[
    {
        "image_filename": "designv10_2_0000588_j.jmapro.2021.02.021-Figure20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000588_j.jmapro.2021.02.021-Figure20-1.png",
        "caption": "Fig. 20. The contour of longitudinal residual stress distribution in Case 5.",
        "texts": [
            " Through the above comparison between the calculated and measured mechanical results, it can be summarized that the established simulation model here is reliable for mechanical analysis. Fig. 18 shows the calculated longitudinal RS distributions in cases 1\u20136 along line 1 and line 2. From Fig. 18, it can be found that the magnitude of longitudinal compressive RS along line 1 increases with the number of layers as in Fig. 18(a), while the magnitude of longitudinal tensile RS along line 2 increases as in Fig. 18(b). This is because the magnitude of bending deflection increases with the number of layers as shown in Fig. 19. Combined with Fig. 20, it can be understood that the magnitude of RS in the substrate increases with the layer number. It should be mentioned that the magnitude of RS in the substrate varies sharply first but then slowly with the layer number as in Fig. 18. This is because the bending deformation changes fast at first but then slowly with the layer number as in Fig. 19. It should be noted that the longitudinal RS is in tension at the beam area in Case 1 and Case 2, while that is in compression in the other cases as seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003942_1.1334379-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003942_1.1334379-Figure4-1.png",
        "caption": "Fig. 4 Mechanism of occurrence of kinematic error due to assembly errors",
        "texts": [
            " The small amplitude, high frequency, components superimposed on this fundamental are believed to occur due to the teeth placement errors. We propose the following explanation of the mechanism of occurrence of the error. The slight misalignment of the circular spline due to assembly errors and/or shaft deflection would cause the flexspline teeth to move deeper ~depth A! into the circular spline on one side of the major axis of the wave generator ellipse than on the opposite side ~depth B!, as shown in Fig. 4. Higher depth of meshing on one side results in moving the load ~for the same motor revolution! faster when the wave generator traverses that side ~angle u1 590\u00b0 in Fig. 4! which in turn results into the negative slope on the kinematic error waveform ~load leads the motor!. During the next 90 degree ~angle u2! of wave generator rotation the load now lags the motor producing positive slope on the kinematic error waveform. This serves as a basic mechanism of occurrence of the fundamental harmonic of the kinematic error based on assembly errors. The basic mechanism remains the same for other assembly errors. 2.2 Flexibility Induced Component of the Kinematic Error. In this section, we show that the kinematic error measured under typical motion of the harmonic drive is composed of the pure component discussed in the previous section as well as a second component induced by the stiffness of the harmonic drive gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.70-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.70-1.png",
        "caption": "Fig. 5.70: A pump driven by 5 microactuators. According to [Mizu93]",
        "texts": [
            " 190 5 Microactuators: Principles and Examples The microactuator was manufactured by the bulk micromachining technique and the sputtering technique using (100) silicon. The membrane consisting of a SiOz layer and a NiCrSi alloy layer will buckle out by 35 f.,tm when a pres sure of 1 kPa is generated. A prototype was subjected to 50,000 work cycles, showing no wear problem. To prove the practicability of this light-operated actuator, researchers have developed and built an original micropump which uses several of these microactuators to realize a worm-like motion, Fig. 5.70. 5.7 Thermomechanical Actuators 191 Five microcells were serially arranged in a diaphragm structure and covered by an acrylic plate; the whole device was mounted onto a glass plate. Two glass capillaries with an inner diameter of 0.9 mm are connected to both sides of the channel to transport the liquid to and from the pump. If there is liquid in the inlet capillary, the diaphragm can be moved in a fashion of passing fire buckets by supplying laser light successively to each microcell. Thereby the liquid is pumped through the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure18-1.png",
        "caption": "Fig. 18. Motion branch of evolved 4R linkage. (a) Motion branch of 4R mechanism (b) Its prototype.",
        "texts": [
            " The screws and the corresponding constraint-screw multiset of the mechanism can be written as follows: S r l1 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 11 = ( 0 , 0 , 0 , 0 , 0 , 1 ) T S r 12 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 13 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 14 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 21 = ( 0 , 0 , 0 , 0 , 0 , 1 ) T S r 22 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 23 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad (21) 24 Apparently, the number of independent loops l is 1. According to Eqs. (9) and (10) , card \u3008 S r \u3009 = 8 , dim S r = 4 . Hence, the mobility is m = 4 \u2212 6(1) + 8 \u2212 4 = 2 . When the evolved 4R linkage moves to the position as shown in Fig. 18 , the axes of joints B 2 , B 4 intersect with an arbitrary angle, but not coincident. The total constraint-screw multiset of the mechanism can be written as follows: S r l1 = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 S r 11 = ( 0 , 0 , 0 , 0 , c \u03c6 s \u03c6 , 1 )T S r 12 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 13 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 14 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 S r 21 = ( 0 , 0 , 0 , 0 , \u2212 s \u03c6 c \u03c6 , 1 )T S r 22 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 23 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 24 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23ad (22) where \u03c6 ( \u03c6 = 0 , \u03c0 ) denotes the angle between the Y-axis and line OB 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure10-1.png",
        "caption": "Fig. 10. Coordinate systems Ss and Sw and worm installment.",
        "texts": [
            " The next step was done by the patent proposed by Litvin et al. [14] that has provided the exact determination of the thread surface of a generating worm that might be applied for grinding and cutting of face gears. The paper covers the solution to the following problems of the design of a grinding worm: (1) Determination of crossing angle between the axes of the shaper and the worm. (2) Determination of worm thread surfaces. (3) Avoidance of singularities of the worm thread surface. (4) Dressing of worm thread surface. Fig. 10 shows fixed coordinate systems Sa, Sb, and Sc applied for illustration of installment of the worm with respect to the shaper. Moveable coordinate systems Ss and Sw are rigidly connected to the shaper and the worm. Axis zs (it coincides with za) is the axis of rotation of the shaper. Axis zw (it coincides with zc) is the axis of rotation of the worm. Axes zs and zw are crossed and form a crossing angle 90 kw. The upper (and lower) sign corresponds to application of a right-hand (left-hand) worm. The shortest distance between axes zs and zw is designated as Ews",
            " Tangency of surfaces Rs and R2 is provided because the normals to Rs pass through point P (Figs. 11 and 14). Step 2: Tangency of surfaces Rs and Rw at point P is observed, if the following equation of meshing between Rs and Rw is satisfied at P [8]: N\u00f0s\u00de v\u00f0sw\u00de \u00bc 0: \u00f03\u00de Here N\u00f0s\u00de is the normal to Rs; vector v \u00f0sw\u00de is determined as v\u00f0sw\u00de \u00bc v\u00f0s\u00de v\u00f0w\u00de, where v\u00f0s\u00de and v\u00f0w\u00de are the velocities of point P of the shaper and the worm. Using Eq. (3), we obtain after derivations that kw \u00bc arcsin rps Ns\u00f0Ews \u00fe rps\u00de : \u00f04\u00de Here rps is the pitch radius of the shaper, and Ews (Fig. 10) is the shortest distance between the axes of the shaper and the worm. The magnitude of Ews affects the dimensions of the grinding worm and the conditions of avoidance of surface singularities of the worm (see below). The meshing of the worm and the shaper is schematically illustrated in Fig. 12. 3.3. Analytical consideration of simultaneous meshing of surfaces Rs, Rw, and R2 Designations Rs, Rw, and R2 indicate surfaces of the shaper, worm, and face gear, respectively. Simultaneous meshing of Rs, Rw, and R2 is illustrated in Fig",
            " 14) determined by the equations xs \u00bc rbs\u00bdcos\u00f0hs \u00fe gs\u00de \u00fe hs sin\u00f0hs \u00fe gs\u00de ; ys \u00bc rbs\u00bd sin\u00f0hs \u00fe gs\u00de hs cos\u00f0hs \u00fe gs\u00de ; zs \u00bc us: \u00f05\u00de Here us and hs are surface parameters; parameter gs determines half of the width of the space on the base cylinder; rbs is the radius of the base cylinder. Parameters hs and gs are shown in Fig. 14; parameter us is directed along the zs axis. The upper and lower signs in equation of ys\u00f0hs\u00de correspond to profiles I and II, respectively. Step 2: The worm surface Rw is determined in coordinate system Sw (Fig. 10) by the following equations [8]: rw\u00f0us; hs;ws\u00de \u00bcMws\u00f0ws\u00ders\u00f0us; hs\u00de; \u00f06\u00de orw ous orw ohs orw ows \u00bc fws\u00f0us; hs;ws\u00de \u00bc 0: \u00f07\u00de Here vector function rw\u00f0us; hs;ws\u00de is the family of shaper surfaces Rs represented in Sw; matrix Mws\u00f0ws\u00de describes coordinate transformation from Ss to Sw; Eq. (7) is the equation of meshing between Rs and Rw. Parameters \u00f0us; hs\u00de in vector function rw\u00f0us; hs;ws\u00de represent the surface parameters of the shaper; parameter ws in rw\u00f0us; hs;ws\u00de is the generalized parameter of motion. We remind that during generation of the worm, the shaper and the worm perform rotations about crossed axes za and zw (Fig. 10). Angles of rotation ws and ww (Fig. 10) are related by the equation ws ww \u00bc 1 Ns \u00f08\u00de where Ns is the number of teeth of the shaper. It is assumed that a one-thread worm is applied. Equation of meshing (7) may be represented as well as [7\u20139] Ns v\u00f0sw\u00des \u00bc fws\u00f0us; hs;ws\u00de \u00bc 0: \u00f09\u00de Vector function rw\u00f0us; hs;ws\u00de and equation of meshing fws\u00f0us; hs;ws\u00de \u00bc 0 represent the worm thread surface Rw by three related parameters. Surface Rw may be represented in form of two parameters by using the theorem of implicit function systems existence [6,21]",
            " Parameters ww and w2 are the angles of rotation of the worm and the face gear related by the equation ww w2 \u00bc N2 Nw \u00f015\u00de where N2 and Nw are the number of teeth of the face gear and the number of threads of the worm. Usually one thread of worm is applied and Nw \u00bc 1. Parameter lw of translational motion is provided as collinear to the axis of the shaper (see below). The following coordinate systems are applied for derivation of the face gear surface: (i) Fixed coordinate system Sb and Sc where we consider the rotation of the worm (Figs. 10 and 11). (ii) Fixed coordinate system Sm where we consider the rotation of the face gear (Fig. 11). (iii) Movable coordinate system Sw rigidly connected to the worm (Fig. 10) and coordinate system S2 rigidly connected to the face gear. Surface R2 of the face gear generated by the worm is determined by the following equations [7,8,21]: r2\u00f0us; hs;ww; lw\u00de \u00bcM2w\u00f0ww; lw\u00derw\u00f0us; hs\u00f0us;ws\u00de;ws\u00de; \u00f016\u00de or2 ous \u00fe or2 ohs ohs ous or2 ows \u00fe or2 ohs ohs ows or2 oww \u00bc 0; \u00f017\u00de or2 ous \u00fe or2 ohs ohs ous or2 ows \u00fe or2 ohs ohs ows or2 olw \u00bc 0: \u00f018\u00de Here, vector function rw\u00f0us; hs\u00f0us;ws\u00de;ws\u00de \u00bc Rw\u00f0us;ws\u00de \u00f019\u00de represents the worm surface. Function hs\u00f0us;ws\u00de is obtained from equation of meshing (7) by using the theorem of implicit function system existence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000841_j.oceaneng.2020.107131-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000841_j.oceaneng.2020.107131-Figure1-1.png",
        "caption": "Fig. 1. Definition of coordinates and state variables of AUV.",
        "texts": [
            " The stability of the proposed controller is also discussed by analyzing the tracking error dynamics and the model estimation errors. Based on the stability analysis results, the characteristics of the closed loop system (an error dynamics including the TDE error) and tuning guideline of control gains are addressed. The tracking performance of the proposed controller is demonstrated through numerical simulations using REMUS model. For the simplicity, let us consider the control problem of the vehicles having three DOF (surge, sway, yaw) motion in XY plane. Fig. 1 shows the conceptual diagram including coordinate systems. The dynamics of the vehicles in horizontal plane is described as follows (Fossen, 1994): \ud835\udc0c?\u0307? + \ud835\udc02\ud835\udf42 + \ud835\udc03\ud835\udf42 + \ud835\udc20 + \ud835\udc1d\ud835\udc42\ud835\udc46 = \ud835\udf49 + \ud835\udf49\ud835\udc38 (1) where, \ud835\udf42 \u2261 [\ud835\udc62, \ud835\udc63, \ud835\udc5f]\ud835\udc47 denotes a vector of the velocities (surge, sway, yaw) in body-fixed coordinate, {\ud835\udc35}; \ud835\udc0c \u2261 \ud835\udc0c\ud835\udc45\ud835\udc35 +\ud835\udc0c\ud835\udc34 with \ud835\udc0c\ud835\udc45\ud835\udc35 inertia matrix of rigid body dynamics, and \ud835\udc0c\ud835\udc34 added inertia matrix due to hydrodynamics; \ud835\udc02 \u2261 \ud835\udc02\ud835\udc45\ud835\udc35 + \ud835\udc02\ud835\udc34 with \ud835\udc02\ud835\udc45\ud835\udc35 rigid body Coriolis and centripetal matrix, and \ud835\udc02\ud835\udc34 hydrodynamic Coriolis and centripetal matrix; \ud835\udc03 damping matrix; \ud835\udc20 restoring forces; \ud835\udf49 control inputs; \ud835\udf49\ud835\udc38 environmental disturbances; \ud835\udc1d\ud835\udc42\ud835\udc46 coupled dynamics with other states (heave, roll, pitch)",
            " As a result, it is hard and time-consuming to identify the mathematical model of dynamics as well as essential coefficients for the model. Practically, the modeling error is unavoidable, and may degrade tracking performance when the controller is designed based on the model that is not perfect. Due to the underactuated characteristics, only two trajectory variables in the plane having three DOFs can be designed independently. We can set the independent trajectory variables as x, y in {\ud835\udc4a }; the trajectories can be given as the following continuous time functions: \ud835\udc65\ud835\udc51 = \ud835\udc65\ud835\udc51 (\ud835\udc61), \ud835\udc66\ud835\udc51 = \ud835\udc66\ud835\udc51 (\ud835\udc61). (8) As illustrated in Fig. 1, the desired yaw angle, \ud835\udf13\ud835\udc51 , in {\ud835\udc4a } is dependently derived from (8) as follows: \ud835\udf13\ud835\udc51 = \ud835\udc4e\ud835\udc61\ud835\udc4e\ud835\udc5b2(?\u0307?\ud835\udc51 , ?\u0307?\ud835\udc51 ). (9) From (8) and (9) regarding (7), the desired trajectories for the state variables in {\ud835\udc35} are given as follows1: \ud835\udc62\ud835\udc51 = \u221a ?\u0307?2\ud835\udc51 + ?\u0307? 2 \ud835\udc51 , \ud835\udc5f\ud835\udc51 = ?\u0307?\ud835\udc51 . (10) Note that the derivatives of the desired trajectories in (8) satisfying (9) and (10) are given as follows: ?\u0307?\ud835\udc51 = \ud835\udc62\ud835\udc51\ud835\udc50\ud835\udf13\ud835\udc51 , ?\u0307?\ud835\udc51 = \ud835\udc62\ud835\udc51\ud835\udc60\ud835\udf13\ud835\udc51 . (11) 1 Note that ?\u0307?\ud835\udc51 = \ud835\udc51 \ud835\udc51\ud835\udc61 \ud835\udc4e\ud835\udc61\ud835\udc4e\ud835\udc5b2(?\u0307?\ud835\udc51 , ?\u0307?\ud835\udc51 ) = \u2212 ?\u0307?\ud835\udc51 ?\u0307?2\ud835\udc51+?\u0307? 2 \ud835\udc51 ?\u0308?\ud835\udc51 + ?\u0307?\ud835\udc51 ?\u0307?2\ud835\udc51+?\u0307? 2 \ud835\udc51 ",
            " In details, the tracking error along \ud835\udc65\ud835\udc51 and \ud835\udc66\ud835\udc51 are firstly dealt with by using the control input, \ud835\udf49\ud835\udc50 . Note that, if there are lateral disturbances like sea currents, the yaw angle error may be required intentionally to generate lateral force for overcoming the disturbances. In the subsection, the tracking error dynamics of the vehicle having nonholonomic constraint is arranged as strict feedback form in the desired trajectory coordinate, {\ud835\udc37}. The coordinate {\ud835\udc37} is a moving coordinate which follows the desired trajectory: as shown in Fig. 1, the origin of {\ud835\udc37} is (\ud835\udc65\ud835\udc51 , \ud835\udc66\ud835\udc51 ), and the rotation angle of {\ud835\udc37} with respect to {\ud835\udc4a } is \ud835\udf13\ud835\udc51 . By describing the error dynamics in {\ud835\udc37}, one can attenuate the relationship changes between variables in different coordinates (Xia et al., 2019; Peng et al., 2018): if there is no tracking error, \ud835\udc62 affects \ud835\udc37\ud835\udc65 for every \ud835\udf13 . The transform can be easily accomplished as follows (Craig, 1989): [\ud835\udc37\ud835\udc65,\ud835\udc37\ud835\udc66]\ud835\udc47 = \ud835\udc37 \ud835\udc4a \ud835\udc11[\ud835\udc65, \ud835\udc66]\ud835\udc47 \u2212 \ud835\udc37 \ud835\udc4a \ud835\udc11[\ud835\udc65\ud835\udc51 , \ud835\udc66\ud835\udc51 ]\ud835\udc47 , (12) where, \ud835\udc37 \ud835\udc4a \ud835\udc11 denotes the rotation matrix of {\ud835\udc4a } with respect to {\ud835\udc37}, which is obtained as \ud835\udc37 \ud835\udc4a \ud835\udc11 = \ud835\udc4a \ud835\udc37 \ud835\udc11\ud835\udc47 = [ \ud835\udc50\ud835\udf13\ud835\udc51 \ud835\udc60\ud835\udf13\ud835\udc51 \u2212\ud835\udc60\ud835\udf13\ud835\udc51 \ud835\udc50\ud835\udf13\ud835\udc51 ] "
        ],
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    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure21-1.png",
        "caption": "Fig. 21. Coordinate systems Ss, Sw and worm installment.",
        "texts": [
            " (2) Modified geometry of face-gear drives based on application of a shaper that is conjugated to a parabolic rack-cutter. (3) Concept of generation of face-gears by grinding or cutting worms, analytical derivation of worm thread surface, and its dressing. Nomenclature ai\u00f0i \u00bc d; c\u00de pressure angles for asymmetric face-gear drive for driving (i \u00bc d) and coast (i \u00bc c) sides (Fig. 9) Dc change of shaft angle (Fig. 8) DE change of shortest distance between the pinion and the face-gear axes (Fig. 7) Dq axial displacement of face-gear (Fig. 8) kw crossing angle between axes of shaper and worm (Fig. 21) cm shaft angle (Figs. 4, 8, 12) Ri \u00f0i \u00bc s; 1; 2;w\u00de tooth surface of the shaper (i \u00bc s),the pinion (i \u00bc 1), the face-gear (i \u00bc 2) and the generating worm (i \u00bc w) wj \u00f0j \u00bc r; e\u00de angle of rotation of the shaper (j \u00bc r) and the pinion (j \u00bc e) considered during the process of generation (Fig. 11) wi \u00f0i \u00bc s;w\u00de angle of rotation of the shaper considered during the process of generation of the face-gear (i \u00bc s) and the worm (i \u00bc w) (Figs. 12, 21) wi \u00f0i \u00bc 2;w\u00de angle of rotation of the face gear (i \u00bc 2) and the worm (i \u00bc w) considered during the process of generation (Figs. 12, 21) h\u00f0i\u00de j ; u\u00f0i\u00dej \u00f0j \u00bc s; 1\u00de surface parameters of the rack-cutter for the shaper (j \u00bc s) and the pinion (j \u00bc 1), for driving side (i \u00bc d) and coast side (i \u00bc c) (Fig. 9) Ews shortest distance between the axes of the worm and the shaper (Fig. 21) fd parameter that determines location of point Oq (Fig. 9) Li \u00f0i \u00bc 1; 2\u00de inner (i \u00bc 1) and outer (i \u00bc 2) limiting dimensions of the face-gear (Fig. 4) Lis \u00f0i \u00bc 2;w\u00de lines of tangency between the shaper and the face-gear (i \u00bc 2), the shaper and the worm (i \u00bc w) (Figs. 3,13\u201315) Mji, Lji matrices 4 4 and 3 3 for transformation from Si to Sj of point coordinates and projections of vectors Ni \u00f0i \u00bc s; 1; 2;w\u00de number of teeth of the shaper (i \u00bc s), of the pinion (i \u00bc 1), of the face-gear (i \u00bc 2), of the generating worm (i \u00bc w) p circular pitch P diametral pitch rpj \u00f0j \u00bc s; 1\u00de radius of the pitch circle of the shaper (j \u00bc s) and the pinion (j \u00bc 1) (Figs",
            " Designations Rs, Rw, and R2 indicate surfaces of the shaper, worm, and face-gear, respectively. Simultaneous meshing of Rs, Rw and R2 is illustrated by Fig. 20. Shaper surface Rs is considered as the envelope to the family of rack-cutter As surfaces and is represented by vector function Rs\u00f0wr; hr\u00de (see Eq. (9)). Surfaces Rw and R2 are generated as the envelopes to the family of shaper surfaces Rs. We remind that in the new design the shaper is provided with non-involute profile (see Section 3). Fig. 21 shows fixed coordinate systems Sa, Sb, and Sc applied for illustration of installment of the worm with respect to the shaper. Moveable coordinate systems Ss and Sw are rigidly connected to the shaper and the worm. Axis zs (it coincides with za) is the axis of rotation of the shaper. Axis zw (it coincides with zc) is the axis of rotation of the worm. Axes zs and zw are crossed and form a crossing angle 90 kw. The upper (and lower) sign corresponds to application of a right-hand (left-hand) worm. The shortest distance between axes zs and zw is designated as Ews. The crossing angle kw is kw \u00bc arcsin rps Ns\u00f0Ews \u00fe rps\u00de \u00f027\u00de Here rps is the pitch radius of the shaper, and Ews (Fig. 21) is the shortest distance between the axes of the shaper and the worm. The magnitude of Ews affects the dimensions of the grinding worm and the conditions of avoidance of surface singularities of the worm (see below). The worm surface Rw is determined in coordinate system Sw (Fig. 21) by the following equations [8] rw\u00f0wr; hr;ww\u00de \u00bc Mws\u00f0ww\u00deRs\u00f0wr; hr\u00de \u00f028\u00de oRs owr oRs ohr v\u00f0s2\u00des \u00bc fws\u00f0wr; hr;ww\u00de \u00bc 0 \u00f029\u00de Here relative velocity v\u00f0s2\u00des is determined by differentiation and transformation of matrix Mws that are similar to derivations in Section 5.2; vector function rw\u00f0wb; hb;ww\u00de is the family of shaper surfaces Rs represented in Sw; matrix Mws\u00f0ww\u00de describes coordinate transformation from Ss to Sw; Eq. (29) is the equation of meshing between Rs and Rw. Parameters (wr; hr) in vector function Rs\u00f0wr; hr\u00de represent the surface parameters of the shaper; parameter ww is the generalized parameter of motion in the process of generation of the worm by the shaper. We remind that during generation of the worm, the shaper and the worm perform rotations about crossed axes za and zw (Fig. 21). Angles of rotation wws and ww (Fig. 21) are related by the equation ww wws \u00bc 1 Ns \u00f030\u00de where Ns is the number of teeth of the shaper. It is assumed that a single-thread worm is applied. Eqs. (28) and (29) represent the worm surface Rw by three related parameters. We may represent Rw in two-parameter form using the following procedure: i(i) We apply the theorem of implicit function system existence [6,22] and consider that one of the derivatives of fws, say ofws=owr, is not equal to zero. (ii) Then, we can solve equation fws \u00bc 0 by function wr\u00f0hr;ww\u00de 2 C1 and represent the worm surface Rw by rw\u00f0wr\u00f0hr;ww\u00de; hr;ww\u00de \u00bc Rw\u00f0hr;ww\u00de \u00f031\u00de 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000106_tie.2020.3029463-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000106_tie.2020.3029463-Figure1-1.png",
        "caption": "Fig. 1. The topology of the SSRM.",
        "texts": [
            " 2) To further improve anti-disturbance ability and robustness in the case of load disturbances, ATSMC is presented based on the rate of change rate in load torque without the load torque disturbance limit. The remainder of this paper is organized as follows. Section \u2161 presents the novel RL based on DITC system. The proposed ATSMC is given in Section III. To verify the effectiveness of ATSMC, simulation and experimental results are provided in Section I\u2164, followed by the conclusion in Section V. II. A NOVEL REACHING LAW BASED ON DITC SYSTEM Fig. 1 shows the topology of the SSRM with 16/10 stator/rotor poles. The stator of this SSRM consists of an equal number of excited poles and auxiliary poles. The excited poles are wound by windings, while the auxiliary poles are only functioned as flux return paths without any windings. The rotor is made up of a series of discrete segmented-rotors [34]. The total output torque is taken as its control object in DITC. The turn-on, turn-off and continuation states of the conduction Authorized licensed use limited to: Carleton University"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure26-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure26-1.png",
        "caption": "Fig. 26. Contact and bending stresses for proposed geometry of face-gear drive generated with edged-top shaper.",
        "texts": [],
        "surrounding_texts": [
            "Finite element analysis has been performed for the two versions of face-gear drives represented in Tables 1 and 2. For the second version of face-gear drive, it has been also considered the application of a rounded top shaper (Fig. 5), in order to compare the bending stresses at the fillet of the generated face-gear. The finite element mesh of three pair of teeth of version 2 is represented in Fig. 24. Elements C3D8I [5] of first order, enhanced by incompatible nodes to improve their bending behavior, have been used to form the finite element mesh. The total number of elements is 44820 with 58327 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Figs. 25 and 26 show the maximum contact and bending stresses obtained at the mean contact point for the existing and the proposed geometry, respectively. For such examples a traditional edged-top shaper has been applied. Comparison between Figs. 25 and 26 shows that: i(i) Edge contact can be avoided, reducing the magnitude of the maximum contact stress to 40%. (ii) For a considerable part of the cycle of meshing only one pair of teeth is in contact. The max- imum bending stress at the fillet of the existing geometry of face-gear is 43% lower. Fig. 27 confirms that application of a rounded-top shaper (Fig. 5) reduces the bending stresses of the face-gear from 6% to 12% during the cycle of meshing. This enables us to keep the increment of the bending stresses for the proposed geometry less than 40%. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs. 28 and 29). Figs. 28 and 29 illustrate the variation of bending and contact stresses of the face-gear and the pinion during the cycle of meshing for face-gear generated with an edged-top shaper and a rounded-top shaper, respectively. The stresses are represented as functions of unitless parameter / represented as / \u00bc /P /in /fin /in ; 06/6 1 \u00f034\u00de Here /P is the pinion rotation angle, /in and /fin are the magnitudes of the pinion angular positions in the beginning and end of cycle of meshing. The unitless stress coefficient r (Figs. 28 and 29) is defined as r \u00bc rP rPmax ; jrj6 1 \u00f035\u00de Here rP is the variable of function of stresses and rPmax is the magnitude of maximal stress."
        ]
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.13-1.png",
        "caption": "Fig. 8.13 Tire\u2013wheel system with forces acting at tire/road contact point G and at wheel center point O (/ = /0 = \u2212 90\u00b0)",
        "texts": [
            " The above equations show that the torque excitation on a wheel will not cause any radial displacement of a tread ring or any displacement of the wheel center (i.e., T23 = T43 = T53 = 0). This is because the torque will only excite the rotational motion of the tire\u2013wheel system, and the displacement of the tread ring and the displacement of the wheel center are decoupled from the rotational motion. (2) Transfer function from the point contact force to the axle force at a wheel The transfer function from the point force on the contact patch to the force at a wheel is important for riding comfort. Figure 8.13 illustrates a tire\u2013wheel system where the external forces are applied at tire/road contact point G and the resultant forces are generated at the wheel center point O. 8.3 Frequency Response Function of Tires 493 Referring to Fig. 8.13, / = /0 = \u2212 90\u00b0 is satisfied for matrix [T] in Eq. (8.155). The transfer function matrix between the wheel (Hr, X, Z, T, Fx and Fz at point O) and the point on the tire surface (V, W, Pv and Pw at point G) is then given by V W Hr X Z 8>>< >>: 9>>= >>; \u00bc H11 H12 H13 H14 0 H21 H22 0 0 H25 H31 0 H33 0 0 H41 0 0 H52 0 0 H44 0 0 H55 2 6664 3 7775 Pv Pw T Fx Fz 8>>< >>: 9>>= >>; ; \u00f08:156\u00de where the elements of the transfer function [Hij] are shown in Appendix 3. Note that the two transfer functions H12 (the tangential displacement response of the tread ring V to the radial force excitation Pw at the same point) and H21 (the radial displacement response of the tread ring W to the tangential force excitation Pv) have the same magnitude but opposite signs, and they come from the Coriolis effect of the rotating system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.33-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.33-1.png",
        "caption": "Fig. 5.33: Rigid and Elastic Bodies",
        "texts": [
            " Thus the phase shifts of a complete planetary gear can be computed starting from a gear train including the sun gear. Starting with the principles of linear and angular momentum or with Jourdain\u2019s principle of virtual power, the equations of motion for rigid and elastic bodies are derived, see chapters 3.3 on page 113 and 3.4 on page 131. Combining the equations of the single components the differential equations of motion of the whole multibody system can be set up. 5.2 Ravigneaux Gear System 251 The equations of motion of a rigid body represent a base for the description of a multibody system. Figure 5.33 shows a rigid body with mass m, inertial tensor IS regarding the center of gravity S and external force FA \u2208 IR3 and torque MA \u2208 IR3 acting in point A separated from S by the vector rSA. The translational velocity of the center of gravity is called vS \u2208 IR3 and the associated acceleration aS = v\u0307S . The rotational speed is \u03c9 \u2208 IR3. Introducing the vectors of the generalized coordinates q, velocities q\u0307 and accelerations q\u0308 the principles of linear and angular momentum yield the classical multibody equations of motion ( JS JR )T ( mE 0 0 IS )( JS JR ) q\u0308+ + ( JS JR )T [( 0 \u03c9\u0303IS\u03c9 )( mE 0 0 IS )( \u03b9S \u03b9R )] \u2212 ( JA JR )( FA MA ) = 0. (5.73) The dimension of these equations is f, according to the number f of degrees of freedom, q \u2208 IRf . The Jacobians are defined by JS = \u2202vS \u2202q\u0307 and JR = \u2202\u03c9 \u2202q\u0307 . The magnitudes \u03b9S and \u03b9R are generated by the partial time derivation \u03b9S = J\u0307Sq\u0307 and \u03b9R = J\u0307Rq\u0307. Elastic bodies can be integrated into the structure of multibody systems [28]. Figure 5.33 shows an elastic body in undeformed and deformed state as well as several coordinate systems associated with the body: the inertial system I, a reference frame B coinciding with the undeformed body and a body fixed system K for the deformed body. The external force FA \u2208 IR3 and the torque MA \u2208 IR3 are acting in point A. Jourdain\u2019s principle of virtual power leads to the equations of motion of an elastic body in the form \u222b mi ( \u2202Bv \u2202q\u0307 ) (Ba\u2212 BfA)dm = 0 (5.74) where a is the absolute acceleration of the mass element dm and fA \u2208 IR6 the vector of the external forces and moments on the mass element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000262_j.oceaneng.2020.107107-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000262_j.oceaneng.2020.107107-Figure1-1.png",
        "caption": "Fig. 1. Definition of the earth-fixed \ud835\udc42\ud835\udc4b0\ud835\udc4c0 and the body-fixed \ud835\udc34\ud835\udc4b\ud835\udc4c coordinate frames.",
        "texts": [
            " If { \ud835\udc651, \ud835\udc652,\u2026 , \ud835\udc65\ud835\udc5b } \u2208 \u211c and \ud835\udc5d > 0, then (| | \ud835\udc651|| + | | \ud835\udc652|| +\u22ef + | | \ud835\udc65\ud835\udc5b||)\ud835\udc5d \u2264 max(\ud835\udc5b\ud835\udc5d\u22121, 1)(| | \ud835\udc651|| \ud835\udc5d + | | \ud835\udc652|| \ud835\udc5d + \u22ef + | | \ud835\udc65\ud835\udc5b|| \ud835\udc5d). If \ud835\udc5d = \ud835\udc5a\u2215\ud835\udc5b \u2264 1, then | | \ud835\udc651\ud835\udc5d \u2212 \ud835\udc652\ud835\udc5d|| \u2264 21\u2212\ud835\udc5d| | \ud835\udc651 \u2212 \ud835\udc652|| \ud835\udc5d, where \ud835\udc5a and \ud835\udc5b are odd integers. Lemma 3 (Zuo, 2015). If the system satisfies the following ?\u0307? = \u2212\ud835\udc591\ud835\udc60\ud835\udc56\ud835\udc54\ud835\udc5a1 (\ud835\udc65) \u2212 \ud835\udc592\ud835\udc60\ud835\udc56\ud835\udc54\ud835\udc5a2 (\ud835\udc65), \ud835\udc65(0) = \ud835\udc650 (3) then the system (3) is fixed-time stable and the settling time is expressed as \ud835\udc47 \u2264 1 \ud835\udc591(\ud835\udc5a1 \u2212 1) + 1 \ud835\udc592(1 \u2212 \ud835\udc5a2) where 0 < \ud835\udc5a2 < 1, \ud835\udc5a1 > 1, \ud835\udc591 > 0, \ud835\udc592 > 0 As shown in Fig. 1, two coordinate systems are commonly defined. \ud835\udc42\ud835\udc4b0\ud835\udc4c0 is the earth-fixed frame, and \ud835\udc34\ud835\udc4b\ud835\udc4c is the body-fixed frame. An MSV for the 3-DOF nonlinear models with neglecting the motions in heave, pitch and roll can be generally formed as (Zhang et al., 2019c) { ?\u0307?=\ud835\udc45(\ud835\udf13)\ud835\udc63 \ud835\udc40?\u0307? + \ud835\udc36(\ud835\udc63)\ud835\udc63 +\ud835\udc37(\ud835\udc63)\ud835\udc63 = \ud835\udf0f + \ud835\udc51 (4) where the vector \ud835\udf02 = [\ud835\udc65, \ud835\udc66, \ud835\udf13]\ud835\udc47 is the actual positions and heading angle in the earth-fixed frame, consisting of the surge position \ud835\udc65, the Ocean Engineering 201 (2020) 107107 sway position \ud835\udc66, and the heading angle \ud835\udf13 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003676_tia.2006.889826-Figure16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003676_tia.2006.889826-Figure16-1.png",
        "caption": "Fig. 16 illustrates the convergence of all of the closedloop system trajectories to the desired solution (\u03d5 = \u03d5e) on \u03d5\u2013\u2126\u2013R\u0303s space for the same initial conditions of Fig. 12. The proposed estimator (20), (21) improves the system performances in such a way that the limit cycle disappears and the sensorless algorithm succeeds in controlling the machine at low speeds in spite of a relatively important error on U0m(\u03b4\u03bd = \u221210%).",
        "texts": [
            " From the resistance estimator (20), (21) and the mechanical subsystem (19), the model of the augmented system can be obtained as follows: 1 p d dt\u03d5 = g(\u03d5, \u03c1) \u00b7 \u2126 + h(\u03c1) J d dt\u2126 = KfIs cos\u03d5\u2212 \u0393L(\u2126) d dt R\u0303s = \u2212\u03b7 tan\u03c1 Rs+R\u0303s f(\u2126, \u03d5, \u03c1) (22a) with g(\u03d5, \u03c1) = (1 + \u03b4\u03bd) cos(\u03d5 + \u03c1) \u2212 cos \u03c1 + D\u03bd sin \u03c1 cos \u03c1\u2212D\u03bd sin \u03c1 h(\u03c1) = (h\u03bd \u2212 hR) cos \u03c1 cos \u03c1\u2212D\u03bd sin \u03c1 f(\u2126, \u03d5, \u03c1) \u223c= [(1 + \u03b4\u03bd + D\u03bd tan \u03c1) sin\u03d5\u2212D\u03bd cos\u03d5]Kf\u2126. (22b) This nonlinear system has an equilibrium point at \u03d5e \u223c= tan\u22121[D\u03bd/(1 + \u03b4\u03bd + Dv tan \u03c1)]. Knowing that |D\u03bd | is often very little (|D\u03bd | 1), \u03d5e is nearby zero. Using Lyapunov\u2019s linearization method, it can be easily shown that this nonlinear system is locally stable around \u03d5e if It must be noted that the resistance estimation error does not vanish (Fig. 16). Indeed, there is a static error on the estimated resistance which compensates the harmful effects of the inverter irregularities and permits the sensorless control to operate correctly even at low speeds. The projection of the system trajectories in \u03d5\u2013\u2126 plane is shown in Fig. 17. In order to evaluate the proposed method performances, a startup test followed by a speed inversion with \u03b4\u03bd = \u221210% is performed. Initial position error is \u03d50 = \u2212\u03c0/3 rd and the stator resistance is well known. As illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.11-1.png",
        "caption": "Fig. 8.11 Fig. 8.12 Fig. 8.13",
        "texts": [
            " For the occurrence of chaos and some basic concepts of two-dimensional mapping, refer to [5] In what follows, we will introduce the most important mathematical theory in studying the two-dimensional mapping-Smale horseshoe theory. Define a horseshoe mapping f: ie ~ ie (ie = ie2 ) being a diffeomorphism. The mapping f contains two steps: 280 Bifurcation and Chaos in Engineering (a) to stretch ~ to a long strip; see Fig. 8.10; (b) to fold the long strip in the middle so that a horseshoe I(~) is formed; see Fig. 8.11. ~nf(~) is composed oftwo lines, that is, 'P, U'P2 \u2022 See Fig. 8.12. Apply mapping I again to ~n/(~), that is, I(~)n~. See Fig. 8.13. ~ splits into two strips 'P\", ~2 and 'P2 into 'P21 \u2022 'P22 . There are 4! kinds of arrangement model for these four strips, and kth horseshoe mapping. Ik (~) n ~ = 2k vertical strip set. When k tends to ao , the width of the strip tends to zero. It forms a (Cantor's set) x (vertical line). Defining an inverse mapping r': ~ ~ ~ then, 1-': ~ ~ ~ as shown in Fig. 8.14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.25-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.25-1.png",
        "caption": "Fig. 2.25: Moment and Moment of Momentum",
        "texts": [
            " An equally great achievement was the finding of Euler [58], that in addition to Newton\u2019s ideas of momentum the laws for the moment of momentum represent independent mechanical statements and cannot be \u201cderived\u201d from the momentum equations, which is sometimes done in older textbooks of mechanics. In the meantime we know, that the moment of momentum equations as usually applied depend on Boltzmann\u2019s axiom or the symmetry of Cauchy\u2019s stress tensor. For polar materials for example these moment of momentum equations must be supplemented by some expressions including the tensor of moment stresses. We consider some rigid or elastic body under the influence of active and passive forces (Figure 2.25), where the active forces contribute to the motion and the passive forces not. We know, that the moment equation of Newton and the moment of momentum equation of Euler are independent laws not derivable from each other. We furtheron assume, that there will exist an inertial coordinate system, where these equations become valid. Therefore and following an idea of [63] we define these two equations in the form of two axioms and write\u222b B (r\u0308dm\u2212 dFa) = 0, \u222b B r\u00d7 (r\u0308dm\u2212 dFa) = 0, (2.146) where r is a vector in an inertial frame I to a mass element dm of the body B, and (dFa) are active forces. With respect to Figure 2.25 we should note, that the passive forces dFp indicated in that Figure are only passive without internal deformations. We have used the definitions \u201ca\u201d for active and \u201cp\u201d for passive. The idea of active and passive forces being used in continuum mechanics for quite a time is more adequate for our considerations than external and internal forces, though in some cases it means the same. But for unilateral problems the features \u201cactive\u201d and \u201cpassive\u201d change during the motion, and therefore the definitions \u201cexternal\u201d and \u201cinternal\u201d do not help so much. As a reminder: active forces can be shifted along their lines of action, passive forces cannot. From this we state, that active forces produce work and power, passive forces not. According to the equations 2.146 (see also Figure 2.25) we define the momentum by p = \u222b B r\u0307dm, (2.147) which is a coordinate-free representation. The velocity r\u0307 is an absolute velocity, and as always, derivations with respect to time have to be performed in an inertial system. On the other hand it is of course possible to transform these equations into any other coordinate system, for example into a body-fixed frame. We come back to this point in chapter 2.3.4. The fundamental laws considering momentum are the famous three laws of Newton, which possess the quality of axioms",
            "3 Momentum and Moment of Momentum 55 To illustrate this basic law, which we find already in the statements of Galilei [259], we shall use the notation introduced by Euler for the momentum and moment of momentum laws. Referring to Axiom 1 we have no external, thus no active forces, which means \u222b B dFa = 0 and therefore \u222b B r\u0308dm = 0 resulting in p = \u222b B r\u0307dm = constant, (2.148) which represents the law of conservation of momentum. Considering the mass center of a body we get pC = pC0 = \u02d9rCm with rCm = \u222b B rdm (2.149) Axiom 2. The rate of change of the momentum of a body is proportional to the resultant external force that acts on the body. For the mass element of Figure 2.25 we get from the first equation 2.146 r\u0308dm\u2212 dFa = 0 (2.150) which represents also the momentum budget for a point mass. The time derivative of the momentum is mass times acceleration if we are dealing with a constant mass, as in the above equation. For not constant masses the time derivative of the mass must be considered in addition. In terms of our definitions we may write dp d t = F, with p = \u222b B r\u0307dm, and F = \u222b B dFa. (2.151) Taking again the center of mass of the body we come out with m( dvC d t ) = FC "
        ],
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    },
    {
        "image_filename": "designv10_2_0003221_s0094-114x(98)00081-0-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003221_s0094-114x(98)00081-0-Figure1-1.png",
        "caption": "Fig. 1. Five-bar with prismatic actuations.",
        "texts": [
            " In such a case, the dynamic analysis of a leg does not yield all the reaction components at the platformconnection. The required number of equations are, however, found by considering the equilibrium of the platform. The resulting system turns out to be a system of di erential algebraic equations with constraints on the legs. In this section, the dynamic formulation strategy is illustrated with two rudimentary planar manipulators, namely \u00aeve-bar 2-DOF manipulators with prismatic and revolute actuations. In addition, 3-DOF planar manipulators are also discussed in brief. The \u00aeve-bar mechanism shown in Fig. 1 is a 2-DOF regional manipulator with the ende ector at point ``p'', the position of which is denoted by t and gives the generalized coordinates. In this case, as the output-point itself is the platform-connection-point (for the point-platform), the analysis starts with the legs. For each of the legs, denoting the leg vector, leg length and unit vector along the leg by S, L and s, respectively (omitting the leg-index for convenience), the position kinematics yields S t\u00ff b; L kSk; s S=L From this, the centres of gravity of the lower and upper parts of the leg are transformed to a \u00aexed frame at the base point parallel to the global frame and are denoted by rd and ru"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000968_j.addma.2021.102203-Figure24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000968_j.addma.2021.102203-Figure24-1.png",
        "caption": "Fig. 24. Nephogram of distortion along the height direction of the part in different path strategies. (a) path strategy 1. (b) path strategy 2. (c) path strategy 3.",
        "texts": [
            " Even layers are from the middle to both sides, and the trend is similar to the SRM path strategy. Fig. 23 presents the von Mises stress distributions of the load-carry frame part in different path strategies. The maximum residual stress is found at the junction of the ends of the bead and the substrate. In path strategy 1, the von Mises on the substrate presents an asymmetric distribution; in path strategy 2, it is symmetrically distributed. In path strategy 3, stress concentration occurs at the midpoint of the weld bead because of the arc striking and extinguishing at this position. Fig. 24 illustrates the nephogram of distortion along the height direction of the part in different path strategies. The maximum distortions along the height direction of path strategy 1, path strategy 2, and path strategy 3 are 4.775 mm, 4.952 mm, and 4.335 mm, respectively. Therefore, the maximum distortion along the height of path strategy 3 is less than the other two path strategies. The path strategy used in the production of actual parts is path strategy 3. Fig. 25 shows the load-carrying frame in commercial aircraft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure7-1.png",
        "caption": "Fig. 7 Condition of tooth surface tangency",
        "texts": [
            " 18 provides even nonlinear scalar equations that can be solved for the seven nknowns. Equations 19 provides six nonlinear scalar equations or the case of Formate gear. Only two of the components of the ormals need to be used because of n1 = n2 =1. In some cases, owever, even if the iteration of Eq. 18 or 19 is successfully onvergent with high accuracy, the TCA result may not be geoetrically correct. This is because the direction of the third comonent of the normals is not taken into account. To avoid this ituation, a modified algorithm illustrated in Fig. 7 has been deeloped by using two tangent vectors of either tooth surface and a ormal vector of the other 13,14,22 . In this paper, we propose a new modified algorithm with reuced number of iterative equations and stabilized convergence. he main idea is to explicitly represent the displacement paramters 1 and 2 in terms of the functions of the surface parameters s 1 = 1 u1, 1, 1,u2, 2, 2 20 ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 2 = 2 u1, 1, 1,u2, 2, 2 21 Equations 20 and 21 are obtained by directly solving the first equation of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000698_j.matdes.2019.107823-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000698_j.matdes.2019.107823-Figure2-1.png",
        "caption": "Fig. 2. Fiber laser narrow gap welding system and procedure: (a) laser welding system; (b) fibe",
        "texts": [
            " 1 displayed the microstructure of Inconel 617 observedwith opticalmicroscope (OM) and scanning electronmicroscope (SEM). The base metal was austenite, which contained annealing twins in the grain. The grain size varied from 20 \u03bcm to 120 \u03bcm. There were many precipitates that were randomly distributing along the grain observed with (a) OM and (b) SEM. boundaries or inside the grains. Based on the elements analysis, the black block-shaped particle was Ti(C, N), the grey particles were M23 (C, N)6 and the white particles were M6C. Fig. 2 showed the fiber laser system and schematic of the experimental setup of the narrow gap laser welding process. As seen in Fig. 2(a)\u2013(b), the welding system was consisted of an IPG continuous wave solid state ytterbium fiber laser system (YLS-10000) and a wire feeder system (TPS-5000). The maximum power was 10 kW and the beam parameter product was 12.5 mm mrad. The diameter of optical fiber was 0.3 mm, and the Rayleigh length was 10.3 mm. The laser and wire feeder system were controlled by a six-axis KUKA welding robot. Thewirewas fed from the front of laser beam, and itwas adjusted to 30\u00b0 to the sheet plane. The experimental setup and groove geometry of the workpiecewas shown in Fig. 2(c)\u2013(d). The first pass with a thickness of 2 mmwas welded by laser beam. Then the groove was filled by the narrow gap laser welding process with filler wire. The groove had a depth of 9 mm and a width of 2 mm. The groove angle was 4\u00b0. Argon shielding gas with a flow rate of 5 l/min was used to protect the weld metal. For the first pass, a laser power (P) of 2.5 kW, a welding speed (VS) of 3 m/min and a defocused distance (D) of 0 mm were employed. For the rest passes, various parameters were considered to obtain the optimum condition, which mainly included laser power, wire feed speed (Vf), and distance between laser beam and wire (SLW)",
            " Lack of fusion between the root weld bead and the deposited weld metal was formed for No. 4. The relationship between the weld parameter, the weld bead geometry and the defect would be discussed in detail next. The influence of SLW on the lack of fusionwas consideredfirstly. During laser welding process with filler metal, the wire tip was primarily melted by the combination of laser irradiation energy (EL), plasma radiation energy (EP), and molten pool radiation energy (EM) [16]. When SLW of 1 mmwas used, as shown in Fig. 2(d), the weld bead wasn't produced under this condition. The filler wirewasmainlymelted by EM and the wire stuck with the molten pool owing to high melting point and high viscosity of Ni-filler metal. This condition was not presented in Table 2. When SLW of 0 mm was used, as shown in Fig. 3(b), the filler wire was simultaneously melted by EL, EM, and EP. Partial laser energy transmitted into the deep part of the weld metal, resulting in a deep and narrow keyhole, as specimen 3 shown in Table 2. The width of the penetration part was narrower than the width of the groove, and the side wall of the groove could not be fully melted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.50-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.50-1.png",
        "caption": "Fig. 7.50: Experimental Test Set-Up for Verification",
        "texts": [
            " For the judgement of the disturbance behavior, the amplitude frequency response function for zG gripper displacement related to zG gripper force is depicted in Figure 7.49. The resonance peak at the first natural frequency vanishes completely, which indicates gripper oscillations to be well damped. However, the starting amplitude is increased. This is due to the trade-off with the mating tolerance criterion, which reduces the cartesian end-effector stiffness. Experimental Verification The optimized configuration is verified experimentally using the test-setup depicted in Figure 7.50. A rigid rectangular peg is assembled into a rigid hole with a clearance of 0.3 mm in xG-direction and an xG offset of 2 mm using a PUMA 562 manipulator. The desired mating path is a straight line in zG-direction with a length of 60 mm and an assembly time of 0.4 s. Forces are measured using a Schunk FTS 330/30 force-torque sensor installed at the robot\u2019s end-effector. The gripper position is reconstructed by measuring the joint encoder angles using the robot\u2019s forward kinematics. For the judgement of impacts, the time histories of the zG gripper force is considered, Figure 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000897_j.oceaneng.2021.108903-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000897_j.oceaneng.2021.108903-Figure3-1.png",
        "caption": "Fig. 3. Definition of \u03b8dand \u03c8din LOS",
        "texts": [
            " 2. In order to facilitate the statements of the formation controller, the guidance law proposed in (Yu et al., 2019) is adopted. According to (Yu et al., 2019) and (Li et al., 2019), the desired point of each follower AUV is defined as: G. Xia et al. Ocean Engineering 233 (2021) 108903 yid = Remark 1. The tracking guidance law proposed in (Yu et al., 2019) is developed by extending the horizontal virtual vehicle method and line of sight (LOS) method (Z. ping Yan et al., 2015). { \u03b8d \u03c8d shown in Fig. 3 is calculated by LOS method. The detailed derivation process refers to the above references, and the conclusion is given directly here. \u23a7 \u23aa \u23a8 \u23aa \u23a9 \u03b8d = arcsin (z \u2212 zd l ) \u03c8d = arctan ( y \u2212 yd x \u2212 xd ) (16) In the leader-following formation considered in this paper, there is a virtual leader which only provides a reference trajectory and virtual attitude information for the follower AUVs. The formation controller need to be designed for the follower AUVs to keep a predefined distance with respect to its virtual leader"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.55-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.55-1.png",
        "caption": "Fig. 16.55 Shear force distribution in the contact patch",
        "texts": [
            " (7.12) is generated in the direction perpendicular to the applied displacement. Because the lateral shear deformation in one shoulder region of a tire is opposite to that in the other shoulder region, a coupled force is generated in the contact patch. This moment is called the pattern steer moment, because this coupled force or a type of RAT rotates the tire about the z-axis. Koehne et al. [29] conducted FEA of the rotation of a tread block with a parallelogram shape under the loading condition. Figure 16.55 shows that lateral and longitudinal forces are generated in the contact patch even for freely rolling tires owing to the bending deformation in the lateral and longitudinal directions. Furthermore, in driving/braking, a force with a triangular distribution in the circumferential direction is added to the shear force in the freely rolling condition. Blocks having a parallelogram shape have commonly been used for tire patterns. The directions of principal axes of the spring rate of the block (referred to as X- and Y-axes) discussed in Chap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003913_es702335y-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003913_es702335y-Figure1-1.png",
        "caption": "FIGURE 1. (A) Schematic diagram of the flow-injection sensing system. (B) 3-D image of the electrochemical flow-cell.",
        "texts": [
            " The mixture was incubated for different time periods, for example, 5, 10, 30, 60, or 120 min. Then 100 \u00b5L of the above mixed solution was subsequently reacted with an equal volume of 5 mM ATCh for 10 min; 40 \u00b5L of the reaction solution was sequentially injected into the sensing system, and the i-t curves were recorded. Flow Injection Sensing System. The laboratory-built flowinjection system consisted of a carrier, a syringe pump (Model 1001, BAS), a sample injection valve (Valco Cheminert VIGI C2XL, Houston, TX), and a laboratory-built flow-through electrochemical cell (Figure 1A). The total carrier volume was 10 mL, and the sample volume was 40 \u00b5L. All flowinjection analyses were conducted at a flow rate of 200 \u00b5L min-1. The laboratory-built microelectrochemical cell was constructed by sandwiching the SPE between a plastic base and a plastic cover with two holes for the inlet and outlet, respectively. A Teflon gasket with a flow channel was mounted between the SPE and the cover to form a flow cell, in which the SPE was exposed to the cell for the electrochemical detection (Figure 1B). Electrochemical Detection. All electrochemical experiments were carried out with an electrochemical analyzer CHI 660 (CH Instruments, Inc., Austin, TX) connected to a laptop computer. A disposable SPE (Alderon Biosciences) was employed that consisted of a CNT-modified electrode as the working electrode, an Ag/AgCl, and a carbon ring as the reference- and counterelectrodes, respectively. A sensor connector was used to connect the SPE to the electrochemical analyzer. Square wave voltammetric (SWV), cyclic voltammetric (CV), and amperometric measurements were performed with the SPE",
            " For SWV measurements, the potential was scanned from 0 to 1.0 V with a step of 4 mV, an amplitude of 25 mV, and a frequency of 15 Hz. A 0.05 M PBS buffer solution (pH 8.0) was used as the supporting electrolyte for electrochemical experiments. The amperometric measurements were conducted at different potentials (e.g., 0.15 V), and all potentials were referred to the Ag/AgCl reference. We developed a CNT-based electrochemical sensor coupled with a flow-injection system for measurement of ChE activities in biological fluids such as saliva (Figure 1). The assay of enzyme activities in saliva is based on the excellent electrocatalytic properties of CNTs, which makes enzymatic products detectable at low potentials with extremely high sensitivity. The amount of enzymatic products that are generated from ChE enzyme depends on the enzyme activity. Therefore, this sensor can measure ChE activities in saliva by sensitively detecting the electroactive enzymatic products. The detection principle of the sensor is based on the following reaction: acetylthiocholine +H2Of ChE thiocholine + acetate (1) The ChE enzyme in saliva can hydrolyze acetylthiocholine to thiocholine, and the latter can be detected at the CNT- VOL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.7-1.png",
        "caption": "Fig. 7.7",
        "texts": [
            " 2nn Only when t = 0, --, ... , are the point co coordinates of these three cases are the same. Take the solution (x(O) = O,y(O) = 0) of the forced linear vibration eq. (7.59) as an example (see Fig. 7.3). The equation on the revelent rotating plane is <;' = -(0.1<; + 0.975'11)sin2 1.6t + (0.975<; + 0.1'11 + 0.625) sin1.6t cos 1.6t '11' = (0.975<; +0.1'11 +0.625)cos2 1.6t +(0.1<; + 0.975'11) sinl.6tcosl.6t (7.63) 246 Bifurcation and Chaos in Engineering The solution corresponding to C;(O) = 0,11(0) = 0 is shown in Fig. 7.7. Its fixed points are C; = C;A = -0.634, 11 =l1A = 0.06. This satisfies eq. (7.63). When t ~ 00, every solution (as the curve in the figure) tends to this fixed point. Now, we average eq. (7.63), and obtain C;' = -0.065C; - 0.487511 11' = 0.4875C; + 0.0511 + 0.3125 (7.64) The solution with the initial condition C;(O) = 0 and 11(0) = 0 is shown in Fig7.8. Comparing it with Fig. 7.7, we can see the averaging results. The fixed points are the same in both figures. Application of the Averaging Method in Bifurcation Theory 247 The general form of the averaging equation of the non-linear forced vibrating system is x\" +ro~x = E/(X,X') + EFcosrot Using the coordinate transformation x = ~cosrot + T\\sinrot x' . - = y = ~smrot + T\\cosrot ro This means adding a condition ~' cos rot + T\\' sinrot = 0 Substituting (7.66) into (7.65), we have (ro~ - ro 2 }~cosrot + (ro~ - ro 2 )T\\sinrot - ro~'sinrot + roT\\' cosrot = E/( ~cosrot + T\\sinrot",
            " For the original vibration system, the motion finally tends to S or S' , depending upon the initial conditions. These two regions are twinned to each other. The proper change of the initial condition will cause great variation in the final stationary states. 252 Bifurcation and Chaos in Engineering The twinning of the two-attractor regions, however, is not the whole of the problem. Fig. 7.13 is the phase diagram of the averaging equation on the rotating plane. Let us discuss again the phase diagram of the averaging equation and the real equation as shown in Fig. 7.8 and Fig. 7.7. Can we guess the type of Fig. 7.7 from Fig. 7.8 ? It is possible in linear systems, because there is only one equilibrium point A. However, it is rather complicated if we guess the real c; plane curves from Fig. 7.13. Roughly speaking, the periodic wave added to the track line in Fig. 7.13 will not be large if the amplitude is not large. So even if the shape of the dividing line is not as smooth as that in Fig. 7.14, we can still divide the plane into two parallel bands, that is to say, there exist two attractor regions. But, if the amplitude of the disturbing force is large enough, then the amplitude of the wave to be added is large"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.28-1.png",
        "caption": "Fig. 6.28: Timing Chain Drive of the Porsche 911 Carrera",
        "texts": [],
        "surrounding_texts": [
            "Figure 6.29 depicts a roller chain and a bush chain together with their models we shall use. In the case of the bush chains the teeth of the sprocket contact directly the pins fixed in the tab plates, whereas in the case of roller chains we have an additional rolling element reducing the friction in the toothroller-contact by rolling without sliding, at least approximately. The external elements comprising two tab plates and two pins do not have contact with the sprocket teeth. Typical chain pitches are 7 mm, 8 mm and 9.525 mm. Double roller chains are applied for larger loads. They possess an additional tab plate in the middle of the double configuration. The link model follows the dissertation [69] of Fritz, who was the first one to present a detailed simulation model of roller chain systems. In the following we shall give some more details (see also [70], [111] and [201])."
        ]
    },
    {
        "image_filename": "designv10_2_0001098_j.matdes.2021.109985-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001098_j.matdes.2021.109985-Figure2-1.png",
        "caption": "Fig. 2. Dimensions and build platform of a) single struts (SS) and b) tensile specimens (ST).",
        "texts": [
            " 1 shows the scan strategies consisting of in-skin and border patterns for samples with diameters of 0.3 and 2 mm and two build orientations. For a sample with a diameter of 2 mm, two borderlines were observed, and a uniform scan pattern was used for the interior region. On the other hand, only a single borderline and no inskin pattern was used for samples with 0.3 mm diameter. In addition, seven single struts (SS) with diameters of 0.3, 0.4, 0.5, 0.75, 1, 1.5, and 2 mm were created with two build angles of 45 and 90 as shown in Fig. 2a. According to Fig. 2a, struts were built on a solid support such that they could be easily removed using the wire electrical discharge machining (wire-EDM). These sample sizes and build angles were chosen as they were normally found in various lattice structures. SS samples were designed to assist the examination of internal and external defects. Therefore, they were built without handles and relatively small size. On the other hand, the tensile samples (ST) shown in Fig. 2b were made for mechanical testing. Consequently, the ST specimens were noticeably larger than SS ones. The ST samples were also made with varying diameters and two build angles. Nonetheless, only four diameters of 0.3, 0.5, 1, and 2 mm were made for the ST samples. Fig. 2b illustrated the dimension of all ST samples, in which the design of the ST samples was modified according to the standard method for tension testing of metallic materials (ASTM E8/ E8M) [35]. The present study classified defects into internal and external types. Internal defects are voids that could be attributed to the lack of fusion, balling effect, keyholing, and the release of gas trapped in powders [13]. The external defects are the geometrical imperfections which are divided into the undersizing/oversizing, diameter variation and the offset of the strut cross sections [11,24,36]",
            " For example, flat defects such as those from the lack of fusion could be harder to identify with the CT in certain orientations. Table 4 summarized the volume fraction of internal voids for all SS samples. The overall volume fraction was less than 1% for all samples. The SS samples with 45 build angle provided a smaller volume fraction of voids than those with 90 build angle. A similar observation was reported by Awd et al. [43] and Murchio et al. [41]. One possible reason could come from the larger melt pool size in samples with 45 build angle as previously mentioned. In addition, according to Fig. 2a, it was noticed that struts were placed onto the solid substrate by the order of their size. Thus, struts, which were placed in the middle, had a higher possibility to be affected by spattering from neighboring struts. Therefore, it was seen in Table 4 that struts with diameters of 0.75 and 1 mm, which were placed in the middle, had higher volume fraction of voids than those with diameters of 0.3 and 2 mm, which were located at the edges of the build substrate. In addition to the mentioned reason, the sample location on the build plate and their relative direction with the gas flow may also have an impact on internal porosities [44,45]",
            " [47], the yielding behaviors of spherical and non-spherical voids differed by about 5%. 4.4. Influence of local properties and the effect of mCT voxel sizes The competition between defects, residual stress, and microstructures on mechanical response are complicated [48]. In previous sections, we evaluated the effect of internal and external defects. Nonetheless, other factors such as residual stress and microstructural features could also play a very important role in mechanical behaviors. Therefore, the ST samples, as described in Fig. 2, were subjected to the mechanical test. The mean diameters shown Table 5 were used for stress calculation. Fig. 12 illustrated experimental results for stress\u2013strain behaviors of the ST samples. A minimum number of three tests were performed for each condition. Reasonable repeatability in experimental results was seen for all samples. According to Fig. 12, size\u2019s dependent behaviors were greatly discernible. The strain at failure reduced significantly with sample\u2019 size. And the samples with 90 build angle had the greater failure strain than those with 45 build angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.55-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.55-1.png",
        "caption": "Fig. 7.55 Pattern of a studless tire [43]",
        "texts": [
            ", studies have investigated the friction coefficient of a rubber block on ice [40], the effect of sipes on the friction coefficient of tires on ice [41\u201345], the friction coefficient of tires on ice and associated rubber characteristics [46], the tire friction coefficient of tires on ice obtained using an analytical tire model [47] and the relationship between the stiffness and performance of tires on ice [48, 49]. A winter tire with studs had superior performance on ice but produced dust pollution by digging into roads that were not covered by snow or ice. Because tires with studs have been prohibited in many countries, a studless tire, which is a winter tire without studs but with many sipes as shown in Fig. 7.55, was developed. Because it is most difficult to drive a vehicle on ice, research has concentrated on increasing the friction coefficient of tires on ice in Japan. The friction coefficient of a studless tire on ice has more than doubled over a period of 20 years as shown in Fig. 7.56. This large improvement mainly resulted from the introduction of compounding technology and sipe technology. A sipe, which is a narrow groove in a block, increases the friction coefficient on ice by not only absorbing water from the interface of the tire and road but also plowing the ice or snow surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure5.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure5.6-1.png",
        "caption": "Fig. 5.6 Fig. 5.7",
        "texts": [],
        "surrounding_texts": [
            "y = x 2 +2xJ +\u00b7\u00b7\u00b7 (5.33b) 164 Bifurcation and Chaos in Engineering If we substitute eq. (S.33b) into the x',Il' equations of eq. (S.31), we obtain the differential equations of flow restricted to the centre manifold: x' = J.!X - x 2 , Il' = \u00b0 (5.34) From the above equations we know that the trivial solutions of the flow are { X = \u00b0 Il = const { Il = x Il = const (5.3S) The phase portrait on the two-dimensional centre manifold is shown III Fig. S.6. If Il is taken as a control variable and x remains a state variable, then Fig. S.6 is a bifurcation diagram. The solution is stable on three-dimensional subspace, because &\" is a null subspace and y is asymptotically stable. If Il = \u00b0 in eq. (S.31), there is a two-dimensional system { x'=-x 2 y' = _y+x 2 (5.36) The eigenvalues at the origin are \u00b0 and -1 whose corresponding eigenvectors are (1,0) T and (0,1) T, so their centre subspace &C and stable subspace &' are (5.37) Seek a one-dimensional centre manifold. From eq. (5.36) we obtain -(/-,) Xo -, 2 reds x(t) = --, yet) = yoe + Xo -- 1+ xot 1 + xos (S.38) where (xo ,Yo) = (x(O),y(O\u00bb. See Fig. 5.7 for the phase portrait on the x - y plane. Suppose a one-dimensional centre manifold is 7I/c = {[; Jly = hex), h:~ ~ ~, h(O) = 0, Dh(O) = o} (5.39) Centre Manifold Theorem and Normal Form of Vector Fields Calculate h( x) by the power series method, and suppose that y = hex) = ax2 +bx3 +cx4+ ... 165 (5.40) If we substitute eq. (5.40) into the second equation of eq. (5.36), and x' is substituted by the first equation of eq. (5.36) we obtain x2 (2ax + 3bx2 + 4cx3 +- .. ) = (ax 2 +bx3 + cx4 + ... ) _ x 2 To compare the same order terms on both side of the above equation we get O(X2) 0= a-I, :. a = 1 O(X3) 2a =b, :. b = 2! O(X4) 3b=c, :. c = 3! It's easy to see that the coefficients of x\" are (n -I)!. Substituting the above coefficients into eq. (5.40), we get y = hex) = x2 + 2x3 + 3!x4 +-. +K!XK+1+... (5.41) '\" Thus is divergent for any x\"* O. LK!XK+1 is meaningless. However, we can prove K=I that eq. (5.41) is asymptotic and valid if x is small enough. If fee 1 , there exists h and h e e-I ; and hEel for any 1 if fEe\"'. Applying Taylor's theorem to h for I=K+1, we get h(x)=x2+2x3+3!x4+.\u00b7+(K-1)!xK+RK(x). Where RK(x)=h(K+I)(S)xK-1 /(K+1)!,(SE[0,xD is called the Taylor remainder. So in a given interval \\x\\< 0, it follows that lsi::; o. Because h(K+I) is continuous on [-0,0], therefore \\h(K+I) (S)\\::; B (constant); for x e[-o,o], we get \\RK(x)\\::; B\\X\\K+I /(K + I)! = B\\X\\K+I , Therefore (5.42) The above expression is an asymptotic expression rather than a series when x -+ O. This example illustrates that h may not be analytic even though f is. Another approach is used to calculate h(x). Substituting eq. (5.40) into the second equation of eq. (5.36) where x' is substituted by the first equation of eq. (5.36), then x 2 dh = h - x 2 , or dh - -;. h = -1. Multiplying both sides of the dx dx x d [.!.] .!. above expression by ellx , we get dx heX = -eX. The integral of the above expression is hex) = e -;[ C - Je;dx l When x -+ 0+, then e-; -+ 0; and when 1 x -+ 0-, then e X -+ 00. So hex) is not continuous at x = o."
