensors were placed as close to flush as possible with surface with an offset such that the target does not go beyond the range of the sensor. The sensor offset was measured carefully using a Mitutoyos (Aurora, IL) SJ500 profilometer with an accuracy of 1 nm using a special probe enabling measurement of the surface inside the casing (shown in Fig. 7). An illustration of the measurement obtained using the profilometer is shown in Fig. 7 and the sensor offset was calculated as shown. The measured film thickness \u00f0hmeas\u00de includes this offset. hBal can be calculated using hBal \u00bc hmeas Of ; \u00f034\u00de where Of is the sensor offset from the EGM casing. Components of an EGM are expected to deform under pressure and thermal loads. Since the lubrication in the lateral gap is expected to be in the TEHD domain, the deformation of the lateral bushing and the gears are modelled by the FSI\u2013thermal model of the lateral gap and accounted for. The deformation of the casing is an additional factor which will affect the film thickness measurements which is external to the domain of the lateral lubricating interface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure3-1.png",
        "caption": "Fig. 3 (a) Three-legged PPR-PKC; (b) Three-legged PPR-PKC with a PPR V-chain added.",
        "texts": [
            " For convenience, \u03be0, \u03be\u221e, \u03b60 and \u03b6\u221e are used to represent a twist of 0-pitch, a twist of \u221e-pitch, a wrench of 0-pitch and a wrench of \u221e-pitch respectively. Base on the reciprocity condition of screws, we obtain the geometric relation between a twist system and its wrench system as follows: (a1) The axis of \u03be0 is coplanar with the axis of any \u03b60. (a2) The direction of a \u03be\u221e is perpendicular to the axis of any \u03b60. (a3) The axis of \u03be0 is perpendicular the axis of any \u03b6\u221e. Since the motion pattern of an m-legged PPR-PKC [Fig. 3(a)] is the same as a PPR V-chain, we can connect the base and the moving platform of the PPR-PKC with a PPR V-chain without affecting the motion of the moving platform [Fig. 3(b)]. It is apparent that each leg of the PPR-PKC and the V-chain constitute a 3-DOF single-loop kinematic chain. Meanwhile, the wrench 3 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/15/2018 Te system of the original PKC must be the same as that of the Vchain in any one general configuration. Otherwise, the DOF of the moving platform is greater than 3. To facilitate the type synthesis of PPR-PKCs, the conditions for a PKC to be a PPR-PKC can be described as: (1) Each leg of the PKC and a same V-chain constitute a 3-DOF single-loop kinematic chain",
            " 1), the wrench system is a 1-\u03b60-2-\u03b6\u221esystem, which is composed of (a) all the \u03b6\u221e whose axes are perpendicular to the axis of the R joint and (b) all the \u03b60 whose axes are perpendicular to the directions of the P joints and coplanar with the axis of the R joint, and (c) other \u03b6 which are linear combinations the above \u03b6\u221e and \u03b60. One set of basis wrenches of the 1-\u03b60-2-\u03b6\u221e-system is \u03b601, \u03b6\u221e2 and \u03b6\u221e3. For convenience, the axis of the R joint within the PPR V-chain is called a virtual axis, the plane which are parallel to the directions of the two P joints within the PPR V-chain is called a virtual plane. In any general configuration, the wrench system of a PPRPKC [Fig. 3(a)] is the same as that of its V-chain, i.e., a 1-\u03b602-\u03b6\u221e-system (Fig. 1). As the wrench system of a parallel kinematic chain is the union (linear combination) of those of all its legs in a general configuration [40], the wrench system of any leg in a PPR-PKC is a sub-system of its wrench system. Here and throughout this paper, the wrench system of a leg is called a leg-wrench system. In the type synthesis of PMs, one is only interested in the leg-wrench systems in which there is a set of basis Copyright  2004 by ASME rms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001261_1.1479337-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001261_1.1479337-Figure7-1.png",
        "caption": "Fig. 7 Photograph of test rig",
        "texts": [
            " Multiple solutions could be obtained by changing the initial condition; e.g., changing the input angle of inclination of the rotor (ux) resulted in different solutions for the higher speeds. Figure 6 shows the run up solution at 18,000 rpm compared to a solution obtained by using an all zero initial condition. Here, the zero initial condition solution is chaotic. These multiple solutions result from the bearing nonlinearity and should be avoided, as far as possible, by appropriate selection of system parameters. Test Rig Model. Figure 7 shows a photograph of the modeled test rig which is currently being commissioned. The test rig model is the same as that in @10# except three more degrees-of-freedom were added at each bearing as required by the 5DOF modeling. Table 3 gives the relevant parameters for the rotor system while Fig. 9 Peak-to-peak response 19.5 N preload Table 4 Clearance for 2DOF models Preload ~N! 2DOF and 2DOF1i model clearances ~mm! ci ce 19.5 20.20695 20.31356 100 20.59794 20.90597 Transactions of the ASME 16 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002026_tmag.2009.2012785-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002026_tmag.2009.2012785-Figure6-1.png",
        "caption": "Fig. 6. Contours of hysteresis loss. (a) Without skew and (b) 4/3 slot pitch skewed.",
        "texts": [
            " 4 shows the distributions of flux density vectors of SCIM with the 4/3 slot pitch skewed rotor. The flux density vectors of the upper section are larger than those of the lower section. The imbalance of the magnetic flux distributions makes the loss distributions imbalanced in the SCIM with skewed rotor. Fig. 5 shows the contours of eddy current loss. The eddy current loss in the tip of teeth and the surface of the rotor is especially large. From Fig. 5(b), the eddy current loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 6 shows the contours of hysteresis loss. The hysteresis loss concentrates in the upper side in the SCIM with the 4/3 slot pitch skewed rotor due to the skewed rotor. Fig. 7 shows the loss of the SCIM. The iron loss of the SCIM is decreased by the skewed rotor. The calculated total losses agree well with the measured ones. Fig. 8 shows the waveforms of bar-current. The ripple of the bar-current of the motor with the 4/3 slot pitch skewed rotor is smaller than that of the motor with the rotor without skew"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.30-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.30-1.png",
        "caption": "Figure 6.30 and H+. Biconical transmission line showing the principal mode field components 6?@",
        "texts": [
            " Further discussions of monopole of its variations and applications are given in [2,6,7]. The biconical antenna provides moderately broadband performance and it is typically used in the frequency range 30 to 200 MHz. The antenna can be considered as a finite section of the well-known biconical transmission line described in [ 1-3,7]. A biconical transmission line consists oftwo semi-infinite conducting cones of half angle 00 placed symmetrically along the x axis with a gap at the center 0, which is also the origin of a coordinate system shown in Figure 6.30. The line is excited at the gap. It is known that such a line supports the principal or dominant spherical TEM propagating mode having only Eo and H4 components. This mode is analogous to the TEM mode in a conventional two-wire or coaxial line. Detailed modal analysis of biconical transmission lines may be found in the references cited. For an understanding of the characteristics of its principal mode we begin with the source-free Maxwell\u2019s equations V x E = -jwpH V x H = j w e E , (6.210) (6.2 1 1) and in conformity with the geometry we will use a spherical coordinate system",
            " Now, using (6.2 17) and (6.2 15a), we obtain (6.2 18) 276 ANTENNAS AND RADIATION where q = is the intrinsic impedance of the medium. Observe that the first terms i n (6.2 17) and (6.21 3) represent a wave moving away from the center (source) and the second terms represent waves approaching the center (source), meaning they are outgoing and incoming waves. For our semi-infinite biconical line we assume that there is no incoming wave and thus we have the following: (6.219a) (6.2 19b) and E4 = qH4. in Figure 6.30, is given by The voltage between the two conductors, namely between points A and B T-00 which after using (6.17) can be written as with (2) (2). VA = 2A In cot VB == 2B In cot (6.220a) (6.220b) The current density on the upper cone surface J,(r) is J,(r) = f i x H, = i H + / ~ = e ~ ~ , (6.22 1) where f i = 6 is the outward down unit normal on any point on the upper surface and H, is the magnetic field at the upper surface at that point. Using (6.218) in (6.221), we obtain (6.222) The total current at T = r on the upper surface, i.e., the axial current at I ( r ) (see Figure 6.30) is given by Ampere\u2019s law: f H . &! = Ienclosed = I ( r ) , (6.223) BICONICAL ANTENNA 277 which implies After substituting the value of H4 from (6.218) in the above, we obtain which by virtue of (6.220b) can be written as For a semi-infinite biconical line V B = 0 and we obtain the voltage and current along the same line as (6.225) A -jPr V ( T ) = V e which give the outgoing travelling wave on the line. The characteristic impedance of the line is given by (6.226) and is independent of T , that is, the line has uniform characteristic impedance",
            "228) 278 ANTENNAS AND RADIATION and is also independent ofr , when Zc is as given above. Note Zi as given above is purely resistive, where 2, is given by (6.227b). The input impedance Zi of an infinite biconical antenna and ofa single (semi-infinite) cone above a perfect ground plane as functions of the cone half angle are shown in Figure 6.31. Note that when the lower cone of the infinite biconical antenna is replaced by a large ground plane, its input resistance is half that of the former. A finite biconical antenna is obtained by using the two finite cones of length T = t in Figure 6.30. If we assume that an ideal open circuit exists at T = I!, then using the boundary condition I ( ! ) = 0 we obtain by using (6.224) that the current distribution on the antenna is (6.229) that is, for the TEM mode assutned on the antenna, the current distribution is sinusoidal under ideal open-circuit condition. For a finite biconical antenna Schelkunoff [3] defines a boundary sphere of radian 1 as shown in Figure 6.32. Within the sphere, namely for r 5 Q, TEM and higher order modes exist; outside the sphere, namely for r 2 Q, only higher order modes exist"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003420_tps.2013.2246872-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003420_tps.2013.2246872-Figure2-1.png",
        "caption": "Fig. 2. Temperature field calculation model.",
        "texts": [
            " 1) The thermophysical parameters of the windings, permanent magnet, and iron in the circumferential direction are the same, respectively. 2) The air flow and the convection coefficients of the outer surface of the mover are regarded as the same around the circumference in the same axial length. The thermal conduction path inside the motor and the heat convection on the outer surface are mainly distributed along the radius and axis direction. So the temperature field can be simplified from 3-D to 2-D. The FEM model in ANSYS is shown in Fig. 2. The 2-D transient thermal heat transfer equation in cylindrical-coordinate system of the motor is \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 1 r \u2202 \u2202r ( \u03bbrr \u2202T \u2202r ) + \u2202 \u2202 Z ( \u03bbZ \u2202T \u2202 Z ) + Q = \u03c1c \u2202T \u2202 t \u2212\u03bb \u2202T \u2202n \u2223 \u2223 \u2223 \u2223 S1 = 0 \u2212 ( \u03bbZ \u2202T \u2202 Z nZ + \u03bbr \u2202T \u2202r nr )\u2223 \u2223 \u2223 \u2223 St = \u03b1i (T \u2212 Te) (1) where T is the temperature, \u03bbr and \u03bbz are the thermal conductivities in the direction R and Z, respectively, \u03b8a is the heat source density, c is the specific heat capacity, \u03c1 is the component density, S1 is the adiabatic surface, Si (i = 1, 2, 3, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002918_00207179.2014.909948-Figure13-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002918_00207179.2014.909948-Figure13-1.png",
        "caption": "Figure 13. Example 2: Scheme I \u2013 plant states and reference signals (a) x, xd; (b) x\u0307, x\u0307d .",
        "texts": [],
        "surrounding_texts": [
            "Figure 9. Example 1: Scheme II \u2013 tracking error.\nIn this example, we consider dead-zone model (3). The actual plant parameters and dead-zone parameters are respectively given as a1 = a2 = a3 = b = 1, m = 1, br = 0.5, bl = \u22120.6 for simulation. The initial condition of the controlled plant (95) is set to be x(0) = \u22122.5, x\u0307(0) = 3.5.\nD ow\nnl oa\nde d\nby [\nR en\nss el\nae r\nPo ly\nte ch\nni c\nIn st\nitu te\n] at\n2 1:\n41 1\n0 O\nct ob\ner 2\n01 4",
            "Figure 12. Example 1: Scheme II \u2013 designed input v and actual input u.\nD ow\nnl oa\nde d\nby [\nR en\nss el\nae r\nPo ly\nte ch\nni c\nIn st\nitu te\n] at\n2 1:\n41 1\n0 O\nct ob\ner 2\n01 4",
            "Figure 15. Example 2: Scheme I \u2013 parameter estimates.\nD ow\nnl oa\nde d\nby [\nR en\nss el\nae r\nPo ly\nte ch\nni c\nIn st\nitu te\n] at\n2 1:\n41 1\n0 O\nct ob\ner 2\n01 4"
        ]
    },
    {
        "image_filename": "designv10_10_0002676_1.4006791-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002676_1.4006791-Figure6-1.png",
        "caption": "Fig. 6 The forces and moments acting on the DFTV elements",
        "texts": [
            " We observe that the DFTV variator shows relatively small spin coefficients on most part of the ratio range and zero-spin at the unit speed ratio. The SFTV shows instead the largest spin coefficients and the SHTV shows relatively low values, close to the maximum value reached at srID \u00bc 1, on most part of the speed ratio range. Zero spin is obtained, in this case, only at the extreme values of the geometric ratios range. 2.3 Traction Parameter and Efficiency. Dealing with friction drives, we use to define the traction coefficient l\u00bcFT/FN, where FT is the tangential force at the roller\u2013disk interface, and FN is the normal load (see Fig. 6). Also the spin momentum coefficient is defined as v\u00bcMS/(FNr), where MS is the parasitic momentum generated by the spin motion and r the radial 071005-4 / Vol. 134, JULY 2012 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use coordinate of the disk\u2013roller contact point. In Ref. [7], the equilibrium equation for the case of SHTV and SFTV has been already derived, here we focus only on the DFTV. By referring to Fig. 6, the torque balance equation gives FTin r2 FTC rC \u00feMSin cos hDT TBa \u00bc 0 (18) FTC rC FTout r2 \u00feMSout cos hDT TBb \u00bc 0 (19) where the angle hDT\u00bc (p a)/2 (see Fig. 2(a)). In Eqs. (18) and (19), FTC represents the resultant vector of the tangential forces at the roller\u2013roller interface, while the term TB includes the torque losses due to roller bearings (TBR) and to the thrust axial bearing (TBL), namely TB\u00bc TBL\u00fe TBR. According to Refs. [7] and [11], we have expressed the axial bearing loss TBL as TBL \u00bc 4:6 10 5F1:03 R (20) with FR\u00bc 2FN cos h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000775_iros.2000.894664-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000775_iros.2000.894664-Figure3-1.png",
        "caption": "Figure 3: DOFs inside the body",
        "texts": [
            " . . .. -. . :j The robot consists of four active joints, the linear axis 6 1 and three rotational joints &,&,e7 and two passive joints 65 and $6 (see Fig. 2). These two passive joints are not motor driven and have no breaks. They guarantee that no forces are exerted to the entry point t = [t,, t,, tZIT (see Fig. 1). This entry point can be considered as a geometric constraint to the kinematic that binds two degrees of freedom (DOF). As a result, inside the abdomen only four DOFs are left (see Fig.3 ). Additionally the robot consists of another rotatory joint 04, that can be used to suit the geometry to the actual situation. The transformation from the tool-center point frame to the world frame is: with and A ( O i ) representing homogeneous transformations. 2.2 Trocar As already mentioned in Sec. 1 the position of the trocar has a strong influence on the kinematic of the robot. To allow Cartesian control of the tool-tip its position has to be known. One possible solution is to place an electromagnetic tracker a t the entry point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003033_s00170-012-4406-7-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003033_s00170-012-4406-7-Figure6-1.png",
        "caption": "Fig. 6 Relationship between lead angle and B axis angle Fig. 7 C axis angle modification method",
        "texts": [
            " Original and the interpolated cutter location points and the tool axis vectors are shown in Fig. 5. 3.2 NC data correction In Section 2, kinematic modeling of the machine tool is introduced and it is shown that there are multiple possible solutions for B and C axis angles. Therefore, appropriate solution among these candidates has to be chosen. For determining the B axis angle a simple yet effective method is used. For the first CL point in the CL data, lead angle of the tool with respect to workpiece is found, and then the solution having the same sign with the lead angle is chosen. In Fig. 6, the relationship between lead angle and the B axis angle is shown. Lead angle is defined as the rotation angle about Yw which is Y axis of workpiece coordinate frame. Lead angle is calculated as: lead \u00bc atan2 Tx; ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T 2 y \u00fe T2 z q \u00f018\u00de For first CL point modifying the solution for B yields: Following angles for B axis are determined according to previous B axis angle selecting the solution which causes the shortest rotational motion. Modification in C axis angles has to be made as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003985_cjece.2015.2465160-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003985_cjece.2015.2465160-Figure2-1.png",
        "caption": "Fig. 2. Details of the rotor poles displacement.",
        "texts": [
            " To form the phase winding, the coils of the pair of stator poles placed on each stator are connected in series and the corresponding phase windings on the two stators are then connected in parallel. As a result, the 8/6 double-sided AFSRM is a four-phase motor. For the 8/6 double-sided AFSRM shown in Fig. 1, the rotor poles are located symmetrically in both the sides of a rotor core. In other words, the rotor poles in the two halves of the rotor are completely aligned. In the case that the rotor poles are displaced by \u00b1\u03b1\u00b0, a new topology is obtained which is shown in Fig. 2. Due to this displacement, the phase inductance profile of the motor changes as explained hereafter using an analytical method. When the rotor poles in the two halves of the rotor are aligned (Fig. 1), the phase inductance of the 8/6 doublesided AFSRM can be modeled using the Fourier series as follows [10]: L(i, \u03b8) = L0(i) + L1(i) cos(Pr\u03b8) + L2(i) cos(2Pr\u03b8) (1) where \u03b8 is the rotor position, i is the phase current, Pr is the number of rotor poles, and L0(i) = 1 2 [ 1 2 (La + Lu) + Lm ] (2) L1(i) = 1 2 (La \u2212 Lu) (3) L2(i) = 1 2 [ 1 2 (La + Lu) \u2212 Lm ] (4) where La and Lu are the inductance values at the aligned and unaligned positions and Lm is the inductance at the midway between the unaligned and aligned positions. In the case that the rotor poles are displaced by \u00b1\u03b1\u00b0, as shown in Fig. 2, the inductance related to one side of the rotor can be rewritten as Lx (\u03b8, \u03b1)= 1 2 [L0 + L1 cos(Pr (\u03b8\u2212\u03b1)) + L2 cos(2Pr (\u03b8 \u2212 \u03b1))]. (5) And for the other side L y(\u03b8, \u03b1)= 1 2 [L0 + L1 cos(Pr (\u03b8+ \u03b1)) + L2 cos(2Pr (\u03b8+ \u03b1))]. (6) For the 8/6 double-sided AFSRM, when the rotor poles are displaced, the inductance profiles obtained from (5) and (6) and the phase inductance profile are shown in Fig. 3. For the motor without the displacement (Fig. 1), the phase inductance profile calculated using (1) is also shown in this figure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003000_j.measurement.2012.07.005-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003000_j.measurement.2012.07.005-Figure3-1.png",
        "caption": "Fig. 3. (a) Experimental test rig. (b) Schematic rep",
        "texts": [
            " Existence of a misalignment on the system, orders of running speed from 1 to 10 can be seen at the spectrum graph, the vibration amplitude of the two orders (2 ) of the running speed is the biggest than the others. In addition to this, the time waveform graph has a periodic form (nonharmonic). Existence of a mechanical looseness on the rotating machinery, orders of running speed from 1 to 10 can be seen at the spectrum graph, the vibration amplitude of the any orders of the running speed is the random. In addition to this, the time waveform graph has not a periodic form. It has a random form, not periodic. The experimental test rig of direct coupled rotor-bearing system, as shown in Fig. 3, it mainly consists of a steel shaft (27 mm diameter and 1000 mm length) and a centrally located steel disc (1.64 kg weight). The model system is generally used in the industrial machine applications for purpose power transmission or driving unit. The shaft is supported in identical rolling element bearing at its two ends with type of UC 204 SKF ball bearings. Experimental test rig comprises coupling, shaft, disc, two bearing frame bodies, AC velocity control unit and CSI machinery analyzer. System is driven by a 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001650_rob.4620010107-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001650_rob.4620010107-Figure5-1.png",
        "caption": "Figure 5. Rhythmic. motion in one-leg stance.",
        "texts": [
            " In both movements the linear feedback gains of the system are selected to decouple the 10 angles 6: K,=Diagonal Matrix [25,25,25.25,25,25.25,25.25,25]; K,=Diagonal Matrix [lo, 10,10,10.10,10,10.10,10, lo]. These gains correspond to stable poles for the linear system to be all at -5. This means that any transients should dissipate within approximately one second. Two motions of the biped system are considered in this section. The first motion is a rhythmic motion of the left leg and the left thigh (Fig. 5) while the rest of the system remains still. For this motion the nonlinear feedback strategy 110 Journal of Robotic Systems-I 984 is utilized without any delay and without any predictor. The desired motion is further described here. Digital computer simulations of this motion with the above reference signals are shown in Figure 6 . The needed control torques. computed from Eq. (15) are shown in Figure 7. Because of nonlinear feedback and decoupling all other angles remain zero. i.e, the right leg, the right thigh, and the trunk appear to form a stable platform for the rhythmic motion of the left leg and thigh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001758_robot.2008.4543731-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001758_robot.2008.4543731-Figure3-1.png",
        "caption": "Fig 3: Discrete element model of a cable-passing through conduit",
        "texts": [],
        "surrounding_texts": [
            "A. System Governing Equation Consider an infinitesimal cable segment [x, x+dx] with negligible inertia and Coulomb friction acting on it due to contact with the conduit. For this small segment the radius of curvature can be assumed to be constant R(x), where x is the distance of a point along the conduit. Define u(x,t) as the axial displacement of the cable, T(x,t) as the axial cable tension in the. N(x,t) denotes the normal force between the cable and the conduit and f(x,t) denotes the frictional force acting on the cable. When the net axial tension force T(x+dx,t)-T(x,t) = T'(x,t)dx is less than the limiting value of friction the cable segment will not move due to the Coulomb friction, i.e. T . . > T'(x,t) ( , ) 0 ( , ) T'(x,t)dx R x s t u x t and f x t \u00b5 \u2200 \u21d2 = =\u027a (1) On the other hand, when the cable segment moves due to the net axial tension, by force balance along the axial direction: ( , ) ( ) 0 T T x t dx sign u dx when u R \u00b5 \u2032 = \u2260\u027a \u027a (2) To calculate the cable strain Hooke\u2019s law of elasticity is used, modeling cable-conduit system as a linear spring with stiffness keq. The governing strain equation is given by: (x,t) (x,t) T K \u03b5 = (3) where eq k defines the equivalent stiffness of the cable- conduit system give by: 1 1 1 eq cable conduit k k k = + (4) B. Discrete Element Model Partial differential equations in (1) to (3) define the dynamics of the system. However, due to the discontinuous nature of the friction present in the system, it is difficult to solve the equations. Therefore, for computational simplicity, a discrete element formulation is used by dividing the cable into n segments and calculating the displacement and tension of each node at discrete time instants. Consider the i th cable segment between nodes i and i+1. Let T(xi,tj) and u(xi,tj) be the tension and the displacement of the i th node, respectively at time tj. We neglect small variations in radius of curvature over the cable segment, and denote the radius by R(xi). Based on the motion, cable segments can be divided into three different categories. Case 1: When the entire cable segment is moving, since ( ), 0u x t \u2260\u027a , (2) can be integrated to relate the tension and displacements at the two ends as: ( ) ( ) ( ) ( ) ( )1 1 1, , exp ( , ) ( , ) i i i j i j i j i j i x x T x t T x t sign u x t u x t R x \u00b5 + + \u2212  \u2212 = \u22c5 \u2212     (5) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 ( , ) ( , ) ( , ) ( , ) , exp ( , ) ( , ) , , 2 i i j i j i j i j eq i i i j i j i j i i j i j i i eq R x u x t u x t sign u x t u x t k x x T x t sign u x t u x t R x T x t T x t x x k \u00b5 \u00b5 + \u2212 + \u2212 + + \u2212 = \u2212  \u2212 \u2212     + \u2212 \u2248 i (6) Case 2: When the entire cable segment is stationary, the strain and therefore the tension of the segment will not change, i.e. -1 1 1 -1 -1 1 1 -1 ( , ) ( , ) ( , ) ( , ). ( , ) ( , ) ( , ) ( , ). i j i j i j i j i j i j i j i j T x t T x t and T x t T x t u x t u x t and u x t u x t + + + + = = = = (7) Case 3: A part of the cable segment is moving, while the rest of it is stationary. Assume that node i is moving, while node i+1 is stationary. From (7), for the stationary section of the cable segment, j j-1 j j-1 T(x,t ) = T(x,t ) and u(x,t ) = u(x,t ) . The displacement of the stationary section can be approximated by the displacement of the last moving point of the cable segment. Therefore, we can approximate that (6) holds true. On moving one end of the cable initially only a part of the cable moves, and as the tension at the input end changes, motion gradually propagates across the cable. If the first k nodes are moving at some time instant tp, we need to solve for the cable stretch and tension of the first k segments, solving 2k-1 equations simultaneously for tension of the first k nodes, and displacement of node 2 to node k. When the k th cable segment satisfies eq. (5), motion propagates to the next node and node k+1 becomes the last moving node. C. Single Cable Simulation Before simulating the closed loop system, simulations were carried out to characterize the tension transmission across a single cable. A desired motion profile is provided to the actuator end of the cable, and the tension at the two ends of the cable is calculated. Simulation results are plotted in Fig. 4 for two cases: 1. Pretension is high such that the cable does not slack; 2. Pretension is low, such that the cable becomes slack during the motion. These simulation results are similar to the lumped mass model and experimental results performed Kaneko et al. [5, 6], which also justifies the assumption of negligible cable inertia. It has been shown that due to tension losses across the cable, tension transmission may not be continuous across the cable. This leads to a period during which the movement of one end of the cable does not lead to the movement of the other end. The other end starts to move only when the tension change on the first end is significant enough to overcome friction. Thus it follows a backlash type of force transmission profile. D. Closed loop cable-conduit Simulation We extend the simulation of single cable to the case of closed loop system, assuming no slacking at the two pulleys. One end of each cable (cable A and cable B as shown in Fig 5) is fixed to the drive pulley while the other end is anchored to the follower pulley. Apart from the assumption of small cable motion, we can also assume that the nodes on one side of the pulley do not move to the other side. This assumption is reasonable since we always have some part of cable exposed without a conduit where no friction is acting, and therefore can be taken towards the compensation for the cable motion. Similar to the case of single cable described above, the simulations are carried out with the constraints for torsional spring and no slacking at the pulleys, 4 2 ( ) o e o o K T T R\u03c4 \u03b8= \u2212 = \u2212 (8) 3 2 2 o o x x R \u03b8\u2212 = (9) 2 3 x x L+ = (10) where \u03c4o is the torque being applied by the load motor, o \u03b8 is its angular rotation, Ro is the radius of the pulley at the load motor, Ke is the simulated environment stiffness, L is the sum of two cable lengths (with pretension), T1,2,3,4 denote the tension at the four ends of the cable, and x1,2,3,4 denote the position of the corresponding ends. The input motor is provided with a sinusoidal oscillatory motion profile. For each time step the motion of the input motor is calculated and based on that, we determine the \u2018last moving node\u2019 on each side of the pulley, and the tension and displacements of all the nodes up to the last moving node. Consider the time period when one end cable A is moving, while the other end is stationary, i.e. there is some intermediate node on the cable A which is the last moving node. During this period, cable A will act as an independent cable, the motion of which will not affect the motion of cable B. Therefore during the time period when the last moving nodes of the two cables do not coincide, there is no interaction between the two cables and the motion of the two cables can be solved independently. Once the last moving nodes of the two segments coincide, the entire system follows a collective motion. Based on the above analysis, the motion of the system can be divided in two categories, both sides of cable taut, or either side of cable slack. When one side of the cable goes slack the other side still moves as an independent cable. E. Simulation Results Analysis Apart from the backlash profile in motion and torque transmission, several other atypical phenomena are observed. Fig. 6 shows the variation in the tension at the two ends of the cable for both cables, input (load) torque vs output (drive) torque profile, and input vs output angular rotation. For the ease of understanding, various time instances in the motion and the sequence of motion propagation have been marked in Fig. 6, which are described as follows: 1. Drive motor starts to rotate counterclockwise such that cable A is getting stretched, while cable B is released. 2. Motion has propagated across cable B and it starts to move load pulley. Motion has only been propagated in cable A till some intermediate point, and a part of cable A is still stationary. 3. Motion has propagated to the end of cable A, and both cables start to move. 4. Cable B goes slack. 5. Input motor reverses its direction of motion, while cable B still remains slack, load pulley is not moving. 6. Cable B starts to move after getting taut again, and it moves the load pulley. Motion has only propagated in cable A till some intermediate point. Similar to stage 2. 7. Both cables start to move, but in direction opposite to that of stage 3. 8. Cable A goes slack. 9. Cable A remains slack, input motor changes direction of motion, similar to stage 5, but slack cable and direction of motion has been changed. 10. Cable A starts to move after becoming taut, and starts After stage 11, next stage coincides with stage 3, and stages 3-11 keep on repeating thereafter. Based on these stages the motion can be divided into following phases: I. Output pulley not moving (Time interval between stages 1-2, 5-6, 9-10) \u2013 Motion has not propagated to the distal ends (i.e. the load pulley) in either of the cable. The load pulley remains stationary, and it translates to the backlash region in the transmission profile. II. One cable pulling another cable (Intervals 2-3, 6-7, 10-11) \u2013 The tension variation at the two ends of the cable are opposite to each other, i.e. when tension at one end of the cable is increasing (or decreasing), but on the other end it is decreasing (increasing). This translates to the small slope in the torque backlash profile, which has also been referred as soft spring [3]. The motion of the output pulley is influenced only by one cable, while the other cable remains inactive. In this phase one of the cables is not moving, but it is not slack, i.e. the pretension is high enough to avoid any slacking. III. Both cables moving (Intervals 3-4, 7-8, 11-3) - Entire system is moving collectively. This translates to the directly proportional part of the transmission profile. IV. One cable goes slack while other cable keeps moving (Intervals 4-5, 8-9) - Since the motion is governed by one motor, similar to phase II, the slope in the torque as well as theta profile reduces. V. Change of direction of motion of one cable, while From these plots, it is evident that friction not only causes a backlash type of tension transmission profile, but also results in other phenomenon, such as changes in the slope of the transmission, introduction of small slopes in the torque transmission (intervals 6-7, 1-11), as well as opposite tension variations at two ends of the cable. Apart form the transmission profile, all these phases are most predominantly visible in the plot of input torque versus input theta (Fig 7). This also provides evidence that if the state of the system friction is know, the motion of the load pulley and cables can be predicted based on the motion of the drive pulley."