        ]
    },
    {
        "image_filename": "designv10_2_0000604_j.mechmachtheory.2019.103627-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000604_j.mechmachtheory.2019.103627-Figure5-1.png",
        "caption": "Fig. 5. Analytical coordinate of rolling bearing and definition of angular parameters.",
        "texts": [
            " f n ( l ) , l \u2208 [ l n \u22123 , l n ] (15) where f i (l) = A i + B i (l \u2212 l i ) + C i (l \u2212 l i ) 2 + D i (l \u2212 l i ) 3 , (i = 1 , 2 , ..., n \u2212 1) ; l i (i = 0 , 1 , ..., n ) is peak point of the fault contour ( l 0 is the first peak point while l n is the last peak point); A i , B i , C i , D i is the fitting parameter; l is the arc length of the rolling element movement. For the damage shown in Fig. 4 (b), its contour obtained by fitting is shown in Fig. 4 (c). For the convenience of derivation, a coordinate system is built up in Fig. 5 . In this figure, \u03d5d represents the angle between the failure position and the X-axis, \u03b81 is the initial angle between the first rolling element and the X-axis, \u03b8 k is the real-time angle position of the kth rolling element, and \u03d5\u03b8 is the angle between the first roller and the fault position. When there is a local damage in the inner ring or out ring, the impulsive effect will occur when the rolling element passes through the damaged area. Considering the coupling effect of the rolling element [35] , the fault fitting excitation function is formulated as: \u23a7 \u23aa \u23a8 \u23aa \u23a9 h i = H max \u2212 f ( R m ( mod ( \u03b8k , 2 \u03c0) \u2212 \u03d5 1 ) ) h k = h i cos ( 2(i \u2212z) \u03c0 z ) , i \u2208 [ 1 , z ] and i = k \u03d5 1 \u2264 mod ( \u03b8k , 2 \u03c0) \u2264 \u03d5 2 h k = 0 otherwise (16) where \u03d51 denotes the angle between the X-axis and the rolling element when it firstly enters the fault region, \u03d52 denotes the angle between the X-axis and the rolling element when it lefts the fault region, and R m is the pitch radius. W In order to obtain the dynamic response of high-speed ACBB, the rolling element of the bearing is regarded as a nonlinear elastic contact body, and the rolling bearing is simplified as a spring-mass system, where the rolling element is simplified as spring and damping element, as shown in Fig. 5 . In this study, we suppose that the outer ring is fixed. Based on the 2-DOF dynamic model, considering the Hertz contact, fault displacement excitation, gyroscopic torque and centrifugal force of the rolling element, the nonlinear dynamic equations of faulty ACBB are established as follows: \u23a7 \u23aa \u23a8 \u23aa \u23a9 m d 2 x d t 2 + c d x d t + z \u2211 k =1 ( \u03bck K ik \u03b4 3 / 2 ik cos \u03b1ik + \u03bbik M gk D sin \u03b1ik + F ck ) cos \u03b8k = W x m d 2 y d t 2 + c d y d t + z \u2211 k =1 ( \u03bck K ik \u03b4 3 / 2 ik cos \u03b1ik + \u03bbik M gk D sin \u03b1ik + F ck ) sin \u03b8k = W y (17) where x and y respectively denote the vibration displacement of ACBB along the X and Y directions, and the acting forces F ix , F iy are expressed as: \u23a7 \u23aa \u23a8 \u23aa \u23a9 F ix = z \u2211 k =1 ( \u03bcik K ik \u03b4 3 / 2 ik cos \u03b1ik + \u03bbik M gk D sin \u03b1ik + F ck ) cos \u03b8k F iy = z \u2211 k =1 ( \u03bcik K ik \u03b4 3 / 2 ik cos \u03b1ik + \u03bbik M gk D sin \u03b1ik + F ck ) sin \u03b8k (18) where \u03b4 ik is the total contact deformation between the inner and the rolling element, and its definition is given by \u03b4ik = ( x cos \u03b8k + y sin \u03b8k \u2212 h k \u2212 \u03b3 ) cos \u03b1ik (19) In the process of numerical calculation, the Newton\u2013Raphson method is first used to solve the positions and forces of rolling element in a period, and then they are fed into the above high-speed bearing fault dynamic model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003416_tfuzz.2004.834803-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003416_tfuzz.2004.834803-Figure1-1.png",
        "caption": "Fig. 1. Scheme of the delta wing: (a) plan view; (b) end view; (c) side view.",
        "texts": [
            " In addition, to relax the requirement for the uncertain bound in the supervisory controller, an estimation mechanism is incorporated to observe the uncertain bound. Thus, the chattering phenomena of the control efforts can be relaxed. Finally, a comparison between the sliding-mode control (SMC) [19], the fuzzy sliding control (FSC) [24] and the proposed SRFNNC is presented. Simulation results verify the effectiveness of the proposed SRFNNC system in achieving favorable control performance with unknown of system dynamic functions. The delta wing for the wing rock motion control is represented schematically in Fig. 1. This wing has one degree of freedom, and the dynamical system includes the wing (a flat uniform plate) and the parts of the string that rotate with it. The aerodynamic rolling moment is a complex nonlinear function of the rolling angle, roll rate, angle of attack and sideslip angle. The nonlinear wing rock equation of motion for an 80 slender delta wing has been developed by Nayfeh et al. [15]. The differential equation describing the wing rock motion is given by [15], [18] (1) where is the roll angle, an over-dot denotes a derivative with respect to time, is the control effort, is the density of air, is the freestream velocity, is the wing reference area, is 1063-6706/04$20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure2-1.png",
        "caption": "Fig. 2. Pitch circles and tooth profiles of pinion and shaper.",
        "texts": [
            " A brief summary of obtained results is as follows. Localization of the bearing contact between the tooth surfaces of the involute pinion and the face-gear is achieved as follows: (1) The face-gear is generated by an involute shaper with tooth number Ns > Np, where Ns and Np are the tooth numbers of the shaper and the pinion of the drive. Usually, Ns Np \u00bc 2 or 3 for the purpose of localization of bearing contact of the gear drive. (2) The shaper and the pinion of the drive are in an imaginary internal tangency as shown in Fig. 2. (3) We may consider that three surfaces Rs, R2, and R1 are in mesh simultaneously. The surfaces of the shaper Rs and the face-gear R2 are in line tangency at every instant. However, surface R2 and pinion surface R1 are in tangency at a point at every instant since Np < Ns. The tooth surfaces R2 of the face-gear generated by an involute shaper are shown in Fig. 3(a). Lines L2s represent the instantaneous lines of tangency of R2 and shaper Rs, shown on R2. The cross-sections of the face-gear tooth are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000698_j.matdes.2019.107823-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000698_j.matdes.2019.107823-Figure5-1.png",
        "caption": "Fig. 5. Schematic diagram of charpy impact test's specimen.",
        "texts": [
            " Tensile tests at room temperature were conducted by a Zwick-Z100 universal material machine with a speed of 0.5 mm/min. For high temperature test, the specimens were held at 750 \u00b0C, 850 \u00b0C and 950 \u00b0C for 10 min to obtain a homogeneous temperature distribution, and tensile test was done by a ZwickZ50 universal material machine with a speed of 0.5 mm/min. Charpy V impact test was conducted using a 300-J instrumented impact tester. The charpy impact test's specimenwasmachined according to GB264989, and schematic diagramof specimenwas shown in Fig. 5. Vickersmicrohardnessmeasurement of cross-sectionwas carried out under a load of 200gf and a sustaining time of 15 s. r laser; (c) schematic of laser welding procedure and (d) the groove geometry of the joint. The filling-pass welding process was performed. Different parameters were considered to obtain the optimum condition, which mainly included P, Vf, and SLW. Among them, P varied from 2.5 to 3.5 kW, Vf varied from 1 to 2 m/min, and SLW varied from \u22121 to 1 mm. The results were displayed in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure13.73-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure13.73-1.png",
        "caption": "Fig. 13.73 Model of tire contact. Reproduced from Ref. [5] with the permission of Sankaido",
        "texts": [
            " (1) Equivalent mass of a vehicle considering the rotational inertia of all rotating parts (tire\u2013wheel, drive train, engine): Mvehicle!+4%. (2) Equivalent mass of a tire\u2013wheel assembly: Mtire+wheel!+50%. Figure 13.72 shows forces resisting movement in an elementary urban driving cycle as defined by Directive 98/69/EC. This calculation uses a vehicle mass of 1100 kg, aerodynamic drag ACD of 0.65 m2, RRC of 12 kg/t, internal friction of 50 N and engine power of 51 kW. Note 13.3 Load Factor [5] The load capacity in the regulation of JIS (JIS D4202), W (kg), is defined by Fig. 13.73 1008 13 Rolling Resistance of Tires Notes 1009 W \u00bc K 4 10 4 p0:585 D\u00fe S\u00f0 \u00deS1:39; S \u00bc S1 180 sin 1 W1 S1 =141:3; \u00f013:147\u00de where K is the coefficient for the load capacity, p is the inflation pressure (kg/cm2), D is the wheel radius calculated as the product of the nominal rim diameter code and 25.4 (mm), S1 is the section width of a tire (mm), W1 is the wheel width (mm), and S is the virtual section width of a tire when a tire is mounted on the rim, which is 62.5% of the tire width S1. The above equation is derived assuming that when a tire with width S1 is mounted on a rim with widthW1, the cross-sectional shape of the tire is a circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003299_tfuzz.2003.819837-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003299_tfuzz.2003.819837-Figure3-1.png",
        "caption": "Fig. 3. Pole-balancing robot system.",
        "texts": [
            " Two examples on designing tracking controller for pole-balancing robot system and ship autopilot system are given in this section. The former has an unknown input gain function and the latter unknown input gain constant . We shall find the adaptive fuzzy robust tracking controllers by following the design procedures given in the previous section. Simulation results will be presented. To demonstrate the effectiveness of the proposed algorithms, a pole-balancing robot is used for simulation. The Fig. 3 shows the plant composed of a pole and a cart. The cart moves on the rail tracks in horizontal direction. The control objective is to balance the pole starting from an arbitrary condition by supplying a suitable force to the cart. The same case studied has been given in [43]. The dynamic equations are described by (42) where is the angular position from the equilibrium position and . Suppose that the trajectory planning problem for a weight-lifting operation is considered and this pole-balancing robot system suffers from uncertainties and exogenous disturbances"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000960_jiee-1.1921.0036-Figure19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000960_jiee-1.1921.0036-Figure19-1.png",
        "caption": "FIG. 19.",
        "texts": [
            " 15 here), let us endeavour to translate the Another 3-lobed figure of a rather imperfect type is shown in Fig. 18, derived from Fig. 17 (c). It should now be obvious from the examples we have discussed that any winding which yields a vector diagram approximating sufncfently closely to our original lobed figure can be used as a cascade secondary. For instance, (c) in Fig. 17 may be much improved by the addition of some further conductors, thereby making \u2022 it practically equal to Fig. 14. Diagrams of this improved winding and its vector diagram are shown in Fig. 19. Fig. 19 is a vector diagram and diagram of connections for a winding having 36 slots connected as shown, which has merely been built up empirically so as to give a vector polygon as close as possible to \u00abthe ideal curve, which it approaches very closely. No attention has been paid to determining whether such a winding can be arrived at by superposing two other windings, and the principal object of explaining it is to make it clear that this is not in any sense a necessary condition, and that the sole condition to be met is that it shall conform as closely as possible to the ideal curve",
            " Diametrically opposite coils of the second star-connected winding may, however, be permanently connected in parallel, for instance terminals T3 to T7 (Fig. 23) where the even-numbered coils represent the extra winding, and five slip-rings are used to make the other FIG. 37. parallel connections when required. Fig. 37 shows the vector polygon corresponding to this winding. It will be seen that it is remarkably close to the ideal curve shown for the case of five phases in Fig. 25 (a). This winding is clearly a generalization to five phases of the winding shown in Fig. 19. Winding (4).\u2014Another convenient winding for the same purpose is a two-coil-per-slot drum winding having 40 slots (see Fig. 38). A winding having a pitch one to four is wound in these slots, two full and two blank coming alternately, if we consider the upper conductors only. The winding is divided into 10 units, each unit being made up as follows. The turn consisting of the upper conductor of slot 1 and the lower of slot 4 is connected in series reversed with the turn consisting of the upper conductor of slot 4 and the lower of slot 7 by a connection between the lower conductors of slots 4 and 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003426_s0094-114x(97)00094-3-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003426_s0094-114x(97)00094-3-Figure1-1.png",
        "caption": "Fig. 1. Kinematic redundancy and force redundancy.",
        "texts": [
            " On the other hand, static or force singularities in a parallel manipulator restrict its load-carrying capabilities. Hence, the concept that arises as the series\u00b1parallel dual to the kinematic redundancy of serial manipulators is that of static or force redundancy, which has particular importance regarding the avoidance of static or force singularities, the only singularities in the case of simple parallel manipulators and the more challenging ones in the case of other parallel manipulators. For example, the series\u00b1parallel dual of the 2-d.o.f. serial manipulators shown in Fig. 1(a) is the two-legged (and 2-d.o.f. also) parallel manipulator shown in Fig. 1(b), Cartesian position p(x, y) of the end-e ector de\u00aening the task-space coordinates in both cases. In the serial manipulator, inverse velocity transformation is unique at a non-singular con\u00aeguration and not wellde\u00aened at a singularity. Similar is the case of inverse force transformation in the parallel manipulator. In the serial manipulator, singularities are found on two circles in the task-space (completely extended and completely folded poses) and are of kinematic nature. In the parallel manipulator, they are static singularities and are found on the line joining the \u00aexed pivots b1 and b2. Now, considering only the position (and disregarding the orientation) of the end-e ector in the plane, the 3-d.o.f. serial manipulator shown in Fig. 1(c) is a kinematically redundant manipulator having one additional link (and an actuation) in series. For this manipulator, at a given con\u00aeguration, the inverse velocity transformation will be a \u00aebre (an in\u00aenitely many valued function), while the inverse force transformation will be unique. In the same way, a static or force redundancy can be introduced in the parallel manipulator of Fig. 1(b) in the form of an additional leg in parallel getting thereby a statically redundant 2-d.o.f. (3 degree-of-constraint) parallel manipulator shown in Fig. 1(d). For this manipulator, at any given con\u00aeguration, the inverse force transformation is a \u00aebre, while the inverse velocity transformation is unique. This shows the duality of kinematic redundancy of serial manipulators and force redundancy of parallel manipulators. However, it is to be observed here that the redundant serial manipulator of Fig. 1(c) still has an in\u00aenite number of singularities at the completely extended (and possibly completely folded) con\u00aegurations, while the redundant parallel manipulator of Fig. 1(d) is entirely free from singularities as long as the three \u00aexed pivots b1, b2, b3 are non-collinear. This indicates that though the kinematic singularities of serial manipulators remain the same in number{ even after the introduction of redundancy (which merely redistributes the singular poses in the workspace), force redundancy in parallel manipulators may be able to reduce the singularities and even eliminate them completely. This aspect will be discussed in detail for the general case in Section 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure22-1.png",
        "caption": "Fig. 22. For illustration of axodes of worm, pinion and rack-cutter.",
        "texts": [
            " The velocity polygon at M satisfies the relation v\u00f0w\u00de v\u00f0p\u00de \u00bc li : \u00f033\u00de t Here: v\u00f0w\u00de and v\u00f0p\u00de are the velocities of the worm and the pinion at M ; it is the unit vector directed along the common tangent to the helices; l is the scalar factor. Eq. (33) indicates that the relative velocity at point M is collinear to the unit vector it. In order to get the same pinion tooth surface Rr that is generated by rack-cutter surface Rc (Section 3), the generation of Rw can be accomplished considering that three surfaces Rc, Rr and Rw are simultaneously in meshing. Fig. 22 shows the axodes of these three surfaces wherein the shortest distance between pinion and worm axodes is extended. Plane P represents the axode of the rack-cutter. Surface Rw is obtained using the following steps: Step 1. Parabolic tooth surface Rc of rack-cutter is considered as given. Step 2. A translational motion of rack-cutter surface Rc, that is perpendicular to the axis of the pinion, and rotational motion of the pinion provide surface Rr as an envelope to the family of surfaces of Rc (see Section 3). Velocity v1 (Fig. 22) is applied to rack-cutter while the pinion is rotated with angular velocity x\u00f0p\u00de. The relation between v1 and x\u00f0p\u00de is defined as v1 \u00bc x\u00f0p\u00derp; \u00f034\u00de where rp is the radius of the pinion pitch cylinder. Step 3. An additional motion of surface Rc with velocity vaux along direction t\u2013t of skew rack-cutter teeth (Fig. 22) is performed and this motion does not affect surface Rr. Vector equation v2 \u00bc v1 \u00fe vaux allows to obtain velocity v2 of rack-cutter Rc in direction that is perpendicular to the axis of the worm. Then, we may represent the generation of worm surface Rw by rack-cutter Rc considering that the rack-cutter performs translational motion v2 while the worm is rotated with angular velocity x\u00f0w\u00de. The relation between v2 and x\u00f0w\u00de is defined as v2 \u00bc x\u00f0w\u00derw; \u00f035\u00de where rw is the radius of the worm pitch cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001174_j.optlastec.2021.106914-Figure43-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001174_j.optlastec.2021.106914-Figure43-1.png",
        "caption": "Fig. 43. Number of cycles to failure for Inconel 718 super alloy [102].",
        "texts": [
            " Result of fatigue test confirmed the increase in life by 1000 times for the machined Z-oriented specimen. The fatigue strength of the X-oriented/Y-oriented part was found to be 14% more than that of the Z oriented parts. Gribbin et al. [102] examined the low cycle fatigue (LCF) behavior and strength of DMLS processed Inconel 718 super alloy followed by heat treatment and HIP. Samples were subjected to cyclic loading (tension\u2013compression) at a fixed value of strain amplitude. The number of cycles (Nf) required to reach the failure was recorded. Fig. 43 shows the plot for Nf with respect to strain amplitude for the Inconel 718 super alloy. Nf was reduced as a result of rise in strain amplitude. Another sample (wrought Inconel 718) was also developed under the similar condition of heat treatment. Table 7 shows the strain amplitude selected for the LCF experiments. This study reported that developed sample of Inconel had strength as well as LCF properties similar to those of Inconel 718 developed by forging. Nf was found to be reduced with the rise in strain amplitude for the heat treated DMLS sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.71-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.71-1.png",
        "caption": "Fig. 5.71: Model of a Rocker Pin Chain Link [249]",
        "texts": [
            " Therefore the chain link models have to be simple, compact, but nevertheless realistic. To start with the model we consider Figure 5.70. Every chain link represents a rigid body, consisting of several plates and a pair of rocker pins. It has three degrees of freedom qTL = (xL, yL, \u03b1L), which is the maximum number of degrees of freedom in a plane. Therefore, the chain links are kinematically decoupled. The chain links are connected by force elements, acting between the point D of one chain link and the point B of its successor (lower part of Figure 5.71). These force elements take into account the elasticity and damping of the link and the joint. When a link comes into contact with a pulley, the frictional and normal contact forces act on the bolts of the chain link and, therefore, on the link at the point B. Hence, all contact forces acting on one pair of rocker pins are assigned to one link. In Figure 5.71 a left positioned index refers to the coordinate systems, for example \u201dI\u201d for an inertial and \u201dL\u201d for a link-fixed coordiante system. A right index are the coordinates, or angles, or length, themselves. The magnitudes (mL, IL) are the link mass and mass moment of inertia, respectively. 5.5 CVT - Rocker Pin Chains - Plane Model 287 CVT\u2019s transmit power by friction in the contact of the rocker pins with the pulley surfaces. Therefore these contacts need to be considered very carefully. Phenomenologically rocker pins between the pulley sheaves build up in normal direction certain normal forces, which are generated by the elastic deformations of the pins and the sheaves on the one and by the contact constraints on the other side",
            " The most convenient way consists in writing these equations with respect to the reference point (Bi), which is the hinge point of a chain link. The point (Si) marks the center of mass. Hence, the vector rBSi points from (Bi) to (Si). IBi is the matrix of the mass moments of inertia, mBi is the mass, \u03c9i the rotational speed of the body, and Fi and Mi are all active forces and torques acting on the body, including the contact forces between the link and the pulley set and the joint forces between the links. The last one is modeled as a linear spring-damper law with the coefficient of elasticity c and the damping coefficient d (see Figure 5.71): F = c ( rBi+1 \u2212 rDi ) + d rBi+1 \u2212 rDi |rBi+1 \u2212 rDi | ( vBi+1 \u2212 vDi ) (5.115) The point Di belongs to the link i under consideration and the point Bi+1 to it\u2019s successor i + 1. Building all individual equations for each link and combining them in an appropriate way we get finally for the rigid body Bi: Miq\u0308 = hi(q, q\u0307, t) (5.116) These equations of motion for each body are decoupled kinematically as long as no stiction forces occur. Therefore, the mass matrix of the entire system has a block-diagonal structure enabling a symbolic inversion",
            " In contrast to this the azimuthal contact force causes the changes of the tensile force in the corresponding chain link, leading to different tensile force levels in the two strands which agree with the transmitted torque. Measurements have been performed at the Technical University of Munich at the Lehrstuhl fu\u0308r Landmaschinen [231]. In order to compare these measurements with simulation results, it is necessary to determine the distribution of the tensile force on the plates of the chain links. Therefore, an elastostatic model of the chain, including all its components, was established, see Figure 5.71 on page 286. For this purpose the pairs of rocker pins are modeled as bending beams and the plates as linear springs. Neglecting second order effects, only the azimuthal frictional forces and the stretched chain length are adopted from the dynamic simulation as boundary conditions. With this model we obtain the right graph of Figure 5.82 for the tensile force in the clasp plate. The results differ a bit from the results of the model, due to the deformation of the link components. The plate forces are usually significantly different"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003630_027836499201100504-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003630_027836499201100504-Figure4-1.png",
        "caption": "Fig. 4. Definition of the arm angle 1jJ.",
        "texts": [
            " Note that the arm angle 0 is undefined when the wrist point W is anywhere on the line through the shoulder point S containing 11 -even though this is generally not a singular configuration-because in this case the reference plane is not uniquely defined. The angle 0 is also undefined when e and w are colinear, as then the plane SEW is not uniquely defined. In the latter case, the arm is either nearly fully outstretched or folded and is therefore near or at an &dquo;elbow singular&dquo; configuration (Burdick 1988; Wampler 1988b). In such cases, 0 ceases to parameterize the redundancy. To derive the forward kinematic function that gives V) as a function of joint angles, again consider Figure 4. Let w = W - S; e = E - S, and let V denote an arbitrary fixed unit vector (e.g., the unit vector in the vertical direction of the base frame). Let the projection of e onto w be given by d = w(i~T e), w = wlilwll. The minimum distance from the line SW to the point E is along the vector p = e - d = (I - ww )e. The reference plane is the plane that contains both w and the unit vector V. The unit vector in the reference plane that is orthogonal to w is given by ~ = .~/ ~~ ~~~, with f = (w x V) x w. We also define the unit vector fi = pI I IP I I Note that e, w, w, d, w, P, Q, and i can be computed during the forward kinematics iteration ( 1 ), as will be discussed subsequently. The vector I, or equivalently P, is treated as a free vector that can slide along the line SW. In particular, i is moved along the line SW until its base is in contact with the base of vector p at the point d (see Figure 4), so that 0 is the angle from ~ to p. This construction results in where C1j; = cos 1/J and S, = sin 1/J. This gives The result (3) can be simplified somewhat. Defining g = w x V, we have \u00a3 = g x w, and we note that gT 9 = VTg = 0. This means that I and V are coplanar, both lying in the reference plane. Because, in general, the reference plane is spanned by V and w, we have Substituting this result into (2) gives which can be used with (3) to obtain Equation (5) immediately gives the forward kinematic function that maps the joint angles 6 to the arm angle y\u00a7 as: where atan2(y, ~) is defined as in Craig (1986)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.20-1.png",
        "caption": "Fig. 6.20 Two types of lateral displacement under lateral force Q",
        "texts": [
            " The lateral spring rate is defined by the ratio of the lateral force Q to the lateral displacement d as shown in Fig. 6.19. Because the out-of-plane flexural rigidity of 322 6 Spring Properties of Tires the belt is much greater than the sidewall stiffness, the tread ring is assumed to be a rigid ring. The shear deformation of the tread rubber is neglected. The lateral displacement d at the point of lateral loading Q is the summation of the translational lateral displacement d1 and the lateral displacement d2 due to the out-of-plane rotation, as shown in Fig. 6.20. Referring to Fig. 6.20, when the lateral force Q is applied to point A, the translational lateral displacement d1 is expressed as d1 \u00bc Q 2prA =ks; \u00f06:41\u00de where ks is the lateral fundamental spring rate per unit length on the tread surface, and rA is the radius at point A. The lateral spring rate of a tire Rs with respect to the translational lateral displacement is given by Rs \u00bc Q=d1 \u00bc 2prAks: \u00f06:42\u00de Referring to Fig. 6.20, when the lateral force Q is applied to point A, the moment rAQ is applied to a tire. Using Eq. (6.38), the out-of-plane rotation h is obtained as h \u00bc rAQ=Rmz: \u00f06:43\u00de Infla on pressure (MPa) To rs io na ls pr in g ra te R\u2019 m z (k N m /r ad ) theory experiment 175SR13 (5J-14) load: 3kN rB=192 mm rC=251 mm rD=296 mm D=53.5\u00b0 Em=3.5 MPa 0 0.1 0.2 0.3 0 5 10 15 Using Eq. (6.38), the lateral displacement d2 due to the out-of-plane rotation is expressed as d2 \u00bc rAh \u00bc r2AQ Rmz \u00bc\u00bc Q prAks \u00fe p B 2 2kr \u00fe kt rA ; \u00f06:44\u00de where B is the tread width or rim width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000873_sapm194726194-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000873_sapm194726194-Figure1-1.png",
        "caption": "FIG. 1. Forces and stress resultants on element of deformed ring",
        "texts": [
            " Specifically, we consider the elastica problem of the buckled circular ring under uniform radial pressure, the stability problem of closed symmetric rings under any loading which leads to a stability (eigenvalue) problem, the stability problem of a ring which has been pre-stressed into a configuration with large deflections, and the stability of a ring subjected to a uniform pressure applied harmonically in time. Some features of the eigenvalue problems which arise differ in an interesting manner from the more classical forms. 2. The General Equations. The equations of dynamic equilibrium of a curved segment of an elastic strip which is sufficiently thin that the elongation of its center line may be completely neglectedl are readily expressed by equating tp.e moment about the center of curvature, the moment about the point a (Fig. 1), and the radial force, to the corresponding inertia terms. These equations are R'p + tp - M' = zpAI M' - T = 0 - R,p' + q - T' = zAr (1 ) (2) (3) Here R, q, T, M, t, as defined in Fig. 1, are the various stresl:1 resultants and forces acting on the segment; p is the radius of curvature of the segment in the deformed shape; AI, AT, are the components of acceleration referred to the distorted coordinate system; z is the mass per unit length; and 8 is the Lagran gian coordinate taken as the distance along the ring. We adopt such units of length that the points 8 = 0 and 8 = 211\" coincide for any clqsed ring under con sideration. Hence, for an originally circular ring, 8 becomes synonomous with the angular coordinate o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.15-1.png",
        "caption": "Fig. 5.15 Tire shape and interlaminar shear stress",
        "texts": [
            "63) is rewritten as TB \u00bc p 2 \u00f0r2C r2B\u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p A r\u00bcrB \u00bc p 2 \u00f0r2C r2A\u00de2 exp 2 ZrA rB cot2 a r dr 0 @ 1 A \u00f0r2C r2B\u00de2 2 4 3 5 1=2 : \u00f05:65\u00de The tension of the bead core TB also depends on the cord path, and the expressions of TB for the various cord paths are summarized in Table 5.3. The safety factor of the bead wire is defined by the ratio between the static failure stress and the maximum stress of the bead wire, which is calculated using the maximum tension of the bead core. The safety factor of the bead wire is usually less than 10 for a passenger-car tire. 5.3 Effects of the Tire Shape on Tire Properties 261 Referring to Fig. 5.15, the interlaminar shear stress sC acting between bias plies is determined by the condition that the element on a ring does not rotate around the zaxis. The equilibrium of torques due to interlaminar shear stress sC and cord tension tc around the z-axis is given by N d\u00f0tc cos a r\u00de=ds \u00bc rsC2pr; \u00f05:66\u00de where N is the number of ply cords. Using Eq. (5.22), we obtain d ds \u00bc d dr dr ds \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p B d dr : \u00f05:67\u00de Using Eq. (5.67), Eq. (5.66) is rewritten as sC \u00bc N 2pr2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p B d dr tc r cos a\u00f0 \u00de: \u00f05:68\u00de Eliminating tc in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure7-1.png",
        "caption": "Fig. 7. Parabolic profile of pinion rack-cutter in normal section.",
        "texts": [
            " 18) /i (i \u00bc 1; 2) angle of rotation of the pinion (i \u00bc 1) or the gear (i \u00bc 2) in the process of meshing wi (i \u00bc r; 1; 2) angle of rotation of the profile-crowned pinion (i \u00bc r), the double-crowned pinion (i \u00bc 1), or the profile-crowned gear (i \u00bc 2) in the process of generation Dc shaft angle error (Fig. 14) Dk lead angle error Dki (i \u00bc 1; 2) correction of lead angle of the pinion (i \u00bc 1) or the gear (i \u00bc 2) D/2\u00f0/1\u00de function of transmission errors Dwp additional rotational motion of the pinion during the feed motion (Fig. 24) Dsw translational motion of the grinding worm during the feed motion (Fig. 24) DE center distance error (Figs. 12 and 14) Ri surfaces (i \u00bc c; t; r; s; 1; 2;w;D) ac parabola coefficient of profiles of pinion rack-cutter in its normal section (Fig. 7) amr parabola coefficient of the parabolic function for the modified roll of feed motion apl parabola coefficient of plunging by grinding disk or by grinding worm b parameter of relative tooth thickness of pinion and gear rack-cutters EDp shortest center distance between the disk and the pinion (Figs. 18 and 19) Ewp shortest center distance between the worm and the pinion (Fig. 24) ld, lc parameters of location of point of tangency Q and Q , respectively (Fig. 6) lp translational motion of the pinion during the generation by grinding disk (Fig",
            " The rack-cutter for the pinion is provided with a parabolic profile. The profiles of the rack-cutters are in tangency at points Q and Q (Fig. 6(a)) that belong to the normal profiles of driving and coast sides of the teeth, respectively. The common normal to the profiles passes through point P that belongs to the instantaneous axis of rotation P1\u2013P2 (Fig. 5(a)). The parabolic profile of pinion rack-cutter is represented in parametric form in an auxiliary coordinate system Sa\u00f0xa; ya\u00de as follows (Fig. 7): xa \u00bc acu2c ; ya \u00bc uc; \u00f04\u00de where ac is the parabola coefficient. The origin of Sa coincides with Q. The surface of the rack-cutter is denoted by Rc and is derived as follows: ii(i) The mismatched profiles of pinion and gear rack-cutters are represented in Fig. 6(a). The pressure angles are ad for the driving profile and ac for the coast profile. The locations of points Q and Q are denoted by jQP j \u00bc ld and jQ P j \u00bc lc where ld and lc are defined as ld \u00bc pm 1\u00fe b sin ad cos ad cos ac sin\u00f0ad \u00fe ac\u00de ; \u00f05\u00de lc \u00bc pm 1\u00fe b sin ac cos ac cos ad sin\u00f0ad \u00fe ac\u00de : \u00f06\u00de i(ii) Coordinate systems Sa\u00f0xa; ya\u00de and Sb\u00f0xb; yb\u00de are located in the plane of the normal section of the rackcutter (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure21-1.png",
        "caption": "Fig. 21. Installment of grinding (cutting) worm.",
        "texts": [
            ": +34-968-326432; fax: +34-968-326449. E-mail address: alfonso.fuentes@upct.es (A. Fuentes). 0045-7825/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0045-7825(03)00367-0 Nomenclature ai (i \u00bc d; c) normal pressure angle for the driving profile (i \u00bc d) or the coast profile (i \u00bc c) at the point of tangency of mismatched rack-cutters (Fig. 6) b helix angle (Figs. 5 and 8) cDp crossing angle between the disk and the pinion (Figs. 18 and 19) cwp crossing angle between the worm and the pinion (Fig. 21) ki (i \u00bc p;w) lead angle of the pinion (i \u00bc p) or of the worm (i \u00bc w) (Fig. 21) qD radius of generating disk (Fig. 18) /i (i \u00bc 1; 2) angle of rotation of the pinion (i \u00bc 1) or the gear (i \u00bc 2) in the process of meshing wi (i \u00bc r; 1; 2) angle of rotation of the profile-crowned pinion (i \u00bc r), the double-crowned pinion (i \u00bc 1), or the profile-crowned gear (i \u00bc 2) in the process of generation Dc shaft angle error (Fig. 14) Dk lead angle error Dki (i \u00bc 1; 2) correction of lead angle of the pinion (i \u00bc 1) or the gear (i \u00bc 2) D/2\u00f0/1\u00de function of transmission errors Dwp additional rotational motion of the pinion during the feed motion (Fig",
            " The same translational motions are performed by system S1 that performs rotational motion of angle w1 with respect to system Sq. (4) The pinion tooth surface R1 is determined as the envelope to the family of disk surfaces RD gen- erated in the relative motion between the disk and the pinion. The installment of the grinding worm with respect to the pinion may be represented on the basis of meshing of two helicoids. Fig. 20 illustrates the meshing of two left-hand helicoids, that represent the grinding worm and the pinion generated by the worm. Drawings of Fig. 21 yield that the crossing angle is cwp \u00bc kp \u00fe kw; \u00f032\u00de where kp and kw are the lead angles on the pitch cylinders of the pinion and the worm. Fig. 21 shows that the pitch cylinders of the worm and the pinion are in tangency at pointM that belongs to the shortest distance between the crossed axes. The velocity polygon at M satisfies the relation v\u00f0w\u00de v\u00f0p\u00de \u00bc li : \u00f033\u00de t Here: v\u00f0w\u00de and v\u00f0p\u00de are the velocities of the worm and the pinion at M ; it is the unit vector directed along the common tangent to the helices; l is the scalar factor. Eq. (33) indicates that the relative velocity at point M is collinear to the unit vector it. In order to get the same pinion tooth surface Rr that is generated by rack-cutter surface Rc (Section 3), the generation of Rw can be accomplished considering that three surfaces Rc, Rr and Rw are simultaneously in meshing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure1.22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure1.22-1.png",
        "caption": "Fig. 1.22 Shear deformation when stress is applied in the x-direction [1]",
        "texts": [],
        "surrounding_texts": [
            "Kabe [15] compared micromechanics and experimental results for UDCRR, where the elastic constants for composite were Ef = 2.85 GPa, Em = 5 MPa, mf = 0.4 and mm = 0.5 (Fig. 1.24). The relation GLT/ET 1/4 in Eq. (1.113) is in good agreement with the experimental results except for Vf = 0 and Vf = 1. The ratio of GLT calculated using Eq. (1.73) to ET calculated using the Akasaka\u2013Kabe equation (given as Eq. 1.108) agrees with the measurement better than that calculated using the simplified Halpin\u2013Tsai equation (given as Eq. 1.116). 1.5 1.0 0.5 0.5 0 30 60 90 C xs \u00d7E T \u03b8 (deg) Fig. 1.23 Relationship between CxsET and cord angle h [15] 1.6 Mechanics of UDCRR Under an FRR Approximation 37"
        ]
    },
    {
        "image_filename": "designv10_2_0003437_60.866991-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003437_60.866991-Figure2-1.png",
        "caption": "Fig. 2. Rotor position at two different moments in time. The position of minimum air gap is at: a) = 0 rad and b) = =2 rad.",
        "texts": [
            " Mutual inductance between circuits and which are placed on the opposite sides of the air gap, in the case of skewing of rotor bars (or stator slots) is defined to be: (14) where (15) and where is the angle of skewing in radians and is temporarily variable, , [11]. It is well known that for a small level of rotor eccentricity an accurate enough way of describing the air gap length is, [9]: (17) where is the degree of eccentricity, and is the radial air gap length in the case of a uniform air gap. In order to avoid stator-rotor rub . The inverse air gap function can be approximated by the expression: (18) where, (19) Equation (17) is related to the rotor position shown in Fig. 2a). The average radius of the air gap can be described in a similar manner by the expression: (20) where is the average radius of the air gap in a symmetrical machine. In the case of dynamic eccentricity, the self inductance of the stator windings and mutual inductances between stator windings are functions of rotor position, i.e. of the space coordinate . For a known machine layout and given the parameters of the machine stator winding, it is easy to define the winding functions of the stator phases",
            " These values are calculated by numerical integration of expression (13), however, the expression for the winding function (16) can also be applied to the rotor loop . Stator phase\u2013rotor loop mutual inductance is dependent on the rotor position. With the machine winding layout known, the stator-rotor mutual inductance can be easily calculated. By shifting the winding distribution of the rotor loop through the positive angle in a step by step fashion and integrating (14) and (15), the mutual inductance between the stator phase and rotor loop can be obtained for one position of the rotor. For the rotor position given in Fig. 2a), Fig. 4 (top) shows the curves of mutual inductances between stator phases and rotor loop. It is obvious that the value of mutual inductance declines with the rise of the air gap length. For some other moment in time, i.e. some other rotor position, these curves change, for example, the mutual inductances between stator phases and the same rotor loop for the rotor position shown in Fig. 2b) is presented on Fig. 4 (bottom). It is clear that in every rotor position the new curve which describes mutual inductance between stator phase and rotor loop must be known. What is the best method of solving this problem in an iterative procedure? The most obvious way is by the organization of mutual inductance curves in two-dimensional look-up tables. Rows of this matrix should represent values of mutual inductances between stator phase and rotor loop for one rotor position. So, for example, if the machine circumference is discretized in steps of 1 ( rad",
            " The reason for this is that the rotor loop in standard cage rotor induction machine has a quite small pitch, ( for our machine), so the rotor loop in one position of the rotor does not experience a significant change in air gap length. Further, as a result of the rotating position of minimum of air gap length, this situation remains unalterable for all positions of the rotor. For other rotor loops these curves remain the same shape, but with changes in amplitude. So, if rotor loop 1 is at a position of minimum air gap length (Fig. 2a)), the rotor loop 1-stator phase A mutual inductance is given by the stator-rotor mutual inductance for symmetrical machine, but has a greater amplitude. The same is true for rotor loop 1 and stator phase B and C. For the rotor loop which is at position , (loop 20 for our machine) curves of the same shape are valid but with smaller amplitude than in a symmetrical machine and shifted by rad. It is easy to show that it is enough to know the curve of mutual inductance between one stator phase and one rotor loop for the symmetrical machine (all other curves could be obtained by shifting) and multiplying by the following coefficient once, out of the iteration loop, (22) where define initial rotor loop position. So, if the initial rotor position is given by Fig. 2a), and , the rotor loop 1-stator phases mutual inductances are given by the same curves as in the symmetrical machine case, multiplied by . Also, the rotor loop 2-stator phases mutual inductances are given by the same curves as in symmetrical machine ease, multiplied by , and so on. Note that (22) is a good approximation for a medium degree of eccentricity, . The described method was applied to an 11kW, four pole, three phase induction machine. Machine construction parameters and winding details are given in the Appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.31-1.png",
        "caption": "Fig. 5.31: Two prototypes of the chopstick fingers. According to [Arai93]",
        "texts": [
            " Two piezo-driven chopstick-like fingers, each having 6 degrees of freedom, are designed to manipulate micro objects like a human hand, Fig. 5.30. The two-finger design was specially conceived to work in the microworld, where gravity and moments of inertia play only a very minor role. Therefore, two fingers are sufficient for manipu lating microobjects. 5.3 Piezoelectric Microactuators 147 148 5 Microactuators: Principles and Examples Two prototypes of the chopstick microfingers were developed and are shown in Figure 5.31. A parallel link mechanism was used to construct both proto types. It is made up of 6 prismatic piezo connecting elements which are connected to the base plate and end effector. Springs are added to the first prototype to enable the fingers to move continuously and to maintain the hand's stability, Fig 5.31, left. The fingers are made of 50 mm long needles having a tip radius of 30 f.!m. The second prototype has flexible ball joints made of steel, Fig. 5.31, right. They increase the stiffness, thereby increasing the accuracy. An important design goal is to improve the mechanical struc ture in order to expand the work area of the micromanipulator and to improve the dynamic behavior of the actuator. The fingers were improved by repla cing them with a glass pipette with a tip radius of under 1 f.!m. Both finger prototypes are controlled by six piezoelements with a dimension of 2 mm x 3 mm x 8 mm. The diameter of the base plate is 56 mm, that of the end effector is 20 mm and the distance between the plates is 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003456_bf02317861-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003456_bf02317861-Figure1-1.png",
        "caption": "Fig. 1--Schematic of a simple compression experimental setup",
        "texts": [
            " It is shown in this paper that this approach results in different values for the machine compliance factor for different materials. The nonuniqueness of the machine compliance factor is attributed to the inherent nonlinearity of the machine compliance, i.e., the nonlinear dependence of the nonsample displacement on the applied load. Through a set of mechanical tests on a range of materials, it has been demonstrated that it is necessary to characterize this nonlinear compliance relationship for the machine to obtain accurate and consistent measurements. In t roduct ion The simple compression mode of testing (Fig. 1) has several intrinsic advantages in evaluating some of the basic mechanical properties of a material. It is relatively simple, requires only a small amount of the material, has a simple sample geometry, does not require any expensive grips (such as those used in tensile testing) and is immune to instabilities such as necking. As a result, it is being used increasingly in the evaluation of mechanical properties of a number of materials. In particular, it is being used extensively for characterizing the modulus and strength of a variety of composites 2,3 and for studying the strain-hardening behavior of a number of metals 4 and polymers. 5 There are two major disadvantages with the simple compression mode of testing when compared to tensile testing: (i) the interface between the sample and the compression plate can experience significant frictional forces if this interface is not properly lubricated (typically a thin teflon sheet and/or grease is placed at these junctions; see Fig. 1) and (ii) measurement of the actual deformation in the sample is relatively more difficult, since the typical lengths of specimen used in simple compression testing are fairly small and do not allow for direct use of extensometers. While it is possible to use strain gages to measure accurately the strain in the S. R. Kalidindi is Assistant Professor, and Abusafieh and E. El-Danaf are Research Assistants, Department of Materials Engineering, Drexel University, Philadelphia, PA 19104. Original manuscript submitteck August 5, 1996",
            " The goals of our study were to (i) demonstrate that the use of constant values of machine compliance can lead to significant errors in estimating material properties from simple compression tests, (ii) develop suitable techniques for characterizing the nonlinear relationship between the applied load and the nonsample deformation in the loading system and (iii) demonstrate that this characterization produces much improved results for a range of materials on the same testing machine. To this end, we performed a number of end-loaded simple compression tests (Fig. 1) on samples of a range of materials, including polymers, metals and composites, on a single testing machine. The measurements from these tests were critically analyzed, and the results are summarized in this paper. Current Limitat ions We start by first exploring the limitations of the currently used technique for compliance correction. The fundamental concept behind compliance corrections is fairly straightfor- ward and is based on the assumption that the sample and testing fixture can be modeled as a system containing two springs in series",
            " It is highly unlikely that the nonlinear behavior of the machine is due to inelastic deformation in some of the components in the loading system, since the components are all metallic, and any plastic deformation in them should disappear in subsequent runs due to inherent hardening of the metal. Compliance Characterization We used three different techniques to characterize the nonlinear compliance of our testing machine. These are described in detail. Method I: Direct Technique In this technique, the load-displacement relationship for the machine was directly measured using the setup shown in Fig. 1, without any sample between the compression plates. This was accomplished by giving a displacement rate of 1.0 2 1 2 9 VoL 37, No. 2, June 1997 compliance using Methods I and II and a smooth curve-fit to the data mm/min to the actuator and recording the resulting load. The data shown in Fig. 4 for two different tests (numbered l and 2 in Fig. 4) were found to be highly repeatable. Figure 4 indicates two distinct regimes in the compliance behavior of the machine. The first regime involves relatively high amounts of nonsample displacement in the loading system at very low load levels",
            " This regime of the compliance curve is termed the \"initial settling compliance\" in this paper, since this part of the curve reflects the initial settling of the loading fixture and sample (when present). In other words, at the beginning of the test, there is a certain amount of nonsample displacement in the loading system resulting from the lubricant squeezing out o f the junctions between sample ends and compression plates, and the self-alignment of the bottom plate in the ball-and-socket joint (Fig. 1) to bring the sample axis parallel to the loading axis. Note that the magnitude of this effect is very sensitive to sample geometry, sample placement and the type and amount of lubrication. Consequently, in repeated measurements of the compliance of the machine using Method I, we found that the recorded load displacement curves differed from each other by a constant displacement, i.e., all recorded curves were parallel to each other and could be made to coincide with each other by adding or subtracting a constant value from the y-coordinate for each set of data",
            " Note that there is a distinct region at the beginning of the test where practically all of the actuator motion is accommodated by the loading system (nonsample displacement), and the applied load in this regime is extremely small (almost zero). Method II1: Finite Plastic Strains This technique is based on the fact that plastic deformation in metals can be conveniently measured after the test and that the plastic strains can be orders of magnitude larger than the elastic strain. In this technique, large amounts of plastic strain are imposed on metallic samples in simple compression using the setup shown in Fig. 1. In each of the tests, the maximum load applied (at the end of the applied deformation), the actual change in sample length and the total displacement recorded by the actuator are documented. The difference between the recorded actuator displacement and the actual change in sample length gives the nonsam- Experimental Mechanics 9 213 pie deformation corresponding to the maximum load applied during the test. Consequently, each sample will provide a data point on the machine compliance. A set of such tests was performed on samples of aluminum, brass and MP35N, and the data obtained are plotted in Fig~ 6, along with the previous data shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003887_978-94-011-4120-8_41-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003887_978-94-011-4120-8_41-Figure3-1.png",
        "caption": "Figure 3b. Closed loop with RPR sequence generating planar motion",
        "texts": [
            " The five-dimensional subset is the product of five one-dimensional subgroups, which represents an open sequence oflower kinematic pairs (called also Reuleaux pairs). Three degrees of freedom of {S(N)} are obtained by locking two kinematic pairs among the five pairs. To the previous types of obvious possible limbs, we have to add the mechanisms, which result from different ways of obtaining special mechanical bonds. For example, a sequence of three revolute pairs with parallel axes produces the subgroup {G(PI)} of planar displacements (or planar gliding), PI being a plane perpendicular to the rotational axes, of the revolute pairs R2, R3 and R4, (see Fig. 3a). In figure 3a, the axis of the revolute pair R3 may include the point N. Then, we have a limb with 3 converging axes and 2 idle pairs like in figure 2. All sequences (R2 R3 R4) with axes perpendicular to plane PI generate the same mechanical bond. 399 Therefore, we can have the axis of Ra at any position perpendicular to PI and R2, R4 are no longer idle pairs. The subgroup {G(PI)} can be generated by the PI planar pair and also by sequences (pRR, RPR, PPR, PRP) of prismatic pairs P and revolute pairs R, prismatic pairs being parallel to PI, axes of revolute pairs being perpendicular to PI. For example figure 3b is equivalent to figure 3a. The limb mechanism of figure 3b has the structural limb type of the platform that will be described with more details in the next paragraph. Employing these equivalencies, we can design tripods for spherical rotation, which are not trivial. We will highlight a structural type, which is the same than the Tsai translational platform. 4. A rotational platform with three extensible limbs A special case of the previous mechanisms consists of a fixed base and a moving platform, which are connected by three extensible limbs. Each limb is made of a prismatic joint between two elements, which are endowed with two universal joints at their two extremities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003231_s0957-4158(99)00057-4-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003231_s0957-4158(99)00057-4-Figure4-1.png",
        "caption": "Fig. 4. The e ect of K-adaptation on the phase plane.",
        "texts": [
            " The criterion (cost) which is to be minimized is chosen as J 1 2 STS U T cUc 31 The reason behind the selection of the cost function as in (31) is that minimizing (optimizing) the S function results in a minimization of the error, because S is a function of error as de\u00aened in (5) and optimizing Uc results in elimination of chattering and optimization of the control. To make J small it is reasonable to change the parameters (weights) in the direction of the negative gradient of it, i.e. DKj, i \u00ffg @J @Kj, i and DGj, i \u00ffg @J @Gj, i 32 Weight adaptation for the output layer also means the adaptation of the Kmatrix of SMC. The e ect of K-adaptation is presented in Fig. 4. The gradient descent as in (32) for K can be derived as DKj, i \u00ffg @J @Sj @Sj @Kj, i \u00ff g @J @Ucj @Ucj @Kj, i where j 1, . . . , m and i 1, . . . , m 33 The partial derivatives are calculated as @J @Sj Sj, @J @Ucj Ucj , and @Ucj @Kj, i h Si 34 The sliding function in (5) can be rewritten using (17) and the integral of (4) as S G Xd \u00ff X GXd \u00ff G F X B Ueq Kh S dx 35 Taking the partial derivative of (35) and assigning the constants to g ' which are obtained by multiplication of elements of G and B: @Sj @Kj, i \u00ffg 0 h Si x dx 36 The last form of K-adaptation is obtained as DKj, i g1Sj h Si x dx\u00ff g2Ucj h Si 37 The minimization of the corrective controller (Uc) prevents chattering when the system is on the sliding surface or inside the boundary layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000042_c6cs00242k-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000042_c6cs00242k-Figure8-1.png",
        "caption": "Fig. 8 Movement of a Galinstan droplet under the influence of an external field in (a) basic and (b) acidic electrolytes. Figure adapted from ref. 53 with permission from The Royal Society of Chemistry.",
        "texts": [
            " Specifically, in a basic electrolyte, gallium reacts with hydroxide ions producing gallates [Ga(OH)4] that charge the surface negatively and attract positively charged ions to the EDL. The interface can be treated as a parallelplate capacitor obeying the so-called Lippmann equation (eqn (1)) relating surface tension to EDL properties: g\u00f0V\u00de \u00bc g0 C 2 V2; (1) where C is the capacitance of the EDL, V is the potential across the EDL, and g0 is the maximum surface tension at V = 0. When the liquid metal is treated as equal-potential throughout its extent, exposure to an outside DC field causes the surface charge on the droplet to redistribute (Fig. 8a) creating a gradient of V over the droplet\u2019s surface. The electric potential at the cathodic pole becomes greater compared to the anodic pole and, according to eqn (1), the surface tension at the cathodic pole is smaller than that at the anodic pole. The surface tension gradient thus established induces the motion of the droplet towards the anode. This motion is accompanied by an electrochemical oxidation of gallium into b-Ga2O3, which \u2013 if deposited in excess \u2013 can cause the droplet to halt. The motion in acidic medium can be described by the same principles as for the basic electrolyte with the difference that the droplet becomes positively charged, leading to the negative charge accumulation on the outer layer (Fig. 8b). Similar experiments were repeated53 with Galinstan droplets covered with WO3, In2O3 and ZnO nanoparticles, NPs, that have low-pH isoelectric point and in a basic solution have large negative surface charge. Since the NP coating is free to move over the surface of the metal, the externally applied potential acting on the composite liquid\u2013metal/NP EDL strives to minimize surface tension by clearing the NPs from the droplet\u2019s cathodic pole \u2013 droplet motion then ensues. Another means of eliciting directional droplet motion is by light stimuli"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003966_s00422-001-0300-3-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003966_s00422-001-0300-3-Figure1-1.png",
        "caption": "Fig. 1a\u2013c. Overhead views of a cockroach (a), a cartoon of the lateral leg-spring bipedal model during one stride of period s (b), and model details (c). O denotes a fixed \u2018origin\u2019 on the ground, F is the current foot position F 0 (not shown) is the next foot position on the opposite side of the body, and G is the body center of mass (COM). P is the leg attachment point (also called center of pressure, COP) which may move or be fixed with respect to G according to the prescribed position function d\u00f0t\u00de. f1 and f2 are components of force generated in the leg with respect to body axes e1; e2; r\u00f0t\u00de \u00bc \u00f0x\u00f0t\u00de; y\u00f0t\u00de\u00de is the masscenter position with respect to inertial frame ex; ey . h\u00f0t\u00de is the body orientation, and /\u00f0t\u00de is the leg angle relative to body. The leg positions with respect to the body at the start of each step are sketched in gray; b is the leg angle with respect to the body centerline at touchdown. d\u00f0t\u00de, shown in a, is the angle of the mass center velocity v\u00f0t\u00de with respect to the body centerline",
        "texts": [
            " After describing the model in Sect. 2, we: (1) explicitly define stability and provide measures of performance (Sect. 3), (2) estimate parameters for a specific insect as a test case and assess how well the model captures and explains steady gaits over a range of speeds including the preferred speed (Sect. 4), and (3) consider geometric size scaling and determine how individual parameter variations affect performance (Sect. 5). The results are discussed and assessed in Sect. 6. The LLS model, illustrated in Fig. 1, and described in detail in Schmitt and Holmes (2000b), consists of a rigid body of mass m and moment of inertia I (in insects, the head\u2013thorax\u2013body unit), that is free to move in the plane under forces generated by two massless, laterally rigid, axially elastic legs, pivoted freely at a point P (generally displaced forward or backward from the center of mass (COM) G), and intermittently contacting the ground at feet F ; F 0 with a 0:5 duty cycle. F ; F 0, and P are pin joints (i.e., with no torques)",
            " In fact the prescribed force studies of Kubow and Full (1999), in which representative forces were applied at foot positions, motivated the present generalized models, which we believe are better suited to represent the effects of mechanical feedback or \u2018preflexes\u2019 in gait stabilization. Further information and detailed analyses of these models appear in Schmitt and Holmes (2000b, 2001). The dynamical behavior of the model (1) is conveniently described in terms of touchdown values of COM velocity magnitude v\u00f0t\u00de \u00bc jv\u00f0t\u00dej \u00bc j _r\u00f0t\u00dej and COM velocity heading d\u00f0t\u00de relative to body axis, body orientation, or yaw angle h\u00f0t\u00de relative to a fixed reference frame, and body angular velocity _h\u00f0t\u00de x\u00f0t\u00de; see Fig. 1. Integration of (1) (Schmitt and Holmes 2000b) produces a stride or step map F specifying these variables at each touchdown instant t \u00bc tn\u00fe1 in terms of their values at the preceeding touchdown t \u00bc tn: \u00f0vn\u00fe1; dn\u00fe1; hn\u00fe1;xn\u00fe1\u00de \u00bc F\u00f0vn; dn; hn;xn\u00de ; \u00f04\u00de where vn \u00bc v\u00f0tn\u00de, etc. Here we retain the terminology of Schmitt and Holmes (2000a,b). In traditional biological usage, heading denotes the COM velocity with respect to compass direction (i.e., the quantity d \u00fe h), and body orientation denotes the angle the body makes with the velocity vector (d)",
            " In all cases a saddle-node bifurcation (Guckenheimer and Holmes 1983) occurs at a critical COM speed v \u00bc vc (or ~k \u00bc ~kc), below which no gaits exist and above which two branches emerge, one potentially stable with relatively small lateral and yaw oscillations (small jdj), and one with large oscillations (large jdj), which is typically unstable. (Bifurcation theory (Guckenheimer and Holmes 1983) implies that in general at most one branch may be stable, but both could be unstable.) For this model, with passive compliant spring legs and fixed COP, the smaller jdj gaits exhibit relative heading and angular velocity stability if d < 0 (hip behind COM), and instability for d > 0; moving-COP gaits are stable provided d moves backward during stance (d1 < 0 in Eq. 3), as shown in Fig. 1b. Stability results from losses/ gains of angular momentum incurred in leg-to-leg Fig. 2. Response to perturbations and stability explanation. The cartoon shows the model recovering from a perturbation to a stable gait (v\u00bc 0:2175;d\u00bc 0:14; h\u00bc 0;x\u00bc 0:9295 with parameters k\u00bc 2:25;m\u00bc 0:0025; I \u00bc 2:04 10 7;d \u00bc 0:0025;b\u00bc 1) applied at the beginning of the third step. The graphs show the state variables at the beginning of each step. The model is neutrally stable in h and v (corresponding eigenvalues jkj of unit magnitude) but asymptotically stable in x ( _h) and d; the corresponding eigenvalues are less than one in magnitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure4-1.png",
        "caption": "Fig. 4. Rounded-top shaper.",
        "texts": [
            " Lines L2s represent the instantaneous lines of tangency of R2 and shaper Rs, shown on R2. The cross-sections of the face-gear tooth are shown in Fig. 3(b). Investigation shows that the surface points of the face gear are hyperbolic ones. This means that the product of principal curvatures at the surface point is negative. The fillet of the face-gear tooth surface of a conventional design (Fig. 3) is generated by the edge of the shaper. The authors have proposed to generate the fillet by a rounded edge of the shaper as shown in Fig. 4 that allows the bending stresses to be reduced approximately in 10%. The shape of the modified fillet of the face gear is shown in Fig. 5. The length of the face-gear teeth has to be limited by dimensions L1 and L2 (Fig. 6) to avoid [8]: (i) undercutting in plane A, and (ii) tooth pointing in plane B. The permissible length of the face-gear tooth is determined by the unitless coefficient c represented as c \u00bc \u00f0L2 L1\u00dePd \u00bc L2 L1 m \u00f01\u00de where Pd and m are the diametral pitch and the module, respectively",
            " For a symmetric gear drive such a value is equal to half of the angular step: wN \u00bc 360 Ns 1 2 \u00bc 6 \u00f031\u00de where Ns is the number of teeth of the shaper. The corresponding worm rotation angle is ww \u00bc \u00f0ws wN \u00de msw \u00bc \u00f018:3 6 \u00de 30 \u00bc 369 that corresponds to 369=360 \u00bc 1:025 turns of the thread of the worm. Considering the two limitations for both sides, we obtain 2.05 as the maximum number of turns of the thread. The goals of stress analysis represented in this section are (i) Comparison of bending stresses at the fillet of two versions of face-gear design: of the edged and rounded fillets (Fig. 4). (ii) Determination of contact and bending stresses and investigation of formation of the bearing contact during the cycle of meshing. The performed stress analysis is based on finite element method [23] and application of general purpose computer program [5]. Finite element method [23] requires the development of a finite element mesh, definition of slave and master contacting surfaces and establishment of boundary conditions. The authors\u2019 approach for application of finite element analysis has the following advantages: \u2022 The generation of finite element models is performed automatically by using the equations of the tooth surfaces and taking into account the corresponding fillets and portion of the rim",
            " We have chosen for stress analysis the gear and pinion tooth surfaces as the master and slave ones, respectively. The development of the finite element model of the face gear is complicated due to the specific structure of the face-gear tooth. Fig. 3(a) shows that the tooth surface of the face gear is formed as a combination of: (i) an envelope to the family of shaper generating surfaces, and (ii) the surface of the fillet generated by the edged top of the shaper (or by the rounded top of the shaper, Fig. 4). The authors could overcome this obstacle by the development of an algorithm that determines the finite elements considering simultaneously the root, fillet, and the active part (the envelope) of the face-gear tooth. Fig. 21(a) and (b) show the finite element models of one-tooth of the pinion and the face gear, respectively. In the case of the pinion tooth model, five finite elements have been considered on the root and fillet portions (Fig. 21(a)). However, in the model of the face-gear tooth (Fig. 21(b)), each longitudinal section, due to its particular length, have to be divided into proper finite elements considering together all portions of the face-gear tooth profile. The finite element analysis has been performed for two versions of face-gear drives of common design parameters represented in Table 3. The versions correspond to face-gear drives with conventional and rounded fillet, respectively (Fig. 4). The finite element mesh of five pair of teeth of version 2 is represented in Fig. 22. Elements C3D8I [5] of first order enhanced by incompatible modes to improve their bending behavior have been used to form the finite element mesh. The total number of elements is 67,240 with 84,880 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Fig. 23 shows the whole finite element model of the gear drive. Figs. 24 and 25 show the maximum contact and bending stresses obtained at the mean contact point for gear drives of two versions of fillet (see Fig. 4). It is confirmed that the bending stresses are reduced more than 10% for the face gear generated with a rounded-top shaper in comparison with the face gear generated with a edged-top shaper. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs. 24 and 25). The obtained results show the possibility of an edge contact in face-gear drives by application of involute pinion. Avoidance of edge contact requires the changing of the shape of the pinion profiles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.2-1.png",
        "caption": "Fig. 8.2 Vibration modes of a tire",
        "texts": [
            " 450 8 Tire Vibration (1) Eccentric vibration Referring to Eq. (6.52), the eccentric spring rate Rd of the rigid ring model is expressed as Rd \u00bc prD kr \u00fe kt\u00f0 \u00de; \u00f08:1\u00de where kr and kt are fundamental spring rates per unit length in the radian and circumferential direction at the radius of the belt rD. The total mass of the tread M is given by M \u00bc 2prDm; \u00f08:2\u00de where m is the mass of the tread per unit length in the circumferential direction at the radius of the belt rD. The eccentric vibration mode is shown in Fig. 8.2a. Using Eqs. (8.1) and (8.2), the fundamental frequency of eccentric vibration f is obtained as f \u00bc 1 2p ffiffiffiffiffi Rd M r \u00bc 1 2p ffiffiffiffiffiffiffiffiffiffiffiffi kr \u00fe kt 2m r : \u00f08:3\u00de Equation (8.3) is modified when the combined mass of the two sidewalls m0 per unit length in the circumferential direction is considered. If the sidewall mass m0 is assumed to be located at the radius of the belt rD, Eq. (8.3) can be rewritten as f \u00bc 1 2p ffiffiffiffiffiffiffiffiffi kr \u00fe kt 2m0 q m0 \u00bc m\u00fe am0; \u00f08:4\u00de where a is the modification parameter used to define the equivalent mass m0 and is expressed by1 a \u00bc 1 3 1\u00fe rD rD \u00fe rB : \u00f08:5\u00de (2) Lateral vibration Referring to Eq. (6.42), the lateral spring rate of a tire Rs is given as Rs \u00bc 2prDks: \u00f08:6\u00de 1Note 8.1. 8.1 Vibration Properties of Tires 451 The lateral vibration mode is shown in Fig. 8.2b, and the fundamental frequency f is given by f \u00bc 1 2p ffiffiffiffiffiffiffiffiffiffi Rs M \u00bc r 1 2p ffiffiffiffi ks m r : \u00f08:7\u00de When the combined mass of the two sidewalls m0 per unit length in the circumferential direction is considered, Eq. (8.7) can be rewritten as f \u00bc 1 2p ffiffiffiffi ks m0 q m0 \u00bc m\u00fe am0; \u00f08:8\u00de where a is the modification parameter used to define the equivalent mass m0 and is given by Eq. (8.5). (3) Out-of-plane torsional vibration The out-of-plane torsional vibration is torsional vibration around the vertical axis of a tire and is shown in Fig. 8.2c. Referring to Eq. (6.38), the torsional spring rate Rmz is given as Rmz \u00bc pr3Dks \u00fe p b=2\u00f0 \u00de2rD kr \u00fe kt\u00f0 \u00de; \u00f08:9\u00de where b is the belt width of a tire. The moment of inertia of a tire around the vertical axis is given by Iz \u00bc pr3Dm: \u00f08:10\u00de Using Eqs. (8.9) and (8.10), the fundamental frequency of out-of-plane torsional vibration f is given as 452 8 Tire Vibration f \u00bc 1 2p ffiffiffiffiffiffiffiffiffiffiffiffi Rmz Iz \u00bc s 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 m ks \u00fe b 2rD 2 kr \u00fe kt\u00f0 \u00de ( )vuut : \u00f08:11\u00de When the combined mass of the two sidewalls m0 per unit length in the circumferential direction is considered, Eq",
            "11) can be rewritten as f \u00bc 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 m0 ks \u00fe b 2rD 2 kr \u00fe kt\u00f0 \u00de s m0 \u00bc m\u00fe am0; \u00f08:12\u00de where a is the modification parameter used to define the equivalent mass m0 and is given by Eq. (8.5). (4) In-plane rotational vibration The in-plane rotational vibration is torsional vibration of the tread ring around the tire axle. Referring to Eq. (6.54), when the tread is twisted, the rotational spring rate of a tire is given as Rt \u00bc 2pr3Dkt: \u00f08:13\u00de The polar moment of inertia around the tire axle, Ip, is given by2 Ip \u00bc 2pr3Dm: \u00f08:14\u00de The rotational vibration mode is shown in Fig. 8.2d, and the fundamental frequency of rotational vibration around the tire axle f is given by f \u00bc 1 2p ffiffiffiffiffiffiffiffiffi Rt Ip \u00bc s 1 2p ffiffiffiffi kt m r : \u00f08:15\u00de When the combined mass of the two sidewalls m0 per unit length in the circumferential direction is considered, Eq. (8.15) can be rewritten as f \u00bc 1 2p ffiffiffiffi kt m0 q m0 \u00bc m\u00fe am0; \u00f08:16\u00de where a is the modification parameter used to define the equivalent mass m0 and is given by Eq. (8.5). 2Problem 8.1. 8.1 Vibration Properties of Tires 453 Sakai [11] derived the natural frequencies of tires with one point of contact",
            " The kinetic energy of the sidewall and tread T is expressed by T \u00bc 1 2 mv2 \u00fe 1 2 Za 0 m0 a v x a 2 dx \u00bc 1 2 v2\u00f0m\u00fe 1 3 m0\u00de; \u00f08:200\u00de where a is the radius of the tread, m0 is the combined mass of the two sidewalls, and m is the mass of the tread. Equation (8.200) shows that the kinetic energy of the sidewall is equal to the kinetic energy where the equivalent mass m0=3 is located on the tread. Notes 525 Another model for a was proposed by Nakajima, who derived the equivalent mass using the cylindrical model shown in Fig. 8.2. Suppose that the velocity of the sidewall v(r) linearly changes from the bead to the tread and is expressed by v\u00f0r\u00de \u00bc vD r rB\u00f0 \u00de rD rB ; \u00f08:201\u00de where vB and vD are, respectively, the velocities at rB and rD. The kinetic energy of the sidewall T is expressed by T \u00bc 1 2 ZrD rB 2pqhv2rdr \u00bc pqhv2D rD rB\u00f0 \u00de3 3rD \u00fe rB\u00f0 \u00de 12 rD rB\u00f0 \u00de2 \u00bc pqhv2D rD rB\u00f0 \u00de 3rD \u00fe rB\u00f0 \u00de 12 ; \u00f08:202\u00de where q is the density of the sidewall and h is the thickness of the sidewalls. The combined mass of the two sidewalls m0 is given by m0 \u00bc 2pqh r2D r2B : \u00f08:203\u00de Using Eqs. (8.202) and (8.203), the kinetic energy of the sidewalls T is rewritten as T \u00bc m0v2D rD rB\u00f0 \u00de 3rD \u00fe rB\u00f0 \u00de 24 r2D r2B\u00f0 \u00de \u00bc m0v2D 3rD \u00fe rB\u00f0 \u00de 24 rD \u00fe rB\u00f0 \u00de \u00bc 3rD \u00fe rB 12 rD \u00fe rB\u00f0 \u00de 1 2 m0v2D: \u00f08:204\u00de The equivalent combined mass of the two sidewalls and a are given by equivalent mass for both sidewalls \u00bc 3rD \u00fe rB 12 rD \u00fe rB\u00f0 \u00dem 0 ! a \u00bc 3rD \u00fe rB 12 rD \u00fe rB\u00f0 \u00de : \u00f08:205\u00de Another model for a assumes that the acceleration linearly changes from the bead to tread. As shown in Fig. 8.2, we suppose that acceleration in the z-direction at radius r is denoted \u20acz and acceleration in the z-direction at the belt is denoted \u20aczD. \u20acz is expressed by m treadm\u2019side wall a xFig. 8.44 Equivalent mass of the sidewall 526 8 Tire Vibration \u20acz \u00bc \u20aczD r rB\u00f0 \u00de=\u00f0rD rB\u00de: \u00f08:206\u00de The inertia force of the sidewalls per unit circumferential length F is given by F \u00bc 2 rD ZrD rB \u20aczqhrdr \u00bc 2q rD ZrD rB \u20aczD r rB\u00f0 \u00de rD rB hrdr \u00bc 2q\u20aczD rD rD rB\u00f0 \u00de Zr1 r0 r2 rBr hdr \u00bc 2qh\u20aczD rD rD rB\u00f0 \u00de 1 6 rD rB\u00f0 \u00de2 2rD \u00fe rB\u00f0 \u00de \u00bc qh r2D r2B 3rD \u20aczD 1\u00fe rD rD \u00fe rB ; \u00f08:207\u00de where q is the density of the sidewalls",
            "24 Figure 14.55a shows the region of polygonal wear for the relation between the number of tire rotations per second f (=X/2p) and the number of sides of the polygon N at k \u00bc 2:9 10 14 m=N. The solid line indicates the unstable region for polygonal wear r is positive while the dotted line indicates the stable region where r is negative. X1 (=f1/f) is the ratio of the primary natural frequency f1 to f. The primary natural frequency of the mode shape is the frequency of the eccentric vibration in Fig. 8.2 and is 70\u201380 Hz for a truck/bus radial tire. Figure 14.55b shows the value of r at N = 10. The magnitude of the positive value of r indicates the tendency of instability. 24Note 14.13. 14.10 Diagonal Wear and Polygonal Wear 1081 The following conclusions are drawn from Fig. 14.55. (i) The shape of the polygonal wear of tires is a regular polygon, where the number of sides is an integer. The region of instability is located on the left side of the curve of X1; i.e., (number of tire rotations per second) < (primary natural frequency of vertical vibration)/(number of sides of the polygon)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003884_robot.1990.126246-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003884_robot.1990.126246-Figure2-1.png",
        "caption": "Figure 2. Illustration of pattem parameters.",
        "texts": [
            " This phase begins at the moment when the forefoot leaves the ground and terminates as the heel strikes. As a consequence, there are four phases - support, deploy, swing, and place - for a leg during a complete walking cycle. Here the term \"phase\" is also used to describe the status of a leg. During the single-support phase, one leg is in the support phase, while the other leg is in the swing phase. In this section, we shall generate the biped walking trajectory specified by the parameters TI, T2, T4, S, H, A, Ay, and A=, as illustrated in Fig. 2. 2T1 is the time interval for the supporting phase, T2 is the time interval for the deploy phase, T3 is the time interval for the swing phase, and T4 is the time interval for the heel-contact (place) phase. These time intervals are measured according to one leg in a complete walking cycle. Since the left and right legs are a half-cycle shift along the time axis, the cadence T, defined here as the time necessary for one walking cycle, is equal to 4T1. The step length S is the distance that separates the two successive supports"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure16-1.png",
        "caption": "Fig. 16 Coordinate systems Sj and Se",
        "texts": [
            " System So is connected to he machine element 8 and represents the work head offset setting ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 motion Fig. 13 . Sw is connected to the work 8 and represents the work rotation with angular parameter Fig. 14 . System Se is connected to the eccentric setting element and represents the radial setting Fig. 15 . System Sj is connected to the tilt wedge base element which performs rotation relatively to the eccentric element to set the swivel angle j Fig. 16 . System Si is connected to the cutter-head carrier which performs rotation relatively to the tilt wedge base element to set the tool tilt angle i Fig. 17 . Through the coordinate transformation from Si to Sw, the position vector and the unit tangent at the current cutting blade point P can be represented in the coordinate system Sw, namely rw = Mwiri u, 20 tw = Mwiti u, 21 where Mwi is a resultant coordinate transformation matrix and is formulated by the multiplication of the following matrices representing the sequential coordinate transformations from Si to Sw, Mwi = MwoMopMprMrsMsmMmcMceMejM ji 22 where matrices Mwo , Mop Em , Mpr Xp , Mrs m , Msm Xb , Mmc , Mce s , Mej j and M ji i can be obtained directly from Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-42-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-42-1.png",
        "caption": "Figure 4-42. Dead-time effect: (a) measured current trajectory with sixth harmonics and reduced fundamental; (b) as in (a), with deadtime compensation (fs = 200 Hz ).",
        "texts": [
            "36 produces a nonlinear distortion of the average voltage vector trajectory uav. Figure 4-41 b shows an example. The distortion does not depend on the magnitude u* of the fundamental voltage and hence its relative influence is very strong in the lower-speed range where 4.5. Open Loop Schemes 177 u is small. Since the fundamental frequency is low in this range, the smoothing action of the load circuit inductance has little effect on the current waveforms, and the sudden voltage changes become clearly visible, Figure 4-42a. As a reduction of the average voltage occurs according to equation 4.36 when one of the phase currents changes its sign, these currents have a tendency to maintain their values after a zero crossing, Figure 4-43a. The situation is different in the generator mode of the machine. The average voltage then suddenly increases, causing a steeper rise of the respective phase current after a zero crossing. The machine torque is influenced in any case, exhibiting pulsations in magnitude at six times the fundamental frequency in the steady state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000932_j.jii.2021.100218-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000932_j.jii.2021.100218-Figure12-1.png",
        "caption": "Fig. 12. (a) 3D model of the part, (b) Transverse section of the 21st layer.",
        "texts": [
            " In order to filter out the most accurate solution, all the solutions are input to the SVR forward model as three input variables. Then, after comparing the value of (OD,BH) produced based on predicted solutions and the value of desired (OD,BH), the optimal solution will be filtered out. The problem that using 2-dimension input parameters to predict 3-dimension output parameters has been addressed at the expense of computer memory. The performance of the proposed algorithm and system was evaluated through the fabrication of a real-world workpiece, whose 3D model is shown in Fig. 12(a). The detailed fabrication process and relevant discussion are provided in this section. In this case study, the raw material was aluminium 4043 and CMTpulse welding method. The first step is to slice the 3D model into 39 layers including 3 base layers and 36 body layers (with the predetermined 2 mm layer height). As the 3D model illustrated in Fig. 12 (a), the shape of each layer is a \u2018doughnut\u2019 with a changing diameter. As shown in Fig. 12(b), the welding torch will move circularly to fill each layer with a number of weld beads. Thus, the overlapping distance of each weld bead varies for adjacent layers. To generate the near-net shape of the part, the welding parameters have to be constantly adjusted for each layer. However, it is difficult for the conventional bead modelling method to generate accurate welding parameters for all layers. As shown in Fig. 13(a), layers will be divided into a few groups and the same set of welding parameters will be selected to fabricate the target part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003316_0094-114x(95)00068-a-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003316_0094-114x(95)00068-a-Figure1-1.png",
        "caption": "Fig. 1. A general six-in-parellel SPS platform manipulator.",
        "texts": [
            " It was first demonstrated numerically that the problem may in general have at most 40 nonsingular solutions and this bound has been verified using several different mathematical arguments. The problem is reformulated in this report using a classical representation of rigid-body displacements: Study's soma coordinates, or equivalently, dual quaternions. This provides a much simpler analytical proof of the upper bound of 40. Moreover, the simple form of the equations may be useful in further studies of the problem. Consider a platform manipulator as shown in Fig. 1, consisting of a moving \"end plate\" supported from a \"base plate\" by six extensible \"legs\". On the end plate there have been selected six points having vector coordinates b0 . . . . , b5 in the reference frame of the body. For each of these there is a corresponding point in the base plate having vector coordinates a 0 , . . . , as, resp., in the fixed reference frame. At any particular position p and rotation R of the end plate, there will be unique squared distances L2i = (p + R b i - ai)T(p + R b i - ai), i = 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001121_j.matdes.2021.109685-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001121_j.matdes.2021.109685-Figure1-1.png",
        "caption": "Fig. 1. A schematic of the laser powder bed fusion (LPBF) process.",
        "texts": [
            " The graph theory method has the potential to serve LPBF practitioners as a rapid physics-based approach to guide part design and identify suitable processing parameters in place of expensive and time-consuming empirical trial-and-error optimization. 2021 The Authors. Published by Elsevier Ltd. This is anopenaccess article under the CCBY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction deposited onto the build plate using a blade (recoater) or roller- Overview Laser powder bed fusion (LPBF) is a metal additive manufacturing process in which a layer of material in powder form is deposited on a build plate (powder bed) and selectively melted using energy from a laser [1]. As shown in Fig. 1, in LPBF the powder is type mechanism. After a layer of powder is melted by the laser, a fresh layer of powder is deposited, and the process repeats until an entire part is built. Contemporary LPBF systems are typically equipped with a 250\u2013500 W fiber laser with an operating wavelength in the near infrared region (1050\u20131070 nm). The laser is scanned in the horizontal plane using a pair of galvanometric mirrors, with the typical scanning velocity in the range of 500\u20131000 mm s 1. The LPBF process continues to evolve as the process of choice for creation of complex, high-value components, particularly in the aerospace, tool and die, automotive, and biomedical industries [2,3]",
            " The lifting of the recoater blade reduces the possibility of the recoater impacting a smaller part. (d) to avoid spatter and debris from one part interfering with others, the parts are spaced with at least 5 mm gaps between each other and in a staggered manner. (e) The parts were located to facilitate the exhaust of soot particles away from a fresh deposited layer. The gas flow in this machine was from the front to the back of the machine which is shown with arrow in Fig. 4; noting that the gas exhaust port is to far-side from the door as seen in Fig. 1 and Fig. 3. Hence, the laser melted the parts in the reverse order of the gas flow \u2013 the laser processes the parts from back to front of the build plate. By processing parts closer to the exhaust port first minimizes the chance of soot particles interfering with parts that are yet to be melted. Two cone-shaped parts of height 20 mm were produced. We varied the inclination of the slant edge of the cone to the horizontal defined as the overhang angle. We built cones with the slant edge inclined at two overhang angles, namely, Z = 40 and Z = 45 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003565_tie.2003.817488-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003565_tie.2003.817488-Figure8-1.png",
        "caption": "Fig. 8. Coordinations and parameters.",
        "texts": [
            " We choose an adaptable background to make the background separation module work robustly [27]. The outputs from these two modules are compared in the clustering process. Only the common regions are conveyed to the calculation of a moment module, and the two\u2013dimensional (2-D) positions of the regions are calculated. Since a DIND has a database of the height of a color bar, one DIND is able to estimate the position of a color target. The 2-D positions of color targets in the image coordination are converted to 3-D positions in camera coordination. From Fig. 8, there exists the following relationship between camera coordination and world coordination, where is the pose, is the rotational matrix and is the translation matrix (1) These matrices are found from the calibration process of a DIND, based on Tsai\u2019s algorithm. After the target detection procedure, to get rid of errors, the 2-D Euclidean distances between the detected targets are checked. If the distance is too long or too short, the detected targets are neglected. Even after this, the result may still contain recognition errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.1-1.png",
        "caption": "Fig. 4.1 Model of a two-ply belt structure [1]",
        "texts": [
            " The interlaminar shear strain of a loaded tire causes a failure in the adhesive rubber layer of belt ends, and this strain microscopically consists of the intra-cord shear strain and inter-cord shear strain. The thickness of the adhesive rubber layer of a currently available tire tends to be low to satisfy requirements of material sustainability and low rolling resistance. Because the thinness of the rubber layer deteriorates the belt durability, a precise model for the belt structure, such as that of discrete lamination theory (DLT), is required to analyze the intra-cord and inter-cord shear strains. Akasaka and Shouyama [1] developed the DLT shown in Fig. 4.1 under the following assumptions. (i) The tire belt consists of two plies and an adhesive rubber layer and has infinite length. (ii) The cord is a square-shaped beam for which the sectional area is Af, the in-plane flexural rigidity is Df, the extensional rigidity of the cord is Ef and the cord distance is d, which is much longer than the side length of the square cord h0. \u00a9 Springer Nature Singapore Pte Ltd. 2019 Y. Nakajima, Advanced Tire Mechanics, https://doi.org/10.1007/978-981-13-5799-2_4 189 (iii) The cord is modeled by a beam, and the adhesive rubber layer is modeled by a plate",