        ]
    },
    {
        "image_filename": "designv10_10_0001165_0954406021525331-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001165_0954406021525331-Figure2-1.png",
        "caption": "Fig. 2 Equivalent joints aligning with creases",
        "texts": [],
        "surrounding_texts": [
            "In the highly competitive consumer product market, packaging in the personal product range including cosmetics and perfumery requires frequent changes in type, shape and closing method. New cartons come out frequently, with fancy types and attractive shapes and with various closing methods. The dif culty arises in carton packaging automation when changing over from one type of carton to another where manual effort is still required. This affects the consistency in quality control and incurs labour injuries to the wrists due to the constant twisting motion in various carton folding processes.\nThough research has been carried out in the study of residual moment [1] by applying the nite element method, with results con ned to a local bending motion of a carton panel, little study has been made until recently with respect to a carton motion. Akella and coworkers [2, 3] introduced a exible xture approach for folding a carton where a collision-free algorithm was employed to search a motion path in a con guration space of a carton to generate a folding sequence. The work has a general impact but con nes itself to a particular type of rectangular carton.\nThe concept of carton folding can be categorized as folding sequence, path planning and folding process. Though not much literature is available on carton manipulation and carton folding, a similar concept can be found in sheet metal folding, where a CAPP (computer aided process planning) was used based on a tolerance tree [4] to generate bending sequences. De Vin et al. [5] introduced a heuristic search method based on a sequence search to minimize handling steps and to select tools. Radin et al. [6] developed a two-stage algorithm for determining the bending sequence and for searching for lower cost solutions without violating its time constraints. Gupta and Guo [7] proposed an automated robotic system for planning and executing bending on sheet metal blanks. Wang [4] dissociated the sheet metal products into components that ease manufacturing in cutting, bending and assembly.\nTo apply these results to carton folding and to analyse a carton motion, a new concept is required to model a carton. In 1997 Dai and Rees Jones [8] proposed a new model to describe and present a carton as a mechanism. By presenting carton creases which are dominant elements in carton folding as revolute joints and considering carton panels which do not need to bend during a carton folding process as mechanism links, a carton can be presented as an equivalent mechanism. A metamorphic mechanism [9] is hence produced. The new mechanism has typical characteristics and changes its mobility during motion. A correlation between a carton and this equivalent, metamorphic mechanism was proposed [10] and mobility in this type of mechanism\nof a foldable/erectable kind was analysed based on the theory of screws [11].\nA foldable carton is produced from a cardboard or hard-back paper that is cut and creased and prepared with xing aps or integral locking devices. The process of folding a carton in a packing assembly operation is regarded as a succession of moves from one distinct con guration to another, in which anticipated changes in shape are governed by the geometry of crease lines and the dimensions of panels. Hence, the possibility for panels to move and the priority of movement into successive distinct con gurations are determined by the kinematic geometry.\nThis paper focuses on the manipulation in a carton folding process, investigates the folding sequence of cartons and provides a folding trajectory based on the directed graph theory [12] and kinematic transformation of an equivalent, metamorphic mechanism. The mechanism is analysed and con guration changes are characterized. The algorithm is then developed by identifying the active guiding joints and by generating the hereditary connectivity in sequence analysis. The approach aims to give a feasible packaging sequence of a foldable carton and to give a trajectory for providing the position and orientation for manipulating ngers in carton folding manipulation. An origami-type carton is used in demonstrating the manipulation process and the con guration changes in carton folding. The work addressed in this paper is an essential step towards the manipulation control of a packaging process for a programmable automatically controlled robotic packaging unit.\n1. Directed graphs (digraph) are denoted as Gd Q, E , consisting of a set of nodes Q q1, , qn and a set of arcs, E, of ordered pairs of nodes. Vectors q1, , qn are con guration vectors at the geometric centre of panels. Matrix Q is a con guration matrix consisting of n con guration vectors. 2. The adjacency matrix is denoted as A aij\u0160 for a graph formed by a set of nodes given by q1, , qn. It can further be speci ed as aij i=j 1 if qi and qj are adjacent, aij i=j 0 if qi and qj are not adjacent and aij i j 0. 3. The upper triangular adjacency matrix (UTAM) is obtained from the upper triangular part of an adjacency matrix with zeros in the lower triangular part of the matrix. 4. The hereditary connectivity matrix H hi, j\u0160 is generated from an adjacency matrix by taking column connectivity and its hereditary connectivity. Each entry, hi, j, of the matrix is a homogeneous\nProc Instn Mech Engrs Vol 216 Part C: J Mechanical Engineering Science C17101 # IMechE 2002",
            "transformation between two panels corresponding to the row and column numbers. 5. A path of a foldable carton G from qinit to qgoal is a continuous map t [13], where [0, 1] ?C , with t 0 qinit and t 1 qgoal. Vectors qinit and qgoal are the initial and target con gurations of the path respectively.\nA carton is formed by a combination of different geometric shapes. It generates various states from its transportation to its folding process and to its nal completed pack. The initial state of a carton is at, as shown in F ig. 1. Taking creases of a carton as joints and panels as links, a carton fold can be presented as an equivalent mechanism (F ig. 2). This mechanism has a characteristic that changes its link number and consequently changes its mobility during motion. When endlink 5 in the gure is attached to link 1, equivalent to at 5 being attached to panel 1, the mechanism changes its structure and mobility and forms a new con guration state (F ig. 3). This presents a metamorphic mechanism [9] that allows a mechanism representation of a carton. It can be seen that, during motion, the main part of the mechanism changes from a ve-bar serial kinematic chain in F ig. 2 to a four-bar closed-loop kinematic chain in Fig. 3. This facilitates the study of folding motion of artefacts, fancy gift packs and paper folds.\nThe nature of the changeable mobility of a metamorphic mechanism represents the con guration changes of artefacts and foldable cartons during carton folding. The mobility of an equivalent metamorphic\nmechanism can be derived from a Kutzbach\u2013Grubler criterion [14], which is dependent on the type of pairs and constraints as follows:\nm mc mo b n \u00a1 g \u00a1 1 g go 1\nwhere mc is the mobility in closed loops, mo is the mobility in open loops and is equal to number of joints, go, in open loops, b the order of the screw system formed by joint axes of a closed loop, n the number of links in a closed loop and g the number of joints in a closed loop.\nThe use of the above equation to the equivalent mechanism of a carton can be illustrated with respect to the two con guration states of the origami-type carton in Figs 2 and 3. The attened con guration of the equivalent mechanism in F ig. 2 is an open-loop kinematic chain. The mechanism has 12 joints and subsequently go is equal to 12. The mechanism in this\nC17101 # IMechE 2002 Proc Instn Mech Engrs Vol 216 Part C: J Mechanical Engineering Science",
            "con guration state hence has a mobility of m mo 12. When the mechanism changes its con guration state to an erectable con guration in F ig. 3, the mechanism becomes a mixture of both open loops and a closed-loop kinematic chain. The closed loop is formed by links 2, 3 and 4 and a combined link 1(5) by attaching link 5 with link 1. The link number in the closed loop is 4 and the joint number is 4. Hence the closed loop becomes a four-bar submechanism. Since this submechanism [15] has planar motion only, the order of the screw system formed by the four joint axes is 3. F rom equation (1) this gives the mobility of the closed-loop submechanism mc 1. The open loop in F ig. 3 has eight joints and gives mo go 8. Hence, the mobility at the erectable con guration state of the equivalent mechanism is m 1 8 9. The mobility of the equivalent mechanism then changes to 9 at its erectable con guration state, presenting a new mechanism structure.\nThe graph representation of the equivalent mechanism in F ig. 2 is given in F ig. 4. The graph of the new structure of the metamorphic mechanism after the con guration change is given in F ig. 5.\nThe above approach can be applied to complex cartons which require a concerted effort for carton folding. In particular, complex origami-type cartons are a challenge to automatic carton folding. F rom this section, a typical type of origami carton is presented to investigate the carton folding manipulation and to illustrate the algorithms and the approach in this paper. The carton with both a attened con guration and a folded con guration is illustrated in F ig. 6. The equivalent mechanism model is introduced in F ig. 7 by taking crease lines as revolute joints and panels as links. It can be seen that the mechanism consists of four spherical submechanisms which centre at O1, O2, O3 and O4 respectively. The graph representation is given in F ig. 8.\nA carton can now be presented in a new class of mechanism which changes its mobility during motion. The folding sequence of a carton can hence be obtained from the analysis of the equivalent mechanism and its\nProc Instn Mech Engrs Vol 216 Part C: J Mechanical Engineering Science C17101 # IMechE 2002"
        ]
    },
    {
        "image_filename": "designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000868_(sici)1521-4001(199904)79:4<281::aid-zamm281>3.0.co;2-v-Figure5-1.png",
        "caption": "Fig. 5. Influence of residual stress on the elastic rotational stresses in (a) hollow disc and (b) solid disc, Predictions by Tresca (- - - -) and von Mises (\u00b1 \u00b1 \u00b1 )",
        "texts": [
            " It appears that Tresca magnitudes are greater but nowhere do they exceed 25% of the yield stress. Also, the sense of both sRr and sRq oppose those of von Mises within the prior elastic zone. We should only need to measure the residual hoop strain at the outer diameter to establish which criteria is more realistic. 3.3 Net stress distributions Residual compressive stresses may be exploited when it is desirable to reduce hoop tension. For instance, residuals can remove the concentration in tensile stress around surface defects when a hollow disc rotates at high speed. Fig. 5a shows how this is achieved when the disc in question is designed to rotate at 6300 rev/min. This is an elastic speed equal to 75% of the speed required to initiate plasticity. The continuous lines in Fig. 5a are the Lam e elastic stresses found from eqs. (1a, b). The hoop stress reaches its maximum of 0.56Y in tension within the bore. The radial stress attains a maximum of 0.18Y at a radius of riro p . Had this disc been pre-spun at an elastic-plastic speed of a 11000 rev/min the elastic distributions would be altered by the presence of the residuals determined by Mises and Tresca earlier. The net stress distributions (broken lines) shown are found from adding the two distributions. They reveal that net hoop compression exists in the bore. This stress peaks in tension at the prior interface radius which differs between the two criteria. The net radial stresses are also reduced. The internal net stresses in a solid disc are much more strongly dependent upon the yield criterion used to establish the residuals. Fig. 5b shows the elastic stresses (continuous lines) for a speed 9000 rev/min, which again is 75% of the speed required to initiate plasticity within the said disc. These show that both sq and sr fall gradually from maximum values of 0.57Y at the centre. Adding to these the residuals established earlier within Figs. 4a, b results in the net distributions shown as broken lines. Magnitudes are lowered beneficially to 0.38Y at the bore. Peak stresses occur at the prior interface radii of magnitudes 0.45Y \u00ff 0:6Y "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure5.2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure5.2-1.png",
        "caption": "Figure 5.2 two-wire; (b) coaxial; (c ) parallel plate; (6) microstrip. Longitudinal and transverse views of selected TEM transmission lines: ( a ) open",
        "texts": [
            " Moreover the variation of the phase velocity with frequency during transmission may be such that distortions will be introduced through dispersion of the signal if it contains multiple frequencies. For such conditions an analysis of transmissions lines is carried out by applying field theory concepts. We will consider the important class of transverse electromagnetic (TEM) lines that are widely used in a variety of applications. In such lines the propagating waves contain electric and magnetic fields that are predominantly transverse to the direction of propagation ( z direction in Figure 5.1). Longitudinal and transverse plane views of selected TEM lines are shown in Figure 5.2. It is assumed that the lines are excited at the left hand side so that energy is propagated along the z direction. As shown, the z direction is defined as the longitudinal direction along which the energy propagates; also observe that each line has a constant (or uniform) transverse cross section (in the xy plane) along the longitudinal direction. This is why the lines shown here are also called uniform transmission lines. For the purpose of illustration, consider the coaxial line in Figure 5.2b is fed at the left-hand side. It can be shown that the field configuration within the coaxial region is entirely transverse, meaning the fields consist of E = 6Ep, H = 4H4, and E, = H , = 0 in the present case. The average power flow in the line is S,, = Re[ iE x HI = EpH@2, meaning in the longitudinal z direction, and the fields are TEM type. Similar considerations indicate that the two-wire line of Figure 5.2a ideally sustains a predominantly TEM type of field configuration. It can be shown that the fields here consist of E = iE,, H = ijHy, and E, = H , = 0, thereby propagating energy in the z direction. Neglecting the edge effects, it is simple to visualize that the fields within the parallel plate region of the line in Figure 5 . 2 ~ will consist of E = ?Ex, H = cHy, E, = H , = 0, and hence the energy propagation is in the z direction. The microstrip line in Figure 5.2d does not support strictly a TEM mode of fields; it does contain a small E, component. Generally, E, is neglected and 142 TRANSMISSION LINES TELEGRAPHER\u2019S EQUATIONS: QUASI-LUMPED CIRCUIT MODEL 143 it is assumed that the fields within the microstrip region are only E = iE, and H = $Hy thereby transmitting energy in the z direction. It should be noted that all four lines shown in Figure 5.2 require two conductors, as is true for all TEM transmission lines. We will assume that the medium within the line is homogeneous and is characterized by PO, E O E ~ , a; 0 is assumed to be very small, meaning dielectric loss is very small. The conductivity of the conductors used is ac. A rigorous way to analyze the lines in Figure 5.2 is to consider them as boundary value problems where the required fields are obtained from Maxwell\u2019s equations and then apply the proper boundary conditions. We will not proceed in this complicated way but follow a simpler method called quasi-lumped circuit theory. This method involves modifying the lumped circuit model so that the finite time ofpropagation through the line is taken into account [ 1,3,4]. Intuitively, it is argued that the resistance, conductance, inductance, and capacitance associated with the line are distributed continuously along the length of the line. We shall represent them by lumped parameters R, G, L, C, respectively on a per unit length basis. Although these parameters are different for different lines shown in Figure 5.2, it is then possible to use a single quasi-lumped circuit model for each. Thus the model for a section of the line between z and z + dz (or between AD and BC) is shown in Figure 5.3 at time t , where the instantaneous values of the voltage and currents or u ( z , t ) and i ( z , t ) are as shown, and R is the resistance in ohms per unit length of the line, 144 TRANSMISSION LINES G is the conductance in mhos per unit length of the line, L is the inductance in henries per unit length of the line, and C is the capacitance in farads per unit length of the line",
            "85) LINE PARAMETERS 163 where PL is the power consumed by the load. Equation (5.85) indicates that for maximum power transfer to the load, rL should be as small as possible, or in other words, the VSWR S should be as close to unity as possible, which means that the load should be matched to the line (for an ideal match, l?L = 0). So far in our discussion we have used a transmission line model characterized by a continuous distribution of lumped circuit parameters R, L, C, and G per unit length of the line. This model applies to all TEM lines shown in Figure 5.2; however, the circuit parameters applicable to each line are determined by its geometry, material constituents, and environment. The relevant parameters can be determined analytically by treating the line as an electromagnetic boundary value problem. Such treatment can be found in most textbooks on electromagnetics and transmission lines [ 1,2,4,5]. We will follow here simplified and approximate methods [8] to obtain the required values that are sufficiently accurate for practical use. Detailed derivation and analysis may be found in the references cited",
            ", at t = O+) values of voltage and current as (5.129a) Z(z, t ) = Z(O,O+) = I\" = 2, + 2\" ' (5.1 29b) TRANSIENTS ON TRANSMISSION LINES 183 and note that v ( z , t ) / i ( z , t ) = V ~ / l o = 20, as it should be. Let us now assume that steady state or final state is obtained at time t = t o (= 00). Under the steady state condition the equivalent circuit can be represented as shown in Figure 5.20. Due to the nature of the voltage source, under steady state condition, the voltages at A-A\u2019 and B-B\u2019 are the same and using the circuit shown in Figure 5.2O(b) we obtain them as (5.130a) i ( 0 ,oc ) = i ( d , m ) = I , = 2, + Z L (5.1 3 Ob) 5.8.2 Transient Values We assume that at time t = O f , a voltage and a current wave of amplitude the load ZL along the z direction with velocity (5.13 1) where L, C are the per unit length inductance and capacitance of the line. The time taken by both waves to reach the load is d tl = - W (5.132) 184 TRANSMISSION LINES TRANSIENTS ON TRANSMISSION LINES 185 On reaching the load, the waves suffer reflection at the load",
            " The voltage and current reflection coefficients at the generator end are r G and - r G , respectively, where The voltage and current waves at A-A' at time 2 t f are ~ ( 0 , 2 t ; ) = v+ + v-(1 + rc) = vo + rLvo + rGrLvo (5.136) (5.1 37a) The reflected waves will proceed toward the load where they will be reflected and the process will continue back and forth until the steady state is obtained (which, ideally, will take infinite time in the present case). Instead of tracing the voltage and current waves back and forth, it is easier to keep track of the process by using the bouncing (or lattice) diagrams shown in Figure 5.2 1 and 5.22, respectively. The diagrams are graphical representations of the voltage and current waves as they travel back and forth between the generator and the load. They can be used to estimate the transient duration before the steady state is reached. For example, the steady state voltage at (l, t + m) or z = (d - l, t + m) is obtained by adding up the contributions at A, B, C, D, E , . . . , and similarly for the current wave. 186 TRANSMISSION LINES TRANSIENTS ON TRANSMISSION LINES 187 188 TRANSMISSION LINES Figures",
            " The total voltage (or current) at any position ( z = d - e, or t) can be determined by drawing a vertical line through the point ( z or 1') and then adding the voltages (or current) of all the zig-zag segments intersected by the line between time t = 0 and t. For example, the voltage and current buildup at the generator and load terminals are as indicated at the appropriate locations on Figure 5.21 and Figure 5.22, respectively. The voltage and current at the load and generator terminals can be obtained similarly from the bounce diagrams, and they are as given below: I = { I o , From Figure 5.2 1 it is seen that the steady state value of the voltage at the load is for0 5 t < 2 t l I. - rr. Io, fo r2 t l 5 t < 4 t l . V ( Z = d , t + m) = vo + rLvO +rGr2,v, + r&r2vo + r&rtvo + . . . 00 n=O 1 + rL 1 - rGrL . = v, (5.138) Introducing the value of r L , rc; (from (5.134) and (5.136)) in (5.138) and using (5.129a) for VO we obtain: MEASUREMENTS 189 which is the same as V, given by (5.129a). Hence it is compatible with the equivalent circuit in Figure 5.20b. Similarly, from Figure 5.22 the steady state current at the load end ( z = d, or l = 0) is 30 q d , t = W) = io(i - rL) X(rGrLy n,=O 1 - rL 1 - rGrL = I0 (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000694_0094-114x(96)84593-9-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000694_0094-114x(96)84593-9-Figure2-1.png",
        "caption": "Fig. 2. Two reciprocal screws on a body.",
        "texts": [
            " These direction lines can be rotational axes when the motion is rotational. In the direction in which the pitch h = oo, the motion can only be translation. I f h has a value other than 0 or oo, the motion will be the screw motion. It can be concluded that if a body is subjected to a reciprocal screw $~, i.e. a constraining force, its rotations will be restricted, except for those around the axes sharing the same plane with Sr. I f a screw system applies two reciprical screws on a body, as shown in Fig. 2, for simplicity and generality, we can suppose these two reciprocal screws as, $ ~ = ( 0 0 1;0 - l 0) $ ~ = ( 0 1 0;0 0 0) There are two methods for determination of the possible motions under the constraints of these two line vectors. The first method is to use the screw expression. Adding two line vectors, we have, J ~ = $ ~ + $ ~ = ( 0 1 1;0 --1 O) 1002 Z. Huang et al. where f = x//2, h = - 1/2, ( / m n) T = (0 1/x/~ l/x//2) r, (p q r) T = (0 -- l/x//2 0) T, from equation (4), we have, 1~ = (1/2 0 0) T",
            " These two reciprocal screws $~ and $~ are perpendicular and intersect with each other. Four motion screws are, $ ~ = ( 0 1 1;0 0 1), h=\u00bd l $\u2022=(0 - 1 1;0 0 --1), h = - ~ $~ '=(1 0 0;0 0 0), h = O $ ~ = ( 0 0 0;1 0 0), h = oo Any other possible motions are the linear combination of these four screws. Another method for determination of the motion screws is the observation method. From Fig. 1, it can be seen that translation is possible in the direction orthogonal to $~ and $L and the axis intersecting with $~ and $~ can be the rotating axis, as shown in Fig. 2. We can verify the agreement of these two methods, for example, $ ~ = $ ~ + $ ~ n = 2 ( 0 0 1;0 0 0), rotation $ ~ = $ ~ + $ T + 2 5 ~ = 2 ( 0 0 1;1 0 0), rotation $ ~ = $ ~ + $ ~ = ( 1 0 1;0 0 0), rotation When the body is subjected to three reciprocal screw line vectors, i.e. three constraining forces, all its translational motions in three-dimensional space are constrained, and its possible motions are three rotations. However, any of these rotational axes must intersect with three line vectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure21-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure21-1.png",
        "caption": "Fig 21 Friction factor - performance comparator for intensity of heat generated (FEB)",
        "texts": [
            " The author has introduced a similar study 43 which gives, on a comparative basis, the accumulative work done around the bearing (at every 10 \u00b0 of bearing arc) during a complete load cycle. This may indicate to some extent the severity of high local temperatures which could aggravate both wiping and fatigue damage. The approach differs from Ross and Slaymaker in that the reciprocal of the film thickness is used in the analysis rather than the eccentricity (the bearing surface being more sensitive to film thickness). The development of a friction factor map which can be used as a comparator indicating the intensity of heat generated around the bearing is shown in Fig 21. This figure relates to the VEB big end bearing study case. The centre part shows the, now well-recognised, journal centre orbit TR I B O L Q G Y in te rna t i ona l 157 on a horizontaI plane. The upper figure shows the first part of the process for a particular crank angle and journai position. The heights of the vertical bars shown are proportional to the frictional work done on each 10 \u00b0 arc of bearing surface. This process is repeated throughout the 720 \u00b0 of crankshaft rotation and a!t the friction values (height of vertical bars) are summed and averaged at each l 0 \u00b0 of bearing arc. The lower diagram in Fig 21 shows the resultant E\u00d7perimentol a Predicted 600 ._= ~E o 400- o 200 Gt~cier ~ / j ~ experiment~ 0 C Feed pressure, ber 2 4 6 overall friction factors, and gives a comparison oi: the accumulated frictional work done as particular positio.<~.s around the bearing\u00b0 E xperimentN support A few years ago the National Engineering Laboratorms we:e very active m a joint program of research with Perkins Engines with the prh~dpat aim of providing h~proved design methods for engine bearings. W L Cooke\u00b0 formerly at NELo supervised the experimental work ~here, which was suppo; ted by the UK Departmem of Industry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002328_978-90-481-9689-0-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002328_978-90-481-9689-0-Figure11-1.png",
        "caption": "Fig. 11 The comparative stress diagram for the two analyzed cases.",
        "texts": [
            " The dynamic maps obtained can give important data for the analysis of the behavior of the knee joint in two cases: first, for the normal walking and second, for the sectioned ligament. These diagrams show that the less stressed surfaces are determined in the first case for the normal walking and the most stressed areas are obtained for the second case. These surfaces are located on menisci, tibial plateau and posterior crisscross ligament. Using these dynamic maps decomposed in frames 313 D. Tarnita et al. (static maps), the information can be structured in the different ways, such comparative diagrams that shows the differences between the analyzed cases. In Figure 11 an example was presented for these kinds of analysis which shows the major differences of the maximal stress between the two studied cases. In this figure it was determined that the maximal stress for the second case is 3.54 times bigger than the walking studied case. 314 Numerical Simulations of the Virtual Human Knee Joint The 3DP (three-dimensional printing) is a rapid prototyping technology, used to create complex three-dimensional parts directly from a computer model of the part, with no need for tooling [4, 5]",
            " dia dt = 1 L (ua \u2212 cm \u00b7\u03c9 \u2212R \u00b7 ia) (4) d\u03c9 dt = 1 J (cm \u00b7 ia \u2212\u03c9 \u00b7b\u2212Mext) (5) where R represents the resistance of the armature, L the electric inductance, J is the rotor\u2019s moment of inertia, cm is the machine constant, b represent the friction coefficient and ia is armature current, Mext \u2013 external torque (Mr raxM). Taking note of Equations (4) and (5), a flow chart was developed. This flowchart represents the model of the DC motor presented in Figure 10. 589 O. Tatar et al. The characteristics of the motor are: b = 2.6 \u00b710\u22126 [Nm/ rad/s], L = 6 \u00b710\u22123 [H], R = 3[\u2126 ], J = Ir = 1.5 \u00b710\u22126 [kg m2], cm = 5.7 \u00b710\u22123 [Nm/A]. Therefore, the initial response of the system with KP = 1, KI = 0, KD = 0 is presented in Figure 11. After the optimisation the resulting constants are: KP = 5.294, KI = 0.07686, KD = 0.0238. In a corresponding way, the response during an time period is also obtained (Figure 12). 590 The Modular Robotic System for In-pipe Inspection In the near future, field tests will be conducted with the system and the prototype will be adjusted according to the obtained results. This paper presents a wheeled in-pipe modular robotic system. A very impor-tant design achievement of the in-pipe modular robotic system is the adaptability to variable inner diameters of the pipes",
            " A good mechanism was proposed in [5] and the scheme is shown in Figure 10. The reference x0y axes are placed according to the Schmidt Analysis [9]. Schmidt has made the classical Stirling Analysis in 1871. Using the same reference it can replace the sin function of compression cylinder, in the Schmidt Analysis by a new displacement function, in order to develop a new isothermal analysis of the engine. But this one is not good enough regarding the phases of the two pistons. In order to improve this situation a mechanism as shown in Figure 11 was proposed in [3]. The analysis of the dwell mechanism begun in [3] and it reveals the expected displacement functions yC(t) and yE(t) and the phase relation between them. The proper phase relation demonstrates that the mechanism is good for the application that it is focused on. Second, it must show that yE(t) has a dwell large enough level, in accordance with the expansion stroke time of the expansion cylinder. Implementing the displacement functions from [3] in a computer program and proceeds to a numerical derivation it obtains the velocity and the acceleration functions",
            " In order to view the configuration of the torque at element (1) it implements equations (1) to system equation (8) into the computer program that was used in [4]. The torque diagram is shown in Figure 14. It could be observed that torque presents a positive maximum along the dwell angle of the compression cylinder (in the torque diagram the sign (+) is under the 0x axis). The torque diagram configuration is a reliable argument to sustain the attempt to improve the PV diagram of classical Stirling engine (with two slide-crank mechanisms, see Figure 3) using the proposed linkage (Figure 11). Movement, velocity and acceleration functions of the compression cylinder (piston) prove that the proposed linkage is able to perform a dwell in a proper phase position. Torque function of the crank presents a maximum point along the dwell angle of the compression cylinder. The two diagrams prove that the paper makes a step award to improve the Stirling engine design. 1. Ataera, E.O. and Karabulutb, H., Thermodynamic analysis of the V-type Stirling-cycle refrigerator, International Journal of Refrigeration, 28:183\u2013189, 2005"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000689_s0094-114x(02)00030-7-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000689_s0094-114x(02)00030-7-Figure3-1.png",
        "caption": "Fig. 3. Initial, final position and trajectory.",
        "texts": [
            "0 s of motion the terminal element reaches the position 0~rO0;TCP t\u00bc5 sj \u00bc 0:62 0:30 0:11\u00bd T m. In order to imple- ment the simulation proposed in this example, a simulation program was written in FORTRAN based on the method explained in Section 4.2. The program written in double precision and runs on a 400 MHz Pentium II PC. The linear system was solved using Cholesky decomposition and the fourth/fifth order Runge\u2013Kutta technique is used to integrate the differential equations. In the integration process, a tolerance of 1 10 6 is used and an interval of 0.1 s is employed. Fig. 3 shows the robot in the initial position; the planned trajectory; and the final position. In order to obtain the generalized forces that cause the end effector to describe the programmed trajectory, the inverse dynamic problem for every instant has been solved, using as input data the results of the resolution of the inverse kinematic problem. Fig. 4 shows a block diagram of the procedure, where the superscript \u2018\u2018 \u2019\u2019 denotes the generalized coordinates, velocities, and accelerations obtained by the numerical integration of the method developed in this work"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003306_tmag.2017.2665639-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003306_tmag.2017.2665639-Figure4-1.png",
        "caption": "Fig. 4. (a) IM internal geometry, slots, rotor bars and placement of the ITSC. (b) 2D IM external geometry for the FEA. The units dimentions are milimiters (mm).",
        "texts": [
            " For the purpose of creating the ITSC, the motor was dismantled and 8 center taps were performed in the IM phase \u201ca\u201d as depicted in Fig. 3(a). The winding profile of the phase \u201ca\u201d with one of the fault cases is shown in Fig. 3(b). Four cases of the fault were performed with a fault severity factor of 42/510 (8.2%). The 4 cases were conducted in the following positions of the phase winding \u201ca\u201d: : , : , : and : . indicates the position where 1, 2, 3, 4 . The fault resistance is imposed 0.67 \u03a9. The complete geometry of the IM is depicted in Fig. 4(a) and (b). The stator consist of an iron core M19 USS with 36 slots numbered as in Fig. 3(b). The rotor bars are made of Aluminum 3.8e7 Siemens/m and there are 44 of them. The air gap is 0.31 mm. The FE simulation is performed by strong coupling simulation between FE and circuit analysis. The FE is used to model the phase \u201ca\u201d as the combination of 7 coils (6 healthy and 1 faulty windings) all connected in series to form the phase. The faulty circuit part is connected as a step-down autotransformer configuration where is added as in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure11-15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure11-15-1.png",
        "caption": "FIGURE 11-15 Determination of the longitudinal location of the center of gravitv using the weighing method.",
        "texts": [
            " The locations determined experimentally are then often useful in estimating the center of gravity location of a new tractor design. Only the weighing method for center of gravity location will be discussed in this section. Several other methods are discussed in the suggested readings at the end of the chapter. Given the tractor weight W, and wheelbase, L = hit cos 8 It + h2' cos 82\" the longitudinal location, e = xc!': = hit cos 8 It, of the center of gravity may be 304 MECHANICS OF THE TRACTOR CHASSIS found by placing the front axle of the tractor on a scale to determine force Rf (fig. 11-15). Then (78) As a check, the reaction Rr may be found and the distance L \u20ac determined, Since most tractors are approximately symmetrical about the vertical plane perpendicular to the axles and passing midway between the wheels, the lateral location of the center of gravity will normally be quite close to this plane. Given the wheel tread setting, the lateral location may be found by weighing one of the sides of the tractor. Again weighing the other side can serve as a check. The measurements required for finding the longitudinal and lateral lo cations of the center of gravity are straightforward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001900_978-1-4020-8829-2_11-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001900_978-1-4020-8829-2_11-Figure2-1.png",
        "caption": "Fig. 2. Computation of dual angle between two line vectors",
        "texts": [
            " The scalar and cross products of two dual vectors are respectively defined as follows [10]: A\u0302 \u00b7 B\u0302 = a \u00b7 b + \u03b5 [a \u00b7 (r2 \u00d7 b) + b \u00b7 (r1 \u00d7 a)] , = a \u00b7 b + \u03b5 [(r1 \u2212 r2) \u00b7 (a \u00d7 b)] , = ab cos \u03b8 \u2212 \u03b5 [(ss ) \u00b7 (ab sin \u03b8s )] , = ab [cos \u03b8 \u2212 \u03b5s sin \u03b8] = ab cos \u03b8\u0302 , (6) A\u0302 \u00d7 B\u0302 = a \u00d7 b + \u03b5 [a \u00d7 (r2 \u00d7 b) + (r1 \u00d7 a) \u00d7 b] , = a \u00d7 b + \u03b5 [(a \u00b7 b) (r2 \u2212 r1) + r1 \u00d7 (a \u00d7 b)] , = ab {s sin \u03b8 + \u03b5 [s cos \u03b8s + sin \u03b8 (r1 \u00d7 s )]} , = abS\u0302 (sin \u03b8 + \u03b5s cos \u03b8) = abS\u0302 sin \u03b8\u0302 . (7) Table 2 summarizes the result of different dual vectors products for different cases of relative position of line vectors. The dual angle between the two line vectors A\u0302i = ai + \u03b5 (si \u00d7 ai) , (i = 1, 2) must be computed. The computational steps are described in the following and are justified by the geometry depicted in Fig. 2. 1. Compute the dual vectors E\u0302i = A\u0302i\u2225\u2225\u2225A\u0302i \u2225\u2225\u2225 , (i = 1, 2). (8) 2. Compute their cross product E\u03023 = E\u03021 \u00d7 E\u03022\u2225\u2225\u2225E\u03021 \u00d7 E\u03022 \u2225\u2225\u2225 . (9) 3. Compute cosine and sine of the dual angle \u03b8\u0302 between the two line vectors cos \u03b8\u0302 = E\u03021 \u00b7 E\u03022 , (10a) sin \u03b8\u0302 = E\u03021 \u00d7 E\u03022 \u00b7 E\u03023 . (10b) 4. Compute dual angle \u03b8\u0302 = atan2 ( sin \u03b8\u0302, cos \u03b8\u0302 ) = \u03b8 + \u03b5h . (11) The procedure is not valid if line vectors are parallel. In this case, there is an infinite set of dual vectors E\u03023. With reference to the geometry of Fig. 3, we want to compute the sum A\u0302 = A\u03021 + A\u03022 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001776_978-1-4684-6632-4-Figure10-1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001776_978-1-4684-6632-4-Figure10-1-1.png",
        "caption": "FIGURE 10-1 Method of determining maxi mum value of shearing force for variolls levels of vertical loading.",
        "texts": [],
        "surrounding_texts": [
            "10 TRACTION\nTransmitting engine power to the drawbar in agricultural and other off highway vehicles is achieved through traction devices, namely wheels and tracks. Of the three principal ways of transmitting tractor-engine power into useful work-power takeoff, hydraulic, and drawbar-the least efficient and most used method is the drawbar. Basic configurations of wheels and tracks are modified to meet special operating conditions in various parts of the world. The predominate traction device is the pneumatic tire. The majority of this chapter deals with the theory and operating parameters of pneumatic tires for agricultural tractors. Terminology used in this chapter conforms, when possible, to ASAE Standard: ASAE S296.2.\nTraction Mechanics\nTraction is developed by the interaction of mechanical devices with soil. The ory, experimental studies, and field tests provide the general nature of these interactions for analysis and design of tractive systems. Central to design of traction systems is the development of performance equations. Freitag (1985) indicates that performance equations have devel oped by use of theoretical, analog, and empirical approaches. Owing to the complexities of soil-traction device interactions, the theoretical approach has not yielded readily usable solutions for the designer. However, it does provide general performance response for a particular combination of soil-vehicle parameters.\nMohr-Coulomb Failure Criteria\nApplication of the Mohr-Coulomb criteria to a soil-plate(lug) situation pro vides insights into the nature of plate (lug) loading and soil shear behavior. If a plate of width b and length I is equipped with lugs sufficiently long, such that an area A = bl shears off as in figure lO-l(a), we find that the force required is usually dependent upon both the normal force and the area.\n240",
            "MOHR-COULOMB FAILURE CRITERIA\n241\nIf we plot maximum values of F against W (as in figure 10-2), we find for soils having some cohesion that F does not approach zero as Wapproaches zero. If the maximum values are plotted for a soil that has both cohesion c and internal friction <1>, the result will be similar to figure 10-2. The equation for such a curve is\nF = Ac + W t.an <I>\nor F = A (c + jJ tan <1\u00bb\nwhere jJ = W/A is the average normal soil pressure and A is the area.\nFor a track\np W\nbl\n( 1)\n(2)\n(3)",
            "242\nTRACTION\nwhere b is the width of the track and Z is the length of the track in contact with the soil. Uniform pressure is assumed.\nFor a rubber tire, the \"footprint\" is approximately in the shape of an ellipse (fig. 10-3) for which case\np w 0.78bZ\n(4)\nIf we know the soil values c and <1>, the maXImum soil thrust can now be approximated by equation 2."