            " (4) Total strain energy of a two-ply bias laminate The total strain energy of a two-ply bias laminate U is defined by the volume of the reference area S and the half thickness of the two plies h + h0: U \u00bc Uf \u00feUr \u00feU0: \u00f04:39\u00de The total strain energy of the two-ply bias laminate U is expressed by U \u00bc Ema 2 e20K0 \u00fex2K1 \u00fe 2e0xK2 \u00fe 2e0/\u00f0b\u00deK3 \u00fe 2e0w\u00f0b\u00deK4 \u00fe 2x/\u00f0b\u00deK5 \u00fe 2xw\u00f0b\u00deK6 \u00feK7 Rb 0 w2dy\u00feK8 Rb 0 /02dy\u00feK9 Rb 0 w02dy\u00fe 2K10 Rb 0 /0w0dy \u00feK11 Rb 0 /00 cos a w00 sin a\u00f0 \u00de2dy 8>>>>< >>>>: 9>>>>= >>>>; ; \u00f04:40\u00de where XH \u00bc x Em \u00bc Emhb=\u00f01 m2m\u00de: \u00f04:41\u00de The constants Ki (i = 0,\u2026,11) can be calculated if the belt structure and material properties are given. These equations for Ki (i = 0,\u2026,11) can be easily implemented in Mathematica or MATLAB.6 6Appendix 1. 202 4 Discrete Lamination Theory Suppose that the tensile external force T is applied to a two-ply bias laminate. The volume V with half-width b, half thickness of the laminate h + h0 in Fig. 4.1 and length a in Fig. 4.2 is expressed by V \u00bc Tae0=4: \u00f04:42\u00de The stationary condition of the potential P for the entire system is given by dP \u00bc d U V\u00f0 \u00de \u00bc Ema de0 e0K0 \u00fexK2 \u00fe/\u00f0b\u00deK3 \u00few\u00f0b\u00deK4 T 4Em n o \u00fe dx xK1 \u00fe e0K2/\u00f0b\u00deK5 \u00few\u00f0b\u00deK6f g \u00fe d/\u00f0b\u00de e0K3 \u00fexK5\u00f0 \u00de\u00fe dw\u00f0b\u00de e0K4\u00fexK6\u00f0 \u00de \u00feK7 Rb 0 wdwdy\u00feK8 Rb 0 /0d/0dy\u00feK9 Rb 0 w0dw0dy\u00feK10 Rb 0 /0dw0dy \u00feK10 Rb 0 w0d/0dy\u00feK11 Rb 0 /00 cos a w00 sin a\u00f0 \u00de d/00 cos a dw00 sin a\u00f0 \u00dedy 2 6666666666664 3 7777777777775 \u00bc 0: \u00f04:43\u00de Applying integration by parts to Eq. (4.43) and considering that /(y) and w(y) are odd functions with respect to y, we obtain de0 e0K0 \u00fexK2 \u00fe/\u00f0b\u00deK3 \u00few\u00f0b\u00deK4 T 4Cm \u00fe dx xK1\u00fe e0K2 \u00fe/\u00f0b\u00deK5 \u00few\u00f0b\u00deK6f g \u00fe d/\u00f0b\u00de e0K3 \u00fexK5\u00fe/0\u00f0b\u00deK8 \u00few0\u00f0b\u00deK10 /000\u00f0b\u00de cos a w000\u00f0b\u00de sin af g cos aK11\u00bd \u00fe dw\u00f0b\u00de e0K4 \u00fexK6\u00few0\u00f0b\u00deK9 \u00fe/0\u00f0b\u00deK10 \u00fe /000\u00f0b\u00de cos a w000\u00f0b\u00de sin af g sin aK11\u00bd \u00fe d/0\u00f0b\u00de /00\u00f0b\u00de cos a w00\u00f0b\u00de sin af g cos aK11\u00bd dw0\u00f0b\u00de /00\u00f0b\u00de cos a w00\u00f0b\u00de sin af g sin aK11\u00bd : \u00fe Zb 0 K11 cos a /\u00f0IV\u00de cos a w\u00f0IV\u00de sin a K8/ 00 K10w 00 n o d/dy \u00fe Zb 0 K11 sin a /\u00f0IV\u00de cos a w\u00f0IV\u00de sin a K9w 00 K10/ 00 \u00feK7w n o dwdy \u00bc 0 \u00f04:44\u00de Euler equations are derived from Eq",
            "15 Distribution of interlaminar shear stress ratio szx=e0 at the cross section x = 0 [1] Further research is required because the maximum value of the sawtooth distribution may be the initiation point of belt failure. Figure 4.16 shows the interfacial shear stress ratio sC/e0 of a two-ply laminate with a bias angle a = 30\u00b0 along the y-axis. The interfacial shear stress ratio is a maximum at the center of the belt. Akasaka also developed DLT under bending moment. Suppose that the bending moment M0 is applied to a two-ply bias laminate as shown in Fig. 3.21. The displacement in the thickness direction is constrained and the bias laminate is modeled using the discrete model as shown in Fig. 4.1. Referring to Eqs. (3.141) and (4.19), the displacements under the bending moment can also be expressed by adding nonperiodic displacements to the periodic displacements of Eq. (4.3): u \u00bc jxy\u00fe hw\u00f0y\u00de\u00fe jy\u00f0 \u00def \u00f0n\u00de v \u00bc jx2=2\u00fe h/\u00f0y\u00de\u00fe f0\u00f0s\u00def \u00f0n\u00de ; \u00f04:99\u00de where j is the curvature of bending deformation while w(y) and /(y) are, respectively, functions related to extension or compression both in the width direction and longer direction due to the bending deformation. Comparing Eq. (4.19) with Eq. (4.99), the tensile strain e0 in displacement u is replaced by \u2212jy, jx2/2 is added to the displacement v of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000720_j.surfcoat.2020.125646-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000720_j.surfcoat.2020.125646-Figure2-1.png",
        "caption": "Fig. 2. (a) Actual and (b) schematic of laser beam intensity profile.",
        "texts": [
            " Inconel 718, a nickel based super alloy with potential application in aerospace industry was used as substrate with dimensions of 25 mm \u00d7 25 mm \u00d7 8 mm. Chemical composition of the substrate and metal powder used in the present work are presented in Tables 1 and 2 respectively. A 2 kW Yb-fiber laser (IPG photonics, YLR 2000) operating at 1.07 \u03bcm wavelength, capable of operating in both CW and modulated modes was used as the energy source. The laser beam has a multimode intensity profile with high intensity at the center and two annular rings of relatively low intensities [37]. Fig. 2 shows the actual and schematic of laser beam intensity profile along with pyrometer temperature detection zone, whose implications will be discussed in a subsequent section. An in-house designed and fabricated co-axial laser cladding head, integrated to the laser module through optical fiber, mounted on a 5-axis CNC was used for the deposition process. A plano-convex lens with 200 mm focal length was used in laser cladding head to focus the 16 mm collimated laser beam coming out of the laser system",
            " 8 (a)\u2013(f) show schematic of clad track geometrical aspects and the effect of scan speed and preheating temperature on it i.e. clad width, height, melt depth, area and dilution, respectively. All geometrical aspects of clad tracks including dilution increased with substrate pre-heating temperature and reduced with increasing scan speed. Though the laser beam diameter was ~1.6 mm (encompassing 86% laser power), the clad track width on substrate at ambient temperature was less than the beam diameter; However, it exceeded beyond the beam diameter on pre-heated substrates. As shown in Fig. 2, the laser intensity reduces along radial direction, and therefore there will be a certain radial distance from the center of the beam where the melting point of powder/ substrate would reach forming the track and beyond that powder would remain un-melted. With the preheating the surface absorptivity tends to increase enhancing the absorbed laser power, both these, i.e. preheating and higher absorbed laser power could widen the radial extent up to which melting of powder/substrate could take place",
            " However, with preheating the temperature gradient in the substrate gets reduced which causes a decrease in the cooling rate (Fig. 9(b)). It is interesting to note that the heating rate i.e. rate at which laser power is induced into the cladding zone which is supposed to be dependent on the laser scan speed alone also showed a decreasing trend with increasing substrate preheating temperature. The increased thermal conductivity of Inconel 718 substrate with increased preheating temperature [43] could be one of the reasons. Another reason is as the following: As shown in Fig. 2(b), as the laser beam having multimode intensity profile approaches the zone at which pyrometer is focused, the temperature value slowly rises beyond the detection limit of pyrometer (~800 \u00b0C) and reaches a maximum value. The time taken to reach the pyrometer detection limit depends on the initial substrate temperature. Therefore, in the case of substrate with preheating, the temperature crosses this limit earlier compared to substrate at room temperature. However, the Table 5 Material properties [25,44,45]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.9-1.png",
        "caption": "Fig. 7.9: Properties of the Boundary Curve: \u2212 \u2212 \u2212 \u2212 \u2212 Trajectory Source (eqn.()), \u2212\u00b7\u2212\u00b7\u2212\u00b7\u2212 Trajectory Sink (eqn.()), \u2014\u2014\u2014 Allowed for Trajectories (eqn.())",
        "texts": [
            " From this we find the following properties of the boundary curve s\u0307 = s\u0307max: \u2022 trajectory sink parts with the property (s\u03072)\u2032max < [(s\u03072)\u2032E,min](s\u03072=s\u03072max), (7.39) \u2022 trajectory source parts with the property (s\u03072)\u2032max > [(s\u03072)\u2032E,max](s\u03072=s\u03072max), (7.40) \u2022 arcs being allowed for trajectories due to special constraints (equations (7.37) and Figure 7.8b ); here we have [(s\u03072)\u2032E,min](s\u03072=s\u03072max) < (s\u03072)\u2032B,max < [(s\u03072)\u2032E,max](s\u03072=s\u03072max) (7.41) Each boundary curve can be partitioned into these three regimes. Figure 7.9 depicts an example of a three-link robot tracking a straight line. With these preparations we are able to construct the minimum-time solution applying the procedure below (for illustration see also Figure 7.10): \u2022 Start at s = 0 and s\u0307 = 0, evaluate an extremal with maximum acceleration, follow it to the end of the trajectory or to the point where it disappears at a trajectory sink (Figure 7.10a). \u2022 Start at s = sF and s\u0307 = 0 and track an extremal with maximum deceleration until it meets the acceleration extremal starting from s = 0 or until it intersects its originating point at the s\u0307max-curve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure16-1.png",
        "caption": "Fig. 16. Illustration of transmission errors and shift of bearing contact on the pinion tooth surface of a profile-crowned gear drive caused by Dc: (a) function of transmission errors with error Dc \u00bc 30; (b) path of contact when no errors are applied; (c) path of contact with error Dc \u00bc 30.",
        "texts": [
            " 14). Such errors cause discontinuous linear functions of transmission errors which result in vibration and noise, and may cause as well edge contact wherein meshing of a curve and a surface occurs instead of surface-to- surface contact (see Section 9). In a misaligned gear drive, the transmission function varies in each cycle of meshing (a cycle for each pair of meshing teeth). Therefore the function of transmission errors is interrupted at the transfer of meshing between two pairs of teeth (see Fig. 16(a)). New approaches for computerized design, generation and application of the finite element method for stress analysis of modified involute helical gears are proposed. The basic ideas proposed in the developed approaches are as follows: ii(i) Line contact of tooth surfaces is substituted by instantaneous point contact. i(ii) The point contact of tooth surfaces is achieved by crowning of the pinion in profile and longitudinal directions. The tooth surface of the gear is a conventional screw involute surface",
            " 15, 16(b) and (c)). (3) Error DE of shortest center distance does not cause transmission errors. The gear ratio m12 remains constant and of the same magnitude m12 \u00bc x\u00f01\u00de x\u00f02\u00de \u00bc N2 N1 : \u00f028\u00de However, change of DE is accompanied with the change of radii of operating pitch cylinders and the operating pressure angle of cross-profiles (Fig. 12). (4) The main disadvantage of meshing of profile-crowned tooth surfaces is that Dc and Dk cause a dis- continuous linear function of transmission errors as shown in Fig. 16(a). Such functions cause vibra- tion and noise and this is the reason why a double-crowned pinion instead of a profile-crowned one is applied. Errors Dc and Dk cause as well the shift of the bearing contact on the pinion and gear tooth surfaces. Our investigation shows that the main defects of the gear drive for the case wherein L 6\u00bc 0 and Dc 6\u00bc 0 are the unfavorable functions of transmission errors, similar to the one shown in Fig. 16. We remind that errors of shaft angle and lead angle cause a discontinuous linear function of trans- mission errors (see Section 4) and high acceleration and vibration of the gear drive become inevitable. Longitudinal crowning of the pinion tooth surface, in addition to profile crowning, is provided for transformation of the shape of the function of transmission errors and reduction of noise and vibration. The contents of this section cover longitudinal crowning of the pinion by application of a plunging generating disk"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003960_s0039-9140(03)00125-5-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003960_s0039-9140(03)00125-5-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of a Ru-complex modified CCE in 0.1 M phosphate buffer (pH 2) solution containing (a) 0 and (b) 2.86 mM L-cysteine. \u2018c & d\u2019 as \u2018a & b\u2019 for bare CCE. Scan rate 10 mV s 1.",
        "texts": [
            " In amperometric experiments the modified CCEs rotated by contact them with a Methrom drive shaft. The electrochemical response of a Ru-complex modified CCE was previously reported [33]. The catalytic oxidation of L-cysteine and glutathione at the Ru-complex modified CCEs has been examined to evaluate the feasibility of using the electrodes in electro-catalysis and electro-analysis. In order to test the electrocatalytic activity of the Ru-complex doped CCEs, the cyclic voltammograms were obtained in the absence and presence of these compounds. Fig. 1 shows cyclic voltammograms for the electro-catalytic oxidation of Lcysteine at the bare and modified CCEs in 0.1 M phosphate buffer (pH 2). Upon the addition of 2.86 mM L-cysteine, there is a dramatic enhance- ment of the anodic peak current and the cathodic peak current disappeared (Fig. 1b), which indicate a strong catalytic effect. The anodic peak potential for the oxidation of L-cysteine at Ru-complex modified CCE is about 800 mV while at the bare electrode the L-cysteine is not oxidized until 1200 mV (Fig. 1d). Thus, a decrease in overpotential and enhancement peak current for L-cysteine oxidation is achieved with the modified electrode. The same behavior was observed for glutathione at the surface of modified CCE. Fig. 2 shows the dependence of the voltammetric response of mod- ified CCE on the L-cysteine concentration with the addition of L-cysteine (0.9 /2.86 mM). There was an increase in the anodic peak current and a decrease in the cathodic peak current. Plot of Icat vs. L-cysteine concentration was linear in the concentration range 0",
            " Ip 0:496nFAD1=2(nF=RT)1=2Cs (5) where D and Cs are the diffusion coefficient (cm2 s 1) and the bulk concentration (mol cm 3) other symbols have their usual meaning. Low value of Kcat results in values of the coefficient lower than 0.496. For low scan rate (5 /20 mV s 1) the average value of this coefficient was found to be 0.40 for a Ru-modified electrode with a coverage 3 /10 9 mole cm 2, a geometric area (A ) of 0.0314 cm2 in 3.75 mM glutathione at pH 2. The diffusion coefficient (D ) value calculated by chronoamperometry method and it was about 4.2 /10 5 cm2 s 1. According to the approach of Andrieux and Saveant and using Fig. 1 Ref. [35], the average value of Kcat was calculated to be 2.5 /103 M 1 s 1. The values of diffusion coefficient and catalytic rate constants for L-cysteine are 3 /10 5 cm2 s 1 and 2.1 /103 M 1 s 1, respectively. Since at concentrations suited for cyclic voltammetry, the oxidation of L-cysteine or glutathione in aqueous solution passivated the composite electrode, the amperometry under stirred conditions or the flow injection analysis with amperometric detection is employed rather than cyclic voltammetry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.36-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.36-1.png",
        "caption": "Fig. 2.36: Journal Bearing",
        "texts": [],
        "surrounding_texts": [
            "Nonlinear damping behavior in machines and mechanisms is very diverse. Material damping, friction in all components having relative motion with respect to other components, damping in all connecting elements like screws or press fits are a few examples. The mounts connecting the motor with the automobile body consist of visco-elastic springs with a progressive characteristic. Surveys of nonlinear damping my be seen from the literature ([47], [266]). A practically reasonable measure of damping is the \u201crelative damping\u201d defined as the friction losses per cycle, which is proportional to the area enclosed by the hysteresis cycle (Figure 2.37). The mechanical losses due to such a hysteresis behavior is the integral for one cycle WD = \u222e \u03c3d\u03b5, or WD = 1 T t+T\u222b t FTDvreldt, (2.213) which represents in the first case the work of damping per volume [Nm/m3] for arbitrary \u03c3 \u2212 \u03b5 \u2212 curves, in the second case the damping work in [Nm]"
        ]
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.7-1.png",
        "caption": "Fig. 6.7: Pressure sensor using the resonance principle. According to [Tilm93]",
        "texts": [
            " The sensor unit is made by anisotropically etching (110) silicon and then fastening it to a pyrex substrate through anodic bonding. The prototype of the capacitive microsensor had a nominal capacitance of 1 pF. Measurements in this range can easily be handeled by commercially available microelectronic measuring devices. It was possible to measure very small forces with a resolution of 20 nm (0.01-10 N). The same structure can be used as a positioning unit for nanorobots. Resonance sensor for measuring pressure In Figure 6.7, a pressure resonance sensor is shown. The device consists of a silicon substrate, a diaphragm and three transducers equally spaced on the annular diaphragm. Each transducer consists of two resonators which oppose each other. If a pressure is applied to the diaphragm, the deformation causes the resonant frequencies of the resonators 1 and 2 to increase or decrease, respectively. The frequency difference between the two resonators serves as the output signal of the sensor. By averaging the measurements of the three resonator transducers, it is possible to compensate for errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.21-1.png",
        "caption": "Figure 7.21 shows the maximum shear stress normalized by the average compressive stress r0 when the shape factor S is changed. The figure reveals the critical friction coefficient for there to be no slippage at the edge of the block. For example, because the maximum shear strain is a maximum at S = 1.05, the friction coefficient must be larger than 0.58 for there to be no slippage at the edge of a block in compression.",
        "texts": [],
        "surrounding_texts": [
            "The substitution of Eq. (7.66) into Eq. (7.77) yields\nsxzjz\u00bc0\nr0 \u00bc Sn\n1 2 \u00fe 4 p2 \u00fe p2 12 S 2 ; \u00f07:78\u00de\nwhere\nr0 is the average compressive stress\nFigure 7.20 shows the shear stress distributions on the lower surface of a compressed block calculated using Eq. (7.78) (Akasaka\u2019s model) and Eqs. (7.28) and (7.36) (Horton\u2019s model). The parameters used in these calculations are a = 30 mm, h = 8 mm, G = 1 MPa and F/a = 0.3 MPa. The two models provide similar distributions.\nThe shear stress sxz has a linear distribution and a maximum value at n = \u00b11. Substituting n = 1 into Eq. (7.78), the maximum shear stress smax\nxz of Akasaka\u2019s model is given as\nsmax xz\nr0 \u00bc S 0:905\u00fe 0:822S2 : \u00f07:79\u00de\n0 0.2 0.4 0.6 0.8\n1 1.2 1.4 1.6\n-1 -0.5 0 0.5 1\n\u03c3zz|z=h/ \u03c30\n\u03be\nHorton\nAkasaka\nFig. 7.19 Contact pressure distribution of a block in compression\n7.3 Properties of the Block in Contact with the Road 399",
            "(3) Fundamental equations for the case of a finite or zero friction coefficient\nKim and Park [20] extended Akasaka\u2019s study by including the slip condition. In their analysis, a block with a flat surface was pressed on a flat surface and only the area near the block edges gradually slipped in compression. Their analysis may be a little different from the analysis of the block of a rolling tire. Because a tire has double curvatures in the lateral and circumferential directions, a block begins connecting with a road from the run-in edge of the block to the run-out edge of the block. The lateral displacement at the edges of the area where the block is in contact with the surface may therefore be larger than that given by their model.Nakajima\n0.8\n\u03c4xz|z=h/ \u03c30\n400 7 Mechanics of the Tread Pattern",
            "also modified Eq. (7.51) to consider the block deformation of a rolling tire and expressed the displacements u and w as\nu \u00bc sin pz h \u00feB h z h ax w \u00bc c z h ;\n\u00f07:80\u00de\nwhere B(h \u2212 z)/h is introduced to consider the nonzero lateral displacement u at z = 0. The substitution of Eq. (7.80) into Eq. (7.55) yields\nexx \u00bc sin pz h \u00feB h z h a\u00fe 1 2 sin pz h \u00feB h z h\n2\na2\nezz \u00bc c h \u00fe 1 2 c h 2 \u00fe 1 2 p h cos pz h B h\n2\na2x2\ncxz \u00bc p h cos pz h B h 1\u00fe sin pz h \u00feB h z h a ax:\n\u00f07:81\u00de\nWhen the friction coefficient is zero, the shear stress is zero on the contact surface of the block. This requirement yields\ncxz x\u00bca 2;z\u00bc0\u00bc 0 ) p h B h 1\u00feBaf g \u00bc 0: \u00f07:82\u00de\nFrom Eq. (7.82), the condition of zero friction coefficient is obtained as\nB \u00bc p; \u00f07:83\u00de\nwhere\nSimilar to Eqs. (7.52) and (7.53), the increase in volume due to the barrel deformation DV and the decrease in volume due to the compressive deformation DV 0 are given by\nDV \u00bc aah 2 p \u00fe B 2\nDV 0 \u00bc ac:\n\u00f07:84\u00de\nBecause the incompressibility of rubber requires the relation DV \u00bc DV 0, the unknown parameter c is determined by\n7.3 Properties of the Block in Contact with the Road 401"
        ]
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.28-1.png",
        "caption": "Fig. 8.28 Fig. 8.29",
        "texts": [
            "075 and 0.325 at the hyperbolic fixed point 294 Bifurcation and Chaos in Engineering A (0.7, 0.7) and the gradients of the characteristic direction are 1 :3075 and 1 :0.325; the characteristic line is the stable and unstable manifolds of the linearized system at point A. In order to obtain the unstable manifold of the non-linear system we take a certain point on the small segment AB of the characteristic line of 1 :3.075. After many iterations, this will expand into an unstable manifold as shown in Fig. 8.28, namely the solid line ABCDEFG ... . At the beginning this curve approximates to a straight line, but then it gradually begins to bend owing to the influence of the non linear term. When it returns to A, the bending amplitude and oscillating amplitude become bigger and bigger. We can draw the stable manifold by the inverse transformation cp-l in the same way. But for the symmetry, we make the solid line ABCDEFG ... a mirror reflection in OA and then obtain the stable manifold AIHGFED, represented by the broken line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003228_a:1008914201877-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003228_a:1008914201877-Figure15-1.png",
        "caption": "Figure 15. Joint names and reference positions for the excavator.",
        "texts": [
            " Thus, when the left hand side of a particular rule evaluates to true, its corresponding command gets sent to the excavator. The rules get re-evaluated at a fixed rate as state information is obtained, 10 Hz for example, during the execution of the excavator\u2019s motion. Fig. 14 shows the script rules for the truck loading task. The numbers in boldface are one example set of script parameters, which will be described in more detail below. The \u03b8 \u2019s are the excavator\u2019s state, in this case the angular positions of the joints. The definitions of the joints along with their lines of reference are shown in Fig. 15. The commands are desired angular joint positions. Notice that each joint has its own separate script. Therefore, only one rule per joint may be active at a time. The script parameters are computed before each loading pass starts using the information about the truck\u2019s location and the desired dig and dump points which it receives from the truck recognizer, dig point planner, and dump point planner software modules respectively. There are two types of script parameters, those which appear in the left hand side of the script rules and affect which commands are sent by the planner, and the joint commands themselves which appear on the right hand side of the rules"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure6-24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure6-24-1.png",
        "caption": "Figure 6-24. Cross section of a hybrid PM induction machine, showing simplified block diagram of open loop voltsper-hertz control scheme.",
        "texts": [
            " In contrast to the trapezoidal PMAC drive, the sinusoidal version of closed loop current regulation conventionally requires at least two current sensors to directly measure the phase currents. (The third phase current can be inferred from the other two because of the assumed wye connection, so that iA + iB + ic = 0.) Open-Loop V\\Hz Control. As discussed briefly in Section 6.1.1, buried-magnet PMAC machines can be designed with an induction motor squirrel cage winding embedded along the surface of the rotor as sketched in Figure 6-24. This hybridization adds a component of asynchronous torque production so that the PMAC machine can be operated stably from an inverter without position sensors. This simplification makes it practical to use a simple constant volts-per-hertz (V/Hz) control algorithm as shown in Figure 6-24 to achieve open loop speed control for applications such as pumps and fans that do not require fast dynamic response. According to this approach, a sinusoidal voltage PWM algorithm is implemented which linearly increases the amplitude of the applied fundamental voltage amplitude in proportion to the speed command to hold the stator magnetic flux approximately constant. The open loop nature of this control scheme makes it necessary to avoid sudden large changes in the speed command or the applied load to avoid undesired loss of synchronization (pull-out) of the PMAC machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000721_j.sna.2020.111973-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000721_j.sna.2020.111973-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of the designe",
        "texts": [
            " With the distance of \u221a 3R in between, the two identical circular electrical coils can generate a uniform-gradient magnetic field near the center of the two coils by applying the equal amount of electrical current to the respective coils in opposite direction, known as gradient-field Maxwell coil. A magnetic flux gradient induces a magnetic gradient force to the magnetic material. The magnetic gradient force in the magnetic flux gradient can be estimated as [28] F = V(M \u00b7 \u2207)B (2) The schematic of the fabricated electromagnetic coil system is indicated with its specifications in Fig. 2. The fabricated electromagnetic coil system consists of two coil pairs functioned as Helmholtz and Maxwell coils in order to generate the uniform magnetic fields and the magnetic flux gradient, respectively. The electromagnetic coil system is intended to be horizontally and manually rotatable around the center of the system, utilizing thrust ball bearings. The Helmholtz coil produces a uniform magnetic field capable of magnetizing and aligning the microrobot to the targeted direction. The J. Jeong, D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000286_j.optlaseng.2019.05.020-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000286_j.optlaseng.2019.05.020-Figure8-1.png",
        "caption": "Fig. 8. Thermal image by infrared cameras: (a) the melt pool (circular beam spot) [72] , (b) the entire part including the melt pool [70] .",
        "texts": [
            " Then the thermal metrics of the melt pool, such as the hermal gradient at the trailing edge and the area, can be extracted to uild a 3D representation demonstrating their evolution during the enire printing process, as shown in Fig. 7 (c) and (d). These 3D spatial r v n fi o p t i t c c b i 3 m a a c u a a v e i r econstructions are useful in understanding the melt pool characteristic ariations and have a potential for assessing part quality (e.g., discontiuity and microstructure). Infrared camera is another useful tool for fulleld thermal imaging [68] . Fig. 8 presents the typical infrared images f the melt pool and DLD process using Fe-based alloy and Inconel 718 owder, respectively, directly showing the surface temperature distribuion [70,72] . However, the melt pool is undergoing complicated physcal changes leading to a nonconstant emissivity. Accordingly, similar o single-color pyrometers, the use of unvarying emissivities in infrared amera measurements (0.3 for Fe-based alloy and 0.1 for Inconel 718) an result in inaccurate and unreliable results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003302_s0967-0661(01)00105-8-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003302_s0967-0661(01)00105-8-Figure2-1.png",
        "caption": "Fig. 2. Frames and joint variables.",
        "texts": [],
        "surrounding_texts": [
            "The experimental comparison is carried out on a twojoints planar direct drive prototype robot manufactured in the laboratory (IRCCyN) (Figs. 1\u20133), without gravity effect. The description of the geometry of the robot uses the modified Denavit and Hartenberg notation (Khalil & Dombre, 1999). The robot is directly driven by two DC permanent magnet motors supplied by PWM choppers. The dynamic model depends on eight minimal dynamic parameters, including four friction parameters: v \u00bc ZZR1 Fv1 Fs1 ZZ2 LMX2 LMY2 Fv2 Fs2 T ; ZZR1 \u00bc ZZ1 \u00feM2L 2; where L is the length of the first link, M2 the mass of link 2, ZZ1 and ZZ2 the drive side moment of inertia of links 1 and 2, respectively, LMX2 and LMY2 the first moments of link 2 multiplied by the length L of link 1, Fv1;Fs1;Fv2;Fs2 are the viscous and coulomb friction parameters of links 1 and 2, respectively. The inverse dynamic model used to compute WLS is written as Eq. (3): where C2 \u00bc cos\u00f0q2\u00de and S2 \u00bc sin\u00f0q2\u00de: The direct dynamic model necessary to compute the extended Kalman filtering algorithm is written as Eq. (11) with q \u00bc q1 q2 T and s \u00bc t1 t2 T : M \u00bc M11 M12 M12 ZZ2 \" # ; M11 \u00bcZZR1 \u00fe ZZ2 \u00fe 2LMX2C2 2LMY2S2; M12 \u00bcZZ2 \u00fe LMX2C2 LMY2S2: The joint position q and the current reference VT (the control input) are collected at a 100Hz sample rate while the robot is tracking a fifth order polynomial trajectory. This trajectory has been calculated in order to obtain a good condition number Cond\u00f0Ww\u00de \u00bc 290 and Cond\u00f0U\u00de \u00bc 100: This means that it is an exciting trajectory taking the whole trajectory all over at the time of the test. Both methods are performed in a closed loop identification scheme (simply joint PD control), using the same data q and s; where each torque sj is calculated as sj \u00bc GTjVTj ; where GTj is the drive chain gain which is considered as a constant in the frequency range of the robot dynamics. Fig. 4 presents the torque of motors 1 and 2."
        ]
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure4-1.png",
        "caption": "Fig. 4. Schematic generation of face-gear tooth and limitation of the tooth length by magnitudes L1 and L2.",
        "texts": [
            " 12, 21) wi \u00f0i \u00bc 2;w\u00de angle of rotation of the face gear (i \u00bc 2) and the worm (i \u00bc w) considered during the process of generation (Figs. 12, 21) h\u00f0i\u00de j ; u\u00f0i\u00dej \u00f0j \u00bc s; 1\u00de surface parameters of the rack-cutter for the shaper (j \u00bc s) and the pinion (j \u00bc 1), for driving side (i \u00bc d) and coast side (i \u00bc c) (Fig. 9) Ews shortest distance between the axes of the worm and the shaper (Fig. 21) fd parameter that determines location of point Oq (Fig. 9) Li \u00f0i \u00bc 1; 2\u00de inner (i \u00bc 1) and outer (i \u00bc 2) limiting dimensions of the face-gear (Fig. 4) Lis \u00f0i \u00bc 2;w\u00de lines of tangency between the shaper and the face-gear (i \u00bc 2), the shaper and the worm (i \u00bc w) (Figs. 3,13\u201315) Mji, Lji matrices 4 4 and 3 3 for transformation from Si to Sj of point coordinates and projections of vectors Ni \u00f0i \u00bc s; 1; 2;w\u00de number of teeth of the shaper (i \u00bc s), of the pinion (i \u00bc 1), of the face-gear (i \u00bc 2), of the generating worm (i \u00bc w) p circular pitch P diametral pitch rpj \u00f0j \u00bc s; 1\u00de radius of the pitch circle of the shaper (j \u00bc s) and the pinion (j \u00bc 1) (Figs",
            " The surfaces of the shaper Rs and the face-gear R2 are in line tangency at every instant. However, surface R2 and pinion surface R1 are in tangency at a point at every instant since Np < Ns. The tooth surfaces R2 of the face-gear generated by an involute shaper are shown in Fig. 3(a). Lines L2s represent the instantaneous lines of tangency of R2 and shaper Rs, shown on R2. The cross-sections of the face-gear tooth are shown in Fig. 3(b). The tooth length of the face-gear has to be limited by dimensions L1 and L2 (Fig. 4) to avoid undercutting that occurs in plane A, and tooth pointing in plane B [8]. A unitless coefficient c defines the tooth length and is represented as c \u00bc L2 L1 m \u00f01\u00de Coefficient c depends on the gear ratio and other design parameters (see Section 3). The face-gear tooth surface has a fillet (Fig. 3(a)) that might be generated by (i) the edged top of the shaper tooth, or (ii) a rounded top of the shaper tooth (Fig. 5). Investigations show that application of a shaper with a rounded top enables the bending stress to be reduced by 12% (see Section 8)",
            " Derivations similar to those applied in Section 4.1 are based on the following procedure: Step 1: We obtain the family of pinion rack-cutters represented in coordinate system S1 as r1\u00f0ue; he;we\u00de \u00bc M1e\u00f0we\u00dere\u00f0ue; he\u00de \u00f011\u00de where matrix M1e describes coordinate transformation from Se via S n to S1 (Fig. 11(b) and (c)). Step 2: Using the equation of meshing between the rack-cutter and the pinion, we obtain ue\u00f0we\u00de \u00bc xeNye yeNxe rp1Nye we \u00f012\u00de Generation of R2 by a shaper is represented schematically in Fig. 4. We apply for the derivation of R2 (see Fig. 12): (i) movable coordinate systems Ss and S2, rigidly connected to the shaper and the face-gear, respectively, and (ii) fixed coordinate system Sm and Sp, rigidly connected to the housing of the generating equipment. Surface R2 of the face-gear is determined as the envelope to the family of shaper surfaces Rs. Surface R2 has to be determined as a regular one, therefore undercutting has to be avoided. We use in the derivations the concept of relative velocity v\u00f0s2\u00des between the shaper and the face-gear and the basic theorem of avoidance of surface singularities [8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003838_s0301-679x(03)00094-x-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003838_s0301-679x(03)00094-x-Figure4-1.png",
        "caption": "Fig. 4. Friction measurement set-up with compensating counterweight.",
        "texts": [
            " Summing up the load components, he found that for 10, 15 and 20 balls in the bearing, the total load-carrying capacity divided with the maximum load on one ball was the number of balls divided with 4.37. To be on the safe side, he gave the famous equation: P0 5\u00b7P /z (1) where P0 = maximum load on one ball; P = maximum load on one ball; and z = number of balls. For friction calculations, he also found that the sum of the radial forces around the circumference of the bearing was 1.2 times the external load. Stribeck designed and manufactured a friction torque measurement rig, which automatically compensated for the weight of the different moving parts, see Fig. 4. He was thereby able to measure the small friction with high accuracy. He found that for small amounts of lubricant in the bearings, the friction was independent of the temperature. His experiments were run at 65, 100, 130, 190, 380, 580, 780 and 1150 rpm, starting with the lowest speed. When decreasing the speed from 1150 rpm, Stri- beck noticed that the friction was lower than during the speed increase despite almost constant temperature. He assumed that the friction decrease was due to running in of the surfaces, as this phenomenon was much stronger for rough surfaces than for polished surfaces, where the friction was not changed by running in"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003788_an9921701657-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003788_an9921701657-Figure3-1.png",
        "caption": "Fig. 3 Schematic diagram of implantable glucose enzyme electrode (from ref. 26)",
        "texts": [
            "24JS This polymer class is particularly attractive for such use, as it has already been tried and evaluated in vivo for prosthetic devices, and has some claims to biocompatibility. Polyurethanes can be coated over planar microfabricated electrodes, or on needle-type enzyme electrodes. They probably present a tortuous microporous barrier to substrate diffusion while allowing freer passage for 0 2 . A recent design for an implantable oxidase based glucose sensor26 has deployed the electrode sensor surface along the needle shaft rather than at the tip, as is usual, to facilitate membrane coating (Fig. 3). Future membrane fabrication technologies will probably lead to further improvement in membrane bulk properties to optimize mass transport and bioreagent immobilization; also, differential control over surface interfacial properties through surface derivatization will be possible. Thus, in one study, by partial ozonolysis of an isoprene-propoxysilane copolymer layer, it has proved possible to create highly controlled pores that are tailored for enzyme attachment ,27 and recently, plasma deposition of diamond-like carbon on pre-formed membranes has led to improved surface properties for sensors interfaced with blood"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003948_978-3-642-48819-1-Figure2.10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003948_978-3-642-48819-1-Figure2.10-1.png",
        "caption": "Fig 2.10.1 Triangular plate in constrained motion",
        "texts": [
            " -ide.n;t[c.a\u00a3 c.ompone.n-t6 a\u00a3ong the. t\u00a3ne. c.onne.c.t-ing them. Proof: Let a and 9 be the position vectors of two points, A and B, of a rigid body in motion. Thus, for any configuration, (b-a). (b-a)=const (2.10.1) from the rigidity condition. Differentiating both sides of eq. (2.10.1), (1')-a) \u2022 (b-a) =0 or, alternatively, (2.10.2) This theorem is used to check the compatibility of the given velocities of a rigid body in subroutine INSCRU of Sect. 2.9. Exercise 2.10.1 The triangular plate of Fig 2.10.1 is constrained to move in such a way that vertex C remains on the Z-axis, while vertex A remains on the X-axis and side AB remains on the X-Y plane. Vertex C has a velocity ~c=-5~zm/sec. i) Determine the velocity of vertices A and B ii) Determine the angular velocity of the plate iii) Locate the instant aneous screw axis of the motion of the plate, and cbmp'ute the pi t.ch of its screw. 149 150 THEOREM 2.10.2 (Aftonhold-Kennedy). Given ~htee nigid bodie6 in mo~on, ~e /te6uLUng ~htee in6.taM .6C1tW a.Xe6 ha.ve one COJrnlon noJtma.l iMeMec:ti.ng all ~htee a.Xe6. Proof: Referring to Fig 2.10.2 let SB and Sc be the instant aneous screw axes of bodies Band C, respectively, with respect to body Ai let ~B and ~C be the relative sliding velocities of the instant screws SB and Sc' with respect to A. Finally, let Q and Q be the relative angular velocities of bodies Band -B -C C, respectively, with respect to body A,and ~, the common normal to SB and SC' joining both axes. It will be shown that the third instant screw axis, SB/C' passes through the common normal B*C*. Let P be any point of the three-dimensional Euclidean space, with position vector r. Points P ,P and P of bodies A, B and C, coincide at P. Let ABC v , v and v be the velocities of each of these points. Furthermore, ~p-~ ~PB ~pc let v be the relative velocity of PB with respect to Pc and let B* and C* be the points in which the common normal intersects SB and Sc' B* ~B Fig. 2.10.2 Instantaneous screws of two bodies in motion with respect to a third one. Thus, Y=YpB-YpC= = (YB+gB;)-(YC+gc(;-\u00a3\u00bb)= =YB/C+gB/C!+gc\u00a3 .. p - W -B (2.10.3) * 151 It is next shown that, if P is a point of the relative instant aneous screw axis SB/C' then it lies on the line defined by points B* and C*. This is done * v ~B/C is to be interpreted as the relative velocity of B* with respect to C*. 152 via the minimization of the quadratic form T <P(;)=y y <P (:) has an extremum at a point :0 where its gradient vanishes",
            "6) Since r is parallel to vector ~, the -0 common normal to axes SB and Sc' then SB/C passes through line B*C*, q.e.d. IExercise 2.10.3 Show that~, as given by eq. (2.10.6), is parallel to ~. One application of the Aronhold-Kennedy Theorem arises in the pitch-surface synthesis of the coupling of two bodies whose relative motion is the composition of sliding and rotation, as is the case in hypoid gears. This is shown in the following example. Example 2.10.1 Let L1 and L2 be the non-intersecting non-parallel axes of two shafts required to be coupled. These axes are shown in Fig 2.10.3. In order to have the most efficient coupling, it is required that this takes place along points of minimum-magnitude relative velocity, i.e. on the axis of the instantaneous screw of shaft 2 with respect to shaft 1. 153 From Theorem 2.10.2, that set of points constitutes line L3 , normal to the Y-axis, a distance a from L1 ; Hence, line L3 is determined by distance a and angle a. Point Q, the intersection of line L3 and the y-axis is found from the minimum condition on the relative velocity magnitude",
            "c.:t to C ..L6, and only ..L6, the.Jte. e.wt La'l.>.p.ll. 06 both Band C w..t:th Ilel.>pe.c.:t to A and :thel.>e. ..Ln:teJL6e.c.:t, :the. ..L . a.p.ll. 06 B wilh Ilel.>pe.c.t to C paM..Lng thllough the. I.>a..td ..Ln:teJL6e.c.:t..ton. FWt:the.JtmOlle., aU thlle.e. axel.> Me. c.opi.a.nM. IExercise 2.10 . 4 Prove Corollary 2.10.2. As an application of Corollary 2.10.2, solve the following problem. Example 2. 10.2 (Kane(2.9 )~ A shaft, terminating in a truncated cone C of semivertical angle a, see Fig 2.10.4, is supported by a thrust bearing consisting of a fixed race R and four identical spheres S of radius r. When the shaft rotates about its axis, S rolls on R at both of its poi nts of contact with R, and C rolls on S. Proper choice of the dimension b allows to obtain pure rolling of C on S. Determine b Fig 2.10.4 Shaft rotating on thrust bearings. * Taken from: Kane, T.R., Dynamics, Dr. Thomas Kane R C 817 Lathrop Drive Stanford, CA - 94305 8 -_-+_J '-----L-_ __ 8 156 Solution: From Corollary 2.10.2, if all C, Sand R move with pure rolling rel~tive motion, then the i.a's.p.r. all coincide at one common point. Clearly, the i.a.p.r. of C with respect to S is the cone element passing through the contact point (between C and S), whereas the i.a.p.r. of C with respect to R is the symmetry axis of C. The intersection of those two axes is the cone apex, which henceforth is referred to as point o. Length b is now determined by the condition that the i.a.p.r. of C with respect to R passes through o. Now, two points of this axis are already known, namely, the two points of contact of S on R, henceforth referred to as points P1 and P2 . Then, the geometry of Fig 2.10.5 follows I'\" b I ----''i~. r..., Fig 2.10.5 Instantaneous axes of pure rotation of bodies C, Sand R of Fig 2.10.4. From Fig 2.10.5 it is clear that axis SSR makes a 45\u00b0 angle with axis SCR. Let T be the contact point between C and S. From a well-known theorem of plane geometry, Applying the Pythagorean Theorem to triangle OT'T, But and Hence, Also, -2 OT -2 OT OT' b - rcos6 T'T = b + r + rsin6 2r2 (1+sin6)+2br(1+sin6-cos6)+2b2 I2b OP2 (2.10.13) (2.10.14) (2.10.15a) (2.10.15b) (2.10.16) (2.10.17a) (2.10.17b) Substitution of eqs. (2.10.16) and (2.10.17 a and b) into eq. (2.10.13) yields from which, r(1+sin6)+b(sin6-cos6)=0 b=r 1 + sin6 cos6-sin6 (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.48-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.48-1.png",
        "caption": "Fig. 11.48 Gyro-moment at high speed (Note 11.18). Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [
            " This is different from the dynamic properties of the cornering force and the self-aligning torque because the cornering force is gradually generated with rolling distance, while a tire instantaneously deforms and generates camber thrust when a camber is applied to the tire. The dynamic cornering properties of tires at high speed are important because they relate to the vehicle response to rapid and small steering changes on a highway. These properties are different from the dynamic properties at low speed because not only the gyro moment induced by the wheels and tires, but also the vibration of the tire tread must be considered for the dynamic properties at high speed. Figure 11.48a shows that, when a slip angle is suddenly applied to a radial tire by steering a wheel at high speed, the tread area near the contact patch of the radial tire deforms laterally owing to the gyro-moment, and at the same time, the tread in the upper area deforms laterally in the opposite direction. The lateral displacement at the contact patch due to the gyro-moment delays the generation of the side force. The delay of the side force decreases with the increasing lateral spring rate of the tire and the decreasing mass moment of inertia. When a slip angle is suddenly applied to a bias tire, there is only partial tread deformation and the gyro-moment thus slightly affects the delay of the response in the bias tire. Figure 11.48b shows that, when a slip angle is suddenly applied to a radial tire from the road, or a flat-belt machine, at high speed, a force acts on the tire from the road. The force deforms the tire in the lateral direction and a gyro-moment in the counterclockwise direction around the vertical axis is then generated. Because the front part of the tire is twisted to the left while the back part of the tire is twisted to the right, the gyro-moment reduces the slip angle and thus increases the delay of the side force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003951_1.2898878-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003951_1.2898878-Figure1-1.png",
        "caption": "Fig. 1 A model of universal hypoid generators",
        "texts": [
            " The UGM incorporates the UMC, which defines the achine settings in a dynamic manner by polynomials as Ra = Ra0 + Ra1q + Ra2q2 + Ra3q3 + Ra4q4 Xb = Xb0 + Xb1q + Xb2q2 + Xb3q3 + Xb4q4 sr = sr0 + sr1q + sr2q2 + sr3q3 + sr4q4 Em = Em0 + Em1q + Em2q2 + Em3q3 + Em4q4 Xp = Xp0 + Xp1q + Xp2q2 + Xp3q3 + Xp4q4 m = m0 + m1q + m2q2 + m3q3 + m4q4 j = j0 + j1q + j2q2 + j3q3 + j4q4 i = i0 + i1q + i2q2 + i3q3 + i4q4 1 ere, q is the cradle rotation angle, Ra is the ratio of generating oll, Xb is the sliding base, sr is the cutter radial setting, Em is the ffset, Xp is the work head setting, m is the root angle, j is the wivel angle, and i is the cutter head tilt angle, respectively. Figure 1 illustrates the kinematical description of the machine ettings of a model of universal hypoid generators. Each machine etting is represented by a moving element whose motion is decribed a polynomial function in terms of cradle rotation angle. e call the machine settings represented by Eq. 1 the universal otions. The universal motions can be implemented on CNC hyoid gear generating machines by machine software. The first erms in Eq. 1 represent traditional basic machine settings. There re a total of 40 8 5 coefficients in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003630_027836499201100504-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003630_027836499201100504-Figure2-1.png",
        "caption": "Fig. 2. Robotics Researcjt model K-1207 link frame assignment.",
        "texts": [
            " Mapping from Joint Space to End-Effector Coordinates The Robotics Research model K-1207 arm is a 7-DOF manipulator with nonzero offsets (denoted by the nonzero link lengths ai, i = 1, - - -, 6) at each of the joints, as shown in Figures 1 through 3. Denavit-Hartenberg (DH) link frame assignments are given in accordance with the convention described in Craig (1986) and Yoshikawa (1990). This assignment results in the interlink homogeneous transformation matrix where 0; denotes the ith joint angle (Craig 1986). The D-H parameters for the K-1207 arm are given in Table 1. at Kungl Tekniska Hogskolan / Royal Institute of Technology on March 7, 2015ijr.sagepub.comDownloaded from 471 The link frame assignments for the K-1207 are given in Figure 2, where the arm is shown in its zero configuration. The link i coordinate frame is denoted by Ft, with coordinate axes (5~i, ~i, Fi) and origin 0~,. The associated interlink homogeneous transformation matrices, z-ITi\u2019 i = 1, ~ ~7, are easily found from the above expression evaluated for the D-H parameter values listed in Table 1. If the link length parameters az, i = 1, - - -, 6 are set to zero, the 7-DOF all-revolute anthropomorphic arm described in Hollerbach (1984) is retrieved; we call this arm the zero-offset arm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure14.31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.31-1.png",
        "caption": "Fig. 14.31 Model of irregular wear of tires due to fore\u2013aft forces [27]",
        "texts": [
            " Differential sliding always occurs if there is a difference in the contact length between the center and edges. To improve the wear due to differential sliding, a particular cross-sectional shape is used for grooves in a process referred to as crowning. r1 r2 tire 1 tire 2 \u0394r (1) Model of the irregular wear of tires Hanzaka and Nakajima [25] developed the model of the progression of step-down wear. The irregular wear of tires due to fore\u2013aft forces can be analyzed using the wear model of dual tires discussed in Sect. 14.8.2. Figure 14.31 shows the model of the irregular wear of tires due to fore\u2013aft forces, where h is the thickness of the tread rubber, d is the step of irregular wear of the rib, Dr is the difference in the radii of the tire center and tire shoulder (Fig. 14.31a) or the difference in the radii of normal wear and irregular wear (Fig. 14.31b). Because Dr corresponds to the difference in radii for a dual tire, the definition of Dr depends on which areas mainly interact with each other. For example, when irregular wear is due to inter-rib interaction, Dr is defined as in Fig. 14.31a. Meanwhile, when irregular wear is due to intra-rib interaction, Dr is defined as in Fig. 14.31b. 1056 14 Wear of Tires Suppose that the contact shape is rectangular, the contact lengths in the region of normal wear and irregular wear are, respectively, l0 and l, and the step of irregular wear is d. Because the contact length l and maximum contact pressure pm of a tire with irregular wear cannot be analytically solved, they are calculated through FEA. In FEA, part of a rib is dented by d, and l and pm are obtained at the center of the dented area as shown in Fig. 14.32. d and l change with the step of irregular wear as functions of l \u00bc l0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 d=dm4 p pm \u00bc pm0 1 d=dm\u00f0 \u00de; \u00f014:110\u00de where pm0 is the maximum contact pressure in the region of normal wear while dm is the critical step of the irregular wear where the region of step-down wear does not make contact with the road"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure3-1.png",
        "caption": "Fig. 3. Structure of face-gear tooth: (a) contact lines L2s and fillet; (b) cross-sections of face-gear tooth.",
        "texts": [
            " Usually, Ns Np \u00bc 2 or 3 for the purpose of localization of bearing contact of the gear drive. (2) The shaper and the pinion of the drive are in an imaginary internal tangency as shown in Fig. 2. (3) We may consider that three surfaces Rs, R2, and R1 are in mesh simultaneously. The surfaces of the shaper Rs and the face-gear R2 are in line tangency at every instant. However, surface R2 and pinion surface R1 are in tangency at a point at every instant since Np < Ns. The tooth surfaces R2 of the face-gear generated by an involute shaper are shown in Fig. 3(a). Lines L2s represent the instantaneous lines of tangency of R2 and shaper Rs, shown on R2. The cross-sections of the face-gear tooth are shown in Fig. 3(b). The tooth length of the face-gear has to be limited by dimensions L1 and L2 (Fig. 4) to avoid undercutting that occurs in plane A, and tooth pointing in plane B [8]. A unitless coefficient c defines the tooth length and is represented as c \u00bc L2 L1 m \u00f01\u00de Coefficient c depends on the gear ratio and other design parameters (see Section 3). The face-gear tooth surface has a fillet (Fig. 3(a)) that might be generated by (i) the edged top of the shaper tooth, or (ii) a rounded top of the shaper tooth (Fig. 5). Investigations show that application of a shaper with a rounded top enables the bending stress to be reduced by 12% (see Section 8). TCA is designated for simulation of meshing and contact of surfaces R2 and R1 and enables the influence of errors of alignment on transmission errors and shift of bearing contact to be investigated (see Section 6). The advantage of the involute face-gear drive is that errors of alignment do not cause transmission errors [8]",
            " The derivations and computations mentioned above may be simplified using proposed relation between the curvatures of the generating and generated surfaces [8]. Investigation of R2 shows that surface R2 has elliptical (K > 0) and hyperbolic (K < 0) points (Fig. 17). The common line of both sub-areas is the line of parabolic points. The dimensions of the area of surface elliptical points depend on the magnitude of the parabola coefficient as of the shaper rack-cutter. Surface R2 of existing design contains only hyperbolic points (Fig. 3(b)). This procedure is applied for simulation of meshing and contact of pinion and face-gear tooth surfaces. The algorithm of TCA is based on simulation of continuous tangency of surfaces R1 and R2 that is accomplished as proposed in [8]. The TCA procedure is based on application of the following coordinate systems: (i) movable systems S1 and S2 that are rigidly connected to the pinion and gear, respectively, and (ii) fixed coordinate system Sf where the tangency of contacting surfaces R1 and R2 is considered (see Section 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.2-1.png",
        "caption": "Fig. 11.2 Comparison of theoretical tire models for cornering. Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [
            " Performance criteria of the force and moment of tires are introduced to improve the cornering performance of a vehicle. Furthermore, the effect of alignment on the cornering performance of a vehicle is explained by the force and moment of tires. Tire models of vehicle dynamics are categorized as theoretical and empirical models. Theoretical models are mechanical models used to calculate the force and moment of a tire, and they can be further categorized as several types of model as shown in Fig. 11.1. The solid model in Fig. 11.2a does not consider deformation of the carcass or tread ring (belt), the rigid ring model in Fig. 11.2b considers deformation of the carcass but not of the tread ring, the flexural (elastic) ring model in Fig. 11.2c considers deformation of the carcass and tread ring, and the finite element (FE) model in Fig. 11.2d is used in FEA [1, 2]. The treads of all theoretical models except the finite element model are modeled using the brush model in which \u00a9 Springer Nature Singapore Pte Ltd. 2019 Y. Nakajima, Advanced Tire Mechanics, https://doi.org/10.1007/978-981-13-5799-2_11 707 small elements of tread rubber are deformed independently of the direction of the applied force like bristles of a brush. The cross-sectional deformation of the solid model is shown in the right figure of Fig. 11.2a. The side force is generated by shear deformation of the tread rubber, and the shear displacement increases until the sliding point at which the shear force is equal to the static frictional force. The tread slides laterally after passing the sliding point, and the tread moves back to the original position at the trailing edge. The side force of a tire is expressed by Side force \u00bc Z A lateral spring rate of tread per unit area\u00f0 \u00de \u00f0displacement of tread\u00de dA; \u00f011:1\u00de where A is the contact area. In the rigid ring model of Fig. 11.2b, the tread ring behaves like a rigid body. However, the ring can deform in torsional and lateral directions because the ring is supported by carcass springs. When the rigid ring model rolls with the slip angle a, there is a lateral displacement and lateral slip. A comparison of Fig. 11.2b with Fig. 11.2a shows that the differences are the rigid body displacement y0 of the center of the ring and torsional displacement. The side force of the rigid ring model is also given by Eq. (11.1). The adhesion region is from point O to point A, while the slip region is from point A to the trailing edge (x = l). Meanwhile, the string model is used in the transient analysis of a vehicle for simplicity. The elastic ring model of Fig. 11.2c is used for the analysis of a radial tire. When the belt is represented by a beam, the model is called a beam model. Fiala [3] approximated the in-plane deformation of the beam using a parabola and neglected the effect of belt tension; his model is called the Fiala model. When the elastic ring model rolls with slip angle a, the tread shear deformation of the elastic ring model 708 11 Cornering Properties of Tires 11.1 Tire Models for Cornering Properties 709 shown by slanted lines is smaller than that of the rigid ring model owing to the bending deformation of the tread ring",
            " Various physical tire models have been proposed. SWIFT was developed by TNO on the basis of the studies of Zegelaar [17] and Maurice [18], F-Tire was developed by Gipser [19\u201322], RMOD-K was developed by Oertel and Fandre [23], and the Hankook tire model was developed by Gim et al. [24\u201327]. Those models are used for describing not only cornering phenomena but also the riding comfort of the vehicle/suspension/tire system. Lugner et al. [28] published a paper comparing these models. The finite element model as shown in Fig. 11.2d presents the tire shape and construction in detail and can be used to quantitatively predict the cornering performance of a tire. However, because the finite element model is computationally expensive, the application for the vehicle dynamics is limited and the model is mainly applied in tire development. Meanwhile, an empirical model is a mathematical model that fits measurements made in an indoor test and is used for the vehicle dynamics. The most famous model is the Magic Formula proposed by Pacejka [1]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003227_s100510170283-Figure22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003227_s100510170283-Figure22-1.png",
        "caption": "Fig. 22. Geometry considered to evaluate the effect of tip geometrical hindrance on the half-height width (2L) of the topographical section profiles measured by AFM on nanowires: (a) Ratio of wire (R) to tip apex (r) radii smaller than (1/ sin\u03b1\u2212 1), (b) R/r larger than (1/ sin\u03b1\u2212 1).",
        "texts": [
            " Although less pronounced as the angle \u03d5 tends towards zero (M \u2016 z\u0302), this effect may indeed occur whatever the angle of the cylinder magnetisation. In conclusion, the interpretation of MFM contrasts recorded in the lift mode on samples having sharp topographical features may require to take into account the exact trajectory of the magnetic probe. Furthermore, in the presence of additional side contrasts, a MFM image may no longer be seen as a simple mapping of the magnetic charges in the sample. The effect of tip geometrical hindrance, sketched in Figure 22, is intrinsic to most scanning force microscopy techniques. It may only be considered as negligible when the size of the probe is much smaller than that of the topographical features to be imaged. If this condition is not fulfilled, sharp features of the sample surface, as our nanowires, can act as imaging protrusions so that the topographical profiles reflect to a certain extent the shape of the probe rather than that of the samples [39]. Such a geometrical effect limiting the spatial resolution and giving rise to an apparent broadening of the sample features unavoidably occurs in the case of our nanowires since the curvature radii of the tips used are in the range of 30 to 50 nm (according to the manufacturer), that is comparable to the lateral size of the nanowires. Assuming the simple tip-sample geometry outlined in Figure 22, an expression for the half-height width of the topographical profile may be obtained, which depends on the ratio of the wire (R = \u03c6/2) to tip apex (r) radii. If R/r is smaller than (1/ sin\u03b1 \u2212 1) (Fig. 22a), it is the hemispherical apex of the tip that is in \u201ccontact\u201d with the sample when the tip is located at y\u2212 yc = \u00b1L (Fig. 22a). Then, 2L reads 2L = 2 \u221a R2 + 2rR. (D.1) If, on the contrary, R/r is larger than (1/ sin\u03b1 \u2212 1) (Fig. 22b), it is one of the flat faces of the square-based pyramidal tip that is in \u201ccontact\u201d with the wire (Fig. 22b) and 2L is given by 2L = 2 [ 1 + tan2(\u03b1/2) 1\u2212 tan2(\u03b1/2) ] R+ 2 ( 1\u2212 sin\u03b1 cos\u03b1 ) r. (D.2) The intrinsic lateral broadening of the topographical profiles across the nanowires was estimated using these two equations. The shaded area in Figure 10e shows what the profile half-height width would be for \u03b1 = 17\u25e6 (manufacturer\u2019s data) and tip apex radii ranging between 30 to 50 nm if the tip geometrical hindrance were the only source of broadening. It is clear from Figure 10e that a significant part but not the whole broadening of the wire profiles may be attributed to intrinsic geometrical effects (see Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000630_tro.2021.3060969-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000630_tro.2021.3060969-Figure12-1.png",
        "caption": "Fig. 12. Lateral grip force and maximum pull force measurement. (a) Diagrams of the force measurement setups. (b) Pictures of the force measurement setups. (c) Lateral gripping force and maximum vertical pulling force at changing pressures for three diameters of cylindrical objects.",
        "texts": [
            "4% of the gripper\u2019s initial length), and the maximum opening angle of the gripper is 140\u25e6 at 143 kPa (initial angle as 0\u25e6). Through the aforementioned efforts, the gripper is able to grasp various objects, from short and tiny ones, to long and thick ones. To quantitatively evaluate the gripper\u2019s grasping capability, we set up two apparatuses to measure its gripping force. We 3-D printed several pieces of semicircular structure with varying dimensions and assembled them together to form three cylinders with diameters as 6, 10, and 14 cm. In the first setup [left column on Fig. 12(a) and (b)], we located a load cell (Zhongnuo, range: 50 N, accuracy: 0.1% FS) in between the semicirculars, and when the gripper enveloped the cylinder, the horizontal grip force can be measured [45]. Because our gripper can envelop an object when performs a power grasp, the grip force is distributed all along the object surface. Thus, in the second setup [right column on Fig. 12(a) and (b)], we measured the maximum vertical force by pulling the cylinder downward, in which the load cell is located at the bottom of the cylinders. In Fig. 12(c), we could see that the 14-cm cylinder\u2019s horizontal grip force is the largest, yet its vertical pull force is the smallest; whereas the 6-cm cylinder\u2019s horizontal grip force is smallest, yet its vertical pull force is the largest. This is due to that, for a small cylinder, the gripper fingers envelop it from the top to bottom, leading to a distributed force not only horizontally, but also vertically from the bottom up. For the pinching of the gripper, the tip blocked force in Fig. 10(f) should be an equivalent measurement for a two-finger gripper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000556_j.mechmachtheory.2021.104265-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000556_j.mechmachtheory.2021.104265-Figure6-1.png",
        "caption": "Fig. 6. Configuration of the industrial manipulator.",
        "texts": [
            " Then \u03b83 = \u03b834 \u2212 \u03b84 . (22) After that, the revolute joint variables \u03b85 and \u03b86 can be obtained, respectively, according to the conditional formulas (8) and (9). \u03b85 = atan2 ( \u22121 , 0 ) \u2212 atan2 ( a y c 1 \u2212 a x s 1 , \u2212a z c 34 + s 34 ( a x c 1 + a y s 1 ) ) , (23) \u03b86 = atan2 ( 1 , 0 ) \u2212 atan2 ( \u2212c 34 ( o x c 1 + o y s 1 ) \u2212 o z s 34 , \u2212n z s 34 \u2212 c 34 ( n x c 1 + n y s 1 ) ) , (24) The rigid body and coordinate frame attachments of the industrial manipulator with skew offset wrist are illustrated in Fig. 6 , and its D-H parameters are shown in Table 2 . According to the three principles in Section 3.3 , the origin of the second joint and the fourth joint in Fig. 6 are selected as the cut points, and the corresponding deformation is Eq. (13) . Then, according to the conditional Eqs. (4) and (5) of reconnecting the two sub-chains, four equations containing only \u03b81 , \u03b82 , \u03b83 , and \u03b86 can be obtained. According to conditional Eq. (5) s 23 ( \u2212c 1 A 23 \u2212 s 1 B 23 ) \u2212 c 23 C 23 = cos \u03b2, (25) where A 23 = \u2212a x c \u03b2 + o x c 6 s \u03b2 + n x s \u03b2s 6 , (26) B 23 = \u2212a y c \u03b2 + o y c 6 s \u03b2 + n y s \u03b2s 6 , (27) C 23 = a z c \u03b2 \u2212 o z c 6 s \u03b2 \u2212 n z s \u03b2s 6 . (28) According to conditional Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure17-1.png",
        "caption": "Fig. 17. Generation of pinion by grinding disk.",
        "texts": [
            " Longitudinal crowning of the pinion tooth surface, in addition to profile crowning, is provided for transformation of the shape of the function of transmission errors and reduction of noise and vibration. The contents of this section cover longitudinal crowning of the pinion by application of a plunging generating disk. The same goal (double-crowning) may be achieved by application of a generating worm (see Section 6). The approach is based on the following ideas: ii(i) The profile-crowned surface Rr of the pinion is considered as given. i(ii) A disk-shaped tool RD that is conjugated to Rr is determined (Fig. 17). The axes of the disk and pinion tooth surface Rr are crossed and the crossing angle cDp is equal to the lead angle on the pinion pitch cylinder (Fig. 18(b)). The center distance EDp (Fig. 18(a)) is defined as EDp \u00bc rd1 \u00fe qD; \u00f029\u00de where rd1 is the dedendum radius of the pinion and qD is the grinding disk radius. (iii) Determination of disk surface RD is based on the following procedure [6,7]. Step 1. Disk surface RD is a surface of revolution. Therefore, there is such a line LrD (Fig. 18(c)) of tan- gency of Rr and RD that the common normal to Rr and RD at each point of LrD passes through the axis of rotation of the disk [6,7]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.55-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.55-1.png",
        "caption": "Fig. 6.55: Check Valve Principle and Chracteristic",
        "texts": [
            " Experience shows that for these cases the influence of gap eccentricity can be approximated by simply modifying the geometrical coefficient \u03b1\u2206p according to [61] in the following form \u03b1\u2206p = \u2212A h2 12\u03b7l ( 1 + 1, 5\u03b53 ) with \u03b5 = e h . (6.132) \u03b5 is the relative eccentricity with 0 \u2264 \u03b5 \u2264 1. As the influence of the gap height h is with h3 very large, we get for a displaced piston with contact on one side an increase of the volume flow in the gap by a factor of 2.5. Many tensioners apply check valves to avoid a reflow of the oil into the supply system. Check valves typically have a spherical closure configuration in addition with a spring, which is sometimes omitted depending on the tensioner position. Figure 6.55 illustrates a typical design. Tensioner dynamics must be described very carefully, because it influences the chain dynamics in a dominant way. From this we have to take into consideration all motion elements, solid and fluid, the motion of the sphere, the fluid motion through the annular areas produced by the sphere motion and all fluid deviations. From many experiments with large and small check valve models we take the following route: We model the most important loss represented by the annulus flow between the sphere and the housing in detail and regard additional losses by a contraction coefficient \u03b1V related to the orifice behaviour of the valve. This theoretical-empirical combination reduces data processing but at the same time makes experiments necessary to measure the coefficients \u03b1V . Going back to Figure 6.55 we write the momentum equation in the form 6.5 Hydraulic Tensioner Dynamics 403 mV v\u0307 = A (pA \u2212 pE) + ApV , (6.133) with the fluid mass mV of the valve volume under consideration. The nonlinear pressure loss pV depends on the flow velocity v and on the annular area given by the sphere position. We apply for that the orifice equation pV = \u2212\u03c1 2 A2 \u03b12 VA 2 V |v| v = \u2212\u03b6V \u03c1 2 |v| v, (6.134) where A is the input cross section, and the area AV (xK) can be calculated from Figure 6.55 AV (xK) = 2\u03c0xKrK sin(\u03b3) cos(\u03b3) + \u03c0x2 K sin(\u03b3) cos2(\u03b3) (6.135) With decreasing flow areas AV the characteristics become steeper and reach in the limiting case the form of a bilateral constraint. On the other hand, these characteristics can be approximated quite realistically by a complementarity. See for both possibilities the chapters 4.2.2.1 and 4.2.2.2 on the pages 193 and following. Practical observations of tensioners indicate a pressure rise at the beginning of the piston\u2019s motion with a closing check valve"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure11.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure11.3-1.png",
        "caption": "Fig. 11.3",
        "texts": [
            " The asymptotic expression of the buckling solution can be obtained using the singular perturbation method [176]. o~---.... Fig. 11.2 2. The Buckling of a Bar with an Asymmetric Defect (11.13) In the buckling problem discussed above, suppose the bar is straight and symmetrical. When compression P exceeds the critical load, the bar yields by buckling, but we do not know whether the bar bends up or down. In fact, a real bar has some asymmetric defects, such as some small original bending, asymmetry of the trachoma and so on. These affect the buckling behaviour of the bar. For example, the bar shown in Fig. 11.3, bends up slightly. (i.e. 8 > 0) when it is free from a compressive load. In giving the bar a compressive load, the bar bends in continuously towards the direction of the original bending. But if the original bend is small, when the load P increases, the transversal displacement increases very slowly at first until P reaches the critical load of the symmetric bar. Then the transversal displacement increases quickly. This P buckling state of an asymmetric bar is shown in Fig. 11.4. Let fl = E1 be a horizontal co-ordinate, and the maximum torsion angle (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000408_j.jfranklin.2019.05.016-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000408_j.jfranklin.2019.05.016-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed OX o Y o and body-fixed AXY coordinate frames of an ASV.",
        "texts": [
            " Simulation studies and iscussions are carried out in Section 4 . Section 5 concludes this paper. . Problem formulation An ASV kinematics and dynamics can be modeled by [42] \u02d9 \u03b7 = R(\u03c8) \u03c5  \u0307 \u03c5 = J ( \u03b7, \u03c5) + \u03c4 + \u03c4\u03b4 (1) here ( \u03b7, \u03c5) = \u2212C ( \u03c5) \u03c5 \u2212 D ( \u03c5) \u03c5 \u2212 g( \u03b7, \u03c5) (2) ere, \u03b7 = [ x, y, \u03c8] T is the 3-DOF position ( x , y ) and heading angle ( \u03c8) of the ASV, = [ u, v, r] T is the corresponding linear velocities (u, v) , i.e., surge and sway ve- ocities, and angular rate ( r ) in the body-fixed frame, see Fig. 1 , \u03c4 = [ \u03c41 , \u03c42 , \u03c43 ] T nd \u03c4\u03b4 := MR T ( \u03c8) \u03b4( t ) with \u03b4(t ) = [ \u03b41 (t ) , \u03b42 (t ) , \u03b43 (t )] T are control inputs and mixed isturbances, respectively, and R(\u03c8) = [ cos \u03c8 \u2212 sin \u03c8 0 sin \u03c8 cos \u03c8 0 0 0 1 ] with the following prop- rties: R T (\u03c8) R(\u03c8) = I, \u02d9 R (\u03c8) = R(\u03c8) S (r) , \u2200 \u03c8 \u2208 [0, 2\u03c0 ] and R T (\u03c8) S (r) R(\u03c8) = (\u03c8) S (r) R T (\u03c8) = S (r) where S (r) = [ 0 \u2212r 0 r 0 0 0 0 0 ] , the inertia matrix M = M T > 0, the kew-symmetric matrix C ( \u03c5) = \u2212C T ( \u03c5) , and the damping matrix D ( \u03c5) are given y M = [ m 11 0 0 0 m 22 m 23 0 m 32 m 33 ] , C ( \u03c5) = [ 0 0 c 13 ( \u03c5) 0 0 c 23 ( \u03c5) \u2212c 13 ( \u03c5) \u2212c 23 ( \u03c5) 0 ] , and D ( \u03c5) = [ d 11 ( \u03c5) 0 0 0 d 22 ( \u03c5) d 23 ( \u03c5) 0 d 32 ( \u03c5) d 33 ( \u03c5) ] here m 11 = m \u2212 X \u02d9 u, m 22 = m \u2212 Y \u02d9 v, m 23 = mx g \u2212 Y \u02d9 r, m 32 = mx g \u2212 N \u02d9 v, m 33 = I z \u2212 \u02d9 r; c 13 ( \u03c5) = \u2212m 11 v \u2212 m 23 r, c 23 ( \u03c5) = m 11 u; d 11 ( \u03c5) = \u2212X u \u2212 X | u| u | u| \u2212 X uuu u 2 , d 22 ( \u03c5) = Y v \u2212 Y | v| v | v| , d 23 ( \u03c5) = \u2212Y r \u2212 Y | v| r | v| \u2212 Y | r| r | r| , d 32 ( \u03c5) = \u2212N v \u2212 N | v| v | v| \u2212 N | r| v | r| and 33 ( \u03c5) = \u2212N r \u2212 N | v| r | v| \u2212 N | r| r | r| "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001036_jsen.2021.3066424-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001036_jsen.2021.3066424-Figure4-1.png",
        "caption": "Fig. 4. The developed grasper device. (a) The schematic diagram of the surgeon operating surgical tools [28]. (b) The 3D structure of grasper device [26].",
        "texts": [
            " The type of the catheter is different; therefore, the slave manipulator should be applicable for different sizes of the catheters. Authorized licensed use limited to: University of Prince Edward Island. Downloaded on June 06,2021 at 07:26:18 UTC from IEEE Xplore. Restrictions apply. A. Grasper Device The grasper device, like a doctor\u2019s hand, which can clamp and release the guidewire and catheter. So, from the perspective of simulating the doctor\u2019s hand, a grasper device for the guidewire and catheter collaborative operating system was developed, and the structure is shown in Fig.4. Besides, the shell of the grasper device was printed by a 3D printer, with the length of 11cm, the width of 3cm, and the height of 3cm. Fig.5 shows the working principle of the grasper device. It can be described as in the initial state, the guidewire and the catheter are clamped by the sliding block (Thumb) and the sliding block (Index finger) due to the elastic force of springs. To increase the friction between the surgical instruments and the grasper device, and prevent excessive clamping force from damaging the guide wire and catheter, the part where the inner surface of the sliding block in contacts the outer surface of the guidewire and catheter are filled with rubber"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.46-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.46-1.png",
        "caption": "Fig. 12.46 New pattern geometry for a formula one tire [44]",
        "texts": [],
        "surrounding_texts": [
            "(1) Application of CFD simulation to hydroplaning CFD simulation was first applied to analyze hydroplaning using a two-dimensional Reynolds equation including the fluid/structure interaction [38, 39]. Threedimensional CFD simulation has since been applied to analyze hydroplaning using the Navier\u2013Stokes equation including the free surface and a turbulence model [40, 41]. Three requirements in simulating the hydroplaning of a tire are the fluid/structure interaction in a three-dimensional model, the analysis of a rolling tire and the modeling of a practical tread pattern geometry. Although the fluid/structure interaction has been considered in the previous hydroplaning simulations [38\u201340], the other two requirements have not been considered. Seta and Nakajima et al. [42\u201344] R at io o f l oa d of c on ta ct ar ea a nd to ta l l oa d Velocity : V (km/h) mmth0 0 0.5 1.0 0 50 100 150 1 1 1 1 1 1 2 5 10 20 Fig. 12.38 Road retention rates for various water depths and speeds (reproduced from Ref. [19] with the permission of Guranpuri-Shuppan) inflation pressure (kPa) contact length (mm) contact width (mm) 210 250 170 210 250 130 98 100 91 160 103 130 103 100 103 R oa d re te nt io n ra te : K Velocity: V (km/h) 0 0.5 1.0 0 50 100 Fig. 12.39 Road retention rates for various inflation pressures and speeds (reproduced from Ref. [19] with the permission of Guranpuri-Shuppan) 12.2 Hydroplaning 843 first established a new numerical procedure for hydroplaning in which the three requirements are considered and applied the procedure in the design of a tire pattern. They used the commercial explicit code MSC.Dytran whereby the tire was analyzed through FEA with a Lagrangian formulation and the fluid was analyzed using a FVM with an Eulerian formulation [45]. Furthermore, the interface between the tire and fluid was modeled by adopting general coupling. Because dynamic hydroplaning that occurs in region A of Fig. 12.26 is mainly studied, they ignored the viscosity of water. Using the same procedure proposed by Seta and Nakajima et al., the patent of which was granted for Bridgestone in 2002 [46], studies were conducted on the critical hydroplaning speed [47, 48], the effect of the tire pattern on hydroplaning [49] and the braking distance on a wet road [50, 51]. Osawa and Nakajima of Bridgestone [52] developed the riblet wall technology that suppresses the turbulence inside the main groove by CFD and validated to improve the hydroplaning of a tire. (2) Validation of hydroplaning simulation The hydroplaning simulation of a rolling tire with a practical tread pattern is shown in Fig. 12.40, where water drains into the two circumferential grooves and lateral grooves. The velocity of the tire is 60 km/h, the tire size is 205/55R16, the inflation pressure is 220 kPa, and the load is 4.5 kN. Prescribed velocities are applied to the tire model in the horizontal and rotational directions. The coefficient of friction between the tire and road is zero. The depth of water is 10 mm, and flow boundaries around the water pool are wall boundaries through which no water can flow. An explicit FEA/FVM scheme is applied in this simulation, and water flow is evaluated after the hydrodynamic force becomes stable. Figure 12.41 compares the prediction and measurement of water flow. The photograph taken through a glass plate shows the water flow of a rolling tire. The water depth is 10 mm, and the velocity is 60 km/h in the prediction and experiment. Although the viscosity of water is ignored in this simulation, the prediction of water flow is in good qualitative agreement with the measurement. (3) Global\u2013local analysis for hydroplaning simulation The hydroplaning analysis of a rolling tire requires much computational time, particularly for a tire with a practical pattern for the whole tread. A new procedure based on global\u2013local analysis was therefore developed to predict the water flow around a practical tread pattern [42]. In the scheme of global\u2013local analysis as shown in Fig. 12.42, a rolling tire with a blank tread is first analyzed in global analysis considering the fluid/structure interaction. The history of the displacement of the belt is then obtained in the global analysis. After the practical pattern model is glued to the belt model, the prescribed velocities calculated from the displacement of the global analysis are applied to the belt in local analysis. The local analysis is run as a separate analysis. Because the local model is more precise than the global model, the nodal coordinates in the local model are not necessarily the same as 844 12 Traction Performance of Tires those in the global model. The prescribed velocities in the local model are thus determined using element interpolation functions. The local analysis also considers the fluid/structure interaction. Because the local model is independent of the global model, the effect of a small change in the tread pattern design on hydroplaning can be analyzed by changing only the local model. The computational time can thus be reduced in this global\u2013local analysis. 12.2 Hydroplaning 845 (4) Development of a new pattern design through hydroplaning simulation Global\u2013local hydroplaning simulation is conducted to develop new pattern technology. To control water flow around the tread pattern, the three-dimensional design of the block shape is studied. The water flow around the block tip can be made smooth by a sloped block tip, which is shown in Fig. 12.43. Typical dimensions of the block tip are given in the figure, and the depth of the tread pattern is 8 mm. Two rolling tires are simulated with and without the sloped block to study the effect on hydroplaning. The water flow of the tire with the sloped block becomes smoother than that of the tire without the sloped block as shown in Fig. 12.44, indicating that the sloped block avoids an increase in the hydrodynamic pressure around the block tip. The measurement of the tire hydroplaning velocity shows a 1-km/h improvement due to the sloped block, demonstrating that the sloped block is effective in improving the hydroplaning performance. A new wet pattern for a Formula One tire is designed through hydroplaning simulation. Hydroplaning readily occurs in motorsport owing to the high speeds of racing, but tread patterns have been designed through trial and error according to the designer\u2019s experience. The procedure of pattern design begins with the simulation of a tire with a blank tread. The predicted streamline of a front tire is 846 12 Traction Performance of Tires asymmetric owing to the camber angle, while the predicted streamline of a rear tire is symmetric as shown in Fig. 12.45. The velocity is 200 km/h, and the water depth is 2 mm in this calculation. The groove geometry on the tread is then designed according to the predicted streamline. Because the streamline indicates where water tends to flow out of the contact patch, water can be effectively drained by grooving voids having the same geometry as the streamline on the blank tread as shown in Figs. 12.45 and 12.46. The alignment of grooves of front and rear tires gradually changes from the circumferential direction in the center area to the lateral direction in the shoulder area. The groove configuration becomes asymmetric for the front tire because the centerline of the contact area is not located at the center of the tire geometry owing to the camber angle. The hydrodynamic pressure of the control pattern and newly designed pattern is shown in Fig. 12.47. The numbers in parentheses are hydrodynamic force indexes, which show that the hydroplaning performance is better for the newly designed pattern. The lap time of a tire with the new pattern was shorter in a field test. Finally, the groove geometry on the block of the new wet pattern for a Formula One tire is designed. The water drainage on the block can be further improved by adding a small void called a sipe. Global\u2013local analysis is conducted to predict the 12.2 Hydroplaning 847 848 12 Traction Performance of Tires water drainage on the block as shown in Fig. 12.48. The hydrodynamic pressure is largely reduced by adding the sipe, and the lap time in a field test was shortened by adding sipes. (5) Riblet wall to improve hydroplaning Osawa and Nakajima [52] developed the riblet wall technology inside main grooves that makes the near-wall turbulence structure smooth as shown in Fig. 12.49. Using the CFD, the vorticity on a flat surface is found to be larger than that on a surface with riblets (the riblet wall). Because the turbulent flow contacts with the vertices of riblet on the riblet wall, the vorticity is suppressed on the riblet wall. The riblet wall technology was applied to main grooves of a passenger tire and validated to improve the hydroplaning performance in the proving ground. New pattern (65)Control pattern (100) 12.2 Hydroplaning 849"
        ]
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure2.10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure2.10-1.png",
        "caption": "Fig. 2.10: Microspectrometer (LIGA method). According to [Menz93a]",
        "texts": [
            " After the measurement, the sample is discharged, the sensor rinsed by means of a second micropump and recalibrated with a reference liquid. This analyzer requires a very small amount of expensive chemicals compared with conven tional ones. The micropumps used here are described in more detail in Sec tion 4.2.6 after the introduction of the LIGA-technique. The microspectro- meter, which is to be integrated in the above-described microanalysis in strument, is described in [Miill93] and [Hage95]. The principle function of the optical measurement system is depicted in Figure 2.10. The microspectrometer consists of several polymer layers and was made with the LIGA method. A glass fiber which is positioned within a shaft, trans mits the incoming light to the sensor base where it is directed toward a serrated, self-focussing reflection grid. There, the light is split into its spectral constituants and retransmitted through the sensor base. Inside this base the light is deflected by a 45\u00b0 prism and brought to a photodiode array for detec tion. The grid is made of PMMA and has about 1,200 serrations, which are about 3 t-tm wide and 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure15.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure15.14-1.png",
        "caption": "Fig. 15.14 Model of a radial tire using a beam with tension on an elastic foundation. Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [
            " Sakai [2] and Krylov and Gilbert [17] expressed the external force using Dirac\u2019s delta function. Meanwhile, Metrikine and Tochilin [16] expressed the external force using an infinite number of Dirac delta functions with an interval of the circumferential length of the tire, because the tire is considered a cylinder. They showed that the standing wave occurs backward of the moving load (i.e., backward of the trailing edge of the tire). Referring to Eq. (11.64), the governing equation for the model in Fig. 15.14 is m d2w dt2 \u00feEI d4w dx4 Tx d2w dx2 \u00fe krw \u00bc Pd\u00f0x\u00de; \u00f015:46\u00de where w is the vertical displacement, m is the mass from the bead to tread per unit circumferential length, EI is the out-of-bending flexural rigidity of the beam, Tx is the circumferential tension, and kr is the fundamental radial spring rate. 15.4 One-Dimensional Model of a Standing Wave \u2026 1147 Assume that the solution to Eq. (15.46) is w \u00bc A sin j x v/t : \u00f015:47\u00de Equation (15.47) means that a wave of A sin (jx) with wave number j propagates at phase velocity v/"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003669_j.automatica.2004.05.017-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003669_j.automatica.2004.05.017-Figure3-1.png",
        "caption": "Fig. 3 depicts an example of a family of nested Lyapunov regions, where the dimensions of the respective individual regions, Gp, have been chosen such that each of them is tangent to the straight lines, kT px=u0 and kT px=\u2212u0, arising from the relation, |kT px| u0, restricting the values of the control parameter. This tangential construction guarantees a good exploitation of the control signal\u2019s constraints during regulation cycles. The largest region Gp must include X0.",
        "texts": [],
        "surrounding_texts": [
            "The initial concept for a soft VSC proposed by Kiendl (1972) and Kiendl and Schneider (1972) is a systematic extension of their discontinuousVSC lacking sliding modes. The subcontrollers of this discontinuous VSC are chosen in a manner rather similar to those described in the example of the preceding section. The control\u2019s selection strategy is based on nested, positively invariant sets. In order to explain this control, we start off by describing the discontinuous case in the section that follows. Stelzner (1987) improved the method for designing such controls. As mentioned in the introduction, Wredenhagen and B\u00e9langer (1994) developed the same VSC in a later work. In a second section, we describe the concept of a soft VSC employing nested Lyapunov functions proposed by Kiendl and Schneider. This concept was taken up and further developed into soft VSC employing implicit Lyapunov functions in (Adamy, 1991). In the process of extending this kind of control, the final step has thus far been that of (Niewels & Kiendl, 2000, 2003; Niewels, 2001, 2002), where the implicit Lyapunov approach was generalized to the case ofVSC employing multivalued Lyapunov functions and robustness was proven. Since the direct method of Lyapunov\u2019s stability theory (Hahn, 1967; Rouche, Habets, & Laloy, 1977; Sastry, 1999) is essential to all controls described in this paper, we shall briefly review it here for the convenience of readers.We start with the following well-known theorem: Theorem 1. The differential equation, x\u0307= f(x) with a continuous function f , having an equilibrium state, x=0, has a unique solution. If there exists a function v(x) having continuous partial derivatives and if (A1) v(0) = 0, (A2) v(x)> 0, x = 0, (A3) v\u0307(x)< 0, x = 0, then the equilibrium state, x = 0, will be asymptotically stable and v(x) will be called a \u201cLyapunov function.\u201d For stable linear systems, x\u0307=Ax, it will always be possible to compute a Lyapunov function, v(x) = xTRx, having a positive-definite matrix, R, by solving the so-called \u201cLyapunov equation,\u201d ATR + RA= \u2212Q, (8) for an arbitrary positive-definite matrix, Q. If there exists a Lyapunov function, v(x), for a system, x\u0307 = f(x) and G = {x | v(x)< c} (9) is bounded, then G is a positively invariant set that is also called a \u201cLyapunov region,\u201d i.e., a region for which every trajectory that starts therein never leaves it."
        ]
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.61-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.61-1.png",
        "caption": "Fig. 5.61: CVT-Drive, Example LUK/PIV System",
        "texts": [
            " The advantage of a CVT configuration consists in a perfect adaptation to the drag-velocity hyperbola, the disadvantage in a lower efficiency due to power transmission by friction and in a somehow limited torque transmission. An additional advantage of the CVT\u2019s is the possibility of very smoothly changing the transmission ratio without any danger of generating jerk. Figure 3.9 on page 113 depicts an example from industry. The following pictures give an impression of the systems and the components. They are of general importance though the configurations shown correspond to the LUK/PIV chain system. The operation of a chain- or beltdriven CVT is for the various configurations always the same. Figure 5.61 depicts the main features. The chain or the belt moves between two pulleys with conically shaped sheaves. One side of these pulleys possesses a movable sheave controlled by a hydraulic system. The other side id fixed. Reducing or increasing the distance between the pulley sheaves forces the chain or belt to move radially upwards or downwards thus changing the transmission ratio of the CVT. We have a driving pulley A (Figure 5.61) with an incoming torqe M1, with a pressure force FP,1 and a resulting rotational speed \u03c9, and we have a driven pulley B with the outgoing torque M2 and a pressure force FP,2. The control of these hydraulic pressure forces represents one of the crucial points for CVT operation. Some important components of CVT drives are pictured in Figure 5.62. On the left one pulley is depicted with its axially fixed sheave with a mechanical torque sensor on the same side, with the movable sheave and the hydraulic chamber, and as indicated with a rocker pin or a push belt element between the sheaves"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003487_tcst.2004.843130-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003487_tcst.2004.843130-Figure2-1.png",
        "caption": "Fig. 2. Structure of double-inverted pendulum.",
        "texts": [
            " Then by the manipulations like (19), the control law can be derived as shown in (28) at the bottom of the page where and are the estimated coupling factors which are adapted by the following fuzzy inference systems: (29) (30) with the adaptive laws shown in (31)\u2013(32) at the bottom of the next page, in which and are the positive learning rates; and are the parameter vectors; and are the regressive vectors; and where . Also, and are restrained to be positive. Similarly, this (28) idea can be extended to even higher order systems by introducing the hierarchical sliding surface. The concept diagram of this HFSM control system is depicted in Fig. 1. A double inverted pendulum system is simulated and a comparison between the proposed HFSM and the FSM decoupling control is demonstrated. The structure and controlled states of double inverted pendulum are shown in Fig. 2. Its dynamics are described as: (33) where is the angle of the pole 1 with respect to the vertical axis, is the angular velocity of the pole 1, is the angle of the pole 2 with respect to the vertical axis, is the angular velocity of the pole 2, is the position of the cart, is the velocity of the cart, is the applied force to move the cart and is the disturbance. The system equations are given in [7]. In the simulations, the parameters are chosen as 1 Kg; 0 m; 9.8 m/s ; and 0.05 /s . For the coupling factor tuning in (11), same membership functions are defined for and "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.29-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.29-1.png",
        "caption": "Fig. 2.29: Sliding and Static Friction",
        "texts": [
            " For ideal classical inelastic impacts either the relative velocity is zero and the accompanying normal constraint impulse is not zero, or vice versa. The scalar product of relative velocity and normal impulse is thus always zero. For the more complicated case of an impact with friction we shall find such a complementarity in each phase of the impact. Friction in one contact only is characterized by a contact condition of vanishing relative distance and by two frictional conditions, either sliding or sticking (see Figure 2.29). A typical property of contacts, whatsoever, is the fact, that kinematic magnitudes indicating the beginning of a contact event become a constraint at that time instant, where a contact becomes \u201cactive\u201d. For example: a nonzero normal distance between two bodies going to come into contact indicates a \u201cpassive\u201d contact state with zero normal constraint force. In the moment it is zero, then the relative distance represents a constraint accompanied by a constraint force, and the contact is \u201cactive\u201d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003951_1.2898878-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003951_1.2898878-Figure5-1.png",
        "caption": "Fig. 5 Trace of generating roll",
        "texts": [
            " In addition, change of zero-order ratio of generating roll Ra0, offset Em0, work head Xp0, and root angle m0 also introduces second-order profile and spiral angle modifications. Change of zero-order cutter radial setting sr0 primarily introduces spiral angle change. We notice that the universal motions are higher-order polynomials in terms of the generating roll angle q. Application of higher-order motions will diagonally modify the tooth surfaces along the trace of generating roll, as shown in Fig. 5. On the concave tooth flank, the rolling direction is from toe top T1 to heel bottom H2 . However, the rolling is from heel tip H1 to toe bottom T2 on the convex side. Therefore, normally, the first-, JULY 2008, Vol. 130 / 072601-3 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use c p c c 3 s o i s b m T p o l 0 Downloaded Fr Table 2 and 3 show the difference surfaces 1 and 2 of the oncave side and convex side, respectively, corresponding to a ositive change of first-, second-, third-, and fourth-order coeffiients of ratio of generating roll Ra and radial setting Sr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000556_j.mechmachtheory.2021.104265-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000556_j.mechmachtheory.2021.104265-Figure4-1.png",
        "caption": "Fig. 4. Configuration of RC manipulator.",
        "texts": [
            " (4) ~(5), obtain the IK solutions of the other four joint variables except for \u03b8 i and \u03b8 i + 1 using the existing elimination method of the three-DOF manipulator. Step 3: Solve \u03b8 i by using Eq. (6) or (8), and solve \u03b8 i + 1 by using Eq. (7) or (9) based on the results of step 2. Three examples are developed in this section to show more details of the proposed method and its advantages. The trigonometric equations used in this section\u2019s derivation can be referred to in the appendix in the literature [55] . The rigid body and coordinate frame attachments of the RC manipulator [42] are illustrated in Fig. 4 , and its D-H param- eters are presented in Table 1 . The symbolic variables in Table 1 are substituted into Eq. (2) to obtain the forward kinematics formula of the RC manipulator EE. The target value of EE is a symbolic function in the form of Eq. (3) . According to the three principles in Section 3.3 , the origin of the third joint and the fifth joint in Fig. 4 are selected as the cut points, and the corresponding deformation is Eq. (14) . Then, according to the conditional Eqs. (4) and (5) of reconnecting the two sub-chains, four equations containing only \u03b81 , d 2 , \u03b83 , and \u03b84 can be obtained. According to conditional Eq. (4) l 4 c 34 + l 3 c 3 = p z \u2212 h 1 \u2212 a z d 6 , (15) l 4 s 34 + l 3 s 3 = ( a y d 6 \u2212 p y ) s 1 \u2212 ( p x \u2212 a x d 6 ) c 1 , (16) l 2 = ( p x \u2212 a x d 6 ) s 1 \u2212 ( p y \u2212 a y d 6 ) c 1 \u2212 d 2 . (17) from now on, s i and c i denote sin \u03b8 i and cos \u03b8 i , s ij and c ij are denoted as sin( \u03b8 i + \u03b8 j ) and cos( \u03b8 i + \u03b8 j ), respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure5-5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure5-5-1.png",
        "caption": "Figure 5-5. Illustration of a sinusoidal pulse width modulation technique.",
        "texts": [
            " The motor now tends to rotate much more smoothly at low speed. Torque pulsations are virtually eliminated and the extra motor losses caused by the inverter are substantially reduced. To counterbalance these advantages, the inverter control is complex, the chopping frequency is high (typically 500-2500 Hz for GTOs and up to 5,000 or more for BJT transistors), and inverter losses are higher than for the six-step mode of operation. To approximate a sine wave, a high-frequency triangular wave is compared with a fundamental frequency sine wave, as shown in Figure 5-5. When the low-frequency sine waves are used with 120\u00b0 phase displacement, the switching pattern for the six inverter devices ensues. 5.2. Inverters for Adjustable Speed 217 Synchronous Versus Asynchronous Modulation. If the carrier and modulation are to be synchronized, there must be a fixed number of carrier cycles in each modulation cycle. If this number is chosen to give a \"good\" sinusoidal current waveform at low frequency, say, at 1 Hz, then the ratio of carrier frequency to fundamental frequency will be in the neighborhood of 100-200 kHz",
            " Whereas the carrier frequency must be a fixed ratio of fundamental frequency at moderate and high speed to prevent undesirable \"subharmonics\" from appearing, asynchronous operation of the carrier frequency becomes acceptable at low speeds where the effect of the differing number of carrier cycles per modulation cycle is small. However, a change over to synchronous operation is required at some speed, and some type of \"phase locking\" technique must be introduced to achieve the synchronization. While Figure 5-5 provides a good picture of the modulation process, once the possibility of using a microprocessor is introduced, the \"analog\" solution obtained by the intersection of a triangle wave and a sine wave becomes only one of many possibilities. This so-called \"natural modulation\" can be replaced to advantage by \"regular modulation\" in which the modulating waveform is piece wise constant, that is, sampled at the carrier frequency. An example of carrier and modulated waveforms for such a scheme is reproduced in Figure 5-7 for a switching ratio of 9 [5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-4-1.png",
        "caption": "Figure 2-4. Cross section of an induction motor.",
        "texts": [
            " Electrical Machines for Drives \u2022 A limit on the constant power speed range due to increased difficulty in commutation at low values of flux \u2022 A relatively low maximum rotor speed limited by mechanical stress on the commutator \u2022 Relatively high cost For high-performance applications, the maximum torque that a commutator motor can produce is limited by the current that the commutator can switch without excessive sparking. Typically, this is in the range of two to five times the continuous rated current [4]. 2.4. INDUCTION MOTORS Most induction motors are designed to operate from a three-phase source of alternating voltage [1, 5, 6]. For variable speed drives, the source is normally an inverter that uses solid-state switches to produce approximately sinusoidal voltages and currents of controllable magnitude and frequency. A cross section of a two-pole induction motor is shown in Figure 2-4. Slots in the inner periphery of the stator accommodate three phase windings a, b, and c. The turns in each winding are distributed so that a current in a stator winding produces an approximately sinusoidally distributed flux density around the periphery of the air gap. When three currents that are sinusoidally varying in time but displaced in phase by 120\u00b0 from each other flow through the three symmetrically placed windings, a radially directed air gap flux density is produced that is also sinusoidally distributed around the gap and is rotating at an angular velocity equal to the angular frequency \u03c95 of the stator currents",
            " The continuous values of the rms linear current density Kr in the rotor and Ks in the stator are limited by many of the same heat dissipation considerations as discussed for the commutator motor. These limitations on flux density and current density are the main factors in establishing the base continuous torque Tb of the motor. The force per unit of rotor surface area and thus the rated torque are roughly comparable for induction and commutator motors of the same rotor radius r and effective length \u00cd. The base angular velocity wb of the motor will be fixed by the needs of the mechanical load to be driven. For the two-pole motor shown in Figure 2-4, the 2. Electrical Machines for Drives required base value of angular frequency of stator currents UJS will differ from ub only by the angular frequency \u03c9\u0386 of the rotor currents. Figure 2-5 shows the relation between the angular velocity and the torque for a number of values of stator frequency. For small values of the slip frequency u>R, the torque is seen to be proportional to wR. For motoring action, UJR has a positive value. To produce regeneration with reversed torque, the load will drive the mechanical angular velocity to a value greater than that of the stator angular frequency making the value of wR negative; that is, the sequence of the rotor currents is reversed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.4-1.png",
        "caption": "Fig. 2.4: Typical constraint examples",
        "texts": [
            " A well-known example is the rolling disc, which at the same time is an example with the minimal possible number of degrees of freedom for a non-holonomic system, namely three [93]. The rolling condition for rolling without sliding cannot be integrated to come out with a holonomic equality, because a change of the orientation includes also a change in the position. These properties will have significant consequences for the development of the differential principles. A more detailed discussion of constraints can be found in [180], [93], [27] or [63]. Figure 2.4 depicts some typical constraints. The pendulum on the left represents a holonomic constraint depending only on the position of its mass. As long as the mass connection remains under tension we have a bilateral constraint. The sledge example represents also a holonomic, bilateral constraint as long as the sledge does not detach from the ground. In doing so we get a unilateral constraint with contact- and detachment-phases. The wheel example includes a non-holonomic constraint, because in the general case the function f(x\u0307, y\u0307, \u03b2\u0307, \u03b1) = 0 cannot be integrated to give then a position-dependent constraint. This is possible only, if the wheel follows exactly a straight line by rolling without sliding. Then we can roll back the wheel coming exactly to the starting point, and only then the constraint can be integrated. The examples in Figure 2.4 illustrate also the empirical experience, that the constraint forces Fc are in all cases perpendicular to the directions of motion, which later on will give a basis for the principle of d\u2019Alembert-Lagrange. Constraints confine the number of degrees of freedom of a system. In general cases it is not possible to eliminate those degrees of freedom, which are 2.1 Basic Concepts 11 constrained. But for special cases, usually of smaller dimensions, we might succeed in reducing the coordinates to the number of degrees of freedom really existing in the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001172_j.triboint.2021.106856-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001172_j.triboint.2021.106856-Figure11-1.png",
        "caption": "Fig. 11. The simulated pressure distribution nephograms in different pre-tightening force.",
        "texts": [
            " For the FEA model shown in Fig. 6, the pre-tightening force Ni is set to 5000 N, 10000 N, 15000 N, 20000 N, 25000 N and 30000 N respectively, and the friction coefficient is set to 0.15. In order to ensure that the FEA model appears macro slip, the corresponding tangential force is set to 0.2Ni. After the FEA model is solved, we extract the surface pressure data from mating surface, and then determine the maximum radius of the non-zero pressure region. The simulated pressure distribution nephograms are shown in Fig. 11. From the nephograms, the pressure distribution shapes under the different pre-tightening force is basically the same, only the maximum pressure value is different, which is consistent with the experimental result in Ref. [36]. The minimum radius of the pressure distribution area under different preloads is the bolt hole radius: Rmin = 5.50mm. The extracted maximum radius of the pressure distribution area under 5000 N and 15000 N preload are 14.42 mm, and the extracted maximum radius of the pressure distribution area under 10000 N, 20000 N, 25000 N and 30000 N preload are 14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.24-1.png",
        "caption": "Fig. 6.24: Structure of the V10 Timing Gear Train (wi = gear wheel number i, mi = gear mesh number i, (Ix, Iy, Iz) = inertial coordinates), (courtesy VW)",
        "texts": [
            " Again, mechanical and mathematical modeling follows the paths presented in chapter 6.1, where detailed mathematical models have been established. Mainly due to the backlashes within the meshes of the gears, but also due to some components like clutches or ancillary equipment, the system dynamics is highly nonlinear and as a rule cannot be linearized around some operating point. We tried to do that for the 5-cylinder engine timing train, but without success. The structure of the VW V10 Diesel engine is illustrated by Figure 6.24. The timing gear with gear wheels only is located at the backside of the engine, between engine housing and the drive train clutch. The VR-angle between the two 5-cylinder motor blocks is 90\u25e6. The left camshaft drives the valves and the injection pump pistons of the cylinders (1 to 5) and the right camshaft those of the cylinders (6 to 10). The crankshaft, here the wheel (w1), drives the two camshafts, on the left side via the gears (2, 3, 4a/4b, 5, 6) and on the right side by the gears (10, 11a/11b, 12, 13)",
            " The necessary transmission ratio for the camshafts is realized by the double gear wheels (4a/4b) on the left and (11a/11b) on the right side. All gear wheels are helical gears with a helix angle of 15\u25e6. With the exception of gear (w31), which is shrinked on the water pump shaft, all gears are supported by journal bearings. Ancillary components are driven in the following way: water pump by gear (w31), oil pump, power steering pump and climate compressor by the wheels (w20) and (w22), the generator with freewheel and elastic clutch by wheel (w40). The origin of the inertial coordinate system is the axis of gear wheel (w1), Figure 6.24. with the z-axis along the crankshaft axis and with the x- and y-axes in the plane of the timing gear system. The mechanical model includes 62 rigid bodies with altogether 137 degrees of freedom, which are interconnected by 207 force elements. Figure 6.25 depicts the main features. The wheels are modeled as rigid bodies with four degrees of freedom, one for rotation and three for translation, which allows to take into account the influence of elastic bearings. As in the 5-cylinder case we neglect tilting motion of the gear wheels, because the bearing tolerances make such tilting nearly impossible",
            " Nevertheless they include some important indications with respect to the maximum forces and torques as a basis for a first sizing up of the design ideas. The maximum torques of the two camshafts are about 260 Nm, approximately the same value for both shafts. The maximum tooth forces in the gear meshes depend also on the loads of the ancillary equipment. According to table 6.7 the loads on the left side are a bit larger than those of the right side, which is due to some ancillary components and in addition to one more wheel in that branch (see also Figure 6.24). The maximum loads on the bearings are also illustrated by table 6.7, where in addition the angle with respect to the positive x-axis is given designating the direction of the corresponding maximum force. The gears of the two main timing gear branches are heavily loaded by the large injection pressures and as the consequence by large torques. As in the case R5 this leads also here to hammering situations, which are always accompanied by very large forces on the gear teeth. The journal bearings thus move always between two extreme positions, which are both equally and heavily loaded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000526_j.ijmecsci.2019.105207-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000526_j.ijmecsci.2019.105207-Figure4-1.png",
        "caption": "Fig. 4. Temperature field and flow field of the molten pool.",
        "texts": [
            " 3 b hows the three-dimensional contour data under a laser scanning microcope. Smoothing pretreatment can reduce the measurement error of the ladding layer due to surface roughness to some extent. Fig. 3 c shows he macroscopic morphology of the cladding layer obtained from the nu- erical model, which has a similar morphology to the experimentally btained cladding layer. Fig. 3 d shows the measured layer size meaurements for experiments and simulations. The error between the two s small, indicating the reliability of the numerical model constructed in his paper. Fig. 4 a and b show the temperature field and flow field of the molten ool. Obviously, the flow pattern inside the molten pool mainly exists n two forms, one is annular convection around the center of the molten ool, and the other is flow from the front edge of the molten pool to the ottom and the back of the molten pool. The two convections together ring fluid near the surface of the molten pool to the interior of the g olten pool, while the primary source of fluid on the surface of the olten pool is the molten alloy powder and the metal that melts on he surface of the substrate. The highest temperature is generated at the aser action point and gradually decreases in the opposite direction of he scanning direction below the metal solidus. The maximum width f the molten pool is about 1100 \u03bcm and the length is about 2940 \u03bcm, hat is, the aspect ratio is about 1:3. Fig. 4 c and d show the velocity eld of the molten pool in a side view and a top view, respectively. The ow velocity of the liquid metal inside the molten pool calculated by he model is about 0.12 m/s, which occurs at the surface of the molten ool toward the point of action of the laser. Therefore, it can be inferred hat there is a point at the surface of the molten pool having a surface ension of 0, which is located in a region where the molten pool flows nward. .2. Convection of molten pool under different conditions The main factors affecting the internal convection of the MLDD weld ool include gravity, Marangoni motion caused by surface tension, and mpact of the shielding gas on the surface of the molten pool",
            " Since the fluid density and specific heat capacity sed in this example vary with temperature, a polynomial function fit is erformed on the fluid density and specific heat capacity as a function f temperature in order to simplify the calculation: = 7796 + 0 . 119 \ud835\udc47 \u2212 (3 . 068 \ud835\udc52 \u2212 4) \ud835\udc47 2 (14) \ud835\udc5d = 1348 \u2212 1 . 963 \ud835\udc47 + 0 . 0016 \ud835\udc47 2 \u2212 (3 . 503 \ud835\udc52 \u2212 7) \ud835\udc47 3 (15) Among them, the fluid density is parabolic fitting, the specific heat apacity is cubic polynomial fitting, and the fitting iteration is based n the Levenberg-Marquardt optimization algorithm [29] . Then P e is onverted into a function related to v and T . In Fig. 4 c, take a line from he front edge of the molten pool to the trailing edge of the molten pool nd obtain the fluid velocity and temperature at each point on the line. ubstituting the temperatures into Eqs. (14) and (15) respectively, the uid density and specific heat capacity at each point on the straight line re obtained, and then P\u00e9clets number at each point on the straight line s obtained from Eq. (13) , as shown in Fig. 10 a. Taking the diffusion of Cr n RCF103 as an example, the solidification parameter of Cr ( Table 3 ) nd the solidification rate in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000535_j.addma.2019.100980-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000535_j.addma.2019.100980-Figure7-1.png",
        "caption": "Fig. 7. Geometry of used fatigue sample [21].",
        "texts": [
            " Mechanical testing samples were stress relieved in vacuum at 650 \u00b0C for 3 h before cutting them from the build plate. The O2 Precision was used to maintain 68 ppm and 1003 ppm oxygen in the atmosphere to determine whether oxygen holds any influence over fatigue behavior. For the following build jobs, the Ti-6Al-4 V powder was sieved and analyzed again. Fatigue measurements were performed on a Roell Amsler REL 2041 with a load cell of 10 kN, according to DIN 50100. The tests were conducted at room temperature using samples machined to Type A shape, as specified in Fig. 7 and Table 2. To investigate the influence of oxygen concentration in the build chamber on the final part quality, the build job was repeatedly built at different oxygen concentrations (0 ppm, 200 ppm, 400 ppm, 600 ppm). The different oxygen concentrations were reached by purging in additional inert gas using the ADDvance\u00ae O2 precision to a defined setpoint and then maintained at the same level over the total build time. In addition, a build job without using the ADDvance\u00ae O2 precision to control the oxygen level was built for further comparison as a benchmark"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.45-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.45-1.png",
        "caption": "Fig. 16.45 RAT and RCF",
        "texts": [
            "44 are given by LF \u00bc CFaa\u00feFPS y \u00feFCT y ; \u00f016:18\u00de AT \u00bc CMaa\u00feMPS z \u00feMCT z ; \u00f016:19\u00de where CFa (=\u2202LF/\u2202a) and CMa (=\u2202AT/\u2202a) are the cornering stiffness and the aligning torque stiffness. Eliminating a using Eqs. (16.18) and (16.19), we obtain 1186 16 Tire Properties for Wandering and Vehicle Pull AT \u00bc CMa=CFa LF\u00feCMa=CFa FPS y \u00feFCT y \u00feMPS z \u00feMCT z : \u00f016:20\u00de Substituting LF = 0 into Eq. (16.20), RAT is given as RAT \u00bc CMa=CFa FPS y \u00feFCT y \u00feMPS z \u00feMCT z : \u00f016:21\u00de Substituting AT = 0 into Eq. (16.20), RCF is given as RCF \u00bc CFa=CMa MPS z \u00feMCT z \u00feFPS y \u00feFCT y : \u00f016:22\u00de Using Eqs. (16.21) and (16.22), the relation of RAT and RCF is given as (Fig. 16.45) RAT \u00bc CMa=CFa RCF: \u00f016:23\u00de Referring to Fig. 16.44, RCF and RAT are expressed as RCF \u00bc CFa a1 a2\u00f0 \u00de RAT \u00bc CMa a1 a2\u00f0 \u00de: \u00f016:24\u00de The relations among RCF, RAT and (a1 \u2212 a2) (denoted ATSP) are a1 a2 \u00bc RAT=CMa \u00bc RCF=CFa: \u00f016:25\u00de RCF, RAT and ATSP are thus interchangeable with each other. Similar to Eq. (16.17), RAT and RCF are decomposed into plysteer and conicity components in the vehicle coordinate system: PRCF \u00bc RCFCW \u00feRCFCCW\u00f0 \u00de=2 CRCF \u00bc RCFCW RCFCCW\u00f0 \u00de=2 PRAT \u00bc RATCW \u00feRATCCW\u00f0 \u00de=2 CRAT \u00bc RAFCW RATCCW\u00f0 \u00de=2; \u00f016:26\u00de where CW and CCW, respectively, denote clockwise and counterclockwise rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.89-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.89-1.png",
        "caption": "Fig. 5.89: Kinematics of an Angled Rocker Pin Joint",
        "texts": [
            " In order to be able to describe the kinematics of a rolling rocker pin joint we need in a first step a specification of the inner contour of a rocker pin, because the two pins of a joint are rolling one on the other along their inner contour. It consists of two symmetrical halves, each is an involute to a circle, and is defined by the two parameters r0 and r (Fig. cvts-contour). The following equations hold true for the upper half (0 \u2264 \u03a8 \u2264 \u03a8max): r0 :=SX0, l(\u03a8) =PX = r0 + r\u03a8, PN =NS = r tan \u03a8 2 . (5.126) The lower half is the reflection of the upper half with respect to the symmetry line SX0. As illustrated in Fig. 5.89 the rocker pins are fixed to the links with their outer contours. It should be noticed, that the symmetry axis of the rocker pin is not parallel to the link plate axis, but it is rotated by the constant angle \u03b4. This fact has been neglected in former models [239], but should be considered when studying the joint kinematics more in detail. Figure 5.89 shows an angled rocker pin joint. The most important kinematical effect consists in an offset \u2206ai between the intersection point X0 of the symmetry axis with the contour of the pin and the intersection point Bi of the two link axes. For common rotational joints (r0 = r = 0) this offset vanishes. The connection between 5.6 CVT - Rocker Pin Chains - Spatial Model 305 the joint angle 2\u03c6i and the offset \u2206ai is calculated by using Eqs. 5.126 and applying some trigonometrical operations: \u03c8i = \u03c6i \u2212 \u03b4, \u03a8i = |\u03c8i| AN = l(\u03a8i)\u2212 r tan \u03a8i 2 , NX0 = r0 + r tan \u03a8i 2 \u2206ai = X0Bi = 1 cos\u03c6i [r0 (1\u2212 cos\u03a8i) + r (\u03a8i \u2212 sin\u03a8i)] (5",
            " ,q T n )T \u2208 IR2n, with qi = (yi, zi)T . (5.128) For developing the chain equations of motion we consider Figure 5.90. We collect the proportionate masses mji of the chain (link plates and pins) in the point Pji. The point Kji denotes the position of the potential contact points Kji on the rocker pins to the pulleys. The position vectors of Pji and Kji can be stated by referring to the angles \u03b1i of the link axes (Figure 5.90). Furtheron we introduce the offset \u2206ai resulting from the rocker pin joint kinematics (Eq. 5.127, Fig. 5.89) and the constant \u2206bi := PjiKji, which describes the position of the body fixed contact point on the pin. The vectors to the above points then write rP1i = qi + \u2206ai ( cos\u03b1i\u22121 sin\u03b1i\u22121 ) rP2i = qi \u2212\u2206ai ( cos\u03b1i sin\u03b1i ) (5.129) rK1i = rP1i + \u2206bi ( cos(\u03b1i\u22121 + \u03b4) sin(\u03b1i\u22121 + \u03b4) ) rK2i = rP2i \u2212\u2206bi ( cos(\u03b1i \u2212 \u03b4) sin(\u03b1i \u2212 \u03b4) ) (5.130) The equations (5.129) refer to the mass points and the equations (5.130) to the contact points. Each of the two rocker pin components possesses its own contact point, which turns out to be quite realistic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003339_s0890-6955(03)00134-2-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003339_s0890-6955(03)00134-2-Figure1-1.png",
        "caption": "Fig. 1. Illustration of hybrid machining",
        "texts": [
            " In this part of the experiment, WG-300 tool inserts were selected in the study of possible increase of tool life and improving surface quality in machining Inconel 718. The operating parameters and experimental procedures were similar to those used in the plasma heating enhanced machining except that liquid nitrogen cooling system was added to cool the tool. The liquid nitrogen cylinder pressure used was 160 Psi. During the machining process, the cutting forces were measured in x, y, and z directions, which were feed force Fx, thrust force Fy, and cutting force Fz, respectively. The experimental setup is shown in Fig. 1. The data was later used to conduct a statistical analysis. Gradual tool wear appears mostly in two ways. One is crater wear, which is concave in shape located on the rake face of the tool formed by the action of chips sliding against the rake surface. The other one is flank wear, which is the result of relative motion between the newly generated work surface and the flank face adjacent to the cutting edge. In this study the tool flank wear is studied since it determines tool life. Fig. 2 shows how the flank tool wear increases with the increase of the cutting length in conventional machining, plasma enhanced machining, and hybrid machining in using WG-300 tool inserts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure2.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure2.3-1.png",
        "caption": "Fig. 2.3 Force and moment acting on a laminated plate",
        "texts": [
            "11) can be expressed in matrix form as Nx Ny Nxy Mx My Mxy 8>>>>< >>>: 9>>>>= >>>; \u00bc Axx Axy Axs Bxx Bxy Bxs Axy Ayy Ays Bxy Byy Bys Axs Ays Ass Bxs Bys Bss Bxx Bxy Bxs Dxx Dxy Dxs Bxy Byy Bys Dxy Dyy Dys Bxs Bys Bss Dxs Dys Dss 2 6666664 3 7777775 e0x e0y c0xy jx jy jxy 8>>>>< >>>: 9>>>>= >>>; \u00f02:12\u00de or simply expressed by N M \u00bc A B B D e0 j ; \u00f02:13\u00de where Aij (i = j = x, y, s) denotes the extensional and shear stiffness, Axs and Ays denote the extension\u2013shear coupling stiffness, Bij denotes the bending/twisting\u2013 extension/shear coupling stiffness, Dij (i = j = x, y, s) denotes the bending and twisting stiffness, and Dxs and Dys denote the bending\u2013twisting coupling stiffness (Fig. 2.3): \u00f0Aij;Bij;Dij\u00de \u00bc XN m\u00bc1 Zhm hm 1 \u00f01; z; z2\u00deE\u00f0m\u00de ij dz \u00f0i; j \u00bc x; y; s\u00de Aij \u00bc XN m\u00bc1 E\u00f0m\u00de ij \u00f0hm hm 1\u00de Bij \u00bc 1 2 XN m\u00bc1 E\u00f0m\u00de ij \u00f0h2m h2m 1\u00de Dij \u00bc 1 3 XN m\u00bc1 E\u00f0m\u00de ij \u00f0h3m h3m 1\u00de: \u00f02:14\u00de 2.1 CLT 63 Matrices [A], [B] and [D] are symmetric matrices because [E(m)] is a symmetric matrix. The 6 6 stiffness matrix on the right side of Eq. (2.12) is therefore also a symmetric matrix. Equation (2.13) can be rearranged as2 e0 M \u00bc a b c d N j ; \u00f02:15\u00de where \u00bda \u00bc \u00bdA 1 \u00bdb \u00bc \u00bdA 1\u00bdB \u00bdc \u00bc \u00bdB \u00bdA 1 \u00bc \u00bdb T \u00bdd \u00bc \u00bdD \u00bdB \u00bdA 1\u00bdB : \u00f02:16\u00de Note that [a] and [d] are symmetric while [b] and [c] are not"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000397_tnnls.2020.3027335-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000397_tnnls.2020.3027335-Figure8-1.png",
        "caption": "Fig. 8. Schematic of the electromechanical system.",
        "texts": [
            " Furthermore, in order to further illustrate the effectiveness of the developed control scheme, we compared with the nonfinite-time control by choosing the same design parameters, NNs, and initial values except the parameter \u03b2. Especially, when \u03b2 = 1, the developed control method becomes a nonfinite-time control scheme. The simulation results are displayed by Figs. 6 and 7. Fig. 6 depicts the curves of the given reference function and outputs of two control schemes; Fig. 7 presents the curves of tracking errors of two control schemes. Example 2 [20]: To further testify the effectiveness of the developed control algorithm, an electromechanical system is provided. The system is shown in Fig. 8. Authorized licensed use limited to: Middlesex University. Downloaded on October 20,2020 at 07:41:13 UTC from IEEE Xplore. Restrictions apply. The system model is expressed as Mq\u0308 + Bq\u0307 + N sin(q) = I L I\u0307 = V0\u2212RI \u2212 KT q\u0307 (57) where M = J/K\u03c4 +mL2 0/(3K\u03c4 )+M0 L2 0/K\u03c4 +2M0 R2 0/(5K\u03c4 ) and B = B0/K\u03c4 and N = mL0G/(2K\u03c4 )+M0 L0G/K\u03c4 , where m is the link mass, J is the rotor inertia, M0 is the load mass, R0 is the load radius, L is the armature inductance, B0 is the viscous friction coefficient, L0 is the link length, R is the armature resistance, KT is the back EMF coefficient, I (t) is the motor armature current, the gravity coefficient is G, and K\u03c4 is the coefficient that features the electromechanical conversion of armature current to torque",
            "1], W\u03023(0) = [0.2, 0.1, 0.1, 0, 0.1, 0, 0.2, 0.1, 0.2, 0.1, 0.1], \u03021(0) = 0.1, \u03022(0) = 0.2, \u03023(0) = 0.1, \u03021(0) = 0.01, \u03022(0) = 0.02, and \u03b1c 1(0) = \u03b1c 2(0) = 0.3. Moreover, in the designed projection operator Pr oj(\u00b7) (5), choose the design parameters as = 0.2 and \u03c2 = 0.2. According to (54), with the selected design parameters and initial values, we can get Treach \u2248 9.54 s. Thus, the simulation results are displayed by Figs. 7\u201310, where Fig. 7 shows the curves of output y(t) and reference function yr (t) and Fig. 8 shows the curves of tracking error e1; Fig. 9 presents the curves of states \u03c72 and \u03c73; and Fig. 10 depicts the curves of controller u. From Figs. 1\u20137 and 9\u201312, it is apparent that the developed control algorithm can ensure that all signals of the controlled system are bounded. Furthermore, output y(t) can track the reference function yr (t) within finite time. In this article, we have researched the finite-time NN adaptive DSC design problem for the SISO nonlinear system. RBFNNs are utilized to approximate the unknown functions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000240_tpel.2018.2809668-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000240_tpel.2018.2809668-Figure2-1.png",
        "caption": "Fig. 2 The electrical model of PMSM with inter turn short fault",
        "texts": [
            " Therefore, speed loop is included in the system for simulating the mechanical response as well. It is worth to mention that, the real time simulation and FEA simulation can be performed simultaneously, which is named as cosimulation. However, co-simulation requires very large computational resource and significant execution time. Therefore, the proposed method divides the co-simulation into two asynchronous simulations and links them by look-up tables. The equivalent circuit model of the PM machine in real time simulation is given in Fig. 2. The resistance of the short path cannot be perfectly zero and hence a fault resistance is introduced into in this model. In this case, the current in the circulating path is divided to two different components. One is the short circuit current is, which flows in the short path; and the other one is the fault current if, which is the current in the shorted turns. Based on Fig. 2, the voltage equations of the stator winding can be derived in (1) mabcfsabcfsabcf dt d eiLirv  (1) where, T abcf ah b c afv v v v   v  Tfcbaabcf iiiii T m ah b c afe e e e   e  Tafcbahm \u03bb                    afafcafbafah afcccbcah afbcbbbah afahcahbahah s LMMM MLMM MMLM MMML L                af c b ah s r r r r 000 000 000 000 r The voltage on the fault resistance is given in (2). f f s af f af a b c ah af b af c af af di r i r i L dt di di di M M M e dt dt dt          (2) The mechanical model of PMSM can be developed by the torque equation, which is given in (3) 2 2 T Tm m e abcf abcf e e dP P T d    \u03bb e i i (3) Since the test motor is surface mount PMSM, only electromagnetic torque is modeled as the torque output"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001204_j.rcim.2021.102115-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001204_j.rcim.2021.102115-Figure2-1.png",
        "caption": "Figure 2. The scheme of full pose measurement for DiaRoM-II by a laser tracker",
        "texts": [
            " Additionally, there is JL = [ I5 01\u00d75 ] for DiaRoM-II, so that the mechanism singularity occurs if and only if J is singular [47]. Therefore, the singularity of D corresponds to the mechanism singularity of DiaRoM-II, which means the proposed FKS algorithm is valid provided X is not too close to the singularity configuration of the parallel robot. As is acknowledged, the pose of a rigid body can be decided by three fixed points relative to it, so a laser tracker can accomplish full pose measurement of a robot by detecting the spatial coordinates of three points attached to its end-effector. Figure 2 presents the scheme of full X. Luo et al. Robotics and Computer-Integrated Manufacturing 70 (2021) 102115 pose measurement for DiaRoM-II by a laser tracker. An auxiliary tool is applied to assist the measurement, which consists of a cylindrical holder to concatenate the spindle and a square plate to support 4 SMRs at its vertexes. Ci (i = 1\u22ef4) are the centers of the SMRs when used, and the nominal dimension of rectangular C1C2C3C4 is a\u00d7 b. The auxiliary tool coordinate system {at : o\u2217 \u2212 x\u2217y\u2217z\u2217} is set up at point C1, with the x*-axis passing through point C2 and z*-axis perpendicular to the square plate",
            " On this account, an improved error modeling method is proposed to overcome the abovementioned problems by transforming the pose error \u0394\u03c7 to the position errors of some feature points, meanwhile introducing corresponding auxiliary tool errors. According to the number of the feature points, three ways are put forward as follows. (1) Using 2 feature points to express the pose of the spindle axis equivalently. It is well known that the 5-DoF pose of a rigid line, except for the rotation about itself, can be decided by 2 different points fixed on it. Therefore, the 5-DoF pose error of the spindle of DiaRoM-II can be substituted by the position errors of 2 points along the spindle axis, such as points D1 and D2 presented in Figure 2. The distance between points Di is set as t0, while di and pi are set to be their coordinates with respect to {ee} and {rt}, respectively. When the spindle is controlled to move from the zero position to some pose by a nominal instruction (o, R), the transformation relation between di and pi can be generated as: pi = o + Rdi, i = 1, 2 (46) where, d1 = [ 0 0 0 ] T , d2 = [0 0 t0 ]T. Subsequently, take the derivative of Equation (46), and the position errors of the feature points can be expressed as: { \u0394p1 = \u0394o \u0394p2 = \u0394o \u2212 t0Re3 \u00d7 \u0394R (47) Finally, rearrange Equation (47) in the matrix form and substitute Equation (45) into it, the proposed error model based on 2 feature points can be obtained as Equation (48), or abbreviated as Equation (49): [ \u0394p1 \u0394p2 ] = JspJ1\u0394\u03bb (48) \u0394\u03c7 2 = J2\u0394\u03bb (49) where, Jsp = [ I3 03\u00d73 I3 \u2212 [t0Re3\u00d7] ] , Ii denotes the identity matrix with dimension i\u00d7 i, [v\u00d7] denotes the skew matrix of vector v, and \u0394\u03c72 denotes the position errors of these 2 feature points along the spindle axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.40-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.40-1.png",
        "caption": "Fig. 5.40: ML Power Transmission of the VARIO series (courtesy AGCO/Fendt)",
        "texts": [],
        "surrounding_texts": [
            "to external requirements. The hydrostat system possesses the great advantage to develop very large torques especially at low speeds and at standstill. Figure 5.3.1 ilustrates the kernel of the power transmission, and Figure 5.41 presents a sketch of the overall system. Following this sketch we recognize that the torque of the Diesel engine is transmitted via a torsional vibration damper (1) to the planet carrier (5) of the planetary gear set (2). The planet gear distributes the power to the sunwheel (4) and the ring gear (3). This ring gear drives via a cylindrical gear pair the hydraulic pump (6), which itself powers the two hydraulic motors (7), where the oil flow from pump to motor depends on the pump displacement angle \u03b1. The hydraulic motors (7) generate a torque according to the oil flow and the motor displacement angle \u03b2. Furtheron, the sun wheel transmits its own torque via a gear pair to a collecting shaft (8), which adds the torques coming directly from the Diesel engine via the sun wheel on the one and coming indirectly from the chain ring gear-hydraulic pump-hydraulic motors on the other side. Thus the collecting shaft (8) combines the mechanical and the hydraulic parts of the torque. This splitting of mechanical and hydraulic power in an optimal way is the basic principle of the stepless VARIO system. As an additional option we may also connect the planet carrier (5) with the rear power take off (PTO) system, which drives all possible rear implements for performing processing of agriculture and forestry. The travel range selector (9) allows switching between 5.3 Tractor Drive Train System 259 slow and fast operation. The outgoing torque will be transmitted to the rear axle by a pinion and to the front axle by a gear pair. The system allows an adaptation of the tractor speed only by an appropriate combination of the displacement angles \u03b1 and \u03b2 without changing the engine\u2019s speed, which means, that the engine\u2019s speed may be kept constant at an optimal fuel efficiency point in spite of varying tractor speeds, of course within a limited speed range. This stepless VARIO-concept represents a type of CVT-system (Continuous Variable Transmission), which results in significant improvements with respect to handling and working performance."
        ]
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.10-1.png",
        "caption": "Fig. 11.10 Tire model with a stretched string [29]",
        "texts": [],
        "surrounding_texts": [
            "(1) Fundamental equations for the string model 718 11 Cornering Properties of Tires x x dx y 0 S1 S1 D fydx ksvdx b/2 b/2 dx x DD   x vS   1            dx x v x vS 2 2 1 v Fig. 11.11 Force equilibrium in a tread element of the string model [29] 11.1 Tire Models for Cornering Properties 719 where v is the displacement of the string in the y-direction and ks, S1, D and fy are, respectively, the lateral carcass spring rate per unit length in the circumferential direction, the tension of the string in the circumferential direction, the shear force and the side force on the contact patch. The shear force D is proportional to the shear angle \u2202v/\u2202x: D \u00bc S2 @v=@x; \u00f011:24\u00de where S2 is the tension related to the shear deformation. We here introduce the equivalent total tension S (=S1 + S2). Using Eqs. (11.24) and (11.23) can be simplified as S @2v=@x2 ksv \u00bc qy: \u00f011:25\u00de Because fy is zero outside the contact patch, Eq. (11.25) can be rewritten as S @2v=@x2 ksv \u00bc 0 for xj j[ a; \u00f011:26\u00de where a is half the contact length. Figure 11.12 shows the deformation of the string model near the contact patch. We also introduce the relaxation length r expressed by r \u00bc ffiffiffiffiffiffiffiffiffi S=ks p : \u00f011:27\u00de Using Eqs. (11.27) and (11.26) is rewritten as r2 @2v=@x2 v \u00bc 0 for xj j[ a: \u00f011:28\u00de If the relaxation length is shorter than the tire circumference, the displacement at the trailing edge v2 is not affected by the displacement at the leading edge v1. Displacements of the string outside the contact patch can be independently solved at the leading and trailing edges: 720 11 Cornering Properties of Tires v \u00bc C1e x=r for x[ a v \u00bc C2ex=r for x\\ a: \u00f011:29\u00de Considering the boundary conditions v = v1 at x = a and v = v2 at x = \u2212 a, we obtain @v=@x \u00bc v1=r for x # a @v=@x \u00bc v2=r for x \" a; \u00f011:30\u00de where x#a denotes that x gradually decreases toward a while x\" \u2212 a denotes that x gradually increases toward \u2212a. Considering that the slope of the string is continuous between the inside and outside of the contact patch at the leading edge, we obtain @v=@x \u00bc v1=r for x \" a; x \u00bc a; x # a: \u00f011:31\u00de (2) Force and moment of the string model The force and moment of the string can be calculated from the displacement in the contact patch v, the lateral carcass spring rate per unit length ks in the circumferential direction and the tension of the string S as shown in Fig. 11.12. The side force Fy is given by Fy \u00bc ks Za a vdx\u00fe S v1 \u00fe v2\u00f0 \u00de=r: \u00f011:32\u00de The self-aligning torque around point O is obtained through the addition of the lateral and circumferential components. The self-aligning torque due to the lateral displacement of the string v is given by M0 z \u00bc ks Za a vxdx\u00fe S a\u00fe r\u00f0 \u00de v1 v2\u00f0 \u00de=r: \u00f011:33\u00de The self-aligning torque due to the circumferential displacement u is given by M z \u00bc Cx Za a Zb 2 b 2 uydxdy; \u00f011:34\u00de where Cx is the shear spring rate of the tread per unit area in the circumferential direction. The total moment Mz is given by 11.1 Tire Models for Cornering Properties 721 Mz \u00bc M0 z \u00feM z : \u00f011:35\u00de Suppose that the lateral displacement of the string in the contact patch v can be expressed by a straight line at a given slip angle a. Neglecting the circumferential displacement u, v is given by v \u00bc a a x\u00fe r\u00f0 \u00de: \u00f011:36\u00de The substitution of Eq. (11.36) into Eqs. (11.32) and (11.33) yields Fy \u00bc CFaa Mz \u00bc CMaa CFa \u00bc 2ks r\u00fe a\u00f0 \u00de2 CMa \u00bc 2ksa r r\u00fe a\u00f0 \u00de\u00fe a2=3 : \u00f011:37\u00de"
        ]
    },
    {
        "image_filename": "designv10_2_0000772_j.precisioneng.2021.01.007-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000772_j.precisioneng.2021.01.007-Figure4-1.png",
        "caption": "Fig. 4. The equivalent SPR chain of the 1st chain.",
        "texts": [
            ", \u03b4\u03b1s5] T is the angle error vector of zero offsets of motors, including 5 error components. The method of building the error model of the ball-screw-actuator can be applied to other parallel machines with this design. Based on the screw theory [5], the actuation wrenches and constraint wrenches are analyzed. The i-th (i = 2,3,4,5) chain is the 6-DOF chain without constraints. The 1st chain is a 5-DOF chain, which is equivalent B. Mei et al. Precision Engineering 69 (2021) 48\u201361 to a SPR chain from the perspective of mechanism. As shown in Fig. 4, the permit twists of the 1st chain in the local reference frame is \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 $T11 = (1, 0, 0; 0, 0, 0) $T12 = (0, 1, 0; 0, 0, 0) $T13 = (0, 0, 1; 0, 0, 0) $T14 = (\u03c91; 0, 0, 0) $T15 = (vr; am1 \u00d7 vr) (22) The constraint wrench of the 1st chain is reciprocal to the permit twists, which can be calculated and obtained as $c = (vr; 0, 0, 0) (23) Thus the constraint wrench is a pure force passing through B1 along the direction of the axis of revolute joint in the 1st chain. The input twist in the 1st chain is $T14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000369_j.ijpharm.2018.02.022-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000369_j.ijpharm.2018.02.022-Figure2-1.png",
        "caption": "Fig. 2. Diagram of (a) generic bioaffinity-type biosensor and (b) generic enzyme-based amperometric biosensor.",
        "texts": [
            " For implanted sensors, which are exposed to the truly vast number of proteins, metabolites, cells, and chemicals present in a physiological environment, this high selectivity is absolutely crucial for accurate operation. The archetypal biosensor has two basic components, the biological element which interacts with the target analyte, and the physical transducer which interacts with the biological element to convert the chemical interaction into a quantifiable signal. Biosensors can be broadly classified into two categories, differentiated by the type of biological component: bioaffinity sensors and biocatalytic or enzymatic sensors (Fig. 2). A diagram of a generic bioaffinity sensor is presented in Fig. 2a. Bioaffinity sensors consist of a physical transducer coated with a thin functionalization layer of \u2018capture molecules\u2019, which bind selectively and typically irreversibly to target analytes. These capture molecules represent the biological recognition element of a bioaffinity sensor, and may be an immobilized film of antibodies, antigens, aptamers, or DNA/ RNA segments. Detection of an analyte is encoded in a transduction signal, such as a measured change in mass, film thickness, charge, dielectric constant, or local-field potential due to the presence of the captured analyte, or the fluorescent signal from an accompanying fluorophore tag",
            " While both oxidase and dehydrogenase enzymes are commonly used in ex vivo biosensors, only oxidases are typically used in vivo as there is an available supply of O2 to regenerate the enzyme. Though enzymatic sensors include those using fluorescent, plasmonic, and voltammetric transducers among others, by far the most common are amperometric designs. Notably, both the first biosensor (Clark and Lyons, 1962) and first implanted biosensor (Sternberg et al., 1989) were amperometric and enzymatic. A diagram of a common amperometric biocatalytic sensor is presented in Fig. 2b. The basic transducer comprises a set of electrodes held at a constant potential difference, with the working electrode coated in a layer of enzyme. Analytes at the enzyme layer undergo a catalyzed reaction and the enzyme is regenerated through the reduction of a mediator compound, which may be naturally present in the body or coimmobilized with the enzyme. The reduced mediator is electrochemically oxidized at the working electrode, resulting in an electric current (nA to \u00b5A) proportional to the local concentration of the target analyte"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000772_j.precisioneng.2021.01.007-Figure20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000772_j.precisioneng.2021.01.007-Figure20-1.png",
        "caption": "Fig. 20. The model and features of the M1_160 test piece: (a) axonometric view; (b) Top view.",
        "texts": [
            " Precision Engineering 69 (2021) 48\u201361 diameter, feed speed and radial depth of cut are chosen to reduce the machining errors induced by post-processing and cutting forces. The tool used in the test is a sintered carbide end mill with the diameter of 12 mm. With a small diameter, the accuracy of tool path generated by the post-processing can be improved. The radial depth of cut in the process of finish machining is set as 0.1 mm and the feed speed is set as 250 mm/min to reduce elastic deformation due to cutting forces. The model of the M1_160 test piece is shown in Fig. 20. The detailed features are presented in ISO 10791\u20137:2020. Fig. 21 presents the M1_160 test piece during and after the machining process. The machined M1_160 test piece is measured by the coordinate measurement machine. The measured results of error components are shown in Fig. 22. The maximum error, mean error and standard variance are 52 \u03bcm, 15 \u03bcm and 13 \u03bcm, respectively. It demonstrates that after error compensation, the parallel machining robot has fine performance on three-axis machining. An S-shaped test piece is machined by the five-axis parallel machining robot, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure20-1.png",
        "caption": "Fig. 20. Illustration of simultaneous meshing of shaper, worm, and face-gear.",
        "texts": [
            " The next step was done by the patent proposed by Litvin et al. [10] that has formulated the exact determination of the thread surface of a generating worm providing the necessary conditions of conjugation of the tooth surfaces of the hob, the shaper, and the face-gear, concept of worm design, and avoidance of worm singularities. The worm might be applied for grinding and cutting of facegears. Designations Rs, Rw, and R2 indicate surfaces of the shaper, worm, and face-gear, respectively. Simultaneous meshing of Rs, Rw and R2 is illustrated by Fig. 20. Shaper surface Rs is considered as the envelope to the family of rack-cutter As surfaces and is represented by vector function Rs\u00f0wr; hr\u00de (see Eq. (9)). Surfaces Rw and R2 are generated as the envelopes to the family of shaper surfaces Rs. We remind that in the new design the shaper is provided with non-involute profile (see Section 3). Fig. 21 shows fixed coordinate systems Sa, Sb, and Sc applied for illustration of installment of the worm with respect to the shaper. Moveable coordinate systems Ss and Sw are rigidly connected to the shaper and the worm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure8-1.png",
        "caption": "Fig. 8. Three gears mesh assem",
        "texts": [
            " For each iteration in the analysis, the olver forms the model\u2019s stiffness matrix and solves a system P D D C nd details of their local mesh. f equations. This means that each iteration is equivalent, in omputational cost, to conducting a complete linear analysis. t can be seen that the computational expense of a non-linear nalysis in the solver can be many times greater than for a linear ne. To achieve high accurate result, very fine surface meshes re required for their geometry accuracy and contact accuracy. igh quality meshes for contact surfaces have been obtained y surface-based tie constraint techniques as shown in Fig. 8. he main advantage of this surface-based tie constraint is hat it allows for rapid transitions in mesh density within the odel. Fig. 8(a) shows examples of three helical gears mesh quality nd their assembly. It can be seen from the figure that the whole ear model mesh is quite course for each gear and high quality eshes are only for the contact surfaces. Fig. 8(b) shows the urface local tied constraint applications and this rapid transition n mesh density will make the model run significant fast with igh contact accuracy. . Gear surface pitting failure The gears used for automotive application shown in Fig. 9 re carburised steel (E = 207 GPa and \u03c5 = 0.3) gears. The gear orque is oscillating but with a peak of 440 Nm. Following are he gear specifications: inion 24 teeth heel 24 teeth odule 3 mm ressure angle 25\u25e6 ace width 20 mm rowning 18 m ip relief 61 m ead correction 8 m eak torque 440 Nm river speed 4000 rpm riven speed 4000 rpm oefficient of friction 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.37-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.37-1.png",
        "caption": "Fig. 5.37 Relation of the tire shape to tension in its structure (reproduced from Ref. [20] with the permission of Tire Sci. Technol.)",
        "texts": [
            " Axisymmetric membrane shell theory for structures implies that an equilibrium normal to a surface gives N/ r1 \u00fe Nh r2 \u00bc p; \u00f05:125\u00de 284 5 Theory of Tire Shape where N/ is the meridian membrane force (i.e., sidewall tension) per unit width of the sidewall, Nh is the circumferential membrane force, r1 is the meridian radius of curvature (of the sidewall), r2 is the circumferential radius of curvature as shown in Fig. 5.1, and p is the inflation pressure. 5.6 Nonequilibrium Tire Shape 285 For radial tires, we can assume that in the sidewall area we have Nh \u00bc 0: \u00f05:126\u00de The sidewall membrane force (tension) N/ is therefore expressed by N/ \u00bc r1p: \u00f05:127\u00de Referring to Fig. 5.37, the total belt tension T0 is given as T0 \u00bc ap 2 b 2r1 sin h\u00f0 \u00de; \u00f05:128\u00de where a is the belt diameter, b is the belt width, and h is the angle between the tangent to the carcass line and the belt. Equation (5.128) shows that the carcass ply tension is proportional to the radius of curvature of the sidewall. Conversely, Eq. (5.128) shows that the total belt tension decreases when the carcass ply radius r1 and angle h are larger than those of the conventionally shaped tire for a given belt diameter a and belt width b"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.27-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.27-1.png",
        "caption": "Fig. 7.27: Three Different Types of Contacts Between the Snap Hook and the Chamfer",
        "texts": [
            " The relationship between the linear deformations and the linear elastic reaction forces has then the following form:( Af Am ) = K ( ArAL A\u03d5AL ) \u2208 IR6, (7.98) where Af is the vector of the forces and Am is the vector of the torques acting at the origin of the L frame when the deformations ArAL and A\u03d5AL are imposed. The description of the geometry is easy for the snap fasteners under consideration. The counterpart is a simple cuboid and the hook a polygonal part with six corners. Thus there are three basic possibilities of contact points between the snap hook and the counterpart as indicated in Figure 7.27: corner\u2013 surface (type 1), edge\u2013edge (type 2), and surface\u2013corner (type 3). A contact between the flexible part and the counterpart is not regarded. The location of a contact point is always indicated by two parameters u and v, which will be needed later in the equations of the force equilibrium. When the snap hook and the counterpart get in contact the parts will slide on each other and the hook will be displaced and twisted. In order to determine this movement and the accompanying forces we have to calculate the equilibrium position between these two parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.89-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.89-1.png",
        "caption": "Fig. 5.89: Design of the polymer actuator. According to [Guo95)",
        "texts": [
            " A prototype of a microcatheter was developed with two integrated guide wires and a liquid channel [Guo95). Through the channel physiologic solutions or contrast media can be transported. Attached to each guide wire is a polymer film actuator which enables the catheter to be bent, Fig. 5.88. The guide wire consists of two electric conductors covered by a wire sheath and the actual actuator, an ionic conducting polymer film. The end of this film is embedded between two flat platinum electrodes, Fig. 5.89. In order to bend the tip of the catheter, a defined voltage is applied to both electrodes of the desired actuator. This voltage causes the polymer gel to expand at the ca thode side, which results in a movement of the film actuator towards the anode side. The actuator tip bends in a circular manner, making it possible to control the radius of this bend (and with this the position of the catheter) with the voltage applied to the electrodes. The special features of these actuators, compared to other actuation principles like SMA or bimorphic materials are quick response and low driving voltage, about 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000231_tie.2021.3073313-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000231_tie.2021.3073313-Figure8-1.png",
        "caption": "Fig. 8. The rigid body model of the needle insertion device. (a) shows the forces exerted on the shaft of linear motion and (b) shows the forces of rotary motion.",
        "texts": [
            "2Hz, 2850.76Hz and 9114.6Hz, the corresponding vibration modes were shown in Fig. 7. It can be noted that the vibration modes of the first three order resonance frequencies all happened on the T shape beam structure, including bending and torsional vibrations. After accomplishing the structural design, it is necessary to perform the dynamic simulation to validate the design and predict the system behavior before prototyping. The simplified rigid body model of the needle insertion device is shown in Fig. 8. The translation and rotation of the shaft are separately transferred from the reciprocal longitudinal and flexural movement of the driving foot. In the linear motion direction, the shaft is subjected to the driving friction force Fl on the contact surface with the driving foot and the external resistance forces fg coming from the bearing friction and external needle-tissue interaction forces. Around the rotation axis, the shaft is mainly subjected to the rotation driving friction force Fr and the resistance torque Tg",
            " 8 needle tip diameter, penetration velocity, insertion angle, contact stiffness, would directly influence the interaction force. The output force of the needle insertion device also determined the insertion result. In our experiment, the maximum insertion force of the needle insertion device was characterized by the blocking force of the translational movement. As shown in Fig. 20, the blocking forces under different driving voltages were tested. All measurement results fluctuate slightly around 32 mN. According to Fig. 8, the blocking force was generated by the driving friction force Fl, which was influenced by the contact normal force. All the measurements were conducted under the same contact normal force, the blocking force just nearly kept constant under different driving voltages. Compare to the insertion forces tested in [13], the blocking force was adequate to perform the insertion whose force peak was 9.33 mN. The insertion force could be significantly improved by using the adjustment mechanism to increase the normal force, under the condition that a power amplifier with faster charge and discharge time was utilized to restrain the backward motion introduced by the extra friction force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.106-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.106-1.png",
        "caption": "Fig. 5.106: Coordinate sets of one finite element [282].",
        "texts": [
            " Generally, the coordinate set used for this attempt cannot be used for coupling different elastic bodies to one discretized structure. On the other hand, finite element (FE) approaches offer coordinate sets designed for coupling adjacent elements. These different advantages of both, MFR and FE, can be maintained, if two coordinate sets are used. The following formalism is described in detail in [282], see also [81]. The internal coordinate set qi = (yS , zS, \u03d5S , \u03b5\u0303, al, \u03b2l, ar, \u03b2r)T \u2208 IR8 (see Figure 5.106a) is used to evaluate the equations of motion for one single finite element. This set is inspired by MFR-ideas: yS , zS , \u03d5S describe the rigid body movements of the finite element, \u03b5\u0303 gives an approximation for the longitudinal strain and al, \u03b2l, ar, \u03b2r describe the bending deflections. The global coordinate set qg = (y1, z1, \u03d51, a1, a2, y2, z2, \u03d52)T is used as second coordinate set (see Figure 5.106b) for coupling different finite elements to a discretized description of one structure. This FE-inspired set is used for time integration of the entire dynamical system. The correlation between both coordinate sets is shortly explained below. A constraint on position level is developed and derived to gain dependencies on velocity and acceleration level. These equations are used to transform the equations of motion of one single finite element into a form in terms of the global coordinates. The coordinate sets qi and qg of one single finite element are subjected to an explicit equality constraint: qi = Q(qg) \u2208 IR8 (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003878_s101890170060-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003878_s101890170060-Figure8-1.png",
        "caption": "Fig. 8. (a) The ordering of a rod with polar angle \u03b8 to the director n\u0302 and azimuthal angle \u03c6 in the xy-plane. (b) A freely jointed polymer, composed of such rods, with end-to-end vector R.",
        "texts": [
            " The modulus ratio is < 1 around the transition, rapidly crosses over to > 1 below Tni and saturates to a sizable value > 1 at low temperatures. The direction of uniaxial nematic order, the director n\u0302, is taken to be along z\u0302 in the matrix form of Q. The degree of uniaxial order, Q, is given microscopically by the average Q = \u300832 cos2 \u03b8 \u2212 1 2 \u3009, where \u03b8 is the angle between the long axis of a mesogenic rod and the director. The degree of biaxiality is measured by the order parameter b = 3 2 \u3008sin2 \u03b8 cos 2\u03c6\u3009 and determines how the angular freedom (\u03c6) of rods in the plane perpendicular to n\u0302 is restricted, see Figure 8a. In some cases the elongated molecules are also sufficiently asymmetric in their crosssection that their molecular interactions spontaneously induce biaxial order. We consider intrinsically uniaxial systems; those spontaneously ordering with Q = 0, b = 0, and examine only biaxiality induced by external strains. The phenomenological expansion of the nematic freeenergy density, Fn, of a nematic fluid to the required quartic order in the order parameter Q is [3] Fn = 1 3ATr ( QQ ) \u2212 4 9BTr ( QQQ ) + 2 9C Tr ( QQQQ ) + ",
            " The chain then suffers an extreme and rapid elongation as the temperature drops and the backbone order parameter grows. Much larger derivatives, DQ and Db, can thus arise than in the simplest model, that of chains of freely jointed rods, that we shall adopt below. It may, in cases where extreme anisotropy is observed, be necessary to revert to more complicated models. A freely jointed rod chain end-to-end vector is the sum of the component rod vectors. Let the rods be of length a, the \u03b1-th link forming an angle \u03b8\u03b1 with the director and an azimuthal angle \u03c6\u03b1, see Figure 8. Let the unit vector of the \u03b1-th rod be u\u0302(\u03b1). The the polymer\u2019s end-to-end vector is R = a \u2211N \u03b1=1 u\u0302(\u03b1). The shape tensor is, on rearranging (5), = 3 Na \u3008RR\u3009 = 3a N \u2211 \u03b1\u03b2 \u2329 u\u0302(\u03b1)u\u0302(\u03b2) \u232a . (23) Being freely jointed, there is no correlation between directions u\u0302(\u03b1) and u\u0302(\u03b2) on different links \u03b1 and \u03b2, whence\u2329 u\u0302(\u03b1)u\u0302(\u03b2) \u232a only survives when \u03b1 = \u03b2 and gives \u3008u\u0302u\u0302\u3009, the same for all links. The coordinate projections, in the frame where the director is along z, that is n\u0302 = z\u0302, are uz = cos \u03b8, ux = sin \u03b8 cos\u03c6 and uy = sin \u03b8 sin\u03c6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.52-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.52-1.png",
        "caption": "Fig. 5.52: Load Example",
        "texts": [
            "94) which can be decomposed to the three equations for the unknowns (h, \u03b2, \u03b3) \u03b3 = arcsin ( rTF lK (sin\u03d5TF cos\u03d5K \u2212 cos\u03d5TF sin\u03d5K cos\u03b1) ) \u03b2 = arcsin ( rK \u2212 rTF (sin\u03d5TF sin\u03d5K + cos\u03d5TF cos\u03d5K cos\u03b1) lK cos \u03b3 ) h =rTF cos\u03d5TF sin\u03b1 + lK cos\u03b2 cos \u03b3 (5.95) The results of these equations are illustrated in Figure 5.3.2. To get an idea of the forces resulting from the above kinematical consideration we investigate a simplified case with no rotational speed difference, \u03d5T \u2212\u03d5K = 0, and a piston pressure according to Figure 5.52. The pistons possess at one end spherical bearings, which allow a force tranfer only in the direction of the piston axis to the driving flange. This direction for one piston is defined by DeK,k = \u2212 cos\u03b2 cos \u03b3 \u2212 sin\u03b2 cos \u03b3 sin \u03b3  k =\u21d2 DFK,k =Fp,k \u2212 cos\u03b2 cos \u03b3 \u2212 sin\u03b2 cos \u03b3 sin \u03b3  k , (k =1, 2, \u00b7 \u00b7 \u00b7 9) (5.96) The reference coordinates are piston drum fixed. The forces can be decomposed into three components and then summarized for all nine pistons, regarding their individual position and orientation. Before showing the results we transform the forces from the piston drum \u201dD\u201d to the driving flange \u201dF\u201d by the transformation (Figure 5.52) 5.3 Tractor Drive Train System 269 FFK,k =Fp,k  \u2212 cos\u03b1 cos\u03b2 cos \u03b3 \u2212 sin\u03b1 cos\u03b2 cos \u03b3 cos\u03d5 + sin\u03b1 cos\u03b2 cos \u03b3 sin\u03d5  k , (k = 1, 2, \u00b7 \u00b7 \u00b79) (5.97) A numerical evaluation indicates, that axial forces of the pistons are large on both, drum and flange; whereas tangential and radial forces are only large on the driving flange, see Figures 5.3.2 and 5.3.2. To establish the equations of motion of the complete system we have to combine the above models and to supplement them by the appropriate models for the oil hydraulics and the axial drum bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure9-1.png",
        "caption": "Fig. 9. A derived origami-inspired 8R kinematotropic metamorphic mechanism. (a) 8R kinematotropic metamorphic mechanism (b) Its prototype.",
        "texts": [
            " 8 (b) with the conditions that: a 12 = a 23 = a 34 = a 45 = a 56 = a 61 = c { \u03b112 = \u03b134 = \u03b156 = \u03b3 \u03b123 = \u03b145 = \u03b161 = \u2212\u03b3{ d 1 = d 3 = d 5 = 0 d 2 = d 4 = d 6 = 0 (3) where a i (i +1) denotes length of link i (i + 1) , \u03b1i (i +1) is twist of link i (i + 1) , d i is referred as offset of joint i , \u03b8i is the angle of rotation from x i and x i +1 about axis z i , c > 0 and \u03b3 \u2208 ( 0 , \u03c0) based on the geometrical conditions. It can be identified from the DH parameters that this 6R mechanism is a threefold-symmetric Bricard linkage [55] . Hence, the subtle relevance of origami and Bricard linkage is emerged by the construction approach. In this section, a special 8R kinematotropic metamorphic mechanism is extracted from origami as shown in Fig. 9 . It is composed of eight equal links connected with eight revolute joints. These joints are denoted by E, B 1 , F, B 2 , G, B 3 , H, and B 4 , respectively. The twist angle \u03b1 of adjacent joints is \u03c0/ 2 , the parameters of the derived origami-inspired 8R mechanism are as follows: a 12 = a 23 = a 34 = a 45 = a 56 = a 67 = a 78 = a 81 = a { \u03b112 = \u03b134 = \u03b156 = \u03b178 = \u03c0/ 2 \u03b123 = \u03b145 = \u03b167 = \u03b181 = \u2212\u03c0/ 2 { d 1 = d 3 = d 5 = d 7 = 0 d 2 = d 4 = d 6 = d 8 = 0 (4) where a i (i +1) denotes length of link i (i + 1) , \u03b1i (i +1) is twist of link i (i + 1) , d i is referred as offset of joint i , \u03b8i is the angle of rotation from x i and x i +1 about axis z i , a > 0 based on the geometric conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.39-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.39-1.png",
        "caption": "Fig. 2.39: Typical Model of a Press Fit [26]",
        "texts": [],
        "surrounding_texts": [
            "For some nonlinear systems we might be able to generate a linear approximation by representing the nonlinear hysteresis curves by linear ones. With respect to Figure (2.37) we then must approach the closed hysteresis of the right picture by the ellipse-shaped curve of the left side by watching the condition, that the enclosed area must be the same for both cases, the real nonlinear one and the approximate linear one. Many methods are available to perform such an approximation ([148], [187], [47] or [60]). 3 Constraint Systems Es ist die na\u0308chste und in gewissem Sinne wichtigste Aufgabe unserer bewussten Naturerkenntnis, dass sie uns befa\u0308hige, zuku\u0308nftige Erfahrungen vorauszusehen, um nach dieser Voraussicht unser gegenwa\u0308rtiges Handeln einrichten zu ko\u0308nnen. (Heinrich Hertz, Die Prinzipien der Mechanik, Einleitung, 1894) The most direct, and in a sense the most important task, which our conscious knowledge of nature should enable us to solve is the anticipation of future events, so that we may arrange our present affairs in accordance with such anticipation. (Heinrich Hertz, The Principles of Mechanics Presented in a New Form, authorized English translation by D.E. Jones and J.T. Walley; London, New York, Macmillan, 1899)"
        ]
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.13-1.png",
        "caption": "Fig. 8.13: Inverted Pendulum Model",
        "texts": [
            " Human walking is characterized by two phases, not considering here the phase without ground contact taking place only for running. The two phases are the single- and the double-support phases. For the single-support phase we have stance for one foot and swing for the other one. For the double-support phase we have stance for both feet. During walking we have a periodic change of single- and double-support phases. The inverted pendulum model provides a simple model for a also simple control design, which for small speeds might be a first approach. Figure 8.13 illustrates the model. The momentum equation for the total system writes M x\u0308S = \u2212G+ F ext, (8.63) which includes the gravity forces G and some external forces F ext. The vector xS represents the coordinates of the machine\u2019s center of mass. As long as the machine mass is constant, we get from equation (8.63) the correct motion of the center of mass without simplifications. With respect to the moment of momentum equations we are not able to reduce the machine\u2019s overall moment of inertia to a constant value",
            "64) which is a simplification, because on the one side the moments of inertia of the machine are not constant, and on the other side the moment of momentum of the machine might change even for a not moving trunk but with moving legs or arms. Astonishingly enough, the rough approximation as introduced above is quite nicely confirmed by experiments, and it is therefore used by many research teams around the world. For JOHNNIE we apply that for real-time computations, but not for simulations. 8.3 Walking Trajectories 533 For the following trajectory consideration we assume, again approximately, that we have an upright gait for T ext = 0. According to Figure 8.13 only forces are acting in the zero-moment-point and no torques. From this we get also only forces along the connecting line from the ZMP to the system center of mass. With a prescribed vertical acceleration z\u0308S,ref of the center of mass the horizontal accelerations can be calculated by  x\u0308S y\u0308S z\u0308S  =  (g + z\u0308S,ref)xS\u2212xZMP zS\u2212zZMP (g + z\u0308S,ref)yS\u2212yZMP zS\u2212zZMP z\u0308S,ref  (8.65) These equations can be solved for some prescribed vertical motion, for exam- y [m ] ple one of the magnitudes zS,ref , z\u0307S,ref , z\u0308S,ref "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003496_s0956-5663(00)00085-3-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003496_s0956-5663(00)00085-3-Figure6-1.png",
        "caption": "Fig. 6. Lineweaver\u2013Burk plot for inhibition of urease immobilised in biosensor form by Hg(II) ions. Inhibition time: 15 min; , no inhibitor; , 1.0 mM and , 2.0 mM Hg(II).",
        "texts": [
            "0 mM although in the last case the total recovery of enzymatic activity was much less possible \u2014 after 30 min regeneration only 80% of initial activity of urease was obtained. For the inhibition of urease immobilised in CPG reactor by phenylmercury acetate described in the literature [18] also smaller slope of calibration curve was observed than for Hg(NO3)2 but the linear range was the same for both forms of mercury The mechanism of Hg(II) ion inhibition was also studied by measuring of initial rate of potential change for different concentration of mercury(II) and of urea. The results of these measurements shown in Fig. 6 in the form of Lineweather\u2013Burk plot suggested noncompetitive inhibition of urease immobilised in PVC layer at the surface of iridium oxide electrode. Also Liu Fig. 5. Calibration curves for different forms of mercury obtained after 30 min of inhibition. Concentration of added urea, 1.0 mM; , Hg(NO3)2; , HgCl2; , Hg2(NO3)2; , PhHgCl. Table 2 Parameters of calibration curves for different mercury forms ConcentrationParameters of calibration curve Hg form Linear range (mM)Slope (%/dec) Correlation for 50% inhibition (mM) 56"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure29-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure29-1.png",