        ]
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure15-1.png",
        "caption": "Fig. 15. Temperature distribution of the finger plate when the relative magnetic permeability of the press plate is 50.",
        "texts": [
            "html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 8 It can be seen from Fig. 14 that the temperature of the stator-end copper winding which contacts the stator end core is relatively high (about 52.6 \u00b0C). However, the temperature of the stator-end copper winding nose is relatively low (about 44.3 \u00b0C). When the relative magnetic permeability of the press plate is 50, the highest temperature and average temperature of stator-end copper winding are 54 \u00b0C and 52.1 \u00b0C, respectively. Fig. 15 shows the temperature distribution of the finger plate when the relative magnetic permeability of the press plate is 50. It can be seen from Fig. 15 that the highest temperature of the finger plate is 52.5 \u00b0C, which occurs in the contact area between the stator end core and finger plate. The main reason for this is that fluid velocity around the surface of the short finger plate is low. In addition, the loss and temperature of the stator end core are high under the end leakage magnetic field. The heat of the stator end core transfers to the finger plate. When the relative magnetic permeability of press plate is 50, the highest temperatures of the long and short finger plates are 49"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.25-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.25-1.png",
        "caption": "Figure A.25 Flux of A through a surface S.",
        "texts": [
            "R , V R = -X + -9 + --z ax a y d z 1 1 a 1 1 a 2 R dX 2 R dY + -2 ( z - 2 \u2019 ) - ( z - Z \u2019 ) i = - -2(x - X\u2019)- (X - X I ) ? + - -2(y - y\u2019)-(y - y\u2019)Q 1 a R az d 1\u2018 v (A) - = - d x ( R ) * - x + - : y ( i ) y + ; ( i ) \u2019 - - 1 ( x - x\u2019)2 + ( y - y\u2019)Q + ( z - z\u2019)2 R2 R R 1 R R R3 R2 R R2 . V\u2018R = -VRandV\u2019 (4) = -V (4). - - - - - - - - - - Note that (A. 74a) Therefore (A.74b) R V\u2019R= -UR ,U\u2018 A.9.4 Flux of a Vector Given a vector A in space one can define an elementary vector surface d s = fi d s as shown in Figure A.25. This may be part ofa closed (or open) surface S. (Note: f i is outward normal if d s is part of a closed surface; for an open surface positive normal is defined in the :right-hand rule sense.) Thus for a finite open surface S the totaljux (of A) through S is by definition @ = A . d s . I For a closed surface, the total outward flux is (A.75) (A.76) VECTOR CALCULUS 447 The total outward flux through a closed surface is a measure of a source or sink inside. The divergence of a vector A at a point P, abbreviated as div A = V "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure3.17-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure3.17-1.png",
        "caption": "Figure 3.17 Optical transmission through a fiber using total reflection.",
        "texts": [
            "269a) in medium 2 can be given by (3.282) Equation (3.282) indicates a wave decaying in amplitude in the z direction and propagating in the y direction. In other words, it is a surface wave in the less dense medium and propagating along the interface. Example 3.6 Total reflection explains the operating principle for optical transmission through fibers. The optical signal enters the fiber A-A at an angle 8i, suffers total reflections as it propagates along the fiber, and finally exists at an angle 8i through the end B-B (see Figure 3.17). What should E , be so that the fiber can handle all angles of incidence? REFLECTION AND REFRACTION (TRANSMISSION) OF PLANE WAVES 107 For total reflection we need I9 2 8, or sin I9 2 -1, meaning sin2 I9 2 l/&. Snell\u2019s law requires 6 sin 4 = & sin Qt So for Snell\u2019s law we need E,. 2 1 + sin2 19i. The maximum value of the incident angle is 7r/2. Thus er 2 2 can accommodate all angles incidence. Commonly used materials for fibers are quartz, for which er !x 3.78, and glass, for which E , !x 6.78. The Brewster angle is the angle of incidence for which the reflection coefficient vanishes, meaning a total transmission occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003089_tiga.1968.4180895-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003089_tiga.1968.4180895-Figure1-1.png",
        "caption": "Fig. 1. Winding arrangement of an idealized three-phase induction motor.",
        "texts": [
            " Each harmonic voltage may then be applied separately and the responses added by superposition. The higher applied voltage harmonics include components of positive, negative, and zero sequence nature. Even the straightforward case of steady-state operation with a motor voltage waveform that is invariant with load impedance (as, for example, motor speed and torque) involves considerable algebra. [1] -[4] This paper deals with the more general problem of a three-phase induction motor with symmetrically triggered pairs of thyristors in series with the stator windings (Fig. 1). Both the winding voltages and motor currents have different nonsinusoidal waveforms that depend on the triggering-angle and the load impedance. The Fourier method previously mentioned cannot conveniently be applied in this case. A logical approach is to obtain a set of equations suitable for numerical solution. WINDING VOLTAGES IN TERMS OF CURRENTS AND INDUCTANCE COEFFICIENTS FOR AN ARBITRARY INSTANTANEOUS SPEED In order to apply analytical methods based on the principle of superposition, certain simplifying assumptions are made regarding the motor",
            " The author is with the University of Bradford, Bradford, Eng- land. 1) Saturation, hysteresis, and eddy currents are ignored. 2) All saliencies such as slot and teeth effects are neglected so that the spatial magnetomotive force and the flux waves are considered to be sinusoidally distributed. 3) The uniformly distributed windings of the machine may be represented by equivalent lumped circuits. Balanced, three-phase sinusoidal voltages of constant magnitude and frequency are supplied to the terminals A, B, and C (Fig. 1). The connecting link between a stator winding and a pair of thyristors is denoted by the symbols A', B', or C'. All quantities in the following analysis are in per unit referred to the stator (excitation) windings. The instantaneous angular displacement between the axis of stator coil A'B and rotor coil a (Fig. 1) is denoted by B. In terms of the instantaneous mechanical angular velocity w(t), w(t) = dt = PA (1) where p is the differential operator d/dt. In terms of synchronous angular velocity w, and per unit slip s, w(t) = (1 - s)W, pw (t) = -pSWs = P2' * (2) SHEPHERD: THREE-PHASE INDUCTION MOTOR WITH THYRISTOR VOLTAGE CONTROL Let it now be assumed that each pair of stator windings (Fig. 1) has a constant mutual inductance coefficient M, and that each pair of rotor windings has a constant mutual inductance represented by M2. The mutual coupling between a stator winding and a rotor winding is assumed to be a simple trigonometric function of the angular rotor position, varying from zero when a pair of coil axes are perpendicular to a maximum M12 when the pair of coils is in adjacent alignment. At the instant shown in Fig. 1, for example, the effective mutual inductance coefficient between coils A 'B and a is M12 cos 6. The self-inductance coefficients of Fig. 1 bear subscripts corresponding to the terminology of the windings themselves. For example, the self-inductance coefficient of winding A'B is LA,B and the self-inductance coefficient of winding a is La. Each stator winding is assumed to have a resistance R1, and each rotor winding, a resistance R2. The thyristors are presumed ideal, having no voltage drop when conducting current. The phase voltages of the six-loop system (Fig. 1) are given by (3)-(8): eA'B = RliAB + PLAIBiAB + PMl(iBC + iCA) + pM12 X [ia cos 6 + il cos (6 + 120) + i4 cos (6 - 120)] (3) eBeC = RliBC + pLB'CiBC + pM(iCA + iAB) + pM12 X[ia cos(6 - 120) + ib cos 6 + i- cos (6 + 120)] (4) ec'A = RliCA + pLc'AiCA + pMl(iAB + iBC) + pM12 X [ia cos (6 + 120) + ib cos (6 - 120) + 4c cos 6] (5) ea = R2ia + pLaia + pM2(ib + i4) + pM12 X [iAB cos 6 + iBccos (6 - 120) + icA cos (6 + 120) ] eb = R2i + pLbi6 + pM2(i + ia) + PM12 X [iAB cOs (6 + 120) + iBC COS 6 + iCA COS (6 - 120)] e- = R24 + pLC4 + pM2(ia + ib) + PM12 X [iAB COS (6 - 120) + iBc cos (6 + 120) + iCA COS 6 ]. (6) L2 is introduced, defined by (10): La = Lb = L- = L2 + M2. (10) The sum of the instantaneous currents iA, iB, and ic in the supply lines in Fig. 1 is zero at all times: iA + iB + iC = 0. (11) Also, the sum of the instantaneous rotor currents ia, ib, and i4 is zero at all times: i a + ib + c = 0 - (12) The three instantaneous stator phase currents iAB, iBCI and iCA will not equal zero, in general. Let the instantaneous sum be denoted by the symbol i, as in (13): itAB + tBC + iCA = i (13) Substituting (9), (12), and (13) into (3)-(5), eliminating i, results in a more compact form for the stator winding voltage equations: eA'B = (R1 + pLl)iAB + pMli - /3pMl2 X [ia sin (6 - 60) + ib sin 6 ] eB'e = (R1 + pLl)iBc + pMli + v3pM12 X [ia sin 6 + ib sin (6 + 60)] (14) (15) eC,A = (R1 + pLl)icA + pMli + V3pMM2 X [-ia sin (6 + 60) + ib sin (6 - 60)]. (16) Similarly, substituting (10) and (12) into (6)-(8) results in a more compact form for the rotor loop voltage equations: ea = (R2 + pL2)ia + PM12[iAB cos 6 + iBC cos (6 - 120) (17)+ icA cos (6 + 120) ] eb = (R2 + pL2)ib + pM12 [iAB cos (6 + 120) + iBC cos 6 + iCA cos (6 - 120) ] ec= -(R2 + pL2) (ia + i4) + pM2 [iAB COS (6 - 120) + iBC cos (6 + 120) + iCA cos 6 ]. (19) With a short circuit applied across the rotor terminals (7) a, b, and c in Fig. 1, the following relationships are true: ea- eb = eb- eC = e. - ea = 0. (8) It is assumed that the self-inductances of the three stator windings are identical. In order to simplify the terminology a self-inductance coefficient L1 is introduced, defined by (9): LA'B LB'C = LC'A = L1 + Mi. (9) Similarly it is assumed that the self-inductances of the rotor windings are identical. A self-inductance coefficient (20) Combining (20) with (17)-(19) eliminates ea, eb, and e- from the rotor loop voltage equations: 0 = (R2 + pL2)(ia - ib) + O3pM12[iAB sin (6 + 60) + iBC sin (6 - 60) -iCA sin 6] 0 = (R2 + pL2)(ia + 2i) + V3PM12[-iAB sin + iBC sin (6 + 60) + iCA sin (6 - 60)] 0 = -((R2 + pL2)(2ia + ib) + V3pM12[+iAB (21) (22) X sin (6 - 60) -iBC sin 6 + icA sin (6 + -60)]",
            " (38) The five system equations (34)-(38) may be written more compactly in the following matrix form: 306 SHEPHERD: THREE-PHASE INDUCTION MOTOR WITH THYRISTOR VOLTAGE CONTROL eA BB [Rfl eB'C ecA = 01 + p(Li + M1) pM1 pM, E + Fp B-Dp pm, R1 + p(Li + M1) pM1 -A-Cp E + Fp pM, pM, R1 + p(Li + M1) B-Dp -A-Cp A +Cp -B + Dp -E-Fp R2 + Lp2 R2 + Lp2 B-Dp E + Fp -A-OCp -R2-pL2 2(R2 + pL2) j The 5 X 5 matrix in (39) is defined as the operational impedance matrix; where A = -wX/$3M12 cos(wt - 60) for the first period: eB mstX - r, x, 2.r eA'B = Em sin wst 0, 0, 7r + 0 B = -wV3M12 cos wt C = -V\\a/3J12 sin (wt - 60) D = + \\/3VM12 Sill wt E = + wV3M12 cos (wt + 60) F = + /3Mr.12 sin (wt + 60). Coefficients A, B, and E have the dimension of impedance since motor speed w is related to the synchronous angular frequency co, by a dimensionless constant. The six loop system of Fig. 1 is thus represented by the five loop equations in the matrix, for operation at any fixed speed w with any shape of applied voltage waveforms. Measured waveforms of stator winding voltage and current for the induction motor connection (Fig. 1) are given in the oscillograms shown in Fig. 2 While either thyristor of a given pair is conducting, the winding voltage of the phase coincides (very nearly) with the corresponding supply voltage. The excitation functions of the thyristor controlled motor, represented as the voltages column matrix in (39), are then segments of sinusoids. When current is blocked in a given winding, a voltage still appears across the winding due to mutual coupling, but this induced voltage does not form part of the excitation function. In Fig. 2(c) it is seen that the induced voltage is highly dependent on motor speed at a fixed triggering angle. Measured torque-speed curves for a 3-hp, 50-Hz wound-rotor motor, controlled by the connection of Fig. 1, were given previously[5] together with an approximate method for calculating the torque at a given speed and thyristor triggering angle. Assumed stator voltage and current waveforms are given in Figs. 3 and 4 for triggering angles of 60\u00b0 and 1200, respectively. The waveforms and conduction angles are drawn so as to be typical of experimental observations in which the precise form of the induced stator voltages, shown dotted, is not known. The excitation voltages, indicated by solid lines, are defined by (40)-(42) eBIC = Em sin (w,st- ) ec'A = Em sin (wst + 7r 27r x - -, x + 3 3 7r 2wr 3' 3 27r Xr x - -, x + -,27r 3 3 0, + -2 + 3 3 (41) (42) The extinction angle x in voltage eA,'B of Fig",
            "111'1121 In the present case, determination of the extinction angle for operation at a fixed speed and triggering angle requires manipulation of the solution of current equations (51)-(55). It is concluded that to solve the set of simultaneous equations (39) for the condition of constant rotor speed, a numerical form of solution must be employed or the equations must be linearized by some suitable transformation of variables. A transformation of variables that leads to an analytic solution of the induction motor equations for constant speed sinusoidal operation was originally suggested by Park.[II] The fluxes and magnetomotive forces of the six windings in Fig. 1 may be resolved along two perpendicular axes which are stationary in the stator, [14] [1[1] rotating synchronously, [161 or rotating at the rotor velocity. Krause and Thomas have developed transformation equations for an arbitrary reference frame. [17] The Park transformation was applied to a set of equations similar to (39) with the nonsinusoidal voltages (Fig. 2) by resolving the system variables along two perpendicular axes rotating anticlockwise at the synchronous speed wv,, following the method of Fitzgerald and Kingsleyv[181 which is based on the classic paper by Brereton et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001642_rnc.1154-Figure10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001642_rnc.1154-Figure10-1.png",
        "caption": "Figure 10. Phase trajectory of errors when r > 2e with r \u00bc 0:053 and e \u00bc 0:025:",
        "texts": [
            " Chattering is completely eliminated and trajectory is confined inside the boundary layer as shown in Figure 5. If r > 2e r ; condition (26) is violated, chattering occurs across the sliding manifold. With r \u00bc 0:042 and e \u00bc 0:025; chattering starts to occur but the trajectory is finally confined to the boundary layer as shown in Figure 8. When r \u00bc 0:051 and e \u00bc 0:025; more severe chattering occurs as depicted in Figure 9. When r \u00bc 0:053 and e \u00bc 0:025; the chattering does not converge as shown in Figure 10. If condition (26) does not hold, the system cannot eliminate chattering and DSM does not exist. A slight variation in the sliding mode gain can alter the system stability. Hence, condition (26) plays a crucial role in the design of DSM. Copyright # 2006 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control 2007; 17:803\u2013828 DOI: 10.1002/rnc In this paper, we consider the design of a DSM observer for a class of nonlinear systems to robustly estimate the system states when uncertainties or unknown input is present in the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003820_1.4039386-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003820_1.4039386-Figure2-1.png",
        "caption": "Fig. 2 Ball and raceway groove curvature centers positions",
        "texts": [
            " The first coordinate system (OXYZ) is a global coordinate system and the X axis coincides with the bearing center axis; the second coordinate system (o0 x0y0z0) is a moving coordinate system and the coordinate origin o0 coincides with the center of ball; and the third coordinated system (OL gn) is a contact coordinate system. To determine the relation between the external load and displacement of ball bearing, let us assume that the outer ring is fixed and the inner ring rotates with the spindle at a constant speed xi, and the revolution and rotational angular speeds of ball are xm, xx0 , xy0 , xz0 . In addition, the displacements of the inner ring relative to the outer ring are dx; dy; dz; hy; hz and the external loads acted on inner ring are Fx;Fy;Fz;My;Mz. 2.1 The Interaction Between the Ball and Raceway. Figure 2 gives the relative positions of ball center and raceway groove curvature centers of ball bearing. As the external loads and rotation speed are zero, the initial positions of ball and raceway groove curvature centers are Ob, Oi, Oo, respectively. With the increase of rotational speed and external loads, the centers of ball and inner raceway groove curvature move to O0b, O0i, and the distances between the inner and outer raceway groove curvature centers in the horizontal and vertical directions can be expressed as A1k \u00bc \u00f0ri \u00fe ro D\u00desin ao \u00fe Dak A2k \u00bc \u00f0ri \u00fe ro D\u00decos ao \u00fe Drk 8< : (1) where ri, ro, and D denote the inner and outer raceway groove curvature radii and ball diameter, respectively. ao is the initial contact angle. The displacements of inner ring relative to outer ring at angular position wk can be written as Dak \u00bc dx \u00fe hy cos wk hz sin wk Drk \u00bc dy sin wk \u00fe dz cos wk ( (2) As shown in Fig. 2, the geometry equations can be obtained by the Pythagorean theorem X2 1k \u00fe X2 2k \u00f0ro 0:5D\u00fe dok hok\u00de2 \u00bc 0 \u00f0A1k X1k\u00de2 \u00fe \u00f0A2k X2k\u00de2 \u00f0ri 0:5D\u00fe dik hik\u00de2 \u00bc 0 8< : (3) 053301-2 / Vol. 140, MAY 2018 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 03/22/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use where dik and dok are the ball-raceways contact deformations, and hik and hok are oil film thicknesses in contact areas. The ballraceways contact forces can be expressed by the Hertz contact theory Qik \u00bc Kikd 1:5 ik Qok \u00bc Kokd 1:5 ik 8< : (4) where Kik and Kok denote the deflection coefficients of ball-raceways contacts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001726_j.wear.2007.05.007-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001726_j.wear.2007.05.007-Figure2-1.png",
        "caption": "Fig. 2. Schematic view of the FZG gear test rig.",
        "texts": [
            " he equilibrium temperature at constant operating conditions is direct indication of power losses, since a lower equilibrium emperature indicates higher energetic efficiency, lower friction oefficient, smaller oil oxidation and a longer oil life [9]. The gear efficiency tests had two main objectives: (i) meaurement of the equilibrium temperature of the lubricant, at ifferent operating conditions (torque and speed), and (ii) the valuation of the wear protection provided by each gear oil. The esults obtained were compared with similar results obtained ith carburized steel gears. .1. Operating conditions in gear power loss tests All the gear tests were performed on the well known FZG ack-to-back spur gear test rig, shown in Fig. 2, and the gears sed are similar to standard FZG type C gears [15] (pinion, 6 teeth; wheel, 24 teeth; modulus, 4.5 mm; center distance, 1.5 mm). The tests were performed with both gear oils using a ide range of speed and torque conditions, corresponding to nput powers between 0.5 and 86.4 kW, as shown in Table 3. he hertzian contact pressures at the gear pitch point, coresponding to each FZG load stage (or torque level), and he number of cycles for each combination of torque and peed are also presented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001824_0169-8141(86)90012-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001824_0169-8141(86)90012-0-Figure2-1.png",
        "caption": "Fig. 2. Free body diagram of the forearm.",
        "texts": [
            " The reaction forces and moments at the joint centre could be determined from the equation of dynamic equilibrium at the segment. At the adjacent body segment, these reaction forces and moments became action forces and moments with the opposite sign. A free body diagram for this second segment was then drawn and the reaction forces a n d moments determined through dynamic equilibrium. The calculations proceeded from the forearms to the lower legs through the arms, torso, hip, and upper legs. The reaction forces in the lower legys and feet became the ground reaction forces. Figure 2 shows the complete free-body diagram of the forearm. The equations involved in the calculation of forces and moments are given below: Force equations at segment n Fx(Bn)-F~(An)+ Wx(n)=m(n) 'A,(Gn) (18) Fy(Bn) - Fy(An) + Wy(n) -- re(n). Ay( On) (19) F~(Bn)-F~(An)+ W~(n)=m(n).A~(Gn) (20) Moment equations at segment n MAAn)- F,(S,)-p, -Fy(An) .qn = l:,(n). Q:,(n) - - \u2022 \u2022 (21) M . ( B , , ) - + ( B , , ) . p , + Fx(An).qn = Iy(n). Qy(n) - [ I , (n ) - Ix (n ) ] .W, (n ) .W~, (n ) (22) M~( Bn) - M~(An) = I~(n) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001107_1.1564064-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001107_1.1564064-Figure2-1.png",
        "caption": "Fig. 2 A multi-degree-of-freedom lumped parameter model of a hypoid geared rotor system",
        "texts": [
            "org/about-asme/terms-of-use Downloaded F surface are generally perturbed from its theoretical position. The LTE term in Eq. ~3! denoted by DuL is generally periodic with mesh frequency, and is a function of gear rotation position and applied load. It can be expressed in the Fourier expansion form as DuL~u!5e01( r51 n ~erc cos~rvm~u2u0!!1~ers sin~rvm~u2u0!!, where vm is fundamental gear mesh frequency and u0 is initial position angle of the pinion. Consider a generic drive train system comprising of a hypoid gear pair, a mechanical source and a load element as shown in Fig. 2. Each gear is modeled as a rigid conical body attached to a torsionally flexible shaft that is supported by compliant rolling element bearings represented by a set of discrete stiffness and damping elements @32#. Note that the nominal rotations of the pinion and gear are about Y 1 and Y 2 respectively. Furthermore, only the torsional coordinates of the driver uE and load u0 are modeled as their translation coordinates that are normally decoupled from those of the gears by use of flexible coupling design",
            " and ~6a!, the averaged mesh stiffness km can be shown to be km 5W0 /(ly (1)DuL2\u00ab0)5Wo /(eL2\u00ab0), where eL is the translation form of LTE in the mesh force line-of-action direction. Similar expressions of the mesh stiffness are also used by O\u0308zgu\u0308ven and Houser @13# and Blankenship and Singh @18#. Hence, the instantaneous km is a function of load, tooth errors, tooth modifications and gear rotation position. Accordingly, the equations of motion for the 14 degrees-of-freedom ~DOF! system shown in Fig. 2 incorporating loaded transmission error term eL are given by IEu\u0308E1kt1 ~uE2u1!1ct1 ~ u\u0307E2 u\u03071!52T1 , (8a) JUNE 2003, Vol. 125 \u00d5 375 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F @M 1#$q\u03081%1~h~1 !T 2mg~1 !T ! f ~dd2eL!1@C1b#$q\u03071%1@K1b#$q1% 5$Fext ~1 !%, (8b) @M 2#$q\u03082%2~h~2 !T 1mg~2 !T ! f ~dd2eL!1@C2b#$q\u03072%1@K2b#$q2% 5$Fext ~2 !%, (8c) IOu\u0308O1kt2 ~uO2u2!1ct2 ~ u\u0307O2 u\u03072!52T2 , (8d) where IE and IO are the mass moment of inertias of the driver and load, kt1 and kt2 are the torsional stiffnesses of the input and output shafts, ct1 and ct2 are the input and output shaft damping coefficients, T1 and T2 are the mean torques of the driver and load, $Fext (l) % is the external load vector acting on the gear member l, and the mass, stiffness and damping matrices of shaft-bearing components are given by @M l# , @Klb# and @Clb# respectively",
            " The pitch uzl and yaw uxl angular coordinates of both the pinion (l51) and gear (l52) are neglected as they were found to be unimportant in the earlier work by Cheng and Lim @22#. Furthermore, the formulation is transformed into a positivedefinite system using a1(t)5u12uE , a2(t)5ly (2)u22ly (1)u1 , and a3(t)5u22uO , which separates out the rigid body rotational mode and improves computational efficiency. The numerical solution of the proposed set of nonlinear, time-varying equations of motions governing the torsional and translational vibrations of the hypoid geared rotor system illustrated in Fig. 2 is obtained by applying the 5/6th order Runge-Kutta integration routine with adaptive time step capability. As part of the solution scheme, the second order differential form of Eq. ~8! must be casted in the state-space domain generally given by a\u0307 i5 f i(a1 ,a2 , . . . ,a18), where i51,2, . . . ,18. The calculation generates the time domain steady-state vibratory response, which can be processed to provide either mesh frequency or order spectrum. A summary of the proposed computational approach is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001450_detc2006-99628-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001450_detc2006-99628-Figure4-1.png",
        "caption": "Fig. 4 Selection of actuated joints for the 3-R\u030b(RRR)ER\u030b parallel mechanism with both spherical and translational modes.",
        "texts": [
            " By assembling the legs listed in Table 4, their variations, and legs with a wrench system of order 0, a large number of parallel mechanisms with both spherical and translational modes such as the two parallel mechanism shown in Fig. 2 can be obtained. Without considering the variation of legs, as it can be seen from Table 4, one can obtain 43 types of 3-legged parallel mechanisms with both spherical and translational modes with identical types of legs. According to the validity condition for actuated joints of translational parallel mechanisms [19] and spherical parallel mechanisms [8], one can find that the three joints located on the base can be used as actuated joints in both the translational mode [Fig. 4(a)] and the spherical mode [Fig. 4(b)] of the 3- R\u030b(RRR)ER\u030b parallel mechanism. However, these three actuated joints are not sufficient to change the parallel mechanism from one operation mode to another since they cannot fully control the motion of the moving platform in the lockup\u2194translation configuration [Fig. 3(b)] or the lockup\u2194rotation configuration 8 nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 03/11/2018 T [Fig. 3(d)]. In order to change operation modes, four joints, including the three joints located on the base and the second joint in one of the legs, should be actuated [Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000951_jsvi.1995.0132-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000951_jsvi.1995.0132-Figure1-1.png",
        "caption": "Figure 1. A rotating shaft subject to moving loads and axial forces.",
        "texts": [
            " The present matrix formulation is simple in form with the resulting equations of motion in matrix form are amenable to numerical computations. The effects of axial forces, which have not been considered in the past studies, are included in the present formulation. The present formulation is also applicable for a load moving at a speed which is an arbitrary prescribed function of time. The effect of perturbation on the constant axial velocity of the moving load is also investigated. The shaft considered is an axisymmetric uniform shaft of length L rotating about its longitudinal axis and simply supported at its two ends, as shown in Figure 1. A co-ordinate system is assumed to be fixed in the inertial frame, with the X axis parallel to the undeformed longitudinal axis of the rotating shaft. Two moving loads PY and PZ are applied in the directions of the Y and Z axes with a common prescribed varying speed u in the X direction. This prescribed varying velocity is usually called the axial velocity of the moving loads. The shaft is assumed to be spinning with a constant rotational speed denoted by V. The deformation of the shaft is assumed to be governed by Timoshenko\u2019s beam theory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003250_s10846-015-0301-4-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003250_s10846-015-0301-4-Figure4-1.png",
        "caption": "Fig. 4 Visualization of the proposed vehicle in this paper",
        "texts": [
            " On the other hand Ryll\u2019s study [23] is based on a \u201cquadrotor with tilting propellers\u201d. Jeong et al. [24, 25] study on omni-directional aircrafts with VTOL and CTOL (Conventional take off and landing) modes are also an enthusiasm for our study on the tilt-roll capable quadrotors. Our previous study [26, 27], was based on a tilt-roll rotor quadrotor that can rotate their rotors in the same direction by tilting and/or rolling movements. A regular type quadrotor is given in Fig. 3 and illustration of the proposed quadrotor with tilt-roll-able motor geometry is introduced in Fig. 4 for comparison. The goal of this study is to; \u2022 Design adaptation of a regular quadrotor aiming for better stability and robustness. \u2022 Derive the dynamical model of the proposed vehicle. \u2022 Enhanced maneuver capabilities in constrained environments. \u2022 Change the tilt and roll angles of rotors independently from each other for better adaptability. \u2022 Handle the disturbances more efficiently that occur from nature, environment and hardware imperfections. \u2022 Simulate, compare and improve the quadrotor\u2019s performance in terms of robustness, reaching to the destination in lower time, have environmentfriendly structure to operate vast numbers of scenarios"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003154_s11071-013-1125-z-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003154_s11071-013-1125-z-Figure9-1.png",
        "caption": "Fig. 9 Contact modeling",
        "texts": [
            " (17) The second type of equilibrium equations is the dynamic equilibrium where the (i) h\u2217 harmonic force of the tooth mesh and the (ii) 1st Fourier order of the contact forces corresponding to the fundamental frequency f are taken into account: \u039b\u0304(\u03c9) \u00b7 \u03b7\u0304(1) = f\u0304(h \u2217) TM + f\u0304(1) NL, \u039b\u0304D(\u03c9) \u00b7 \u03b7\u0304(1) D = f\u0304(1) NL,D, (18) \u03c9 = 2\u03c0f being the angular frequency of the excitation, \u039b and \u039bD the diagonal dynamic stiffness matrices of the gear and damper, respectively: \u039b\u0304(\u03c9)pp = \u03bbp \u2212 \u03c92 + i \u00b7 2\u03c9\u03b6p \u221a \u03bbp, \u039b\u0304D(\u03c9)dd = \u03bbDd \u2212 \u03c92 + i \u00b7 2\u03c9\u03b6Dd \u221a \u03bbDd , with \u03b6p and \u03b6Dd the pth and d th modal damping ratios of the gear and damper and f\u0304(h \u2217) TM = \u03a6T p \u00b7 F\u0304(h\u2217) TM , f\u0304(1) NL = \u03a6T p \u00b7 F\u0304(1) NL, f\u0304(1) NL,D = \u03a6T Dd \u00b7 F\u0304(1) NL,D. (19) In order to couple the ring damper to the gear, two types of contact elements are used (see Fig. 9), i.e., contact elements (c.e.s) and penalty elements (p.e.s). 6.1 Contact elements The c.e. is the source of friction damping since it simulates slip-stick-lift off contact states. The original formulation of this 2-dofs c.e. is developed in [15] for the forced response of frictionally damped systems. It is characterized by 1D tangential motion, normal motion with respect to the contact area, and three parameters: the tangential contact stiffness kt , normal contact stiffness kn, and friction coefficient \u03bc",
            " The static (15) and dynamic (18) balance equations of the two structures are therefore coupled by the contact forces of the contact model without any preliminary static analysis of the system to compute the static normal preloads N0 as it was originally described in [15]. In the following, the constitutive equations for N(t) and T (t) are given. The direct coupling of the static and dynamic quantities affects first of all the calculation of the contact normal load N(t), which can be computed as N(t) = { kn \u00b7 v(0) + kn \u00b7 v(1)(t) if contact, 0 if lift off. (21) Referring to Fig. 9, where the positive direction of relative displacements and forces is shown, the contact occurs if N(t) is greater than zero, and therefore Eq. (21) takes the form N(t) = max [ kn \u00b7 v(0) + kn \u00b7 v(1)(t),0 ] , (22) where N(t) is determined without any need of a preliminary static analysis to compute the static normal load N0 used in the original formulation since it is dependent on v(0) when the bodies are in contact; otherwise, N(t) is null if lift-off occurs. Three states describe the contact state during one period of motion: stick, slip, and lift off",
            " In the third case, the static tangential displacement u(0) is low enough to induce a negative slip (T (t) = \u2212\u03bcN(t)) during the first unloading cycle, but then the stabilized hysteresis cycle is perfectly elastic with a minimum tangential force equal to the lower Coulomb limit value \u2212\u03bcN(t). In this case, the static value T (0) is set equal to the minimum allowable value of the static tangential force T (0) min. 6.2 Penalty elements The p.e.s are unilateral constraints placed at the front and rear sides of the ring damper (see Fig. 9). They are used to avoid an undetermined static offset of the ring damper during calculation. Two states only are possible: normal stick and lift off. Since only a variable normal load at the contact is modeled, Eq. (22) is sufficient to model the contact behavior at the side walls of the damper. With the above-listed refinements of the constitutive equations of the c.e.s and p.e.s shown in Fig. 9, it is possible to couple the static and dynamic balance equations of the gear and ring damper computing a unique cycle of contact forces for any possible contact conditions. The static and dynamic balance equations of the gear and ring damper written in modal coordinates according to HBM (Eqs. (23) and (26)) represent the set of nonlinear equations in the frequency domain to be solved to compute the forced response of the system in terms of modal amplitudes \u03b7(0), \u03b7\u0304(1), \u03b7 (0) D , and \u03b7\u0304 (1) D "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003669_j.mechmachtheory.2014.09.002-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003669_j.mechmachtheory.2014.09.002-Figure6-1.png",
        "caption": "Fig. 6. Equivalent generated motion with respect to the gear coordinate system.",
        "texts": [
            " On the other hand, when Sb is chosen [1], the result is directly obtained in Sb, but the expression of the cradle motion in Sb is more complicated because it is involved in two rotation operations. Both of these coordinate systems can be applied in the proposed approach, and Sb is chosen as an example to show the convenience of the proposed approach. When the generating process is considered in a three dimensional Euclidean space E3 b , where the gear and Sb are fixed, the generating process can be treated as an equivalent generated motion as shown in Fig. 6. While the gear is fixed in E3 b , the head- cutter not only rotates about the cradle axis with an angle \u03d5c but also rotates about the gear axis with another angle\u2212 \u03d5b. Then tooth surfacemodel is formed as the envelope surface of the family of the head-cutter surfaces. In order to calculate this envelope surface, it is necessary to describe the instantaneous configuration of the head-cutter surfaces with respect to Sb. This can be implemented with the HTM which transfers the head-cutter surfaces from Sg to Sb, and it can be represented as Mbg \u03d5c\u00f0 \u00de \u00bc M11 M12 M13 M14 M21 M22 M23 M24 M31 M32 M33 M34 0 0 0 1 2 664 3 775: \u00f067\u00de The details about the derivation of Mbg(\u03d5c) and its componentsMi,j(i = 1, 2, 3; j = 1, 2, 3, 4) are given in Appendix A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002950_iros.2011.6094959-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002950_iros.2011.6094959-Figure2-1.png",
        "caption": "Fig. 2. A view of our robotic system for needle insertion",
        "texts": [
            " Finally, by adding the quasi-static solution introduced by \u03c6(x, t) to the homogenous solution obtained using the residue theorem, the complete dynamic response of the beam can be derived. For example, for the second sub-beam \u03c92(x, t) = 1 2\u03c0i \u222b +\u221e \u2212\u221e (\u222b L l1 g(x, x\u0303;\u03c6)f\u0303(x\u0303, t)dx\u0303 ) ei\u03c6t d\u03c6 +C(x)Fc(t), l1 < x \u2264 L (15) For more details on the mathematical method explained in brief, readers can refer to [7]\u2013[9]. IV. IMPLEMENTATION AND EXPERIMENTS Experimental studies of the proposed method were carried out using a state-of-the-art robotic system which has been fully designed and constructed in our lab [19]. The manipulator shown in Fig. 2 is capable of inserting, rotating, and orienting the needle with an acceptable accuracy. A Nano43 force/torque sensor (ATI Industrial Automation) with six degrees of freedom (DOF) that is attached to the needle holder and an Aurora electromagnetic tracker (Northern Digital Inc.) are the external sensing devices for providing feedback signals. Two desktop computers for control and data capturing were interfaced through a UDP connection over ethernet. The robot is controlled using a PID controller at the rate of 1kHz while force data are acquired at the rate of 100Hz after being smoothed by a moving average filter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001923_tac.2007.900831-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001923_tac.2007.900831-Figure2-1.png",
        "caption": "Fig. 2. The PVTOL vehicle.",
        "texts": [
            " This, of course, may not always be the case, and the reality depends on both the choice of f (z), and the nonlinear functions g (z; ) and h (z; ). However, an alternative nonlinear design methodology for the class of systems (1) has been presented that is likely to improve performance. Fig. 1 shows an interesting graphical interpretation of the two control laws. By designing u1 as an appropriate function of , the resulting interconnection term 2 is always perpendicular to g (z; ) such that k 2k is minimized with respect to u1. A free body diagram of the PVTOL aircraft is shown in Fig. 2. A simplification of the system\u2019s dynamics as given in [1] is _x1 =x2 _x2 = u1 sin + u2 cos _y1 = y2 _y2 =u1 cos + u2 sin g _ =! _! =u2: (11) Here x1; y1, are horizontal and vertical displacements, and x2; y2 horizontal and vertical velocities of the vehicle\u2019s center of gravity, respectively. The variable is the roll angle, ! the roll rate, g gravitational acceleration, u1 primary thrust input and u2 roll control input. Here 2 + represents the input coupling between the roll control input and translational dynamics, resulting in the system being nonminimum phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003495_s00332-016-9294-9-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003495_s00332-016-9294-9-Figure3-1.png",
        "caption": "Fig. 3 Strains of two different configurations of a sheet: i The configuration \u03d51 maps the sheet to a section of a cylinder with E = 0, and H = 0, ii the configuration \u03d52 is an in-plane extension of the sheet with E = 0, and H = 0",
        "texts": [
            " We introduce extrinsic strain tensors for configurations of surfaces that depend on the second fundamental form as follows. The extrinsic deformation tensor \u2208 (S2T \u2217H) is defined as the pull-back of the spatial second fundamental form := \u03d5\u2217\u03b2. In components, AB = Fa AFb B\u03b2ab. We define the extrinsic material strain tensor as H := 1 2 ( \u2212 B) and the extrinsic spatial strain tensor as \u03b7 := 1 2 (\u03b2 \u2212 \u03b8), where \u03b8 := \u03d5\u2217B. Note that \u03b7 = \u03d5\u2217H . As an example, consider two different configurations of a sheet shown in Fig. 3. The configuration \u03d51 is an isometry between the sheet and a section of a cylinder, and therefore, E = 0. However, note that since the out-ofplane geometry has changed, we have H = 0. On the other hand, \u03d52 is an in-plane deformation of the sheet with E = 0, and H = 0. The pull-back of the Gauss and the Codazzi equations (3.1) of the surface (\u03d5(H), g) by \u03d5 read (Angoshtari and Yavari 2015) RC(X,Y , Z,W) = (X, Z) (Y ,W) \u2212 (X,W) (Y , Z), (3.3a) ( \u2207C X ) (Y , Z) = ( \u2207C Y ) (X, Z), (3.3b) where \u2207C andRC are, respectively, the Levi\u2013Civita connection and the Riemannian curvature of the Riemannian manifold (H,C)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003439_1464419313513446-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003439_1464419313513446-Figure5-1.png",
        "caption": "Figure 5. Flexible bearing cut view at roller j position.",
        "texts": [
            " Having established the radial and axial displacements as well as raceway tilt at the position of each interface node, the elastic deflection of the outer raceway can now be interpolated at the roller positions. For this purpose, a linear interpolation is used because it has been found to be sufficiently precise while providing high computational performance. The bearing ring deflections at roller j position shown in Figure 3(a) for the six-dof model are now slightly modified to include the deflections of the outer ring, as shown in Figure 5. Subscript ij designates the inner ring coordinate system rotated about its z-axis into the roller j position and oj designates the equivalent coordinate system of the outer ring relative to the reference node translated into the bearing centre along the x1 axis and rotated into the roller j position. Since the interface nodes are located at the centre of the outer raceway, the rotation oj only impacts the contact alignment and not the contact deflection. The approach of the two raceways measured orthogonally on the roller axis at the roller j centre is thus j \u00bc \u00f0 zj zoj\u00de sin\u00f0 o\u00de \u00fe \u00f0 xj xoj\u00de cos\u00f0 o\u00de \u00f012\u00de The total relative misalignment between the raceways is j \u00bc cos\u00f0 j \u00de y sin\u00f0 j \u00de x oj \u00f013\u00de The raceway approach and misalignment of the flexible bearing at roller j position defined in equations (12) and (13) have identical physical interpretation as equations (5) and (6) for the six-dof model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001961_978-3-540-73719-3-Figure1.10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001961_978-3-540-73719-3-Figure1.10-1.png",
        "caption": "Fig. 1.10. Engine thrust forces",
        "texts": [],
        "surrounding_texts": [
            "The aim of the shock absorbers is to dampen the forces transmitted by the wheels and to dissipate the energy due to the touchdown of the aircraft during landing. Seen from the aircraft, the shock absorbers filter the vertical forces from the wheels. Seen from the wheels, they filter the vertical load variations due to the pitch and roll moments. The forces generated by these types of shock absorbers can be represented simply using stiffness and damping elements dependent respectively on the compression and the compression rate of the landing gear leg. To do this, it is possible to directly use graphs obtained from tests or functions such as polynomial functions identified on the basis of these graphs. The force then obtained is oriented in the landing gear axis. If the landing gear concerned has a non-negligible inclination (with regard to the aircraft coordinate system) this force must then be projected into the aircraft coordinate system. As the influence of a possible inclination of a landing gear on the longitudinal and lateral behaviour of the aircraft is very indirect and extremely small, the shock absorbers are considered, throughout the study, as oriented along the aircraft coordinate system \u201cvertical\u201d axis. 14 M. Jeanneau"
        ]
    },
    {
        "image_filename": "designv10_10_0001030_0956-5663(95)96894-5-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001030_0956-5663(95)96894-5-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the glucose biosensor: working",
        "texts": [
            " All other reagents were of analytical grade and were used without further purification. Human blood samples with known glucose content were obtained from the Division of Endocrinology, the School of Medicine, University of New Mexico. The blood samples were obtained from normal (non diabetic) subjects on the day of the measurement. Heparin was added to these blood samples in order to prevent clotting. No preservatives were used. Plasma was obtained from these samples by centrifugation, and used in the electrode tests the same day. Figure 1 shows a cross-sectional schematic of the glucose biosensor, which was based on the hydrogen peroxide measuring principle. The sensor consists of two parts: an amperometric electrode system and an enzyme micro-bioreactor. A three-electrode amperometric scheme is used: a platinum wire (diameter 0.25 mm, length 4 mm) working electrode (1); a silver/silver chloride reference electrode (In Vivo Metric, electrode (I), silver/silver chloride reference electrode (2), counter electrode (3), sensor housing (4), glucose diffusion membrane (5), immobilized enzyme (6), inlet recharge tube (7) and exhaust discharge tube (8)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002889_j.triboint.2013.05.002-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002889_j.triboint.2013.05.002-Figure1-1.png",
        "caption": "Fig. 1. Schematic view of the rolling bearing assembly.",
        "texts": [
            " The formulations are the following: ESTF and ESTR are Notation and units a ASTM D341 reference kinematic viscosity (cSt) C0 ellipticity parameter (\u2013) dm rolling bearing mean diameter (mm) En contact equivalent Young modulus (Pa) Fa axial load (N) G material parameter (\u2013) Grr factor depending on the bearing type, bearing mean diameter and applied load (\u2013) Gsl factor depending on the bearing type, bearing mean diameter and applied load (N mm) h0 centre film thickness \u00f0\u03bcm\u00de h0C thermal corrected centre film thickness \u00f0\u03bcm\u00de Krs starvation constant for oil bath lubrication (\u2013) KZ bearing type related geometry constant (\u2013) L thermal parameter (\u2013) m ASTM D341 viscosity parameter (\u2013) Mexp bearing friction torque measured experimentally (N mm) M\u2032rr rolling friction torque (N mm) Msl sliding friction torque (N mm) Mdrag friction torque of drag losses (N mm) Mseal friction torque of seals (N mm) Mt internal bearing friction torque (N mm) n ASTM D341 viscosity parameter (\u2013) n rotational speed (rpm) R1 geometry constant for rolling friction torque (\u2013) RXi curvature radius of element i in x direction (\u2013) RX equivalent radius of curvature in x direction (\u2013) RYi curvature radius of element i in y direction (\u2013) RY equivalent radius of curvature in y direction (\u2013) S1 geometry constant for sliding friction torque (\u2013) s piezoviscosity parameter (\u2013) S sliding factor of the roller/ball (\u2013) t piezoviscosity parameter (\u2013) T operating temperature (K) Tref reference temperature (K) U speed influence parameter (\u2013) U1 linear speed of ball (m/s) U2 linear speed of ring (m/s) VI viscosity index (\u2013) W load parameter (\u2013) \u03b1 piezoviscosity coefficient (Pa\u22121) \u03b1t thermal expansion coefficient (\u2013) \u03b2 thermoviscosity coefficient (1K\u22121) \u03b7 dynamic viscosity (Pa s) \u03d5bl sliding friction torque weighting factor (\u2013) \u03d5ish inlet shear heating reduction factor (\u2013) \u03d5rs kinematic replenishment/starvation reduction factor (\u2013) \u03d5T thermal reduction factor (\u2013) \u03ba viscosity ratio (\u2013) \u039b specific film thickness \u00f0\u03bcm\u00de \u03bcbl coefficient of friction in boundary film lubrication (\u2013) \u03bcEHD coefficient of friction in full film lubrication (\u2013) \u03bcsl sliding coefficient of friction (\u2013) \u03bc bearing coefficient of friction (\u2013) \u03bd kinematic viscosity (cSt) \u03bd1 required kinematic viscosity (cSt) \u03b8 operating temperature (1C) \u03b8c stabilization temperature (1C) \u03b8s stabilization temperature (1C) \u03c10 density at reference temperature (g/cm3) \u03c1 density (g/cm3) s composite surface roughness ball/ring (m) s1 RMS surface roughness ball (m) s2 RMS surface roughness ring (m) \u03c4 shear stress (Pa) biodegradable ester base oils; MINR is a mineral base oil; MINE is formulated with hydroprocessed group III base oil and a PAMA thickener; PAGD is a polyalkylene glycol and PAOR is a polyalphaolefin base oil with an ester compatibilizer. Table 1 displays the wind turbine gear oils physical properties as well as their chemical composition. A detailed description on the physical properties can be found on previous works [26,27]. 3. Rolling bearing assembly and test procedures The rolling bearing tests were performed on a modified FourBall machine, where the Four-Ball arrangement was replaced by a rolling bearing assembly, as shown in Fig. 1. This assembly was developed to test several rolling bearings and measure the friction torque as well as the operating temperature in several different points. A detailed presentation of this assembly can be found in [25]. The rolling bearing assembly is divided in two parts: the shaft adapter (6), directly connected to the machine shaft and supporting the bearing upper race (5); a lower race support (2) and the bearing lower race (3), both clamped to the bearing housing (1). In operation, the internal bearing torque (or friction torque) is transmitted to the torque cell (11) through the bearing housing (1). The friction torque was measured with a piezoelectric torque cell KISTLER9339 A, ensuring high-accuracy measurements (71 N mm) even when the friction torque generated in the bearing was very small compared to the measurement range available. This assembly includes five thermocouples (I\u2013V), measuring temperatures at strategic locations (see Fig. 1) which are used to monitor the temperature inside the bearing assembly (IV), near to the rolling bearing and the lubricant (III) and to evaluate the heat evacuation from the bearing housing into the surrounding environment (I, II and V). The system is also monitored by two thermocouples to monitor the chamber and room temperatures. Considering the rolling bearings dimensions, the contact geometry is defined according to Eq. (1). 1 RX;Y \u00bc 1 2 1 RX;Y\u00f01\u00de \u00fe 1 RX;Y\u00f02\u00de \u00f01\u00de For the axial loads tested (700 and 7000 N) each element of ball-raceway contact reach the conditions presented in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001787_0094-114x(87)90010-3-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001787_0094-114x(87)90010-3-Figure3-1.png",
        "caption": "Fig. 3. Extreme reach of a reference point on the workspace.",
        "texts": [
            " (13) -] U~Uz(I -- COk+2) UxSk ~2 | - - UxSO~ + 2 0 J U~(1--C0k+2)+C0k+2 U:Sk+2 0 1 surfaces, the Jacobian determinant is of rank less than 3, When the manipulator is in the position of extreme reach, it is simple to show that the instantaneous motion of the wrist center must be on a surface perpendicular to the vector joining the wrist center to the reference point from which the reach is being measured. The Jacobian surfaces shown in Section 4 are the only surfaces where the wrist center is constrained to move on a surface. Thus, the wrist center is at a maximum/minimum reach when the perpendicular to the Jacobian surface passes through the reference point (see Fig. 3). In other words, each point on these Jacobian surfaces is at a maximum/minimum reach with reference to the points lying on the perpendicular to the Jacobian surface at that point. In general, for a 6R manipulator it is obvious there will be 32 such points for a given reference point. The one for the absolute maximum, the one for the absolute minimum and those remaining will denote the relative maximum/minimum. The Jacobian analysis of workspaces of mechanical manipulations a I = 2 6 . 7 * a 4 = 8 6 , 0 \u00b0 01 = 3 2 04 = 4 S t = 0 a2 = 1 2 3 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002600_1.4004962-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002600_1.4004962-Figure2-1.png",
        "caption": "Fig. 2 Waviness at inner race and outer race",
        "texts": [
            " In other words, the respective spring force comes into play when the instantaneous spring length is shorter than its unstressed length; otherwise the separation between ball and race takes place and the resulting force is set to zero. An unbalance force (Fu) is acted due to rotating of rotor with inner race. 2.1 Race Waviness. An important source of vibrations in ball bearings is waviness. These are imperfections with varying amplitude across the circumference of the outer and inner surface of the bearing components as shown in Fig. 2. The characteristic wavelengths of the imperfections are much larger than the dimensions of the Hertzian contact areas between the balls and the guiding races. The number of waves per circumference is denoted by the wave number. Waviness imperfections cause variations in the contact loads when the bearing is running. The magnitude of the variation depends on the amplitude of the imperfection and the nonlinear stiffness in the contact. Due to the variations in the contact loads, vibrations are generated in the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000613_ac9704218-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000613_ac9704218-Figure2-1.png",
        "caption": "Figure 2. Scheme of the screen-printed electrodes before (A) and after (B) adaptation to a microwell.",
        "texts": [
            " The P+ traces were extracted from the stock solution under these conditions, but S- was partially extracted, too, and its final concentration was evaluated to be\u223c0.5 \u00d7 10-2 M by square wave voltammetry (SWV) at a CPE. Preparation of Disposable Nafion-Coated Screen-Printed Electrodes (Nafion-SPE). A conductive carbon ink was prepared by thoroughly hand-mixing graphite powder and a polystyrene/mesitylene mixture. A commercial conductive carbon ink (Minico M3021-1RS, W. R. Grace) was also used in a few cases. A manual screen-printer was used to produce disposable SPEs. An array of six electrodes, each of them corresponding to the pattern shown in Figure 2A, was printed on a flexible polyester film (Staedler film for overhead projection) by forcing the conductive ink to penetrate through the mesh of a screen stencil (77 threads cm-1). Each SPE consisted of a disk as the working surface (3.5 mm diameter), a conductive track (20 mm \u00d7 1 mm), and a square extremity (25 mm2) for the electrical contact. After drying for 1 h at room temperature, an insulator layer was spread manually over the conductive track, leaving the working disk area ready for Nafion modification",
            "31 Equipment and Electrochemical Measurements. An EG&G Par 273 potentiostat interfaced to an IBM XT 286 computer system with a PAR M270 software was used for cyclic voltammetry (CV) at a fixed potential scan rate of 50 mV s-1 and for SWV. The SWV parameters are given in a previous work.28 The electrochemical experiments were carried out at room temperature in small glass vials, with a working volume of 5 mL. A few measurements were performed in a cell of small volume (50- 250 \u00b5L) corresponding to the SPE-adapted microwell depicted in Figure 2B. The bottom of a commercial microwell was removed and replaced by a Nafion-SPE. Solutions were not deaerated unless otherwise stated. For the accumulation procedure, a Nafion-SPE was immersed in the vial containing the analyte solution (P+), shaken to enhance the mass transfer to the working electrode surface. The modified SPE was wedged in the vial to avoid its rotation during shaking. After preconcentration, the accumulated product P+ was determined by connecting the modified SPE, the Ag/AgCl (3 M NaCl) reference electrode, and the platinum wire counter electrode to the potentiostat",
            "17 It shows that the maximal velocity (Vm) is not yet reached at the substrate concentrations used in these experiments, since the velocity corresponds to Vm/2 when the substrate concentration is equivalent to Km. The low detection limit of AP at a Nafion-SPE allows one to envision very sensitive enzyme immunoassays. However, they dictate working with small volumes of liquid because of the expensive reagents used (antibody, label, etc.) and of the small quantities of samples assayed (serum, urine, blood, etc.). Therefore, the Nafion-SPE was stuck successfully to the bottom of a microwell of 300 \u00b5L (Figure 2B), making it possible to work with solution volumes within the range 50-250 \u00b5L, well adapted to enzyme immunoassays. Preliminary results have shown that stronger shaking conditions are needed for the accumulation of P+ and that the signal is decreased as the assay volume is reduced owing to a nonnegligible extraction of P+ within the Nafion film and, therefore, its depletion in solution.46 It was verified that P+ did not adsorb on the microwell wall. For example, the relative electrode responses of 0",
            " The indirect electrochemical determination of AP can be achieved at subfemtomolar levels at a disposable Nafion-SPE using the enzyme substrate S- and a 1 h incubation period. Considering the simple fabrication procedure of the Nafion-SPEs and the low cost of their mass production ($\u223c0.03 of raw material), their applications in enzyme immunoassays are very promising. An AP detection limit of 8 \u00d7 10-20 mol/200 \u00b5L (\u223c50 000 AP units) can be envisioned insofar as the previous results can be extrapolated to small volumes (Figure 2B). Work is in progress to replace the wire Ag/AgCl reference electrode of the microwell-shaped cell shown in Figure 2B by a screen-printed Ag/AgCl electrode and to achieve ultrasensitive enzyme immunoassays. We thank the Agence Nationale de la Valorisation de la Recherche (A.N.VA.R.) for financial support of this reseach. Received for review April 23, 1997. Accepted August 1, 1997.X AC9704218 (46) To be published. X Abstract published in Advance ACS Abstracts, October 1, 1997. 4694 Analytical Chemistry, Vol. 69, No. 22, November 15, 1997"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000828_robot.1997.620041-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000828_robot.1997.620041-Figure4-1.png",
        "caption": "Fig. 4 Zero Moment Point, (ZMP)",
        "texts": [
            " This structure is strong against falling down of the robot and it looks smart and more similar to human. 4 Conditions for Continuous Walking In this section, we consider the conditions for stable walking. Biped locomotion robots must be controlled under the possibility of falling down. Therefore the reference trajectory of biped locomotion robots must be generated without falling down. We must consider many kinds of conditions for Continuous walking without falling down as follows; a e 5 Conditions of Zero Moment Point(ZMP) The moment is generated by the floor reaction force and torque. Figure 4 shows the concept of Zero Moment Point, where p is the point that T, = 0 and Ty = 0 , T,, Ty represent the moments around x axis and y axis generated by reaction force F,. and reaction torque T,. respectively. The point p is defined as the Zero Moment Point (ZMP). When the ZMP exists within the domain of the support surface, the contact between the ground and the support leg is stable. where pzmp denotes a position of ZMP. S denotes a domain of the support surface. This condition indicates that no rotation around the edges of the foot occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001261_1.1479337-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001261_1.1479337-Figure1-1.png",
        "caption": "Fig. 1 5DOF model coordinate systems",
        "texts": [
            " All four models consider individual ball rolling elements and use Hertzian contact theory ~@5#! to model the nonlinear stiffness of the bearing. Whereas complicated functions are used for stiffness, constant damping is used to represent the effects of lubrication and friction. Cage influences are ignored though the spacing of the rolling elements is assumed constant. Two-Degrees-of-Freedom Model Without Inertia \u201e2DOF\u2026. This was the model investigated previously ~@10#!. Of the five DOF shown in Fig. 1, only the x and y DOF are used. Contact or loss of contact is considered for each rolling element. Ignoring rolling element centrifugal load effects, the inner and outer race contact deformations can be combined so that the overall contact deformation for the j th rolling element, d j , is given by d j5x cos f j1y sin f j2ci2ce . (2) Summing the contact forces for each rolling element in the x and y directions gives H f x f y J 5Kp( g jd j nH cos f j sin f j J (3) where g j5H 1 for d j.0 0 for d j<0 and f j5 2p~ j21 ",
            " With known d i , all parameters, including the inner and outer race contact forces, can be obtained and transformed into the global degreesof-freedom. Note that when inertia is ignored, contact is lost when d is negative but with centrifugal load, the inner race can lose contact even though there is still contact with the outer race. The critical value of d when contact is lost, dc , occurs when d i50. Hence contact with the inner race is lost when d<dc , where dc5S mrevc 2Dp 2Kpe D 1/n . (8) Five-Degrees-of-Freedom Model \u201e5DOF\u2026. As shown in Fig. 1, this model ~@11,12#! includes not only the radial displacements of the inner race but also the rotations about the x and y-axes and the axial displacement. Two coordinate systems are used. The inner race coordinate system (x ,y ,z ,ux ,uy) corresponds to the degrees-of-freedom of the rotor at this point and has its origin at the center of the bearing. The local rolling element coordinate system (r ,Z ,Q) defines the position of the inner race center of curvature for each rolling element and has its origin at the nominal position of the inner race center of curvature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002732_1.4025196-Figure8-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002732_1.4025196-Figure8-1.png",
        "caption": "Fig. 8 Robust optimization of PPTE: optimal tooth surface (total) modifications corresponding to the three proposed robustness measures",
        "texts": [
            " The following four tooth surface modifications were selected as design variables x, with their user-specified bounds: \u2022 Profile crown x1, 0 x1 50lm \u2022 Lead crown x2, 0 x2 50lm \u2022 Profile slope x3, 25lm x3 25lm (pressure angle variation) \u2022 Lead slope x4, 25lm x4 25lm (helix angle variation) The operating torque range was \u00f0Tl \u00bc 10Nm; Tu \u00bc 500Nm\u00de, while m\u0302 \u00bc 0 was held fixed. All of the three previously defined robustness measures were used to construct the three corresponding robust counterparts of PPTE, namely F \u00f0PPTE\u00de u (uniform distribution), F \u00f0PPTE\u00de t (triangular distribution), and F \u00f0PPTE\u00de w (worst-case scenario). Their minimization resulted in the following tooth surface modifications, shown in Fig. 8: x u \u00bc \u00f0x1u; x2u; x3u; x4u\u00de \u00bc \u00f014; 2; 0; 0\u00delm x t \u00bc \u00f013; 3; 3; 1\u00delm x w \u00bc \u00f09; 2; 3; 1\u00delm The corresponding PPTE functions are plotted versus torque in Fig. 9, along with the results obtained in Ref. [14]. It is straightforward to notice that the three proposed, purposeoriented robustness measures matched expectations. Minimization of F \u00f0PPTE\u00de u resulted in low PPTE throughout the whole torque Journal of Mechanical Design DECEMBER 2013, Vol. 135 / 121005-7 Downloaded From: http://solarenergyengineering"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002136_tmech.2010.2089530-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002136_tmech.2010.2089530-Figure3-1.png",
        "caption": "Fig. 3. Walking configuration in steady state. The rectangles represent the foot boundaries and the thick and thin lines represent the CoM trajectories in single support phase and double support phase, respectively. The small circles represent the initial/final CoM positions for left/right support phase.",
        "texts": [
            " When the robot follows a given CS, it is assumed that its state is in steady state and ZMP variation is not utilized. These assumptions correspond directly to a walking pattern that represents steady-state motion for the 3D-LIPM in which the particular solutions of (6) are zero. In this situation, the WS at the end of each single support phase is identical. This state is considered as a desired WS. To translate the CS into the desired WS, it is enough to observe only one period of the walking configuration in steady state, as shown in Fig. 3. According to the CS, sagittal and lateral motions are generally nonsymmetrical for both left and right legs with different single and double support times, step lengths, and walking directions. Since the robot\u2019s state is in steady state without ZMP variation, the walking configuration can be fully described by initial or final WS for both left and right leg support phases. In terms of implementation, the CoM is controlled to travel with constant velocity during double support phase for a specific time Tdl/r for double support from left/right to right/left movement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001376_icca.2005.1528213-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001376_icca.2005.1528213-Figure3-1.png",
        "caption": "Fig. 3. PC-104 computer system.",
        "texts": [
            " The last servo is to control angles of tail rotor blades, where a closed-loop comprises the gyro, servo and helicopter to stabilize the azimuth of the helicopter automatically. Manipulator can control the ight by sending wireless control signals through the transmitter on the ground. We present in this section the detailed description of each component in the simple avionic system, which includes the PC-104 computer system, sensors such as the NAV-IMU sensing unit and RPM sensor, servo controller and wireless communication device. A. PC-104 Computer System As mentioned earlier, the airborne computer system is the PC-104 computer system as shown in Figure 3. The PC104 is an industrial embedded computer system with good ability of anti-vibration. The size of the printed circuit boards (PCB) in this industrial computer system is 96 x 90 mm. The system consists of four pieces of PCBs, i.e., a main processing board, a serial communication board, an A/D data acquisition board and a DC-to-DC converter board. They are connected through the ISA bus with the anti-shock pin-andsocket connection socket. A real-time operation system (RTOS) is required for the airborne computer system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002991_icra.2014.6906613-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002991_icra.2014.6906613-Figure3-1.png",
        "caption": "Fig. 3. (a) Leg extension 3D-SLIP (b) and long jump 3D-SLIP models to capture the salient requirements of producing a maximum-span running long jump. Following touchdown (TD) both models include a linear spring with stiffness k s that is driven by a linear actuator. Ground contact terminates at liftoff (LO) when the spring reaches its rest length. The long jump 3DSLIP model employs a main mass m1 and small mass m2 which together equal the total mass m. Mass 2 is attached to the spring leg at fixed radius r2 via a nonlinear spring-damper. This mass is initialized along the leg at touchdown, but drifts off the leg throughout stance.",
        "texts": [
            " The whole-body humanoid control approach is summarized in Section IV which enables the performance of 16 on the jumping result were investigated by varying parameter values. The model parameters were first adjusted visually and then calculated using a genetic optimisation algorithm. MODEL DESCRIPTION AND VERIFICATION The leg as a linear spring In a first approach to long jumping we a model will be considered in which the leg operates as a spring. This gives basic insights into the influence of geometric parameters and the role of leg stiffness. 30 ms before the take-off. Fig. 3 Experimental result for the ground reaction force Fg and the instantaneous leg stiffness kdyn as a function of the time.Fig. 2. Experimentally observed vertical ground reaction forces and leg stiffness for a human long jump, from [7]. The passive peak at the beginning is attributed to a forceful foot plant which decelerates the leg mass. 978-1-4799-3685-4/14/$31.00 \u00a92014 IEEE 222 a running long jump in 3D dynamic simulation. Concluding remarks are provided in Section V. While the standard 3D-SLIP model of locomotion can be used to describe the CoM dynamics of running with good fidelity, it lacks the capability to describe important characteristics of a running long jump",
            " In addition, human long jump data displays a passive ground reaction force (GRF) peak at the beginning of stance. Two modifications to the 3D-SLIP model are described below which provide the ability to capture these characteristics. In order to capture the leg lengthening effects found in human long jumping, active lengthening may be added to the 3D-SLIP model. Here, this lengthening is modeled through the incorporation of a linear actuator in series with the SLIP spring. This modification is shown in Fig. 3(a). The model consists of a point mass m and leg that experiences phases of stance and flight. The mass follows ballistic dynamics in flight wherein the massless leg is positioned for upcoming stance. Following touchdown (TD), a Hookean spring with constant k s imparts forces onto the mass. The period of stance ends at liftoff (LO) when the spring once again reaches an unstretched length. Here, forward motion is assumed in the positive x-direction. The dynamic evolution of the point mass is intended to describe the center of mass of a larger system",
            " Forward running jumps are dominated by motion in the positive x-direction, and thus \u2713 c and ` a are monotonically increasing. In addition to active lengthening, human long jumpers plant their stance foot more forcefully prior to takeoff, resulting in a large force peak that decelerates the stance leg mass. This force peak injects additional vertical impulse, which is a key requirement of jumping for distance. The foot plant behavior can be introduced through the addition of a second mass to the Leg Extension SLIP model, shown in Fig. 3(b). In this model, the mass m2 represents the stance leg mass, and is connected to the SLIP leg at a fixed distance r2 through a nonlinear spring-damper. The large mass m1 is positioned at radius r1 and is still driven by the SLIP spring. Similar to before, the spring produces forces f s = k s (r1,0 + ` a r1) (5) directed along \u02c6 r. These forces act only on m1. To describe the position of mass m2, coordinate vectors \u02c6 x2 and \u02c6 y2 are attached to and rotate with the SLIP leg. Combined with \u02c6 r these provide a coordinate system with rotation matrix: R = \u21e5 \u02c6 x2 \u02c6 y2 \u02c6 r \u21e4 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002497_j.conengprac.2010.02.014-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002497_j.conengprac.2010.02.014-Figure5-1.png",
        "caption": "Fig. 5. The presented embedded system fitted into the (custom-built) landing gear of a small-scaled Vario Benzin helicopter. Springs and dampers are used to filter out vibrations from the main rotor blades.",
        "texts": [
            " A central problem observed on-board helicopters is the 25 Hz vibrations induced by the main rotor blades. These vibrations generate a large amount of noise on the inertial sensors. In practice, these noises totally overwhelm the useful signals. Fortunately, it is possible to solve this issue by using well-chosen noise dampers. On the presented helicopter, it was decided that the micro-controller and the sensors would all be located on a board which would be physically connected to the frame of the helicopter through four spring\u2013damper systems (see Fig. 5). Experiments conducted on a vibrating table have shown that it was advantageous to keep the embedded system as compact and as rigid as possible. The total weight of the subsystem is about 600 g. Some of the batteries are attached to it to bring the weight close to 1.8 kg. This enabled the use of off-the-shelf dampers yielding appropriate cut-off frequencies. MV801-5CC dampers from PaulstraTM were chosen for their ability to work with low masses vibrating at low frequencies. With these, the obtained vibration damping is satisfactory, with a cut-off frequency around 9 Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001261_1.1479337-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001261_1.1479337-Figure2-1.png",
        "caption": "Fig. 2 5DOF model parameters",
        "texts": [
            " includes not only the radial displacements of the inner race but also the rotations about the x and y-axes and the axial displacement. Two coordinate systems are used. The inner race coordinate system (x ,y ,z ,ux ,uy) corresponds to the degrees-of-freedom of the rotor at this point and has its origin at the center of the bearing. The local rolling element coordinate system (r ,Z ,Q) defines the position of the inner race center of curvature for each rolling element and has its origin at the nominal position of the inner race center of curvature. The outer race center of curvature is used as a reference point. Figure 2 shows the various parameters used. Note that rp , the radial coordinate of the nominal center of curvature of the inner race, is not related to Dp . For the j th ball, the displacement of the inner race center of curvature, u, is related to the displacement of the inner race, d ~treated as a known input quantity for the forcing function! according to u5$ur uz uQ%T5@R#d5@R#$x y z ux uy% T (9) OCTOBER 2002, Vol. 124 \u00d5 985 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F where @R#5F cos f j sin f j 0 2zp sin f j zp cos f j 0 0 1 rp sin f j 2rp cos f j 0 0 0 2sin f j cos f j G 335 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure15-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure15-1.png",
        "caption": "Fig. 15 2-RPU-UPU PPR-PMs.",
        "texts": [
            "org/ on 01/15/2018 Term (d) substitute one or more P joints each with a planar parallelogram [18, 27]; (e) substitute two of three successive P joints with a spatial parallelogram [42]; (f) substitute one or more R joints in the leg with a ci-\u03b6\u221esystem each with a coaxial H joint. For example, PPR-PMs proposed in [33] are in fact the variations of the PPR-PMs shown in Fig. 14, which are obtained by (a) substituting a combination of two successive R joints with non-parallel axes with a U joint and (b) replacing the unactuated P joints each with a planar parallelogram. Figure 15 shows a 2- RPU-UPU PPR-PM under our current investigation. It is in fact obtained from the 2-(RPR)ERC-RA(RPR)Y RA PPR-PMs shown in Fig. 12(b) by substituting a combination of two successive R joints with non-parallel axes with a U joint. Virtual chains have been introduced to represent the motion patterns of 3-DOF motions. A procedure for the type synthesis of Copyright  2004 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Dow 3-DOF PPR-PMs has also been proposed. Using the proposed procedure, 3-DOF PPR-PMs are synthesized in three steps: (a) Type synthesis of legs, (b) Type synthesis of 3-DOF PKCs and (c) Selection of actuated joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000931_095440502760291808-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000931_095440502760291808-Figure7-1.png",
        "caption": "Fig. 7 Molten pool edge determination for infrared image",
        "texts": [
            " The pulsating illumination synchronized with the high-speed shutter on the camera suppresses the intensive light from the molten pool and ensures the successful acquisition of clear images of the molten pool. The ordinary images acquired from the high-shutter-speed camera are processed with a Canny edge detector to \u00aend the edge of the molten pool [18]. By mapping the position of the edge of the molten pool from the ordinary image to the corresponding infrared image through a coordinate transformation, it is determined that a grey level of 70 represents with enough accuracy the transition between the molten pool and the surrounding solid (Fig. 7). HEAT INPUT CONTROL BASED ON INFRARED SENSING The LBAM system consists of four subsystems: a 1 kW Nd:YAG laser source, a metal powder delivery system, a three-axis positioning system and an infrared image acquisition system. The three-dimensional metal part is produced layer by layer by synchronizing the X\u00b1Y\u00b1Z motion, the Nd:YAG laser and the injection of metal powder. The infrared image acquisition system takes the images of the molten pool in real time and calculates the dimensions of its area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003033_s00170-012-4406-7-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003033_s00170-012-4406-7-Figure5-1.png",
        "caption": "Fig. 5 Spherical interpolation, a example CL data, b original tool movement, c interpolated tool movement",
        "texts": [
            " Dividing m to several intervals provides the interpolated CL data. P !\u00bc P ! i\u00fe1 P ! i :m\u00fe P ! i T !\u00bc R\u00bd T!i \u00f016\u00de The spherical interpolation matrix is given in Eq. 17. R\u00bd \u00bc k2x 1 h\u00bd \u00fe h kxky 1 h\u00bd kzg kxkz 1 h\u00bd \u00fe kyg kxky 1 h\u00bd \u00fe kzg k2y 1 h\u00bd \u00fe h kykz 1 h\u00bd kzg kxkz 1 h\u00bd kyg kykz 1 h\u00bd \u00fe kzg k2z 1 h\u00bd \u00fe h 2 4 3 5 g \u00bc sin\u00f0\u0394\u03b8m\u00de h \u00bc cos\u00f0\u0394\u03b8m\u00de \u00f017\u00de Spherical interpolation is implemented using an example CL data. Original and the interpolated cutter location points and the tool axis vectors are shown in Fig. 5. 3.2 NC data correction In Section 2, kinematic modeling of the machine tool is introduced and it is shown that there are multiple possible solutions for B and C axis angles. Therefore, appropriate solution among these candidates has to be chosen. For determining the B axis angle a simple yet effective method is used. For the first CL point in the CL data, lead angle of the tool with respect to workpiece is found, and then the solution having the same sign with the lead angle is chosen. In Fig. 6, the relationship between lead angle and the B axis angle is shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002667_1.3567962-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002667_1.3567962-Figure1-1.png",
        "caption": "FIG. 1. Schematic of Optomec LENS process for multitrack deposition.",
        "texts": [
            " In this process, a coaxial head consisting of four radially symmetrical powder flow nozzles and optics moves over the surface of a substrate with powder material delivered coaxially with the laser beam.5 The corresponding schematic of the processing head with nozzle configurations can be found in Ref. 5. The moving laser beam locally melts a small surface of the substrate and the current track, leaving a solidified track behind. After scanning some distance, the beam turns off and then it moves to the starting point of the previously deposited track with a certain offset and begins to clad a second adjacent track as seen in Fig. 1. By lifting the head by certain height, a second-layer powder material can be deposited on the existing layer in the same manner. The fiber laser beam is Gaussian with a half divergence angle of 2.7\u00b0 and focused into a 0.5 mm spot at 9.525 mm down the nozzle tip. The assumptions made in the model include incompressible liquid flow in the molten pool while considering velocity fluctuation, immediate powder melting at the free surface,2 and neglection of shielding gas pressure and turbulence on the molten pool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002309_j.jsv.2010.05.014-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002309_j.jsv.2010.05.014-Figure1-1.png",
        "caption": "Fig. 1. Approximated spring and damper linear model.",
        "texts": [
            "e., OnbOe. In other words, the changes in the oil film stabilize fast enough not to influence the harmonic response. Also the pressure dependent relations of the fluid properties have to be evaluated with the transient model. The Dowson and Higgins [14] density\u2013pressure relation and the Roelands equation for the viscosity\u2013pressure relation, as presented in Larsson [15], were applied. Considering the oil film as a set of linear spring and damper, the EHL contacts become a linear dynamic system. Fig. 1 shows this simplified model of the problem, as initially proposed by Wijnant and Wensing [11]. This simple approach is very useful to understand the complete bearing dynamic system. Previously, when dealing only with the dry contact model, the same situation occurs, only without the damping, provided by the oil film, and the stiffness being the one from the Hertzian contact model. In this case, the equation of motion can be rewritten as 1 X2 n d2H0 dT2 \u00feC1 dH0 dT \u00feK1H0 \u00bc 1 (7) The contact forces generated at the inner and outer raceways contacts are adjusted to a set of stiffness and damping coefficients, given by K1 and C1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000967_20.877808-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000967_20.877808-Figure9-1.png",
        "caption": "Fig. 9. Distributions of eddy current loss in permanent magnet (n = 5).",
        "texts": [
            " 6 shows the results of the divided model using the conventional method and that using our - method with double nodes technique. It is clarified that the results using our - method with double nodes technique agrees with the results using the method. Furthermore, it is clarified that the divided model has large advantage to decrease the eddy current in comparison with the standard model. Figs. 9 and Fig. 10 show the distributions of eddy current loss in the permanent magnets. The results of the divided model using our - method with double nodes technique agrees with the results using the method as shown in Fig. 9. From Fig. 10, it is found that the eddy current loss at the surface of the permanent magnet is large. Furthermore, the eddy current loss of the rotation direction side is larger than that of the opposite side. Fig. 11 shows the effect of division of the permanent magnet on the eddy current loss. It is clarified that the eddy current loss decrease strongly as the number of division of permanent magnet n increases. Table I shows the discretization data and CPU time. The number of time step for 1 cycle of eddy current waveforms is 30"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002427_iros.2011.6095091-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002427_iros.2011.6095091-Figure3-1.png",
        "caption": "Fig. 3. Around hip joint of Pneumat-BS. We transmit the force of the muscles by PE braided lines.",
        "texts": [
            " For example, sartorius (\u266f10) is a bi-articular muscle which has the function of knee flexion, hip flexion, hip external rotation, and hip abduction. Thus, using the three-dimensional arrangement of the muscles, the structure is more similar to the human musculoskeletal structure. Since there are infinite ways to arrange muscles on a musculoskeletal robot, it is difficult for the designer to decide it in advance. For this reason, we designed the system so that the location and points of origin of the muscles can be easily changed. Fig. 3 shows the joint drive system around the hip joint of the robot. The hip joint of the robot is driven by 9 muscles (\u266f8\u223c\u266f16). To drive a redundant system like this, we adopted a drive system to put PE braided lines through polyacetal bearings. This structure enables us to easily rearrange the pathway of the muscles and make it possible to generate appropriate joint torques. Fig. 4 shows standard human femur, and the femur part of Pneumat-BS (CAD, photograph). The angle of inclination of the human femur and the projection of the greater trochanter to the side increase the moment arm of the gluteus medius (\u266f10)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000588_s0022-5096(98)00100-8-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000588_s0022-5096(98)00100-8-Figure1-1.png",