        "caption": "Fig. 29. Illustrations of: (a) the volume of designed body, (b) auxiliary intermediate surfaces, (c) determination of nodes for the whole volume, and (d) discretization of the volume by finite elements.",
        "texts": [
            " (3)) and module m \u00bc 1 mm. This section covers stress analysis and investigation of formation of bearing contact of contacting surfaces. The performed stress analysis is based on the finite element method [17] and application of a general computer program [3]. The developed approach for the finite element models is accomplished as follows [1]: Step 1. Tooth surface equations of pinion and gear and portions of corresponding rim are considered for determination of the volumes of the designed bodies. Fig. 29(a) shows the designed body for onetooth model of the pinion of a helical gear drive. Step 2. The designed volume of each tooth of the model is divided into six subvolumes using auxiliary intermediate surfaces 1\u20136 as shown in Fig. 29(b). Step 3. Node coordinates are determined analytically considering the number of desired elements in lon- gitudinal and profile directions (Fig. 29(c)). Step 4. Discretization of the model by finite elements (using the nodes determined in previous step) is accomplished as shown in Fig. 29(d). Step 5. Setting of boundary conditions is accomplished automatically and are shown in Fig. 30(a) and (b) for the case of a three-tooth model. The following ideas are considered: iii (i) Nodes on the two sides and bottom part of the portion of the gear rim are considered as fixed (Fig. 30(a)). i (ii) Nodes on the two sides and the bottom part of the pinion rim form a rigid surface (Fig. 30(a) and (b)). (iii) A reference nodeN (Fig. 30(b)) located on the axis of the pinion is used as the reference point of the previously defined rigid surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure20-1.png",
        "caption": "Fig. 20. Schematic illustration of: (a) boundary conditions for the pinion and the face gear, and (b) rigid surfaces applied for boundary conditions of the pinion.",
        "texts": [
            " We emphasize that all nodes of the finite element mesh are determined analytically and the points lying on the surfaces the tooth belong to the real gear tooth surfaces. Step 4: Discretization of the model by finite elements (using the nodes determined in previous step) is accomplished as shown in Fig. 19(d). Step 5: Setting of boundary conditions for the gear and the pinion are accomplished automatically under the following conditions: (i) Nodes on the two sides and bottom part of the portion of the gear rim are considered as fixed (Fig. 20(a)). (ii) Nodes on the two sides and the bottom part of the pinion rim form a rigid surface (Fig. 20(a) and (b)). Such rigid surfaces are three-dimensional structures that may perform translation and rotation but cannot be deformed. (iii) The advantage of consideration of pinion rim rigid surfaces mentioned above is as follows: (a) their variables of motion (its translation and rotation) are associated with a single point chosen as the reference point M; (b) point M is located on the pinion axis of rotation (Fig. 20(b)); (c) reference point M has only one degree of freedom (rotation about the pinion axis) and all other degrees of freedom are fixed; (d) the torque T in rotational motion is applied directly to the pinion at its reference node M (Fig. 20(b)). Step 6: The contact algorithm of the finite element analysis computer program [5] requires definition of contacting surfaces. The proposed approach enables to identify automatically all the elements of the model required for the formation of such surfaces. The contact algorithm requires as well definition of master and slave surfaces. Generally, the choosing of a master surface is based on the following considerations [5]: (i) it is the surface of the stiffer body of the model, or (ii) the surface with coarser mesh if the contacting surfaces are located on structures with comparable stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure24-1.png",
        "caption": "Fig. 24. Schematic of generation: (a) without worm plunging; (b) with worm plunging.",
        "texts": [
            " 18) /i (i \u00bc 1; 2) angle of rotation of the pinion (i \u00bc 1) or the gear (i \u00bc 2) in the process of meshing wi (i \u00bc r; 1; 2) angle of rotation of the profile-crowned pinion (i \u00bc r), the double-crowned pinion (i \u00bc 1), or the profile-crowned gear (i \u00bc 2) in the process of generation Dc shaft angle error (Fig. 14) Dk lead angle error Dki (i \u00bc 1; 2) correction of lead angle of the pinion (i \u00bc 1) or the gear (i \u00bc 2) D/2\u00f0/1\u00de function of transmission errors Dwp additional rotational motion of the pinion during the feed motion (Fig. 24) Dsw translational motion of the grinding worm during the feed motion (Fig. 24) DE center distance error (Figs. 12 and 14) Ri surfaces (i \u00bc c; t; r; s; 1; 2;w;D) ac parabola coefficient of profiles of pinion rack-cutter in its normal section (Fig. 7) amr parabola coefficient of the parabolic function for the modified roll of feed motion apl parabola coefficient of plunging by grinding disk or by grinding worm b parameter of relative tooth thickness of pinion and gear rack-cutters EDp shortest center distance between the disk and the pinion (Figs. 18 and 19) Ewp shortest center distance between the worm and the pinion (Fig. 24) ld, lc parameters of location of point of tangency Q and Q , respectively (Fig. 6) lp translational motion of the pinion during the generation by grinding disk (Fig. 19) m module m12, mwp gear ratios between pinion and gear and between worm and pinion, respectively Mij matrix of coordinate transformation from system Sj to system Si n \u00f0j\u00de i , N \u00f0j\u00de i unit normal and normal to surface Rj in coordinate system Si Ni number of teeth of pinion (i \u00bc 1; p), gear (i \u00bc 2) or worm (i \u00bc w) p1, p2 screw parameters of the pinion and the gear, respectively ri radius of pinion (i \u00bc p1; p), gear (i \u00bc p2) or worm (i \u00bc w) pitch cylinder rd1 dedendum radius of the pinion r i radius of pinion (i \u00bc p1) or gear (i \u00bc p2) operating circle (Fig",
            " The process of such enveloping is based on application of two independent sets of parameters of motion [7,12]: (i) One set of parameters relates the angles of rotation of the worm and the pinion as mwp \u00bc x\u00f0w\u00de x\u00f0p\u00de \u00bc Np Nw \u00bc Np; \u00f036\u00de Fig. wherein the number Nw of worm threads is considered as Nw \u00bc 1 and Np is the teeth number of the pinion. 23. Contact lines Lcr and Lcw corresponding to meshing of rack-cutter Rc with pinion and worm surfaces Rr and Rw, respectively. (ii) The second set of parameters of motion is provided as a combination of two components: (1) trans- lational motion Dsw of the worm that is collinear to the axis of the pinion (Fig. 24(a)); (2) small rotational motion of the pinion about the pinion axis that is determined as Dwp \u00bc Dsw p ; \u00f037\u00de where p is the screw parameter of the pinion. Analytical determination of a surface generated as the envelope to a two-parameter enveloping process is represented in [7]. The schematic of generation of Rr by Rw is shown in Fig. 24(a) wherein the shortest center distance is shown as extended one for the purpose of better illustration. In the process of meshing of Rw and Rr, the worm surface Rw and the profile-crowned pinion surface perform rotation about crossed axes. The shortest distance is executed as Ewp \u00bc rp \u00fe rw: \u00f038\u00de Surfaces Rw and Rr are in point tangency. Feed motion of the worm is provided as a screw motion with the screw parameter of the pinion. Designations in Fig. 24(a) indicate: (1) M1 and M2 points on pitch cylinders (these points do not coincide each with other because the shortest distance is illustrated as extended); (2) x\u00f0w\u00de and x\u00f0p\u00de are the angular velocities of the worm and profile-crowned pinion in their rotation about crossed axes; (3) Dsw and Dwp are the components of the screw motion of the feed motion; (4) rw and rp are the radii of pitch cylinders. We have represented above the generation by the worm of a profile-crowned surface Rr of the pinion. However, our final goal is the generation by the worm of a double-crowned surface R1 of the pinion. Two approaches are proposed for this purpose. Additional pinion crowning (longitudinal crowning) is provided by plunging of the worm with respect to the pinion that is shown schematically in Fig. 24(b). Plunging of the worm in the process of pinion grinding is performed as variation of the shortest distance between the axes of the grinding worm and the pinion. The instantaneous shortest center distance Ewp\u00f0Dsw\u00de between the grinding worm and the pinion is executed as (Fig. 24(b)) Ewp\u00f0Dsw\u00de \u00bc E\u00f00\u00de wp apl\u00f0Dsw\u00de2: \u00f039\u00de Here: Dsw is measured along the pinion axis from the middle of the pinion; apl is the parabola coefficient of the function apl\u00f0Dsw\u00de2; E\u00f00\u00de wp is the nominal value of the shortest distance defined by Eq. (38). Plunging of the worm with observation of Eq. (39) enables to provide a parabolic function of transmission errors in the process of meshing of the pinion and the gear of the proposed version of modified involute helical gear drive. Conventionally, the feed motion of the worm is provided by observation of linear relation (37) between components Dsw and Dwp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000862_j.isatra.2020.12.059-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000862_j.isatra.2020.12.059-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems for an AUV.",
        "texts": [
            " \u03bbmax(\u00b7) and \u03bbmin(\u00b7) are denoted as the maximum and minimum eigenvalue of a matrix, respectively. Moreover, the operator \u2299 denotes the Hadamard product. r 2. Mathematical model and preliminaries The problem formulation is conducted in this section. Firstly, two coordinate systems are given to facilitate the mathematical modeling. Then, the nonlinear dynamics of the AUV is given on the basis of the above coordinates. Finally, some properties that will be utilized in the subsequent analysis are presented. It is convenient to use the earth-fixed frame and body-fixed frame, as shown in Fig. 1, to study the motion of an AUV in 3-D space. Particularly, there are two generalized coordinate vectors \u03b7 \u2208 R6 and \u03d1 \u2208 R6 that need to be explained. \u03b7 = [x, y, z, \u03c6, \u03b8, \u03c8]T denotes the position and attitude in terms of the NED frame, where x, y, z is the position and \u03c6, \u03b8, \u03c8 is the attitude of the AUV. \u03d1 = [u, v, w, p, q, r]T denotes the velocities of the AUV in terms of the body-fixed frame, where u, v, w are the linear velocities and p, q, r are the angular velocities. Based on the above definitions and descriptions taken from reference [26], the kinematic and kinetic equations of AUVs can be described as: \u03b7\u0307 = J (\u03b7)\u03d1 (1) (MRB + MA)   M \u03d1\u0307 + (CRB(\u03d1) + CA(\u03d1))   C (\u03d1) \u03d1 + D(\u03d1)\u03d1 + g(\u03b7) = \u03c4\u03d1 + \u03c4d (2) where J (\u03b7) is formed as: (\u03b7) = [ J1(\u03b7) 03\u00d73 03\u00d73 J2(\u03b7) ] (3) In (3), one has 1(\u03b7) = \u23a1\u23a2\u23a3c\u03c8c\u03b8 \u2212s\u03c8c\u03c6 + c\u03c8s\u03b8s\u03c6 s\u03c8s\u03c6 + c\u03c8c\u03c6s\u03b8 s\u03c8c\u03b8 c\u03c8c\u03c6 + s\u03c8s\u03b8s\u03c6 \u2212c\u03c8s\u03c6 + s\u03c8c\u03c6s\u03b8 \u2212s\u03b8 c\u03b8s\u03c6 c\u03b8c\u03c6 \u23a4\u23a5\u23a6 (4) J2(\u03b7) = \u23a1\u23a2\u23a31 s\u03c6t\u03b8 c\u03c6t\u03b8 0 c\u03c6 \u2212s\u03c6 0 s\u03c6/c\u03b8 c\u03c6/c\u03b8 \u23a4\u23a5\u23a6 (5) with s(\u00b7) = sin(\u00b7), c(\u00b7) = cos(\u00b7), t(\u00b7) = tan(\u00b7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.11-1.png",
        "caption": "Fig. 3.11: Relative Kinematics for Recursion",
        "texts": [
            " In this case we must regard the forces coming from this external tree via its last connection. If we have chains things are more simple, because there are no side-trees or chains whatsoever, and the recursions are straightforward. Therefore it is very important to choose a good division of the overall system leading to simple topological substructures. We again come back to chapter (2.2.4) and start the first forwardrecursion with the relations (2.52) and (2.49), which write in the coordinate system Bi (see also Figure 3.11) Bi r\u0307IBi =ABiBi\u22121 [(Bi\u22121 r\u0307IBi\u22121 + Bi\u22121 r\u0307Bi\u22121Bi)+ + (Bi\u22121 \u03c9\u0303IBi\u22121 + Bi\u22121 \u03c9\u0303Bi\u22121Bi) \u00b7 Bi\u22121 rBi\u22121Bi ], Bi \u03c9IBi =ABiBi\u22121 \u00b7 (Bi\u22121 \u03c9IBi\u22121) + Bi \u03c9Bi\u22121Bi . (3.108) The relative translational and rotational velocities between the bodies Bi\u22121 and Bi are Bi r\u0307Bi\u22121Bi and Bi \u03c9Bi\u22121Bi , respectively, written in the Bi-system. These two velocities depend directly on the generalized velocities q\u0307i given by the possible degrees of freedom of the connection between the two bodies Bi\u22121 and Bi. These degrees of freedom depend on the configuration of the interconnection: we may have a rotatory joint with rotational degrees of freedom, very often only with one degree of freedom, or we may have a connection with translational relative motion in the form of linear guideways or the like",
            "57)) Bi r\u0308IBi = ABiBi\u22121 \u00b7 Bi\u22121 [r\u0308IBi\u22121 + (r\u0308Bi\u22121Bi + \u02d9\u0303\u03c9IBirBi\u22121Bi+ + 2\u03c9\u0303IBi r\u0307Bi\u22121Bi + \u03c9\u0303IBi \u03c9\u0303IBirBi\u22121Bi)] Bi \u03c9\u0307IBi = ABiBi\u22121 \u00b7 (Bi\u22121 \u03c9\u0307IBi\u22121 + Bi\u22121 \u03c9Bi\u22121Bi \u00b7 Bi\u22121 \u03c9IBi\u22121)+ + Bi \u03c9\u0307Bi\u22121Bi . (3.109) The indices Bi\u22121 on the left side of the brackets indicate, that all magnitudes within the brackets are written in the body-fixed coordinate system Bi\u22121. The structures of these two equations are obvious, it composes the absolute 3.3 Multibody Systems with Bilateral Constraints 121 accelerations of the predecessor body with the relative accelerations between the two bodies. According to Figure 3.11 and to the equations (2.48) to (2.52) we can establish the following relations Bi rBi\u22121Bi =Bi [rHi\u22121 + \u2206rHi\u22121Hi + rHi ] = h0i + HTiqi, h0i =rHi\u22121 + rHi , \u2206rHi\u22121Hi = \u2206r = HTiqi Bi \u03c9\u0303IBi =ABiBi\u22121 \u00b7 (Bi\u22121 \u03c9\u0303IBi\u22121) \u00b7ABi\u22121Bi + Bi \u03c9\u0303BiBi\u22121 Bi r\u0307Bi\u22121Bi =Bi \u2206r\u0307Hi\u22121Hi = HTiq\u0307i + H\u0307Tiqi, Bi \u03c9Bi\u22121Bi =Bi \u2206\u03c9 = HRiq\u0307i, HTi \u2208 IR3,6, HRi \u2208 IR3,6 qi \u2208 IR6, (3.110) where the vector qi represents the joint degrees of freedom and contains accordingly three relative coordinates of translation, for example x,y,z in the case of a local Cartesian frame, and three relative coordinates of rotation, for example \u03b1, \u03b2, \u03b3 in the case of Cardan angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000629_j.conengprac.2021.104763-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000629_j.conengprac.2021.104763-Figure1-1.png",
        "caption": "Fig. 1. Configuration of a typical quadcopter.",
        "texts": [
            " The contribution of this paper is presenting a real-time adaptive robust framework for flight control of quadrotors based on the AFTSMC method. The flight control does not require any prior knowledge of system characteristics such as rotor parameters, mass value, the center of mass position and moment of inertia matrix. The control performance is assessed experimentally. Therefore, the control robustness is evaluated in the presence of frame vibrations, instability of blade rotation and drone mass imbalance. The configuration of a typical quadrotor and its body frame (\ud835\udc31\ud835\udc01-\ud835\udc32\ud835\udc01- \ud835\udc01) are shown in Fig. 1. The origin of the body frame is considered t the mass center of the quadrotor. It is assumed that the inertial rame (x-y-z) and the body frame are aligned at the beginning of the quadrotor flight. The given quadrotor has four rotors (\ud835\udc56 = 1 to 4). Every rotor produces a thrust vector \ud835\udc39\ud835\udc56 exerted on the body frame of the quadrotor n the direction of \ud835\udc33\ud835\udc01. Every thrust vector generates a torque vector \ud835\udc47\ud835\udc56 a a t t \ud835\udc33 \ud835\udc39 w b t r \ud835\udc65 round the mass center of the quadrotor. If the rotation of the quadrotor bout x-axis is called by the roll angle \ud835\udf19, the rotation about y-axis by he pitch angle \ud835\udf03 and the rotation about z-axis by yaw angle \ud835\udf13 , then he resultant torques generated by four motors around the \ud835\udc31\ud835\udc01, \ud835\udc32\ud835\udc01 and \ud835\udc01 can be represented by \ud835\udc47\ud835\udf19, \ud835\udc47\ud835\udf03 and \ud835\udc47\ud835\udf13 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure7-1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure7-1-1.png",
        "caption": "Figure 7-1. Motors for large-drive systems and their voltage and current characteristics.",
        "texts": [
            " The motors for large drives are three-phase AC machines with conventional design at the electrical and magnetical side: \u2022 Synchronous motors \u2022 Slip ring asynchronous motors \u2022 Induction motors In many cases, however, they have to be adapted at the mechanical side to meet the specific requirements of the load machines. DC motors are not well suited for large drives. Due to their mechanical collector, they are expensive and subject to wear, and their voltage, speed, and power ratings are too much limited. Synchronous motors and induction motors (Figure 7-1) are converter controlled via their three-phase stator windings. Synchronous motors for variable speed drives have, in most cases, solid turbo rotors, especially when used in high-speed applications. The rotor carries a DC excitation winding that has to be fed via slip rings or\u2014in high-speed applications\u2014brushless via a rotating transformer and a rotating diode rectifier. Due to the DC excitation the rotor of the synchronous motors can be built with a wider air gap. Therefore, they are mechanically robust",
            " Synchronous motors are well proven as high-power and high-speed drives. The wound rotor with its inherent dissymmetry, however, limits the maximum speed to about 7000 rpm [34]. Induction motors are cheap and robust because of their simple squirrel cage rotor. They have the potential for high-power and high-speed drives. Solid rotor bodies with buried cages and magnetic bearings are means to extend the maximum speed up to about 10,000 rpm at 6 MW and 18,000 rpm at 3 MW. 7.4. Motors for Large Drives 337 Slip ring asynchronous motors (Figure 7-1) are connected to the AC system with their three-phase stator, whereas the three-phase wound rotor is converter controlled via slip rings. They can be built for very high power ratings. The wound rotor and the slip rings, however, limit the rated speed. When designing converter controls for AC drives one has to focus on the motors: the selection of the converter circuits and the design of the control structure strongly depend on the characteristics of the motors. How three-phase motors work is not easy to understand, when looking only at the three-phase quantities of the windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000887_j.mechmachtheory.2020.104055-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000887_j.mechmachtheory.2020.104055-Figure3-1.png",
        "caption": "Fig. 3. Model of a gear tooth without TSW.",
        "texts": [
            " As shown in Fig. 2 , TSW only leads to variation of tooth profile [3] . Hence, only the energy stored in the tooth varied. TSW alters all three mesh stiffness terms. Considering TSW, the new analytical expressions for the three mesh stiffness terms are derived below. Previously, the potential energy method has been employed to derive the energy stored in a single gear tooth [2 , 14 , 27 , 46] . In these models, the ESG tooth is modeled as a cantilever beam fixed on the gear root circle (GRC), as shown in Fig. 3 . The three terms of energy stored in a perfect gear tooth with meshing force can be generally described as: U b = F 2 2 k = \u222b d [ F (d \u2212 x ) cos \u03b11 \u2212 F h sin \u03b11 ] 2 2 E I x dx (3.3) b 0 U s = F 2 2 k s = \u222b d 0 3 F 2 cos 2 \u03b11 5 G A x dx (3.4) U a = F 2 2 k a = \u222b d 0 F 2 sin 2 \u03b11 2 E A x dx (3.5) where E refers to the Young\u2019s modulus, G refers to the shear modulus, k b , k s and k a denote the bending, shear, and axial compressive mesh stiffness, respectively, h refers to the distance from the mating point on gear to the tooth central line, d indicates the distance from the contact point on gear to the gear root, A x is the area of the tooth section, I x refers to the moment of inertia of the tooth section, and x is the distance from the tooth section to the tooth root"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003544_jra.1987.1087145-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003544_jra.1987.1087145-Figure3-1.png",
        "caption": "Fig. 3. Link with more than two joints.",
        "texts": [
            " We have 0 0 0 : 1 u i = caisej cajcej -Sa j isa:ei i2i c l i I (1) jP j = [ di - risaj ricai] =. (2) The orientation of frame j with respect to frame i is defined by \u2018Aj =jA r. (3) Note that in the open-loop robots we will have only the foregoing case, and j will be equal to i - 1. 2) If joint j has more than two joints, two cases are to be considered. a) If Xj is the common perpendicular to Zj and Z j , then the matrix \u2019Ti will be defined as in case 1. b) If Xj is the common perpendicular to Zj and another joint axis as 2, (Fig. 3), an auxiliary frame j \u2019 will be defined 0882-4967/87/1200-0517$01.00 0 1987 IEEE 518 IEEE JOURNAL OF ROBOTICS AND AUTOMATION, VOL. RA-3, NO. 6, DECEMBER 1987 8 . A where ai = 0 for i rotational and ai = 1 for i translational, u i is equal (1 - ai). Let us define Qi = a;Oi + air;. Note that frame 1 can always be defined such that el = y1 = a1 = dl = q 1 = 0 by taking frame 0 in coincidence to frame 1 when q1 =- 0. The terminal frame n can always be defined such that e , = y, = q, = 0 by taking X , aligned to Xa(,) when q, = 0 (where a ( n ) represents the joint antecedent to n)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure30-1.png",
        "caption": "Fig. 30. Schematic illustration of: (a) boundary conditions for the pinion and the gear, and (b) rigid surfaces applied for boundary conditions of the pinion.",
        "texts": [
            " The designed volume of each tooth of the model is divided into six subvolumes using auxiliary intermediate surfaces 1\u20136 as shown in Fig. 29(b). Step 3. Node coordinates are determined analytically considering the number of desired elements in lon- gitudinal and profile directions (Fig. 29(c)). Step 4. Discretization of the model by finite elements (using the nodes determined in previous step) is accomplished as shown in Fig. 29(d). Step 5. Setting of boundary conditions is accomplished automatically and are shown in Fig. 30(a) and (b) for the case of a three-tooth model. The following ideas are considered: iii (i) Nodes on the two sides and bottom part of the portion of the gear rim are considered as fixed (Fig. 30(a)). i (ii) Nodes on the two sides and the bottom part of the pinion rim form a rigid surface (Fig. 30(a) and (b)). (iii) A reference nodeN (Fig. 30(b)) located on the axis of the pinion is used as the reference point of the previously defined rigid surface. Reference point N and the rigid surface constitute a rigid body. (iv) Only one degree of freedom is defined as free at the reference point N , as rotation about the pinion axis, while all other degrees of freedom are fixed. Application of a torque T in rotational motion at the reference point N allows to apply such torque to the pinion model. Step 6. The contact algorithm of the finite element analysis computer program [3] requires definition of contacting surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.39-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.39-1.png",
        "caption": "Fig. 6.39: Elastic Camshaft and Sprocket Carrier",
        "texts": [
            " We assume approximately, that the radial forces cancel out and that only a frictional torque acts in the joints. This torque MR is evaluated using a smooth and measured friction characteristic. It must also be added to the equations of motion in the form hG,i = . . . + JTRezMR hG,j = . . .\u2212 JTRezMR, (6.58) which has to be evaluated a bit further with respect to the overall structure of the equations of motion [69]. 6.4 Bush and Roller Chains 377 Elastic Camshafts One key component of timing gear systems is the elastic camshaft carrying the sprocket wheel and a couple of additional masses (Figure 6.39). We get correspondingly a number of additive terms in the equations of motion. The elastic displacements are always very small, so that we can linearize with respect to elastic motion. This linearized form writes in principle [69] Mq\u0308R+ ( Del +DLag + 2\u2126G ) q\u0307R + ( Kel +KLag + \u2126NLag + \u2126\u0307K\u2126\u0307 + \u21262K\u21262 ) qR + g = h, (6.59) with the vector and matrix elements to be evaluted in the following: M : mass matrix, G : gyroscopic matrix from rotational excitation, Kel : stiffness matrix of elastic deformation, Del : damping matrix of elastic deformation, KLag : stiffness matrix of the bearings, NLag : matrix of the non-conservative bearing forces DLag : damping matrix of the bearings, K\u2126\u0307 : matrix due to rotational acceleration, K\u21262 : matrix of centrifugal forces (rot. excitation), F : force vector from rotational excitation, h : force vector of excitations and external forces. Elastic Camshafts - Shaft Element As a first component of the camshaft we consider the elastic shaft itself characterized by its kinematics and dynamics. In all cases we refer to the theory presented in the chapters 3.3 on the pages 113 ff. and 3.4 on the pages 131 ff. An elastic shaft can be cut into small discs as indicated in Figure 6.39. The motion of such a disc element includes the reference rotation as given by the engine, the rigid body motion and the elastic deformations, assumed to be small in our case. The kinematics of the reference system is given by the transformation matrix ARI from the inertial to the reference system and by the rotational velocity and acceleration, which yields ARI =  cos\u03a6 sin\u03a6 0 \u2212 sin\u03a6 cos\u03a6 0 0 0 1  , R\u03c9R =I\u03c9R =  0 0 \u2126  , R\u03c9\u0307R = I \u03c9\u0307R =  0 0 \u2126\u0307  . (6.60) We choose the following sequence of rotations for the disc element (see chapter 3",
            " Therefore the transformation from the reference system R to the body system K comes out with AKR = E \u2212 \u03d5\u0303R = E \u2212 \u0303\u2212v\u2032u\u2032 \u03d5  =  1 \u03d5 \u2212u\u2032 \u2212\u03d5 1 \u2212v\u2032 u\u2032 v\u2032 1  (6.61) From these preliminaries we can evaluate the absolute angular velocity and acceleration formulated in the body-fixed frame by K\u03c9K = \u2212v\u0307\u2032 \u2212\u2126u\u2032 +u\u0307\u2032 \u2212\u2126v\u2032 \u03d5\u0307 + \u2126  K \u03c9\u0307K = \u2212v\u0308\u2032u\u0308\u2032 \u03d5\u0308 + \u2126 \u2212u\u0307\u2032 \u2212v\u0307\u2032 0 + \u2126\u0307 \u2212u\u2032 \u2212v\u2032 1  (6.62) The equations of momentum will be evaluated in the reference system R and therefore we need the position of the center of mass in that coordinates. The radius vector from O to H follows from the vector chain (Figure 6.39) RrOH = ARI uR0 vR0 0 + 0 0 z + uv 0  , (6.63) from which we get the absolute velocity and acceleration by the expression 6.4 Bush and Roller Chains 379 RvH = u\u0307v\u0307 0 + \u2126 \u2212vu 0  , Rv\u0307H = u\u0308v\u0308 0 + 2\u2126 \u2212v\u0307u\u0307 0 + \u21262 \u2212u\u2212v 0 + \u2126\u0307 \u2212v\u2212u 0  . (6.64) The elastic deformations are approximated by a RITZ approach, which writes uel(z, t) = uT (z) qu(t) = uT qu : bending in u-direction vel(z, t) = vT (z) qv(t) = vT qv : bending in v-direction \u03d5el(z, t) = \u03d5T (z) q\u03d5(t) = \u03d5T q\u03d5 : torsion (6.65) This ansatz makes a separation of position- and time dependent magnitudes possible",
            "77) For an additional rigid mass we have to add similar terms including the inertia tensor I = diag(A,B,C) and the following simple integrals\u222b \u03c1Adz \u2192 m, \u222b \u03c1Ixdz \u2192 A, \u222b \u03c1Iydz \u2192 B, \u222b \u03c1Ipdz \u2192 C. (6.78) External Forces External forces acting on the sprocket shaft are gravitational forces, forces entering from the cams and the valve mechanism and finally forces generated by the tensioners for the guides. In some cases gravitational forces might be neglected. Otherwise it is If = \u03c1Agdz (6.79) with the gravitational vector g being inertially fixed (see Figure 6.39). The additional force contribution to the equations of motion results from a transformation into the reference system, from there into the configuration space and finally from an integration along the shaft. If we have in addition a rigid mass, we get a second term representing the gravitational effect of this rigid mass. Altogether this yields hR = . . . + \u03c1 l\u222b 0 AJTTdzARIg + . . . + mJTT0ARIg (6.80) At the sprocket shaft boundary we have the forces and torques coming from the individual valve trains; they depend for stationary operation on the cam position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000017_s11071-019-05348-0-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000017_s11071-019-05348-0-Figure2-1.png",
        "caption": "Fig. 2 Geometrical parameters for gear body deformation",
        "texts": [
            " 1 h Distance from the point of contact to the center line of the tooth E Young\u2019s modulus v Poisson\u2019s ratio W Tooth width Ix , Ax Moment of inertia and the area of section at the distance x from the base along the tooth center line kb, ks, ka Bending stiffness, shearing stiffness, axial stiffness \u03b4f Additional deformationof the tooth caused gear body kf The stiffness related to the additional deformation of gear body L*,M*,P*,Q* Coefficients expressing the additional deformation of the tooth Sf Defined in Fig. 2 \u03b4h Local contact compliance b Half width of the contact region on the tooth rp, rg Radius of curvature at the point of contact of gear and pinion vp, vg Poisson\u2019s ratio of pinion and gear Ep, Eg Young\u2019s modulus of pinion and gear hxp, hxg Distance from the point of contact to the center line of the tooth of the gear and pinion along the line of action direction kh[F] Local contact stiffness of tooth pair under load F Jp, Jg Mass moments of inertia of pinion and gear Ks[F] Mesh stiffness of single tooth pair under the load F K [F] The overall mesh stiffness of mesh gears under the load F kl Load-independent stiffness including bending, shear, axial stiffness and additional stiffness caused by gear body kli Load-independent stiffness of tooth pair i khi [F] The local contact stiffness of tooth pair i \u03b4 Total deformation of the tooth at the contact point ei Initial separation of the potential contact tooth pair i Eip, Eip Profile error of tooth pair i of pinion and gear \u03b7ip, \u03b7ig Profile modification of tooth pair i_ of pinion and gear \u03bbp, \u03bbg Eccentricity error of pinion and gear \u03b4i Deformation of the tooth pair i Fi Load on the tooth pair i Lsfi Load sharing of tooth pair i Tp Input torque on the pinion Tg Output torque on the gear cm Linear damping element e No-load transmission error hm, hi Contact coefficient rbp, rbg Radius of the base circle of the pin- ion and the gear fs Rotational frequency of pinion fm Mesh frequency With the rapid increase in the wide application of the gear transmission system in different areas [1\u20133], such as automotive, wind turbine and rail traffic, the research on dynamic characteristics of the gear transmission system has become more and more significant for improving the gear transmission stability and controlling the vibration and noise",
            "Theyused theFourier series to represent the displacement, stress and external load and assumed that the inner circle displacement of the ring is constrained, while the outer circle is subject to normal and shear stress. Finally, the additional deformation caused gear body can be expressed as \u03b4f = F cos2 \u03b11 EW { L\u2217 ( d Sf )2 + M\u2217 ( d Sf ) +P\u2217 ( 1 + Q\u2217 tan2 \u03b11 )} (3) The coefficients L*, M*, P* and Q* are fitted by polynomial functions, and they can be found in Ref. [32]. W is the tooth width. Sf is defined as shown in Fig. 2. This method was further extended by Chen et al. [33] to amore general case in the presence of gear tooth root crack fault. The stiffness related to the additional deformation of gear body is kf = F \u03b4f (4) The local contact compliance is composed of line contact deflection and the compression of each tooth from the contact point to the tooth center line in LOA direction. Based on the different simplifications, there are several forms of local contact compliance equation, where the detailed formulas on the local contact deformation can be found in the Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003669_j.automatica.2004.05.017-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003669_j.automatica.2004.05.017-Figure8-1.png",
        "caption": "Fig. 8. The functions (x) and (x) for the case where they are functions of a single variable, x.",
        "texts": [
            " (77). Since these are undesirable effects, we impose additional restrictions on p by demanding that \u2212P p P, (93) where P is a large positive number. Combining Inequalities (91)\u2013(93), we obtain (x) p (x), (94) where the bounds involved depend upon the state vector, x, as follows: (x) =   u0 \u2212 kTx lTx , lTx \u2212u0 + kTx P \u2212P, \u2212u0 + kTx P < lTx< u0 + kTx P , \u2212u0 \u2212 kTx lTx , lTx u0 + kTx P (95) (x) =   \u2212u0 \u2212 kTx lTx , lTx \u2212u0 \u2212 kTx P P, \u2212u0 \u2212 kTx P < lTx< u0 \u2212 kTx P , u0 \u2212 kTx lTx , lTx u0 \u2212 kTx P (96) Fig. 8 presents plots of the functions (x) and (x) for the case where they are functions of a single variable, x. We next choose the function, r(p, x)> 0, used in the selection strategy (89) such that inequality (94) will be satisfied. Recall that compliance with the control constraints (76) will also be maintained in this case. A suitable choice for r is the function r(p, x) =   ( 1 \u2212 (x) p ) + 0 (x) p , p (x) 0, (x)<p< (x) ( 1 \u2212 (x) p ) + 0 (x) p , p (x) (97) such that Eq. (89) represents an anti-windup system, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000486_j.ymssp.2019.04.056-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000486_j.ymssp.2019.04.056-Figure5-1.png",
        "caption": "Fig. 5. (a) ente",
        "texts": [
            " For type 2, lrs_max = min (lze_max, lrs_max, hmin), the rolling element has contact with the top edges of defect area (green radial arcs in Fig. 3), and has no contact with the bottom surface of defect area. For type 3, hmin = min (lze_max, lrs_max, hmin), the rolling element has no contact with the top edges of the defect area (green radial arcs in Fig. 3), and has contact with the bottom surface of defect area. The contact form between the rolling element and the defect area depends on the minimum value of lze_max, lrs_max and hmin. Fig. 5(a) and (b) shows the relative displacement of the rolling element moving towards the bottom of defect area in normal direction under the condition of type 1. This relative displacement is the normal distance between the blue solid line and the red dotted line, which can be described by lze1\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bduj\u00f0t\u00de ud1 q ro \u00fe rocos\u00bduj\u00f0t\u00de ud1 \u00f0ud1 6 uj\u00f0t\u00de < uc\u00de lze1\u00f0t\u00de \u00bc lze max \u00f0uj\u00f0t\u00de \u00bc uc\u00de lze1\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bdud2 uj\u00f0t\u00de q ro \u00fe rocos\u00bdud2 uj\u00f0t\u00de \u00f0uc < uj\u00f0t\u00de 6 ud2\u00de 8>>< >>: \u00f015\u00de where ud1 and ud2 are the angular positions of the highest point (point a and point a00) of the edge of defect area on the radial cross-section, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003239_s0032-5910(01)00283-2-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003239_s0032-5910(01)00283-2-Figure1-1.png",
        "caption": "Fig. 1. A schematic of the impact apparatus.",
        "texts": [
            " In these experiments, spherical particles of aluminium oxide, 5 mm in diameter, fell under gravity onto an inclined, thick glass anvil. A sequence of images was formed on a single frame using a digital camera with strobe illumination, and measurements obtained using commercial image processing software. These direct measurements of particle position yield the speeds, angles and rotation before and after impact, and hence other useful quantities, such as normal and tangential coefficients of restitution, e and e , and the trajectory of the contactn t patch. The experimental system is shown schematically in Fig. 1. Before impact, the particle is held at the appropriate height above the anvil by a small-diameter vacuum nozzle. \u017d .When the particle is released without spin it falls through an optical-fibre triggering device, and an electronic system generates a sequence of pulses to control the camera and the strobe light to produce a single frame of images in a predetermined manner. The digital image is transferred to a PC for measurement using a commercial image processing package. To obtain reliable results it is necessary to ensure that impacts under any set of conditions are highly reproducible, and also that measurements of these events are accurate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.5-1.png",
        "caption": "Fig. 8.5",
        "texts": [
            " Its singular point 0(0,0) corresponds to having no convection; other singular points correspond to simple convection. Singular point 0(0,0) is a fixed point. When p = 0, this fixed point is not hyperbolic, but it is stable (a vague attractor); when 0 < p < 1, it is a stable hyperbolic sink; when p> 0, it is an unstable saddle. It has a Hopfbifurcation when p=24.74. The integral curve passing through every point (non-singular) is unique in three-dimensional space xyz, but its projection can be self-transversal on a certain coordinate plane, so chaos may exist. Figure 8.5 shows the space figure of the Lorenz attractor. This figure gives a typical phase portrait calculated by numerical integral. It starts from the initial point in the neighbourhood of 0(0,0,0). The parameters are cr = 10.p = 8/ 3.p = 28 . It can be seen from Fig. 8.5 that the phase portrait circles between two discs, and will never repeat, but also will never go far away. Figure 8.6 is the projection of the phase portrait onto the xy plane. This phase portrait is self-transversal. Brief Introduction to Chaos With the development of the study on chaos and strange attractors, much work has been done on the properties 40 of the Lorenz equation at different parameter values. t 30 Most work is based on the z assumption that (J = 10 and p = 8/3 , with P as an adjustable parameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003467_tvcg.2005.13-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003467_tvcg.2005.13-Figure7-1.png",
        "caption": "Fig. 7. A bar manipulated with a position constraint (left), an orientation constraint (middle), and a position/orientation constraint (right). The position constraints are represented by yellow spheres and the orientation constraints are represented by RGB axes.",
        "texts": [
            " We employed semi-implicit integration for m decoupled equations because it was easy to implement and the derivation for manipulation constraints became simple. We have not encountered numerical instabilities with a time step size of h = 1/30 second in all our experiments. The possible overdamping effects can be attenuated using theta-integration or Newmark integration. Alternatively, one can use either IIR digital filters suggested in [10] or the closed form solution given in [8]. Finally, we note that all these approaches have the same time complexity becausem equations are already decoupled. orientations (see Fig. 7). We formulate these manipulation constraints as hard constraints. Constraints for velocity and acceleration can be developed in a similar way. Note that orientation constraints for a deformable body have not been addressed in previous studies. Such constraints are possible in our formulation because it explicitly takes into account the mean orientation of each node, based on the infinitesimal strain tensor analysis. Let be the number of constrained points and let uk c be the 3 -dimensional vector consisting of the desired displacements of the constrained nodes at a time step k",
            " 6b is the time-series plot of the average magnitude of nodal displacements in the case of gravitational magnitude 9:8m=s2, in which we can observe a subtle difference in the frequency of oscillation. It is interesting to note that, if measured relative to the error of linear modal analysis, the error of modal warping in the dynamic analysis (Fig. 6a) is larger than that in the static analysis (Fig. 5a). It results from the aforementioned difference in the frequency of oscillation. This experiment demonstrates the manipulation capability of our technique. Fig. 7 shows, from left to right, the resultant deformations in the cases of only position constraints, only orientation constraints, and both position and orientation constraints. For the case of position constraints, the constrained node was identical to the exercised node. For the case of orientation constraints, however, the set of exercised nodes had to be extended to include nodes neighboring the constrained node. To demonstrate how the manipulation constraints can be used to animate deformable parts of a character, we simulated a character whose only deformable part was its potbellied torso (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003302_s0967-0661(01)00105-8-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003302_s0967-0661(01)00105-8-Figure1-1.png",
        "caption": "Fig. 1. SCARA robot.",
        "texts": [],
        "surrounding_texts": [
            "The experimental comparison is carried out on a twojoints planar direct drive prototype robot manufactured in the laboratory (IRCCyN) (Figs. 1\u20133), without gravity effect. The description of the geometry of the robot uses the modified Denavit and Hartenberg notation (Khalil & Dombre, 1999). The robot is directly driven by two DC permanent magnet motors supplied by PWM choppers. The dynamic model depends on eight minimal dynamic parameters, including four friction parameters: v \u00bc ZZR1 Fv1 Fs1 ZZ2 LMX2 LMY2 Fv2 Fs2 T ; ZZR1 \u00bc ZZ1 \u00feM2L 2; where L is the length of the first link, M2 the mass of link 2, ZZ1 and ZZ2 the drive side moment of inertia of links 1 and 2, respectively, LMX2 and LMY2 the first moments of link 2 multiplied by the length L of link 1, Fv1;Fs1;Fv2;Fs2 are the viscous and coulomb friction parameters of links 1 and 2, respectively. The inverse dynamic model used to compute WLS is written as Eq. (3): where C2 \u00bc cos\u00f0q2\u00de and S2 \u00bc sin\u00f0q2\u00de: The direct dynamic model necessary to compute the extended Kalman filtering algorithm is written as Eq. (11) with q \u00bc q1 q2 T and s \u00bc t1 t2 T : M \u00bc M11 M12 M12 ZZ2 \" # ; M11 \u00bcZZR1 \u00fe ZZ2 \u00fe 2LMX2C2 2LMY2S2; M12 \u00bcZZ2 \u00fe LMX2C2 LMY2S2: The joint position q and the current reference VT (the control input) are collected at a 100Hz sample rate while the robot is tracking a fifth order polynomial trajectory. This trajectory has been calculated in order to obtain a good condition number Cond\u00f0Ww\u00de \u00bc 290 and Cond\u00f0U\u00de \u00bc 100: This means that it is an exciting trajectory taking the whole trajectory all over at the time of the test. Both methods are performed in a closed loop identification scheme (simply joint PD control), using the same data q and s; where each torque sj is calculated as sj \u00bc GTjVTj ; where GTj is the drive chain gain which is considered as a constant in the frequency range of the robot dynamics. Fig. 4 presents the torque of motors 1 and 2."
        ]
    },
    {
        "image_filename": "designv10_2_0000486_j.ymssp.2019.04.056-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000486_j.ymssp.2019.04.056-Figure3-1.png",
        "caption": "Fig. 3. Diagram of the simplified three-dimensional geometry of the localized defect on the outer raceway, with outer raceway radius ro1, outer raceway groove radius ro2, radial cross-section of the defect area aa00b00b, axial cross-section of the defect area cc00d00d, top edges of defect area (green and blue arcs), and minimum depth of the defect area hmin.",
        "texts": [
            " Second, the rolling element reaches the center of defect area, and the displacement that moving towards the bottom of defect area reaches a maximum value. Third, the rolling element leaves the center of defect area and moves towards the top of defect area. Finally, the rolling element exits the defect area. Diagram of the motion path of the rolling element passing through the defect area: (a) reach the edge of defect area; (b) enter defect area; (c) reach ter of defect area; (d) move towards the top of defect area; (e) exit defect area. Fig. 3 shows the simplified three-dimensional geometry of the localized defect on the outer raceway, where ro1 and ro2 are the outer raceway radius and outer raceway groove radius; aa00b00b and cc00d00d are the cross-sections of the defect area on the radial center plane (xooyo plane) and the axial center plane (zooyo plane) of the bearing, respectively. Since the surface of the raceway is a curved surface, the top edges of defect area are composed of two radial arcs with radius of curvature ro1 (green arcs) and two axial arcs with radius of curvature ro2 (blue arcs)",
            " The geometric relationship between the defect area and the rolling element is defined as lo0a \u00bc lo0e \u00bc rb; loa \u00bc loc \u00bc ro1; lab \u00bc la00b00 \u00bc lmn \u00bc hmax1; lzn \u00bc hmin1 lo0c \u00bc lo0s \u00bc rb; lo00c \u00bc lo00s \u00bc ro2; lcd \u00bc lc00d00 \u00bc luv \u00bc hmax2; lrv \u00bc hmin2 hmin1 \u00bc hmin2 \u00bc hmin 8>< >: \u00f012\u00de where rb is the radius of the rolling element; hmax1 and hmin1 are the maximum and minimum depth of the defect area on the radial cross-section, respectively; hmax2 and hmin2 are the maximum and minimum depth of the defect area on the axial cross-section, respectively; hmin1 is equal to hmin2, making them equal to hmin in Fig. 3, and is given by In the radial and axial cross-sections, the maximum displacements of the rolling element moving towards the bottom of defect area in normal direction are lze and lrs in Fig. 4(a) and (b), respectively, which can be described by lze max \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro12sin 2\u00f0uc ud1\u00de q ro1 \u00fe ro1cos\u00f0uc ud1\u00de lrs max \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro22sin 2\u00f0u0 c u0 d1\u00de q ro2 \u00fe ro2cos\u00f0u0 c u0 d1\u00de 8>< >: \u00f014\u00de where uc and u0 c are the center angular positions of the defect area on the radial and axial cross-sections, respectively; ud1 and u0 d1 are the angular positions of the highest points (point a and point c) of the edge of defect area on the radial and axial cross-sections, respectively; ud and u0 d are the circumferential angular extents of defect area on the radial and axial crosssections, respectively. The contact form between the rolling element and the defect area can be classified into three types according to the values of lze_max, lrs_max and hmin, and the motion path of the rolling element passing through the defect area will be significantly different under these three types. For type 1, lze_max = min (lze_max, lrs_max, hmin), there are no contact between the rolling element and the top edges of defect area (green radial arcs in Fig. 3) as well as the bottom surface of defect area. For type 2, lrs_max = min (lze_max, lrs_max, hmin), the rolling element has contact with the top edges of defect area (green radial arcs in Fig. 3), and has no contact with the bottom surface of defect area. For type 3, hmin = min (lze_max, lrs_max, hmin), the rolling element has no contact with the top edges of the defect area (green radial arcs in Fig. 3), and has contact with the bottom surface of defect area. The contact form between the rolling element and the defect area depends on the minimum value of lze_max, lrs_max and hmin. Fig. 5(a) and (b) shows the relative displacement of the rolling element moving towards the bottom of defect area in normal direction under the condition of type 1. This relative displacement is the normal distance between the blue solid line and the red dotted line, which can be described by lze1\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bduj\u00f0t\u00de ud1 q ro \u00fe rocos\u00bduj\u00f0t\u00de ud1 \u00f0ud1 6 uj\u00f0t\u00de < uc\u00de lze1\u00f0t\u00de \u00bc lze max \u00f0uj\u00f0t\u00de \u00bc uc\u00de lze1\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bdud2 uj\u00f0t\u00de q ro \u00fe rocos\u00bdud2 uj\u00f0t\u00de \u00f0uc < uj\u00f0t\u00de 6 ud2\u00de 8>>< >>: \u00f015\u00de where ud1 and ud2 are the angular positions of the highest point (point a and point a00) of the edge of defect area on the radial cross-section, respectively. Fig. 6(a) and (b) shows the relative displacement of the rolling element moving towards the bottom of defect area in normal direction under the condition of type 2. The rolling element and the top edges (green radial arcs in Fig. 3) of defect area are in contact at position j1 and separated at position j2. Before the rolling element contacts with the top edges as well as after it separates from the top edges, the relative displacement is equal to lze(t) in type 1. The motion path of the rolling element during contact with the top edges is equivalent to moving along the arc line (xx00 in Fig. 6) between the contact position j1 and the separate position j2, and the relative displacement is equal to lsr_max in Eq. (14) constantly",
            " When the rolling element passes through the defect area, the value of the parameter associated with the defect area (dd(t) in Eq. (5)) is abruptly changed, which causes a drastic change in dbj(t), and finally excites the impulse response of the bearing system. In this paper, the contact form is divided into three types according to the three-dimensional geometric relationship between the rolling element and the defect area. Since the influence of the radial top edges of defect area (green arcs in Fig. 3) on the motion path of rolling element has not been fully considered in previous research, the contact form that this research focuses on is type 2. However, the correlation calculations for type 1 and 3 are still necessary, because the geometrical dimensions of the defect areas corresponding to different contact forms can be quantified by calculation, and the key influencing factors of the motion path of rolling element are further revealed. The actual geometrical dimensions of the defect areas satisfying the above three types are shown in Fig",
            "\u2019s model [17]), the contact model proposed in this paper considers the interaction of the rolling element and the defect area in three-dimensional space. The contact of the rolling element with the radial top edges of the defect area has a great influence on the motion path of the rolling elements, which has not been fully considered in previous research. Fig. 12(a)\u2013(d) shows the relative displacements of the rolling elements calculated by the two-dimensional contact model, since the contact between the rolling element and the radial top edges (green arcs in Fig. 3) of defect area was not considered in the calculation, the motion path of rolling element can be calculated by using type 1 (Fig. 12(a), (b)) and type 3 (Fig. 12(c), (d)) that proposed in Section 3.4, respectively. Fig. 12(e)\u2013(h) show the relative displacements of the rolling elements calculated by the three-dimensional contact model, the contact of the rolling element with the radial top edges of the defect area was taken into account in the calculation. By comparing the motion path of rolling element in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000588_j.jmapro.2021.02.021-Figure28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000588_j.jmapro.2021.02.021-Figure28-1.png",
        "caption": "Fig. 28. Contours of transverse shrinkage in Case 5 and Case 7 (under clamping) (enlarged 10 times).",
        "texts": [
            " 27(b), it can be found that the variation in the restraint condition of the substrate has an obvious effect on the magnitude of transverse RS in the substrate but almost has no influence on that in the beam overall except the first very few layers. J. Sun et al. Journal of Manufacturing Processes 65 (2021) 97\u2013111 This is because only the first few layers connected or very close to the substrate can be strongly restrained by the substrate, while the latter layers can still relatively freely deform learned from Fig. 28. Although the WAAM process is quite similar to the multi-pass welding and SLM process from the perspective of the simulation and manufacturing process, RS distribution in the WAAM components shows obvious differences compared to that in the multi-pass welds and SLM parts. From this work, one can see that the longitudinal RS on the last layer in the WAAM aluminum components becomes compression if the height of beam is larger than a certain value, which is about 20 mm in the current work. This has been proved by the measurements in the paper [33]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001036_jsen.2021.3066424-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001036_jsen.2021.3066424-Figure6-1.png",
        "caption": "Fig. 6. The principle of force detection mechanism for the catheter or guidewire. (a) The axial force detection. (b) The torque detection.",
        "texts": [
            " The release of the guidewire and catheter is achieved by two stepping motors (LIKO MOTOR, 20BYGH 30-0604A-ZK3M5). The stepping motor provides the thrust of the sliding block, when the thrust is greater than the elastic force of springs, the guidewire and the catheter can be released by the grasper device. We have completed the simulation experiment of the grasper device in Ref. [26]. Compared with the previous design [27], the clamping effect is better. B. Force Detection Mechanism The principle of force detection mechanism for the guidewire or catheter is show in Fig.6. Fig.6 (a) is the principle of the axial force detection mechanism for the catheter or guidewire, Fig.6 (b) is the principle of torque detection mechanism for the guide wire or catheter. As shown in Fig.6 (a), a load cell is adopted to detect the axial force between the guidewire or catheter and the vascular environment in real time. The output shaft of the load cell is connected to the grasper device, and the linear sliding rail is installed on the bottom of the grasper device. This design can transmit the axial force of the guidewire or catheter to the load cell, when the slave manipulator moves in linear direction, once the guidewire or catheter is subjected a force, the grasper device will collide with the output shaft of load cell, the load cell will output axial force information. The load cell used in this paper can detect forces in the range of -5N to 5N. Fig.6 (b) is the principle of torque detection for the guidewire or catheter. A dynamic torque sensor is used to detect the force of the guidewire or catheter in real time when the guidewire or catheter rotates. Due to the influence of the blood flow rate and viscosity, a force will be generated when the slave manipulator rotates in the radial direction. The force will be collected by the dynamic torque sensor through the synchronous belt. Then, the dynamic torque sensor will output radial force information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-2-1.png",
        "caption": "Figure 2-2. Cross section of a commutator motor.",
        "texts": [
            ", for position control systems), acoustic noise, shape, volume, acceptability in hazardous environments, reliability, manufacturability, fail-safe features, initial cost, and present value of total lifetime cost, including the cost of energy. 2.3. COMMUTATOR MOTORS Commutator motors, also known as direct current (DC) motors, have been widely used for variable speed drives for many years. Because of their long history and wide acceptability, it is convenient to begin with an examination of some key properties of these motors to establish a basis of comparison for the other variable frequency machine types to be discussed later. Figure 2-2 shows a cross section of a commutator machine. A number of iron poles, typically four or six, project inward from a cylindrical iron yoke. A field coil encircles each pole, and these coils are normally connected in series with sequentially opposite polarity. Current in a field coil produces a magnetic flux in the air gap between the pole and the central rotating armature, the flux returning through adjacent oppositely directed poles. The armature is made of iron laminations and has axially directed slots in its outer surface to accommodate current carrying conductors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.12-1.png",
        "caption": "Fig. 6.12: Angle-measuring microsensor. According to [Ueno91]",
        "texts": [
            " At the moment, there are various principles being used for these measurements; the contact free optical and magnetic methods are the most significant ones for MST. Magnetic sensor to measure angular displacement In robotics it is necessary to exactly control the movements of robot arms and legs or other components having rotating joints. Source [Ueno91] des cribes a microsensor which can measure very exactly an angular displace ment by using the Hall effect. The concept of the entire system is shown in Figure 6.12. The sensor consists of a rotor which has a row of teeth on its bottom. The rotor faces a stator which contains several Hall sensors and electronic circuits. A permanent magnet is located under the Hall sensors, producing a magnetic field. When the rotor moves, the teeth passing by the Hall sensor change the magnetic field. This change is picked up by the Hall sensors and they produce voltage signals. The measuring process is shown in the form of a block diagram in Figu re 6.13. The sensor field covers exactly one notch and one tooth of the rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure1.15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure1.15-1.png",
        "caption": "Fig. 1.15 Force equilibrium of shear in subregion B",
        "texts": [
            "79) yields 1 ETB \u00bc ffiffiffiffiffi Vf p EfT \u00fe 1 ffiffiffiffiffi Vf p Em : \u00f01:81\u00de Hence, ETB in subregion B is expressed by ETB \u00bc Em 1 ffiffiffiffiffi Vf p 1 Em EfT : \u00f01:82\u00de 24 1 Unidirectional Fiber-Reinforced Rubber The transverse Young\u2019s modulus of RVE, ET, is derived using the parallel model and expressed by ET \u00bc sf s ETB \u00fe s sf s Em: \u00f01:83\u00de The substitution of Eqs. (1.80) and (1.82) into Eq. (1.83) yields ET \u00bc 1 ffiffiffiffiffi Vf p Em \u00fe ffiffiffiffiffi Vf p Em 1 ffiffiffiffiffi Vf p 1 Em EfT : \u00f01:84\u00de (2) Shear modulus of a composite Referring to Fig. 1.15, the equations of the shear force equilibrium and the compatibility relation are similarly derived for subregion B: sf \u00bc sm \u00bc sLT ; \u00f01:85\u00de cm\u00f0s sf\u00de\u00fe cfsf \u00bc cLTs: \u00f01:86\u00de The stress/strain relationships are cf \u00bc sf=GfLT cm \u00bc sm=Gm cT \u00bc sT=GLTB; \u00f01:87\u00de where GfLT, Gm and GLTB are, respectively, the shear modulus of the fiber on the L\u2013 T plane and the shear moduli of the matrix and subregion B. Using Eqs. (1.80) and (1.87), Eq. (1.86) is rewritten as GLTB \u00bc Gm 1 ffiffiffiffiffi Vf p 1 Gm GfLT : \u00f01:88\u00de 1",
            " Applying a similar derivation as used for Eq. (1.81), the transverse loss factor of composite \u03b7T is expressed as11 gT \u00bc gfT ffiffiffiffiffi Vf p ET EfT \u00fe gm 1 ffiffiffiffiffi Vf p ET Em ; \u00f01:130\u00de where \u03b7fT and EfT are the transverse loss factor of the fiber and transverse Young\u2019s modulus of the fiber. ET is the transverse Young\u2019s modulus of a composite defined by Eq. (1.84). The assumption of transverse isotropy gives gT \u00bc gZ ; \u00f01:131\u00de where characteristics are the same for the T-direction and Z-direction in Fig. 1.15. Furthermore, the shear loss factor for the in-plane shear damping of a composite, \u03b7LT, is given by gLT \u00bc gfLT ffiffiffiffiffi Vf p GLT GfLT \u00fe gm 1 ffiffiffiffiffi Vf p GLT Gm ; \u00f01:132\u00de where \u03b7fLT and GfLT are the shear loss factor of the fiber and the shear modulus of the fiber. GLT is the in-plane shear modulus of a composite defined using Eq. (1.89). The out-of-plane shear loss factor of a composite, \u03b7TZ, is given by gTZ \u00bc gfTZ ffiffiffiffiffi Vf p GTZ GfTZ \u00fe gm 1 ffiffiffiffiffi Vf p GTZ Gm ; \u00f01:133\u00de where \u03b7fTZ and GfTZ are the out-of-plane shear loss factor of the fiber and the out-of-plane shear modulus of the fiber"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.32-1.png",
        "caption": "Fig. 6.32: Kinematics of a Link",
        "texts": [
            " The dynamics of a chain roller does not influence the vibration of the chain drive in any substantial manner. Hence the roller is not considered as a separate body. The motion of a chain link is given by the translational vector rL and the rotational vector \u03d5L. For the planar motion it is sufficient to consider the displacements in x- and y-direction and the rotation about the zaxis. The following transformation gives a relation between these configuration coordinates qL and the system coordinates zL (Figure 6.32): rL = xLyL 0  , \u03d5L =  0 0 \u03d5L  , zL = ( rL \u03d5L ) , qL = xL yL \u03d5L  , zL = QL qL =  1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 qL . (6.40) The coordinate system of a link is fixed in the reference point HL. A second reference point NL of a link is displaced by the pitch vector a. Chain Joints Due to the low chain tension and the time varying excitations of the camshafts, we regard both the backlash and the oilwhip in a chain joint. Using the theory for journal bearings, the forces acting on the pin and bushing consist of two parts",
            " Mq\u0308 = h+ \u2211 JT F + W\u03bb \u2208 IRf (6.44) The matrix M is the symmetric and positive definite mass matrix, the vector h includes all forces formulated already and directly in the q-space, the sum includes all forces and torques given in the six-dimensional Euclidean space making a transformation with JT necessary, and the last term indicates contact forces. Chain Elements of the Free Strands We start with the chain elements of the free strands, that means with elements without contacts to the sprocket toothing. Figure 6.32 and the equations (6.40) give a first description. From these equations we immediately derive the velocities related to the reference point H of the link: vG = x\u0307Gy\u0307G 0  , \u03c9G =  0 0 \u03d5\u0307G  , (6.45) with the accompanying Jacobians (see eq.(6.40)) JT = \u2202vG \u2202q\u0307G = 1 0 0 0 1 0 0 0 0  , JR = \u2202\u03c9G \u2202q\u0307G = 0 0 0 0 0 0 0 0 1  . (6.46) As we need the pitch vector a in inertial coordinates we have to evaluate the transformation from the link G to an inertial frame I by AIG = cos\u03d5G \u2212 sin\u03d5G 0 sin\u03d5G cos\u03d5G 0 0 0 1  . (6.47) 6.4 Bush and Roller Chains 375 The momentum of a link and its time derivative can easily be determined using the center of mass velocity p =m(vG + 1 2 aIG\u03c9\u0303Ga) = m(JT \u2212 1 2 aIGa\u0303JR)q\u0307G p\u0307 =m(JT \u2212 1 2 aIGa\u0303JR)q\u0308G + 1 2 aIG\u03c9\u0303G\u03c9\u0303Ga (6.48) Due to the symmetry of the link the inertia tensor of the link is diagonal. For a change of the reference point we have (Figure 6.32) IH = IS \u2212 1 4 ma\u0303a\u0303 (6.49) Analogously to the momentum we get for the moment of momentum and its time derivative L =LS + 1 2 a\u0303p = IS\u03c9G + 1 2 ma\u0303vG \u2212 1 4 ma\u0303a\u0303\u03c9G L =IH\u03c9G + 1 2 ma\u0303vG = ( IHJR + 1 2 ma\u0303JT ) q\u0307G, L\u0307 = ( IHJR + 1 2 ma\u0303JT ) q\u0308G + 1 2 m\u03c9\u0303Ga\u0303 vG\ufe38 \ufe37\ufe37 \ufe38 =0 (6.50) Due to the plane model the representations of the moment of momentum are the same for link and inertial coordinates. The share of the link dynamics with respect to the overall dynamics can now already be summarized. We get for the mass matrix MG = m ( JTTJT \u2212 1 2 JTT a\u0303JR + 1 2 JTRa\u0303JT ) + JTRIHJR, (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure5-1.png",
        "caption": "Fig. 5 Kinematical model of hypoid generators",
        "texts": [
            " However, the machine tool settings and the tooth surface generation model might be derived from the traditional cradle-style mechanical machines because computer codes have been developed to \u201ctranslate\u201d the machine settings and motions defined with the mechanical machines into the motions of the six axes of CNC hypoid gear generators, which move together in a numerically controlled relationship with changes in displacements, velocities, and accelerations to implement the prescribed motions and produce the target tooth surface geometry. In this paper, a new generalized kinematical model of the face hobbing process is developed, which is based on the modeling of physical mechanical spiral bevel and hypoid gear generators. Figure 5 shows the kinematical model of a mechanical generator consisting of eleven motion elements listed in Table 1. The cradle represents the generating gear, which provides generating roll mo- Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use t n s s A c i m c J Downloaded Fr ion between the generating gear and the generated work. In the on-generated process, the cradle is held stationary. Face hobbing machine settings are: 1 ratio of roll Ra; 2 liding base Xb; 3 radial setting s; 4 offset Em; 5 work head etting Xp; 6 root angle m; 7 swivel j; and 8 tool tilt i. lthough the kinematical model in Fig. 5 is based on the mechanial machines, considering the ability of modern CNC machines, nstead of considering constant basic machine tool settings, we ay generally represent the machine settings as functions of radle rotational increment , namely, Ra = Ra0 + Rac 6 Xb = Xb0 + Xbc 7 s = s0 + sc 8 Em = Em0 + Emc 9 Xp = Xp0 + Xpc 10 m = m0 + mc 11 Fig. 4 Model of Phoenix\u00aeII hypoid generators ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 j = j0 + jc 12 i = i0 + ic 13 The first terms in Eqs",
            " Typically, the machine settings can be represented in higher order polynomials in terms of the cradle increment angle , namely, Ra = Ra0 + Ra1 + Ra2 2 + \u00af + Ra6 6 6a Xb = Xb0 + Xb1 + Xb2 2 + \u00af + Xb6 6 7a s = s0 + sc1 + sc2 2 + \u00af + sc6 6 8a Em = Em0 + Em1 + Em2 2 + \u00af + Em6 6 9a Xp = Xp0 + Xp1 + Xp2 2 + \u00af + Xp6 6 10a m = m0 + m1 + m2 2 + \u00af + m6 6 11a j = j0 + j1 + j2 2 + \u00af + j6 6 12a i = i0 + i1 + i2 2 + \u00af + i6 6 13a Equations 6a , 7a , 8a , 9a , 10a , 11a , 12a , and 13a can be considered as a conceptual extension of traditional modified roll, helical motion, and vertical motion defined on the mechanical universal machines to all machine settings which are represented by the motion elements of the kinematical model Fig. 5 . The representation of dynamic machine settings can be applied to the sophisticated modification of the tooth surfaces and the optimization of contact characteristics, through which the higher order coefficients of the polynomials can be determined. Tool Geometry The Gleason face hobbing process uses TRI-AC\u00aeor PENTAC\u00aeface hobbing cutters. Face hobbing cutters are different from face milling cutters. The cutter heads accommodate blades in groups. Normally, each group of blades consists of an inside finishing blade and an outside finishing blade with mean point M located at a common reference circle see Fig",
            " 8 and can be defined as a multiplication of three homogeneous matrices as Mtb = M M M 17a where M , M , and M are represented as, M = cos sin 0 0 \u2212 sin cos 0 0 0 0 1 0 0 0 0 1 17b M = 1 0 0 0 0 cos sin 0 0 \u2212 sin cos 0 0 0 0 1 17c M = cos \u2212 sin 0 Rbcos sin cos 0 Rbsin 0 0 1 0 0 0 0 1 17d Coordinate system Si is used to represent the rotation of the cutter head with an angular displacement . From Fig. 6, one can obtain the transformation matrix Mit and ri = Mit rt u = ri u, 18 ti = Mit tt u = ti u, 19 Applied Coordinate Systems Up till now, no paper has been found regarding exact modeling of face hobbing process. Mathematical modeling of face milling process has been developed and well known 7\u20139 . Both face milling and face hobbing processes can be virtually modeled using the mechanical cradle-style hypoid generator shown in Fig. 5. In comparison with the existing description of the cradle-style hypoid generators, this paper describes the kinematics of a universal hypoid generator in several major different aspects: a two independent rotations related to the work axis, cutter-head axis and cradle axis are considered; b the machine tool settings are represented as functions of cradle increment angle , instead of etry of blades Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use c a l s w m v b s C t r p r t s s w p t t J Downloaded Fr onstants; c the applied coordinate systems are directly associted with the physical machine motion elements and visually ilustrated; d the machine is virtually \u201cdisassembled\u201d to clearly how each machine setting and the associated motion elements as ell as the applied coordinate systems; and e a generating curve the edge of a tool blade , instead of a conical surface for face illing , is considered as the generating element. Following proides the detailed description. In order to mathematically describe the generation process, we reak down the relative motion elements of the kinematical model hown in Fig. 5 and attach a coordinate system to each of them. oordinate system Sm Fig. 9 , called the machine coordinate sysem, is connected to the machine frame and considered as the eference of the relative motions. System Sm defines the machine lane and the machine center. System Ss is connected to the sliding base element 11 and repesents its translating motion. System Sr Fig. 10 is connected to he machine element 10 and represents the machine root angle etting. System Sc Fig. 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.16-1.png",
        "caption": "Fig. 7.16",
        "texts": [
            "ro '( +pC.,I\u00bb) + AI(l) cos(ro '( +p~I\u00bb+ ... i \\3 i The first harmonic solution has already been obtained. The second solution is unstable. The third subharmonic solution is what we want to determine. We can see, therefore, that the component of the harmonic wave is somewhat weaker, i.e. A?) < A?), when harmonic solution exists. When ro = ro', the occurrence of subharmonic solutions is determined by the initial conditions. The phase diagram of the averaging equation on the rotating plane is shown in Fig. 7.16. There are seven singular points on plane S . The origin gives out a harmonic solution; of the three saddle points two give out an unstable subharmonic solution; three focus points give out a stable subharmonic solution. Part of the curves pass through two boundary lines, which divide the S plane into the attractive regions of a harmonic wave solution and the attractive regions of a subharmonic solution respectively. 7.4.4 The Present State ofthe Art ofthe Duffing Equation Study The Duffing equation can be of the following types: x\"+ox'+x+x3 = Fcosro( x\" + ox' + x - x 3 = F cosro( x\" + ox' + x 3 = F cosro( x\"+ox'-x+x3 = Fcosro( (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure36-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure36-1.png",
        "caption": "Fig. 36. Contact and bending stresses in the middle point of the path of contact on pinion tooth surface for modified involute helical gear drive wherein an error Dc \u00bc 30 is considered: edge contact is avoided.",
        "texts": [
            " 33 and 34 illustrate the variation of contact and bending stresses for the pinion and the gear, respectively. The stress analysis has been performed as well for the example of a conventional helical involute drive with an error of the shaft angle of Dc \u00bc 30 (Fig. 35). We remind that the tooth surfaces of an aligned conventional helical gear drive are in line contact, but they are in point contact with error Dc. The results of computation show that error Dc causes an edge contact and an area of severe contact stresses. Fig. 36 shows the results of finite element analysis for the pinion of a modified involute helical gear drive wherein an error Dc \u00bc 30 occurs. As shown in Fig. 36, a helical gear drive with modified geometry is free indeed of edge contact and areas of severe contact stresses. The discussions above allow to draw the following conclusions: (1) A new geometry of modified involute helical gears, based on the following ideas, has been proposed: (a) The pinion of the gear drive is double-crowned and therefore the pinion tooth surface is mis- matched of an involute helicoid in profile and longitudinal directions. (b) The gear tooth surface is designed as a conventional screw involute helicoid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.41-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.41-1.png",
        "caption": "Fig. 6.41 Cut section showing the tire construction. Reproduced from Ref. [5] with the permission of Tire Sci. Technol.",
        "texts": [
            "120) through \u03b7 and f can be explicitly expressed as @j @rc \u00bc 4rrc sin/D B2 @j @/D \u00bc 2r cos/D B @l @rc \u00bc 2rc sin2 /D ZrP rB r2 r2c r2D r2 G3=2 dr @l @/D \u00bc B sin/D cos/D ZrP rB r2 r2c 2 G3=2 dr @l @rP \u00bc Bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 sin2 /D r2P r2c 2q G \u00bc B2 A2 A \u00bc r2 r2c sin/D B \u00bc r2D r2c ; \u00f06:121\u00de where rP is an intermediate variable that is replaced with r in the integration of Eq. (6.119). (4) Comparison of calculation and experimental results Yamazaki [5] compared calculation and experimental results for the lateral fundamental spring rate. An experiment was performed for a passenger-car belted radial tire sized 175SR14 (wheel: 5J-14) using an apparatus similar to that shown in Fig. 6.26. A cut section of the tire is drawn in Fig. 6.41, and the calculation used the values rB = 192 mm, rC = 251 mm, rD = 296 mm, /D = 53.5 deg, r B \u00bc 230mm, r D \u00bc 275mm, h1 = 12 mm, h2 = 6 mm, h3 = 11 mm, Em = 3.5 MPa, EmB = 28.7 MPa, EmD = 5 MPa, where Em and h2 are Young\u2019s modulus and thickness of the sidewall, EmB and h1 are Young\u2019s modulus and thickness of the bead filler, and EmD and h3 are Young\u2019s modulus and thickness of the tread rubber. Because Young\u2019s modulus and thickness vary with position r, the integration of Eq. (6.119) must be performed in three regions: rB r B, r B r D and r D rD",
            " w /\u03b4 r D \uff52(mm) 200 250 300 1.0 0 0.5 Fig. 6.53 Radial displacement w at radius r of the sidewall (calculation). Reproduced from Ref. [5] with the permission of Tire Sci. Technol. 6.4 Fundamental Spring Rates Based on the Equilibrium Shape \u2026 363 6.5 Modification of Yamazaki\u2019s Model 6.5.1 Modification of Yamazaki\u2019s Model Nagai et al. [19] modified Yamazaki\u2019s model by considering the location of the neutral plane for bending deformation of the sidewall, Young\u2019s modulus of the carcass and the location of point D in Fig. 6.41. Yamasaki assumed that the neutral plane for bending deformation was located on the inner carcass, but FEA shows that the neutral plane in the prediction of ks is located at the middle of the turnup ply and downward ply as shown in Fig. 6.55, where the red color indicates tensile stress in the radial direction and the blue color indicates compressive stress. When the R ad ia l s pr in g ra te k r( M N /m 2 ) theory experiment 175SR14 (5J-14) load: 3kN rB=192 mm rC=251 mm rD=296 mm \u03a6D=53.5\u00b0 Em=3",
            "168), kr(r) is also expressed as kr\u00f0r\u00de \u00bc kbendingr \u00f0r\u00de\u00fe kextensionr \u00f0r\u00de kbendingr \u00f0r\u00de \u00bc 2 rD ZrD rB Emh3r 12 1 m2m g\u00f0r\u00de2 Bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p dr kextensionr \u00f0r\u00de \u00bc 2 rD ZrD rB Emh Vm 1 m2m f\u00f0r\u00de2 r Bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p dr: \u00f06:173\u00de Using Eqs. (6.172) and (6.173), the contributions of bending and extensional deformation at radius r of the sidewall to the fundamental spring rates can be evaluated. The rubber materials of the sidewall area in Fig. 6.41 are bead filler, gum chafer, sidewall and tread. Figures 6.57 and 6.58 show half of the integrand of Eq. (6.172), which is the contribution of each rubber material in one sidewall to ks(r) at radius r. Figure 6.59 shows the contribution of bending and extensional components of ks(r) in one sidewall calculated by adding bending and extensional components of each material at radius r. 366 6 Spring Properties of Tires Figure 6.57 shows that the bead filler and tread rubber outside the belt end largely contribute to ks in bending deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.8-1.png",
        "caption": "Fig. 3.8: Virtual displacement of a mass element",
        "texts": [],
        "surrounding_texts": [