        "caption": "Fig[ 1[ The coupling of director rotation to antisymmetric and symmetric shears[ \"a# The coupling D0 of the director to the rotation u\u2212v relative to the matrix[ The director is n9 in the relaxed state[ \"b# The coupling D1 of the director rotation to a symmetric shear\\ that is where no rotation of the solid matrix is involved[ The director responds by rotating by u\u2212v[",
        "texts": [],
        "surrounding_texts": [
            "The free energies for both large and small distortions of nematic elastomers are derived within statistical mechanics and continuum elasticity\\ respectively[ These yield the non!linear and linear constitutive relations[ 1[0[ Statistical mechanical analysis Consider a polymer chain of length L[ In an isotropic melt it has random con_gur! ations with a Gaussian end to end probability distribution p\"R# \u00bd exp \"\u22122R1:1aL# characterised by its second moment \u00f0RiRj\u0141 0 1 aLdij\\ that is by a spherical gyration \"or shape# tensor lij adij where a is known as the e}ective step length and is sus! ceptible to measurement in a melt by neutron scattering[ In a nematic melt the elements of a chain are orientationally ordered[ The distribution of chain shapes is then also anisotropic] p\"R# \u00bd exp 0\u2212 2 1L RTl \u22120R1 \"0# where the second moment is now either a prolate or oblate spheroid^ \u00f0RiRj\u0141 0 2 l ijL with l 2 l> 9 9 9 l_ 9 9 9 l_ 3[ \"1# See Fig[ 0 for a prolate example[ Orientational order in a uniaxial nematic is charac! terised by a tensor order parameter Qij Q\"2ninj\u2212 0 1 dij# where Q \u00f0P1\"cos u#\u0141 with u the angle between the nematic ordering direction n and a rod!like component of a conventional nematic ~uid or\\ in this case\\ with the rods in a polymer chain[ P1 is the second Legendre Polynomial\\ the angular function that transforms as a second rank tensor under rotations and characterises quadrupolar order[ A prolate chain has Q\u00d7 9 for its backbone elements and thus\\ l> \u00d7 l_] an oblate chain has the converse[ The connection with shape is easily seen if \"1# is rewritten as] l l_d \u00a6\"l>\u2212l_#n n[ \"2# When the ends of a chain are crosslinked into a network\\ so that it forms a strand of a percolating network\\ mechanical distortions of the body in turn distort the end Fig[ 0[ Nematic chains*their shape and its role in networks[ \"a# A strand with end to end vector R9[ The shape tensor l 9 characterising the distribution of R9 is shown as a prolate spheroid[ The director is n9[ Crosslinks are shown as ,] parts of other network strands to which the test strand is connected are indicated by lighter lines[ The solid in which the strand is embedded is shown undistorted with a transverse lineal dimension of 0[ \"b# The span R9 is deformed a.nely to R by the application of deformations l \"a transverse extensional component of value l is shown for illustration with arrows indicating the stretch#[ The actual chain shapes no longer re~ect the distribution p\"R# optimal at the current conditions of temperature and the current director \"which has not been permitted to rotate#[ Hence the entropy drops\\ in turn increasing the free energy[ \"c# The rotational response of l and n to both extensional and simple shear \"d# strains[ The distribution is shown rotated at constant shape*this combination of l and d is evidently soft[ to end distribution away from the optimal form that characterises the relaxed state at the current temperature[ The free energy then rises[ The resistance to shape change is thereby largely entropic in origin[ Under the a.ne deformation of crosslinks approximation\\ commonly used for such networks\\ the change in free energy is easily calculated[ Let R9 be the span at the instant of crosslinking\\ with \u00f0R9iR9j\u0141 0 2 l 9ijL characterising p\"R9#\\ let the deformation lij 1Ri:1R9j carry R9 \"a.nely# to the current span R l R9 and let the current conditions be such that p\"R# be given by \"0# with moment determined by \"1#[ Then the free energy of a strand is the average of ln p\"R# over the probability p\"R9# of its formation] F \u2212kBT\u00f0ln p\"R#\u0141R9 kBT 2 1L \u00f0\"l R9#Tl \u22120\"l R9#\u0141R9 kBT 1 Tr \"l 9l Tl \u22120l #[ \"3# We assume for the moment that the crosslinking conditions are also those of the relaxed state \"l 9#[ The shape l is that pertaining to the distribution of polymers on imposing l [ The temperature being unchanged\\ the underlying nematic order is largely0 as in the relaxed state before l is imposed\\ but with a possible change in n as the nematic distribution rotates to better accommodate l [ Most of our paper is concerned with this additional freedom a nematic elastomer possesses to respond to imposed strains[ The free energy density f derives from \"3# via the number density n of network strands] f nkBT 1 Tr \"l 9l Tl \u22120l #[ \"4# Network ~uctuations\\ ignored within the a.ne deformation approximation\\ arise when we allow junction points to move randomly\\ subject to the constraint that they are connected by several attached strands to the network[ In that case \"4# remains the sum of the strand contributions \"3#\\ but it has a trivial multiplicative prefactor re~ecting the loss of freedom on binding crosslinks into the network[ For instance this factor is 0:1 for four!functional linkers[ Thus\\ the form \"4# for f in isotropic elastomers is known to be useful\\ indeed up to high strains[ Eventually other e}ects intervene such as _nite extensibility and entanglements[ In nematic elastomers\\ \"4# has been accurately followed to several 099)s[ The dramatic and novel e}ects thrown up by the nematic element in \"4# are so pronounced as to mask the quali_cations we have mentioned for classical elastomers and we shall ignore them at this level[ We shall return \"in Sections 3[2 and 4# to more subtle and important deviations from \"4# 0 Because of the wide disparity of the nematic and rubber elastic energy scales\\ imposed strains change the nematic order rather little[ For soft deformations\\ the elastic energy is zero and the nematic state\\ already being that of minimal energy\\ does not change at all in magnitude but only in direction as l is imposed[ arising from nematic ~uctuations and other e}ects of non!ideality which yield semi! softness[ The prefactor kBT in f points to the entropic origin of rubber elasticity[ The shear modulus of classical rubber is m\u00bd nkBT and sets the energy scale for all elastomers[ It is several orders of magnitude less than that required for volume change\\ the bulk modulus[ Elastomers\\ including nematic elastomers\\ essentially deform at constant volume\\ that is the Poisson ratio is 0:1[ From f stems the constitutive relation s \"l # between stress and deformation in the usual way[ We shall interchangeably refer to the constitutive relation via f or s [ 1[1[ Continuum elasticity The elastic free energy density of an incompressible elastic body of uniaxial sym! metry is characterised by three elastic \"shear# moduli\\ m9\\ m0\\ m1 which govern the symmetric strain o [ We follow Olmsted|s frame!independent form of the energy \"Olmsted\\ 0883#[ Additionally in nematic solids de Gennes recognised \"de Gennes\\ 0879# that the internal degree!of!freedom Q \\ characterised by n if we _x the magnitude of the order Q\\ couples to both symmetric and antisymmetric strains\\ see Fig[ 1[ The free energy is then f 0 1 m9\"n = o = n#1\u00a60 1 m0\"n g o g n#1\u00a60 1 m1\"n = o g n#1 \u00a60 1 D0\"n g \"u\u2212v##1\u00a6D1n = o = \"n g \"u\u2212v##[ \"5# The antisymmetric part of the strain\\ ui 0 1 oijk 1Rj:1R9 k gives the rotation of the matrix] the director has been rotated by v[ Relative rotation is directly penalised \"D0# or couples \"D1# to o in \"5#[ The de Gennes couplings D0 and D1 have an energy scale m but\\ equally\\ must vanish in the isotropic phase[ D0 must scale at least like mQ1\\ since it cannot depend on the sign of Q[ D1 scales like Q since the sign of the director rotation induced by symmetric shear must be di}erent in oblate and prolate elastomers["
        ]
    },
    {
        "image_filename": "designv10_10_0001105_robot.2001.933160-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001105_robot.2001.933160-Figure1-1.png",
        "caption": "Figure 1: Anatomy of the Conro module",
        "texts": [],
        "surrounding_texts": [
            "a set of self-contained modules in a particular configuration; the actions of the robot are the result of the coordinated actions of its modules. These actions can be controlled using a master-slave approach only i f the master can m a p the particular configuration of the robot to one that it already knows how t o control. In this paper we discuss how to describe this configuration using graphs, how to discover a robot configuration and how to identify it as a particular known configuration. T h e methodology used i s very general and can be applied easily t o other modular robots. Experimental results f o r Conro quadrupeds and snakes are presented.\n1 Introduction Reconfigurable robots are made of modules that can be assembled into different shapes and thus, require a flexible control to handle a variety of configurations. These robots are classified as homogeneous or heterogeneous depending on whether the robot uses a single type of module or many. They can also be classified as lattice-based depending on whether their modules are organized in a grid (in either 2-D or 3-D) or not.\nReconfigurable robots have been the subject of active research. Examples of reconfigurable robots are those of Unsal et. a1 [l], Murata et. a1 [2], Tomita et. a1 [3], Kotay et. a1 [4], and Yim et al. [5], among others, who have worked on lattice-based robots in both 2-D and 3-D. These robots are homogeneous with highly symmetrical modules, e.g., triangular and hexagonal modules for planar robots and cubic and dodecahedral modules for robots that move in 3-D. Lattice-based robots require their modules to rotate or slide along their adjacent modules to change their shape. Among the non-lattice-based robots we find\n*A. Castano was with the Information Sciences Institute at the University of Southern California during the performance of this work. Presently he is with the Jet Propulsion Laboratory at the California Institute of Technology, Pasadena, CA 91109 USA (e-mail: Andres.CastanoQjp1.nasa.gov).\nthe Polypod and Polybot robots of Yim [6] and the Conro robots [7]. These robots change their shape by extending limbs that can connect to any part of their bodies thus changing their topology. In contrast with the lattice-based types, these robots do not require to reconfigure in order to move; they can adopt a shape and then use a configuration-dependent gait.\nThe modules of the Conro robot are self-contained robots themselves; they have their own CPU, power supply, sensors, actuators and communication systems. The control of a Conro robot can be seen as the control of a distributed system where each module needs to be controlled correctly to achieve an overall robot motion. To control the robot using a masterslave approach, the master must identify the robot configuration as one of the preprogrammed configurations that it already knows how to control. This paper discusses our representation and identification of such configurations which can be adapted to other modular and reconfigurable robots.\nThis paper is divided as follows. In Sec. 2 we describe the Conro module and discuss the need to discover the configuration of a Conro robot and identify it as a known configuration. In Sec. 3 we present a general representation of a module and a modular robot. The case of Conro is treated as an instance of the representation. In Secs. 4 and 5 we describe the discovery and identification of the robot configuration, respectively. The experimental results, carried out on Conro quadrupeds and snakes, are discussed in Sec. 6. Finally, we present our conclusions in Sec. 7.\n2 The Conro module 1, is a selfsufficient robot composed of a passive and an active connectors, to allow it to attach to other modules, and a body, that serves as a frame for the motors, power supply, and electronics [7], [8]. Three lateral faces of the passive connector have pins that can be inserted into holes on the face of the active connectors of other modules, thus creating structures. Hence, a module The Conro module, shown in Fig.\n0-7803-6475-9/01/$10.000 2001 IEEE 3503",
            "has four docking ports: three on the passive connector and one on the active connector. Each port has an infrared pair that serves as a serial link, to establish communication with adjacent modules, and as a guidance system, to assist in the docking process of two modules. The axes of the motors lie at the joints of the connectors and body and give the module a pitch and a yaw degrees of freedom. The length of the module is 108 mm and its weight is 115 g.\nA Conro robot (e.g., snake, hexapod) is formed by joining several modules together. This distributed system can be controlled using a distributed approach (e.g., [9]), a centralized master-slave approach, or a combination of both. In the master-slave approach a single module or an external host computer controls the robot. Consider the case where a Conro robot has just been assembled and powered up. Before the master can control the robot, it must identify its configuration because different configurations use different gaits and obey different kinematic and dynamic equations.\nTwo steps are needed to identify a robot configuration. First, as shown in Fig. 2 , the master needs to discover the configuration of the robot, i.e., it needs to describe the robot using some suitable representation. Second, it must identify the configuration by comparing it against a catalog of configurations that the master already knows how to control. If the configuration is identified, the master can map the representation of the robot to that in the catalog and control the robot using preprogrammed routines that control the cataloged configuration. If the configuration is not identified, the master cannot control the robot using configuration-dependent routines.\n3 The representation of a modular robot must take into account that a module might have multiple ports and that there might be multiple ways to connect two The graph of a modular robot\nmodules using the same two ports. A remarkable effort to formalize this representation was made by Cheri and Burdick and is described in a series of papers that follow [lo]. They represented a configuration using a matrix called the assembly incidence matrix (AIM). The AIM is a function of the way in which the modules of the robot are labeled, i.e., the labels are part of the matrix itself. Hence, two non-isomorphic AIMs might actually represent the same robot and thus it is not possible to directly compare two configurations; a step of cycling the labels of one of the AIMs to make it isomorphic with the other AIM is necessary.\nIn this section we represent a modular robot using directed graphs (digraphs). In contrast with the representation of Chen and Burdick and those of others (e.g., [2], [3]), a graph-only representation of the robot reduces the complexity of matching two robot configurations to exactly that of the isomorphism-complete class, i.e., there is no need to cycle permutations of labels. Furthermore, it can take into account multiport modules, multiconnector ports and loop structures. However, unlike the representation of Chen and Burdick, this representation is defined for static structures, i.e., extensions that address the kinematics or dynamics of the robot are not considered.\nThe basic Conro module, shown in Fig. 3.a, has four ports. Any of the ports of the passive head can be connected to the port of the active connector of another module in any of two orientations, \u201cbelly-up\u201d or \u201cbelly-down\u201d. We denote the ports of the module as fi and the orientations of the port as d i .\nWe want to find a graph representation of the module that can be used to identify, without ambiguities, any legal robot Configuration. In the connectivitygraph representation, a module is represented as a vertex (see Fig. 3.b) and a connection between modules, as an edge, as in the case shown in Fig. 2 . This graph describes the topology of a robot but cannot be used to uniquely identify configurations with modules that can be connected to each other using different ports, i.e., if a module with n ports can be connected to any of",
            "the n ports of another module, then there are n! ways in which the two modules can be connected, many of which might be topologically different.\nThe Conro module is a multiport module and thus, we cannot use a connectivity graph to uniquely identify a configuration. For example, the two configurations shown in Figs. 4.a-b have the same connectivity graph shown in Fig. 4.c (a module has been colored for visualization purposes). A way to distinguish between configurations of multiport modules is to use the labels of the ports in the representation. In this case a suitable representation of the module is that shown in Fig. 3.c, where tlie module is represented by its ports, i.e., a vertex represents a port while an edge indicates that two ports either belong to the same module or belong to two connected modules.\nOur goal is to find a graph-only representation of a robot that would allow us to distinguish between dif-\nferent configurations regardless of their labelings, i.e., the unlabeled version of the graph must be sufficient to identify the configuration. Unfortunately, the direct use of the labeled-graph representation of a robot with multiport modules leads to ambiguous unlabeled graphs. Figures. 5.a-b show the labeled graphs of the two configurations shown in Figs. 4.a-b. We can see that the unlabeled version of both graphs is the same.\nThe problem of how to make the \u201clabel\u201d itself a part of the graph can be solved in various ways. In our case, we mapped the labeled graph in Fig. 3.c to the digraph in Fig. 6.a by extending an edge from port fi to port f, for i < j , i.e., vertex fi has n - i edges leaving it or, equivalently, it has i - 1 edges arriving to it, where n is the number of ports of the module. This digraph unambiguously represents a multiport module because it is rigid, i.e., it has no automorphisms and thus, there is only one way to interpret it [ll]. Hence, we can now represent robots built with multiport modules without ambiguity. For example, the two configurations shown in Figs. 4.a-b have the digraph representations shown in Figs. 6.b-c, respectively. An inspection shows that the corresponding unlabeled digraphs, indeed, are not isomorphic. The graph representation of Fig. 3.c preserves the symmetries of the module while the digraph representation of Fig. 6.a destroys it; modules that have partial symmetries can be represented using a combination of both representations."
        ]
    },
    {
        "image_filename": "designv10_10_0002587_s11668-010-9422-z-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002587_s11668-010-9422-z-Figure1-1.png",
        "caption": "Fig. 1 Dismounted samples of failure bearing",
        "texts": [
            " Based on the analysis and relevant discussion, failure prevention methodologies for similar grease-lubricated roller bearing were developed. FT-IR with KBr discs, XRD with Co K\u03b1 radiation, and TGA under N2 purge were applied to investigate the structural and thermal characteristics of the greases. Besides that, microstructures of the greases and the wear marks on the bearing inner-ring surface were observed by SEM. Chemical compositions of the bearing material were determined by photoelectric direct reading spectrometry and the material hardness (HRC) was also measured. Figure 1 displays the external morphology of the detached bearing. It is obvious that the raceway surfaces of the bearing inner ring were worn heavily and there were large number of pits and debris on the surface. The inner-ring surfaces were a red-brown color and appeared polished which may the result of direct contact between the rollers and the raceway during operation. Also, the lubricating grease was found to be solidified and pushed out of the bearing track. Characterizations of the Lubricating Grease Samples of used greases from the failed bearing were identified by FT-IR, XRD, SEM with EDS, and TGA, and was then compared with the fresh greases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002596_we.447-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002596_we.447-Figure4-1.png",
        "caption": "Figure 4. Solid model of GRC gearbox installed on wind turbine bedplate.8",
        "texts": [
            "1002/we 639 issues in design, reliability and behavior of the rotating machinery in wind turbines. The paper details some aspects of the state of the art in simulation technology and design approaches used in the industry. The GRC is a program run by the NREL National Wind Technology Centre to determine the reasons for premature failure that are common in gearboxes in wind turbines. The GRC focuses on three areas of research: drive train modeling and analysis, full-scale dynamometer testing and fi eld testing. Figure 4 shows a solid model of the GRC gearbox as it would be installed in the wind turbine nacelle and Figure 5 the corresponding system (excluding the hub) under test at the NREL dynamometer test facility in Golden, Colorado. Wind Energ. 2011; 14:637\u2013651 \u00a9 2011 John Wiley & Sons, Ltd. DOI: 10.1002/we 640 Two 750 kW gearboxes have had some redesign from the original arrangement and been modifi ed to allow a comprehensive instrumentation package (over 150 channels) that provides measurements of tooth root strains on the ring gear, raceway strains on the planet bearings, defl ection of the planet carrier, temperatures near the bearings, input and output torque and speed and more"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001938_0020-7403(76)90006-0-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001938_0020-7403(76)90006-0-Figure3-1.png",
        "caption": "FIG. 3. Cylindrical projectile with back-spin, partially submerged. The velocity of the surface element dA relative to the water is v'. Angles ~bo and $w are as defined",
        "texts": [
            ", agrees well with the empirical relationship (equation (1)) and with the relationship deduced by Johnson and Reid 1 from Birkhoff's pressure law (0~ = 17'5/V'0r) deg.). A small error in the numerical value of the constant in equation (13) would undoubtedly be revealed by an accurate numerical treatment, in which the denominator in equation (3) is not assumed constant. The forces acting on a cylindrical projectile, possessing back-spin about its axis with angular velocity oJ and moving in a plane perpendicular to its axis, will now be considered. The velocity of the water relative to an element of surface dA, v ' , may be deduced from Fig. 3 in Fig. 2. which shows the direction of spin. The angles ~b, ~bo and ~bw are as shown in Fig. 2. The lift force acting on the element is where and 7r s i n a dL 4 + ~ sina PV'~COs~b dA (14) v'2=(v+acocos~b)2+(aoJsin~b)2 (15) s i n a = sin ~b cos 3' - c o s ~b sin 3'. (16) We assume that ato .~ v and neglect terms in a2toz/v 2. The angle 3' is therefore small, and v '2 ~ v 2 + 2atov cos ~b (17) a t o . sin y = 3' = '~ ' - sm ~b (18) sin a = sin d' - - ~ sin cb cos d'. (19) For a cylinder of length 1, dA = al d~b, and making the approximation that the denominator in equation (14) is equal to 5",
            " A moderate amount of spin will cause a significant change in 0~ ; for example, a value of atolv = +(1]3) will increase 0c from 18.7/X/(tr) deg. (no spin) to 23.1/X/(tr) deg. A similar amount of top-spin (ato/v =-(113)) would decrease the critical angle to 12.9/X/(tr) degrees. While, according to this theory, there would be no lift force acting on a totally submerged cylinder without spin, it is instructive to note that when back-spin is applied a submerged cylinder experiences a lift (from equation (21)) of 2~r 2, L = --~ pa lvto (26) where the positive sense of to is shown in Fig. 3. The criteria for critical incidence applied in deducing equations (11) and (23) are therefore not strictly true, since the lift force does not become zero when 4'w = ~r ; the value of 0c expressed in equation (25) forms a lower bound to the true value (or, in the case of top-spin, an upper bound). The exact influence of an increase in lift force on the rebound angle and velocity of the projectile can only be deduced by a numerical treatment of the equation of motion of the body. However , an increase in the ratio; R =l i f t force /dragforce (27) must lead to a decrease in the energy dissipated by the drag force and hence to an increase in rebound velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002839_s10514-013-9343-2-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002839_s10514-013-9343-2-Figure5-1.png",
        "caption": "Fig. 5 a Desired future landing posture after the fall control time. T0 s and T0 n are the transformation of the support and the non-support foot with respect to the global frame. Ts n is the desired transformation matrix from the support foot to the non-support foot to attain the desired landing posture. b Desired current robot posture to realize the desired landing posture. For a robot that is toppling, the support foot rotates about the CoP, P , towards the reference point Q. We model a free joint at P . Without external forces, the joint angle should increase. The leg joints are controlled to satisfy Ts n computed in (a)",
        "texts": [
            " Assuming that the robot possesses an IMU in the trunk, the foot rotation angle can be estimated by noting the mismatch between the trunk orientation angles as computed by the IMU and by the robot joint angle sensors. With this information, we implement a leg controller to ensure that the swing foot is flat as it touches down on the ground. Since we assume that the CoP does not change during the fall, the CoP is modeled as a passive rotational joint about which the support foot rotates, as shown in Fig. 5. The support foot rotation is estimated using the inverted pendulum models without control. The transformation of the non-support foot with respect to the global frame T0 n is determined by the desired stepping location. The transformation of the support foot T0 s is estimated by simulating the inverted pendulum model. Therefore, the desired transformation matrix from the support foot to the non-support foot Ts n can be computed as, Ts n = (T0 s ) \u22121T0 n . (8) If the joints are controlled according to Ts n before the nonsupport foot hits the ground as in Fig. 5b, the robot is expected to step on the desired location by gravity, Fig. 5a. We can compute joint velocities needed to move the swing leg using Eq. 4. Although an appropriate stepping action (including foot lifting) can exert powerful influence on the future motion of the falling robot, in some cases it still may not be sufficient to control the robot to fall in the right direction. In these cases we employ a approach called inertia shaping, which attempts to systematically control the robot\u2019s centroidal angular momentum through the kinematic control of its overall inertia matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure16-1.png",
        "caption": "Fig. 16 Envelope of the tooth face of the face-gear with the shaper cutter",
        "texts": [
            " 15, e1 can be obtained as follows: e1 \u00bc Rc\u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rc\u2212Rt\u00f0 \u00de2\u2212 W=2\u00f0 \u00de2\u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 t \u2212 W=2\u00f0 \u00de2 qr \u00f026\u00de In Fig. 15, O0A is the radius of the arc, O1A, and O2B are the radii of the tool, CD is the theoretical error of e1, andO1O2 is the cutting width W. To satisfy the requirements of machining, the tooth face of the face-gear needs to be enveloped for several times with the shaper cutter. e2 is affected by the number of envelopes and the position of the swing angle, as shown in Fig. 16. e2 at any position of the tooth face of the face-gear can be expressed as follows: e2 v;w\u00f0 \u00de \u00bc min h1 v;w\u00f0 \u00de; h2 v;w\u00f0 \u00de;\u2026; hn v;w\u00f0 \u00def g; v;w\u00f0 \u00de\u2208\u22112 \u00f027\u00de Where \u22112 is the tooth face of the face-gear, v and w are the position parameters of the tooth face of the face-gear, hi is the distance between one point of the tooth face of the face-gear, and the ith tooth face of the shaper cutter. As shown in section 4.1, e1 is relevant to the step distance, and it increases with the increase of w, while e2 is related to the number of envelopes and the position of the swing angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001650_rob.4620010107-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001650_rob.4620010107-Figure1-1.png",
        "caption": "Figure 1. Five-link biped model.",
        "texts": [
            " one- or two-foot stance, and \"This work was supported by NSF under Grant no. ECS 820 1240. Journal of Robotic Systems, 1 (1 ), 101 -1 1 6 (1 984) Q 1984 by John Wiley & Sons, Inc. 0471 -2223841'01 01 01 -1 6$04.00 102 Journal of Robotic Systems-1 904 jumping in the air are presented in Sec. 111. One particular strategy of nonlinear control with computation delay and predictive algorithms is discussed in Sec. IV. Digital computer simulations of a rhythmic movement are presented in Sec. V. II. EQUATIONS OF MOTION The five-link biped is shown in Figure 1. The Newton-Euler formalism developed in Ref. 2 is followed here. The translation vector of the center of gravity of each rigid body is expressed by a 3-vector in the inertial coordinate system. The rotation of each rigid body is described by six state variables: three Euler angles and the three components of the angular velocity-vector W expressed in a body coordinate system-along the body\u2019s principal axes. The connections between the joints are expressed by a set of holonomic constraints. Further restrictions at the joints are expressed by nonholonomic constraints",
            " These simulations confirm the effectiveness of the control strategy, and the predictor performance. While the present study is somewhat removed from application to human movement, some hypotheses may be conjectured, for example, (1) the necessity of nonlinear feedback and (2) the presence of anticipatory (predictive) mechanisms in the spinal circuits or in the muscle dynamics\" to account for the transmission delays in the reflex loops. APPENDIX For simplicity and to avoid duplication, a11 variables in the equations below are defined as in Ref. 2. Define the distance vectors (see Fig. 1) L, and K. as follows: L , = [000.235]' KI = [0 0 -0.2671' L2 = [000.184]r K2 = [OO -0.247Ir K,, = [000.184Ir L 4 = [ O 0 -O.247lr K5 = [000.235]' Ls = [0 0 -0.2671' L3 = 100.138 -0.2801 K3 = [0 -0.138 -0.2801. Hemami and Zheng: Dynamics and Control of Motion 115 m 3 ~ 3 = - [ O O ~ ~ ~ ~ T + r3 + r4 I, m4Z4 = -[oom,g]'- r4 + rs = f, + KK4A6Fs - LL,A:F4 - R4 A4 + A:A, T4 - T: Is W, = fs - LL5 ATI', + A:A4 R, A5 + A:A, Ts The input torques at the joints are described by vector T : m S x s = -[oomSg]r- rs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001623_iros.2004.1389998-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001623_iros.2004.1389998-Figure2-1.png",
        "caption": "Fig. 2. Two difrcrcni paths lor which Ihc mouse rcadings are the same",
        "texts": [
            " Each mouse measures its movement along its horizontal and vertical axes. If the robot makes an arc of circumference, it can he shown that also each mouse will make an arc of circumference, which is characterized by the same center and the same arc angle (but with a different radius). During the sampling time, the angle a between the x-axis of the mouse and the tangent to its trajectory does not change. This implies that, when a mouse moves along an arc of length 1, it measures always the same values independently from the radius of the arc (see Figure 2). So, considering an arc with an infinite radius (Le,, a segment), we can write the following relations: ?E = Icos(a) (1) g = Isin(a). (2) From Equations 1 and 2, we can compute both the angle between the x axis of the mouse and the tangent to the arc: a = arctan ( S ) ~ (3) and the length of the covered arc: otherwise (4) We hypothesize that, during the short sampling period, the robot moves with constant translational and rotational speeds. This implies that the robot movement during a sampling period can be approximated by an arc of cucumference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001036_s0022112005006117-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001036_s0022112005006117-Figure1-1.png",
        "caption": "Figure 1. (a) Illustration of the centreline of a spheroidal particle; (x, y, z) are global Cartesian coordinates, and (x \u2032, y \u2032, z\u2032) are instantaneous coordinates with origin at the particle centre. (b) Discretization of the surface of a prolate spheroid with aspect ratio e = 4 into (i) 32 or (ii) 128 elements, and of (iii) an oblate spheroid with aspect ratio e = 0.25 into 128 elements. For clarity, each quadratic element has been subdivided into four flat sub-elements.",
        "texts": [
            " For the most accurate computations, the combined numerical error due to the particle discretization, double-layer density discretization, and numerical integration is less than 1.0%. Our main objective is to describe the motion of a freely suspended spheroidal particle in wall-bounded simple shear flow. The particle position at any instant is determined by the coordinates of the particle centre, xc, and by the orientation of the particle unit director pointing along the particle axis of revolution, d, as illustrated in figure 1(a). The unit director is a free vector defined by the meridional angle, \u03b8 =\u0398 , and azimuthal angle, \u03d5 = \u03a6 , as dx = cos\u0398 , dy = sin\u0398 cos\u03a6 , and dz = sin\u0398 sin\u03a6 . To reconstruct the particle surface, we generate a spheroid of revolution along the x-axis with centre at the origin, rotate it around the z-axis by the angle \u0398 , rotate it once again around the x-axis by the angle \u03a6 , and then translate it to the position xc. The particle centre translates according to the equation dxc/dt = V , and the director angles evolve according to the equations d\u0398/dt = W\u03b8 and d\u03a6/dt =W\u03d5/ sin\u0398 , where W = \u2126 \u00d7 d, and W\u03b8 = \u2212 sin\u0398Wx + cos\u0398(cos\u03a6Wy + sin \u03a6Wz), W\u03d5 = \u2212 sin\u03a6Wy + cos\u03a6Wz",
            " Consider the motion of a prolate spheroid with long semi-axis a and short semi-axis b, where e \u2261 a/b > 1 is the particle aspect ratio. To establish a point of reference and further validate the numerical method, we first discuss the motion of a spheroid with aspect ratio e = 4 in infinite simple shear flow. Figure 2(a) shows a graph of the angular velocity of rotation around the z-axis plotted against the particle inclination angle, \u0398 , for the left-to-right symmetric configuration corresponding to \u03a6 = 0. In this computation, the particle surface was discretized into 32 quadratic elements, as illustrated in figure 1(b)(i). The dotted, dashed, and dot-dashed lines correspond respectively to element polynomial expansion orders m = 1, 2, and 3, and the solid line represents Jeffery\u2019s (1922) exact solution described by \u2126z = d\u0398 dt = \u2212k 2 ( 1 \u2212 e2 \u2212 1 e2 + 1 cos(2\u0398) ) . (3.2) In spite of the small number of elements, the numerical results for m =2 and 3 are in excellent agreement with the analytical predictions. Jeffery\u2019s formula shows that a spheroid with an infinite aspect ratio, e = \u221e, remains aligned with the flow in the streamwise orientation, \u0398 = 0, and rotates with angular velocity \u2126z = \u2212k in the transverse orientation, \u0398 = \u03c0/2",
            " The circular symbols in figure 2(b) trace the orbits of the inclined director computed with 32 elements, element expansion order m =2, and time step k\u2206t =0.10. The hardly visible solid lines threading the data represent Jeffery\u2019s analytical predictions described by dx = sin \u03be cos \u03c7 , dy = sin \u03be sin\u03c7 , and dz = cos \u03be , where \u03be is a meridional angle defined with respect to the z\u2032-axis, and \u03c7 is the azimuthal angle subtended between the x \u2032-axis and the projection of the director in the x \u2032y \u2032-plane, as shown in figure 1(a). The Jeffery orbits are described by tan2 \u03be (e2 sin2 \u03c7 + cos2 \u03c7) = J2, where the orbital constant J varies between zero and infinity. When \u0398 = \u03c0/2, and correspondingly also \u03c7 = \u03c0/2, the particle axis lies in the y \u2032z\u2032-plane, \u03be = \u03c0/2 \u2212 \u03a6 and J = e cot\u03a6 . The excellent agreement between the numerical and the analytical results demonstrates the accuracy of the numerical method. Next, we consider the motion of the prolate spheroid in wall-bounded shear flow. The circular orbit corresponding to \u03a6 = 0 was considered by Hsu & Ganatos (1994) for large and moderate particle-centre to wall separations, d/a > 2",
            " Hsu & Ganatos (1994) tabulate truncated Fourier series approximations for the particle translational and angular velocities in terms of the particle inclination angle, \u03b1 = \u03c0 \u2212 \u0398 , with an error on the order of 4%. The present results agree with their expressions within this tolerance. In the simulations presented in the remainder of this section, the particle surface was discretized into 128 isoparametric elements supporting second-order expansions, m = 2, and the time step was set to k\u2206t =0.10. Figure 3 illustrates the effect of a plane wall on the Jeffery orbits for particle to wall distance d/a = 1.25 and 1.0, as shown in figure 1(b)(ii). The circular symbols represent the results of the numerical simulations, and the nearly coincident solid lines represent the Jeffery orbits for infinite flow. Because of the reflection symmetry of the flow with respect to the particle centre, the director orbits remain symmetric with respect to the y \u2032z\u2032- and z\u2032x \u2032-planes in the presence of the wall. Surprisingly, the wall has only a moderate effect on the director orbits, even when the particle is in close proximity and nearly touches the wall"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001630_robot.1987.1087758-Figure1.2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001630_robot.1987.1087758-Figure1.2-1.png",
        "caption": "Figure 1.2. Finding the mounting position of a robot hand equipped with tactile sensors, by solving a homogeneous transform equation of the form",
        "texts": [],
        "surrounding_texts": [
            "sensor. This yields a homogeneous transform equation of the moving the robot and observing the resulting motion of the form AX=XB, where A is the change in T, due to the a rm movement, B is the resulting sensor displacement, and X is the sensor position relative t o T,. A and B are known, since A can be computed from the encoder values and B can be found by the sensor system. The solution to an equation of this form has one degree of rotational freedom and one degree of translational freedom. In order t o solve for X (the sensor position) uniquely, it is necessary t o make two arm moveA,X=XB, and A,X=XB,. A closed-form solution to this sysments and form a system of two equations of the form: tem of equations is presented. The necessary condition for a unique solution is that the axes of rotation of A, and A, are neither parallel or antiparallel to one another. The theory is supported by simulation results.\n1. Introduction\ntransform equation of the form A X = X B, where A are B are The investigation into the solution of the homogeneous known and X is unknown, is motivated by a need t o solve for the position between a wrist-mounted sensor and the manipulator wrist center (T,).\nMuch research has been done on using a sensor t o locate an object. The three-dimensional position and orientation of an ob'ect can be found by monocular vision, stereo vision, denselsparse range sensing, or tactile sensing. Monocular vision locates an object using a single view, and the object dimensions are assumed to be known aprlori [2,6,8,10,13,22,29,31,32]. Stereo vision uses two views instead of one so that the range information of feature points can.be found [1,6,12,14,20,24,32]. A dense range sensor scans a reglon of the world and there are as many sensed points as i ts resolution allows [3,7,17,25]. A sparse range sensor scans only a few points, and If the sensed points are not sufficient to locate the object, additional points will be sensed [5,15,16]. Tactile sensing is similar to sparse range sensing In that i t obtains the same information: range and surface normal of the sensed points [4,15,16].\nA sensing system refers to object positions with respect t o a coordinate frame attached to the sensor, but robot the sensor information for a robot task, the relative position motions are specified by the wrist positions. In order t o use between the sensor and the wrist must be known.\nobstacles to obstruct the measurement path, the points of Direct measurements are difficult because there may be interests may be inside a solid and unreachable, and the coordinate frames may differ in their orientations. The measurement path can be obstructed by the geometry of the sensor or frames that are unreachable includes T, and the camera the robot, the sensor mount, wires, etc. The coordinate frame: T, is unreachable because it is the intersection of three link axes, the camera frame is unreachable because its\nCH2413-3/87/0000/1666$01.00 0 1987 IEEE\norigin is at the focal point, inside the camera. Instead of direct measurement, we can compute the camera position by displacing the robot and observing the changes in the sensor frame using the sensor system. This method works for any sensors capable of finding the three-dimensional position and orientation of an object. Figures 1.1 and 1.2 show the cases of sors. In both examples, a homogeneous transform equation of a monocular vision system and a robot hand with tactile senthe form A X=X B is formed, where A is the movement of the robot, B is the resulting displacement of the sensor, and X is the unknown transform between the sensor and the robot wrist. Let T,] and Te2 be the robot wrist positions before and after the motion, respectively. Since T,I and TB2 can be calculated by the robot controller from the joint encoder values, A can be calculated by A=T,]-lT,? Similarly, if OBJ, and OBJ, are the object positions wlth respect ot the sensor before and after the motion, the displacement of the sensor can be calculated by B=OBJ,OBJ,-l.\nera mounting position.\nAX=XB. A is the robot motion, B is the resulting motion of the hand coordinate frame, and X is the mounting position of the hand.\n1666",