            "We have seen and we shall see that in more details in the next chapters, that the triad momentum equation, moment of momentum equation and a set of suitable constraints allows to establish the equations of motion. The principles of mechanics offer another possibility to evaluate these equations, though in most cases the methods connected with these principles are better suited for small systems. For large systems the so-called Newton-Euler-equations represent a more adequate basis. We distinguish between differential principles and minimal principles ([180], [27]). The principles of Hamilton and of Gauss may be considered both ways. The idea of minimal principles is closely related to the origin of Euler\u2019s variational calculus, which allows in many cases the representation of differential equations by a direct optimization problem. Instead of solving the differential equations one may solve directly the optimization problem, a method, which is often used in continuum mechanics and in all fields of physics.\nIn the following we shall consider a selection of principles, which are also used in applications of practical relevancy. Beyond such aspects of utilitarianism principles offer a deep insight and understanding of the mechanical fundamentals. We shall not consider these principles in connection with nonsmooth dynamical properties, because we prefer more the straightforward way using the moment and moment of momentum equations together with the appropriate constraints for a derivation of the equations of motion [200]. Readers interested in that topic should have a look into the books [87] and [177].\nWe apply Newton\u2019s second law in the form of Lagrange to the mass element of Figure (3.8), which might be constrained by some surface \u03a6(rc) = 0. We get\nr\u0308dm = dF = dFa + dFp, (3.32)\nthe forces dF being subdivided into active (applied) forces dFa and into passive (constraint) forces dFp. An integration of this equation over the whole body B yields\u222b B r\u0308dm = \u222b B dF = \u222b B (dFa + dFp). (3.33)\nThe subdivision into applied and constraint forces follows an often used classical concept. In many cases, though, it might be more convenient to use the concept of active and passive forces (see chapter 2.1.2). The magnitude dFa is",
            "3.2 Principles 101\nan active force, and the magnitude dFp a passive one. For contact processes we should keep in mind, however, that passive forces may become active ones or vice versa, for example for transitions stick to slip or slip to stick in the tangential direction of a contact. As already mentioned active forces generate work and power, passive forces not. For simplicity we shall consider the force dFp as a passive constraint force, which means with respect to Figure (3.8) the component perpendicular to the constraint surface. The tangential component, if any, we would have to add to the applied force dFa.\nAs indicated in Figure(3.8) we assume that the mass element dm will be shifted by a virtual displacement \u03b4r. Such a virtual displacement will produce virtual work, and we get together with equation(3.32) for the mass element\n(dF\u2212 r\u0308dm)T \u03b4r =0\n(dFa \u2212 r\u0308dm)T \u03b4r =\u2212 (dFp)T \u03b4r = \u2212\u03b4Wp. (3.34)\nWe have assumed in Figure (3.8) a holonomic constraint \u03a6(rc) = 0, which makes the derivations a bit more transparent. We could have chosen of course a more complicated constraint (see for example [180]). Anyway, the constraint does not allow any kind of motion, also not any kind of virtual displacement, but only such displacements which are compatible with\n\u03b4\u03a6 = ( \u2202\u03a6 \u2202r )\u03b4r = (grad\u03a6)\u03b4r = 0 with r \u2208 IR6, \u03a6 \u2208 IRm. (3.35)\nA possible geometric interpretation is obvious. The m constraints \u03a6(r) span within the system space of r altogether m constraint surfaces, the surface normals of which are proportional to (grad\u03a6). The vanishing scalar product [(grad\u03a6)\u03b4r = 0] implies that\n(grad\u03a6) \u22a5 \u03b4r. (3.36)",
            "The normal vector on this constraint surface is n = (grad\u03a6)/|(grad\u03a6)|, which together with the two relations (3.34) and (3.36) give the comparison\n(grad\u03a6) \u22a5 \u03b4r, \u21d2 n \u22a5 \u03b4r, \u21d2 dFp \u22a5 \u03b4r, (3.37)\nfrom which we conclude, that the normal vector n and the passive force dFp are perpendicular to the virtual displacement \u03b4r indicating the following: The passive forces have the same direction as the normal vector to the constraint surface, hence, the passive forces are always perpendicular to the constraint surface, and the motion, virtual or real, can only take place within these surfaces. With respect to a certain point, motion takes place within the tangent plane of this point given by equation (3.35) (see also Figure 3.1). This confirms our earlier statement: motion takes place on the constraint surfaces, in the tangent spaces, all passive constraint forces are assembled within the normal spaces.\nFrom these arguments we conclude that the mechanical magnitudes as components of the tangent spaces must be always orthogonal to those of the normal spaces, or more concrete, passive constraint forces are orthogonal to displacements on the tangent plane in a point of the constraint surface. The above arguments form the main basis for the principle of d\u2019Alembert in the setting of Lagrange ([187], [27], [93]):\npassive (constraint) forces do no work: \u222b B (dFp)T \u03b4r = 0. (3.38)\nConstraint forces are alway passive forces, and they are \u201clost forces\u201d, according to a statement of Daniel Bernoulli, \u201clost forces\u201d in a sense that they do not contribute to the motion of a mechanical system. But these lost constraint forces keep things together telling the motion where to go. The motion itself will be realized only by the active forces. Therefore we get from the equations (3.33) and (3.34)\u222b B (r\u0308dm\u2212 dFa)T \u03b4r = 0 (3.39)\nFor the static case (r\u0308 = 0) this equation includes the principle of virtual work ([258], [147])\u222b B (dF)T \u03b4r = \u03b4W = 0 (3.40)\nMany textbooks of mechanics, especially dynamics, give a nice explanation of the above equations, which possess the character of an axiom. This explanation will be discussed in the following, because it allows a better understanding of constrained dynamics. The terms of the equation"
        ]
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure16-1.png",
        "caption": "Fig. 16. Bifurcation configuration of evolved 6R linkage. (a) Bifurcation configuration of 6R mechanism (b) Its prototype.",
        "texts": [
            " The corresponding constraint-screw multiset can be derived as follows: S r l1 = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 S r 11 = ( 1 , 0 , 0 , 0 , lp c \u03b1s \u03b2 , 0 )T S r 12 = ( 0 , 1 , 0 , \u2212 lq c \u03b2s \u03b1 , lq c \u03b1 s \u03b12 s \u03b2 , lq c \u03b1 c \u03b2s \u03b12 )T S r 13 = ( 0 , 0 , 1 , ln c \u03b2s \u03b1 , \u2212 ln c \u03b1 s \u03b12 s \u03b2 , \u2212 ln c \u03b1 c \u03b2s \u03b12 )T \u23ab \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 S r 21 = ( 1 , 0 , 0 , 0 , lp c \u03b1s \u03b2 , 0 )T S r 22 = ( 0 , 1 , 0 , \u2212 lq s \u03b1c \u03b2 , lq c \u03b1 s \u03b12 s \u03b2 , \u2212 lq c \u03b1 s \u03b12 c \u03b2 )T S r 23 = ( 0 , 0 , 1 , \u2212 ln s \u03b1c \u03b2 , ln c \u03b1 s \u03b12 s \u03b2 , \u2212 ln c \u03b1 s \u03b12 c \u03b2 )T \u23ab \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23ad (19) Apparently, the number of independent loops l is 1. According to Eq. (9) and Eq. (10) , card \u3008 S r \u3009 = 6 , dim S r = 5 . Hence, the mobility is m = 6 \u2212 6(1) + 6 \u2212 5 = 1 . In view of the special DH parameters, when the evolved 6R linkage moves to the position as shown in Fig. 16 . It is obvious that the number of independent loops l is 1. Thus, the constraint-screw multiset can be derived as follows: S r l1 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 11 = ( 1 , 0 , 0 , 0 , 0 , f c \u03b8 ) T S r 12 = ( 0 , 1 , 0 , 0 , 0 , f s \u03b8 ) T S r 13 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 21 = ( 1 , 0 , 0 , 0 , 0 , \u2212 f c \u03b8 ) T S r 22 = ( 0 , 1 , 0 , 0 , 0 , \u2212 f s \u03b8 ) T S r 23 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad (20) where \u03b8 denotes the angle between the Y-axis and line OG, f is the length of OG"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003951_1.2898878-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003951_1.2898878-Figure3-1.png",
        "caption": "Fig. 3 Definition of a local coordinate system",
        "texts": [
            " Coordinate system S0 x ,y ,z is introduced by the tooth surface generation modeling 15\u201317 . It is rigidly fixed to the gear or pinion member with z axis coincides with the axis of the gear or pinion. In the case of inverse engineering, the target tooth flank form may be numerically represented by the measured coordinates of a group of grid points of a master hypoid pinion or gear. In order to visually represent the tooth flank form error, a local coordinate system S X ,Y , is defined for each side of tooth flank and shown in Fig. 3. We assume that the positive direction of axis is the same as that of the tooth surface normals whose positive directions are defined as pointing out of the tooth from inside to outside. Under such assumption, a positive error indicates a thicker tooth than the target one, and a negative error indicates a thinner tooth. The concave and convex tooth surfaces are rotated at angles 1 and 2, respectively, so that at the reference point coordinate, y =0. The nominal data of the grid points of the convex and con- cave tooth surfaces are then transformed into the same coordinate Transactions of the ASME 6 Terms of Use: http://www",
            " Using a reression method, the error surfaces can be represented by polynoials of two variables up to sixth order as 1 = a1X + a2Y + a3X2 + a4XY + a5Y2 + \u00af + a27Y 6 2 = b1X + b2Y + b3X2 + b4XY + b5Y2 + \u00af + b27Y 6 7 ere, 1 and 2 are errors of concave and convex side tooth suraces, respectively. The goal of the correction process is to compensate for error urfaces 1 and 2 by an appropriate correction of the universal otion coefficients. Since coordinates X and Y correspond to the ooth profile and lengthwise directions, respectively Fig. 3 , the oefficients in Eq. 7 indicate specific geometric meanings. For ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 instance, a1 and a2 are first-order errors or pressure angle and spiral angle errors, respectively; a3, a4, and a5 are second-order errors in profile, warping, and lengthwise curvatures; and so on. Using the universal motions represented by Eq. 1 , we may minimize the higher-order components of the error surfaces 1 and 2. For a face-mill single-side process, the correction calculation is separately conducted on each tooth side and the tooth thickness error is directly corrected to the nominal thickness using the machine stock divider"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000288_tie.2019.2921296-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000288_tie.2019.2921296-Figure1-1.png",
        "caption": "Fig. 1. The Quanser 3-DOF helicopter experimental platform.",
        "texts": [
            "278-0046 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Index Terms\u2014Three degrees-of-freedom helicopter, backstepping control, neural networks. I. INTRODUCTION AS one of the laboratory helicopter, Quanser three degreesof-freedom (3-DOF) helicopter (Fig. 1) has been widely used for controller design and analysis due to some similarities between its dynamic features and those of the real one, such as high nonlinearity, strong coupling and underactuation. The control design for Quanser 3-DOF helicopter can be separated into two classes: two channels regulation and three channels regulation. Two channels regulation mostly means that the travel angle is set to free move, and the rest two attitude angles (elevation and pitch angles) are under control. To list some representative results, the authors in [1] presented a robust control for the elevation and pitch motions of a 3- DOF helicopter by using output-regulation theory and signal compensation technique",
            " the effectiveness and advantages of our control method are verified by four sets of contrastive experiment results. The rest of paper is organized as follows. The 3-DOF helicopter system description and its state space model are given in section II. The controller design procedure and stability analysis are presented in section III and section IV, respectively. Section V shows the experimental results, and followed by section VI which concludes this paper. The three degrees-of-freedom (3-DOF) helicopter system shown in Fig.1 consists of five modules: the propeller section, the arm section, the active disturbance system (ADS) section, the base section and a counterweight. The propeller section including two direct current (DC) motors and two propellers, which generates control forces; the arm section is used to connect the center of the helicopter body, the base and the counterweight; the ADS section can create disturbances by driving a sliding block to move back and forth; the base section is used to support the helicopter system, and a counterweight is located at the other end of the arm to adjust the effective mass of the helicopter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000633_admt.202100007-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000633_admt.202100007-Figure1-1.png",
        "caption": "Figure 1. Schematics of LIG direct laser writing on polyimide sheets. a) Gantry scan system of the CO2 laser. b) Galvanometric system of the UV laser. c) Schematic representation of the line-scan with spacing d during the laser synthesis.",
        "texts": [
            " The DLW procedure consisted in the irradiation and carbonization of commercially available polyimide sheets, more specifically Kapton, using i) a continuous CO2 laser (10.6\u00a0 \u00b5m) equipped with a computer driven gantry holding a focusing lens (Redsail M500) or ii) a diode-pumped Nd:YVO4 pulsed UV laser (355\u00a0 nm) (Inngu Laser), equipped with a galvanometric head comprising a f-theta lens. The DLW of graphene electrodes is accomplished through linear spaced passages of the laser beam onto a polyimide film, at a given speed (Vlaser) and at an appropriate line separation d (see Figure\u00a0 1) so that both continuity and structural integrity of the overall film are attained. The IR and UV LIG writing parameters were selected based on previous works of the group and are summarized in Table S1 in the Supporting Information. While the scan in the IR system is done by moving the laser focusing head, in the UV system the laser beam is analogously steered using a galvanometric head, with the f-theta lens assuring focus conditions across all the processed area. After DLW, the 50 mm2 LIG samples are thoroughly and repeatedly cleaned with isopropanol and DI water"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000658_rpj-07-2019-0182-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000658_rpj-07-2019-0182-Figure9-1.png",
        "caption": "Figure 9 EBM system, schematic representation of a commercialized system by Arcam, Sweden (a) (Additive Manufacturing, 2019), a machine developed by IWB, Germany (b) (Sigl et al., 2006) and Tsinghua University, Beijing (c) (Guo et al., 2015)",
        "texts": [
            " In the market, there is only one company, Arcam, which provides the commercial system. It has developed four EBM units which are different in size and designed according to the applications, as shown inTable V. In these systems, multi-beam technology is provided, which enables several standard scanning strategies for optimized sintering. For process validation, Arcam provides inbuilt highresolution camera LayerQam for defect detection and xQam for built-in X-ray diffraction system. The schematic representation of the Arcam is given in Figure 9(a). Formedical applications, Arcam has developed several implants, which have been used by patients too with a positive response (AdditiveManufacturing, 2019). Apart from Arcam, three other research institutes have developed machines for study. However, the details of these equipment are not mentioned in detail anywhere. Out of these three, one is Institute of Machine Tools and Industrial Engineering of the Technical University of Munich, Germany, which has developed indigenous machine of 10 kW, 100kV power. Theymodified the existing Pro-beammachine shown in Figure 9(b) (Sigl et al., 2006; Kahnert et al., 2007). Furthermore, Tsinghua University Beijing has developed a unique system of 3 kW, 60kV and 50mA for dual-material processing simultaneously for a single layer. This is a unique configuration claimed by the author for functionally graded material (FGM) (Guo et al., 2015) (Table VI). Apart from this, the exchangeable build tank of 200 200 200 and 250 250 250 mm3 are given in this machine for spreading of mixed powder on the build plate, as shown in Figure 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.3-1.png",
        "caption": "Fig. 7.3 Shear spring rate of the tire block pattern (where the lower surface is not constrained in the thickness direction)",
        "texts": [
            " The total shear displacement d is expressed by [2] d \u00bc d1 \u00fe d2 \u00bc f h AG \u00fe 2 f \u00f0h=2\u00de3 3EI ; \u00f07:1\u00de where E is Young\u2019s modulus of rubber, G is the shear modulus of rubber, and f is the shear force applied to the lower surface. I and A are, respectively, the moments of inertia of the cross section of the block and contact area: I \u00bc a3b=12 A \u00bc ab ; \u00f07:2\u00de where b is the block width in the direction perpendicular to the page. Equations (7.1) and (7.2) and the relation G = E/3 for rubber yield the block rigidity (i.e., shear spring rate of the block) K1: K \u00bc f d \u00bc abE 3t 1\u00fe 1 3 h a 2h i : \u00f07:3\u00de Meanwhile, when the lower surface does not stick to the road, the deformation of the block is shown in Fig. 7.3 and different from the deformation in Fig. 7.2. The block rigidity is expressed by [3]2 Total shear displacement Shear Bending 1Note 7.1. 2See Footnote 1. 7.1 Shear Spring Rate of the Tire Block Pattern 377 K \u00bc f d \u00bc abE 3t 1\u00fe 4 3 h a 2h i : \u00f07:4\u00de The value of 1/3 in the denominator of Eq. (7.3) and the value of 4/3 in the denominator of Eq. (7.4) are related with the ratio of bending displacement to shear displacement. These values depend on the boundary condition of the lower surface. When the ratio of bending displacement to shear displacement is denoted a, Eq",
            " The small pitch has the lower void volume ratio than the large pitch, because the pitch variation changes the circumferential length but slot angle in Fig. 7.65a. Hence, the tread thickness of the small pitch becomes thinner than that of the large pitch. The difference of the tread thickness between the small and large pitches worsens the radial force variation (RFV). Furthermore, Fig. 7.65b shows that the calculated block rigidity per area of the large pitch is larger than that of the small pitch owing to the bending deformation of Fig. 7.3. The difference of the block rigidity between the small and large pitches, especially in the circumferential direction (a = 90\u00b0), worsens the RFV and the tangential force variation (TFV). Ishiyama and Nakajima of Bridgestone [55] developed the optimization technology to minimize the difference of block rigidity and the tread thickness between the small and large pitches, which is called the flat force block. The design variables are slot angles and void depths at sides of a block. Figure 7.66 shows the effect of the flat force block that the slot angles of 0\u00b0, 14\u00b0 and 20\u00b0 are applied to large, 7",
            "00R20 185/70HR14 Construction Bias Radial Radial Inflation pressure (kPa) 725 725 170 Load (kg) 2400 2700 350 Axle Rear Rear Front Course 320 km/cycle 100% paved road 400 km/cycle 70% highway, 30% ordinary 320 km/cycle 100% paved road j1 0.0184 0.0215 0.0341 j2 0.208 0.0754 0.0193 Reproduced from Ref. [16] experiment 0 20 40 5 10 15 Distance of travel (103km) W ea r d ep th (m m ) tire A tire B tire C calculation Fig. 14.14 Comparison of tire wear between the calculation and fleet test. Reproduced from Ref. [15] with the permission of JSAE 1036 14 Wear of Tires Gough [17] used a cantilever beam to represent belt deformation that consists of shear deformation d1 and bending deformation d2 as shown in Fig. 7.3. A lateral load P is applied to the center of contact patch of length L with Young\u2019s modulus d \u00bc d1 \u00fe d2 \u00bc PL 4AG \u00fe PL3 48EI ; \u00f014:50\u00de where A is the cross-sectional area and I the area moment of inertia of the beam. (Note that we are considering the in-plane loading in the tire footprint.) Recasting the above equation in the form of stiffness KGough (i.e., so-called Gough stiffness) and using typical tire dimensions for A, I and L that Gough related to the relaxation length of a tire, we obtain KGough \u00bc P d \u00bc EG L 4A E\u00fe L3 48I G : \u00f014:51\u00de In general, the above equation can be rewritten as KGough \u00bc AxxAss=\u00f0C1Axx \u00feC2Ass\u00de; \u00f014:52\u00de where Axx and Ass are, respectively, the circumferential and shear moduli of the cord\u2013rubber laminate in the tread region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.59-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.59-1.png",
        "caption": "Fig. 5.59: Active endoscope using shape memory actuators. According to [Esashi93]",
        "texts": [
            " The present trend towards minimal invasive therapy requires that precise catheter systems with active guidance will be available to enable the surgeon to enter the various cavities of the human body or to direct them into a specific branch of a blood vessel. In [Esashi93] the development of an active endoscope was described which uses springs made from shape memory alloy. These springs produce the for ce for allowing a defined trajectory which is needed to perform a complicated motion in minimal-invasive surgery, Fig. 5.59. The prototype is 215 mm long, has a diameter of 13 mm and consists of 5 active segments. Each of the seg ments can be moved by 1 mm diameter SMA springs which are controlled by a microprocessor. picts the catheter design. Three SMA wires are encased in a flexible plastic 180 5 Microactuators: Principles and Examples actuator body; each wire has a diameter of 150 f.A.m. There is an electrical connector on each end of the SMA wires to which the electric voltage can be applied. The wires contract when an electric current is applied to them, causing a temperature increase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.32-1.png",
        "caption": "Fig. 8.32 Movement of a rigid wheel rolling over a step [29]",
        "texts": [
            " The inclination angle of the follower with respect to the horizontal corresponds to the effective forward slope by. w(X) and by are expressed by w\u00f0X\u00de \u00bc fb X ls=2\u00f0 \u00de\u00fe fb X \u00fe ls=2\u00f0 \u00de 2 tan by \u00bc fb X ls=2\u00f0 \u00de fb X\u00fe ls=2\u00f0 \u00de ls ; \u00f08:197\u00de where X is the longitudinal position of the wheel center. A parameter lf in the left figure of Fig. 8.31, the so-called offset, controls the position of the basic curve with respect to the beginning of the step in the road profile. The basic curve is used as a building block with which to compose the basic profile for an arbitrarily shaped obstacle. As shown in Fig. 8.32, the path of the center of the rigid wheel corresponds to a circle with the same radius a as the rigid wheel. The shape of the basic curve corresponds well with the curve of the rigid wheel response. The length of the curve lb is thus expressed as 514 8 Tire Vibration lb \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 a hstep 2q : \u00f08:198\u00de Nondimensional parameterization is used for the length and offset of the basic curve: a \u00bc plba0 ls \u00bc pls2l lf \u00bc plf lb: \u00f08:199\u00de where a0 is the unloaded tire radius, l is the half contact length, and plb, pls and plf are fitting parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001151_tsmc.2021.3051335-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001151_tsmc.2021.3051335-Figure1-1.png",
        "caption": "Fig. 1. Desired formation pattern.",
        "texts": [
            " ,N}, where \u03b7i = [xi, yi, \u03c8i]T coordinated in the Earth-fixed frame denote the ith MSV\u2019s outputs with vessel position (xi, yi) and yaw angle \u03c8i, J(\u03c8i) are the rotation matrices, \u03bdi = [ui, \u03c5i, ri]T expressed in the bodyfixed frame denote the velocities with surge velocity (ui), sway velocity (\u03c5i), yaw velocity (ri), M = MT > 0 denotes the inertia matrix (including added mass), C(\u03bdi) are the total Coriolis and centripetal acceleration matrices, D(\u03bdi) denote the uncertain hydrodynamic damping matrices, (\u03b7i, \u03bdi) = [ 1, 2, 3]T \u2208 R 3 denote the unmodeled dynamics, \u03c4i \u2208 R 3 Authorized licensed use limited to: UNIVERSITY OF WESTERN ONTARIO. Downloaded on May 26,2021 at 08:41:12 UTC from IEEE Xplore. Restrictions apply. represent the control inputs, and \u03c4d,i \u2208 R 3 denote the unknown time-varying disturbances. Consider a desired formation pattern consisting of a virtual vessel with virtual center Od and N actual vessels with N vertices (each vertex i, i \u2208 N denotes the center of gravity of each vessel), as shown in Fig. 1. The virtual vessel moves along the reference trajectory \u03b7d that is designed according to the actual task, and each vessel moves along the reference trajectory \u03b7r,i generated from \u03b7d, i.e., \u03b7r,i = \u03b7d + \u03b7\u2217 i (2) where \u03b7\u2217 i are constant vectors specified by the designer. To learn the homogeneous modeling uncertainties cooperatively, each vessel needs to interact with its neighbor agents. The undirected graph G = (V, E) is employed to model the interaction among MSVs, where V = {\u03d11, . . . , \u03d1N} is the set of vertices indexed by each vessel, and E \u2286 {(\u03d1i, \u03d1k)|\u03d1i, \u03d1k \u2208 V, \u03d1i = \u03d1k} denotes the edge set"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.60-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.60-1.png",
        "caption": "Fig. 5.60: Schematic representation of a MAC actuator. According to [Fuku93]",
        "texts": [
            " The pharmaceutical in the microcapsule is pushed out due to the volume increase of the polymer gel. When the pump space is completely occupied by the gel, the medicine is fully injected and the cycle is completed. The duration of the cycle depends on the concentration difference between the polymer gel solution and the ambient solution. A pump prototype had a diameter of 5 mm, was 9.8 mm long and had a weight of 0.7 g. The semipermeable membrane was made of a 70 f.tm thick cellulose sheet. Polymer microcatheter For the microcatheter presented in Figure 5.60, alternative actuation prin ciples are being investigated. A prototype of a microcatheter was developed with two integrated guide wires and a liquid channel [Guo95). Through the channel physiologic solutions or contrast media can be transported. Attached to each guide wire is a polymer film actuator which enables the catheter to be bent, Fig. 5.88. The guide wire consists of two electric conductors covered by a wire sheath and the actual actuator, an ionic conducting polymer film. The end of this film is embedded between two flat platinum electrodes, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.39-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.39-1.png",
        "caption": "Fig. 5.39: Typical Modern Tractor Concept (courtesy AGCO/Fendt)",
        "texts": [
            "3 Tractor Drive Train System 257 Power tansmissions of tractors represent the most complicated drive train units of nearly all transportation systems. They must meet a large variety of very hard requirements, and in the last one, two decades the demands for more versatility, flexibility and comfort for the driver increase continuously. Tractors are supposed to do all kind of agricultural work, but also to fulfill many requirements of forestry, and additionally tractors should be able to move along normal roads with reasonable speed and safety. Figure 5.39 pictures a typical modern tractor concept with a very sophisticated drive train system. This altogether leads to very complex drive trains, for which modern CVTconcepts offer significant advantages. They may operate with some given speed independently from the engine speed thus running the motor at the point of best fuel efficiency. It offers advantages for all implements by generating an optimal power distribution between driving and working. The German company Agco/Fendt as one of the leading enterprises of modern tractor technologies developed for that purpose a very efficient power transmission including for low speeds a hydrostatic drive and for larger speeds a gear system with the possibility of mixing the power transmission according to external requirements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure8.16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure8.16-1.png",
        "caption": "Fig. 8.16: Operating principle of the swimming robot: robot design (left) and motion principle of the fins (right). According to [Fuku95)",
        "texts": [
            " The rod of the robot is 60 mm long and the length of the legs is 35 mm. The force which could be transmitted by the tip of the rod was 6.8 mN in the downward direction and 3.2 mN in the upward direction. ' Piezoelectric swimming microrobot A concept of a swimming microrobot was introduced in [Fuku95). The robot can be used as a mobile platform for an industrial application, e. g. to inspect pipelines or as a miniaturized device for medical purposes to inspect blood vessels. The robot motion is obtained by vibrating fins using piezoactuators, Fig. 8.16. The multilayer stacked piezoelements exert high forces but their displacement is small. However, they can easily operate a lever mechanism. In this mic rorobot, a small 8 ~m stroke of the piezoelements is magnified 250 times to generate a secondary motion of about 2 mm. The swim motion is accom- plished with two 32 mm long fins and a lever mechanism, as shown in Figure 8.16. The resulting propulsion force was 10\u00b74 N for forward motions and 2 x 10\u00b75 N for backward motions. The robot has a length of 34 mm and a width of 19 mm. The fins provide the robot with one rotational and one translational degree of freedom, enabling it to move forward and evade obstacles in its path. The robot was able to move at a speed of 30 mm/s at an operating fre quency of the piezoelements of 100-350 Hz and a voltage of 150 V. Levitated mobile unit with optical power supply Usually, miniaturized mechanical actuator systems have problems with high friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-17-1.png",
        "caption": "Figure 4-17. Reference waveforms with added zero-sequence systems: (a) with added third harmonic; (b), (c), (d) with added rectangular signals of triple fundamental frequency.",
        "texts": [
            " Pulse Width Modulation for Electronic Power Conversion Measured waveforms obtained with the suboscillation method are displayed in Figure 4-16. This osciUogram was taken at 1 kHz switching frequency and m \u00ab 0.75. Modified Suboscillation Method. The deficiency of a limited modulation index, inherent to the suboscillation method, is cured when distorted reference waveforms are used. Such waveforms must not contain other components than zero- 4.5. Open Loop Schemes 157 sequence systems in addition to the fundamental. The reference waveforms shown in Figure 4-17 exhibit this quality. They have a higher fundamental content than sinewaves of the same peak value. As explained in Section 4.2.4, such distortions are not transferred to the load currents. There is an infinity of possible additions to the fundamental waveform that constitute zero-sequence systems. The waveform in Figure 4-17a has a third harmonic content of 25% of the fundamental; the maximum modulation index is increased here to mmax = 0.882 [11]. The addition of rectangular waveforms of triple fundamental frequency leads to reference signals as shown in Figure 4-17b through Figure 4-17d; a limit value of mmax2 = \\/37r/6 = 0.907 is reached in these cases. This is the maximum value of modulation index that can be obtained with the technique of adding zero-sequence components to the reference signal [12, 13]. Sampling Techniques. The suboscillation method is simple to implement in hardware, using analog integrators and comparators for the generation of the triangular carrier and the switching instants. Analog electronic components are very fast, and inverter switching frequencies up to several tens of kilohertz are easily obtained",
            " The reference signal is w*(r) = w/mmax \u25a0 sin 2\u03c0/\u038a t, and the sampled values w*(0 in Figure 4-22 form a discretized sinefunction that can be stored in the processor memory. Based on these values, the switching instants are computed on-line using equation 4.25. Performance of Carrier-Based PWM. The loss factor S of suboscillation PWM depends on the zero-sequence components added to the reference signal. A comparison is made in Figure 4-23 at 2 kHz switching frequency. Letters \"a\" through \"d\" refer to the respective reference waveforms in Figure 4-17. The space vector modulation exhibits a better loss factor characteristic at m > 0.4 as the suboscillation method with sinusoidal reference waveforms. The reason becomes obvious when comparing the harmonic trajectories in Figure 4-21. The zero vector appears twice during two subsequent subcycles, and there is a shorter and a subsequent larger portion of it in a complete harmonic pattern of the suboscillation method. Figure 4-15 shows how the two different on-durations of the zero vector are generated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-37-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-37-1.png",
        "caption": "Figure 4-37. (a) Two sections of optimized current trajectories having dif-",
        "texts": [
            " Pulse Width Modulation for Electronic Power Conversion Figure 4-35. Loss factor S of synchronous optimal PWM: (a) for comparison at/s = 300 Hz; (b) modified space vector modulation; (c) space vector modulation. ^ i Figure 4-36. Switching state sequences of a quarter cycle: (a) space vector modulation; (b) synchronous optimal modulation (k refers to the switching-state vectors uk as defined in Figure 4-9, time axis not to scale). minimum harmonic distortion, as the one shown in the left half of Figure 4-37a. An assumed change of the operating point at / = ty commands a different pulse pattern, to which a different steady-state current trajectory is associated. Since the current must be continuous, the actual trajectory resulting at t > tx exhibits an offset in space, Figure 4-37b. This is likely to occur at any transition between pulse numbers since two optimized steady-state trajectories rarely have the same instantaneous current values at any given point of time. The offset in space is called the dynamic modulation error \u03b4(\u03ae [53]. This error appears instantaneously at a deviation from the preoptimized steady state. The dynamic modulation error tends to be large at low switching frequency. It is therefore almost impossible to use a synchronous optimal pulse width modulator as part of a fast current control system",
            " The fundamental current loop is shown there in the upper portion of Figure 4-60. It operates very slowly as it need not contribute to the dynamic performance. Fast current changes subdivide in three categories: the unavoidable harmonics \u00cd A J J ( \u00cd ) , commanded transients itr(t), which include transients generated by the load, and the dynamic modulation error \u03b4(\u03ae; hence, 4.6. Closed Loop PWM Control 189 dW = ', i(0 + \u00abi-CO + *A\u00bb(0 - \u00bf(0 (4.37) The dynamic modulation error was introduced with reference to Figure 4-37; it is an inherent imperfection of any voltage-controlled pulse width modulator [53]. Representing the commanded transients i,r(t) as a separate component in equation 4.37 classifies the harmonic current /\u00bf\u201e(f) as a steady-state quantity, which is indicated by the additional subscript ss. Therefore, ih ss(t) can be reconstructed from the optimal pulse pattern in actual use. The optimal patterns, by definition, also refer to the steady state. Using equation 4.36, the dynamic modulation error can be then determined from the measured machine current is(t) and the commanded values \u00a1{ (t) and i\u201e{t)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure14-1.png",
        "caption": "Fig. 14. Tip relief for the current design.",
        "texts": [
            " The modified lead correction s 37 m instead of the original designed 8 m. The second micro-geometry modification is the gear tooth rofile tip relief. Fig. 13 shows the result from the original esign, 61 m and it shows the second gear tooth started in ontact. This tip relief is over relieved resulting in tip contact pitting failure. K. Mao / Wear 262 (20 c s t t o w t p t o a r u r 6 c m m s o o p b s m T a ontribution too late, contact ratio low and concentrated contact tress at the lowest point of single tooth contact. Fig. 14 shows he modified design with 36 m tip relief and it can be seen from he figure that the tip contact contribution started earlier than the riginal design in Fig. 13. More contact ratio and load sharing ill be achieved from the modified design without causing high ip local contact. R [ [ [ [ [ 07) 1281\u20131288 1287 Crowning of 10 m on pinion and 8 m on wheel gear is roducing even contact stress between the centre of the gear and he edges at the required torque and it can be concluded that the riginal design of crowning is adequate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure20-1.png",
        "caption": "Fig. 20 Model of a hypoid gear drive",
        "texts": [
            " The vectors are considered and represented in the coordiate system Sw that is connected to the work. A unit cradle angular elocity, i.e., c=1 might be considered. The equation of meshing s applied for determination of generated tooth surfaces. The tooth surface generation model described above is applied o the left-hand work members. For the right-hand members, the nitial cradle angle q0 in Fig. 15 should be replaced by \u2212q0. Figres 18 and 19 show a pair of mating pinion and gear tooth suraces of a face hobbed hypoid gear drive Fig. 20 , which is genrated by using the developed equations. ooth Contact Analysis (TCA) Tooth Contact Analysis TCA is a computational approach for nalyzing the nature and quality of the meshing contact in a pair f gears. The concept of TCA was originally introduced by The leason Works in the early 1960s as a research tool and applied to piral bevel and hypoid gears 16\u201318 . Application of TCA techology has resulted in significant improvement in the developent of bevel gear pairs under given contact conditions",
            "org/about-asme/terms-of-use 1 Downloaded Fr for generated gear r2 = r2 u2, 2, 2 n2 = n2 u2, 2, 2 t2 = t2 u2, 2, 2 f2 u2, 2, 2 = 0 33 for non-generated gear r2 = r2 u2, 2 n2 = n2 u2, 2 t2 = t2 u2, 2 34 322 / Vol. 128, NOVEMBER 2006 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 Further, the mating tooth surfaces are transformed into a common coordinate system Sf that is connected to the frame of the gear drive and with origin Of located at the theoretical crossing point of the gear axis. The relationship of coordinate systems in Fig. 21 simulates the running meshing of the gear pair shown in Fig. 20 and incorporates the adjusting parameters E, G, P, and . In case of spiral bevel gear drives, E0=0 is assumed. The axes Z1 and Z2 coincide with the rotation axes of the pinion and the gear, respectively. The origins O1 and O2 of systems S1 and S2 would be at the theoretical crossing point if the adjusting param- hing of design A Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use e r t b o M b f t o es J Downloaded Fr ters G=0 and P=0 are assumed. Denoting 1 and 2 as the otational motion parameters of the pinion and the gear respecively shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000964_j.surfcoat.2021.127010-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000964_j.surfcoat.2021.127010-Figure1-1.png",
        "caption": "Fig. 1. (a) and (b) Schematic of laser cladding operation, (c) view from the top of one of the cladded samples.",
        "texts": [
            " To perform the initial adjustment of the device and find the range of coating parameters, a preliminary coating on GTD-111 samples was carried out following the studies in the literature [15,20]. Based on the initial microstructure of the coating, a wide range of parameters was selected. The average power (Pav), scanning speed (V), and powder feeding rate (F) employed for this study are presented in Table 2. The schematic of the laser cladding operation and the top-view of the cladded samples are shown in Fig. 1. After the laser cladding process, the cross-sections of the samples were obtained by wire-cutting. The cut samples were subjected to metallographic steps, including sanding and polishing with Al2O3 diamond paste, to aid microstructural observation. Four pieces were cut from each sample. Electro etching solution with 12 mL H3PO4 + 40 mL HNO3 + 48 mL H2SO4 compound at 6 V for 5 s was also used to detect the substrate and coating. When the specimens were ready, digital images were taken using an optical microscope from the cross-sectional surfaces of the cladding layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001038_j.mechmachtheory.2021.104352-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001038_j.mechmachtheory.2021.104352-Figure2-1.png",
        "caption": "Fig. 2. Description of localized defect;(a) geometrical constraint relationships;(b) outer raceway defect.",
        "texts": [
            " As can be expected, the localized defect not only occurs on the inner and outer raceways, but also occurs on the balls [1] . For simplification, this study focuses on the defect on the outer raceway. In many researches with the displacement excitation functions, the cube-shaped defect is a preference [ 1 , 5 , 31 ]. However, with this kind of defect, it is hard to consider the geometrical relationship in the defect region. Hence, the defect shape presented by Cui et al.[ 32 , 33 ] is adopted here, which can be described with the scale \u03c6 f ,the position angle \u03c6 f and the depth h . As shown in Fig. 2 (a) and (b), when the ball is located in the defect-free area, the geometrical relationship between the ball center and the raceway centers is the same as the normal case. However, when the ball enters into the defect area, the geometrical relationship will change and the abrupt variations in load and friction will occur. Owing to the geometric constraints caused by the ball surface and the raceway surface, the movements of the ball cannot strictly follow the change of defect depth. The effective defect depth profile is as follows [ 32 , 33 ]: d ( \u03d5 j ) = { min ( h, r b + R o ( cos \u03b2 j \u2212 1 ) \u2212 \u221a r b 2 \u2212 R o 2 ( sin \u03b2 j )2 ) \u03d5 j \u2208 [ \u03c6 f \u2212 0 ",
            " 5 \u03c6 f (2) In most of the dynamic models, the displacement excitation function is directly included in the load-deformation relationship. However, when the dynamic behaviors of the ball are considered, whether the ball interacts with the bottom surface of the defect depends on the movements of the ball center. Actually, the effective defect depth profile should be employed to provide the constraint of motion which can be equivalent to the displacement of the outer raceway groove curvature center. With this way, the axial and radial distances between the inner and outer raceway groove curvature centers (see Fig. 2 (a)) can be modified as [ 24 , 30 ]: { A a j = ( r i + r o \u2212 d ) \u00b7 sin \u03b10 + \u03b4a \u2212 \u03b8y i sin \u03d5 j + \u03b8z i cos \u03d5 j \u2212 d ( \u03d5 j ) \u00b7 sin \u03b10 A r j = ( r i + r o \u2212 d ) \u00b7 cos \u03b10 \u2212 \u03b4ry cos \u03d5 j \u2212 \u03b4rz sin \u03d5 j \u2212 d ( \u03d5 j ) \u00b7 cos \u03b10 (3) where r i and r o represent the inner and outer raceway groove curvature radii respectively, \u03b10 is the initial contact angle, d denotes the ball diameter, and i is the radius of the locus of inner raceway groove curvature centers. \u03b8y and \u03b8z are the angular misalignments of the inner ring, which describe the relationship between the coordinate system ( O i \u2212 x i y i z i ) and the inertial coordinate system ( O \u2212 xyz). \u03b4a , \u03b4ry and \u03b4rz are the displacements of the inner ring in the inertial coordinate system. As shown in Fig. 2 (a), the interactions between balls and raceways are not only influenced by the defect depth profile, but also influenced by the positions of ball centers. In the figure, O 1 , O 2 and O b represent the raceway groove curvature centers and the ball center respectively in the initial state. Under a given external load, the inner raceway groove curvature center moves to O \u2032 2 and the ball center moves to O \u2032 b . In the defect case, the effective outer raceway groove curvature center moves to O \u2032 1 , and O 1 O \u2032 1 denotes the effective defect depth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003482_mssp.1996.0072-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003482_mssp.1996.0072-Figure1-1.png",
        "caption": "Figure 1. Dynamic model of a pair of spur gears; for the sake of simplicity mesh stiffness, damping and error of only a single pair of meshing teeth are shown.",
        "texts": [
            " Moreover, the solution is more accurate and more reliable than solutions obtained by numerical integration or by approximate equations achieved neglecting or simplifying some terms in the equation of motion. A pair of spur gears can be modeled using two disks coupled by non-linear mesh stiffness, mesh damping and excitation due to gear errors. One disk (the driving gear) has radius R1 and mass moment of inertia I1, and the other (the driven gear) radius R2 and mass moment of inertia I2; the radii R1 and R2 correspond to the radii of the base circles of the two gears, respectively (Fig. 1). The transmission error, which is defined as the difference between the actual and ideal positions of the driven gear, is usually expressed as a linear displacement along the line of action. The sign convention used for the transmission error is positive behind the ideal position of the driven gear. If gears are analysed that have a low contact ratio o (i.e. 1Q oQ 2), so that one or two tooth pairs mesh simultaneously, the non-linear equation of motion [3, 9] for the dynamic transmission error x (m) can be written as mx\u0308+ g1(x\u0307, t)+ g2(x\u0307, t)+ f1(x, t)+ f2(x, t)=W0, (1) where x=R1u1 \u2212R2u2, m= I1I2/(I1R2 2 + I2R2 1), W0 =T1/R1 =T2/R2, (2\u20134) and for j=1, 2 fj(x, t)=6kj(t)[x\u2212 ej(t)] 0 when x\u2212 ej(t)q 0 when x\u2212 ej(t)E 0 (5) gj(x\u0307, t)=6qkj(t)[x\u0307\u2212 e\u0307j(t)] 0 when x\u2212 ej(t)q 0 when x\u2212 ej(t)E 0 (6) where fj(x, t) and gj(x\u0307, t) are the elastic and damping forces, respectively, for the meshing tooth pair j, W0(N) is the static load, m (kg) the equivalent inertia mass of the gear pair, T1 and T2 the driving and driven torques (Nm), and u1 and u2 the angular displacements (rad) of the two gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003751_s0924-0136(02)00846-4-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003751_s0924-0136(02)00846-4-Figure1-1.png",
        "caption": "Fig. 1. Five degrees of freedom model for grinding spindle.",
        "texts": [
            " The objective of the present paper is to study the effect of initial axial preload on the vibration behavior of the grinding machine spindle. A five degrees of freedom model is utilized to simulate the dynamical behavior of the grinding machine spindle. The numerical scheme presented by Aini et al. [10] and refined by Alfares and Elsharkawy [11] is implemented in the present study. Malkin\u2019s [12] experimental measurements for the grinding forces as a function of grinding wheel wear rate percentage for five different workpiece materials are used to simulate external loading on the grinding machine spindle. Fig. 1 shows a schematic representation of a grinding machine spindle supported by a pair of angular contact ball bearings. The bearings are identical and in a back-to-back configuration. The degrees of freedom are three translations Nomenclature a0 distance from the center of gravity to the position of the applied grinding forces (m) a1 distance between the left bearing and the center of gravity (m) A distance between centers of curvature of inner and outer race grooves (m) b1 distance between the right bearing and the center of gravity (m) Cd bearing diameteral clearance (m) DCd radial interference (m) d bearing pitch diameter (m) di inner race diameter (m) do outer race diameter (m) D ball diameter (m) E Young\u2019s modulus (N/m2) Fx(t) grinding force component in the x-direction (N) Fy(t) grinding force component in the y-direction (N) Fz(t) grinding force component in the z-direction (N) g acceleration of gravity (m/s2) I moment of inertia (kg m2) K total stiffness coefficient per ball (N/m3/2) ms mass of the shaft (kg) mg mass of the grinding wheel (kg) M total mass, M \u00bc ms \u00fe mg (kg) n number of balls in a bearing set Pr axial preload (N) r radii of curvature of bearings rings (m) t time (s) W load per ball (N) x, y, z Cartesian coordinate set (m) X, Y, Z displacements along x, y, z (m) Greek letters a contact angle (rad) ap preload contact angle (rad) a0 unloaded contact angle due to interference fit of bearings (rad) d elastic deflection at each contact (m) y ball center angular displacement n Poisson\u2019s ratio f rocking motion of spindle about x-axis (rad) F rocking motion of spindle about y-axis (rad) O angular velocity of the spindle (rpm) Oc cage set angular velocity (rpm) Subscripts i left hand bearing counter ir inner race j right hand bearing counter L left hand bearing or outer race R right hand bearing 0 initial conditions Superscripts "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.7-1.png",
        "caption": "Fig. 2.7: Frame Relations",
        "texts": [
            " To give an example: for unilateral contact problems it makes sense to represent the surface coordinates of the bodies in a parametric form (see Figure 2.6 and chapter 2.2.6): r = x(u, v) y(u, v) z(u, v)  (2.4) The basic elements of kinematics are translation and rotation. In addition, and mostly confined to special cases, we have projections and reflections (see for 2.2 Kinematics 15 example [3] and [155]). We shall focus on the first two movements. Considering mechanical systems requires a precise and unique definition of coordinate frames. In the following we shall use an inertial base I, and several body-fixed bases B or Bi and R or Ri (Figure 2.7). A vector v is a component of the vector space V, v \u2208 V, and it can be represented in any of the mentioned coordinate systems. From the standpoint of dynamics it is convenient to describe mechanical systems in different frames, and therefore we need a transforma- tion from one frame to any other one. From Figure 2.7 we easily can describe the vector chain in a coordinate-free form rIRi = rIBi + rBiRi , (2.5) where the indices (I, Ri, Bi) stand for the origins of the bases and for the bases themselves. The property of the necessary coordinate transformation can be nicely illustrated by the transformation triangle, which relates graphically the representation in different coordinate systems (see Figure 2.8). We apply for these representations the convention: KI(v) = Iv \u2208 IR3, KB(v) = Bv \u2208 IR3, KR(v) = Rv \u2208 IR3",
            " The complete transformation matrix is then the result of the above successive rotations. We come out with: AIB = AI,\u03b1Ainter,\u03b2AB,\u03b3 =( cos \u03b2 cos \u03b3 \u2212 cos \u03b2 sin \u03b3 sin\u03b2 cos\u03b1 sin\u03b3 + sin\u03b1 sin\u03b2 cos \u03b3 cos\u03b1 cos \u03b3 \u2212 sin\u03b1 sin\u03b2 sin\u03b3 \u2212 sin\u03b1 cos \u03b2 sin\u03b1 sin\u03b3 \u2212 cos\u03b1 sin\u03b2 cos \u03b3 sin\u03b1 cos \u03b3 + cos\u03b1 sin\u03b2 sin\u03b3 + cos\u03b1 cos \u03b2 ) (2.19) With the knowledge of the coordinates and coordinate transformation we have established a basis for deriving the expressions for velocities and for accelerations in the various possible coordinate systems. Let us first go back to Figure 2.7 and simplify this figure a bit for our purposes (see Figure 2.13). We go from the I-system into the B-system, or vice versa, and we consider in both systems the coordinates of the point P. The translation follows from that Figure by rOP = rOQ + rQP . (2.20) According to chapter 2.2.2 the rotation of coordinate system B with respect to I can be described by the matrix ABI , if we go from I to B and by AIB , if we go from B to I. Applying this matrix we can express the coordinates in one frame by those in the other frame, for example Ir =AIB Br Br =ABI Ir, (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003791_3477.662755-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003791_3477.662755-Figure5-1.png",
        "caption": "Fig. 5. The five rotational DOF robot.",
        "texts": [
            " Equation (35) is the sum of the vectors representing the lengths and the offsets of the links. Since the vectors are the unit vectors defining the orientation of the and axis, respectively, the unit vector of the axis of the last coordinate system is calculated by the vector product of the and vectors, as is shown in (36). To illustrate the application of the algorithms and for better understanding of the physical significance of the transformation parameters, the kinematic equations for a five degree of freedom articulated robot have been formulated. The robot shown in Fig. 5 has five rotational degrees of freedom. The local coordinate system and the parameters of each link have been defined according to D\u2013H notation. The formulation of the kinematic equations of a robot based on homogeneous transformation can be found in any robotics text book, therefore it is not presented in this paper. Following the second algorithm the formulation of the kinematic equations of the five degree of freedom robot starts by the calculation of the vectors by replacing the link parameters from Table II in (14)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000500_j.jmatprotec.2020.116906-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000500_j.jmatprotec.2020.116906-Figure10-1.png",
        "caption": "Fig. 10. Triaxial melt tracks and microstructure of SLMed maraging steel in milling: (a) ABT sample, (b) ABS sample, (c) relationship between feed force direction and melt tracks for ABT, (d) relationship between transverse force direction and melt tracks for ABT, (e) relationship between feed force direction and melt tracks for ABS, and (f) relationship between transverse force direction and melt tracks for ABS.",
        "texts": [
            " (2017) also found that the cutting force was higher when milling the additively manufactured 316L steel parts with building direction of 0\u25e6 (corresponding to the ABT in this study) than that of the parts with building direction of 90\u25e6 (corresponding to the ABS in this study). From Fig. 4, the microstructure of the ABT and ABS samples is different. The former features cellular structures and the latter consists of a large number of strip structures, which can lead to different effects on the cutting forces. To further investigate the difference in cutting forces between ABT and ABS samples, the microstructure and melt track morphologies contacting the cutting tool were analyzed in detail, as shown in Fig. 10. It can be seen that the feed direction is simultaneously perpendicular and parallel to the melt tracks when milling ABT sample (as shown in Fig. 10c) comparing to that only perpendicular to the melt tracks when milling ABS sample (as shown in Fig. 10e). Because breaking the material along melt tracks is more difficult than that vertical to melt tracks, the feed force of milling ABT sample is a slightly higher. The transverse directions for milling both ABT and ABS samples are simultaneously perpendicular and parallel to the melt tracks, as shown in Fig. 10d and f. Therefore, the transverse force values are almost the same. As for the higher axial force for the ABT sample than that for the ABS sample, it is due to the higher hardness of the ABT sample, resulting in difficult deformation of the ABT sample along the building direction. In addition, the higher yield strength along building direction than that vertical to the building direction also leads to the increase of ability to resist deformation for the ABT sample. As reported by Suryawanshi et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003429_cvpr.1991.139677-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003429_cvpr.1991.139677-Figure1-1.png",
        "caption": "Fig. 1. The displacement of a rigid object from one position to another can be described as a screw motion.",
        "texts": [],
        "surrounding_texts": [
            "LA1 and LA2 intersect at a point or LAC is parallel to LA2. The latter cannot happen because we know O A l r which is twice the angle between P, , and P I 2 161, is nonzero. Therefore, LAe is well-defined. Finally, L A is not perpendicular to LA2 as long as O A l # a. In summary, for the alternative approach to work, it is required that O A 1 # a and LAl and LA2 do not intersect. When this is not true, there exist two solutions for R x but a unique solution for tx.\n4 ) LA1 and LA2 are both ambiguous. That is, d A 1 = d A 2 = 0 and OA, = O m = a. In this case, L A is perpendicular to LA, and LA2 (Fig. 6). As a result, the sign ambiguities of LA1 and LA2 cannot be resolved no matter whether LAC is well-defined or not. Therefore, there exist two solutions for R x . If LA, is not parallel to LA2, tx has a unique solution; otherwise tx has one degree of freedom.\nSimilar to Case 1, we have RAC = RA1 and tx = tA1 + tA2. Thus the screw axis LAC is parallel to LA, and is welldefined if tA2 . nAl # 0. In this case the angular constraint can be applied (as in Case 3) to fix the signs to LA1 and LB1; thus, R x can be uniquely determined and tX has one degree of freedom. When tA2.nAl= 0, both LA, and L& are ambiguous and consequently R x has two solutions. When tA2 is parallel to LAI, A, becomes coaxial with A,; the problem cannot be solved.\n6. Conclusion\nThe aim of this paper was to demonstrate the use of screw theory for motion problems. The screw motion is a unique description of rigid transformations. We have exploited the strengths of the screw motion description for head-eye calibration. We have shown that the rotational and translational parameters should not be decoupled, for otherwise the generality and efficacy of the resulting algorithm would be adversely affected.\nWe have proved that the rotation angle and the screw translation are invariant with respect to coordinate transformation, and that the problem can be solved by finding the rigid transformation that aligns the camera screw axes with the corresponding robot screw axes. The screw congruence theorem derived here can be used to compute the head-eye transformation, to verify the correspondence between robot and camera motions, and to resolve the sign ambiguity of screw axes.\nFor well-defined screws, we have shown that the necessary and sufficient condition of a uniqueness solution for the head-eye geometry is that the screw axes of two robot motions are either skew or intersecting lines. For undefined or ambiguous screws, we have shown that a partial solution or even a complete solution may be obtained by investigating the screw geometry of composite motion. The screw motion theory has been considered mathematically elegant but of no practical use Ill]. To the contrary, we found it extremely useful. We hope that the work reported here will inspire more\n5) LA1 is ambiguous, LA2 is undefined.\nthoughts on the use of screw theory for motion research.\nAcknowledgements\nThe author wishes to thank Prof. Berthold Horn at MIT for bringing the ==XI3 (X unknown) problem to his attention. He would also like to thank Dr. Kicha Ganapathy for his interest in this work.\nReferences\nR. S . Ball, A Treatise on the Theory of Screws, Cambridge Univ. Press, 1900. M. K . Bartschat, \u201cAn automated flip-chip assembly technology for advanced VLSI packaging,\u201d Electronic Components Conference, 1988, 335-341. 0. Bottema and B. Roth, Theoretical Kinematics, Elsevier North-Holland, 1979. M. Chasles, \u201cNote sur les proprigtes g6ne\u2018rales du systBme de deux corps semblables entre eux, places d\u2019une maniBre quelconque dans l\u2019espace; e t sur le dkplacement fini, ou infiniment petit d\u2019un corps solide libre,\u201d Bulletin des Sciences Math Cmatiques d e Firussac, XJV, 1831, 321-326. H. H. Chen, \u201cMotion and depth from binocular orthographic views,\u201d Proc. Second Int\u2019l Conf. Computer vision, 1988, 634-640. H. H. Chen, \u201cScrew triangle and its applications for motion vision,\u201d in preparation. H. H. Chen, \u201cPose determination from line-to-plane correspondences: Existence condition and closedform solutions,\u201d to appear in IEEE Trans. Pattern Analysis Machine Intell. J . Chou and M. Kamel, \u201cQuaternions approach to solve the kinematic equation of rotation, A,A, = A,Ab, of a sensor-mounted robot manipulator,\u201d Proc. IEEE Int\u2019l Conf. Robotics Automat., 1988, 656-662. F. M. Dimentberg, The Screw Calculus and Its Applications in Mechanics, (in Russian), Moskow, 1965, (English translation: AD 680993, National Technical Information Service, Virginia).\n- I\n[lo] M. A. Fischler and R. C. Bo\u2019lles, \u201cRandom sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography,\u201d Comm. ACM, vol. 24, no. 6, 1981,\n1111 H Goldstein, Classical Mechanics, 2nd ed., Addison-Wesley, 1980. (121 R. Horaud, B. Conio, and 0. Leboulleux, \u201cAn analytic solution for the perspectlve 4-point problem,\u201d Computer Vision, Graphics, and Image Processing, vol. 47, 1989, 33-44.\n381-395.\n1131 B. K . P. Horn, Robot Vision, MIT Press, 1986. (141 Y. Hung, P-S. Yeh, and D. Harwood, \u201cPassive\nranging to known planar point sets,\u201d Proc. IEEE Int\u2019l Conf. on Robotics and Automat., 1985, 80-85. (151 Y. Liu, T. S. Huang, and 0. D. Faugeras, \u201cDetermination of camera location from 2-D to 3-D line and point correspondences, IEEE Trans. Pattern Analysis and Machine Intell., vol 12, no. 1, 1990, 28-37.",
            "1161 Y. C. Shiu and S. Ahmad, \u201cFinding the mounting position of a sensor by solving a homogeneous transform equation of the form AX=XB,\u201d IEEE Trans. Robotics and Automat., vol. 5, no. 1, 1989,\n1171 G. Strang, Linear Algebra and Its Applications, 3rd ed., Harcourt Brace Jovanovich, 1988. 1181 R . Y. Tsai, \u201c A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenzes,\u201d IEEE J . Robotics and Automat., vol. RA-3, no. 4, 1987, 323-344. 1191 R. Y. Tsai and R. K. Lenz, , \u201cReal time versatile robotics hand/eye calibration using 3D machine vision,\u201d Proc. IEEE Int\u2019l Conf. Robotics Automat., Philadelphia, PA, 1988, 554-561. 1201 J. S.-C. Yuan, \u201c A general photogrammetric method for determining object position and orientation,\u201d IEEE Trans. Robotics and Automat., vol. 5, no. 2,\n16-29.\n1989, 129-142."
        ]
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.42-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.42-1.png",
        "caption": "Fig. 6.42: Contact between Link and Sprocket",
        "texts": [
            " J\u2217 G = ( E3\u00d73,\u2212r\u0303K ) , J\u2217 L = ( E3\u00d73,\u2212Rrollerplaten\u0303 ) wG\u03bb = QT GJ \u2217T G ( n\u2212 vrel |vrel| \u00b5t ) \u03bb, wL\u03bb =\u2212QT LJ \u2217T L ( n\u2212 vrel |vrel| \u00b5t ) \u03bb. (6.102) Contact between a Sprocket and a Link Regarding the contact between a sprocket and a link we achieve very simplified relations for the normal velocity and acceleration. Due to the fact that the toothing contour is composed of circles, it is sufficient to consider the center of these contour circles. For this purpose we use the vector d from the reference point HL to the contour center MK (Figure 6.42). Applying the radius RK of the contour in the contact areas, according to Figure 6.34 with RK,toothprofile = RTP and RK,seatingcurve = \u2212RSC , the distance vector rD results in rD =d\u2212 nRK , r\u0307D =d\u0307+ RKtb T\u2126S , r\u0308D =d\u0308+ RKn(bT\u2126S)2 + RKtb T \u2126\u0307S (6.103) After some transformations the equations (6.98), (6.99) and (6.100) can be written as gn = nTd\u2212RK , g\u0307n = nT d\u0307, g\u0308n = nT d\u0308+ ( tT d\u0307 )2 nTd . (6.104) Contact Configuration For establishing the complementarities we have to evaluate forces and accelerations, which characterize the relevant contact configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003688_b003483p-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003688_b003483p-Figure2-1.png",
        "caption": "Fig. 2 Cyclic voltammograms of chitosan HRP modified enzyme electrode in 0.02 M deoxygenated phosphate buffer (pH 7.0) containing 1 mM hexacyanoferrate(II). (a) Without and (b) with 0.93 mM H2O2. Scan rate 5 mV s21.",
        "texts": [
            " The improved electrode response in the presence of glutaraldehye could be due to the cross-linking reactions between the amino groups of chitosan and the aldehyde group of glutaraldehyde, and amino groups of HRP enzyme and the aldehyde group of glutaraldehyde. HRP enzyme and chitosan could not be cross-linked directly except via the glutaraldehye acting as a \u2018bridge\u2019. This cross-linked film matrix may provide a high enzyme loading, and a stable film matrix for enzyme immobilization.19\u201321 Thus leading to less leakage of enzyme from the biosensor surface. Fig. 2 shows the cyclic voltammogram of the enzyme electrode in an unstirred 0.02 M deoxygenated phosphate buffer (pH 7.0) containing 1 mM hexacyanoferrate(II). Without H2O2, the HRP electrode only gives the electrochemical behaviour of hexacyanoferrate(II) in solution [Fig. 2 (a)]. There is a pair of quasi- 1592 Analyst, 2000, 125, 1591\u20131594 D ow nl oa de d by U ni ve rs ity o f A ri zo na o n 16 D ec em be r 20 12 Pu bl is he d on 0 4 A ug us t 2 00 0 on h ttp :// pu bs .r sc .o rg | do i:1 0. 10 39 /B 00 34 83 P reversible anodic and cathodic waves. In the presence of 0.93 mM H2O2, the cathodic peak current increased significantly [Fig. 2 (b)]. This indicates that H2O2 oxidizes hexacyanoferrate(II) to hexacyanoferrate(III) in the presence of HRP, and the hexacyanoferrate(III) is subsequently reduced at the surface of the electrode. In the absence of hexacyanoferrate(II) in the phosphate buffer, no observable response was seen when H2O2 was added. Thus, no direct electron transfer between HRP immobilized in cross-linked chitosan film and CPE was observed. The effect of applied potential on the biosensor response is shown in Fig. 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000349_tec.2020.2995902-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000349_tec.2020.2995902-Figure12-1.png",
        "caption": "Fig. 12. Flux density distribution of SPM motors calculated by FEA. (a) Motor A. (B) Motor B. (c) Motor C.",
        "texts": [
            " To validate the proposed analytical model, two 4-pole/18slot SPM motors (Motor A and Motor B) and one 8-pole/36slot SPM motor (Motor C) are analyzed by FEA and the proposed method. The main parameters of Motor A are the same as those in Table I, and the parameters of Motor B and Motor C are listed in Table II. The nonlinear B-H curves of the core materials are shown in Fig. 11. Motor A and Motor B have similar parameters, except the direction of magnetization and the length of air-gap. Motor A has a smaller air-gap length than Motor B, so they have different levels of saturation. Fig. 12 shows the flux density distribution of the motors with both rotor eccentricity (e=0.5mm) and magnet defects (\u0394Br =0.1T, \u0394\u03b1p=0.05, \u0394\u03c4=0.5\u00b0) calculated by FEA, it is observed that Motor A has the most severe saturation degree, followed by Motor B, and the saturation degree of Motor C is the lightest. The air-gap flux densities under open-circuit condition calculated by the analytical model are compared with the FEA results. To show the effect of saturation, the FEA calculations are performed for both linear and nonlinear permeability cores",
            " In addition, with the increase of saturation degree of the motor, the amplitude difference of the radial air-gap flux density calculated by the nonlinear and linear model will also increase. It can be seen from Fig. 13 that without considering the core nonlinearity, the maximum errors of the amplitude of air-gap flux density for the SPM motors are 8.7%, 4.2% and 3.4%, respectively, which shows that Motor A has the most severe saturation degree and the saturation degree of Motor C is the lightest. This conclusion is consistent with the calculation results shown in Fig. 12. The cogging torque calculated by the analytical model is compared with the FEA results. Fig. 14 shows the cogging torque waveforms over a pole pitch of the SPM motors with both rotor eccentricity (e=0.5mm) and magnet defects (\u0394Br =0.1T; \u0394\u03b1p=0.05; \u0394\u03c4=0.5\u00b0). It is observed that the cogging torque waveform calculated by the analytical model and FEA has the same variation trend, but the error also exists. The comparison of the maximum values of cogging torque calculated by FEA and the analytical model is shown in Table III"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001038_j.mechmachtheory.2021.104352-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001038_j.mechmachtheory.2021.104352-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems and multi-body interactions:(a) bearing components;(b) cage-guiding surface interaction;(c) inner ring and shaft;(d) ball-pocket interaction;(e) cage.",
        "texts": [
            " In particular, instead of using the displacement excitation function as the previous dynamic models, the model in this study considers the localized defect effects in the geometrical constraint relationships. By solving the multi-DOF dynamic model with these considerations, the localized defect with different sizes and at different positions in angular contact ball bearing will be considered in detail. After the comprehensive analysis, the influence of the defect on the dynamic behaviors of the bearing will be finally studied. To describe the motions of all the movable components in the dynamic system, seven coordinate systems are defined as shown in Fig. 1 . The inertial coordinate system ( O \u2212 xyz) is fixed at the center of the outer race, which is considered as a fixed body. In this coordinate system, the x axis is along the outer ring axis and the ball position angle \u03d5 j is determined. The azimuth coordinate system ( O b \u2212 x b y b z b ) is established on the ball center to model the motions of six freedom degrees. The body-fixed coordinate systems ( O i \u2212 x i y i z i ) and ( O c \u2212 x c y c z c ) are set up for the inner ring and the cage respectively, which are coincident with the principal axes of the elements",
            " 5 d+ \u03b4oj , cos \u03b1oj = X r j \u2212d ( \u03d5 j ) \u00b7cos \u03b10 r o \u22120 . 5 d+ \u03b4oj (5) Under high speed, the ball-pocket interaction and the cage-guiding surface interaction count a lot in the dynamic system. During the time between the defect entry and exit events, the abrupt changes in load and friction between balls and raceways will also change the cage performance, thus in turn affecting the dynamic characteristics of other components. To investigate the motions of cage, two coordinate systems are established on the cage center as shown in Fig. 1 . The cage coordinate system ( O c \u2212 x g y g z g ) is employed to consider the cage-guiding surface interaction and the body-fixed coordinate systems ( O c \u2212 x c y c z c ) is employed to describe the ball-pocket interaction. In the transverse plane, the moving cage with the rotation speed \u03c9 c is supported by the oil film between the cage land and the guiding surface ( Fig. 3 ). The relative movements between the interacting surfaces not only result in the oil film pressure, but also lead to the friction moment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-11-1.png",
        "caption": "Figure 4-11. Space vector trajectories of nonoptimal (upper patterns) and optimized modulation techniques (lower patterns): (a) and (c) current trajectories; (b) and (d) stator flux trajectories.",
        "texts": [
            "5, while the flux linkage vector is derived from the measured phase voltages by subsequent integration. The flux linkage trajectory is erroneous at lower fundamental frequency since the voltage drop across the winding resistance is normally neglected. The harmonic content of a steady-state trajectory is observed as the deviation from its fundamental component, with the fundamental trajectory describing a circle. Although deviations in amplitude are easily discernible, differences in phase angles have equal significance. The example in Figure 4-11 demonstrates that a nonoptimal modulation method, Figures 4-1 l a and 4-1 lb , produces both higher deviations in amplitude and in phase angle as compared with the respective optimized patterns shown in Figures 4-1 lc and 4-1 Id. 152 4. Pulse Width Modulation for Electronic Power Conversion The modulation index is the normalized fundamental voltage, defined as m = \u2014 \u2014 (4.22) Ml six-step where u\u00a1 is the fundamental voltage of the modulated switching sequence and u\\ six-step = 2\u03b9/(//\u03c0 the fundamental voltage at six-step operation",
            " A set of switching angles that minimize the harmonic current (d -> min) is shown in Figure 4-34. Figure 4-35 compares the performance of a d -> min scheme at 300 Hz switching frequency with the suboscillation method and the space vector modulation method. The improvement of the optimal method is due to a basic difference in the organization of the switching sequences. Such sequences can be extracted from the stator flux vector trajectories Figure 4-1 lb and Figure 4-1 Id, respectively. Figure 4-36 compares the switching sequences that generate the respective trajectories in Figure 4-11 over the interval of a quarter cycle. While the volt-second balance over a subcycle is always maintained in space vector modulation, the optimal method does not strictly obey this rule. Repeated switching between only two switching-state vectors prevails instead, which indicates that smaller volt-second errors, which needed correction by an added third switching state, are left to persist throughout a larger number of consecutive switchings. This method is superior in that the error component that builds up in a different spatial direction eventually reduces without an added correction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure4.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure4.11-1.png",
        "caption": "Fig. 4.11",
        "texts": [],
        "surrounding_texts": [
            "universal unfolding G of g is topologically equivalent under a small perturbation, that is the bifurcations have a generality. These bifurcation diagrams are considered persistent. But for other value of a, the bifurcation diagram of G would change its property under a small perturbation, that is, the bifurcation is degenerate. These bifurcation diagrams are considered non-persistent. We point out that non-persistent sets or transition sets in unfolding parameter space are of three cases: bifurcation point set, hysteresis set and double limit point set. Thus we put forward the following four definitions. Definition 4.16 Let G:;e x;e x ;ek ~ ;e be a universal unfolding of g:;e x ;e ~ ;e . Then we can define: a) bifurcation point set B = {a E;ekI3(x,A) E;e x;e such thatG = Gx = G, = 0 at (x,A,a)} b) hysteresis set H= {a E;ekI3(x,A) E;eX;e, such that G=Gx =Gxx =0 at (x,A,a)} c) double limit point set D = {a E;ek 13(x1'X2 ,A) E;e x ;e X ;e,Xj oF- x2 such that G = xGx = 0 at (x, ,A,a),i = 1,2} d) transition set L = B U H U D . The transition set is the set of unfolding parameters corresponding to the non-persistent bifurcation diagrams of G(x,A,a). It is a hyperplane in ;ek. The transition set includes three cases: the bifurcation, hysteresis and double limit point set. When we consider only small perturbations, or we restrict the parameter in the neighbourhood 11/ of ;ek, the transition set divides parameter space into several regions, in which diagrams of G are persistent. Consequently we can obtain all the perturbed bifurcation diagrams SUbjected to a small perturbation. Example 16. Consider the perturbed bifurcation diagrams of h(X,A) = x 3 - Ax. Suppose H is a universal unfolding of h: H(x,A,a,p) = x 3 - Ax + a + px 2 . Since Hx = 3x 2 - A +2px, H, = -x, Hxx = 6x +2P then B = {a = A}, H = {a = \u00a3}, D = ~ and transition set = L= BUH. 27 Figure 4.10 gives all the curves of I which divides: the parameter space into four regions and the diagrams on each region and I. All the singular points of equation H = 0 are limit points but not double limit points. The bifurcation diagram has the bifurcation point on the bifurcation point set B and the hysteresis point on the set H. Liapunov-Schmidt Reduction We now return to the Euler buckling equation. 117 Example 17 If the weight of the structure and the non-symmetry of the spring are taken into consideration in example I, two parameters E and () should be introduced. Suppose that the system is in the static state. Now consider the static bifurcation. The potential energy of the system is written as - 1 2 V(x,A.,E,8) = -(x-8) e2A.(cosx-l)+Esinx 2 and the static state is described by the following equation We can identify eq. (4.62) as the perturbation of eq. (4.46). Expanding G(x,A.,E,8) at (x,A.) = ( o,~) , we have 118 Bifurcation and Chaos in Engineering 1 3 1 2 1 G(X,A,E,8) = --x + -EX + 2(A - -)x + (8 - E) + hot 6 2 2 (4.63) Now introduce the transfonnation X 3~ E Y=--, J.l=v6(1-2A), a=8-E, p=--V6 2V36 and we have (4.64) Since we need to consider the diagrams only in the neighbourhood of the origin, the higher tenns in H can be omitted. That means we only need study the bifurcation diagrams of the equation / - AY + a + pi = 0 which is the universal unfolding of l- Ay. The diagrams of this equation are shown in Fig. 4.10. Returning to the parameters E and 8, we can obtain the diagrams of the original system. To end this section we give some notes as follows: 1) If the generality of the diagrams is taken into consideration, we know that the diagrams of G are generate if a ~ L, and degenerate if a E L / {a} with the degenerate degree less than a = o."