            "Matrix equations of the form A X = X B have been discussed in linear algebra [ll]; however, no known work has been done for homogeneous transform equations, in which case the matrices are much more restricted and a geometric interpretation is desired. Using Gantmacher\u2019s method, the solution to the 3x3 rotational part of X (R,) is any linear combination of n linearly independent matrices: R,=k,M,+ * * . +k,Mn, where n is determined by properties of eigenvalues of RA and R, (rotational parts of A and B), k,, . . . ,kn are arbitrary constants, and M,, . . . M, are linearly independent matrices. Gantmacher\u2019s solution IS for general matrices; the given solution may not be a homogeneous transform. To restrict the solution to homogeneous transforms, we must impose the conditions that the 3x3 rotational part of the solution be orthonormal and that the righthanded screw rule is satisfied. These restrictions will result in non-linear equations in terms of k , . . . k,. There are many disadvantages using this method: (1) Only iterative solutions are possible, since non-linear equations are involved. (2) Iterasolutions. Different initial estimates will converge to different tive solutions are not useful when there are infinite number of solutions, and it is not possible to generalize the solutions. (3) The solution cannot be expressed symbolically. (4 Geometric interpretation of the solution is not possible an d the conditions for uniqueness cannot be specified in geometrical terms.\nArbitrary Axis 2. Homogeneous T r a n s f o r m s and Rotation about an\nHomogeneous transforms [28 can be viewed as the relative position and orientation o i a coordinate frame with respect to another coordinate frame. The lements of a homogeneous transform T\nLo 0 0 1 1 We also denote [nX,ny,nzlT as a, [ o ~ , o ~ , o , ] ~ as 0, and [aX,ay,a,lT as a. n, 0, and a can be interpretated as unit vectors which indicate the x, y , and z directions of coordinate frame T; p can be viewed as the origin of T. The vectors n, 0, a and p are referenced with respect t o a frame represented by a transform to which T is post-multiplied. If there is no frame to the left of T, then n, 0 , a, and p will be vectors relative to the world or absolute frame.\nWe will refer to the upper-left 3x3 submatrix of T as the\norientation of the coordinate frame. A rotational submatrix rotational submatrix since it contains information about the can be expressed as a rotation around an arbitrary axis. From [28], the matrix representing a right-hand-rule rotation of 0 around an axis [kX,ky,k,lT is :\n1 kxkxvers8+cos8 kykxversO-k,sinO k,k,vers0+kysin8\nRot(k,B)= kxkyversO+k,sinO kykyversO+cos8 k,kyversO-kxsinO\nkxk,vers8-k,sin0 k,k,versO+k,sinO k,k,versO+cosO\nwhere verso = (1-cos0). (2.2)\nIn this paper, we will follow the convention tha t O<S<r. From Paul\u2019s text [28], we have the following two equations:\ncos0 = -(nx+oy+a,-l) 1 2 (2.3)\nand\nSince 0<8<7r, we only take the positive sign of Equation 2.4. Thus, we have only one solution for 8:\n0 = atan2(~(o,-a~~+(ax-n~+(ny-o~~,nx+oy+a,-l). (2.5) We can now find k using 0 computed by Equation 2.5. The set of equations used depends on whether n,, oy, or a, is most\npositive. Prom Paul\u2019s text, if nx is most positive,\n(2.6a)\nk =A k=& 2kxvers6\u2019 \u2019 2kxvers0 \u2019\na +n (2.6b,c)\nwhere sgn(e)=+l if e20 and sgn e)=-1 if e<O. (Note that our definition of sgn(e) is different I rom that in Paul\u2019s text. We will discuss this further on.) If oy is the most positive,\nFinally, if a, is the most positive,\n(2.7a)\n(2.7b,c)\nverso (2.8a)\nk =A a +n 0, +a, k =- x 2k,versO\u2019 2k,versO.\n(2.8b,c)\nFrom a geometric point of view, when O=X, there are two solutions to k, one opposite to the other. Also, when O=n, we can see from Equation 2.2 tha t 0,-a 4, a,-n,=O, and ny-ox=O. In this case, we can use either sgn(O)=+l or sgn(O)=-1 for Equation 2.6a, Equation 2.7a, and Equation 2.8a; we have two solutions for k. However, i t is desirable to use some convention so t h a t we can solve for k uniquely even when O=T. To do this, we can modify Paul\u2019s definition for the sgn function. In Paul\u2019s text, sgn(0) can be either +1 or -1. We define sgn(O)=+l, so t h a t we have unique 0 and k for each rotational matrix.\nA general rotational matrix can be represented as the exponent of a skew-symmetric matrix [26,23]:\nY\n0 -k, k,\nRot(k,O) = eKa, where K = (2.9)\nnot equal to identity are 1, d e , and e-J\u2019. Let ejs and e-\u2019\u2019 be Lemma 1: The eigenvalues of a general rotation matrix denoted by X and X. Then 0 can be calculated by:\nmatrix. See [33], or both [21] and [28f Proof: This is a well known roperty of a rotational\n0\nLemma 2: For a general rotation matrix not equal to identity, the eigenvector corresponding to the eigenvalue 1 can be expressed as a vector with real components and is either parallel or antiparallel to the axis of rotation. The other two eigenvectors cannot be expressed as real vectors.\nProof: Follows from Lemma 1 and Fisher\u2019s thesis [9]. More details can be found in a technical report [33]. 0\ntat ive if and only if their axes of rotation are parallel or Lemma 3: Non-identity rotational matrices are commuantiparallel to one another. Proof: Follows from Lemmas 1 and 2. See [33] for more details.\n3. Solut ion to the E q u a t i o n A X = X B\nand translational components, A X = X 8 becomes Dividing a homogeneous transform into its rotational"
        ]
    },
    {
        "image_filename": "designv10_10_0001598_j.ijmecsci.2006.06.013-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001598_j.ijmecsci.2006.06.013-Figure5-1.png",
        "caption": "Fig. 5. Comparison of gear set vs. number of teeth. Fig. 6. Specific unit of gerotor pump.",
        "texts": [
            " Geometrical parameters and operating conditions perform the volumetric characteristics and the maximum contact stress. Most influential parameters were found to be the operating pressure and the number of teeth. Owing to the fact that for lubricating pumps, operating pressure is relatively low and can therefore be excluded from the focus of this analysis. With regard to the contact stress, the influential parameter is also the minimum radius of curvature of the internal gear. For a chosen PZ9e285 gear set with geometrical parameter of Table 1, Fig. 5 depicts the maximum contact stress and the volumetric characteristics vs. number of teeth, where Qs is the pump-specific flow, a dimensionless form of the volumetric capacity cv useful to compare performance of various types of gearing. It can be observed that the evolution of the volumetric characteristics and the maximum contact stress (syy) are opposite. While the volumetric characteristics become better as the number of teeth increases, the contact stress becomes worse. And vice versa. Note that there is a significant inflexion point between the 10th and 11th teeth where the maximum contact stress suffers an important increase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003784_iccar.2017.7942651-Figure5-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003784_iccar.2017.7942651-Figure5-1.png",
        "caption": "Figure 5. SuperBot connectors and kinematic structure",
        "texts": [
            " EXPERIMENT AL RESULTS In our previous work in [15], we developed a high fidelity, physics-based 3D simulator capable of simulating hundreds of physically-connected robot modules. This simulator provided us with an appropriate testbed to evaluate PSO as a high-DOF IK solver because, by connecting robot modules one on top of another, we could build manipulators with incrementally increasing numbers of DOF. Due to its general kinematic structure and dexterity, we elected to use simulated SuperBot [2] modules. Each SuperBot module can itself be viewed as a 3 DOF manipulator (see Fig. 5 for a visualization). Fig. 4 gives the DR parameters of a SuperBot module when viewed as a manipulator where its front dock is the base and its back dock is the end-effector. By connecting n SuperBot modules on top of one another front-to-back, we generate a 3n -DOF manipulator whose end-effector is the back dock of the topmost module. Since the modules have identical kinematics, the forward kinematics model of the entire manipulator is obtained by multiplying the individual transformations for each module"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001083_0956-5663(91)80011-l-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001083_0956-5663(91)80011-l-Figure2-1.png",
        "caption": "Fig. 2. Schematic view of the experimental set-up.",
        "texts": [
            " The size of submerged gel beads was measured after magnification by an overhead projector with an accuracy of 50pm . The activity of the immobilized yeast cells was determined at 30\u00b0C on a batch of gel beads, incubated in a medium containing 5 . 5% minerals according to Evans et al. (1970) and the desired glucose concentration, adjusted to pH 7-0. The conversion rate of the gel beads was measured with a glucose macrosensor (Yao, 1983) at various glucose concentrations . Micro-electrode measurements Micro-electrode measurements were performed at 30\u00b0C in a rectangular 100 ml vessel, shown in Fig. 2. Mixing was accomplished by bubbling air, nitrogen or oxygen through the solution . Dissolved 257 oxygen was measured with a commercial oxygen probe (YSI, model 5331). The glucose microelectrode was calibrated for a series of dissolved oxygen concentrations at each glucose concentration. Biofilm particles were fixed in the centre of the vessel by entomological-specimen needles . The micro-electrode was introduced in the biofilm with a motor-driven micromanipulator, having a 1-pm accuracy. The position of the electrode tip could be examined with a stereo microscope "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003796_j.prostr.2017.07.166-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003796_j.prostr.2017.07.166-Figure4-1.png",
        "caption": "Fig. 4: FEM results: equivalent Von Mises stress distribution for load case 1 (a), 2 (b) and 3 (c); strain distributions for load case 1 (d),(e), and load case 3 (f).",
        "texts": [
            " Three load cases were considered, as described in Fig.3. A linear static analysis (SOL 101) was performed by the FEM code MSC Nastran (Version 2014.0.0-CL305068). Under load case 1, the symmetry of component and the loading condition made the stress, displacement and reaction forces distributions symmetrical with respect of the middle longitudinal plane of the bracket, being identified by coordinates y,z. The maximum value of the equivalent Von Mises stress (296 MPa) was found at the edge below the plane identified by node 1, as shown in Fig. 4a. A fairly large stress values were also detected at the lower little arms near nodes 104 and 105, respectively. A maximum displacement of 0.5 mm was detected. The load case 2 looks as an anti-symmetric loading condition, with respect of plane y,z, thus leading to a distribution of the equivalent Von Mises stress almost symmetric. Its maximum value (185 MPa) was found near constraints 105 and 106. Additional high stresses were detected at the rear arms, near 101 to 104 nodes. Those areas could be particularly critical, because of the small thickness and the likely presence of defects (see tomographic analysis of EBM brackets)",
            " A reference ratio between those loads is defined by the required testing procedure. Particularly, the YL is 1.25 times the LL and the UL is twice the LL. During the tests, transducers equipping the testing machine monitored and recorded the values of applied load and crosshead displacement. In each test, strain gauges were applied to measure the strain and to compare experimental and numerical results. They were located as Figs.5(d), (e) and (f) show, thus covering those areas which the FEA found critical for stress and strain (see Fig.4). It might be noticed that these brackets provide a specific function within the frame of a larger industrial system, being non disclosable. Basically it was required that no material yield occurs up to the application of the YL and no rupture occurs up to the UL application. Fatigue tests were also performed on both the EBM and SLM components. A sinusoidal load with a load ratio R=1 with a maximum value equal to the Limit Load was applied, at 5 Hz. Two load cases were considered, according to the set-ups described in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002860_s12239-013-0077-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002860_s12239-013-0077-0-Figure2-1.png",
        "caption": "Figure 2. Schematic of a full-toroidal CVT including one roller and two disks.",
        "texts": [
            " Conventional CVTs have low efficiency and difficult in control. Also they are larger and heavier than manual transmissions. However, no research was conducted on kinematic and geometrical optimization of full-toroidal CVTs. In this paper, Particle Swarm Optimization (PSO) algorithm is used to maximize power transmission efficiency of fulltroidal CVT and minimize its mass. It\u2019s necessary to find the power transmission efficiency as a function of kinematic and kinetic parameters to perform optimization. Figure 2 represents a schematic full-toroidal CVT, where r22 and r0 are curvature radius of roller and disk, respectively. \u03b3 is rotation angle of the roller (positive direction is clockwise). r1 and r3 are the distance between rotation axis of disk and contact points. As the input disk rotates, it forces the roller to rotate around axis OA, and similarly the rotation is transmitted to the output disk. By rotation of the roller around the axis perpendicular to sketch plane and passing through O, \u03b3 changes and consequently speed ratio is altered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003145_j.mechmachtheory.2013.09.013-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003145_j.mechmachtheory.2013.09.013-Figure1-1.png",
        "caption": "Fig. 1. A mobile manipulator on a six d.o.f. moving base.",
        "texts": [
            " For the second part of the proposition, Z 1 0 exp xad\u03be dx \u00bc Z 1 0 exp xe\u03c9 1 x2\u2225\u03c9\u22252 xe\u03c9; xew ; exp xe\u03c9 \u00fe \u2202 \u2202\u03bcj\u03bc\u00bc1exp xhe\u03c9\u03bc 03 3 exp xe\u03c9 24 35dx: Since the matrix commutator is a bilinear operator, and the integral operator and partial derivative can commute, \u222b 1 0 exp xad\u03be dx \u00bc \u222b 1 0 exp xe\u03c9 dx 1 \u03c9k k2 e\u03c9; ew ;\u222b 1 0 exp se\u03c9 dx \u00fe \u2202 \u2202\u03bcj\u03bc\u00bc1\u222b 1 0 exp xhe\u03c9\u03bc dx 03\u00f13 \u222b 1 0 exp xe\u03c9 dx 264 375: Using Eq. (15) and substituting h \u00bc \u03c9Tw \u03c9k k2, one can show the second part of the proposition. \u25a1 6. Case study In this section, the kinematic analysis of amobilemanipulatormoving on a spacecraft is performed to elaborate the computational aspects of the proposed formulation for Forward and Differential Kinematics of open-chainmulti-body systems. The spacecraft can be considered as a six-d.o.f. moving base for themobilemanipulator that is shown in Fig. 1. Themulti-body systemMS(6) = {(Bi,Ai)|i = 0,\u2026, 6, Bi \u2282 Ai} consists of two branches and six joints. The first branch consists of B0 to B5. The secondbranch contains B6 and joint six is its last joint. Joint one is a free joint, the second joint is a nonholonomic three-d.o.f. planar joint, the next joint is a three-d.o.f. spherical joint and the rest of the joints are one-d.o.f. revolute joints. The coordinate frames assigned to A0,\u2026,A6 at the initial configuration are shown in Fig. 2. In the sequel, the joint parameters are specified, and Forward and Differential Kinematics maps of MS(6) are determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-Figure6.26-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-Figure6.26-1.png",
        "caption": "Figure 6.26 ground. Geometry and the coordinate system used for the horizontal dipole above flat",
        "texts": [
            "200) AF = [2 cos(ph cos S)] for perfect ground ~ [ e ~ b h c o s @ + I've-3PhCoS6] for imperfect ground. (6.201) For perfect ground, (6.199) indicates the far field amplitudes at P will have maxima and minimal nulls at the following angles: emin = cos-1 (+) 2 n + 1 , (6.202) where n = 0,1,2, . . . . Observe that the field amplitude is maximum when P is at the ground surface (i.e., On,,, = ?r/2 for n = 0). The analysis of a horizontally oriented Hertzian electric dipole above a plane earth is similar. The geometry and the coordinate system used for the dipole of moment yI0 d t are shown in Figure 6.26. In the present case, the dipole fields not being symmetrical around the z axis (i.e., they are 4 dependent), it is convenient to express the fields in terms of the angle 4 measured from the y axis toward the observation point P. Thus the incident and reflected fields at P can be expressed as (6.203) ANTENNAS ABOVE GROUND 269 where cos + = ? . y = sin 0 sin 4. The direct and reflected fields at P can be expressed by where Rh is the plane wave reflection coefficient appropriate for the horizontal dipole case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001967_0094-114x(78)90041-1-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001967_0094-114x(78)90041-1-Figure3-1.png",
        "caption": "Figure 3. A dependent l ink within a loop.",
        "texts": [
            " The moment vector of a body about a point is the product of its mass and the position of its mass centre from this point in a given reference system. A convention is adopted such that a summation is zero if the upper limit is less than the lower limit, e.g. if k is less than 2 in eqn (1). The preceding section implies that a counterweight must be attached to each and every moving link to obtain a force balance. This is not necessarily so. The conditions under which links may be left uncounterweighted and how links such as these are balanced are now examined. Consider a loop of links one of which is a frame link, say QRSTQ in Fig. 3. The term loop will be used to describe a loop of links which unless otherwise stated contains no prismatic joints. Link P of this loop is a general polygonal link and has a point mass M fixed at an arbitrary point A. Mehmke's theorem [5] implies that the locus of a point on a rigid body can be expressed as a linear function of the loci of two other body points. Hence, the locus of any mass centre fixed in link P can be expressed as a function of the loci of two of the joints of P. Therefore, if P is connected to the frame link by two revolute jointed chains of links, the loci of the mass centres fixed in P can be related to the kinematics of the two attached chains of links",
            " Thus to balance a chain of links at the kth link, at which there will have been k - 1 previous stages, the general condition to be satisfied is k - I /~k \" Ak' ei~k + ink' rk' e ~k + Ik\" ~ (ran + P,,) = 0. (17) n=l The actual points about which the balance defined by each of these s conditions occurs are the s joints connecting the links. Thus the positions of the counterbalanced mass centres are sequentially transferred from joint axis to joint axis down the chain. Appendix 2. To Establish the Dependency Within a Loop The position with respect to Q (see Fig. 3) of a general point A fixed in link P is pp \u2022 ei~'p = Io - ei(\u00b0p+'o)+ ~ m lj. ei\u00b0~. (18) ./=1 Now from the closure condition of the loop it can be stated that ~,'l,e'S'+lpe is~+ \u00a3 liei\u00b0'=O. (19) i = I j = p + l Hence, using the relationship 1~ + I'~. e ~''. = 1o. e~'o (20) and substituting eqn (19) into (18) gives - I on \" el\u00b0~ = ~ \" e\"';+') \" f~'l li \" e\u00b0' + ~\" ei{%+') \" j~p+,\u00a3 ', \" ei~. (21) Thus the position of the general fixed point A in P can be represented by the summation of two vectors B and C(not to scale in Fig. 3) where B and C come from eqns (21) such that B = \"e ~'5+=~\" \"e ~\u00b0~ (22) p i = l and C=/~ 'C(%+=)\" i=p+t \u00a3 1~ ' e~\u00b0~' (23) For convenience, the angles (i.e. 0 i, j = p + 1, p + 2. . . s) in the p + 1 to s chain will be measured from the other joints of the links (instead of referring the position of the mass centre to the joint between the kth and ( k - l)th link, the one connecting the (k + l)th link to the kth link is used) such that \u00a3 lj\" e iej = \u00a3 l i \u2022 e i(e~+'~. (24) j : p + l j=p+l Hence eqn (23) becomes C = / ~ "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001102_acc.2004.1383652-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001102_acc.2004.1383652-Figure2-1.png",
        "caption": "Fig. 2. Height Yenus time and exaggerated v i m at lint bounce.",
        "texts": [
            " Equation (3) gives the motion of the ball during contact with the ground and applies only when I 5 0. Bounce behavior, involving deformation, restitution, and then rebound, requires an underdamped solution for which w,j > 0 or The \u201csteady\u201d or rest solution, applying after the bounces have died out, can be obtained by setting t i 00 in eq. (3). The equilibrium position is ( 4 k m - c\u2019) > 0. and when 121 5 1z-l there will be no further bounces. It follows that the number of bounces is finite. A. Time of Contacl The time of contact, AT, for the first bounce, shown in exaggerated view in Figure 2, is the time from when the ball reaches 5 = 0 after being dropped to the time it first comes back to z = 0. Mathematically, the contact time is the first finite solution of the equation z(AT) = 0, i.e., it is the minimum non-zero solution of e x p ( - g ) - F = O , (6) which in general has multiple solutions. Although eq. (6) is difficult to solve analytically, it can be solved numerically. Alternatively, an approximate solution can be obtained. Start by writing eq. (3) in the rearranged form, z = -- U0 exp (-\u201ct) sinWdt -+ 3 x W d 2m k - [exp (-5) (Cm W d t +- C sinwdt) - 13 2m 2 w (7) Assuming << 1, which is reasonable for a bouncing ball such as a ping-pong ball, the second term on the righthand side in (7) can be neglected and z can be approximated as U0 z = -- exp (-f t ) sin wdt "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001491_1.1876437-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001491_1.1876437-Figure1-1.png",
        "caption": "Fig. 1 A schematic drawing of a 6-axis CNC hobbing machine",
        "texts": [
            " Using computer graphics, a three-dimensional tooth surface of curvilinear-tooth gears can be plotted. In addition to developing a mathematical model for cylindrical gears with curvilinear shaped teeth cut by a hob cutter, this study investigates the relationship between tooth surface deviations and machinetool settings. The proposed mathematical model, which is capable of simulating the gear cutting process for the CNC hobbing with a hob cutter, can facilitate gear manufacturers to design and manufacture curvilinear-tooth gears. Figure 1 depicts a schematic drawing of a 6-axis CNC hobbing machine, where axes X, Z, and Y represent the functions of the radial feed, axial feed and hob shift of the hob cutter, respectively; Axes A, B, and C are the hob\u2019s swivel axis, hob\u2019s spindle axis and worktable axis, respectively. Some axes of the CNC hobbing machine are fixed while some axes rotate with a specific relationship during the manufacturing process. For example, in the manufacturing of helical and spur gears, axes X and A are fixed and in the manufacturing of worm gears, axes A, X, and Z are fixed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.30-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.30-1.png",
        "caption": "Figure A.30 AS,. (b) Elementary surface AS, with contour A&. (a) Open surface S with contour L divided into a number ofelementary surfaces",
        "texts": [
            " In the cylindrical system, d z (A.91) and in the spherical system of coordinates + + - a 8 84 r sin8 aq5 dr 1 [ 1 [aA+ sin8 dAo] V X A = - - - r sin8 (A.92) Stokes\u2019s theorem plays a role as important as Gauss\u2019s theorem in vector analysis. It states that when A is a continuous function of position, P I. x A - d s = (A.93) where S is an open surface, L is its condition, and the integration contour is defined in the right-hand sense. Consider a surface S broken up with elementary surfaces AS,, as in Figure A.30a. Apply the definition to the elementary surface ASi: V x A . AS, . ii = A . d&, Al?i contour of ASi, (A.94) ! where dei is along the perimeter of A&. As we evaluate the closed line integral for each At, and AS, (Figure A.30b) and sum it up, some cancellation would occur. We are then left with an integral along the contour of S: . J 2 (A.95) for2 --+ 00: L V x A - d s = A - d , where $ A . clt? is the net circulation integral of A around a closed path; it is a measure of another vector-field property, namely the curling up (or rotation) of the field lines. Hence this is called curl or circulation. 4;, 454 VECTORS AND VECTOR ANALYSIS Show that the vector function A. = -32 + ZQ satisfies Stokes's theorem Js V x A . ds = $' A "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003154_s11071-013-1125-z-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003154_s11071-013-1125-z-Figure3-1.png",
        "caption": "Fig. 3 Gear mode shapes for (a) nd = 1 and (b) nd = 2. White lines represent the nodal diameters",
        "texts": [
            " The dynamic system that includes friction contacts is usually the assembly of two or more substructures, which are modeled by FEM. In this paper, the primary structure is the gear, shown in Fig. 1a, made of NS identical sectors, while the secondary structure is the ring damper (Fig. 2), characterized by a circular shape and by a cut along its axial direction, performed to insert it into the rectangular groove located under the rim of the gear and shown in Fig. 1b. The gear is a cyclic symmetric structure, and its mode shapes (Fig. 3) have special features: \u2013 The modal amplitudes of points located at the same relative position of different sectors have a harmonic distribution along the hoop direction and form an integer number of waves along that direction. \u2013 For this reason, mode shapes can be grouped according to the number of nodal diameters nd, i.e., nodal lines crossing the axis of rotation where the modal displacement is null. Also, nodal circles are a common feature of modes of cyclic symmetry structures; in this case, the nodal line is a circle centered on the axis of rotation",
            " The FE models of a dummy bevel gear and its ring damper, shown in Figs. 1 and 2, respectively, are used as a test case for the proposed method. In detail, the gear has NS = 21 teeth, which are modeled straight and parallel to the generators of the gear cone. Figure 12 shows the first five modal families of the gear spanning the whole set of possible nodal diameters; they are web-dominated mode shapes since the observed natural frequency values become larger as the number of nodal diameters increases. The letters a and b indicate the two mode shapes shown in Fig. 3, which occur respectively for fnd1 = 443 Hz and fnd2 = 1278 Hz. In the present paper, the nonlinear analyses are performed around the nd2 resonance (point b in Fig. 3) of the first mode family, characterized by 0 nodal circles. The analysis is performed by retaining the 0th and 1st harmonic terms of the periodical quantities (e.g., displacements and forces) as described in the previous sections. In terms of tooth meshing forces FTM, which provide the required excitation to the gear, it means that, according to Eq. (2) with z = 1, harmonic components corresponding to h\u2217 = 23 and h\u2217 = 19 are to be considered. In this case, the resonance crossing between the nd2 natural frequency fnd2 and the backward traveling wave excitation is investigated corresponding to h\u2217 = h1 = 23"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003231_s00332-013-9174-5-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003231_s00332-013-9174-5-Figure6-1.png",
        "caption": "Fig. 6 Collision avoidance of two dipoles. (a) Trajectories of the two dipoles. The blue and red dashed lines are the paths of the dipoles if they act independently without interacting with each other. (b) Orientation angles versus time. (c) Trajectories depicted on a torus. Parameter values are = 1/2\u03c0 , z1(0) = \u22124.5, z2(0) = \u22123.5 \u2212 2.5i, \u03b11(0) = 0, \u03b12(0) = \u03c0/6 (Color figure online)",
        "texts": [
            " (2012) for two finite dipoles in an unbounded plane. However, the interaction of two dipoles in an unbounded plane is simpler in the sense that one can identify the set of initial conditions that give rise to collision. In the doubly periodic domain, the set of initial conditions that lead to collision seems to be dense in the space of all initial conditions (based on a range of numerical simulations not shown here for brevity). Collision avoidance The hydrodynamic coupling between two dipoles could induce collision avoidance, as shown in Fig. 6a. Figure 6b plots the change in the dipoles\u2019 orientation as a function of time. As the two dipoles approach each other, their orientations change drastically and collision is avoided. The trajectories of the dipoles are represented on a torus in Fig. 6c. We emphasize that this collision avoidance behavior is a result of the hydrodynamic coupling, only with no external control. That is, the fluid medium plays the role of a collision avoidance mechanism for certain approach conditions. Again, numerical evidence (results not shown here) suggests that the set of initial conditions leading to collision avoidance is dense in the space of all initial conditions. Synchronization The most remarkable interaction mode of the two dipoles is the synchronization mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001521_0301-679x(83)90058-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001521_0301-679x(83)90058-0-Figure2-1.png",
        "caption": "Fig 2 JournaZ centre orbits - various solutions obtained /?o~-~ the VEB study case: ( a/ Booker 'shor~ bear~Jvg,. \"b ~ ~itc,~.e L;L'ff (opt. short bearing), (c) Genera! Motors research (finite e h m e n t yrogramL (d) General Motors reseamk 'rapid e ~ w ~': program), (e) Glacier Metai Co. Lid. (with f i lm his~ow,. (t) Gf.acier Metal Co Ltd . /wi thou~ ffIriq his'to~7/ {gj U~vivee~)f'y ,At Sussex lignite bearing mass effects), (h) Unhersily o f Sussex \" one-dime~esio~al solution raass e\u00a3~ec~s)",
        "texts": [
            " All these changes bring the Simplified and quick method~ Many data oresentation techniques shown in this pape; relating to the VEB big end stud}, case use EooKer's short oearing Mobility solution. The ~Mobi!ity' coT:co-or :qas been successfully applied over the last t 5 years, ano. ~.z explained in detail elsewhere u~\u00b0'~ . its great at t ract ion is the way ~L splits journal movement into two con:~onents squeeze and whirl, which enab!e a FulI orbi! to be caicu lated ver)/ rapidly with no reiterative caicuiations a~ each time step. For completeness the ~short bearing' VEB )e~r hal centre orbit is included in the new %urvev' a f orbits in Fig 2a (supplementing those in Ref I\",~ and the variation fn minimum film thickness at different times tLroughot~.~ the load cycle (defined by crank angle) is shown i~: Fig 3. 148 ~983 Voi !8 N< '3 A second part of Booker's work was to produce a clearance circle film pressure map ~2 giving the ratio of the maximum hydrodynamic pressure to the specific load at any point in the clearance circle. The inset diagram in Fig 4 shows the clearance circle film pressure map with the VEB orbit superimposed. Note that this orbit is not plotted relative to space - the conventional method - but on a clearance map which is effectively being moved in an angular sense throughout the cycle, such that the direction of the applied load is always downwards",
            " This is an important and valuable technique when using the Mobility method. The maximum oil film pressure is obtained from these relationships and its variation throughout the load cycle is shown in the main part of Fig 4. At GEC in the UK Ritchie n developed a new semianalytical method for predicting the journal centre orbit; it uses an easily obtained optimized short bearing solution which has improved accuracy at high eccentricities over the standard short bearing method; the orbit of the VEB big end bearing is shown in Fig 2(b). This looks very similar to a general finite bearing orbit and apparently only took 16 seconds to run on an IBM 370/145 computer (several years ago). The minimum oil film thickness of 0.0033 mm (0.00013 inches) is compared in Table 1 with values from other sources (including the results of a GEC finite bearing program using the 'stored data' approach - see next section). It is seen to be within the scatter band of the more rigorous finite bearing methods, but still maintains the advantage of a rapid solution",
            "5 '~o :3 importance of using the oil film history program where such problems might be encountered. The same principles have been applied to the VEB big end bearing study case and the predicted journal centre paths with and without oil film history are shown in Figs 2(e) and (f) respectively. This derating effect of film history for a completely circumferentially grooved bearing was not at first expected by the author. However, the effect is fairly pronounced as seen on the right hand side of the orbit, Fig 2(e), and the local film thickness (see Table 1).was reduced from 0.0036 mm (0.00014 inches) to 0.0023 mm (0.00009 inches), a significant amount. Different trends in film thickness (ratio) throughout the load cycle are compared in Fig 8. The top graph shows (by the thickness of the line) the similarity between the finite bearing prediction from different sources (including Perkins Engines Ltd 17). Tile middle graph shows experimental results from the VEB engine I , and the lower graph shows the predictions considering oil film history",
            " The part of the orbit associated with appied 1gads which are rotating in the opposite direction to the journal appear to be most affected, a]though the minimum fi]m thickness remained unchanged. Metal Dede also considered the VEB study case and assumed the effective mass ~o correspond \"co the rotating mass compon ent of the connecting rod. The resu!ting journal centre orbits from, the 2-D finite bearing solution and the more rapid one-dimensional solution are shown in Figs 2(g) and 2(h) respecdve]y. In Fig 2(h)most o f the orbit appears ~o be unaffected by the mass inertia effec-q akhough the normaly sharp point, at the beginning of the reversed dire..'.\" tion phase of the orbit, has disappeared completely {t is claimed that the mass inertia effec~ of the ] ourna~ within the bearing clearance space may be sigmfican2 in main bearings adjacent ~o a flywheel Progress in other areas Oi! f l ow predictions Oi] f low ~'rom an engine bearing is an important factor i~ the design procedure. I t is required in the heat ba i~ce to determine the operating temperavdre and oil viscosity~ and is helpful when estimating oil pump ~+, capa Q Unfor tunately it is a very difficult parameter ~o predict accurately - I i \u00b0 ",
            " The test results for the simulated VEB bearing with a circumferential groove are shown in Fig 22. The experimental orbit is surprisingly similar in shape to that predicted by Glacier (short bearing theory) for the same operating conditions. Cooke infers in the NEL report that the orbit shape is quantitatively realistic although the positioning of the orbit within the clearance space may not be exact. The blunt point on the orbit at position A may be due to the inertia effect of the massive housing yoke in accordance with comments relating to the predictions from the University of Sussex (Fig 2(h)). Experimental oil flow results for the simulated VEB bearing with different feed pressures are shown in the lower part of Fig 22, together with feed pressure flow (Qp) predictions carried out by the author. The comparison with the NEL results is good, suggesting that the feed pressure flow predictions may, at least for a circumferentially grooved bearing, be adequate for design purposes. A more commonly used oil feed arrangement for big end connecting rod bearings is through a drilling in the shaft",
            " It was interesting to note that negauve pressures of between ] 6 and 17 atmosphere~ were recorded during some tests. The VEB s tuey case (load as Fig i ( b ) ) w a s again simuiatcd on the rig and measurements of film pressure against time for twelve posztions around the beanng were recorded With positive and negative film pressures it was possi%ie re deduce the corresponding film extents for various crank angles and positions on the beanng. The results of\" this work speciaily carried out for tNs paper, are in Fig 2& This can be compared with t~e film extem map in Fig 2-; showing the positive pressures around the toad ~ine penmen. Also of interest are the regions where the film tNckness >.:,_: predicted to increase let areas marked A). These positions are very dose to the measured negauve pressure regions in Fig 28. A further indication of the tendency towards film rupture and the possibb dove,or> merit of these negative oil film pressures is shown i~ t~e rupture region map iv_. Fig 30. Again there is a remarkabb correspondence between Fig 28 and ~ig 30 in a negative pressure region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002813_icarcv.2012.6485313-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002813_icarcv.2012.6485313-Figure1-1.png",
        "caption": "Figure 1. AUV wall following task",
        "texts": [
            " (7) The different methods of simulating hydrodynamic effects further increase the variance in performance of the various dynamic simulation packages. The physics abstraction layer (PAL) system and the underlying dynamic simulation systems employed are described in [1], and the hydrodynamics models in [2]. IV. APPLICATION: WALL FOLLOWING FOR AN AUTONOMOUS UNDERWATER ROBOT To test the applicability of the multiple simulation paradigm in complex environments a control system for an autonomous underwater vehicle was implemented for a wall following task. This scenario is depicted in Fig. 1. The task is to maintain a specified distance \u201cx\u201d from the wall by controlling the orientation of the AUV. A. Vehicle Hardware The test vehicle for the experiment was the \u201cMako\u201d AUV. The Mako is a two-hull, four-thruster configuration, measures 1.34 m long, 64.5 cm wide and 46 cm tall. The vehicle comprises two watertight hulls machined from PVC separately mounted to a supporting aluminum skeletal frame. Two thrusters are mounted on the port and starboard sides of the vehicle for longitudinal movement, while two others are mounted vertically on the bow and stern for depth control [6]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001313_0471746231-FigureA.10-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001313_0471746231-FigureA.10-1.png",
        "caption": "Figure A.10 surface S. Vector representation of elementary surfaces ds where ds is part of an open",
        "texts": [],
        "surrounding_texts": [
            "Case 1. = ( 2 2 - 21) 2 + ( y 2 - y1) y + ( z 2 - z1) 2 :. PI A Z P 2 = = ( 2 2 - 21) 2 + ( y 2 - y1) 6 + ( z 2 - z1) 2 21 1'2 [ b 2 - 2d2 + ( y 2 - y1)2 + ( 2 2 - z1) IP121 422 VECTORS AND VECTOR ANALYSIS which represents the unit vector directed from PI to P2. Case2. Frequently we identify P ( : z ly , z ) and P\u2019(z\u2019,y\u2019,z\u2019) as the field and source points, respectively (Figure A.9b): + I . r\u2019 = OP identifies the source point r = OP identifies the field point + R = vector directed from the source to the field point. VECTOR SURFACE ELEMENT 423 We now have R = r - r\u2019 = (z ~ z\u2019) i + (y - y\u2019) f j + ( z - z\u2019) 2 (A.19a) (A. 19b) = 5 = (z - z\u2019) i + (y - y\u2019) f j + ( 2 ~ z\u2019) 2 R [(z - z\u2019)2 + (y - y\u2019)2 + ( z - z I ) 2 ] 112 Expressions (A. 19a) and (A. 19b) are extensively used in various field problems. A.4 VECTOR SURFACE ELEMENT Consider an elementary (open) surface of arbitrary shape of area ds shown in Figure A. 1 Oa. A vector surface element ds is represented by a vector whose magnitude is equal to the surface area d s and whose direction is specified by the unit positive normal (vector) of the surface. When ds is part of an open surface, as in Figure A. 1 Oa, positive fi is taken in the direction that a right-hand screw would advance when the screw is placed perpendicular to the surface and is turned along the periphery or contour C such that the area d s is always on the left-hand side. 424 VECTORS AND VECTOR ANALYSIS For a closed surface, f i is always directed away from the volume enclosed by the surfaces, of which ds is a part of as in Figure A. 106."