        ]
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.2-1.png",
        "caption": "Fig 7.2",
        "texts": [
            "3 The Geometric Description of The Averaging Method Consider a two-dimensional system x\u00b7 +co~x = Eg(X,X') E\u00ab 1 (7.55) Using the method of the first part of this chapter, and taking the transformation x = acoscp y = -acoo simp (7.56) where a and cp are functions in t, the averaging equation of the first approximation is 242 Bifurcation and Chaos in Engineering cia E \u00a3x( . ). d - = --- g a cos <p,-aID 0 sm<p sm<p <p dt 21tIDo d<p =IDo __ E_ rg(acos<p,-aIDosin<p)cos<pd<p dt 21tID oa .t. (7.57) Next, we will give the geometric explanation. See Fig. 7.2. The coordinate of phase point P on the phase plane (x,y = ;J is (x,y). The coordinate on the rotating phase plane c; with an angular speed IDo is (c;, TJ), so c; = acos9, TJ = -asin9, 9 = <p-IDot Point P will also draw the relevant track. The differential equation in polar coordinate (a,9) is da = _~ g(acos(IDot + 9),- aID 0 sin(IDot + 9)) sin(IDot + 9) dt IDo d9 = --E-g(acos(IDot +9),- aID 0 sin(IDot + 9)) COS(ID ot +9) dt aID 0 These are non-autonomous equations on the plane c; . Generally speaking, the track can be self-transversal on the plane c; "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure5-1.png",
        "caption": "Fig. 5. Rounded top of the shaper tooth.",
        "texts": [
            " The tooth length of the face-gear has to be limited by dimensions L1 and L2 (Fig. 4) to avoid undercutting that occurs in plane A, and tooth pointing in plane B [8]. A unitless coefficient c defines the tooth length and is represented as c \u00bc L2 L1 m \u00f01\u00de Coefficient c depends on the gear ratio and other design parameters (see Section 3). The face-gear tooth surface has a fillet (Fig. 3(a)) that might be generated by (i) the edged top of the shaper tooth, or (ii) a rounded top of the shaper tooth (Fig. 5). Investigations show that application of a shaper with a rounded top enables the bending stress to be reduced by 12% (see Section 8). TCA is designated for simulation of meshing and contact of surfaces R2 and R1 and enables the influence of errors of alignment on transmission errors and shift of bearing contact to be investigated (see Section 6). The advantage of the involute face-gear drive is that errors of alignment do not cause transmission errors [8]. However, the path of contact of the involute face-gear drive is oriented along the surface cross-section, and errors of alignment cause the shift of the bearing contact as shown in Fig",
            " Step 4: Knowing wr, it is easy to get the unit normal to the shaper determined as ns\u00f0wr\u00de and then determine the unit normal to the worm surface determined as nw\u00f0wr;ww\u00de \u00bc Lws\u00f0ww\u00dens\u00f0wr\u00de \u00f033\u00de Step 5: The data (xw; yw; zw; nw) is sufficient for the installment of the tool (a plane or a disk) using a CNC machine. The goals of stress analysis represented in this section are: ii(i) Comparison of contact and bending stresses of two versions of geometry of face-gear drives: of existing and proposed geometry. i(ii) Comparison of bending stresses of two versions of face-gears: with edged and rounded top (Fig. 5). (iii) Determination of contact and bending stresses and investigation of formation of the bearing contact during the cycle of meshing. The performed stress analysis is based on finite element method [24] and application of general purpose computer program [5]. Finite element method [24] requires the development of a finite element mesh, definition of slave and master contacting surfaces and establishment of boundary conditions. The authors\u2019 approach for application of finite element analysis has the following advantages: (a) The generation of finite element models is performed automatically by using the equations of the tooth surfaces and taking into account the corresponding fillets and portion of the rim",
            " (c) Finite element models are developed numerically at the chosen contact point of the path of contact. Stress convergence is assured because there is at least one point of contact between the contacting surfaces. (d) Finite element models of three pairs of teeth are applied and therefore the boundary conditions are far enough from the loaded areas of the teeth. Finite element analysis has been performed for the two versions of face-gear drives represented in Tables 1 and 2. For the second version of face-gear drive, it has been also considered the application of a rounded top shaper (Fig. 5), in order to compare the bending stresses at the fillet of the generated face-gear. The finite element mesh of three pair of teeth of version 2 is represented in Fig. 24. Elements C3D8I [5] of first order, enhanced by incompatible nodes to improve their bending behavior, have been used to form the finite element mesh. The total number of elements is 44820 with 58327 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives",
            " 25 and 26 show the maximum contact and bending stresses obtained at the mean contact point for the existing and the proposed geometry, respectively. For such examples a traditional edged-top shaper has been applied. Comparison between Figs. 25 and 26 shows that: i(i) Edge contact can be avoided, reducing the magnitude of the maximum contact stress to 40%. (ii) For a considerable part of the cycle of meshing only one pair of teeth is in contact. The max- imum bending stress at the fillet of the existing geometry of face-gear is 43% lower. Fig. 27 confirms that application of a rounded-top shaper (Fig. 5) reduces the bending stresses of the face-gear from 6% to 12% during the cycle of meshing. This enables us to keep the increment of the bending stresses for the proposed geometry less than 40%. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs. 28 and 29). Figs. 28 and 29 illustrate the variation of bending and contact stresses of the face-gear and the pinion during the cycle of meshing for face-gear generated with an edged-top shaper and a rounded-top shaper, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure13-1.png",
        "caption": "Fig. 13. Illustration of simultaneous meshing of shaper, worm, and face gear.",
        "texts": [
            " 10) is the shortest distance between the axes of the shaper and the worm. The magnitude of Ews affects the dimensions of the grinding worm and the conditions of avoidance of surface singularities of the worm (see below). The meshing of the worm and the shaper is schematically illustrated in Fig. 12. 3.3. Analytical consideration of simultaneous meshing of surfaces Rs, Rw, and R2 Designations Rs, Rw, and R2 indicate surfaces of the shaper, worm, and face gear, respectively. Simultaneous meshing of Rs, Rw, and R2 is illustrated in Fig. 13. Shaper surface Rs is considered as a given generating one. Surfaces Rw and R2 are generated as the envelopes to the family of a shaper surface Rs. Step 1: Shaper surface Rs is represented as an involute surface of a spur gear (Fig. 14) determined by the equations xs \u00bc rbs\u00bdcos\u00f0hs \u00fe gs\u00de \u00fe hs sin\u00f0hs \u00fe gs\u00de ; ys \u00bc rbs\u00bd sin\u00f0hs \u00fe gs\u00de hs cos\u00f0hs \u00fe gs\u00de ; zs \u00bc us: \u00f05\u00de Here us and hs are surface parameters; parameter gs determines half of the width of the space on the base cylinder; rbs is the radius of the base cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.65-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.65-1.png",
        "caption": "Fig. 5.65: Simplified Impact Velocities",
        "texts": [
            " It undergoes a velocity jump leading to the impact at the entrance or the exit of the pulley. Assuming that the entering (or leaving) pin possesses the same velocity as the initial (end) point of the polygon course, we can write the components of the velocity changes as \u2206vimpact,t,r = 2r\u03c9R sin \u03d5G 2 cos \u03d5G 2 cos\u03d1, \u2206vimpact,t,a = 2r\u03c9R sin2 \u03d5G 2 , \u2206vimpact,n = 2r\u03c9R sin \u03d5G 2 cos \u03d5G 2 sin\u03d1. (5.105) 5.4 CVT Gear Systems - Generalities 281 The indices n, t, r, a stand for normal, tangential, radial and azimuthal directions, respectively, see Figure 5.65. The impact velocity \u2206vimpact comprises normal and tangential components with respect to the pulley surface, of which the tangential radial part includes also an axial component due to the cone angle of the pulley. Both, the azimuthal and the radial velocity components, generate a frictional impact, where the azimuthal component \u2206vimpact,t,a accelerates the chain link, and the radial component \u2206vimpact,t,r decelerates it. Additionally we have a velocity component \u2206vimpact,n perpendicular to the pulley surface, which represents a normal impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.46-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.46-1.png",
        "caption": "Fig. 16.46 Cornering property and vehicle motion at a small slip angle",
        "texts": [
            " CRCF is the conicity component of RCF, and CRAT is the conicity component of RAT, which is related to the manufacturing process. (2) Residual lateral force and moment for a vehicle axle The previous section discussed vehicle pull only in terms of the properties of the tire whereas this section discusses vehicle pull in terms of the axle force and moment of the vehicle, which is the summation of forces and moments of left and right tires. When the driver grips the steering wheel to drive a vehicle straight ahead, the lateral force of the axle is zero and the torque RAT is generated at a2 as shown in Fig. 16.46a. To keep the vehicle moving straight, the driver needs to provide a torque around the king-pin shaft to balance RAT of the front axle. Meanwhile, when a vehicle is driven hands free, the torque around the king-pin shaft is zero and RCF is generated at a1 for the front axle, as shown in Fig. 16.46b. The vehicle starts turning because of this RCF and then changes from a transient state immediately after hands-free driving to a steady state. In the steady state, the lateral force of the front axle is RCF, while the lateral force of the rear axle is Lf/ Lr RCF, where Lf and Lr are, respectively, distances between the center of gravity of the vehicle and the front and rear axles. Note that the contribution of RCF of the front axle to the vehicle pull is greater than that of the rear axle as we will discuss later"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003794_robot.1991.131747-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003794_robot.1991.131747-Figure3-1.png",
        "caption": "Figure 3: 3-wheels example",
        "texts": [
            " The component of this velocity in the plane of the wheel is : [ - s i 7 ~ ( 0 + P + 7) ; COS(& + P + 7) ; dcosy + Icos(P + -y)]lz(tr)i + dcosyb + R$ (6) and the component orthogonal to the wheel : (7) [cos(u + p + y) ; sin(cr + p + y) ; dSi71-1 + ISZlZ(P + y)]R(d) i + dSi?Zyb where R(6') is a ( 3 x 3) orthogonal rotatioil matrix : [ ',\" si;$ ; R(6') = -si,n@ cos0 0 ) (8) These expressions will be used in the next sections to explicit the pure rolling and non slipping conditions. 2.3 Generalized coordinates We use a lower index notation to identify the quantities relative t,o ea.ch wheel. Throughout the paper, we sha.11 examine in more details the particular case of %wheels robots represented in Fig. 3 : the 2 front wheels (index 2 and 3) have a fixed orientation while the orientation of wheel 1 is varying. The theory is easily extended to robots with an arbitrary number of wheels (see [4]). According to our previous description, the geometry of the wheels is completely described by the following set {Ri, l i , 4 , ai, 71, P t , 4i ; i = 1 , ' . . , 3 ) The reference poiiit Q is tlie center of the segment BzB3 (see Fig. 3). The Insis vector X I is aligued with BZB3. The geometric characteristics are : 37r Wheel 1 : R1 = R, 11 = L , dl = d , cy1 = T, P1 = P , 71 = E . 2 L Wheel 2 : Rz = R, 12 = L , $2 = 0 , a2 = 0, p2 = 0, yz = 0. Wheel 3 : p3 = 0 , 73 = 0. R3 = R, 13 = L , d3 = 0 , a3 = T , The robot motion is then completely described by the following vector of 7 generalized coordinates : 2.4 The pure rolling conditions, i.e. the fact that the component of the velocity of the contact point of the wheel with the ground in the plane of the wheel is zero, are deduced from (6) : Kin e ina t ic a1 c o ii strain t s Jl(3)NQK + JZP = 0 (10) w i t h - s i n p cos@ - LSi1 ",
            " Moreover, it is easy to check that the input matrix PTG'(p) has full ra.nk for the two considered configurations, see eq. (21) ) ( 2 2 ) , (30). Consequently, for any (111, U?) there exists one aiid only one static state feedback u ( B , O , ~ ~ ) such that the system of' equations (37) in the variables ( t , 71) reduces to : 171 = U 1 ,j. = e = 0 2 i = - 7 / i S i l Z O I lj = ']ICOSO (38) { - 0 = 112 4.2 Input-ouput feedback linearization Colisider for instance a point Q1 whose coordinates in tlie frame attached to tlie robot are (0 , - 11) (see Fig. 3). Define a.s outputs the position of Ql in the plane equation (29) is rewrit,teii as follows : P T l W ( d ) P 7 j + P?'p(B,Q,P,P,77) = PTC(P)U (34) It follows that Inpul-output linearization is therefore possible because the matrix of tlie coefficients of V I and 02 bas full rank, for any 8 , provided h is not zero. In order to analyse the internal stability we introduce the following change of coordinates c = a(<, 17) : (< deuoLlllg IIOW L h t - L'ector (i y 8 ) T ) i i i order to constitute a diffeomorpliisni, whose inverse is given by : cos8 s i n 8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.31-1.png",
        "caption": "Fig. 8.31 Basic curve and effective plane height for the stepped road when using the two-point follower model [29]",
        "texts": [
            "30 are determined by fitting the curves to either experiment or simulation results obtained for the elastic ring model. Zegelaar [21] extended Bandel and Monguzzi\u2019s idea to express the geometric filter by combining one basic curve with a two-point follower model. The two-point follower model can be applied to an arbitrary road profile. Schmeitz [29] further extended Zegelaar\u2019s model to a three-dimensional model and improved the two-point follower model by introducing the tandem egg model. This section reviews the two-point follower model. Figure 8.31 shows the basic curve and the effective plane height for a stepped road when using the two-point follower model. The step road is transformed to a smooth curve by the basic curve fb, which is expressed by a quarter sine wave with length lb and step height hstep = hb. The parameters of the effective plane can then be obtained by moving with a two-point follower having (horizontal) length ls over a single basic curve fb, as shown in the left figure of Fig. 8.31. When the two points of the follower move along the basic curve fb, the midpoint describes a curve that Effective plane angle Effective plane height Fig. 8.30 Composition of the effective road surface from basic curves for a trapezoid cleat [21] 8.4 Tire Models Rolling Over Cleats (Ride Harshness) 513 represents the effective height w(X). The inclination angle of the follower with respect to the horizontal corresponds to the effective forward slope by. w(X) and by are expressed by w\u00f0X\u00de \u00bc fb X ls=2\u00f0 \u00de\u00fe fb X \u00fe ls=2\u00f0 \u00de 2 tan by \u00bc fb X ls=2\u00f0 \u00de fb X\u00fe ls=2\u00f0 \u00de ls ; \u00f08:197\u00de where X is the longitudinal position of the wheel center. A parameter lf in the left figure of Fig. 8.31, the so-called offset, controls the position of the basic curve with respect to the beginning of the step in the road profile. The basic curve is used as a building block with which to compose the basic profile for an arbitrarily shaped obstacle. As shown in Fig. 8.32, the path of the center of the rigid wheel corresponds to a circle with the same radius a as the rigid wheel. The shape of the basic curve corresponds well with the curve of the rigid wheel response. The length of the curve lb is thus expressed as 514 8 Tire Vibration lb \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 a hstep 2q : \u00f08:198\u00de Nondimensional parameterization is used for the length and offset of the basic curve: a \u00bc plba0 ls \u00bc pls2l lf \u00bc plf lb: \u00f08:199\u00de where a0 is the unloaded tire radius, l is the half contact length, and plb, pls and plf are fitting parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003794_robot.1991.131747-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003794_robot.1991.131747-Figure2-1.png",
        "caption": "Figure 2: Characterization of a wheel",
        "texts": [
            " Define a. reference point Q on tlie h ~ l l e y , and a basis ( 2 1 , 2 2 ) a,ttached to the trolley (sec, Fig.1). The position of the trolley in the plane is completely specified by the following 3 variables : 0 2 ~ y : the coordinates of the reference point Q in the inertial frame, 0 tr : the orientation of the basis {zl , 22) with respect to the inertial basis. We define the vector as : E = (.c y try ( 5) 2.2 Characterization of a wheel W e iiow characterize the position of a particular wheel (see Fig. 2). Consider the mobile frame {Q, 2 1 , 2 2 ) a.t(,aclied to the trolley. T h e center B of the wheel is cuiiiic~ctecl to the trolley by a rigid rod -4B (of constaiit Ic i igh d ) , which can rotale a.round a. fixed vertical axis itt, :I. T h e position of this point il with respect to talle trolley is specified by 2 constants : the length 1 a.iicl t,lic> angle CY. The rotation angle of the rod AB with respect to &A is denoted p. The orientation of tht, 1)la.ne of the wheel with respect to AB is given Iby the constant angle et"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003429_cvpr.1991.139677-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003429_cvpr.1991.139677-Figure2-1.png",
        "caption": "Fig. 2. Transformations between coordinate frames.",
        "texts": [
            " As the robot moves to a new location, the position and orientation of the camera relative to the fixed world can be determined by using control points or lines a t known positions in space. This is the well-known camera location determination problem and many techniques have been developed to solve the problem [lo], [14], 1121, (201, [15], (71, [18]. Given the robot and camera motions, we want to find the position and orientation of the camera relative to the robot. Because the camera is mounted rigidly on the robot, the transformation from coordinate frame FA through FL to FL is the same as the transformation from FA through F B to Fk, as shown in Fig. 2. Therefore, A X - X B (1) Rx - R A R x R E (2) tx RA tx + t A - R x t B (3) or where A is the robot motion, B is the induced camera motion, and X is the robot-to-camera coordinate transformation to be determined. 2.3 Previous Work Several researchers have investigated the solution of (1). Chen (51 investigated the relationship between great circles on a quaternion sphere and proposed a linear method for solving a binocular motion problem (with different unknowns). In the context of head-eye calibration, Shiu and Ahmad [16] were apparently the first to attack the problem and to report a mathematical solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000488_tmech.2019.2945525-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000488_tmech.2019.2945525-Figure4-1.png",
        "caption": "Fig. 4 Overlay of the manipulator insertion configurations throughout the workspace",
        "texts": [
            " Three of the screws with sliding blocks attached to the Ni-Ti rods transfer rotational motion of the flexible shafts to translational motion of the Ni-Ti rods (Fig. 2 (d)). The last one with a sliding block is used to drive the motion of the VS mechanism. The anti-backdrive characteristic of the screws enables the end-effector a stable state, reducing the risk of injuring the patient when the motor doesn't work. 4) Workspace Characterization As for workspace coverage [34], one manipulator is moved in its configuration space as shown in Fig. 4. It demonstrates that the ability to bend is more than 45\u00b0 and to translation is more than 50 mm for the manipulator under master-slave configuration, which indicates the reachable area covers the entire oropharynx. The sketch of the head is drawn with its size based on the existing research [27]. As shown in Fig. 2 (f), a parallel mechanism with 3-PRS joint chains is adopted as the master device in the master side. Three displacement sensors (LPZ-200, FIAYE Electric Co., Ltd.) attached to its P joints are used to record the position of them"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000955_taes.2021.3068434-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000955_taes.2021.3068434-Figure1-1.png",
        "caption": "Fig. 1. The structure of a quadrotor UAV with the body frame and inertial frame.",
        "texts": [
            " The safety control design algorithm is presented in Section III, including the fault estimation, ISM-based safety control law, and their rigorous closed-loop stability analysis. Moreover, the results of numerical simulations and flight tests are presented to verify and validate the proposed safety control strategy in Section IV. Finally, Section V concludes the paper. This section presents the nonlinear quadrotor UAV model and the actuator fault model, which can provide a basis of the proposed safety control design. Two reference frames and their corresponding coordinate systems are used to describe the attitude and position of the quadrotor UAV. As shown in Fig. 1, Body Frame (BF) is assumed to be at the center of gravity of the quadrotor UAV, where x-axis (xB) is pointing head, y-axis (yB) is pointing left, and z-axis (zB) is pointing upwards. Moreover, Inertial Frame (IF) is assumed to be at the center of the flight field, where x-axis (xI ) is pointing towards the north, y-axis (yI ) is pointing towards the west, and z-axis (zI ) is pointing towards upwards. In this paper, the take-off point of flight experiment is set to be (0, 1, 0) in IF. The transformation vector from BF to IF can be expressed as: REB = C\u03c8C\u03b8 \u2212S\u03c8C\u03c6 + C\u03c8S\u03b8S\u03c6 S\u03c8S\u03c6 + C\u03c8S\u03b8C\u03c6 S\u03c8C\u03b8 C\u03c8C\u03c6 + S\u03c8S\u03b8S\u03c6 \u2212C\u03c8S\u03c6 + S\u03c8S\u03b8C\u03c6 \u2212S\u03b8 C\u03b8S\u03c6 C\u03b8C\u03c6  , (1) where \u2126b = [\u03c6, \u03b8, \u03c8] T represents pitch, roll, and yaw angle between BF and IF",
            " In comparison to [34], the convergence time of the designed fault estimator is independent of initial conditions, which is more suitable for the quadrotor UAV safety requirement. From a control aspect, the proposed safety controller explicitly takes transient estimation error into consideration, while this type of error is not handled in [34]. Remark 6. In comparison to [32], this paper adopts a retrofit controller architecture to eliminate the transient errors. The proposed safety controller shown in Fig. 1 compensates the faults and unknown disturbances, while the baseline control algorithm remains unchanged during the fault compensation process. In addition, the proposed safety control method has the potential for a wide variety of baseline controllers because of its robustness to estimation errors. The fault estimation mechanism can be formed by different observers according to the fault characteristics. In other words, the tailorability of the proposed scheme is promising. In this section, both numerical simulation and real-world flight tests are carried out to demonstrate the effectiveness of the proposed safety control strategy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.42-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.42-1.png",
        "caption": "Fig. 7.42: Work Space Restrictions",
        "texts": [
            " \u2022 Position and orientation of the gripper are restricted by external constraints, such as obstacles within the working space, or the requirement that the parts should be assembled on a workbench with a given height. Position and orientation are calculated using the robot\u2019s forward kinematics, so that geometrical constraints can be stated in Cartesian space. For simplicity in our example, we restrict the robot\u2019s position to a cube, the edges of which are parallel to the base coordinate frame B of the robot, see Figure 7.42: Brmin \u2264B rG(q0) \u2264B rmax . (7.152) Orientation restrictions are expressed using the rotational gripper transform AGB. In the example, we choose the orientation to be restricted such that the zG direction should have a negative component in the xB- and the zB-directions, which means that the mating direction points downwards away from the robot\u2019s base. Example: Rectangular Peg-in-Hole Insertion We illustrate the method with the position controlled insertion of a rigid rectangular peg into a hole using a PUMA 562 manipulator, starting from the reference configuration q0,ref ,Kp,ref ,Kd,ref defined in equation (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003458_j.ymssp.2005.02.009-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003458_j.ymssp.2005.02.009-Figure1-1.png",
        "caption": "Fig. 1. Diagram of the 26 degrees of freedom dynamic model of two pairs of gears in mesh.",
        "texts": [
            " The result of this investigation showed that the amplitude and phase modulation of the vibration signal is affected differently for both the tooth spall and the crack. The model developed here is based on a two-stage reduction gearbox [6], where gears 1\u20134 have teeth numbers of 23, 45, 25 and 47, respectively. The overall gearbox reduction ratio is given as \u00f045 47\u00de=\u00f023 25\u00de which is equivalent to a reduction ratio of 3.678. There are a total of 26 degrees of freedom (dof) in the model and a schematic diagram of the model is shown in Fig. 1. The vertical direction \u00f0xi\u00de in the model has been aligned with the pressure line of the gear mesh for modelling convenience. The major assumptions, which the dynamic model is based upon, are, (i) resonances of the gearbox casing are neglected, (ii) shaft mass and inertia are lumped at the bearings or the gears, (iii) shaft transverse resonances are neglected, (iv) input and output shaft torsional stiffness is ignored (flexible coupling torsional stiffness is very low), (v) gear teeth profiles are without runout errors, (vi) the teeth are straight along the axial face width without crowning"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.88-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.88-1.png",
        "caption": "Fig. 5.88: Structure of the microcatheter. According to [Guo95)",
        "texts": [
            "8 mm long and had a weight of 0.7 g. The semipermeable membrane was made of a 70 f.tm thick cellulose sheet. Polymer microcatheter For the microcatheter presented in Figure 5.60, alternative actuation prin ciples are being investigated. A prototype of a microcatheter was developed with two integrated guide wires and a liquid channel [Guo95). Through the channel physiologic solutions or contrast media can be transported. Attached to each guide wire is a polymer film actuator which enables the catheter to be bent, Fig. 5.88. The guide wire consists of two electric conductors covered by a wire sheath and the actual actuator, an ionic conducting polymer film. The end of this film is embedded between two flat platinum electrodes, Fig. 5.89. In order to bend the tip of the catheter, a defined voltage is applied to both electrodes of the desired actuator. This voltage causes the polymer gel to expand at the ca thode side, which results in a movement of the film actuator towards the anode side. The actuator tip bends in a circular manner, making it possible to control the radius of this bend (and with this the position of the catheter) with the voltage applied to the electrodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.32-1.png",
        "caption": "Fig. 7.32: Mating Experiments",
        "texts": [
            " The description of the hole is the same, we only have to replace the index ()1 by the index ()2, where R2 = 20.0mm and r2 = 6.0mm. Between the to mating partners three potential contact points exist: number peg hole 1 torus 1 \u2190\u2192 torus 2 2 cylinder 1\u2190\u2192 torus 2 3 torus 1 \u2190\u2192 cylinder 2 The position of the robot for the insertion task was \u03b30 = (\u22128.4\u25e6,\u2212152.8\u25e6,17.9\u25e6, 0.0\u25e6,\u221244.9\u25e6,\u22128.4\u25e6)T . The initial displacement of the robot with respect to the axis of the hole was 2.1mm in the xG\u2013direction and 1.3mm in the yG\u2013direction (see G\u2013frame in Figure 7.32 for detailed explanation). The mating trajectory was 80mm along the zG\u2013axis. In Figure 7.33 we see the first results from the insertion. The peg and the hole are displayed from two sides. On the two parts we recognize the trace of the contact points. On the left side we see the point of the first contact between the two chamfers, due to the initial displacement. The workpieces are then sliding along the chamfers, until there is a transition of the contact point to the cylinder of the peg. In this situation, the peg touches the chamfer along a straight line, as long as only one point is in contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure5.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure5.2-1.png",
        "caption": "Fig. 5.2",
        "texts": [
            "5) 156 Bifurcation and Chaos in Engineering where K = xoe- I/y\", and XO and Yo are the mean values of x and y when t = o. The manifold of the linearized system is The phase portrait is shown in Fig. 5.1. '3f/S = {(x,y)lx,y satisfy (5.3)} '3f/' = {(O,y)lx,y E~} We shall now discuss the phase portrait from eq. (5.5). When y tends to 0 in 1 1 II v 00 the negative direction, that is y '\" -0, y = -0 = -00, so that x = Ke . = Ke- '\" O. When y tends to 0 in the positive direction, x'\" 00, so that the derivative of the phase portrait is not continuous. It is easy to see that of '3f/c is not unique, see Fig. 5.2 . In order to ensure that the derivative of the phase portrait at (0,0) is continuous, take the expression for the centre manifold '3f/c as '3f/ C (, I x~O, when y>o ) = ~(XJY) x=Ke'II', when y:So (5.6) C h 0 dx 0 C C c For '3f/ w en y> , x = 0 dy = -; = 0, i.e. '3f/ is a tangent to S ; lor y::;; 0, x = Kelly, when y tends to zero in the negative direction, we obtain dx = 0, so that dy '3f/c is a tangent to SC too. The derivative of '3f/c at (0,0) is unique, see Fig. 5.3. There are different centre manifolds for different K at (0,0), i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure5-1.png",
        "caption": "Fig. 5 Illustration of hook,",
        "texts": [
            " In the grinding process, Toprem and Table 1 Kinematics of face milling versus face hobbing Pinion Gear Process Generated Generated Formate Face milling Generating roll: w=Ra c Generating roll: w=Ra c c=0 Intermittent indexing Intermittent indexing Intermittent indexing Face hobbing Generating roll: w=Ra c Generating roll: w=Ra c c=0 Continuous indexing: w=Rtw t Continuous indexing: w=Rtw t Continuous indexing: w=Rtw t Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use F o b d e r a a c a m s f c s H r n i s p J Downloaded Fr lankrem can be easily obtained by dressing the grinding tool. In rder to obtain a continuous tooth surface, the four sections of the lade edge need to be in tangency at connections. Parameter u efines the position of a point on the blade edge. The edge geomtry of three-face sharpened blades is defined by pressure angle , ake angle , and hook angle Fig. 5 . Three-face sharpening is pplicable to both face milling and face hobbing. The blade offset ngle defines the slot position where the blades sit. In most ases, blades are not exactly placed with the front faces in the xial cross section of the cutter head. In the case of the faceilling grinding process, the edge geometry in the axial cross ection of a grinding wheel is considered. We consider that the tooth surface of the generating gear is ormed by the trace of a cutting edge of the tool whose geometry an be defined by the position vector and the unit tangent repreented in the cutter head coordinate system St as rt = Mtb , , ,Rb rb u 3 tt = Mtb , , ,Rb tb u 4a ere, vector rb u and tb u are defined in Fig. 4; matrix Mtb epresents the coordinate transformation from blade face coordiate system Sb to St. Determination of transformation matrix Mtb s based on the geometric description of the rake, hook, and blade lot offset angles shown in Fig. 5 and can be defined as a multilication of three homogeneous matrices as ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 Mtb = M M M 4b where M , M , and M are represented as M = cos sin 0 0 \u2212 sin cos 0 0 0 0 1 0 0 0 0 1 4c M = 1 0 0 0 0 cos sin 0 0 \u2212 sin cos 0 0 0 0 1 4d M = cos \u2212 sin 0 Rb cos sin cos 0 Rb sin 0 0 1 0 0 0 0 1 4e 4 Generalized Tooth Surface Generation Model Today, free-form CNC hypoid generators are widely employed in manufacturing of spiral bevel and hypoid gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure7-27-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure7-27-1.png",
        "caption": "Figure 7-27. Phasor diagram and equivalent circuits according to equations 7.69, 7.70, and 7.71.",
        "texts": [
            "64, which we use to describe the operation of the threephase excited AC machine, can be transferred in a more general form (see equations 7.69-7.71) by introducing the definitions for the magnetizing current IXm, that stator/ rotor windings ration ii, the leakage factor for stator and rotor \u03c3\u03c7 and \u03c32, and the total leakeage factor \u03c3. SL\u00b7 = \u039c \u03a8 , (7.58) %=LxLl+I_2M (7.60) a-^-a-\u00eb-^\u00ea-S\u00b7* (\u03bb64) \u03b7*\\-\u03c8 (7.66) \u03c3 = ( 1 - \u03c3 \u03b9 ) ( 1 - \u03c3 2 ) (7.67) U^MLi-lim (7-69) Zim = / i + \u00bf 2 \" ( l - ^ i ) (7-70) U2 = (\u03cb\u03bb -M \u00b0U \u25a0 \u0399\u03b9) \u25a0 - \u25a0 \u03c4\u03c4^-, (7-71) \u03c9\\ (1-\u03c3 2 ) The phasor diagram and the quivalent circuits for the voltages and currents are shown in Figure 7-27. They are based on equations 7.69-7.71. The figures for the nominal current Iin \u00ab 4/lm and the leakage factors \u03c3\u03c7 \u00ab \u03c32 \u00ab 5% and \u03c3 \u00ab 10% are representative for large slip ring AC machines. The phasor diagram is represented for purely active nominal current I\\ = I\\\u201e. The diagram of the voltages is represented by unfilled phasors. It follows from the equivalent circuit which is based on equation 7.71. The current diagram is made up with filled phasors and based on the equivalent circuit which follows from equation 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.45-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.45-1.png",
        "caption": "Fig. 10.45 External force variation in the time domain for a practical pattern [10]",
        "texts": [
            " Tire noise for the optimized lug shape is one-hundredth that for the magic angle. The optimized lug shape, called the magic shape, depends on the value of a, b and the footprint shape. The optimized magic shape, g(y), of Eq. (10.54) is expressed by the magic angle of only the first term of Eq. (10.54) if a and b have similar values, but it will be very different from the shape of the magic angle if a and b differ greatly. The tire noise model can be easily extended to a complicated pattern as shown in Fig. 10.45. Because tire noise is generated only when a lug rolls into or out from the ground, it is convenient to move edges of the footprint in the pattern to consider the relationship between the pattern and the edge of the footprint. At tire velocity V, the length of this movement becomes VDt at each time interval Dt. When the external force is expressed by a Dirac delta function, tire noise in the time domain can be described by the right graph of Fig. 10.45. The amplitude of the external force is proportional to Dyc(y), where Dy is the lateral component of the length of the lug element between times t and t + Dt and c(y) is the density of the external force at lateral position y. It is obvious that this tire noise model includes the effect of the lug angle discussed in Sect. 10.7 and Dy decreases with increasing lug angle. 622 10 Tire Noise Assuming that the density of the external force is uniform in the meridian direction, the predicted tire noise is given by prediction \u00bc X200 n\u00bc1 cnAn; \u00f010:56\u00de where n is the number of harmonics, An is the parameter of the A-weighted sound level, and cn is the amplitude for the n-th harmonics calculated using the Fourier transform of the external force variation in Fig. 10.45. The predicted tire noise is compared with measurements in Fig. 10.46. Tire noise (A-weighted overall noise) was measured using an indoor drum tester with a 3-m diameter in an anechoic room 10.7 Phenomenological Model for Pattern Pitch Noise 623 at a tire speed of 100 km/h. The prediction is in good agreement with the measurements. Note that the distribution of the density of the external force in the meridian direction and values at the leading and trailing edges need to be measured to further improve predictability",
            " (2) Prediction of the interior noise of a vehicle (air-borne noise and structure-borne noise) employing FEA and a BEM (2-1) Prediction of air-borne noise The interior noise of a vehicle consists of air-borne noise and structure-borne noise as shown in Fig. 10.30. Saguchi et al. [48] first developed a procedure with which to predict the interior noise of a vehicle. They followed Nakajima\u2019s procedure [16, 10.13 Tire Noise Prediction 681 17] of predicting air-borne noise except for the external force estimation. Instead of adopting the procedure of Fig. 10.45, the external force was calculated from the difference in contact pressures between patterned and smooth tires that were predicted by quasi-static rolling contact analysis in Fig. 10.101. A finely meshed finite element model of a tire must be used for prediction of the external force. The external force is then mapped from the fine finite element model to a relatively coarse mesh model for vibration analysis. Although the coarse mesh model lacks a precise reproduction of the tread pattern complexity, it has excellent prediction capabilities for tire vibration up to approximately 1 kHz including the cavity resonance response"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001249_s00170-021-07440-5-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001249_s00170-021-07440-5-Figure5-1.png",
        "caption": "Fig. 5 The nozzle setup of the powder delivery system [78]",
        "texts": [
            ", gas atomization, water atomization, plasma atomization, melt spinning, and various chemical processes [2, 74, 75]. Metal powders produced by each of the listed processes vary in shapes and sizes. The following scheme in Fig. 4 shows the processes that can be used in mass powder production [76, 77]. During the LPD process, the powder conveying subsystem composed of a powder feeder and radial symmetrical nozzle device plays an important role in this process because the additive material exists in the form of powder. Proper design of the nozzle allows the cladding process to be completed in one step [78]. Figure 5 shows one type of nozzle setup applied in the powder delivery system. Currently, deposition nozzles have different designs, different characteristics, and prices. However, they can all be divided into two categories: coaxial nozzles and side nozzles. The coaxial nozzle, which allows the powder stream to flow coaxially with the laser beam, provides the capability of precise deposition due to omnidirectional nature. Nevertheless, the side nozzle has a simple geometry and is easy to be modified, which means that the deposition process can be studied in detail"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003467_tvcg.2005.13-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003467_tvcg.2005.13-Figure4-1.png",
        "caption": "Fig. 4. A bar deformed by modal analysis (red), by modal warping (blue), and by nonlinear FEM (green) under gravity of different magnitudes.",
        "texts": [
            " Then, the problem of simulating deformation is transformed to that of finding the weights of the modes, which results in a significant reduction in computational complexity. This technique can also synthesize geometrically complex deformations with negligible main CPU costs on programmable graphics hardware [10]. However, modal analysis can produce quite unnatural results when applied to bending or twisting deformations of relatively large magnitudes. In particular, the volume of the deformed shape can increase unrealistically, as shown in Fig. 4. These unnatural results are due to the omission of the nonlinear term, which is not negligible for such deformations. In this paper, we propose a new technique that overcomes the above limitations of linear modal analysis. As a result, the proposed technique generates visually plausible shapes of elastodynamic solids undergoing large rotational deformations, while retaining its computational stability and speed. Also, our formulation provides a new capability for orientation constraints, which has not been addressed in previous studies",
            " We used the time step size of h \u00bc 1=30 second in all experiments reported in this section. Model statistics and performance data are summarized in Table 1. Animation clips are available at http://graphics. snu.ac.kr/~mgchoi/modal_warping. This experiment is to compare the results generated by linear modal analysis, modal warping, and nonlinear FEM. We ran the three methods to deform a long bar under different gravities. As for the nonlinear FEM [17], we employed explicit integration and used the time step size h \u00bc 0:001 seconds for numerical stabilities. Fig. 4 shows the snapshots taken at the equilibrium states of the bar. Fig. 5a shows the plot of the relative L2 displacement field error versus gravitational magnitude. We took the result produced by nonlinear FEMas the ground truth. The relative error in modal warping is smaller than that in linear modal analysis, although it increases as the gravitationalmagnitude increases. Fig. 5b is theplot of the relativevolumechangewith respect to the initial volume. It shows that the relative volume change in modal warping is almost identical to that in nonlinear FEM",
            " The motion of the jelly box is driven by the movements of the feet and head of the articulated character; to implement this, a node corresponding to the middle of the two feet is selected and position/ orientation-constrained to follow the average movement of the feet and a node corresponding to the forehead is also position/orientation-constrained to follow the movement of the head. Three snapshots taken during this experiment are shown in Fig. 9a. For comparison, we also applied the traditional modal analysis to this case (see Fig. 9b). In the second example, we applied a dance motion to the flubber shown in Fig. 9c. Because this character has a more articulated shape than that in the previous example, more constraints are required to properly map between the Fig. 5. Error analysis of the bar shown in Fig. 4: (a) The relative L2 displacement field error and (b) the relative volume change with respect to the initial volume. Fig. 6. Error analysis of free vibration: (a) The relative L2 displacement field error summed over space and time and (b) the average magnitude of nodal displacements over time. articulated and deformable characters. We placed one position/orientation constraint at the head and five position constraints at the torso, elbows, and feet (see Fig. 9d). For the flubber, we used a larger number of deformation modes (64 modes) than in the experiments described above; this was necessary to accommodate the wider range of shape variations due to the increased number of constraints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure7-3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure7-3-1.png",
        "caption": "Figure 7-3. Synchronous motor. Illustration of the mode of operation.",
        "texts": [],
        "surrounding_texts": [
            "When designing converter controls for AC drives one has to focus on the motors: the selection of the converter circuits and the design of the control structure strongly depend on the characteristics of the motors. How three-phase motors work is not easy to understand, when looking only at the three-phase quantities of the windings. The usual methods to describe AC machines therefore are not only based on \u2022 Three-phase quantities, but also on their transformation to \u2022 Rotating phasors and to \u2022 Stationary phasors. This is required for two reasons: 1. AC machines are easier to describe mathematically and easier to understand physically when using phasors instead of three-phase quantities. 2. Modern controls are directly based on phasors and their real and imaginary components. The measured three-phase quantities have to be transformed to 7. High-Power Industrial Drives 338 phasors at the inputs of the controls, and an inverse transformation at the outputs has to generate the three-phase quantities to act upon the real \"three-phase-world\" of the high-power converters and motors. This is well known from the literature [16-21]. In our context we therefore don't need to derive this theory. It should, however, be interpreted and illustrated in a physically plausible manner. This will be done with Figures 7-2 and 7-3 for the synchronous motor and Figures 7-4 and 7-5 for the asynchronous motor with slip rings or with squirrel cage rotor. The Synchronous Motor. The synchronous motor with three stator windings a, b, c and the excitation winding e in the rotor is shown in Figure 7-2a. This picture also contains the real axis (Re) of two complex coordinate systems: \u2022 A stator fixed stationary coordinate system \u2022 A rotor fixed coordinate system turning with the rotor. These reference frames are required to transform the following: Three-phase quantities (a); rotating phasors (b) and rotating phasor diagrams (c) for two instants (1) and (2); stationary phasor diagram (d); simplified steady-state motor equations (e). \u2022 Three-phase stator quantities of the voltages Mla\u00bfc, the flux linkages Via,v the currents iiabc and the DC rotor current ie to \u2022 Stator-related ( ) rotating phasors ( ) u ] ; \u03c8 \u00a1 ; i \u03c7 ; / e; or \u2022 Rotor-related stationary phasors (_) Ux; \u03a6^; /,; \u00a1^ = Ie. This is represented in Figure 7-2b. The line diagram in Figure 7-2c shows the transformation algorithms. Figure 7-2d shows the steady-state equations for the stator voltage \u00c7/,, the stator flux linkage \u03a6,, and the electromagnetic torque Te based on stationary phasors. The simplified steady-state motor equations in Figure 7-2d are easy to interpret physically: the torque Te is generated by the force of the magnetic field (represented 340 7. High-Power Industrial Drives by \u03a6 )\u0302 on the current (represented by /[). Jm(Il \u25a0 \u03a8_\u0390) means the product of *j and the perpendicular component of / ] . The stator flux linkage \u03a8 [ is determined by the voltage ( t/, ) and frequency (\u03c9) for the stator. To obtain a good magnetic utilization of the motor the absolute value *i of the flux linkage \u03a6.\u03b9 has to be kept at its rated value by increasing the amplitude U\\ of the stator voltage t/, proportional to the angular stator frequency \u03c9. The rotor follows synchronously to the angular stator frequency \u03c9 = 2\u03c0\u03b7 \u25a0 zp. The stator flux linkage \u03a6[ consists of two components which are generated by the stator current (\u2014\u25ba I\\L\\) and the excitation current (\u2014> IeM). L\u00a1 is the stator inductance and M is the stator-rotor coupling inductance. Equations 7.1-7.7 and the diagrams in Figures 7-3a, b serve the purpose to illustrate the transformation of the^three stator currents iiabc and of the DC rotor current ie to rotating phasors i { and i e for two instants (1) and (2). The transformations are based on the physical idea of three-phase motors where threephase AC currents in three-phase windings generate a rotating field. The DC excitation current ie generates a field which is fixed on the rotor. Mathematically this can be described as follows: the three phase currents iiabc in equation 7.1 are added geometrically in equation 7.3 (each in the direction of its winding axis) and generate a rotating phasor / i = (\u0399\\\u03b2^\u03c8\u03af) \u25a0 ejut in equation 7.4. The DC excitation current ie in equation 7.2 generates a rotor-fixed phasor i e = Ie \u25a0 eJU\" in equation 7.6, which turns together with the synchronously rotating rotor. Both phasors rotate with the same angular frequency \u03c9 = 2\u03c0\u03b7 \u25a0 zp (n: speed; zp: number of pole pairs) relative to the stator (equations 7.4 and 7.6). \u00a1ifl,V = / i C 0 S M + V/ + ^ ) ; Z) = 0\u00b0; -120\u00b0; +120\u00b0; (7.1) ie = h; r1=2/3(/1^o +/I^ i2o0+il^ i2o\u00b0) = 2/3 ^2 h cos(w\u00ed + \u03c8\u03af + D)e~jD = Ixe MeM /i = Iie M I e le ' 6 lg le i l e A c = Re{t\\e+jD) = Re{h \u25a0 e M \u25a0 ej\"' \u25a0 e'D) (7.2) (7.3) (7.4), (7.5) (7.6), (7.7) = /, cos(w? + <pj + D) (7.4 \u2014\u00bb 7.1) Equations 7.1 and 7.4 show clearly in which way amplitude Iu frequency \u03c9, and phase angle \u03c6\u03af of the three-phase currents in equation 7.1 determine the absolute value /1; the stationary unit phasor eJiPi, and the rotating unit phasor eJu\" of the stator-related rotating phasor /1 in equation 7.4. Therefore it is easy to recover the three-phase currents iXabc from the rotating current phasor ix by the inverse transformation in equations 7.4 \u2014* 7.1. f As shown in equations 7.4, 7.5 and 7.6, 7.7 the rotating phasors i\\ ~ \u0399^\u03c8\u03af \u25a0 el\u00b73' and ie ~ Ie \u25a0 \u00bf\u03c91 can be regarded as stationary phasors /, = \u0399\u03bb\u03b5 1\u03c8\u03b9 and Ie multiplied with the rotating unit phasor el\u00b7\". 7.4. Motors for Large Drives 341 In the phasor diagrams in Figures 7-3c, d the stator respectively rotor current phasors are multiplied with the stator inductance L, and the stator-rotor coupling inductance M and summed up geometrically to form the resultant stator flux linkage \u03a6 , ^ ' = (/,L| +IeM)ejut. This illustrates the phasor equations in Figure 7-2d for the voltage C/j and the flux linkage \u03a6, of the stator under the assumption that the stator resistance can be neglected (R\\ \u2014* 0). The phasor diagrams can also serve to illustrate the torque equation. The torque Te is, according to the torque equation, proportional to the area enclosed by the phasor triangle formed by the flux linkages [xLuIeM, and \u03a6,. The Asynchronous Motor. The asynchronous motor with three-phase stator windings is shown in Figure 7-4a. As slip ring motor, it has a three-phase wound rotor accessible via slip rings. As squirrel cage motor it can be regarded as a special case with short-circuited three-phase rotor windings. It is assumed that the variations of the angular rotor speed \u03c9 are slow compared to those of the electrical angular frequencies of the stator \u03c9\u03c7 and the rotor \u03c92. <jj\\dl \u2014 ujt = u>2dt (7.8) These reference frames are required to transform the three-phase quantities x\\a,b,c a n d X2a,b,c (where x \u2014 u or \u03c8 or /) of the stator (index 1) and rotor (index 2) to rotating phasors (\"*) in the stator fixed frame ( '): ~x\u00a1 and ~x2 and in the rotor fixed frame (\" ): ~x\"2 and it\" or to stationary phasors (_) Xt and X2 m t n e rotating frame. The representation of these quantities is shown in Figure 7-4b. Nonsinusoidal transient three-phase quantities of any wave shape can be represented as \"sinusoidal\" quantities with varying amplitude X^2) = ^\u038a(2) (')> frequency \u03c9\u0390(2) = ^i(2) (t), and phase angle \u03c8,\u03972) = <p,\u00b7 (t). The transformation algorithms are shown in the line diagram in Figure 7-4c. Figure 7-4d shows the dynamic phasor equations for the voltages U and flux linkages \u03a6 in stator (index 1) and rotor (index 2) and for the instantaneous value of the electromagnetic torque te as a function of the stator current and flux linkage phasors /, and \u03a6^. Here again we start our illustration with a physical interpretation of the dynamic motor equations in Figure 7-4d: the generation of the torque te is identical to the synchronous motor. Jm(L\\ \u25a0 \u03a6_\u0390) means the product of \u03a6, representing the magnetic field and the perpendicular component of the current /,. The stator flux (a ) A sy nc hr on ou s m ot or , r ef er en ce fr am es R e ro ta tin g\" R e S ta to r (b ) R ep re se nt at io n of th e m ot or q ua nt iti es T hr ee -p ha se q ua nt iti es a , b , c in s ta to r (1 ) an d ro to r (2 ) *i a, b, c = * i co s( J c^ ci f + \u03c6 \u03c7 1 + D ) x ; X = u ; U ^2 a, \u00d6 , c= ^2 C O S (i t0 2 d ( + \u03c6 \u03c7 2 + D ) \u039f \u0393 \u03c8 ; \u03a8 w he re a : 0 = 0\u00b0 , & D = -1 2 0 \u00b0, c D = 1 2 0 \u00b0 o r/ :/ T ra ns fo rm at io ns to r ot at in g ph as or s (\"* ) in th e st at or re la te d (') o r ro to r re la te d (\") c oo rd in at e sy st em . (c ) T ra ns fo rm at io n al go rit hm s x\" , = x ' 1 e -> \"\" Tr an sf or m at io n to s ta tio na ry p ha so rs (_ in th e ro ta tin g co or di na te s ys te m . X i = X ,e \u00a1 ** i X i = X ze \u0399\u03a8 \u03c72 (d ) D yn am ic p ha so r eq ua tio ns o f t he a sy nc hr on ou s m ot or in th e sy nc hr on ou sl y ro ta tin g co or di na te s ys te m \u00fc 1 = /iR 1 + \u00c1 o 1 2 ; 1 + (/ 3; 1/c (r Lk = hf k + \u00c0 \u00b02 \u00cf2 + d \u00e4y df 3 ii= ii\u00ed -i + _ '2 M \u00cd2 = \u00cd2 1 -2 + Il M J\u00cdO , d t= IM '+ \u03c9 \u03af f e = 3/ 2Z p\u00b7 J m (/ r2 i\u00ee ) C\u00db = 2 \u03c0 \u03b7 \u00b7 \u03b6. \u0396\u03c1 = n um be r of p ol e pa irs n = sp ee d * = co m pl ex c on ju ga te d F ig ur e 7- 4. A sy nc hr on ou s m ot or . R ef er en ce f ra m es . R ep re se nt at io n of t he m ot or qu an ti ti es . T ra ns fo rm at io n al go ri th m s. D yn am ic m ot or e qu at io ns . T O I o 3\u00bb es 3 t\u00ed \u00f6 7.4. Motors for Large Drives 343 linkage \u03a6,\u03b9\u2014 determined by the voltage U_x and angular frequency \u03c9\u03c7 applied to the stator (assumption Rx \u2014* 0)\u2014is made up of two components generated by the stator current (\u2014> IXL\\ ) and by the rotor current (\u2014> 72M). L{ is the stator inductance, M is the stator-rotor coupling inductance. The rotor flux linkage \u03a62 can be interpreted in a quite analog manner. Here U2 and \u03c92 are the voltage and angular (slip) frequency applied to the rotor via slip rings. Induction motors have a (short-circuited) cage in their rotor which is not accessible from outside. Therefore, U2 = 0. When controlling the induction motor with a linear voltage frequency characteristic | J7, |~ \u03c9\\ the stator flux linkage \u03a6, can be kept constant at its rated value. This ensures a good magnetic utilization of the induction motor. \u03c92 is the angular slip frequency by which the angular rotor speed \u03c9 = 2-\u03c0\u03b7 \u25a0 zp is lagging behind the angular stator frequency a>! when the motor is in the driving mode. The following steady-state equations 7.9 to 7.12 and the diagrams in Figures 7-5a, b serve the purpose to illustrate the transformation of the three-phase stator and rotor currents i\\a\u00bf\u00bf a nd ha,b,c m equation 7.9 to rotating phasors J'I and i2 in equation 7.11 for two instants (1) and (2) by geometrical addition in equation 7.10. i\\(2)aAc = Ji(2) cos(w1(2)i + <phm + D) (7.9) 7) = 0\u00b0; -120\u00b0; +120\u00b0; ? $ > = \\ {imaefi\u00b0 + imbe +\u00df20\u00b0 + /1(2)c^120\u00b0) (7.10) = 2 / 3 \u03a3 7l(2) COSK2)' + \u03bd/,\u03c1, + D)e'JD D = J1{2)/\"'0> \u00b7 e*\"\u00ae' Z1(2) = 71{2) \u25a0 \u039b (7.11), (7.12) i,(2)eAc = Re{i'Ze+iD) = Mh(i) \u25a0 eM>v \u25a0 e**\u2122* \u25a0 e+\u00bfD) = 7!(2) cos(w1(2)i + \u03c6\u03b7(2) +D) (7.11 ^ 7.9) The rotating phasor / 1(2) = \u0399\u03b9^2)^ \u03c6'\u03971) \u25a0 ejWH2)l can be regarded as stationary phasor /1(2) = I\\(2)e mw multiplied with the rotating unit phasor eMm' (equations 7.11, 7.12). The equations 7.9 and 7.11 show clearly in which way amplitude \u0399\u03c7^, frequency wi(2) and phase angle ipi]{2) of the three-phase quantities determine the absolute value 7i(2), the stationary unit phasor ej,p\"m and, the rotating unit phasor eM<-2)' of the stator (rotor)-related rotating phasor i'1(2) 1(2). Equation 7.11 -\u00bb7.9 shows the inverse transformation i^ \u2014> i\\(2)a,b,cIn the phasor diagrams in Figures 7-5c, d the stator respectively rotor current phasors are multiplied with the stator inductance L\\ and the stator-rotor coupling inductance M and summed up geometrically to form the resultant stator flux linkage 344 7. High-Power Industrial Drives \u03a6,\u03b2'\"1' = (/].\u00a3,! +IeM)e'u'1'. This illustrates the phasor equation of the stator in Figure 7-4e in the steady state {d/dt^_x = 0; \u00a1\u03c9\u03bb\u03ac\u03af = \u03c9\u03c7\u03ae under the assumption that the stator resistance can be neglected {Rx \u2014\u00bb 0). Here again, the area within the phasor triangle of the flux linkages 7iLi,/2Af and \u03a6, is proportional to the generated torque Te\u2014according to the torque equation in Figure 7-5e. 7.5. Converters for Large Drives 345 7.5. CONVERTERS FOR LARGE DRIVES"
        ]
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure25-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure25-1.png",
        "caption": "Fig. 25. Contact and bending stresses for existing geometry of face-gear drive.",
        "texts": [],
        "surrounding_texts": [
            "Finite element analysis has been performed for the two versions of face-gear drives represented in Tables 1 and 2. For the second version of face-gear drive, it has been also considered the application of a rounded top shaper (Fig. 5), in order to compare the bending stresses at the fillet of the generated face-gear. The finite element mesh of three pair of teeth of version 2 is represented in Fig. 24. Elements C3D8I [5] of first order, enhanced by incompatible nodes to improve their bending behavior, have been used to form the finite element mesh. The total number of elements is 44820 with 58327 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Figs. 25 and 26 show the maximum contact and bending stresses obtained at the mean contact point for the existing and the proposed geometry, respectively. For such examples a traditional edged-top shaper has been applied. Comparison between Figs. 25 and 26 shows that: i(i) Edge contact can be avoided, reducing the magnitude of the maximum contact stress to 40%. (ii) For a considerable part of the cycle of meshing only one pair of teeth is in contact. The max- imum bending stress at the fillet of the existing geometry of face-gear is 43% lower. Fig. 27 confirms that application of a rounded-top shaper (Fig. 5) reduces the bending stresses of the face-gear from 6% to 12% during the cycle of meshing. This enables us to keep the increment of the bending stresses for the proposed geometry less than 40%. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs. 28 and 29). Figs. 28 and 29 illustrate the variation of bending and contact stresses of the face-gear and the pinion during the cycle of meshing for face-gear generated with an edged-top shaper and a rounded-top shaper, respectively. The stresses are represented as functions of unitless parameter / represented as / \u00bc /P /in /fin /in ; 06/6 1 \u00f034\u00de Here /P is the pinion rotation angle, /in and /fin are the magnitudes of the pinion angular positions in the beginning and end of cycle of meshing. The unitless stress coefficient r (Figs. 28 and 29) is defined as r \u00bc rP rPmax ; jrj6 1 \u00f035\u00de Here rP is the variable of function of stresses and rPmax is the magnitude of maximal stress."
        ]
    },
    {
        "image_filename": "designv10_2_0003545_0022-0728(95)04522-8-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003545_0022-0728(95)04522-8-Figure8-1.png",
        "caption": "Fig. 8. Catalytic oxidation of ascorbic acid at Na2NiFe(CN) 6 INaNiFe(CN) 6 IPt modified electrode in pH 7.0 phosphate buffer at 20 mV s-t: curve (a) without ascorbic acid; curve (b) with 2.0 mM ascorbic acid.",
        "texts": [
            " 7(a), the peak current decreased and the peak potential moved toward a somewhat more positive value. It was obvious that Nafion \u00ae film reduced the migration rate of Na \u00f7 from solution to the membrane of Na2NiFe- (CN) 6 1NaNiFe(CN) 6. In general, the nickel-hexacyanoferrate film possesses a negative charge. This should decrease the response of ascorbic acid because of the electrostatic repulsion between the film and ascorbic acid. However, experimental results showed that the Na2NiFe(CN)6INaNiFe(CN) 6 could also catalyze the oxidation of ascorbic acid as well as dopamine (Fig. 8). While this modified electrode was further coated with Nation \u00ae, no catalytic current was obtained for ascorbic acid. So the Nafion \u00ae I Na2NiFe(CN) 6 I NaNiFe(CN) 6 modified electrode could be used for the determination of dopamine in the presence of an ascorbic acid concentration as large as 50-fold that of dopamine. A calibration curve of dopamine was obtained in the range of 1.0 \u00d7 10 -4 to 1.5 \u00d7 10 -2 M. This project was supported by the National Natural Sciences Foundation of China. [1] D.O"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000588_j.jmapro.2021.02.021-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000588_j.jmapro.2021.02.021-Figure13-1.png",
        "caption": "Fig. 13. Finite element model and boundary conditions: (a) meshes of layers in cases, (b) boundary conditions without clamps, (c) boundary conditions with clamps, and (d) mesh model in Case 8.",
        "texts": [
            " The temperature-dependent mechanical properties of Al-5356 alloy (filler wire) and Al-6082 alloy (substrate) were obtained from the material database in Simufact.welding software [34] as shown in Fig. 12. It should be mentioned that the strain hardening was ignored in this study because of the strain softening induced by the annealing effect [37,40]. J. Sun et al. Journal of Manufacturing Processes 65 (2021) 97\u2013111 In the present work, the cases in Table 5 were designed and analyzed for clarifying the generation mechanism of RS in the WAAM components. The used meshes of these cases can be seen in Fig. 13. The only difference between cases 1\u20136 was the number of layers. The size of the model in Case 5 was equal to that of the experimental sample as in Fig. 5. The total number of nodes was 62, 728 and that of meshes was 54, 482 in Case 5. The minimum size of the element at the beam area was about 1 \u00d7 1 \u00d7 0.65 mm. The only difference between Case 5 and Case 7 was the application of external clamps. It should be mentioned that the clamps were applied during the WAAM process, but then the clamps were removed when the WAAM component cooled down to the room temperature in Case 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000826_j.apm.2020.11.027-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000826_j.apm.2020.11.027-Figure4-1.png",
        "caption": "Fig. 4 A moving Gaussian heat source heats the semi-infinite substrate",
        "texts": [
            " As a result, the molten pool width is less influenced by the recoil pressure and can be determined by the Eagar-Tsai model ignoring the existence of recoil pressure. An approximate analytical expression of the molten pool width is yielded from the Eagar-Tsai model [12]. In the Eagar-Tsai model, the metal substrate is considered to be semi-infinite, with a moving Gaussian heat source. Furthermore, the morphology of the molten pool surface, as well as the phase change of the metal, are neglected. Rubenchik et al. [24] discuss the reliability of the above simplifications. As shown in Fig. 4, x is defined as the moving direction of the heat source, and z is normal to the metal substrate. Temperature T is solved from the Fourier equation: \ud835\udf0c \u22c5 \ud835\udc50\ud835\udc5d \u22c5 \ud835\udf15\ud835\udc47 \ud835\udf15\ud835\udc61 \u2212 \ud835\udefb(\ud835\udf05\ud835\udefb\ud835\udc47) = \ud835\udc44#(12) where the density \u03c1, specific heat cp, and conductivity \u03ba are considered to be constants. Q is the Gaussian distributed heat source \ud835\udc44 = \ud835\udeff(\ud835\udc67) \ud835\udc43\ud835\udefc 2\ud835\udf0b\ud835\udf0d2 exp (\u2212 (\ud835\udc65 \u2212 \ud835\udc63\ud835\udc61)2 + \ud835\udc662 2\ud835\udf0d2 ) #(13) where, parameters P, \u03b1, and t are laser power, absorptivity, and time-variant, respectively. The boundary condition at z = 0 is \ud835\udf15\ud835\udc47 \ud835\udf15\ud835\udc67 = 0#(14) The temperature field is solved through the combination of Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003919_978-94-015-9064-8_5-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003919_978-94-015-9064-8_5-Figure3-1.png",
        "caption": "Figure 3, i-th leg of the 3-(RRPRR) parallel manipulator",
        "texts": [
            " In the following, maintaining the same topology of the Tsai manipulator, but considering a quite general geometry, such as not intersecting nor perpendicular axes of the revolute pairs in the universal joints, a minimum set of geometric conditions for obtaining a mechanism with a translational platform is investigated. 3. Kinematic model of the 3-(RRPRR) parallel manipulator A kinematic model of the 3-(RRPRR) PM is presented in the this section to study the assembly conditions of the manipulator itself. With reference to Fig. 3, where a schematic of the i-th leg of the 3-(RRPRR) PM is shown, the geometric parameters as well as the variables of motion are given according to the Denavit-Hartenberg notation (Denavit and Hartenberg, 1955). Specifically, the j-th link, j=I,2,3, that belongs to the i-th leg, i=I,2,3, is connected to the G-l)-th link by the j-th revolute pair. A coordinate reference system Sji is chosen fixed to each link with the Zji axis directed along the axis of the j-th revolute pair and positive direction arbitrarily chosen",
            " Moreover: (lji is the angle that axis Zji describes to become parallel to axis Zu+l),i when rotated about axis Xji according to the right hand screw rule; ~i is the shortest distance of axes XO.l),i and Xjj, and is positive if proceeding from link j-I to link j it has the positive direction of the Zji axis; 8ji is the variable of motion of the j-th kinematic pair and it measures the angle that axis XO-l),i describes to become parallel to axis Xji by a rotation about the Zji axis according to the right hand screw rule. Two reference systems Sb and Sp embedded respectively in the base and in the platform are also arbitrarily chosen. In Fig. 3, the unit vector Wji is chosen according to the positive direction of the Zji axis; the unit vector W4i is chosen along the axis of the revolute pair between link 3 and the platfom. In the following, for brevity and without ambiguity, unit vectors Wji and W4i will be often called vectors instead of unit vectors. Inspection of Fig. 3 shows that the position vector Bi of point Bi, foot of the shortest distance d3b and the unit vector W4b both considered as embedded in the platform, can be written in the reference system Sb fixed to the base as functions of the constant geometric parameters aji and (Xjb and the joint variables 9ji and d2b when coordinate transformations are performed through the links of the i-th leg. Since the point Bi and the unit vectors W4i are fixed to the same rigid body, the vectors (B2-B1) and (B3-B1) can be written as a linear combination of the three unit vectors W4i as follows (1",
            " The system can be used to solve the direct as well as the inverse position analysis of the 3-(RRPRR) PM. In these analyses the distance dzi, i=I,2,3, is a given value or a variable, respectively. In order to assemble the platfonn in arbitrarily chosen positions while maintaining a constant attitude with respect to the base it is necessary that the three unit vectors W 4i, i=I,2,3, keep constant in a reference system fixed to the base while the variables of motion can still change. With reference to Fig. 3, each vector W4i, transfonned through the i-th leg in a reference system fixed to the base, for instance the system Sbi with z axis along vector W Ii, x and y axes arbitrarily chosen and mutually orthogonal to z axis to fonn a proper system, can be written as follows with and Gj, ~ r~ 0 0 -s3 ji c3 ji o ~l cU ji -':j,] sU ji cU ji (3) j = 1,2,3 (4) j = 1,2,3 (5) where Hji = Rji Gji, is the 3x3 rotation matrix for vector transfonnation from link j to link j-l of leg i; cO and sO are for cosine and sine respectively; the left hand side vector superscript refers to the reference system where vectors are measured; and Pw 4i is the vector W 4i measured in a reference system Spi fixed to the platfonn having the z axis with the same or opposite direction of vector W4j, and x and y axes arbitrarily chosen and mutually orthogonal to z axis to form a proper system",
            " Moreover, these conditions holding, equations (1) for given values of the leg lengths (d2;, i=I,2,3, given) represent a system of six equations in the six unknowns Sjb j=I,2, i=I,2,3, which provide all the configurations of the 3-TPM manipulator that are possible candidates to maintain a constant orientation of the platform with respect to the base during the motion. 4. Mobility analysis of the 3-TPM manipulator For given values of the leg lengths, that is for given values of the distances dji (see Fig. 3), the 3-TPM manipulator, according to the Grubler criterion, becomes a statically determined structure, and the platform does not have any mobility with respect to the base. Instead, by considering the leg lengths as variables the 3-TPM manipulator, still according to the Grubler criterion, has three degrees of freedom. The question whether the platform has a pure translational motion in its neighborhood or a motion with three dofthat involves translation as well rotation is in order. Thus, the following proposition will be proved. PROPOSITION: If the 3-TPM manipulator is assembled in any non-singular closure configuration that satisfies the conditions (13), by varying the leg lengths, the platform can only have a translational motion with respect to the base. PROOF: With reference to Fig. 3, the angular velocity, (0, of the platform with respect to the base can be written through the i-th leg as follows (0 = IejiW ji j~I,4 where the upper dot stays for differentiation with respect to time. (15) Recalling that condition (6) means that the axes of the revolute pairs of the intermediate link of the leg are parallel to each other, that is (16) for a proper choice of the positive direction of vectors W2i and W3i> if the conditions (16) and (l3) are satisfied, equation (15), for i=I,2,3, represents a system of three vector equations that, after rearrangement, can be written as follows 00 = (911 \u00b1941 )w II +(9 21 +931 )w 21 00 = (9 12 \u00b1942 )w I2 +(922 +932 )w 22 00 = (913 \u00b1943 )w I3 + (9 23 + 9 33 )w23 (17"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.30-1.png",
        "caption": "Fig. 7.30: Snap Fastener with a Plate as Elastic Support",
        "texts": [
            " For every additional contact we obtain three more equations from geometry and three additional unknowns (ui, vi, |LfN |i). The system of nonlinear equations has then the dimension IR6+3n, where n is the number of contacts n = 1, 2 or 3. The transformation into the gripper system is rather simple:( Gf Gm ) = AGL ( LfN +L fR LrGP \u00d7 (LfN +L fR) ) . (7.102) The determination of the stiffness matrix K is still missing. It represents the compliances of the parts. The elastic support might consist of a beam (Figures 7.26 and 7.28) or a plate (Figure 7.30). We apply beam and plate theory, respectively. In a first step we regard the snap fastener from Figure 7.28. According to the picture the displacement in the xA (wx) and yA (wy) direction and the twist around the xA (\u03d5x) and zA (\u03d5z) axes are constrained. The stiffness in these directions would be very high compared to the other elements of K, therefore generating approximately zeros in the first, second, fourth and sixth rows and columns. From beam theory (BERNOULLI\u2013beam) the deflection curve is derived from the following differential equation: EIy(x)w\u2032\u2032\u2032 z (x) = \u2212Fz , Iy(x) = 1 12 (a + x l (b\u2212 a))3c",
            " Measurements were made using again the single axis force measurement machine. Figure 7.29 shows the force vs. distance for the insertion of the upper half of the snap fastener from Figure 7.28. Fx is the force in the direction of insertion, and Fz acts perpendicularly. When mating the complete fitting with both parts, Fx becomes twice as large, and Fz disappears because of symmetry. 7.3 Dynamics and Control of Assembly Processes with Robots 463 Our second example is a snap fastener with a plate as elastic support from Figure 7.30. Here the displacement in the xA (wx) and yA (wy) direction and the twist around the zA (\u03d5z) axes are constrained. ThereforeK contains zeros in the first, second and sixth rows and columns. We assume a KIRCHHOFF plate. The bending is approximated by a Ritz\u2013series wz(x, y) = qTw(x, y), with the coordinates q and the shape functions w. As shape functions we use piecewise defined cubic splines which satisfy the boundary conditions. The coordinates q of the shape functions are found by minimizing the potential \u03a0 = Wi\u2212Wa. We therefore have to solve the variational problem ( \u2202\u03a0 \u2202q )T = 0 with Wi, the elastic energy in the plate: Wi = 1 2 D qT a\u222b 0 b\u222b 0 W T  1 \u03bd 0 \u03bd 1 0 0 0 2(1\u2212 \u03bd) W dy dx q, D = Eh3 12(1\u2212 \u03bd2) , W = [w,xx|w,yy|w,xy] T . (7.105) In these equations a, b and h describe the geometry of the plate according to Figure 7.30, E is the modulus of elasticity and \u03bd is Poisson\u2019s ratio. Wa is the work done by the loads Fz, Mx and My. Let xL and yL be the coordinates of the origin of the L\u2013frame, then Wa = [Fz |Mx|My] +wT (xL, yL) +wT ,y(xL, yL) \u2212wT ,x(xL, yL) q. (7.106) After differentiating the potential with respect to q, we get a system of linear equations. Let q\u0302 be the solution of the equations. The dimension of the system depends on the number of shape functions we use. We then calculate the deformation of the point xL, yL using 464 7 Roboticswz \u03d5x \u03d5y  = +wT (xL, yL) +wT ,y(xL, yL) \u2212wT ,x(xL, yL)  q\u0302. (7.107) For a = 32mm, b = 66mm, h = 3mm, E = 2700N/mm2, \u03bd = 0.3 and xL = 27mm, yL = 48mm, K becomes Fx Fy Fz Mx My Mz  =  0 0 0 0 0 0 0 0 0 0 0 0 0 0 168.5 \u2212455.8 2105.1 0 0 0 \u2212455.8 26794.7 \u22121443.3 0 0 0 2105.1 \u22121443.3 37700.4 0 0 0 0 0 0 0   u v w \u03b1 \u03b2 \u03b3  . (7.108) In Figure 7.31 the results from the experiments and the calculations are shown, for the insertion of the snap fastener from Figure 7.30. Altogether we recognize a good correspondence between theory and experiment for both cases. The force vs. distance graphs show an unsteady shape because of the nonsmooth contour of the snap hooks. It is also observed that the jumps in the mating force are sharper in the calculation than in the measurement. This results from local deformations of the snap hook especially when the contact forces become very high, for example at about 25mm in Figure 7.31. Some Fundaments For this topic we refer to the contributions of [152] and [154]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure7-5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure7-5-1.png",
        "caption": "Figure 7-5. Asynchronous motor. Illustration of the mode of operation: three-phase quantities (a); rotating phasors (b) and rotating phasor diagrams (c) for two instants (1) and (2); stationary phasor diagram (d); simplified steady-state motor equations (e).",
        "texts": [
            "9 shows the inverse transformation i^ \u2014> i\\(2)a,b,cIn the phasor diagrams in Figures 7-5c, d the stator respectively rotor current phasors are multiplied with the stator inductance L\\ and the stator-rotor coupling inductance M and summed up geometrically to form the resultant stator flux linkage 344 7. High-Power Industrial Drives \u03a6,\u03b2'\"1' = (/].\u00a3,! +IeM)e'u'1'. This illustrates the phasor equation of the stator in Figure 7-4e in the steady state {d/dt^_x = 0; \u00a1\u03c9\u03bb\u03ac\u03af = \u03c9\u03c7\u03ae under the assumption that the stator resistance can be neglected {Rx \u2014\u00bb 0). Here again, the area within the phasor triangle of the flux linkages 7iLi,/2Af and \u03a6, is proportional to the generated torque Te\u2014according to the torque equation in Figure 7-5e. 7.5. Converters for Large Drives 345 7.5. CONVERTERS FOR LARGE DRIVES The converters connect the three-phase AC system with the motors and fulfill two main tasks: 1. They convert the voltages and currents of the AC system according to the requirements of the motors. 2. They control the power flow from the AC system to the motor in the driving mode, and vice versa, in the regenerative breaking mode. 1. AC voltage source rectifiers (AC VSRs) 2. DC voltage source inverters (DC VSIs) Both circuits are shown in Figure 7-6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001247_17452759.2021.1905858-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001247_17452759.2021.1905858-Figure11-1.png",
        "caption": "Figure 11. Test artifact for experimental trials (dimensions are in millimetres).",
        "texts": [
            " Due to the limitation of the motion mechanism of the laser scanner and point cloud computational efficiency, the processing time is about 20s for each layer. During the processing time, a nozzle cleaning mechanism is designed to remove the extra material from the nozzle and make sure the fabrication resuming without extra extrusion. The test artifact used is known as the circle-square-diamond test part widely used for assessing the accuracy of computer numerical control (CNC) machines as shown in Figure 11. It is simplified from a standard test artifact defined in both the International Standard ISO 10791\u20137 2014 (International Standard 2014) and the American Standard ASME B5.54 2005 (American Standard 2005). The proposed online laser-based process monitoring and closed-loop control system can also be used with other AM machines, like DED systems (Chen et al. 2020). The laser scanner can provide accurate measurement of the part during the fabrication process. Nevertheless, for some metal AM systems, like SLS, due to high scan speed of laser source, the computational burden of the laser-based dataset may cause delay for real-time control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000419_j.ymssp.2019.106583-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000419_j.ymssp.2019.106583-Figure2-1.png",
        "caption": "Fig. 2. Difference in contact between balls and rings.",
        "texts": [
            " Then with an arbitrary ball j, the azimuth uj is linked with /j as shown in Eq. (9). Bring Eq. (8) and Eq. (9) into Eq. (6) and Eq. (7), and define the torques My and Mz, the rotational motion of the inner ring can also be obtained. For more detailed derivation of the equations, please refer to Ref. [34]. Due to the bearing clearance, there exists difference in the contacts between balls and rings [36], some balls are in contact with the inner and outer rings, while others are not, as shown in Fig. 2. The balls in contact with the inner and outer rings carry the load simultaneously, and are regarded as the loaded balls. The other balls are not in contact with the inner ring, and are regarded as unloaded balls. The unloaded balls are considered to move along the outer ring raceway, and the inner ring is only supported by the loaded balls. In traditional models based on steel bearings [10,21], the balls are considered to carry the load evenly in a specific area defined as the load zone. According to the results in previous works [13,37], the load zone covers the 1/3 symmetrical lower part of the bearing as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003414_87.761054-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003414_87.761054-Figure1-1.png",
        "caption": "Fig. 1. PVTOL aircraft.",
        "texts": [
            "00  1999 IEEE Theorem 1: If one can choose , , and such that the solution to the optimal control problem, denoted by , exists and the following conditions are satisfied: for some such that , then , the -component of the solution to the optimal control problem, is a solution to the robust control problem. We will apply this theorem to design a robust hovering control for V/STOL aircraft. Since we are interested in control of jet-borne maneuver (hovering), we consider a prototype planar vertical takeoff and landing (PVTOL) aircraft. This system is the natural restriction of a V/STOL aircraft to jet-borne maneuver in a vertical-lateral plane. This prototype PVTOL aircraft as shown in Fig. 1 has a minimum number of states and inputs but retains many of the features that must be considered when designing control laws for a real aircraft such as the Harrier. The aircraft state is simply the position, , , of the aircraft center of mass, the roll angle, , of the aircraft, and the corresponding velocities, , , . The control inputs, and are, respectively, the thrust (directed out the bottom of the aircraft) and the rolling moment about the aircraft center of mass. In the Harrier, the roll moment reaction jets in the wingtips create a force that is not perpendicular to the -body axis",
            " Thus, the production of a positive rolling moment (to the pilot\u2019s left) will also produce a slight acceleration of the aircraft to the right. As we will see, this phenomenon makes the aircraft nonminimum phase. Let be the small coefficient giving the coupling between the rolling moment and the lateral force, , on the aircraft. Note that means that applying a (positive) moment to roll to the pilot\u2019s left produces an acceleration, , to the right. In the modeling of the PVTOL aircraft, we neglect any flexure effect in the aircraft wings or fuselage and consider the aircraft as a rigid body. From Fig. 1, we can have the following dynamic model of the PVTOL aircraft: (1) (2) (3) where stands for the gravitational force exerted on the aircraft center of mass and is the mass moment of inertia about the axis through the aircraft center of mass and along the fuselage. For simplicity, we scale this model by dividing (1) and (2) by , and (3) by , to obtain Let us define (4) In addition, from now on, we replace by . Then the rescaled dynamics becomes (5) Obviously, at steady state, , i.e., the thrust should support the aircraft weight to keep it steady"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003446_s00332-002-0493-1-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003446_s00332-002-0493-1-Figure10-1.png",
        "caption": "Fig. 10. The stretch of asymptotic helices in a perversion under tension. The points P1 and P2 are identified on the multicovered ring (left). The helix is stretched in such a way that these two points remain along the same vertical axis (middle and right pictures).",
        "texts": [
            " When a tension T is applied at the ends of the rod, in the direction of the axis of the helix (normal to the plane the ring lies in when no tension is applied), the rod forms a perversion. We calculate the length the spring is stretched by a tension T in the direction of the axes of the asymptotic helices. Consider the unstretched ring, and two material points P1 and P2 on successive rings. In the unstretched state, P1 and P2 occupy the same point in space. When tension is applied, the points separate as two asymptotic helices are created, connected by the perversion (Fig. 10). We assume that the points P1,P2 lie on the same asymptotic helix given by x(s) = 1 \u03bb2 (\u03ba cos(\u03bbs), \u03ba sin(\u03bbs), \u03c4\u03bbs). (58) Taking P1 = x(0), we have P2 = x(2\u03c0 /K ). The distance d between the z-coordinates of P1 and P2 is d = 2\u03c0\u03c4 /\u03bbK . Using the condition that the curvature and torsion lie on the ellipse (50), d is given by d = 2\u03c0 K \u221a K \u2212 \u03ba K \u2212 \u03ba(1 \u2212 ) . (59) 258 T. McMillen and A. Goriely Solving for \u03ba , and using the relation (52) between the tension T and \u03ba , the relation between the tension and d is T = K 3 2\u03c0 d( 1 \u2212 d2 K 2(1\u2212 ) 4\u03c02 )2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.57-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.57-1.png",
        "caption": "Fig. 16.57 Moment in the contact patch due to coupling forces",
        "texts": [
            " Furthermore, in driving/braking, a force with a triangular distribution in the circumferential direction is added to the shear force in the freely rolling condition. Blocks having a parallelogram shape have commonly been used for tire patterns. The directions of principal axes of the spring rate of the block (referred to as X- and Y-axes) discussed in Chap. 7 are different from the moving direction (x-axis) in the parallelogram block of Fig. 16.56. When lateral shear displacement uy is generated 1196 16 Tire Properties for Wandering and Vehicle Pull in a freely rolling tire as shown in the leftmost figure of Fig. 16.57, the fore\u2013aft (x-axis) force is generated by the coupling effect of Eq. (7.12). The pattern steer moment around the z-axis, Mz, is then generated in the contact patch by fore\u2013aft forces as shown in Fig. 16.57. The sign of the moment is minus for the counterclockwise direction. In the second figure from the left in Fig. 16.57, the fore\u2013aft displacement ux is generated in a freely rolling tire. This displacement produces lateral forces that generate a positive moment. The driving and braking forces affect the pattern steer moment and the signs of the moment in driving and braking are opposite. When parallelogram blocks are used in tires with a low aspect ratio and wide tread, the moment due to uy (the leftmost figure of Fig. 16.57) becomes dominant among four mechanisms, because the moment is proportional to the width of the tire. When the tire is narrower or the contact length is longer, the moment due to the displacement ux cannot be neglected. When the tire pattern is asymmetric as shown in Fig. 16.58, the magnitude of circumferential forces may be different in the left and right regions of the contact patch owing to the difference in the shear spring rates of the tread, especially in the driving or braking condition. The difference in circumferential forces generates a moment in the contact patch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000159_j.ijfatigue.2020.105946-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000159_j.ijfatigue.2020.105946-Figure1-1.png",
        "caption": "Fig. 1. Unit cell geometry: (a) parameter definition of in-plane geometry; (b) 3D view of unit cell.",
        "texts": [