        ]
    },
    {
        "image_filename": "designv10_10_0001778_ecc.2007.7068863-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001778_ecc.2007.7068863-Figure2-1.png",
        "caption": "Figure 2. The Energy Stabilized SLIP (ES-SLIP), with an actuator parallel with the spring.",
        "texts": [
            " The standard SLIP consists of a point mass attached to a massless prismatic spring, and it is passive (no torque inputs) and conservative (no energy losses). In this paper, we consider a variant of the SLIP, where the leg force is allowed to be non-conservative. The purpose of this modification is to introduce control authority over the total energy, which, in the standard SLIP, is conserved along solutions, thus precluding the existence of exponentially stable periodic orbits [2], [7]. This system, called the Energy-Stabilized SLIP (ES-SLIP), is presented in Fig. 2. A. ES-SLIP Open-Loop Hybrid Dynamics The derivation of the hybrid model for the ES-SLIP is similar to that of the ASLIP, thus the exposition in this section will be terse. The flight and stance configuration spaces M fQ and M sQ respectively will both be parameterized by the Cartesian coordinates of the COM M M M 2 c c f s( , )x y Q Q Q\u2208 = = \u2282 , where the superscript \u201cM\u201d 3 Notation: let 1 1:f X X\u2192 and 2 2:f X X\u2192 , and define 1 2 1 2:f f X X X\u00d7 \u2192 \u00d7 by ( ) ( )1 2 1 2 1 2( ) ( ), ( )f f x f x f x X X\u00d7 = \u2208 \u00d7 , x X\u2208 ",
            " As in the ASLIP, the ES-SLIP hybrid open-loop dynamics can be written in the following form ( ) ( ) ( )( ) ( ) ( )( ) ( )( ) M M M M M M M M M s s s f ES-SLIP M M M M M M M s f f , , : , , , , x f x g x u x u S x x x u S A\u03c8 \u03c8 \u2212 \u2192 + \u2212 \u2212 \u2192 = + \u2209 \u03a3 = \u0394 \u2208 \u00d7 , (12) where M Mu U\u2208 \u2282 is the input and M 1 fA S\u03c8 \u2208 \u2282 is the touchdown angle (angle of attack), and M M M s :f X TX\u2192 and M M M s :g X TX\u2192 are the system and input vector fields in the stance phase. The switching surface is taken to be the liftoff surface ( ) ( ){ }M M M M M M M M s f s f, , 0S x u X U H x u\u2192 \u2192= \u2208 \u00d7 = , (13) where M M M s f :H TQ U\u2192 \u00d7 \u2192 is defined as ( ) ( )M M M Mc s f el2 2 c c , y H x u F u x y \u2192 = + + . (14) In (14), elF is the elastic force developed by the prismatic spring of the leg. Assuming for definiteness that the spring is linear, ( )2 2 el 0 c cF k r x y= \u2212 + , (15) where k is the spring constant and 0r is the nominal spring length, see Fig. 2. In this work, 0r is taken to be the uncompressed length of the leg. However, these assumptions can be relaxed to allow for spring pretension and nonlinear spring characteristics. B. ES-SLIP Closed-Loop Hybrid Dynamics In order to accommodate perturbations away from the nominal energy, the conservative force elF developed by the springy leg of the standard SLIP is modified to include a nonconservative feedback component M M M( )u x\u03b1= . The purpose of Mu is to stabilize the total energy of the system at a desired level, and is achieved by ( ) ( )M M Mc c c c 2 2 c c E P x x y y x K E x E x y \u03b1 + = \u2212 \u2212 + , (16) where E is the desired nominal energy level, M( )E x is the total energy of the SLIP, and E PK is a positive gain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure7-1.png",
        "caption": "Fig. 7. Component of fluid velocity in the z-axis direction around the surface of stator-end winding.",
        "texts": [
            " The fluid velocity around the surface of lower segment of the stator-end winding is much higher than that around the surface of upper segment of the stator-end winding. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 5 Since the fluid velocity component in the z direction around the surface of stator-end winding is high, Fig. 7 shows the fluid velocity component in the z direction around the surface of stator-end winding. In Fig. 7, the z component of the fluid velocity is positive along the positive z direction, and vice versa. It can be seen from Fig. 7 that the highest fluid velocity component along the z-axis around the surface of the statorend winding is 28.7 m/s, which occurs near the center of the stator-end winding. The press plate can be used to axially clamp the stator core and reduce the magnetic flux leakage in the end region. It is of great significance to study the fluid velocity distribution around the surface of the press plate. Fig. 8 shows the distribution of the fluid velocity around the surface of the press plate and position of the shelter board"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003244_s00170-015-7417-3-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003244_s00170-015-7417-3-Figure4-1.png",
        "caption": "Fig. 4 Planing",
        "texts": [
            " Simultaneously, the unit normal of the shaper ns * is derived as follows: \u21c0ns \u00bc nsx nsy nsz 2 4 3 5 \u00bc \u2202rs\u21c0 \u2202\u03b8s \u2202rs\u21c0 \u2202us \u2202rs\u21c0 \u2202\u03b8s \u2202rs\u21c0 \u2202us \u00bc \u2212cos \u03b8os\u00fe \u03b8s\u00f0 \u00de \u2212sin \u03b8os\u00fe \u03b8s\u00f0 \u00de 0 2 4 3 5 \u00f08\u00de Therefore, the surface equation of the spur face-gear represented by the three parameters us, \u03b8s, and \u03d5s can be obtained r2 \u21c0 us; \u03b8s;\u03d5s\u00f0 \u00de \u00bc M2s \u03d5s\u00f0 \u00de\u22c5rs\u21c0 us; \u03b8s\u00f0 \u00de \u00f09\u00de Simultaneously, meshing equation is represented as N \u21c0 S\u00f0 \u00de \u22c5V \u21c0 S2\u00f0 \u00de \u00bc f us; \u03b8s;\u03d5s\u00f0 \u00de \u00bc 0 \u00f010\u00de After the axial parameter of the shaper is eliminated, the surface equation of the spur face-gear can be simplified as r2 \u21c0 \u03b8s;\u03d5s\u00f0 \u00de \u00bc r2 \u21c0 us \u03b8s;\u03d5s\u00f0 \u00de; \u03b8s;\u03d5s\u00f0 \u00de \u00f011\u00de The expansion equation of the spur face-gear surface which can be represented by two parameters \u03b8s and \u03d5s is obtained x2 \u00bc rbs cos\u03d52 sin\u03d5\u03b8\u2213\u03b8scos\u03d5\u03b8\u00f0 \u00de\u2212 sin\u03d52 i2scos\u03d5\u03b8 y2 \u00bc \u2212rbs sin\u03d52 sin\u03d5\u03b8\u2213\u03b8scos\u03d5\u03b8\u00f0 \u00de \u00fe cos\u03d52 i2scos\u03d5\u03b8 z2 \u00bc \u2212rbs cos\u03d5\u03b8 \u03b8ssin\u03d5\u03b8\u00f0 \u00de 9>>= >>>; \u00f012\u00de Where \u03d5\u03b8=\u03d5s\u00b1(\u03b8os+\u03b8s) and \u03d52= i2s\u03d5s. The unit normal of the spur face-gear surface n2 * is derived as follows: n2 \u21c0 \u00bc n2x n2y n2z 2 4 3 5 \u00bc M2s \u03d5s\u00f0 \u00de\u22c5ns\u21c0 \u03b8s\u00f0 \u00de \u00f013\u00de Planing is widely used in small batch production and rough machining as it is simple in planer tool processing, convenient in installation, and time-saving in preparation. Planing is realized through relative straight motion of a planer tool in the horizontal direction of the workpiece (as shown in Fig. 4.). Not only can planes and grooves be processed but also the molding surface with profile cutter and copying device. Generally speaking, planing can be realized in a squaring machine and a double housing planer. The former planer tool repeats movement with workpiece feeding during every intermittence, and the latter workpiece repeats movement with planer tool feeding during every intermittence. Considering the processing technology and the design parameters of the face-gear, a planer machine is needed with the following functions and characteristics: 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002773_tpas.1966.291548-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002773_tpas.1966.291548-Figure6-1.png",
        "caption": "Fig. 6. Part of the modified circle diagram drawn for two back-to. back induction machines.",
        "texts": [
            " This, of course, is to be expected, because stator resistance losses resulting from magnetizing current remain constant in the back-to-back configuration, while they fall with decreasing stator voltage in the parallel case. The relative magnitude of the term (RfVs,l2/lZ8l2) (1 + cos 4)) is small, particularly when 4 > 7r/2. Phasor Diagram The current in each section of the stator for the parallel connection will be the same, and is given by ISp _ Vs 2 Zs + Zr' (34) The behavior of I,p/2 as the load on the machine changes may be depicted by the familiar circle diagram of the induction motor. Part of this circle diagram is drawn in Fig. 6 where OA = no-load stator current for each section OC, OD = stator currents of the two sections, re- OE OB ACC', ADD' spectively, under load = one half OC + OD, which is one half the total reference phase-line current = stator current of normally-connected induction motor = loci of stator currents of each section as slip varies Circle ACBDA = locus of stator currents OC and OD as 4 varies. OA=I]Vs 2 S=O ZS 2]O<s Zs + Zr, Thus, in the case of this somewhat idealized machine with no core losses or friction and windage losses, the stator current is made up of a magnetizing component OA independent of load, plus a load component AB = -Z,,V,IZ,(Z, + Zr') which varies with slip. Now consider the stator currents of each section in the back-to-back configuration. From (11)-(13), with a slight rearrangement of terms, is, IV1 Z=Vsi 1z-Z(35=Zs Zs(ZS + Zr') 2 (5 126 FEBRUARY SMITH: TWIN STATOR INDUCTION MACHINE = Zrs_V, 1 -2 (36)Z, Z8(Z,+Z7') 2 In terms of OA and AB in Fig. 6, (35) and (36) may be written as Is, = OA + (1-e ) =OC (37) 2 AB1S2=OA + (1 e\"0) =OD. (38)2 It is apparent from (37) and (38) that for a particular value of the slip, the loci of the currents Is, and 12, as 4 varies from 0 to 7r, are the two semicircles ACB and ADB having AB as diameter, as illustrated in Fig. 6. The total stator current per phase in the back-to-back configuration becomes Is1 + Is2 = I, = 2 (OA + AR 1- cos 5= 20E. (39) Equation (39) and Fig. 6 illustrate that the locus of Is/2 OE, as 4 varies from 0 to 7r, is the line AB. The loci of I, and 12 as a function of 4) will, therefore, be a family of circles with slip as parameter, as is demonstrated in Fig. 7. The circular arcs ACC', ADD', AEE', and ABB', shown in Fig. 6, are the loci at a particular value of 4) of the currents I,,, IS2, 1,/2, and IS,/2, respectively, as the slip of the machine varies from S = 0 at a point A towards S = 1. Comparison of Power Factor Reduction of the applied voltage to the ideal machines in the parallel configuration will result in a scale change only for the circle diagram, i.e., O, is independent of Vs. Hence, it follows that the overall power factor of the back-to-back configuration cos 0 is always $ the power factor of the parallel configuration cos 0O",
            " This is the measured counterpart of the theoretical results illustrated in Fig. 7 and shows that under some circumstances stator 128 FEBRUARY P 2 4' SMITH: TWIN STATOR INDUCTION MACHINE 1 can operate at leading power factor and also, as seen from Fig. 10, that stator 2 may deliver power to the supply. The total line current under the various conditions of operation is shown, plotted in polar form, in Fig. 13. Curve A shows the total line current as a function of slip for parallel operation of the machines fed with 247 volts and corresponds to the arc ABB' in Fig. 6, which is the locus of I1p/2. Curves B, D, E, and F (but not C) show the total line current as a function of slip for the back-to-back configurationwhen + = 162.3\u00b0, 124.4\u00b0, 86.5\u00b0, and 48.60, respectively, and correspond to the arc AEE' in Fig. 6, which is the locus of I1/2. Curve C in Fig. 13 is the locus of the total stator current for the parallel configuration when fed with a voltage of ./1 - cos 124.40 X 247 = 220 volts 2 and should be compared with curve D in Fig. 13. As shown in Fig. 8, the torque slip curves are practically identical for the two cases to which curves C and D correspond. Thus, curves C and D confirm the conclusion reached in the sec- 1966 129 IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS tion on \"Comparison of Power Factor.\" The dashed lines in Fig. 13 correspond to AB in Fig. 6. Measured Efficiency When arranged to give identical output power, the total input power in the back-to-back configuration, in terms of the total input power for the parallel configuration, is given by (33) Pin \u00b1P\u00b1in+ RS,2(I +cos 4)). When V8, = 247 volts and 4 = 124.4\u00b0, the term (R, IV,,12/ tZ I2) (1 + cos 4) = 5 watts for the machines under test. No significant difference was measured in the efficiency of the two cases. In practice, the difference would be somewhat greater than this because of the reduction in core losses associated with the reduced voltage applied to the parallel configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.11-1.png",
        "caption": "FIGURE 1.11 Two-wheel vehicle model in a cornering maneuver.",
        "texts": [
            "46) After elimination of the lateral velocity v, we obtain the second-order differential equation for the yaw rate r: Imu\u20acr \u00fe fI\u00f0C1 \u00fe C2\u00de \u00fe m\u00f0a2C1 \u00fe b2C2\u00deg _r \u00fe 1 u fC1C2l 2 mu2\u00f0aC1 bC2\u00degr \u00bc muaC1 _d\u00fe C1C2ld (1.47) Here, as before, the dots refer to differentiation with respect to time, d is the steer angle of the front wheel, and l (\u00bc a \u00fe b) represents the wheel base. The equations may be simplified by introducing the following quantities: C \u00bc C1 \u00fe C2 Cs \u00bc aC1 bC2 Cq2 \u00bc a2C1 \u00fe b2C2 mk2 \u00bc I (1.48) Here C denotes the total cornering stiffness of the vehicle, s is the distance from the center of gravity to the so-called neutral steer point S (Figure 1.11), q is a length corresponding to an average moment arm, and k is the radius of gyration. Equations (1.46) and (1.47) now reduce to m\u00f0 _v\u00fe ur\u00de \u00fe C u v\u00fe Cs u r \u00bc C1d; mk2 _r \u00fe Cq2 u r \u00fe Cs u v \u00bc C1ad (1.49) and, with v eliminated, m2k2u2\u20acr \u00fe mC\u00f0q2 \u00fe k2\u00deu _r \u00fe \u00f0C1C2l 2 mu2Cs\u00der \u00bc mu2aC1 _d\u00fe uC1C2ld (1.50) The neutral steer point S is defined as the point on the longitudinal axis of the vehicle where an external side force can be applied without changing the vehicle\u2019s yaw angle. If the force acts in front of the neutral steer point, the vehicle is expected to yaw in the direction of the force and, if behind, then against the force",
            "10, the difference in slip angle can be measured along the ordinate starting from the value l/R. It is of interest to convert the diagram into the graph shown on the right-hand side of Figure 1.10 with ordinate equal to the difference in slip angle. In that way, the diagram becomes more flexible because the value of the curvature l/R may be selected afterward. The horizontal dotted line is then shifted vertically according to the value of the relative curvature l/R considered. The distance to the handling line represents the magnitude of the steer angle. Figure 1.11 depicts the resulting steady-state cornering motion. The vehicle side slip angle b has been indicated. It is of interest to note that at low speed this angle is negative for right-hand turns. Beyond a certain value of speed, the tire slip angles have become sufficiently large and the vehicle slip angle changes into positive values. In Exercise 1.2 the slip angle b will be used. The direct influence of the pneumatic trails ti may not be negligible. In reality, the tire side forces act a small distance behind the contact centers",
            " The side slip phase response tends to 270 degrees (at larger speeds) which is due to the negative coefficient of ju in the numerator of (1.79). This is in contrast to that coefficient of the yaw rate response (1.77). It is of interest to see that the steady-state slip angle response, indicated in (1.79), changes sign at a certain speed V. At low speeds where the tire slip angles are still very small, the vehicle slip angle obviously is negative for positive steer angle (considering positive directions as adopted in Figure 1.11). At larger velocities, the tire slip angles increase and, as a result, b changes to the positive direction. Exercise 1.2. Four-Wheel Steer at the Condition that the Vehicle Slip Angle Vanishes Consider the vehicle model of Figure 1.16. Both the front and the rear wheels can be steered. The objective is to make the vehicle move at a slip angle b remaining equal to zero. In practice, this may be done to improve handling qualities of the automobile (reduces to first-order system!) and to avoid excessive side slipping motions of the rear axle in lane change maneuvers",
            " Show also the frequency response function d2/d1 (ju) for the amplitude and phase at a speed V\u00bc 30 m/s. Use the vehicle parameters supplied in Table 1.1. From Eqns (1.42) and (1.59) with the same restrictions as stated below Eqn (1.60), the following force balance equations can be derived (follows also from Eqn (1.61)). The effect of the pneumatic trails will be dealt with later on. Fy1 Fz1 \u00bc Fy2 Fz2 \u00bc ay g \u00bc K mg (1.80) where K \u00bc may represents the centrifugal force. The kinematic relationship d \u00f0a1 a2\u00de \u00bc l R (1.81) follows from Eqns (1.44) and (1.51). In Figure 1.11 the vehicle model has been depicted in a steady-state cornering maneuver. It can easily be observed from this diagram that relation (1.81) holds approximately when the angles are small. The ratio of the side force and vertical load as shown in (1.80) plotted as a function of the slip angle may be termed as the normalized tire or axle characteristic. These characteristics subtracted horizontally from each other produce the \u2018handling curve\u2019. Considering the equalities (1.80), the ordinate may be replaced by ay/g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000654_s0967-0661(02)00055-2-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000654_s0967-0661(02)00055-2-Figure2-1.png",
        "caption": "Fig. 2. GARBI body-fixed reference frames showing the six degrees of freedom.",
        "texts": [
            " Due to their global effect on the control performance and robustness, input and output SFs play critical role in the Fuzzy-like PD controller and they have the highest priority in terms of tuning and optimisation (Mudi & Pal, 1999). Analysis of how to investigate their optimal values is presented in this paper. Experimental results of the Fuzzy-like PD controller are presented and discussed extensively in the following sections. The motion study of marine vehicle involves six degrees of freedom as shown in Fig. 2, since six independent coordinates are necessary to determine the position and orientation of a rigid body. The first three co-ordinates surge, sway and heave and their time derivatives correspond to the position and translational motion along the x-, y-, and z-axis. The last three coordinates roll, pitch and yaw and their time derivatives are used to describe orientation and rotational motion. In GARBI the motions in the x and z direction (Surge and Heave) are controlled from the horizontal propellers (T1; T2) and vertical propellers (T3; T4), respectively (Fig. 2). However, no correction in y direction (sway) is applied. The structure of GARBI is designed in such a way that pitch and roll cross-coupling is virtually nonexistent. However, minor coupling appears between yaw and surge only when the vehicle has initial speed. Nevertheless, this coupling is expected and acceptable. Similarly, coupling between yaw and pitch and yaw and depth is also minor and can be neglected. When designing GARBI\u2019s controller it is necessary to compensate for its non-linear dynamics and kinematics, non-linearities due to thrusters and pressure hysteresis, barometer dead-zones, and the noise in yaw and depth measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003843_s12206-018-0635-5-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003843_s12206-018-0635-5-Figure4-1.png",
        "caption": "Fig. 4. Distribution of pressure and sliding velocity across the contact area.",
        "texts": [
            " The expression for \u0245 can be given as [11], 2 2 qr qb h R R L = + , (36) where Rqr and Rqb are the RMS of the surface roughness of the race and the rolling elements, respectively; h is the film oil thickness. Therefore, different \u0245s can be obtained according to Archard wear coefficient Ks. For the mathematical model proposed in the paper, the lubricating status is boundary lubrication, such that \u0245 = 1 and Ks = 1.77\u00d710-8. For the ball-ring interaction, the load and sliding speed vary substantially across the elliptical contact area. Therefore, an accurate calculation can be obtained through substitution. HQu P udxdy= \u00f2\u00f2 , (37) The sliding distribution across the contact area is shown in Fig. 4, where the slip and gyro rotation of the ball are ignored. In Fig. 4, us is the sliding speed included by the self-spin component; ud is the differential sliding speed as the result of the difference in radius of rotation between the ball and rings at the location of contact. According to kinematic analysis, ud and us can be calculated as: 2 2 1/2 2 2 1/2 2 2 1/21 ( ) ( ) [( ) ] 2{1 } 2 ' w j j j j j m i d j DR x R a adu r w - - - - + - = - - , (38) where 2 2 1/2 2 2 1/2' ( ) [( ) ] 2 w j j j jj Dr R R a a= - - + - ( , )j i o= , (39) and 2 2 s su x y w= + . (40) Therefore, Qu can be given as 2 1/2 2 1/2 1/2 [1 ( / ) ] 2 2max [1 ( / ) ] 2 2 3 [1 ( ) ( ) ] 2 ( ) ( ) a b x a a b x a s s d Q x yQu ab a b y x u dydx p w w + + - - - -= - -\u00f2 \u00f2 \u00d7 + + "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002555_physrevlett.107.025506-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002555_physrevlett.107.025506-Figure2-1.png",
        "caption": "FIG. 2 (color online). (a) Schematics of the controlled experiment. A folded sheet is clamped on both sides and maintained at a fixed strain 2y. The force and angle are measured simultaneously. (b) Illustration of the protocol for the fold preparation. The crease is obtained by applying a constant load on a folded sheet into two equal parts during a given time (typically between 10 and 20 min). (c) Superimposed images of the initial stage of the sheet during the unfolding and relaxation processes.",
        "texts": [
            " However, the constants a and b are very dependent on the folding protocol and fluctuate between runs with no monotonic evolution. Apart from showing logarithmic behavior of the relaxation, this experiment does not provide further insights on the unfolding process. We then proceeded to a more elaborate experiment. In the following, we are interested in the behavior of a fold maintained at a fixed \u2018\u2018strain,\u2019\u2019 allowing simultaneous measurements of the force and opening angle. The experiment sketched in Fig. 2 consists in an initially folded sheet that is clamped from both sides to metallic plates. One of the plates is fixed, and the other one is held by a highly resolved 0\u20135N dynamometer free to move horizontally (normal to the direction of the crease) via a microprecision displacement system. As previously, the evolution of the angle \u00f0t\u00de is measured by visualizing the sheet from the side. For all the experiments, the crease preparation was performed by applying a constant load on a folded sheet into two equal parts during a given time (typically between 10 and 20 min)",
            " One can wonder if the relaxation behaviors of the force and the angle are related and representative of the same phenomenon. By taking advantage of the experimental configuration, it seems then possible to determine a relation between the force F, the angle , and the control parameters of the experiment. Moreover, solving such a problem could shed light on the possible mechanisms governing the two different relaxation regimes. The relaxation process is very slow compared to characteristic times associated with elastic wave propagation in the material. Therefore, the experimental configuration of Fig. 2 is always at equilibrium, and the shape of the elastic sheet is governed by the elastica equation BWc ss F cosc \u00bc 0, where s is the curvilinear coordinate along the plate and c \u00f0s\u00de its local slope. When considering one side of the fold (see Fig. 2), the boundary conditions read c \u00f00\u00de \u00bc 0 and c \u00f0L\u00de \u00bc =2. The magnitude of the force F is fixed through the condition y \u00bcR L 0 sinc ds, and the spacing is imposed experimentally. The numerical resolution of this problem is straightforward, and a relation F\u00f0 \u00de is computed for a fixed value of the dimensionless spacing y=L. 025506-2 Figure 4 shows the evolution of the dimensionless force ~F\u00f0 \u00de \u00bc y2F\u00f0 \u00de=BW, for two different experiments using Mylar of the same properties and imposing the same spacing y"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001363_s10008-005-0683-5-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001363_s10008-005-0683-5-Figure6-1.png",
        "caption": "Fig. 6 Current potential curve for a CMGCE in 0.15 M phosphate buffer (pH = 7.0) solution and b the same electrode in a 0.4 mM hydrazine, pH = 7.0 solution (scan rate: 20 mV s 1). c as a and d as b for an unmodified glassy carbon electrode",
        "texts": [
            " The deprotonation of surface-attached materials is also proposed as the origin of coverage decrease by some authors [43]. However, this statement cannot be valid in our case since the surface-bonded catechin remains in its protonated form even at higher pH (see inset in Fig. 5, curve a). Electrocatalytic activity of the CMGCE toward hydrazine oxidation The catalytic oxidation of hydrazine by CMGCE was studied by cyclic voltammetry in 0.15 M phosphate buffer, pH = 7.0, in the absence and in the presence of 0.4 mM hydrazine. The electro-oxidation of hydrazine at a bare glassy carbon electrode is shown in Fig. 6d, where cyclic voltammograms was carried out over the potential range 100 mV to 1,000 mV at 20 mV s 1. Direct oxidation of hydrazine shows the representative irreversible wave. The overall oxidation of the hydrazine by the modified electrode is given in Eq. 1. N2H4 ! N2 \u00fe 4H\u00fe \u00fe 4e \u00f01\u00de Figure 6a, b shows the representative cyclic voltammograms of a CMGCE in the absence and in the presence of 0.4 mM hydrazine. As expected for an electrocatalytic oxidation there is an increase in the anodic peak current of the CMGCEox/CMGCEred redox wave (where CMGCEox is the oxidized form and CMGCEred is the reduced form of the bonded catechin on glassy carbon electrode) in the presence of hydrazine, whereas the reduction peak current has virtually disappeared reflecting the efficiency of the catalytic reaction",
            " This process increases the anodic peak current, while the cathodic peak current is smaller than in the absence of hydrazine. The overall process according to an EC catalytic mechanism can be expressed as shown in Eqs. 2 and 3. CMGCEred! ks CMGCEox \u00fe 2H\u00fe \u00fe 2e \u00f02\u00de 2CMGCEox \u00feN2H4! k0h 2CMGCEred \u00feN2 \u00f03\u00de The rate-determining step is given in Eq. 3 with a rate constant k\u00a2h. Thus, the rate of reaction in Eq. 2 can be considered fast compared to the one in Eq. 3. The catalytic effect can be seen directly when curve a is compared with curve d in Fig. 6. It can be seen that the electrocatalytic-oxidation peak potential (curve b) appear at 225 mV. However, this value is more negative than those previously reported for the other modified electrodes which used in electrocatalytic oxidation of hydrazine [11\u2013 18, 44\u201346] except for only very few other modified electrodes [47]. Thus, a significant decrease in overpotential of hydrazine oxidation at the CMGCE makes it suitable to determine hydrazine by voltammetric detection. The effect of increasing the hydrazine concentration on the voltammetric response of the CMGCE was also investigated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000992_s0043-1648(96)07225-0-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000992_s0043-1648(96)07225-0-Figure2-1.png",
        "caption": "Fig, 2. Point contact rolling surface cell for spall iniliadon and propagation model.",
        "texts": [
            " This paper consists of three pans: damage law applied to each cell in the surface layer leading to spell initiation and propagation; internal stresses and accumulative plastic strain calculation; and multigrid multilevel EHL calculation of pressure and film thickness profiles with dent. 2. Damage law for spali initiation and propagation Spalis generate when a minute piece of metal flakes offthe rolling surface, in this study, the surface layer was divided into many small metal cells as shown in Fig. 2. Each cell is a representative volume element (RVE) in the continuum mechanics point of view, where it is small enough that every physical quantities can be regarded evenly distributed conslants but large enough that it represent an average of the microprocess. For each cell shown in Fig. 3, a damage variable is defined: D--~ (2) v where I'D is the damage volume and V is the total volume of the ceil, and, D = 0 undamaged cell D= I fully damaged cell /'he damage variable can be described as the density of microcracks and cavities ~n RVE due to the local plastic deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001875_s00707-008-0037-3-Figure11-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001875_s00707-008-0037-3-Figure11-1.png",
        "caption": "Fig. 11 Cross section along diameter of annular membrane with sliding outer edge; vertical loading",
        "texts": [
            " An axisymmetric model involving one pile is often used for analytical purposes. Since this is a \u201cunit cell\u201d for one pile in a periodic array, the radial displacement and the slope of the membrane at the outer boundary are assumed to be zero. Also, the membrane directly over the pile is almost flat and then drops sharply into the soil lying outside the pile, so that the membrane is sometimes assumed to be pinned at the edge of the pile, and thus to have an annular shape. The geometry along a diameter is depicted in nondimensional terms in Fig. 11. The vertical loading is assumed to have the constant dimensional value P per unit of undeformed area of the horizontal projection of the membrane. For the GR theory, Pt = P sin \u03c6/[(1 + \u03b5r )(1 + \u03b5\u03b8 )], Pn = P cos\u03c6/[(1 + \u03b5r )(1 + \u03b5\u03b8 )]. (36) For the R theory, the denominators in Eqs. (36) become unity. The right sides of Eqs. (9) and (14) become \u2212(1 \u2212 \u03bd2)r2(sin \u03c6 cos2 \u03c6)p, and the right sides of Eqs. (10) and (15) become \u2212(1 \u2212 \u03bd2)r2(cos2 \u03c6)p, where p = P B/(Eh). Therefore the displacements based on the R and GR theories are the same, as mentioned in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003385_12.2010577-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003385_12.2010577-Figure1-1.png",
        "caption": "Figure 1. Side views of the turbine blade.",
        "texts": [
            " Among the variety of methods for blade inspection9, X-rays and Fluorescent Penetrant Inspection (FPI) have been employed. Laser sintered part dimensional inspection has been successively performed given that very tight geometric tolerances apply for turbine blades. Microstructure of manufactured part has been examined in order to define material properties and fabrication process influence. The turbine blade examined in this study is a 50% scaled version of a compressor blade adopted in a gas turbine (Figure 1). In particular, this type of \u201clow-pressure\u201d blade is employed for first stages where temperatures are lower and greater mechanical strength is needed6. The prototype has been manufactured using an EOSINT M270 titanium version laser sintering system. Machine specifications are given in Table 1. Ti-6Al-4V powder with a mean particle size of 30 \u00b5m has been used in this investigation and alloy chemical composition is listed in Table 2. The powder quality is important to reduce the content of impurities (oxygen, hydrogen and nitrogen), which might negatively affect mechanical properties of laser sintered parts with phenomena like embrittlement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000954_s1359-6454(04)00390-8-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000954_s1359-6454(04)00390-8-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of (a) 3-D melt-po",
        "texts": [
            " It is assumed that in the present analysis the quasisteady state processing conditions are maintained under which the melt-pool shape remains constant with respect to the moving heat source. It is also noted that in this study only the melt-pool shape corresponding to the solidification interface is of interest. Based on the above considerations, the 3-D shape of the melt pool produced by laser surface melting, corresponding to the solidification interface, is assumed to be a segment of an ellipsoid. As shown in Fig. 1, four geometrical parameters (w, l, h, a) are used to depict the melt pool shape, with w being half the maximum width, l being the length between the location of maximum depth (also maximum width) and the trailing point, h being the maximum depth of the melt pool, and a being the angle between the substrate surface and the tangent of the melted trace in the transverse cross-section. It is worth noting that h\u201dw and a\u201d90 for the melt-pool shape obtained from the Rosenthal analytic solution to the temperature field induced by a moving point heat source along the surface of a semi-infinite solid [21,23,24]",
            " The melt-pool length parameter (l) was determined from the 2-D video image of the melt pool or from direct measurements of the melt-pool traces (ripple formation) on the top surface of the melt track. Samples for microstructure analysis were mounted and polished using standard metallographic techniques and etched with a solution containing H2O (100 ml), HCl (100 ml) and CuCl2 (5 g). For convenience of results presentation and comparison, in the computations presented in Sections 4.1\u20134.3, the melt-pool geometrical parameters (w, l, h) excluding the angle a are represented by their relative values using w as the reference parameter. Thus, in the x\u2013y\u2013z reference frame defined in Fig. 1, on the melt-pool interface corresponding to the solidification front, the value of x/w varies from l/w to zero, the value of y/w varies from a minus unit to a unit, and the value of z/w varies from h/w to zero. Effects of variations in the geometrical parameters were studied by changing the ratios l/w and h/w and the value of the angle a. Fig. 3(a) and (b) shows the computational results of dendrite growth velocities and directions on the meltpool solidification interface for a melt pool of the geometrical parameters l/w=1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003831_tie.2018.2826461-Figure6-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003831_tie.2018.2826461-Figure6-1.png",
        "caption": "Fig. 6. Fluid velocity distribution around the surface of the stator-end winding.",
        "texts": [
            " The influence of different relative magnetic permeability values of press plate on the temperature of the end parts is determined with FLUENT commercial CFD software. The relative magnetic permeability of the press plate has an impact on the temperature of the end parts in the turbogenerator. A reasonable selection of the relative magnetic permeability of the press plate can reduce the total loss in the end parts, as well as the production costs. Manganese steel is assumed in this paper. The relative magnetic permeability of press plate could be modified by changing the elemental composition (such as Mn) within the press plate. Fig. 6 shows the distribution of fluid velocity around the surface of the stator-end winding. The highest fluid velocity around the surface of the stator-end winding is 35.6 m/s. It can be seen from the local enlarged panel A in Fig. 6 that the fluid flows to the nose along the upper segment of the stator-end winding. However, it can be seen from the local enlarged panel B in Fig. 6 that the fluid flows to the straight-line part along the lower segment of the stator-end winding. The fluid velocity around the surface of lower segment of the stator-end winding is much higher than that around the surface of upper segment of the stator-end winding. 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 5 Since the fluid velocity component in the z direction around the surface of stator-end winding is high, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000899_156855304773822464-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000899_156855304773822464-Figure3-1.png",
        "caption": "Figure 3. Two kinds of stubbing.",
        "texts": [
            " If the transition between two phases fails, the system cannot evolve anymore. A necessary condition is found to be: PrtdC < 0: (7) This condition comes from the rst equation of (1), which describe the dynamics of the leg length r at the stance phase. In (1), at the moment of touchdown, Mr P\u00b52 and Mg.1\u00a1cos \u00b5/ are positive, and Kl.rtdC\u00a1r0/ D 0 holds. Therefore, if PrtdC > 0, there are no attractive vector elds that constrain the foot to the ground. This prevents the robot from entering to stance phase from ight phase. Note that (7) is not always satis ed. Figure 3 shows such two unfortunate situations. Figure 3a indicates stubbing just after lift-off, while Fig. 3b shows stubbing just before touchdown. The situation Fig. 3b cannot be recovered and should be avoided in advance, while the situation in Fig. 3a can be avoided by retracting the leg during the ight phase (since the foot is mass-less, the leg length is arbitrarily controlled \u2018without in uence on the other dynamics\u2019). For the same reason, the axial velocity of the leg just before lift-off must be positive: Prlo\u00a1 > 0: (8) Fortunately, this condition is automatically satis ed if (7) holds because at the stance phase, only repelling force is applied to the direction of the leg axis [16]. Therefore, (7) is suf cient. Condition (II) is obvious, but it is dif cult to derive the suf cient condition mathematically because the dynamics at the stance phase is non-integrable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003494_tmag.2016.2572659-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003494_tmag.2016.2572659-Figure2-1.png",
        "caption": "Fig. 2. Current superimposition variable flux permanent magnet machine.",
        "texts": [
            " First, the characteristics are computed under vector control. Finally, the computed characteristics are verified by carrying out measurements on a prototype. F Manuscript received. January 23, 2016 Corresponding author: Akira Kohara (e-mail: akira.kohara@ams.eng.oska-u.ac.jp). Digital Object Identifier inserted by IEEE 0018-9464 (c) 2016 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. A. Basic Structure Fig. 2 shows the structure of the proposed CSVFPMM, which consists of a 10-pole rotor and a 12-slot stator that has a single set of windings and 6-pole-pair permanent magnets. The permanent magnets are alternatively magnetized in the direction shown by arrows in Fig. 2, and they function to increase the field magnetic flux density already being generated from the windings. B. Driving Method A 6-phase inverter is used to operate the CSVFPMM using 6- phase coils (A, B, C, D, E, and F), which correspond to 2 sets of 3-phase coils. Therefore, the A and D, B and E, and C and F phases correspond to the U, V, and W phases, respectively. 3-phase AC voltages (Vu, Vv, and Vw) are applied to the A and D, B and E, and C and F phases, respectively, as shown in Fig. 3. DC voltages (+V and \u2013V) are superimposed onto the 3- phase AC voltages"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002596_we.447-Figure9-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002596_we.447-Figure9-1.png",
        "caption": "Figure 9. RomaxWind model of GRC gearbox installed in wind turbine with load case.",
        "texts": [
            " Designers use these models for achieving good alignment of the system under the loads, calculating gear and bearing contact stress and life, optimizing the microgeometry of the gears for increased life and transmission error and predicting the gear vibration magnitudes, as well as for many other purposes. The gearbox model is used in this paper in various forms to illustrate technology and design approaches important to improving wind turbine gearbox reliability, and Figure 7 provides one arrangement where the gearbox is modeled as installed in the NREL dynamometer test cell (Figure 8) Figure 9 provides a model for the purpose of simulating the GRC gearbox as installed in the wind turbine. The load case shown with the fi gure includes a signifi cant off-axis moment as well as loading from rotor mass (wind turbine blades and hub). Large off-axis moments are common in wind turbines, under conditions such as wind direction change, yaw error Wind Energ. 2011; 14:637\u2013651 \u00a9 2011 John Wiley & Sons, Ltd. DOI: 10.1002/we 641 (putting the blades askew to the wind), yawing of the machine and wind shear",
            "1002/we 646 A design analysis needs to be performed to understand the infl uences on the misalignment on the planet gears. If the misalignment can be reduced, then the time-varying contact stress and face load distribution can be reduced. This will in turn decrease vibration and reduce fatigue on the planet gears and planet bearings. For many wind turbine gearbox designs, the alignment of the planetary stage is sensitive to the magnitude of the clearances in the planet carrier bearings (i.e. the bearings that support the carrier). For this model (Figure 9), with the gearbox installed in the turbine, a full factorial study has been performed where the radial internal clearance of the upwind and downwind planet carrier bearings are varied, and the misalignment and face load distribution factor (F\u00dfX and KH\u00df 11) are calculated for each planet position of Figure 10. Note, for the results of Figures 11, 15\u201317, the clearance was assigned as 260 \u00b5m for both carrier bearings. The factorial study (Figure 17) demonstrates how sensitive the misalignment of the sun and planet is to these bearing settings, and designers can use such models to optimize the settings of the bearings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001217_70.240203-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001217_70.240203-Figure3-1.png",
        "caption": "Fig. 3. Simplified PUMA-type 4-DOF robot handling an unknown point-mass load.",
        "texts": [
            " provided that the unknown parameters are updated according to (94) Since H ( q ) is uniformly positive definite, i, in (93) is negative if X is sufficiently large. Note that the control torque in this case becomes (95) where q' = qd - 2 X i - X2G. (96) Obviously, (95) and (96) represent a quasi-computed-torque controller, which would be identical to the well-known computed-torque algorithm [61 if 8 , = 8,. I IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION. VOL. 9, NO. 3, JUNE 1993 B. Case Study In what follows, we consider a 4-DOF manipulator, shown in Fig. 3,with a geometry identical to the first four links of a PUMA 500 robot. Its dynamic parameters are, however, simplified as follows: all four links are of point-mass with ml = m2 = m3 = 2 kg and m4 = 0.5 kg. For the first three links, the mass center of each link is at its midpoint, and the mass center of link 4 is at its distal end. The robot carries a 0.5-kg point-mass load, tracking in the joint space a trajectory specified by c1 + a1 sinwt [ $11 = [ c4 :::::;:;::;4 + a4 cos(wt /4) with c1 = 8 ~ / 9 , c 2 = 27r/3,c3 = 3 ~ / 4 , c 4 = 1 5 ~ / 1 8 , a 1 = 47r/9,a2 = ~ / 3 , a 3 = ~ 1 4 , and a4 = 87r/18 for 0 < t 5 2 s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000943_j.finel.2004.02.002-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000943_j.finel.2004.02.002-Figure2-1.png",
        "caption": "Fig. 2. A part of the generating rack in Fig. 1.",
        "texts": [
            " The operation is similar to that required to generate a helical gear, but instead of being parallel to the axis of the gear, the generating rack is inclined to the axis by the cone angle. The generating rack in Fig. 1 has pressure angle n in the normal plane and pressure angles t+ and t\u2212 in the transverse plane. According to Ref. [12], the relation between these angles is tan tj = tan n cos sec \u2212 j sin tan ; (1) where j is a variable that is equal to 1 or \u22121 (which is denoted with + or \u2212). As a consequence, the generated tooth is not symmetric. The base and pitch radii are de!ned as rbj = r cos tj; r = zm=2 cos : (2,3) Fig. 2 shows a part of the generating rack in Fig. 1. The normal coordinate system Sn is located and oriented such that the xn-axis coincides with the vertical symmetry plane of a space width of the rack, the yn-axis coincides with a normal plane of the rack and the zn-axis coincides with the datum plane. The position of the origin On along the width of the rack is arbitrary. A point on a straight Iank of the rack that will generate a point on an involute helicoid (or surface if the generated gear type is a spur gear) of the gear is located with the position vector rnIj, which is de!ned as rnIj(uIj; vIj) = [ xn Ij yn Ij zn Ij 1 ]T =   uIj cos n j(sr=2 \u2212 uIj sin n) vIj 1   ; (4) where the surface parameters uIj and vIj are the distances which are de!ned in Fig. 2. The tooth thickness of the rack at the datum plane sr is equal to half the pitch or m=2. A point on a !llet surface of the rack that will generate a point on a !llet surface of the gear is located with the position vector rnFj, which is de!ned as rnFj(uFj; vFj) = [ xn Fj yn Fj zn Fj 1 ]T =   \u2212e \u2212 sin uFj j[sr=2 + e tan n + (sec n \u2212 cos uFj)] vFj 1   ; (5) e = ha \u2212 : (6) The surface parameters uFj and %Fj are, respectively, the angle and distance that are de!ned in Fig. 2. A point on a rack root surface that will generate a point on a root surface of the gear is located with the position vector rnRj, which is de!ned as rnRj(uRj; vRj) = [ xn Rj yn Rj zn Rj 1 ]T =   \u2212ha juRj vRj 1   ; (7) where the surface parameters uRj and vRj are the distances that are de!ned in Fig. 2. The transverse coordinate system S t in Fig. 1 is oriented such that the yt-axis is parallel with a velocity vector of the rack and the zt-axis is parallel with the gear axis. The coordinate transformation from the normal coordinate system Sn to the transverse coordinate system S t involves two rotations and is represented by the matrix equation rt = [ xt yt zt 1 ]T =MtaManrn; (8) where Man =   1 0 0 0 0 cos sin 0 0 \u2212sin cos 0 0 0 0 1   ; Mta =   cos 0 sin 0 0 1 0 0 \u2212sin 0 cos 0 0 0 0 1   : (9) The parameters vIj, vFj or vRj represent normal sections of the rack",
            " It can be quite tricky to solve (40) since the involute curve not is de!ned below the base radius. Fig. 4a shows a Iowchart of the algorithm FindBnd, which !rst checks if the tooth pro!le is undercut and if this is the case it determines utFj max by a numerical method such as the secant or the Newton\u2013Raphson method. Finally, it solves (40) by the bisection method (which has the advantage of being very convergent since it belongs to the category of bracketing methods). The interval of the parameter utFj becomes utIFj6 utFj6 =2: (41) From Fig. 2 we conclude that the interval of the parameter \u2019Rj becomes{ \u2019R+(uFR ; w)6\u2019R+6\u2019R+(sr ; w) \u2019R\u2212(sr ; w)6\u2019R\u22126\u2019R\u2212(uFR ; w) uFR = sr=2 + ha tan n + sec n(1 \u2212 sin n); (42,43) where uFR de!nes the boundary between the !llet and root surface. A gear comprises the teeth and the gear body. This paper focuses only on the teeth and the part of the gear body directly under the teeth that is called the rim. Since the geometry of the teeth and rim may be considered to be cyclic symmetric, the model can be constructed using one characteristic tooth sector that comprises one tooth and the part of the rim under the tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0000668_00207170110112241-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000668_00207170110112241-Figure2-1.png",
        "caption": "Figure 2. The simple planar manipulator with two revolute joints.",
        "texts": [],
        "surrounding_texts": [
            "In this section we will consider the control of the simple planar manipulator with two revolute joints shown in \u00aegure 2. Let us \u00aex the notation as follows. For each link i i 1; 2 \u00b3i denotes the joint angle; mi denotes the mass; li denotes the length; lci denotes the distance from the previous joint i 1 to the centre of mass of link i; and Ii denotes the moment of inertia of link i about an axis perpendicular to the plane, passing through the centre mass of link i. Using the well-known Lagrangian equations in classical dynamics, one can show that the dynamic equations of the robot are \u00bd1 \u00bd2 \" # d11 d12 d21 d22 \" # \u00b31 \u00b32 2 4 3 5 c _\u00b32 c _\u00b31 c _\u00b32 c _\u00b31 0 2 4 3 5 _\u00b31 _\u00b32 2 4 3 5 g1 g2 \" # f1 f2 \" # 32 where the coe cients dij ; gi; fi and c are d11 m1l2c1 I1 m2 l21 l2c2 2l1lc2 cos \u00b32 I2 d22 m2l2c2 I2 d12 d21 m2l1lc2 cos \u00b32 m2l2c2 I2 c m2l1lc2 sin \u00b32 g1 m1lc1 g cos \u00b31 m2g lc2 cos \u00b31 \u00b32 l1 cos \u00b31 g2 m2lc2 g cos \u00b31 \u00b32 f1 v1 _\u00b31 f2 v2 _\u00b32 where g is the gravity acceleration, and vi are the viscous friction coe\u00aecients. As it was indicated in } 2, using a proper parametrization, the dynamic equation of the robot can be put in linear dependence of these parameters, and thus, the same is true for the control law as well. In this example the following parametrization is chosen to linearize the parameter dependence. D ow nl oa de d by [ G eb ze Y uk se k T ek no lo ji E ns tit \u00efs u ] at 0 1: 14 2 1 D ec em be r 20 14 It is de\u00aened that the following 2 7 regressor matrix Y Y; _Y; _Yr; Yr whose elements are y11 \u00b3r1 y12 \u00b3r2 y13 2 \u00b3r1 \u00b3r2 cos \u00b32 _\u00b32 _\u00b3r1 _\u00b31 _\u00b32 _\u00b3r2 sin \u00b32 y14 g cos \u00b31 y15 g cos \u00b31 \u00b32 y21 0 y22 \u00b3r1 \u00b3r2 y23 cos \u00b32 \u00b3r1 sin \u00b32 _\u00b31 _\u00b3r1 y24 0 y25 g cos \u00b31 \u00b32 y16 _\u00b31 y26 0 y17 0 y27 _\u00b32 9 >>>>>>>>>>= >>>>>>>>>>; 33 and the unknown dynamical parameters a1 I1 m1l 2 c1 m2l21 I2 m2l2c2 a2 m2l2c2 I2 a3 m2l1lc2 a4 m1lc1 m2l1 a5 m2lc2 a6 v1 a7 v2 9 >= >; 34 As was indicated in } 1, the robot energy can be put in the form E H Y; _Y B. For the robot of this example, the H elements are h1 _\u00b32 1 h2 _\u00b32 2 _\u00b31 _\u00b32 h3 2 _\u00b31 _\u00b31 _\u00b32 \u00a1 \u00a2 cos \u00b32 h4 g sin \u00b31 h5 g sin \u00b31 \u00b32 9 >>>>>>= >>>>>>; 35 and the terms of B are B a1 a2 a3 a4 a5 T Finally, the parametrization of the friction terms is made using the function matrix F _\u00b31 0 0 _\u00b32 \" # 36 and the parameter vector \u00c0 v1 v2 \" # 37 As can be observed, the parameter vector A is formed by the elements of the vector B plus the elements of the vector \u00c0. In the example the following values for the robot\u2019s parameters are assumed m1 2 kg m2 1:4 kg I1 0:5 kg m I2 0:1 kgm v1 0:3 N ms l1 0:8 m lc1 0:4 m l2 0:8 m lc2 0:4 m v2 0:3 N ms 9 = ; 38 Using the values presented in equation (38), the real (unknown) dynamical parameters ai are A 2:04 0:32 0:45 1:92 0:56 0:3 0:3 2 666666666666664 3 777777777777775 39 It should be noted that these parameters are unknown and therefore they are only employed in the dynamic equations of the robot, but not in the controller. The following values have been chosen for the controller parameters \u00b6 diag 10 10 G diag 0:5 0:5 0:5 0:5 0:5 \u00b6f 10 \u00ae 0:1 K 1:5 1:5 diag 0:1 0:1 r 9 11 p 13 15 9 >>>= >>>; 40 and it is assumed that there is an uncertainty around 50% in the dynamical parameters of the robot and therefore these are incorrectly initialized with A\u0302 0 1:5 0:5 0:5 1:0 0:5 0 0 2 666666666666664 3 777777777777775 41 In the example, the robot starts from repose at position Y 0 0 T and the control objective is to follow the desired trajectory Yd 0:3 sin 0:3t \u00ba=2 cos 0:5t sin 0:9t 0:1 0:5 sin 0:3t \u00ba=2 cos 0:5t sin 0:9t 0:3 \" # therefore, the control tracking start with initial position and velocity errors. Figures 3(a) and (b) show the tracking error for the joints. As can be observed, after a small time, both D ow nl oa de d by [ G eb ze Y uk se k T ek no lo ji E ns tit \u00efs u ] at 0 1: 14 2 1 D ec em be r 20 14 Figure 3. Simulation results for the example. (a) Position error for the \u00aerst joint. (b) Position error for the second joint. (c) Control signal for the \u00aerst joint. (d) Control signal for the second joint. (e) Estimated parameters of the system. (f) Sliding variable. D ow nl oa de d by [ G eb ze Y uk se k T ek no lo ji E ns tit \u00efs u ] at 0 1: 14 2 1 D ec em be r 20 14 tracking errors tend to zero. Figures 3(c) and (d) show the control signal for the joints. The signals are smooth because the dynamical composite parameter estimation allows us to use a small sliding gain, since the sliding control only needs to compensate for the unmodelled dynamics and not for the parameter uncertainties. As a result, in the \u00aegures it can be observed that the chattering phenomenon is small. Using the equations for tr (26) and tT (30) with the numerical parameters used in the simulation, a convergence time of less than 25 s is expected. This result agrees with the behaviour shown in the \u00aegures. Finally in \u00aegure 3(e) the time evolution of the estimated parameters is presented which, as observed, tend to the real parameters, and \u00aegure 3(f) shows the time evolution of the sliding variable which can be observed to go to zero."
        ]
    },
    {
        "image_filename": "designv10_10_0001967_0094-114x(78)90041-1-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001967_0094-114x(78)90041-1-Figure4-1.png",
        "caption": "Figure 4. A loop which contains a prismatic joint.",
        "texts": [
            " The chains of counterweighted links by which a dependent link is balanced, but which also exist in loops containing a prismatic joint, will be called counterweighted chains. If a dependent link is pivoted about a frame pivot then one of its counterweighted chains, namely that from the dependent link to the frame pivot, is of zero length. In other words, the mass assigned from the dependent link to this chain is assigned directly to a stationary point. Consequently, zero-length chains need no counterweights. Consider a loop QLMNOQ containing s links two of which, i.e. LM and MN in Fig. 4, are connected together by a prismatic joint. In Appendix III, it is shown that to balance these two links a counterweight does not have to be added to them both. To achieve a force-balance the counterweight condition to be satisfied on link LM is\" I z \u2022 A \u2022 e i# + m k - I \u2022 r k - l \u2022 e %-t + m k \" rk \" e live-n) = 0 (4) where k /~, A and $ m, r and 1, 71 subscript which distinguishes each link and its counterweight from the others in the loop (i.e. starting from one of the frame pivoted links and proceeding round the loop to end at the frame link s), the counterweight parameters as defined in Section 2, the link parameters as defined in Section 2, angle between the reference arcs of links LM and MN",
            " (25) /=p+l Equation (22) shows B to be the chain VUQ which is equivalent to the RQ chain when the length of RQ is factored by l'/lp and then offset from its original position by the angle E'~ + ~-. Similarly, eqn (25) shows C to be the chain ZNQ which is equivalent to the STQ chain when the length STQ is factored by IJIp and then offset from its original position by the angle ~. Appendix 3. Condition Related to a Prismatic Joint Consider the two heavy links, LM and MN, in the loop QLMNOQ of otherwise light links as shown in Fig. 4. Assume that there are s links in the loop. The moment vectors, T~ and To, of the chains MLQ and MNOQ respectively with reference to Q and a frame arc are T~ = i n k _ I \" r k _ I ' e l t O k - ' + v * - d + ~ , , I i e iej ( 2 6 ) j = l and H o w e v e r (27) ok = Ok-, - 7. (28) Hence the moment vector m k \u2022 rk \"e ~* can be re-defined with respect to an arc which radiates from point N in a direction parallel to that of the arc I~-t at L. Consequently eqn (27) becomes k+l Now a moment vector defined with respect to one arc can be translated to any parallel arc that has the same angular motion without affecting the force-balance conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002883_j.acme.2013.12.001-Figure18-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002883_j.acme.2013.12.001-Figure18-1.png",
        "caption": "Fig. 18 \u2013 Contours of equivalent stress according to the Huber\u2013Mises hypothesis for maximum deformation.",
        "texts": [],
        "surrounding_texts": [
            "The results of the performed strength analysis are as follows: contours of deformations, contours of equivalent stress, displacement fields, velocity fields. This paper presents examples of results illustrating the distribution of deformations and stress in the structure at a given moment on a deformed model. Also, the deformation Fig. 16 \u2013 Contours o form is presented at the moment of highest elastic and plastic deformation of bodywork (Figs. 16\u201319). To fulfil the requirements of the Regulation No. 66 of UN/ ECE, for the algorithm and simulation programme the whole energy balance was needed to be plotted. The comparison of the kinetic, internal, hourglass and total energies for the FE bus model is depicted in Fig. 20, which illustrates the kinetic f plastic hinges. energy conversation to internal energy of the whole bus structure. Moreover, the non-physical energy components introduced by the process of finite element modelling and simulating was also plotted. According the Regulation No. 66 of UN/ECE it shall not exceed 5% of the total energy at any time [3]. Since the maximum hourglass energy is 3.5% of the total energy the stated requirement is met."
        ]
    },
    {
        "image_filename": "designv10_10_0000827_robot.2001.933264-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0000827_robot.2001.933264-Figure1-1.png",
        "caption": "Figure 1: A 12-DOF biped robot",
        "texts": [
            " In order to simulate slipping of the foot, the horizontal frictional force between the sole and the ground is set as Pukfvsgn(v5) IvsI 2 E (%I < E , and l f e l < h f v (12) ps f v sgn( v,) otherwise where E is a small number to be used instead of zero in numerical computations; vs is the velocity of the foot relative to the ground; ps and p k are the coefficient of static and dynamic friction, respectively; fe is the horizontal force applied at the foot by the biped robot, and computed by Eqs. (9) and (11); f v , defined by Eq. (7) , is the vertical reaction force generated by the ground. 4 Simulations The effectiveness and the performance of the proposed control are shown in computer simulations. The biped robot used in this paper has a total of 12 degrees of freedom, 6 degrees of freedom in each of its leg, as shown in Fig. 1. And, the dynamic equations and the simulation software developed by Park and Kim [9] are used. The parameters of the environment model used in simulations are shown in Table 1. The pads underneath the feet are 1 cm thick. The hip is normally located 70 cm above the ground during locomotion. The biped robot walks at the speed of 20 cm/s. In the simulations, the reflex control enabled the biped robot to walk on a slippery surface the friction coefficient of which is about 0.3. Slipping occurs at the moment of a landing of the right foot and the left foot is on the normal surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001823_bf00265715-Figure3-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001823_bf00265715-Figure3-1.png",
        "caption": "Fig. 3. Free body diagram of hand-ball segment",
        "texts": [
            " This is based on Newton's Law of F --- ma and d 'Alembert 's principle which stated, 'All external forces and inertial forces form an equilibrium system'. In the forearm segment (Fig. 2), a force mf~ generated by the muscle to produce forearm motion exerted a joint reaction force at the elbow Fe and at the wrist Fw respectively. This force also produced a t o r q u c If(Jr, which likewise exerted a moment M e at the elbow and a moment Mw at the wrist. By the same token, the moving handball segment (Fig. 3), produced a force mh~h which acted across the wrist joint Fw, together with a torque lhSh, which exerted an angular momentum across the wrist joint with a magnitude of Mw. From Newton's Second Law and the Angular Momentum Principle, the differential equations of Y.-S. Hang et al.: Biomechanical Study of the Pitching Elbow 219 mot ion of the two segments are re la ted in such a way that: mf~f = Fo + Fw (1) lf~f = Me -t-/~Iw (2) mh~h = Fw (3) lh~ h = ~ i w (4 ) Subst i tu t ing the value of Fw from equa t ion (3) into equa t ion (1) yields F~ = m f g f - mhah (5) Subst i tut ing the value of 1VIw from equa t ion (4) into equa t ion (2) yields Me = lf~f - lh~ll (6) The value of normal ized elbow force (Fe/me + m0 can thus be obta ined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003402_j.ymssp.2015.04.006-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003402_j.ymssp.2015.04.006-Figure1-1.png",
        "caption": "Fig. 1. (a) Section details of 205/55R16 radial passenger car tyre and (b) tyre FE model.",
        "texts": [
            " In Section 3, obtained rolling tyre modal parameters are compared with experimental results reported by Kindt et al. Also to make an assessment of this procedure, the results obtained, is compared with the mode shapes and resonance frequencies of stationary unloaded, stationary loaded and Steady State Transport rolling tyre. Finally, the conclusions are highlighted in Section 4. Passenger car radial tyre of size 205/55R16 has been chosen to construct a Finite Element model. The size is the same as that used by Kindt et al. [30] in their study. Fig. 1(a) and (b) shows the details of the tyre section and a smooth full tyre model that has been developed. The colour group of the tyre section describes the various components and constructional Please cite this article as: S. Palanivelu, et al., Determination of rolling tyre modal parameters using Finite Element techniques and Operational Modal Analysis, Mech. Syst. Signal Process. (2015), http://dx.doi.org/10.1016/j. ymssp.2015.04.006i details of the tyre. The tyre includes two belts and one ply and one protection ply"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001119_ac00115a031-Figure4-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001119_ac00115a031-Figure4-1.png",
        "caption": "Figure 4. Voltammetry (100 V/s) of 1 mM ascorbate in pH 7.4 phosphate buffer at a cleaved 32 pM carbon fiber microelectrode. Right: voltammogram for ascorbate on untreated carbon with an oxidation wave at > 1100 mV. Left: voltammogram for ascorbate on the electrocatalytic surface of a pretreated electrode with a oxidation wave at 283 mV.",
        "texts": [
            "; Kuhr, W. G.; Wightman, R M. Anal. Chem. (49) Allred, C. D.; McCreery, R L. Anal. Chem. 1992, 64, 444-448. (50) Kovach, P.; Wilson, R L; Ewing, A G.; Wightman, R M.J. Neurosci. Methods 1983,55, 1632-1634. 1984, 10, 215-227. and DOPAC. The Ell2 was 285 mV for the bare surface F i r e 3, bottom left) and 208 mV for the electrocatalytic surface (Figure 3, bottom right). Fast Scan Voltammetry of Redox Species. Ascorbate, which classically has shown an oxidation wave at high overpotentials at 100 V/s (Figure 4, left), exhibits variable voltammetry at bare carbon surfaces. This is dramatically more reversible at an electrocatalytic surface (Figure 4, right). Not only is the overpotential for the oxidation of ascorbate decreased (as evidenced by the large change in the E I / ~ observed under steadystate voltammetric conditions, Table 2), but the apparent kinetics are much faster as well (as shown by the shift in the observed peak potential for the oxidation of ascorbate at fast scan rates, Table 1). This is clearly indicated by a well-defined peak at 283 mV, even at scan rates of 100 V/s (Figure 4, right), rather than the long and drawn out peak of the untreated electrode F i r e 4, left). Several other redox species were examined at 100 V/s as well (Figure 5). Dopamine (Figure 5, top) was marginally less reversible at the electrocatalytic surface than on the untreated carbon surface. However, DOPAC (Figure 5, middle) and uric acid (Figure 5, bottom) are more reversible on the electrocatalytic surface than on an untreated carbon surface. These results are summarized in Table 1. General observations of these data would indicate that the electrocatalytic properties are most dramatic for negatively charged species (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001930_j.nonrwa.2008.02.014-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001930_j.nonrwa.2008.02.014-Figure2-1.png",
        "caption": "Fig. 2. The i th limb of the manipulator [9].",
        "texts": [
            " Here we study an offset 3-UPU (Universal\u2013Prismatic\u2013 Universal) parallel manipulator with an equal offset in its six universal joints, as shown in Fig. 1 [9]. A special 3-UPU parallel manipulator with zero offsets in the six universal joints was proposed by Tsai in 1996 [10,11]. Tsai\u2019s 3-UPU manipulator has three extensible limbs (legs) that connect the base to the mobile platform through universal joints, and it can provide a 3-DOF pure translational motion [9]. Due to zero offsets in the universal joints, the kinematics of the manipulator is simple and straightforward [10]. Fig. 2 shows a schema of the i th limb (i = 1, 2, 3), which connects point B on the mobile platform and point A on the base by a passive universal (U) joint, an active prismatic (P) joint, and another passive universal (U) joint. So, it is called a 3-UPU parallel manipulator [9]. For the convenience of kinematics analysis, three local frames, namely; \u03a31 : O X1Y1 Z1, \u03a32 : O X2Y2 Z2, and \u03a33 : O X3Y3 Z3, are set up and attached to the base in order to represent the position and the first axis of a universal joint",
            " Since each branch limb can be regarded as a 3-DOF serial manipulator with its joint variables {\u03b81i , \u03b82i , L i }. Point Op in a local frame \u03a3i (i = 1, 2, 3) can be represented as:X i Yi Zi  = {Ai Bi } + 0 0 r \u2212  0 0 rp  (i = 1, 2, 3), (8) where {X i , Yi , Zi } is the coordinates of Op in the local frame \u03a3i (i = 1, 2, 3), r is the circumradius of triangle \u2206A1 A2 A3 in the base (shown in Figs. 2 and 3) and rp is the circumradius of triangle \u2206B1 B2 B3 with the circumcenter Op in the mobile platform (shown in Figs. 2 and 4) [9]. From Fig. 2, the vector from Ai to Bi in a local frame \u03a3i (i = 1, 2, 3) is: {Ai Bi } = (L i cos \u03b82i + 2e) cos \u03b81i (L i cos \u03b82i + 2e) sin \u03b81i L i sin \u03b82i  (9) where L i is the length of i th prismatic joint, e is the offset in a universal joint and \u03b81i and \u03b82i are the rotation angles around its corresponding axis (shown in Fig. 2) [9]. Substituting the value of Ai Bi from Eq. (9) into Eq. (8), upon simplifications, yields [9]:X i Yi Zi  = (L i cos \u03b82i + 2e) cos \u03b81i (L i cos \u03b82i + 2e) sin \u03b81i L i sin \u03b82i + dr  (i = 1, 2, 3), (10) where dr = r \u2212 rp. For solving this system of nonlinear equations we can use the homotopy continuation method. Assuming the geometric parameters of the manipulator as: e = 0.182, dr = 0.382, X i = 0.5, Yi = \u22121.5 and Zi = 1, we can rewrite Eq. (10) in the following simultaneous non-linear forms: f = (L i cos \u03b82i + 2\u00d7 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.16-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0002974_b978-0-08-097016-5.00001-2-Figure1.16-1.png",
        "caption": "FIGURE 1.16 \u2018Four-wheel\u2019 steering to make slip angle b \u00bc 0 (Exercise 1.2).",
        "texts": [
            " It is of interest to see that the steady-state slip angle response, indicated in (1.79), changes sign at a certain speed V. At low speeds where the tire slip angles are still very small, the vehicle slip angle obviously is negative for positive steer angle (considering positive directions as adopted in Figure 1.11). At larger velocities, the tire slip angles increase and, as a result, b changes to the positive direction. Exercise 1.2. Four-Wheel Steer at the Condition that the Vehicle Slip Angle Vanishes Consider the vehicle model of Figure 1.16. Both the front and the rear wheels can be steered. The objective is to make the vehicle move at a slip angle b remaining equal to zero. In practice, this may be done to improve handling qualities of the automobile (reduces to first-order system!) and to avoid excessive side slipping motions of the rear axle in lane change maneuvers. Adapt the equations of motion (1.46) and assess the required relationship between the steer angles d1 and d2. Do this in terms of the transfer function between d2 and d1 and the associated differential equation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure7-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure7-1.png",
        "caption": "Fig. 7 Some legs for PPR-PKCs.",
        "texts": [
            "2 ci = 0 Theoretically, any six R and P joints the twists of which are linearly independent together with a PPR Vchain constitute a 3-DOF single-loop kinematic chain. The type of a leg for PPR-PKCs can be represented by a chain of characters representing the type of joints from the base to the moving platform in sequence. By removing the V-chain in a 3-DOF single-loop kinematic chain involving a V-chain, one leg for PPR-PMs can be obtained. For example, by removing the V-chain in an (RRR)E(RR)SV Copyright  2004 by ASME rms of Use: http://www.asme.org/about-asme/terms-of-use Down kinematic chain [Fig. 6(d)], an (RRR)E(RR)S leg [Fig. 7(d)] can be obtained. Figure 7 shows some legs for PPR-PKCs and their leg-wrench systems. The leg-wrench system of the (RRR)ERC leg [Fig. 7(b)] is a 1-\u03b60-1-\u03b6\u221e-system. Its basis can be represented by a \u03b6\u221e whose axis is perpendicular to the axes of all the R joints within a same leg and a \u03b60 whose axis intersects the axes of the RC joint and is parallel to the axes of the R joints within (RRR)E . The leg-wrench systems of the RA(RRR)Y RA leg [Fig. 7(e)] and the (RR)Y (RRR)Y A leg [Fig. 7(f)] are both a 1-\u03b6\u221e-system. The axis of the basis wrench \u03b6\u221e is perpendicular to the axes of all the R joints within a same leg. All the legs for PPR-PMs obtained are listed in Table 1. For legs with ci = 0, one are interested in legs with simple structures: RUS, PUS and UPS legs [1]. By assembling two or more legs for PPR-PKCs shown in Table 1, we obtain PMs in which the moving platform can undergo a PPR motion (Fig. 8). The geometric relation between different legs has also been shown in the notation of legs we proposed in Section 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003624_j.applthermaleng.2015.07.010-Figure1-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003624_j.applthermaleng.2015.07.010-Figure1-1.png",
        "caption": "Fig. 1. Two types of warping deformation.",
        "texts": [
            " Second, large temperature gradient within the friction pair can result in large thermal stress even if it is not subjected to any restrictions. Third, it is assumed that a set of friction pair is composed of one friction disk and one separator disk that aremade of differentmaterials. Even if the efficiency of heat conduction within one of the disks is the same as the other, large thermal stress can also be induced by different thermal properties of thematerials. Two types ofwarping deformation can be observed, as shown in Fig. 1, in the special experimental conditions [1]. There is a rich volume of archival research publications dealing with the thermoelastic problems. The earliest work in this field can be traced back to Barber [2], who conducted a detail investigation on the mechanism for thermoelastic instability (TEI). Many direct transient simulations on the thermoelastic effects were also performed in various research groups (Zagrodzki et al. [3]; Kennedy and Ling [4]; Afferrante et al. [5]) P. Zagrodzki [6] found that thermal deformations could have a great influence on the distributions of normal pressure on the friction surfaces of a multidisc clutch or a brake"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0001186_detc2004-57472-Figure14-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0001186_detc2004-57472-Figure14-1.png",
        "caption": "Fig. 14 Some 3-DOF PPR-PMs of family 2.",
        "texts": [
            " In addition, variations of 3-DOF PMs can be obtained in the following way: (a) substitute a combination of one R and one P joints with parallel axes with a C joint or one of its equivalents [9]; (b) substitute a combination of two successive R joints with non-parallel axes with a U joint; (c) substitute a combination of three successive R joints with concurrent axes with an S joint; 8 loaded From: http://proceedings.asmedigitalcollection.asme.org/ on 01/15/2018 Term (d) substitute one or more P joints each with a planar parallelogram [18, 27]; (e) substitute two of three successive P joints with a spatial parallelogram [42]; (f) substitute one or more R joints in the leg with a ci-\u03b6\u221esystem each with a coaxial H joint. For example, PPR-PMs proposed in [33] are in fact the variations of the PPR-PMs shown in Fig. 14, which are obtained by (a) substituting a combination of two successive R joints with non-parallel axes with a U joint and (b) replacing the unactuated P joints each with a planar parallelogram. Figure 15 shows a 2- RPU-UPU PPR-PM under our current investigation. It is in fact obtained from the 2-(RPR)ERC-RA(RPR)Y RA PPR-PMs shown in Fig. 12(b) by substituting a combination of two successive R joints with non-parallel axes with a U joint. Virtual chains have been introduced to represent the motion patterns of 3-DOF motions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_10_0003470_s12206-015-0901-8-Figure2-1.png",
        "original_path": "designv10-10/openalex_figure/designv10_10_0003470_s12206-015-0901-8-Figure2-1.png",
        "caption": "Fig. 2. Dynamic model of the wind turbine gearbox transmission system.",
        "texts": [
            " For the planetary gear system, each gear was modeled as rigid body and represented using three translational coordinates (x, y, z) and one rotational coordinate (\u03b8). The static coordinates oxyz are defined for the sun gear, ring gear and carrier with the origin in the center of the carrier, respectively. The five moving coordinates ouvw are defined for the planet gears with the origin in the center of the planet gears, respectively. The counterclockwise direction of each component in the corresponding coordinate system is positive. The dynamic model of the high-power gearbox transmission system is established as shown in Fig. 2. \u03b8c,s,r,pi represent the torsional vibration displacement of carrier, sun gear, ring gear and the ith planet gear, respectively. Kcx,sx,rx (Ccx,sx,rx) are the support stiffness (damping) of carrier, sun gear and ring gear in x direction, respectively. Kcy,sy,ry (Ccy,sy,ry) are the support stiffness (damping) of the carrier, sun gear and ring gear in y direction, respectively. Kcz,sz,rz (Ccz,sz,rz) are the support stiffness (damping) of the carrier, sun gear and ring gear in z direction, respectively",
            " xr (yr, zr) represents the vibration displacement of the ring gear in x direction (y direction, z direction), respectively. The 2nd transmission stage consists of three helical planet gears. The equivalent displacements along the line of action for the 2nd transmission stage are similar to 1st transmission stage except for the gear geometry parameters and the position angles of the planet gears. Considering the relative position relationship of the wheel and the pinion in the 3rd transmission stage as shown in Fig. 2(b), the equivalent displacement along the line of action can be represented by [13, 14] cos cos ( )cos( / 2 )cos ( )sin( / 2 )cos ( )sin wp w w wb p p wb p w p wp wb p w p wp wb p w wb wp r r x x y y z z e d q b q b j p a b j p a b b = - + - - + + - - + + - + (3) where \u03b4wp represents the equivalent displacement along the line of action of the 3rd transmission stage. rw (rp) is the wheel\u2019s (pinion\u2019s) base circle radius, respectively. xp (yp, zp) is the vibration displacement of the pinion in x direction (y direction, z direction), respectively",
            " The kinematic equations of the ring gear in the 1st stage are 1 1 ( ) / cos ( ) cos 0 N r r r r rpi rpi r b i N r r rpi rpi b i I C C t K K t q q q q d q b q d b = = + + \u00b6 \u00b6 + + = \u00e5 \u00e5 && & (11) 1 1 ( ) / sin( )cos ( ) sin( )cos 0 N r r rx r rpi rpi r i rp b i N rx r rpi rpi i rp b i m x C x C t x K x K t d f a b d f a b = = + - \u00b6 \u00b6 + + - + = \u00e5 \u00e5 && & (12) 1 1 ( ) / cos( )cos ( ) cos( )cos 0 N r r ry r rpi rpi r i rp b i N ry r rpi rpi i rp b i m y C y C t y K y K t d f a b d f a b = = + + \u00b6 \u00b6 + + + + = \u00e5 \u00e5 && & (13) 1 1 ( ) / sin ( ) sin 0 N r r rz r rpi rpi r b i N rz r rpi rpi b i m z C z C t z K z K t d b d b = = + + \u00b6 \u00b6 + + = \u00e5 \u00e5 && & (14) where Ir is the ring gear\u2019s polar mass moment of inertia. ( )r rq q&& & is the vibration acceleration (velocity) of the ring gear in rotational direction. mr is the mass of ring gear. ( )r rx x&& & is the vibration acceleration (velocity) of the ring gear in x direction. ( )r ry y&& & is the vibration acceleration (velocity) of the ring gear in y direction. ( )r rz z&& & is the vibration acceleration (velocity) of ring gear in z direction. As shown in Fig. 2(a), the planet gears are mounted on the carrier via corresponding bearings; the equivalent displacement between the planet gear and the carrier along the corresponding direction of the bearings are shown in the following: cos sinpiu c i c i pix y ud f f= + - (15) sin cospiv c i c i pi cx y vd f f q= - + - + (16) piw c piz wd = - (17) where \u03b4piu (\u03b4piv, \u03b4piw) is the compression deflection between the carrier and the ith planet gear bearing in u direction (v direction, w direction), respectively. The kinematic equations of the ith planet gear are shown as follows: 1 1 1 1 ( ) / cos ( ) / cos ( ) cos ( ) cos 0 N pi pi spi spi pi b i N N rpi rpi pi b spi spi b i i N rpi rpi b i I C t C t K t K t q d q b d q b d b d b = = = = - \u00b6 \u00b6 - \u00b6 \u00b6 - - = \u00e5 \u00e5 \u00e5 \u00e5 && (18) 1 1 ( ) / ( ) / sin cos N pi pi piu pi piu piu pi i N spi spi pi sp b i m u C u C t u C t u d d a b = = + - \u00b6 \u00b6 - \u00b6 \u00b6 \u00e5 \u00e5 && & (19) 1 1 1 1 ( ) / sin cos ( ) ( ) sin cos ( ) sin cos 0 N rpi rpi pi rp b i N piu pi piu piu i N spi spi sp b i N rpi rpi rp b i C t u K u K t K t K t d a b d d a b d a b = = = = + \u00b6 \u00b6 + - - + = \u00e5 \u00e5 \u00e5 \u00e5 1 1 1 1 1 1 ( ) / ( ) / cos cos ( ) / cos cos ( ) ( ) cos cos ( ) cos cos 0 N pi pi piv pi piv piv pi i N spi spi pi sp b i N rpi rpi pi rp b i N piv pi piv piv i N spi spi sp b i N rpi rpi rp b i m v C v C t v C t v C t v K v K t K t K t d d a b d a b d d a b d a b = = = = = = + - \u00b6 \u00b6 + \u00b6 \u00b6 - \u00b6 \u00b6 + - + - = \u00e5 \u00e5 \u00e5 \u00e5 \u00e5 \u00e5 && & (20) 1 1 1 1 1 1 ( ) / ( ) / sin ( ) / sin ( ) ( ) sin ( ) sin 0 N pi pi piw pi piw piw pi i N spi spi pi b i N rpi rpi pi b piw pi i N N piw piw spi spi b i i N rpi rpi b i m w C w C t w C t w C t w K w K t K t K t s d d b d b d d b d b = = = = = = + + \u00b6 \u00b6 - \u00b6 \u00b6 - \u00b6 \u00b6 + + - - = \u00e5 \u00e5 \u00e5 \u00e5 \u00e5 \u00e5 && & (21) where Ipi is the ith planet gear\u2019s polar mass moment of inertia"
        ],
        "surrounding_texts": []
    }
]