            " In particular, the focus is on the fullyreversed fatigue S-N curves with the goal of investigating the role of the lattice orientation to the printing direction, junction geometry and unit cell size. We use a combination of optical microscopy, electron microscopy and fatigue testing to examine four batches of 3D printed specimens each with selected inclination (0\u00b0 versus 90\u00b0) to the build plane, junction geometry (wide fillet versus sharp fillet), and unit cell sizes (3 mm and 4 mm). The unit cell examined in this work has a regular cubic topology of strut length L and strut diameter t0. At the junctions, the struts are joined by circular arc fillets of in-plane radius R (Fig. 1a). The rationale behind the choice of the cubic unit cell is its simplicity which translates into an easy-to-control relationship between the printing direction and the loading direction of the struts and the possibility of obtaining welldefined fillet radii at the strut junctions. The results here obtained can be transferred to more complex topologies, thus providing insight into the fatigue design of lattice materials. The lattice specimens were 3D printed via L-PBF using a Renishaw machine equipped with a pulsed laser with a nominal power of 200 W and starting from a spherical biomedical grade Ti6Al4V (O2 < 0",
            " A diamond Vickers indenter was used to apply a maximum force of 1 N. The load was applied at a constant 0.1 N/s rate with a dwell time of 10 s. Six measurements were performed on a parallel and a perpendicular section to the printing direction for a specimen of each batch. A set of numerical simulations were carried out to assess the lattice responses in the linear regime only using Ansys\u00ae Mechanical APDL, Release 18.0 (Canonsburg, Pennsylvania, U.S.A). A reduced model consisting of one unit cell (Fig. 1b and, after meshing with 3D 20 node structural continuum elements, Fig. 6) for both the nominal geometry and the as-built geometry was developed with results later compared with their experimental counterparts. For the base material (bulk Ti6Al-4 V), we use the following properties: elastic modulus of 113 GPa and Poisson\u2019s ratio of 0.34. The FE models were used to calculate the fatigue notch factor K f at the filleted joints defined assuming a worstcase scenario of notch sensitivity =q 1 (full notch sensitivity) [23]: = =K K maximum principal stress at the joint nominal homogeneous stressf t (1) Where the nominal homogeneous stress is the ratio between the load on the unit cell and the nominal area of the unit cell (L \u00d7 L)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure9-1.png",
        "caption": "Fig. 9(b) and (c) show schematically the profiles of the rack-cutters of the pinion and the shaper, respectively. Application of both items, (i) and (ii), provide more freedom for observation of the desired dimensions of instant contact ellipse and the predesign of a parabolic function of transmission errors.",
        "texts": [
            " PII: S0094-114X(02)00050-2 The contents of the paper cover: (1) A brief summary of the existing geometry and the output of tooth contact analysis (TCA) computer program developed for simulation of meshing and contact. (2) Modified geometry of face-gear drives based on application of a shaper that is conjugated to a parabolic rack-cutter. (3) Concept of generation of face-gears by grinding or cutting worms, analytical derivation of worm thread surface, and its dressing. Nomenclature ai\u00f0i \u00bc d; c\u00de pressure angles for asymmetric face-gear drive for driving (i \u00bc d) and coast (i \u00bc c) sides (Fig. 9) Dc change of shaft angle (Fig. 8) DE change of shortest distance between the pinion and the face-gear axes (Fig. 7) Dq axial displacement of face-gear (Fig. 8) kw crossing angle between axes of shaper and worm (Fig. 21) cm shaft angle (Figs. 4, 8, 12) Ri \u00f0i \u00bc s; 1; 2;w\u00de tooth surface of the shaper (i \u00bc s),the pinion (i \u00bc 1), the face-gear (i \u00bc 2) and the generating worm (i \u00bc w) wj \u00f0j \u00bc r; e\u00de angle of rotation of the shaper (j \u00bc r) and the pinion (j \u00bc e) considered during the process of generation (Fig. 11) wi \u00f0i \u00bc s;w\u00de angle of rotation of the shaper considered during the process of generation of the face-gear (i \u00bc s) and the worm (i \u00bc w) (Figs. 12, 21) wi \u00f0i \u00bc 2;w\u00de angle of rotation of the face gear (i \u00bc 2) and the worm (i \u00bc w) considered during the process of generation (Figs. 12, 21) h\u00f0i\u00de j ; u\u00f0i\u00dej \u00f0j \u00bc s; 1\u00de surface parameters of the rack-cutter for the shaper (j \u00bc s) and the pinion (j \u00bc 1), for driving side (i \u00bc d) and coast side (i \u00bc c) (Fig. 9) Ews shortest distance between the axes of the worm and the shaper (Fig. 21) fd parameter that determines location of point Oq (Fig. 9) Li \u00f0i \u00bc 1; 2\u00de inner (i \u00bc 1) and outer (i \u00bc 2) limiting dimensions of the face-gear (Fig. 4) Lis \u00f0i \u00bc 2;w\u00de lines of tangency between the shaper and the face-gear (i \u00bc 2), the shaper and the worm (i \u00bc w) (Figs. 3,13\u201315) Mji, Lji matrices 4 4 and 3 3 for transformation from Si to Sj of point coordinates and projections of vectors Ni \u00f0i \u00bc s; 1; 2;w\u00de number of teeth of the shaper (i \u00bc s), of the pinion (i \u00bc 1), of the face-gear (i \u00bc 2), of the generating worm (i \u00bc w) p circular pitch P diametral pitch rpj \u00f0j \u00bc s; 1\u00de radius of the pitch circle of the shaper (j \u00bc s) and the pinion (j \u00bc 1) (Figs",
            " The location and orientation of coordinate systems Sd and Se with respect to Sq are shown in Fig. 8(a). The misaligned face-gear performs rotation about the ze axis (Fig. 8(b)). TCA results shown in Fig. 6 have been obtained for numerical example of design parameters shown in Table 1. The proposed geometry is based on the following ideas: i(i) Two imaginary rigidly connected rack-cutters designated as A1 and As are applied for the generation of the pinion and the shaper, respectively. Designation A0 indicates a reference rackcutter with straight line profiles (Fig. 9). (ii) Rack-cutters A1 and As are provided by mismatched parabolic profiles that deviate from the straight line profiles of reference rack-cutter A0. Fig. 9(a) shows schematically an exaggerated deviation of A1 and As from A0. The parabolic profiles of one tooth side of rack-cutters A1 and As for one tooth side are shown schematically in Fig. 9(b) and (c). (iii) The tooth surfaces R1 and Rs of the pinion and the shaper are determined as envelopes to the tooth surfaces of rack-cutters A1 and As, respectively. (iv) The tooth surfaces of the face-gear R2 are generated by the shaper and are determined by a sequence of two enveloping processes wherein: (a) the parabolic rack-cutter As generates the shaper, and (b) the shaper generates the face-gear. The face-gear tooth surface R2 may be as well ground (or cut) by a worm (hob) of a special shape (see Section 7). (v) The pinion and face-gear tooth surfaces are in point contact at every instant since: (i) rackcutters A1 and As are mismatched (Fig. 9(a)), due to application of two different parabola coefficients, and (ii) the pinion and the shaper are provided with a different number of teeth. (vi) An alternative method of generation of face-gears is based on application of a worm of a special shape, that might be applied for grinding or cutting (Fig. 10). Grinding enables us to harden the tooth surfaces and increase the permissible contact stresses. It will be shown below that the derivation of the worm thread surface is based on simultaneous meshing of the shaper with the face-gear and the worm (see Section 7). Reference rack-cutter A0 has straight line profiles (Fig. 9(a)). Parabolic rack-cutters designated as As and A1 are in mesh with the shaper and the pinion. Parabolic profiles of As and A1 deviate from straight line profiles of A0. Coordinate systems Sq and Sr are applied for presentation of equations of shaper rack-cutter As. Parameters ur and parabola coefficient ar determine parabolic profile of rack-cutter As (Fig. 9(b)). Respectively, coordinate systems Sk and Se are applied for presentation of equations of rackcutter A1. Parameters ue and parabola coefficient ae determine parabolic profile of rack-cutter A1 (Fig. 9(c)). Origins Oq and Ok of Sq and Sk, respectively (Fig. 9(b) and (c)), coincide and their location is determined by parameter fd. The profiles of the rack-cutter are considered for the side with profile angle ad (Fig. 9(a)). The design parameters of reference rack-cutter A0 (Fig. 9(a)) are w0, s0, and ad. Taking into account that w0 \u00fe s0 \u00bc p \u00bc p P \u00f02\u00de we obtain s0 \u00bc p 1\u00fe k \u00bc p \u00f01\u00fe k\u00deP ; w0 \u00bc kp 1\u00fe k \u00bc kp \u00f01\u00fe k\u00deP \u00f03\u00de Here k \u00bc s0=w0, and p and P are the circular and diametral pitches, respectively. The tooth surface of rack-cutter As is represented in coordinate system Sr (Fig. 9(a)) as rr\u00f0ur; hr\u00de \u00bc \u00f0ur fd\u00de sin ad ld cos ad aru2r cos ad \u00f0ur fd\u00de cos ad \u00fe ld sin ad \u00fe aru2r sin ad hr 1 2 664 3 775 \u00f04\u00de Parameter hr is measured along zr axis. Parameter ld is shown in Fig. 9(a). Normal Nr to the shaper rack-cutter is represented as Nr\u00f0ur\u00de \u00bc cos ad \u00fe 2arur sin ad sin ad \u00fe 2arur cos ad 0 2 4 3 5 \u00f05\u00de Similarly we may represent vector function re\u00f0ue; he\u00de of pinion rack-cutter A1 and normal Ne\u00f0ue\u00de. The designed parabolic profiles of rack-cutters As and A1 are represented in Fig. 9. We apply for derivation of shaper tooth surface Rs: (i) movable coordinate systems Sr and Ss that are rigidly connected to the shaper rack-cutter and the shaper, and (ii) fixed coordinate system Sn (Fig. 11(a)). Rack-cutter As and the shaper perform related motions of translation and rotation determined by (rpswr) and wr (Fig. 11(a)). The shaper tooth surface Rs is determined as the envelope to the family of rack-cutter surfaces As whereas considering the equations rs\u00f0ur; hr;wr\u00de \u00bc Msr\u00f0wr\u00derr\u00f0ur; hr\u00de \u00f06\u00de Nr\u00f0ur\u00de v\u00f0sb\u00der \u00bc fsr\u00f0ur;wr\u00de \u00bc 0 \u00f07\u00de Here vector function rs\u00f0ur; hr;wr\u00de represents in Ss the family of rack-cutter As tooth surfaces; matrix Msr\u00f0wr\u00de describes coordinate transformation from Sr to Ss; vector function Nr\u00f0ur\u00de represents the normal to the rack-cutter As (see Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.41-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.41-1.png",
        "caption": "Fig. 8.41 Effect of the Coriolis force on longitudinal and vertical spindle forces for a tire rolling over a cleat. Reproduced from Ref. [24] with the permission of SAE",
        "texts": [
            " The simulation is in good agreement with measurements. Note that the modal stiffness was modified to agree with the natural frequencies, because the natural frequencies of a rolling tire are lower than those of a standing tire. Furthermore, the modal dampings were modified to fit the measured spindle forces. 520 8 Tire Vibration Kido [24] studied the effects of the Coriolis force on longitudinal and vertical spindle forces for a tire rolling over a cleat employing steady-state transfer analysis. Figure 8.41 compares the prediction and measurement at 40 km/h. If rotational effects are included in the calculation, the peak frequency and magnitude of forces agree with the measurements well. For example, the magnitude of the longitudinal force at the peak is different from the measurement, if the Coriolis force and centrifugal force are not considered. 8.4 Tire Models Rolling Over Cleats (Ride Harshness) 521 Kamoulakos et al. [34] first analyzed a tire rolling over a cleat employing explicit FEA and showed that the axle force variation in the time domain qualitatively agreed with measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000127_tsmc.2017.2707241-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000127_tsmc.2017.2707241-Figure6-1.png",
        "caption": "Fig. 6. Single-link robot arm with a gearing connection.",
        "texts": [
            " 1 and 2, it is seen that the proposed method achieves a better tracking performance than the one without performance constraint, especially at the time when the failure occurs. Fig. 3 shows that the trajectories of two hysteretic actuator outputs, which implies that a bigger control gain needs to be provided to guarantee the required tracking performance. In addition, some corresponding adaptive laws are also depicted in Figs. 4 and 5. Clearly these signals are indeed bounded. Consider a robot manipulator in the following Fig. 6. Its gearing connection is described by an symmetric backlash model as (2), and it is well known that its dynamics are shown as follows: x\u03071 = x2 + 0.1 sin(t) x\u03072 = \u2212Mgl J sin x1 \u2212 D J x2 + u + 0.1 cos(t) (62) where x1 and x2 represent the position and velocity of the link, respectively. J is the rotational inertia of the servo motor, and D is the damping coefficient. M is the mass of the object. l represents the distance from the axis of joint to the center of the mass. Their simulated values are specified as J = 1,D = 2,M = 2, and l = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-28-1.png",
        "caption": "Figure 4-28. Carrierless pulse width modulation: (a) signal flow diagram; (b) switching-state vectors of the first 60\u00b0-sector; (c) measured subcycle durations; (d) harmonic spectrum.",
        "texts": [
            " Whenever the carrier signal reaches one of its peak values, its slope is reversed by a hysteresis element, and a sample is taken from a random signal generator which imposes an additional small variation on the slope. This varies the durations of the subcycles in a random manner [26]. The average switching frequency is maintained constant such that the power devices are not exposed to changes in temperature. The optimal subcycle method (Section 4.5.4) classifies also as carrierless. Another approach to carrierless PWM is explained in Figure 4-28; it is based on the space vector modulation principle. Instead of operating at constant sampling frequency 2fs as in Figure 4-20a, samples of the reference vector are taken whenever the duration fact of the actual switching-state vector \u00abact terminates. t.dCl is determined from the solution of Wac t + 'l\u00abl + 1 Jf h |\u00ab2 = 2^\u00b7\u00ab*(0 (4.32) where \u00ab*(/) is the reference vector. This quantity is different from its time discretized value u*(t\u201e) used in equation 4.26a. As u*(t) is considered a continuously time-variable signal in equation 4.32, the on-durations i a c t , / ] , and (1/2/j - t.dCl - tt) of the respective switching-state vectors ua, ub, and u0 are different from the values in equation 4.27, which introduces the desired variations of subcycle lengths. Note that t{ is another solution of equation 4.32, which is disregarded. The switching-state vectors of a subcycle are shown in Figure 4-28b. For the solution of equation 4.32 ux is chosen as ub, and u2 as \u00ab0 in a first step. Once the on-time /act of \u00abact has elapsed, uh is chosen as iiact for the next switching interval, u\\ becomes \u00ab0, u2 becomes ua, and the cyclic process starts again [27]. Figure 4-28c gives an example of measured subcycle durations in a fundamental period. The comparison of the harmonic spectra Figure 4-28d and Figure 4-24 demonstrates the absence of pronounced spectral components in the harmonic current. Carrierless PWM equalizes the spectral distribution of the harmonic energy. The energy level is not reduced. To lower the audible excitation of mechanical resonances is a promising aspect. It remains difficult to decide, though, whether a clear, single tone is better tolerable in its annoying effect than the radiation of white noise. 4.5. Open Loop Schemes 167 technique that the on-duration r0 of the zero vector w0 (or \u00ab7) decreases as the modulation index m increases",
            " Optimal subcycle PWM: (a) signal flow diagram; (b) subcycle duration versus fundamental phase angle with the switching frequency as parameter. The prediction assumes that the fundamental frequency does not change during a subcycle. It eliminates the perturbations of the fundamental phase angle that would result from sampling at variable time intervals [35]. The performance of the optimal subcycle method is compared with the space vector modulation technique in Figure 4-39. The Fourier spectrum is similar to that of Figure 4-28. It lacks dominant carrier frequencies, which reduces the radiation of acoustic noise from connected loads. It was assumed until now that the inverter switches behave ideally. This is not true for almost all types of semiconductor switches. The devices react delayed to their control signals at turn-on and turn-off. The delay times depend on the type of semiconductor, on its current and voltage rating, on the controlling waveforms at the gate electrode, on the device temperature, and on the actual current to be switched"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.109-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.109-1.png",
        "caption": "Fig. 12.109 Tire model (reproduced from Ref. [153] with the permission of Tire Sci. Technol.)",
        "texts": [
            "107 shows that the equivalent shear strain in the soil is concentrates in a narrow band between the top and bottom boxes. Figure 12.108 shows good agreement between the numerical simulation and experimental results. 908 12 Traction Performance of Tires (2) Prediction of the traction performance in different soil conditions The gross traction (GT) and the motion resistance (Rc) can be evaluated from the stress obtained on the surface contacting with soil in the numerical simulation. The tire model used in this simulation is shown in Fig. 12.109. The tire size is 540/ 65R30, the inflation pressure is 240 kPa, and the load is 32.86 kN. The tire is modeled using Lagrangian elements, while a soil bin having a depth of 0.326 m is modeled using Eulerian elements. The coefficient of friction between the tire and the soil surface is ignored. Figure 12.110 shows the calculated rut shape of a tire with a slip ratio of nearly 100% and the calculated cone penetration resistance of soft soil. The tire sinkage is nearly 110 mm, and the result is in good qualitative agreement with common measurement simulation 0 20 40 60 80 0 20 40 60 80 Pressure [kPa] S he ar re si st an ce [k P a] Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.22-1.png",
        "caption": "Fig. 7.22 Fig. 7.23",
        "texts": [],
        "surrounding_texts": [
            "Behaviour 261 From the above discussion, we know that averaging theory provides a method that approximate actual Poincare mapping, or the method of approximation in which the n -dimensional mapping is replaced by the n -dimensional vector field. According to theorem 7.1, the averaging method preserves the local behaviour in the system. For example, the fixed point of the averaging vector field J corresponds to the periodic orbit of eq. (7.34) and the fixed point of p.. But, because there is great difference of generality between the n -dimensional value vector field and the n-dimensional mapping, the global behaviour cannot be preserved directly. Therefore, the property of the global behaviour in J may not reflect that in p., nevertheless, under certain conditions, the global behaviour can still be preserved. Theorem 7.3 If the first approximate averaging system (7.35) is limited to the internal domain V c ;e\" , if the time T flow mapping Po of this system has a limit set that is composed only of hyperbolic fixed points, and if the intersections of the stable and unstable manifolds are all transversal, then, for sufficiently small E > 0, the Poincare mapping P.ID of precise system (7.34) is topologically equivalent to PoID. Proof This theorem is a corollary deduced directly from the averaging theorem (2) and (3). When explained in terms of dynamical systems, the result is derived from the structural stability of the flow of eq. (7.35) when E> O. Yet, the perturbation method cannot be applied directly to the standard equation, because, in eq. (7.39), when E ~ 0, undisturbed system x' = 0 is fully degenerate. On the other hand, let us discuss the equation after scaling 't = Et again. 262 Bifurcation and Chaos in Engineering (7.110) where y' = dy ; in eq. (7.110) there is a disturbing tenn r.T. However, this does not dt affect the use of Growall's estimation about the proof of theorem 7.1. So, we can obtain the same result as in theorem 7.1. Now, let us analyze the example of the Duffing equation again. Checking the phase portrait of eq. (7.73) by the Bendixson criterion, we know that it does not contain any closed orbit. That is to say, there is no closed loop or homoclinic loop. For all (e;,T)) E if? 2 ,we have trace Df = of, + of2 = -2n < 0 (7.111) oe; 8T) So the phase portrait contains fixed points only; as what we analyze here is a two-dimensional system, there is no homoclinic loop, but a saddle point only, and moreover, there is no intersection of the stable and unstable manifolds. The assumption of theorem 7.3 is satisfied, and 1'. and Po are topologically equivalent when r. is very small. In many averaging equations, there is also a periodic orbit in addition to the fixed point. For example, the averaging van der Pol equation produces a Hopf bifurcation, and the periodic orbits are disappeared one after the other at the connection of the saddle points. This is more difficult to treat, but under certain conditions the periodic orbit of the averaging equation is preserved like that of the invariant torus. Theorem 7.4 If there is a hyperbolic periodic orbit Yo in eq. (7.35), then the flow of the suspended system (7.54) has a hyperbolic invariant torus r. near Yo x S'. That is to say, the Poincare mapping 1'. of precise system (7.34) has an invariant closed curve y, near Yo' For a detailed proof of the above theorem refer to [30]. The nonnal hyperbolicity of the invariant set Yo x S' guarantees its persistence (M.W. Hirsh). But while smooth invariant closed curves are existent for both Po and 1'., the dynamics of 1'.ly , are generally quite complex owing to the effects of the resonant vibration. Now, let us analyze eq. (7.110). When r. = 0, there is an orbit of period t in eq. (7.110). When r. ~ 0 , we have the resonance relationship _ mr.T t=- n m,n EZ (7.112) Hence, according to the general principle of mapping on the circle, a smooth closed curve y, is obtained. This is the set containing the periodic points, whose periods m -! depend on r.. When r. ~ 0 they appear or disappear in countable r. bifurcating sequence. The analysis of such resonance motion depends on the small denominators; for further discussion, please see [36]. Application of the Averaging Method in Bifurcation Theory 263"
        ]
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.38-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.38-1.png",
        "caption": "Fig. 6.38: COz microsensor. According to [Heur92]",
        "texts": [
            " The concentrations of C02 in a fluid can be measured with AMO/PTMS (3-amino-propyl-trimethoxysilane/propyltrimeth oxysilane ). The dielectric properties of this material change with the C02 contents in the surrounding of the sensor [Heur92]. This change can be mea sured using a planar interdigital transducer, which makes an indirect C02 measurement possible. The sensor was constructed using a zigzag electrode design on top of which the sensitive material was deposited. The zigzag de- sign has better capacitive properties than the conventional interdigital finger structure, Fig. 6.38. The NiCrAu capacitor was deposited on a glass sub strate. In experiments, the zigzag width was varied between 2.5 ~-tm to 15 ~-tm and the thickness of the sensitive AMO/PTMS layer was varied between 0.9 ~-tm and 1.2 J-tm. The most effective electrode area was 21 mmz. Another interdigital transducer sensor for detecting CO, COz, NOz and water concentrations was introduced in source [Stei94]. The sensor was covered with \u00b7 a sensitive layer of Sn02 which is the most often used oxide semicon ductor material for detecting gases; it can be produced at low cost by the thin film techniques (Chapter 3) and has a high reliability"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001250_j.msea.2021.141539-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001250_j.msea.2021.141539-Figure2-1.png",
        "caption": "Fig. 2. (a) The distribution of WAAM-CMT SS316L nozzles on the pipeline, (b) schematic diagram of standard round rod tensile specimens inside the rough-mouth and narrow-mouth SS316L nozzles, (c) along with their detailed dimensions.",
        "texts": [
            " Besides, in order to remove oxidation layer distributed on the melted pool surface, each layer was thoroughly polished. Otherwise, some oxide particles with high melting point will remain inside the newly formed melting pool, which is detrimental to mechanical properties and corrosion resistance due to the internal inclusion defects accompanied by significant elemental segregation. To test the mechanical properties of the as-deposited SS316L nozzles as well as the interfacial bonding strength with the SS316LN main pipeline, standard round rod tensile specimens were cut along the building direction (seen in Fig. 2), and then both RT and HT tensile tests were performed on the AG-IC 100 KN machine. It should be noted that the metallographic specimens in the XOZ and YOZ plane were respectively cut from the WAAM-CMT SS316L roughmouth nozzle. After standard mechanical ground and polishing, the specimens were firstly characterized by the X-ray diffractometer (XRD7000S) equipped with Cu K\u03b1 radiation to identify possible phases. Afterwards, they were electro-etched in 10% oxalic solution at 1.5 V for 50 s by using electrolyte, and then observed by VHX-1000C optical microscope (OM) and FEI SIRIN200 field emission scanning electron microscope (FSEM)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000360_j.jmapro.2021.03.040-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000360_j.jmapro.2021.03.040-Figure15-1.png",
        "caption": "Fig. 15. Residual stress at 600 mm/s scanning speed, 200 W laser power, and 50 \u03bcm hatch spacing (a) equivalent residual stress (b) X component, (c) Y component, and (d) Z component.",
        "texts": [
            " These slow cooling rates results in lower stress values as layer number increases. These findings are in accordance with previous investigations that the locations of maximum stresses are inside the already deposited layers and equivalent stress values keep decreasing as we move away from the baseplate [15,26]. The equivalent, X, Y, and Z component stress distributions for hatch spacing at the value of 50 \u03bcm, scanning speed at the value of 600 mm/s and laser power at the value of 200 W, are also shown in Fig. 15. As observed from previous discussion and Fig. 15, the stress distribution inside the SLM fabricated component is not uniform and highly location dependent. Therefore, in order to have comparable results, maximum values of equivalent stress before and after baseplate removal in the component are considered as the representative value for a given case. Similarly, maximum values of X and Y component of stress are also considered. The relationship between equivalent stress and scanning speed at constant laser power of 600 W and hatch spacing of 50 \u03bcm is given in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.9-1.png",
        "caption": "Figure 4.9 shows that the strain energy of rubber between cords Ur consists of energies related to in-plane deformation and bending deformation:",
        "texts": [
            " The strain energy of the adhesive rubber layer U0 is obtained by adding the strain energy in the plane strain state to the strain energy of interlaminar shear strain and the flexural strain energy5: U0 \u00bc Emh 2 1 m2m ZZ S u20;x \u00fe v20;y \u00fe 2mmu0;xv0;y \u00fe 1 mm 2 u0;y \u00fe v0;x 2 8>< >: 9>= >;dxdy \u00fe Emh 4 1\u00fe mm\u00f0 \u00de ZZ S w2 x \u00few2 y dxdy; \u00fe Emh3 6 1 m2m ZZ S wx;x w;xx 2 \u00fe wy;y w;yy 2 \u00fe 2mm wx;x w;xx wy;y w;yy \u00fe 1 mm\u00f0 \u00de 2 wx;y \u00fewy;x 2w;xy 2 8>>>< >>: 9>>>= >>; dxdy \u00f04:36\u00de where S is the parallelogram area in Fig. 4.9. The derivatives of Eq. (4.10) with respect to x and y yield u0;x \u00bc e0 1 X1 n\u00bc1 Cn 2pn a sin 2pnx a sin 2pny b0 ( ) v0;y \u00bc h/0\u00f0y\u00de f0\u00f0s\u00de X1 n\u00bc1 Cn 2pn b0 cos 2pnx a cos 2pny b0 f00\u00f0s\u00de 1 sin a X1 n\u00bc1 Cn cos 2pnx a sin 2pny b0 : u0;y \u00fe v0;x \u00bc X1 n\u00bc1 Cn e0 2pn b0 \u00fe f0\u00f0s\u00de 2pn a sin 2pnx a sin 2pny b0 \u00f04:37\u00de 5Note 4.3. 4.1 DLT of a Two-Ply Bias Belt with Out-of-Plane \u2026 201 The derivatives of Eqs. (4.17) and (4.23) with respect to x and y yield wx;x w;xx \u00bc e0 h X1 n\u00bc1 Cn 2pn a cos 2pnx a sin 2pny b0 wy;y w;yy \u00bc f0\u00f0s\u00de h X1 n\u00bc1 Cn 2pn b0 sin 2pnx a sin 2pny b0 \u00fe f00\u00f0s\u00de h 1 sin a X1 n\u00bc1 Cn sin 2pnx a cos 2pny b0 : wx;y \u00fewy;x 2w;xy \u00bc w0\u00f0y\u00de 2X \u00fe 1 h X1 n\u00bc1 Cn e0 2pn b0 \u00fe f0\u00f0s\u00de 2pn a cos 2pnx a cos 2pny b0 \u00f04:38\u00de The substitution of Eqs",
            "110), we obtain 222 4 Discrete Lamination Theory U0 \u00bc Emha 2 1 m2m j2 b3 3 1\u00fe 4 3 f2 \u00fe 2 3 1 mm\u00f0 \u00def1 \u00fe 1 mm\u00f0 \u00de 2 f0 \u00fe 2 3 bh2 1 mm\u00f0 \u00def0 2 664 3 775 2jhmm Rb 0 y/0dy 2j 2 3 1\u00fe mm\u00f0 \u00def3 Rb 0 yf0\u00f0s\u00dedy \u00fe 2 3 1 mm\u00f0 \u00def2 \u00fe 4 3 f1 \u00fe 1 mm\u00f0 \u00de 2 f0 n o Rb 0 f02\u00f0s\u00dedy \u00fe h2 Rb 0 /02dy\u00fe 1 mm\u00f0 \u00de 2 Rb 0 w2dy \u00fe h2 1 mm\u00f0 \u00de 6 Rb 0 w02dy\u00fe h2 3 4 1 sin2 a f0 Rb 0 f002\u00f0s\u00dedy 2 666666666666666666664 3 777777777777777777775 ; \u00f04:113\u00de where f0 \u00bc 1 4h2 P C2 n f1 \u00bc 1 4 P C2 n 2pn a 2 f2 \u00bc 1 4 P C2 n 2pn b0 2 f3 \u00bc 1 4 P C2 n 2pn a 2pn b0 : \u00f04:114\u00de The following approximations and assumption are used for the derivation of Eq. (4.113). (i) Terms including trigonometric functions of higher order are neglected in the integration: Rb 0 F\u00f0y\u00de sin 4pny b0 dy 0 Rb 0 F\u00f0y\u00de cos 4pnyb0 dy 0 : \u00f04:115\u00de (ii) b is assumed to be an integral multiple of b0: b=b0 \u00bc N integer\u00f0 \u00de: \u00f04:116\u00de The total strain energy of a two-ply bias laminate, U (= Uf + Ur + U0), is obtained by integrating over the volume defined by the reference area S of Fig. 4.9 and the half thickness of two plies h + h0. U is expressed by 4.2 DLT of a Two-Ply Bias Belt Without Out-of-Plane \u2026 223 U \u00bc Ema 2 j2K0 2j K1 w0\u00f0b\u00de sin a /0\u00f0b\u00de cos af g\u00bd \u00feK2 Rb 0 yw0dy\u00feK0 2 Rb 0 y/0dy \u00feK3 Rb 0 /02dy \u00feK4 Rb 0 w2dy\u00feK5 Rb 0 w02dy\u00fe 2K6 Rb 0 /0w0dy \u00feK7 Rb 0 /00 cos a w00 sin a\u00f0 \u00de2dy 8>>>>>< >>>>>: 9>>>>>= >>>>>; ; \u00f04:117\u00de where Em is defined by the second equation of Eq. (4.41). The constants Ki (i = 0, \u2026,7) can be calculated using the given belt structure and material properties. These equations forKi (i = 0,\u2026,7) can be easily obtained usingMathematica orMATLAB"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.4-1.png",
        "caption": "Fig 7.4",
        "texts": [
            "61) becomes an autonomous system. No track can be self transversal in the space xy9. de Because - = 1.6, the system has no singular point. The limit periodic dt solution in space xye is a helical line. In fact, the right-hand side of eq. (7.61) is 21t-periodic in e (in the general case, as is eq. (7.58)). So we can only take e E [0,21t), in space xy9 and connect e = 21t with e = O. Equation (7.61) can be taken as defined in the torus space ;e2 x Sl , and the limit periodic solution is a closed track in this space. See Fig. 7.4. We can also study the closed orbit in Fig. 7.4 from another viewpoint. Take a point (xo,Yo) on the cross-section e = 0 as an initial point. The orbit will return to the point (x)' Y)) on the section at t = 21t , or e = 21t. Generally, (XpYI) is different 1.6 from (xo,Yo)' Only when (xo,Yo) = (-0.634, +0.065) can (XpYI) be equal to (xo,Yo)' Therefore, to find a periodic solution is to find whether this return mapping (xo,yo) ~ (XpYI) has any fixed point. This is the method of Poincare mapping. We shall not use this method in this section, but the averaging method",
            "5) and it rotates on the plane xy with a constant angular speed ro. The equation on a rotating plane is C;' = 8(C;. TJ\u00b7l) and TJ' = H(C;. TJ\u00b7l) (7.62) Application of the Averaging Method in Bifurcation Theory 245 Generally speaking, system (7.62) is still non-autonomous. Its terms on the right-hand side contain time t in appearance. If this equation has a stable stationary solution, it will be corresponding to a stable periodic solution of the initial equation. Notice the differences between the following three (refer to Fig. 7.4 and 7.6): (a) The periodic solution on the plane xy is denoted by a circle. (b) The periodic solution at cross-section 2n t = 0, - , ... (that is, the shadowed plane in co Fig. 7.4) is denoted by the fixed point of the mapping. \u00a9 The periodic solution on the rotating plane 0<;'11 is a fixed point (Fig. 7.6). 2nn Only when t = 0, --, ... , are the point co coordinates of these three cases are the same. Take the solution (x(O) = O,y(O) = 0) of the forced linear vibration eq. (7.59) as an example (see Fig. 7.3). The equation on the revelent rotating plane is <;' = -(0.1<; + 0.975'11)sin2 1.6t + (0.975<; + 0.1'11 + 0.625) sin1.6t cos 1.6t '11' = (0.975<; +0.1'11 +0.625)cos2 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000697_j.jallcom.2019.04.287-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000697_j.jallcom.2019.04.287-Figure3-1.png",
        "caption": "Fig. 3. Proportion charts of tensile specimens obtained by laser additive manufacturing.",
        "texts": [
            " The alloys were characterized by X-ray diffractometer (XRD) with a wide 2q range (20e90 ) and the scanning speed is 3 /min. The microhardness of the cross section of melting pool was measured by Victorinox hardness tester (HX-1000) with a load of 50 g and a loading time of 15 s. The specimens obtained by single direction scanning were machined into 10mm 5mm 5mm. After that the density of the alloy was measured by Archimedes method [42]. The tensile tests of the TiC/AlSi10Mg alloys (as shown in Fig. 3) were carried out using a high-precision electronic universal testing machine (AG-100kN) at a strain rate of 1mm/min. Finally, the microstructures of the fracture surfaces were observed by SEM. Fig. 4 shows that the single-track TiC/AlSi10Mg alloys prepared by laser additive manufacturing are well bonded with the substrates. The observed sections were selected perpendicular to the scanning direction, corresponding to the XOZ plane shown in Fig. 3. The satellites [43] at both ends of the molten pool on the upper surface can be observed from Fig. 4a. The pores are mainly located at the top of the molten pool and near the interface between the weld pool and the substrate. This is probably due to the rapid cooling of the upper and lower surfaces of the molten pool. The gas is not able to spill out in a short time due to the rapid solidification of the melt. When the vibration frequency is 546Hz, numbers of satellites on the top surface decreases, as shown in Fig",
            " This is mainly because that strong stirring effect caused by excessively high vibration frequency forms ency micro-vibration. the heated convection in the molten pool, which concaves the upper surface in the middle of the molten pool with the satellite on the top surface and pores inside the pool, as shown in Fig. 4d. The morphologies of the deposited TiC/AlSi10Mg alloys fabricated by laser additive manufacturing under different vibration frequencies are shown in Fig. 5. The observed sections were selected perpendicular to the scanning direction, corresponding to the XOZ plane shown in Fig. 3. It can be observed that the deformation of the top layer of the TiC/AlSi10Mg alloy fabricated at the frequency of 546 Hz and 969Hz is small. In addition, the defects of the alloy fabricated at 969 Hz was least compared with the alloys produced at other conditions, implying that the TiC/AlSi10Mg alloy is best formed at the frequency of 969 Hz. The obvious deformation was found at the top of the alloy without vibration. This is because the increase of the formed layers and the gradual accumulation of defects in each layer, resulting in poor bonding and deformation between the new alloy layer and the formed alloy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.20-1.png",
        "caption": "Fig. 8.20 Fig. 8.21",
        "texts": [
            "37) near the orbit pO, especially the change of the unstable manifold 1fI: and the stable manifold 7et: at pO. To do this, we must transform the non-autonomous system (8.37) into the equivalent suspensory autonomous system: x' = I(x) +Eg(x,9) and 9' = 1, (x,9) E ~2 x Sl (8.38) where Sl = ~ is a circle of circumference T. Note that the flow (x(t),9(t)) generated by system (8.38) is on a three-dimensional manifold, and there may be chaos in this three-dimensional system. Transform a two-dimensional mapping into a one-dimensional mapping SI by using the Poincare mapping, see Fig. 8.20. The plane orbit is a circle, but a fixed point on plane S. We can transform the continuous systems into discrete systems and decrease the dimension of the systems by using Poincare mapping. We take a section of this three-dimensional manifold at to E [O,T]: ~> = {(x,9} E ~2 x SI19 = to}. Define the Poincare mapping ~/. : L I. ~ L I., where mapping ~/. transforms the point (x(to),to) E L '0 into the point returning to L I. that starts from the point (x(to),to) along (x(t+to),9(t+to)), so that we simplify the discussion of system (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000223_j.msea.2020.140279-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000223_j.msea.2020.140279-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic diagram for the vertically manufactured SLMed sample (b) Laser scan strategy applied in the SLM process (c) Dimensions for the tensile sample.",
        "texts": [
            " The strengthening mechanism were studied by analyzing the cellular sub-grain and other microstructures after different heat treatments. Commercial 316L stainless steel powder (20\u201360 \u03bcm) from Shining company (Zhejiang, China) was used to fabricate the SLMed samples. The SLMed samples were fabricated by the SLM machine (EOS 250). The SLMed sample with the following composition (in mass %): 2.52 Mo, 0.57 Si, 0.23 Mn, 0.014 P, 0.006 S, 10.53 Ni, and 16.13 Cr, the rest being Fe. The sample with the dimension of 80 mm \u00d7 20 mm \u00d7 5 mm was vertically manufactured by the SLM machine, as shown in Fig. 1(a). Then, the samples were wire-electrode cutting into the size for the tensile test, as shown in Fig. 1(c). In order to ensure good material density, the parameters of the printing process were optimized (200 W laser power, 950 mm/s scan speed, and 40 \u03bcm powder layer thickness). The scanning direction rotated 67\u25e6after each layer. Then, the samples were further heat treated at four different temperatures (500 \u25e6C, 900 \u25e6C, 950 \u25e6C, 1100 \u25e6C) for 1 h and furnace-cooled. The heat treatment process was conducted under the protection of Ar atmosphere. The heat-treated samples were named as HT500, HT900, HT950 and HT1100, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000536_978-3-030-11981-2-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000536_978-3-030-11981-2-Figure11-1.png",
        "caption": "Fig. 11 Rack profiles with normals",
        "texts": [
            " An example of linear ML is chosen to compare the obtained working sections of all three profiles with profiles determined in accordance with existing reliable programs for involute gears. Figure 10 shows the four meshing links ( , 0, 1, 2) and OY axes for 1 and 2 in two positions: initial i = 0 (profiles are marked with a dotted line) and current i = 3 (profiles are marked with a solid line). All the lines and point are obtained with the help of the computer program; the text is typed in the graphic editor by one of the authors. The image is an \u201caction\u201d image: Now it allows to observe only current contact position of reference points in motion. Figure 11 demonstrates the rack profile obtained for the meshing line in the form of an arc of a circle. Red lines correspond to normal lines to profile. In a contact point, the normal line passes through the pitch point\u2014it represents the accuracy of obtained formulae and algorithms. Figure 12 shows the fragment of three gearings made for ML in the form of an arc of a circle. Figure 12 is obtained with the help of the program used for Fig. 10. Figure 13 represents the rack (Figs. 11, 12) profile radii of curvature diagram",
            " 9a, in addition to automatic static balancing, allows you to additionally limit the dynamic imbalance (Fig. 9b), since during rotation of a dynamically unbalanced rotor, the former declines from its horizontal position, which is fixed by the position switch. HPC-4-7-600 centrifuge, manufactured by Acuitas (Switzerland), with automatic balancing, is shown in Fig. 10 [13]. One of the tasks in the development of centrifugal benches is a casing design. As a rule, in centrifuges of small radius (for example, up to 1 m, Fig. 11a), the casing design is technological and relatively easy to manufacture. Therefore, it is quite reasonable that such a centrifuge has a casing, and a designing engineer always has a desire to locate a rapidly rotating element of a machine, the rotor, inside a protective screen (Fig. 11). with ergonomics rules in relation to heightH of the rotor servicing area. In this case, base 3 is to be fixed to the power floor of test box 4. Figure 12 presents photographs of centrifuges with protective casings. In medium-radius centrifuges [14], for example, from 1 \u2026 1.5 m or more, the casing shall be assembled from different segments, and for installation of the tested products onto the rotor, the casing is to be made with an opening part. In that, all the casing elements shall be sufficiently rigid, while the door itself shall be securely locked, since when the rotor rotates, significant air cores arise, leading to vibrations and excessive pressure acting onto a cylindrical part of the casing [15, 16]. In this case, the casing turns out to be too complex, expensive, and non-technological in manufacture. Therefore, rotors of centrifugal benches designed for simulation of accelerations up to (1 \u2026 1.5) \u00d7 103 m/s2 often has no casings, and centrifuges are installed in separate premises\u2014boxes (Fig. 11b). Rotary-motion feedthrough is to be mounted onto traverse 5, supported by construction structures of the building. At large driving capacities, the centrifuge height dimension becomes significant, and for the location of the rotor service area at a required height, a part of motor 6 has to be placed below the test box floor level, in pit 7, and to get access to motor sensor 8, it is necessary to use manhole 9. The second solution option is to build a protruding base with steps around the centrifuge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.9-1.png",
        "caption": "Fig. 8.9: Contact with Smooth Force Laws",
        "texts": [
            " The unilateral contact laws can also be taken from the kinematics chapter in a suitable form for our specific application g\u0308N \u22650, \u03bbN \u2265 0, g\u0308N\u03bbN = 0, |g\u0307T | =0 \u21d2 |\u03bbT | \u2264 \u00b5\u03bbN , |g\u0307T | =0 \u21d2 g\u0307T = \u2212\u03ba\u03bbT ; \u03ba \u2265 0; |\u03bbT | = \u00b5\u03bbN . (8.34) Smooth Force Laws Another possibility to model contacts of the feet consists in assuming a singlevalued and smooth force law between feet and ground. In many cases of walking machines this corresponds quite well to the real situation, because the feet very often are equipped with some soft rubber material. Figure8.9 illustrates such a contact with springs and dampers in normal and tangential directions. The determination of the necessary spring and damper values may sometimes be cumbersome, they can be measured or evaluated using FEM, for example. Considering the relative kinematics (gN , g\u0307N ) in normal contact direction we get for the normal force In tangential direction we need the point PK where the tangential force applies. We choose for that point the body-fixed position at the beginning of the contact. According to Figure8.9 we come out with the tangential force F T = CT (rPK \u2212 rPE) +DT (r\u0307PK \u2212 r\u0307PE) (8.36) If the force amount |F T | reaches the friction reserve \u00b50FN , then we have sliding with a tangential friction force following Coulomb\u2019s law, namely F T = \u00b5FN . The point PK slides also and with a velocity r\u0307PK =D\u22121 T (F \u2217 T \u2212CT (rPK \u2212 rPE) + r\u0307PE), (8.37) where the sliding friction force will be always directed along the spring-damper force element F \u2217 T = \u00b5FN rPE \u2212 rPK |rPE \u2212 rPK | . (8.38) 8.2 Walking Dynamics 523 Both states, sliding and sticking, must continuously be controled to discover possible changes from sliding to sticking or vice vera"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.33-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.33-1.png",
        "caption": "Fig. 5.33 Tire shapes for various partitioning distributions of tire pressure in the belt (for the same carcass length) (reproduced from Ref. [23] with the permission of Guranpuri-Shuppan)",
        "texts": [
            "5 General Theory for the Shape of Belted Tires 281 partitioned value (a = 0) and partitioned values a = 0.625 and 0.375 in Eq. (5.107). In general, the calculated tire shape with the value of a = 0.375 agrees with the measurement. Figure 5.32 shows the tire shapes for a = 0.375 and various values of fbead0. The bulge in the bead area is small when the bead filler supports the pressure (i.e., the case that fbead0 > 0) and large when the bead filler does not support the pressure (i.e., the case that fbead0 < 0). Figure 5.33 shows tire shapes for various values of fbelt0 (a = 0.25) where the carcass length is constant. When fbelt0 becomes large, the tire shape becomes similar to the shape of the loaded tire or the tire shape with a low aspect ratio. In this calculation, rC is updated by rC + (L0 \u2212 L)/2 instead of fbead0 in Fig. 5.29, where L0 is the target carcass length and L is the calculated carcass length. (4) Control of tire performance through tire shape design Sakai [23] proposed tire shape design that improves the harshness and belt durability of a tire"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure9-12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure9-12-1.png",
        "caption": "Figure 9-12. less motor. Analytical model of brush-",
        "texts": [
            " The brushless motor with a trapezoidal rotor flux distribution provides an attractive candidate, because two of the three stator windings are excited at a time. As a result, the unexcited winding can be used as a sensor [10, 11]; that is, 466 9. Estimation, Identification, and Sensorless Control in AC Drives the speed EMF induced in the unexcited winding is used to determine the rotor position and speed. On the contrary, the brushless motor with a sinusoidal flux distribution excites three windings at a time and the sensorless control algorithm becomes complicated. Figure 9-12 shows an analytical model of a brushless motor where the d-q axis corresponds to an actual rotor position and the \u03b7-\u03b4 axis is a fictitious rotor position. Since the actual rotor position is not known without a position sensor, the aim is to make the angular difference \u0394\u0398 between the fictitious and actual rotor positions converge to zero. Two approaches have been proposed. Both are the estimation of the angular difference by using the detected state variables and the estimated state variables which are obtained from a motor model in the controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003717_robot.1999.769929-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003717_robot.1999.769929-Figure1-1.png",
        "caption": "Figure 1: The sketch of a biped robot with the dynamic forces on the i-th segment. The GCoM is denoted by C.",
        "texts": [
            " The first is the introduction of the FRI point which may be employed as a useful tool in gait planning in biped and other legged robots, as well as for the postural stability assessment in the human. The second contribution is in response to our discussion with other researchers regarding the misconceptions surrounding COP and the CoP/ZMP equivalence. We review the physics behind both the concepts and show that COP and ZMP are identical. 2 FRI point of a biped robot In order to formally introduce the FRI point, we first treat the entire biped robot - a general n-segment extended rigid-body kinematic chain (sketch shown for example purpose in Fig. 1) - as a system and determine its response to the external force/torque. We may employ Newton or d\u2019Alembert\u2019s principles for this purpose. The external forces acting on the robot are the resultant ground reaction force/torque, R and M , acting at the COP (denoted by point P , see Fig. 2), and the gravity. The equation for rotational dynamic equilibrium is obtained by noting that the sum of the external moments on the robot, computed either at its CoM or at any stationary reference point is equal to the sum of the rates of change of angular momentum of the individual segments about the same point",
            " It may be shown that for an idealized rigid foot the COP is situated at a boundary point unless the foot is in stable equilibrium. Since the position of COP cannot distinguish between the marginal state of static equilibrium and a complete loss of equilibrium of the foot (in both cases it is situated at the support boundary), its utility in gait planning is limited. FRI point, on the other hand, may exit the physical boundary of the support polygon and it does so whenever the foot is subjected to a net rotational moment. 3.5 COP and GCoM Referring to Fig. 1, GCoM, C satisfies CG x x m ; g = 0 where G is the center of mass of the entire robot and C m i = M is the total robot mass. Noting that C G C m ; = CGimi, and CG; = C P + PG; we can rewrite Eq. 17 as: Substituting in Eq. 1 we get From above, P and C coincide if (CHci + PG; x miai), = 0 which is possible if the robot is stationary. 4 Conclusions We introduced a new criterion called the FRI point that indicates the state of postural stability of a biped robot. The FRI point is a point on the foot/ground surface, within or outside the support polygon, where the net ground reaction force would have to act to keep the foot stationary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003314_tia.2003.821816-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003314_tia.2003.821816-Figure12-1.png",
        "caption": "Fig. 12. The flux distribution obtained from the finite-element analysis at",
        "texts": [
            " The fluctuation of the magnetic potential resulting from an unbalanced magnetic saturation caused by the radial force windings and is small in comparison with the magnetomotive force . Hence, the fluctuation of the magnetic potential can be ignored. This assumption can be verified with the finite-element analysis. The finite-element analysis is carried out by changing the magnetomotive force of the radial force windings from 0 to the rated value 150 At in the case where the magnetomotive force is constant at 280 At of rated value. The rotor angular position is zero. Fig. 12 shows the flux distribution. In addition, Fig. 13 shows the magnetic flux densities at corresponding points shown in Fig. 12. In analysis results, the magnetic flux densities and M = 150 At and M = 280 At. motive force M in the case where M is constant at 280 At of rated value. in the stator yoke are invariably about 0.6 T in linear region. Therefore, permeance of rotor and stator yokes can be ignored. As the magnetomotive force increases, the magnetic flux densities and increase and decrease, respectively. However, it is seen that the fluctuation of the magnetic flux density is very small. If the magnetic potential fluctuates by means of the unbalanced magnetic saturation, the magnetic flux density ought to fluctuate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003989_978-94-015-9064-8_11-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003989_978-94-015-9064-8_11-Figure1-1.png",
        "caption": "Figure 1. General tendon-driven Stewart platform",
        "texts": [
            " Joint limits and collisions of tendons with the support structure, the platform, or obstacles do not appear in the list because they depend on the realization or environment of a mechanism, rather than theoretical limits. Our objective is to develop optimal designs for general-purpose manipu lators, where the tasks are described only by the number and type of dofs. Thus, it is important to fulfill a minimum standard for the above conditions in a wide area of space, rather then to have excellent standards in a small area needed for a particular task. All geometric quantities are shown in Fig. 1: ICB, Kp are coordinate frames attached to base and platform, respectively; bI , ... ,bm point from KB to the base connection points, and PI, ... ,Pm from ICp to the platform con nection points; r, R give the position and orientation of Kp with respect to ICB. Furthermore, II, ... ,f m are the tendon forces. The sum of all external forces acting on the platform (i. e. all forces except II, ... ,f m, including inertia, gravity etc.) is Ip, and the sum of all external torques is Tp. We assume that: - Tendons are connected by ideal spherical joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure4.33-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure4.33-1.png",
        "caption": "Fig. 4.33: Micromotor using the SLIGA technique. Courtesy of the University of Wisconsin-Madison (Department of Electrical and Computer Engineering)",
        "texts": [
            " In general, electromagnetic microactuators are useful when efficiency is less important than reliability and safety. Rotational electromagnetic micromotor with gears For several years, the SLIGA technique (Section 4.2.5) has been investigated for the manufacture of electromagnetic micromotors [Guck92], [Chri92], (Guck93]. The process allows the making of metallic structures from nickel of only 300 Jtm height. The precision which can be obtained makes it possible to produce various planar micromechanisms, such as electromagnetic reluc tance motors with gears, Fig. 5.43 and Fig. 4.33. The structure produced from galvanically plated nickel is 100 Jtm high and consists of several gears and a reluctance motor. A rotational speed of 10000 rpm is possible. The gap bet ween the motor shaft and the rotor is only 500 nm. This nickel-nickel system has very low friction, which gives the motor excellent dynamic properties. The coil windings of the stator pole are made of an aluminum alloy wire using wire bonding; direct etching of U-like bridges has proven to be problematic. Another use of this design was th"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003740_70.88067-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003740_70.88067-Figure1-1.png",
        "caption": "Fig. 1. Example 1 geometry II = 3.0, I , = 2 .5 , l3 = 2.0.",
        "texts": [
            " Example 1: Comparison with Instantaneous Criteria In the first example, we compare the performance of the algorithm presented in this communication with that of an algorithm that instantaneously maximizes a particular criterion. The integral criterion (2) is defined by G(0, e , t) = 1/2 11 e 11 2, and this is compared for a specific workspace path with the Extended Jacobian method in which the instantaneous criterion g(0) = (det is optimized. (This is the manipulability measure of Yoshikawa [lo]. The Extended Jacobian method also has the property that the trajectories that it generates are periodic if the workspace path is closed (barring an encounter with a kinematic or algorithmic singularity .)) Fig. 1 shows the manipulator geometry and the workspace path of this example. The lengths of the manipulator were 3, 2 .5 , and 2 units for the base, middle, and end link, respectively. The workspace motion consisted of a circle of 2.3 units radius, centered at (2.5, O), traced out counterclockwise in unit time. This brings the end-effector close to the base of the manipulator at the beginning and end of the motion. Recall ([ 1, Example 5 . I]) that the end-effector touching the base of the mechanism defines an algorithmic singularity of the Extended Jacobian method when the criterion function is manipulability"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-20-1.png",
        "caption": "Figure 2-20. Cross section of inset PM motor.",
        "texts": [
            " Above the base speed where the supply voltage limit is reached, the flux linkage is reduced in inverse proportion to the speed, and, from equation 2.13, the torque is inversely proportional to speed squared. 2.8. PM RELUCTANCE MOTORS The surface PM motor considered in Section 2.4 is not amenable to flux reduction as is desired for operation in the constant power range. However, if some of the properties of the reluctance motor are incorporated into the PM machine, effective flux reduction can be achieved. For example, a cross section of an inset-PM motor is shown in Figure 2-20. The magnets are inset into the rotor iron [36]. As a PM motor, the direct axis is aligned with the center of the magnet. Considered as a reluctance machine, its direct axis inductance Ld will be small because of the near unity relative permeability of the magnet material. The quadrature inductance Lq will, however, be relatively large because of its small iron-to-iron gap throughout the quadrature sector. A typical relation between torque and rotor angle for a current-driven inset-PM motor is shown in Figure 2-21",
            " For operation at higher speeds in the constant power range, the angle \u00df is advanced still further toward 180\u00b0. This reduces the torque but also produces a stator flux linkage component that is opposite in direction to that produced by the magnets. The net flux is reduced to the point where the induced voltage is equal to the limiting value of supply voltage. The torque and the flux linkage are therefore controlled by simultaneous adjustment of the magni- 70 2. Electrical Machines for Drives tude and angle of the stator current. Using the motor configuration of Figure 2-20, a constant power speed range of 2-5 can be achieved. Another rotor configuration for a PM reluctance motor is shown in Figure 2-22. In this buried-PM motor, the magnets are directed circumferentially to supply flux to the iron poles, which then produce radially directed air gap flux. The central shaft is nonmagnetic. This type of structure has been widely used with ferrite magnets to achieve a satisfactory value of air gap flux density. The direct axis inductance of this motor is low because its flux path is largely through the low permeability magnets, while the quadrature axis inductance is large because its flux can circulate in and out of each pole face"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure3-1.png",
        "caption": "Fig. 3. Structure of face-gear tooth: (a) lines contact L2s and fillet; (b) cross-section of face-gear tooth.",
        "texts": [
            " Localization of the bearing contact between the tooth surfaces of the involute pinion and the face gear is achieved as follows: (1) The face gear may be determined as the envelope to the family of surfaces of an involute shaper with tooth number Ns > Np, where Ns and Np are the tooth numbers of the shaper and the pinion of the drive. Usually, Ns Np \u00bc 2\u20133. (2) The pinion and the shaper of the drive are in an imaginary internal tangency as shown in Fig. 2. (3) We may consider that three surfaces Rs, R2, and R1 are in mesh simultaneously. The surfaces of the shaper Rs and the face gear R2 are in line tangency at every instant. However, surface R2 and pinion surface R1 are in tangency at a point at every instant since Np < Ns. The tooth surfaces R2 of the face gear generated by an involute shaper are shown in Fig. 3(a). Lines L2s represent the instantaneous lines of tangency of R2 and shaper Rs, shown on R2. The cross-sections of the face-gear tooth are shown in Fig. 3(b). Investigation shows that the surface points of the face gear are hyperbolic ones. This means that the product of principal curvatures at the surface point is negative. The fillet of the face-gear tooth surface of a conventional design (Fig. 3) is generated by the edge of the shaper. The authors have proposed to generate the fillet by a rounded edge of the shaper as shown in Fig. 4 that allows the bending stresses to be reduced approximately in 10%. The shape of the modified fillet of the face gear is shown in Fig. 5. The length of the face-gear teeth has to be limited by dimensions L1 and L2 (Fig. 6) to avoid [8]: (i) undercutting in plane A, and (ii) tooth pointing in plane B. The permissible length of the face-gear tooth is determined by the unitless coefficient c represented as c \u00bc \u00f0L2 L1\u00dePd \u00bc L2 L1 m \u00f01\u00de where Pd and m are the diametral pitch and the module, respectively",
            " Generally, the choosing of a master surface is based on the following considerations [5]: (i) it is the surface of the stiffer body of the model, or (ii) the surface with coarser mesh if the contacting surfaces are located on structures with comparable stiffness. We have chosen for stress analysis the gear and pinion tooth surfaces as the master and slave ones, respectively. The development of the finite element model of the face gear is complicated due to the specific structure of the face-gear tooth. Fig. 3(a) shows that the tooth surface of the face gear is formed as a combination of: (i) an envelope to the family of shaper generating surfaces, and (ii) the surface of the fillet generated by the edged top of the shaper (or by the rounded top of the shaper, Fig. 4). The authors could overcome this obstacle by the development of an algorithm that determines the finite elements considering simultaneously the root, fillet, and the active part (the envelope) of the face-gear tooth. Fig. 21(a) and (b) show the finite element models of one-tooth of the pinion and the face gear, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001127_j.oceaneng.2021.109164-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001127_j.oceaneng.2021.109164-Figure2-1.png",
        "caption": "Fig. 2. BlueROV2 by BlueRobotics company.",
        "texts": [
            " Hence \ud835\udc52\ud835\udc562 = \u2212\ud835\udc50\ud835\udc56\ud835\udc52\ud835\udc561 for all \ud835\udc61 \u2265 0, whose solution is given by \ud835\udc52\ud835\udc561 (\ud835\udc61) = exp ( \u2212\ud835\udc50\ud835\udc56\ud835\udc61 ) \ud835\udc52\ud835\udc561 (0) \ud835\udc52\ud835\udc562 (\ud835\udc61) = exp ( \u2212\ud835\udc50\ud835\udc56\ud835\udc61 ) \ud835\udc52\ud835\udc562 (0) (43) Again considering the assumption \ud835\udc52\ud835\udc561 (0) = 0, \ud835\udc52\ud835\udc562 (0) = 0, then \ud835\udc52\ud835\udc561 (\ud835\udc61) = 0 and \ud835\udc52\ud835\udc562 (\ud835\udc61) = 0 for all \ud835\udc61 \u2265 0. \u25a1 The above means that if the initial conditions of position and velocity of the vehicle match with the initial conditions of the desired trajectory, the trajectory tracking will occur from the beginning, it is \ud835\udc56 = \ud835\udc56\ud835\udc51 for all time. The BlueROV2 is an underwater vehicle used in this work, see Fig. 2. This is an open structure modular vehicle with a dimension of 45.71 cm \u00d7 33.81 cm \u00d7 22.1 cm, a weight of 11.5 kg and a maximum operating depth of 100 m. This underwater robot has 6 thrusters with clockwise and counterclockwise propellers, minimizing torque reactions that allow it to perform decoupled movements in 4 DOF; its structure is made of high-density polyethylene and is complemented by two acrylic tubes that store the electronic components and the LiPo battery. The known physical parameters of the BlueROV2 are defined in Table 1 for more details see Wu (2018)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003254_3-540-45000-9_8-Figure6.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003254_3-540-45000-9_8-Figure6.9-1.png",
        "caption": "Figure 6.9. Definition of polar coordinates for the unicycle",
        "texts": [
            " Another technique which allows to overcome the obstruction of Brockett theorem is to apply a change of coordinates such that the input vector fields of the transformed equations are singular at the origin. This approach has been proposed in [1], where a Lyapunov-like design of a posture stabilizing controller is carried out using a polar coordinate transformation. The control law, once rewritten in terms of the original state variables, is discontinuous at the origin of the configuration space Q. With reference to Figure 6.9, we define the following set of polar coordinates for the unicycle. Let \u03c1 be the distance of the reference point (x, y) of the unicycle from the goal (the origin), \u03b3 be the angle of the pointing vector to the goal w.r.t. the unicycle main axis, and \u03b4 be the angle of the same pointing vector w.r.t. the x axis (orientation error), i.e. \u03c1 = \u221a x2 + y2 \u03b3 = ATAN2(y, x) \u2212 \u03b8 + \u03c0 \u03b4 = \u03b3 + \u03b8. Angles \u03b3 and \u03b4 are undefined for x = y = 0. In practice, during the vehicle motion, when \u03c1 \u2192 0 one must retain the values for \u03b3 and \u03b4 assumed in the final approaching phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.84-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.84-1.png",
        "caption": "Fig. 10.84 Effect of the vibrating position on radiating efficiency. Reproduced from Ref. [66] with the permission of JSAE",
        "texts": [
            " Because the tire sized 225/50R16 has a greater width and lower wedge angle owing to the greater belt tension compared with the tire sized 195/70R14, the former tire has a larger amplification than the latter tire. Iwao and Yamazaki [66] measured the horn effect of a tire as shown in Fig. 10.83. A speaker was buried in the road surface near the contact point of a tire and the road surface. The sound radiated from the speaker was measured with and without the tire present. An amplification effect over 10 dB(A) was observed in the 10.11 Horn Effect 659 frequency range above 300 Hz. Figure 10.84 shows that the radiating efficiency is highest when the angular position is about 10\u00b0 regardless of the lateral position of the measuring microphone. A speaker was buried in the center of the tread surface of the tire in this case. Because the angular position at 10\u00b0 is a point immediately outside the contact area, the speaker vibrates the tire immediately outside the contact area and the sound pressure level thus increases shapely. 195/70R14 225/50R16 2 dB(A) center shoulder Position of speaker So un d pr es su re le ve l (5 00 H z\uff5e 20 00 H z) d B( A) Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure8-1.png",
        "caption": "Fig. 8. For derivation of pinion rack-cutter.",
        "texts": [
            " The locations of points Q and Q are denoted by jQP j \u00bc ld and jQ P j \u00bc lc where ld and lc are defined as ld \u00bc pm 1\u00fe b sin ad cos ad cos ac sin\u00f0ad \u00fe ac\u00de ; \u00f05\u00de lc \u00bc pm 1\u00fe b sin ac cos ac cos ad sin\u00f0ad \u00fe ac\u00de : \u00f06\u00de i(ii) Coordinate systems Sa\u00f0xa; ya\u00de and Sb\u00f0xb; yb\u00de are located in the plane of the normal section of the rackcutter (Fig. 6(b)). The normal profile is represented in Sb by the matrix equation rb\u00f0uc\u00de \u00bc Mbara\u00f0uc\u00de \u00bc Mba\u00bd acu2c uc 0 1 T: \u00f07\u00de (iii) The rack-cutter surface Rc is represented in coordinate system Sc (Fig. 8) wherein the normal profile performs translational motion along c\u2013c. Then we obtain that surface Rc is determined by vector function rc\u00f0uc; hc\u00de \u00bc Mcb\u00f0hc\u00derb\u00f0uc\u00de \u00bc Mcb\u00f0hc\u00deMbara\u00f0uc\u00de: \u00f08\u00de We apply coordinate systems Se and Sk (Fig. 6(c)) and coordinate system St (Fig. 9(b)). The straight-line profile of gear rack-cutter is represented in parametric form in coordinate system Se\u00f0xe; ye\u00de as: xe \u00bc 0; ye \u00bc ut: \u00f09\u00de The coordinate transformation from Sk to St is similar to transformation from Sb to Sc (Fig. 8) and the gear rack-cutter surface is represented by the following matrix equation: rt\u00f0ut; ht\u00de \u00bc Mtk\u00f0ht\u00deMkere\u00f0ut\u00de: \u00f010\u00de The profile-crowned pinion and gear tooth surfaces are designated as Rr and R2, respectively, wherein R1 indicates the pinion double-crowned surface. Profile-crowned pinion tooth surface Rr is generated as the envelope to the pinion rack-cutter surface Rc. The derivation of Rr is based on the following considerations: ii(i) Movable coordinate systems Sc\u00f0xc; yc\u00de and Sr\u00f0xr; yr\u00de are rigidly connected to the pinion rack-cutter and the pinion, respectively (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001767_t-aiee.1918.4765578-Figure18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001767_t-aiee.1918.4765578-Figure18-1.png",
        "caption": "FIG. 18 FIG. 19",
        "texts": [
            " In two-pole turbo-generators with cylindrical field and distributed winding, the flux density is highest in the middle part of the role and is gradually reduced to zero, when approaching a line at right angles to the pole axis. As long as this distribution is the same in two opposite poles and the rotor is in a central position, no unbalanced pull occurs. If, however, one of the coils of one pole is short-circuited, the flux distribution in one pole will be different from that of the other pole, and an unbalanced pull will be set up, rotating with the rotor and producing vibrations of the stator. In Fig. 18 the winding of an a-c. machine is indicated, consisting of 8 coils, the four coils of the upper half being connected in series, as are also the four coils of the lower half. The two paths are connected in parallel. The voltage and periodicity impressed on the two parts are alike, and as both parts consist of the same number of identically situated coils, the total flux passing the upper half will be nearly identical with the total flux in the lower half. Any dissymetry would be practically wiped out by a slight increase of magnetizing current in the one and corresponding reduction of the magnetizing current in the other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.83-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.83-1.png",
        "caption": "Fig. 5.83: Principle of the pneumatically-driven flexible microactuator. Ac cording to [Suzu91]",
        "texts": [
            " Other important parameters to be investigated are higher ranges of operating temperature, higher shearing forces, shorter switching times and a reduction of power con sumption. New types of magnetorheological liquids have been discussed in [Carl94], but there are no assessable results yet. Flexible rubber microactuators A flexible microactuator to be used by miniaturized robots was reported in [Suzu91], [Suzu91a] and [Suzu91b]. The actuator is driven by hydraulic or pneumatic pressure, can be bent in every direction and is designed for use as robot hands or legs for various applications. The structure of this device is shown in Figure 5.83. It is made of rubber reinforced with nylon fibers and has three autonomous actuator chambers. The internal pressure in every chamber can be controlled individually by flexible hoses and valves leading to them. The device can be expanded along its longitudinal axis when the pres sure is increased equally in all three chambers. If the pressure is only in creased in one chamber, the device bends in the opposite direction. The pro- totypes developed so far have a diameter ranging from 1 to 20 mm. Several robot hands and walking machines were produced with them, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000932_j.jii.2021.100218-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000932_j.jii.2021.100218-Figure2-1.png",
        "caption": "Fig. 2. The requirement of overlapping distance and bead height in path planning process.",
        "texts": [
            " In Section 3, the data collection and processing system is presented and the SVMs based modelling algorithm is detailed in Section 4. The effectiveness of the proposed system is examined through the experimental validation and a case study in Section 5, and followed by a conclusion in Section 6. This paper proposes a novel Computer Aided Manufacturing (CAM) system for bead modelling process using arc welding-based AM Fig. 1. The steps of the WAAM process. D. Ding et al. Journal of Industrial Information Integration 23 (2021) 100218 technology. Weld beads are deposited side by side, as demonstrated in Fig. 2, the sliced layer height and offset distance are the same as the desired bead high (BH) and overlapping distance (OD). Thus, the proposed system aims to generate optimal welding parameters and setups to produce the user preferred bead geometry. The overall workflow of an automated bead modelling process for WAAM system is presented in Fig. 3. It consists of three essential modules including, data generation, model creation, and welding parameter generation. All three modules will be called step-by-step when the weld bead model for the selected operation welding mode and filler material does not exist in the current model library"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000420_j.triboint.2020.106200-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000420_j.triboint.2020.106200-Figure7-1.png",
        "caption": "Fig. 7. LBPF Ti6Al4V microstructures of the lateral (XZ plane) surface as a function of the different build-up orientations after heat treatment. BD stands for buildup direction.",
        "texts": [
            " All the as-built specimens presented defects typical of the LPBF process such as weld tracks between layers, attributable to the balling phenomenon, and randomly allocated round-shaped porosity, due to gas entrapment (see Fig. 6 (a)). After heat treatment, a lamellar mixture of \u03b1 and \u03b2 phases was observed inside the columnar prior \u03b2 grains (see Fig. 6 (b)), where the \u03b1 phase is light and the \u03b2 one is dark). The anisotropic microstructure still dominated even if most of the porosities were closed. Along some prior \u03b2 grains boundaries, continuous grain boundary \u03b1 layers (\u03b1GB) formed, as shown in Fig. 6 (c), which is symptomatic of the diffusive nature of the \u03b2-\u03b1 transformation [26]. Fig. 7 reports the LPBF Ti6Al4V microstructures along the XZ plane as a function of the different build-up orientations after heat treatment. Each image shows that the prior \u03b2 grains are aligned along the build-up direction. Such epitaxial growth of columnar \u03b2 grains is attributed to the thermal gradient throughout the workpiece, as previously described. The prior \u03b2 grains appears alternatively dark and light due to the different \u03b1 lamellae orientations. The prior \u03b2 grains width size distribution histograms and their average value for the different samples are presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.43-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.43-1.png",
        "caption": "Fig. 5.43 Displacement in the bead area due to inflation pressure (reproduced from Ref. [21] with the permission of Tire Sci. Technol.)",
        "texts": [
            " 288 5 Theory of Tire Shape The uninflated shape of the TCOT tire has not only a larger radius of curvature in the bead area but also a smaller radius of curvature in the sidewall near the belt than the tire with a natural equilibrium shape. These two elements jointly displace the bead toward the rim, while the displacement in the tread area is larger than that for the tire with a natural equilibrium shape in the radial direction as shown in Fig. 5.42. The former displacement at the bead in the TCOT tire makes the strain at the ply end compressive after the inflation of a tire as shown in Fig. 5.43. This strain works to close the crack at the ply end. The latter displacement in the tread area results in the belt tension being higher in the TCOT tire. This higher tension improves the rolling resistance by 3\u20135% and the belt durability of the TCOT tires. The TCOT shape has a larger radius of curvature in the bead area than the natural equilibrium shape. The carcass ply tension in the bead area is therefore higher for the TCOT tire than for the tire with a natural equilibrium shape. Owing to this tensile effect, the flexural rigidity of the TCOT tire is higher than that of the tire with a natural equilibrium shape in the bead area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.1-1.png",
        "caption": "Fig. 6.1 Spring properties of a loaded tire",
        "texts": [
            " The fundamental spring is related to the stiffness of the tire sidewall, which has ply tension, extensional stiffness, shear stiffness and bending stiffness. The fundamental spring rate can be calculated from the sidewall geometry and inflation pressure or by using an energy method combined with the theory of the natural equilibrium shape. The spring rate of a tire with a rigid ring can be estimated using the fundamental spring rates. The spring properties of tires are routinely measured as the fundamental characteristics of tires. Figure 6.1 shows measurement procedures for the vertical, lateral, longitudinal and torsional springs of a loaded tire. Because the tread deformation is included in the spring of a loaded tire, these springs can be controlled by not only tread stiffness but also sidewall stiffness. Figure 6.2 shows the measured tire spring rates for various tire sizes. Other spring properties are those of the fundamental spring used for a tire model as shown in Fig. 6.3. The tire tread and wheel are connected by the radial \u00a9 Springer Nature Singapore Pte Ltd",
            "50) in the circumferential direction, we obtain the overall force Fz in the z-direction as 326 6 Spring Properties of Tires Fz \u00bc 2 Zp 0 fzrAda \u00bc 2 Zp 0 \u00f0krz sin2 a\u00fe ktz cos2 a\u00derAda \u00bc pzrA\u00f0kr \u00fe kt\u00de: \u00f06:51\u00de The eccentric spring rate Rd of rigid ring model is given by Rd \u00bc Fz=Z \u00bc prA\u00f0kr \u00fe kt\u00de: \u00f06:52\u00de When the tire tread rotates around the wheel axle through the small angle a as shown in Fig. 6.24, the torque My is given by cosz x sinz z The in-plane rotational spring rate Rt is given by Rt \u00bc My=a \u00bc 2pr3Akt: \u00f06:54\u00de When the fore\u2013aft force is applied to a tire as shown in the third figure from the left in Fig. 6.1, the tire deformation of the rigid ring model can be separated into translational displacement d1 and rotational displacement d1 as shown in Fig. 6.25. Using Eqs. (6.52) and (6.54), the overall displacement x is given as x \u00bc d1 \u00fe d2 \u00bc Fx Rd \u00fe r2AFx Rt \u00bc Fx prA kr \u00fe kt\u00f0 \u00de \u00fe Fx 2prAkt : \u00f06:55\u00de The fore\u2013aft spring rate Rx of the rigid ring model is expressed as Rx \u00bc Fx x \u00bc 2prA\u00f0kr \u00fe kt\u00dekt 3kt \u00fe kr : \u00f06:56\u00de The fundamental spring rates are measured using an apparatus such as that shown in Fig. 6.26, where the whole tire tread is clamped"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003466_tac.2004.829615-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003466_tac.2004.829615-Figure1-1.png",
        "caption": "Fig. 1. Finding the periodic solution.",
        "texts": [
            " This suggests the technique of finding the parameters of the limit cycle\u2014via the solution of the complex equation [13] 1 q(A1) = W (j ) (4) where W (j!) is the complex frequency response characteristic (Nyquist plot) of the plant and the function at the left-hand side is given by: 1=q = A1( c1 + jc2)=[4(c 2 1 + c22)]. Equation (4) is equivalent to the condition of the complex frequency response characteristic of the open-loop system intersecting the real axis in the point ( 1; j0). The graphical illustration of the technique of solving (4) is given in Fig. 1. The function 1=q is a straight line the slope of which depends on c2=c1 ratio. This line is located in the second quadrant of the complex plane. The point of the intersection of this function and of the Nyquist plot W (j!) 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 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 with relative degree two driven by the twisting controller a periodic motion may occur in the system. In [3], [6], [10], and [11], the asymptotic second-order SM relay controller was studied. The simplest scalar example of this controller has the form: x = a _x bx k sign(x); a > 0; k > 0. It is shown in those works that this system is exponentially stable (no finite time convergence). In respect to our analysis, from Fig. 1 it also follows that the frequency of the periodic solution for the twisting algorithm is always higher than the frequency of the asymptotic second-order sliding-mode relay controller, because the latter is determined by the point of the intersection of the Nyquist plot and the real axis. Another modification of the twisting algorithm is its application to a plant with relative degree onewith the introduction of the integrator [8]. This will be further referred to as the \u201ctwisting as a filter\u201d algorithm",
            " The above reasoning is applicable in this case as well. 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. In this case, there always exists a point of intersection of theNyquist plot of the serial connection of the actuator, the plant and the integrator and of the negative reciprocal of the DF of the twisting algorithm (Fig. 1). Thus, if an actuator of first or higher order is added to the plant with relative degree one a periodic motion may occur in the system with the twisting as a filter algorithm. However, if the actuator is of second or higher order there is an opportunity for reduction of the amplitude of chattering in the control signal when using twisting as a filter algorithm in comparison with the first order SM control. This reduction is achieved due to the falling character of the magnitude characteristic of the integrator introduced between the discontinuous nonlinear element and the plant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000865_tnnls.2021.3059933-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000865_tnnls.2021.3059933-Figure3-1.png",
        "caption": "Fig. 3. Communication network of four fixed-wing UAVs.",
        "texts": [
            " Note that this article mainly focuses on the FOFTSTC design for networked fixed-wing UAVs, and the proposed control method cannot be directly used to simultaneously handle the state constraints, input saturation, actuator faults, and sensor faults. Moreover, the communication network adopted in this article is a fixed and undirected graph. In formation flight, a switching and directed topology might be practical from the perspective of formation flexibility. These aforementioned issues will be considered in further works. The proposed FOFTSTC scheme is demonstrated on four fixed-wing UAVs through comparative numerical simulations and HIL experiments. The communication network is shown in Fig. 3 and the corresponding adjacency matrix A is set as in (76). The structure and aerodynamic parameters are referred to [36]. In the simulation and HIL experiment, the attitude references are chosen as \u03bcid = \u03bcic\u03c9 2 n/(s 2 + 2\u03c9n\u03bens + \u03c92 n), \u03b1id = \u03b1ic\u03c9 2 n/(s 2 + 2\u03c9n\u03bens + \u03c92 n), and \u03b2id = \u03b2ic\u03c9 2 n/ (s2 + 2\u03c9n\u03bens + \u03c92 n), where \u03c9n = 0.3 and \u03ben = 0.8; \u03bcic steps from 0\u25e6 to 10\u25e6 at t = 2 s and then steps from 10\u25e6 to 0\u25e6 at t = 32 s; \u03b1ic steps from 1.8\u25e6 to 9.8\u25e6 at t = 2 s and then steps from 9.8\u25e6 to 1.8\u25e6 at t = 32 s; \u03b2ic steps from 0\u25e6 to 10\u25e6 at t = 2 s and then steps from 10\u25e6 to 0\u25e6 at t = 32 s; and Authorized licensed use limited to: Univ of Calif Santa Barbara"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003614_b97525-Figure3.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003614_b97525-Figure3.1-1.png",
        "caption": "Figure 3.1. Geometry of the two-dimensional Neo-Hookean block example.",
        "texts": [
            " The new configuration of this active element is computed from the current velocities of the nodes. Subsequently, these velocities are modified by impulses computed based on the new element configuration. Finally, the next activation time for the element is computed as a fraction of the Courant limit and the element is pushed into the queue. Our first example concerns a square block 1 m in size, fixed on one side and traction-free on the remaining three sides, released from rest from a stretched configuration, Fig. 3.1. The block is free of body forces. The material is a compressible Neo-Hookean solid characterized by a strainenergy density of the form: W ( F ) = 1 2\u03bb log2 J \u2212 \u00b5 log J + 1 2\u00b5 tr ( FTF ) , (3.1) where F = D1\u03d5 is the deformation gradient, J = det ( F ) is the Jacobian of the deformation, and \u03bb and \u00b5 are material constants. The values of the material constants used in calculations are: \u03bb = 93 GPa, \u00b5 = 10 GPa, and \u03c1 = 7800 kg/m3. The initial stretch applied to the block is 1.2. The finiteelement mesh contains a distribution of element sizes in order to have a 3",
            " The velocity components are likewise denoted u = (ux, uy, uz) = (u, v, w). Re\u03c4 = u\u03c4\u03b4/\u03bd is the Reynolds number based on the wall-shear velocity, u\u03c4 = \u221a \u03c4/\u03c1, in which \u03c1 is density, \u03c4 is the wall shear, and \u03bd is the kinematic viscosity. The boundary conditions are periodic in the x-and z-directions, and no-slip at y = \u00b1\u03b4. The non-dimensional distance from the wall is defined as y+ = (\u03b4 \u2212 |y|)u\u03c4/\u03bd. Note that the flow is driven by a prescribed unit pressure gradient in the minus x-direction. The problem configuration is schematically illustrated in Fig. 3.1. Two problems are considered: Fully-developed two-dimensional plane channel flow at Re\u03c4=180 and a non-equilibrium three-dimensional channel 230 T. J. R. Hughes and A. A. Oberai flow at Re\u03c4=180 in which a spanwise shearing motion is imposed instantaneously to the fully-developed two-dimensional flow. The approach used is based on that of Moser, Moin, and Leonard [1983], Kim, Moin, and Moser [1987], and Lopez and Moser [1999]. For further details see also Hughes, Oberai, and Mazzei [2001b]. The approach employed utilizes Fourier-spectral discretization in the xand z-directions, and modified Legendre polynomials in the y-direction",
            " First we show that it is always possible to transform to a new gauge where x\u00b5A\u00b5(x) = 0 . A general gauge transformation is specified by a matrix field S(x) \u2208 SO(3), A\u00b5 = SA\u2032 \u00b5St + \u2202S \u2202x\u00b5 St. (3.10) Thus, if we demand that x\u00b5A\u00b5 = 0, we obtain a differential equation for S, x\u00b5 \u2202S \u2202x\u00b5 = \u2212x\u00b5SA\u2032 \u00b5 , (3.11) which can always be solved (locally) by integrating along radial lines in the x\u00b5 coordinates (we choose initial conditions S(0) = I). A geometrical interpretation of this construction is illustrated in Fig. 3.1. In the figure, q0 is the equilibrium shape on shape space SS, F0 is the fiber above it, diffeomorphic to SO(3), and Q0 is a specific configuration on 420 R. G. Littlejohn and K. A. Mitchell the fiber. Relative to some coordinates x\u00b5 on shape space with origin at q0, we draw radial lines emanating from q0, that is, lines with coordinates x\u00b5(\u03bb) = \u03bb\u03be\u00b5, where \u03be\u00b5 is a constant vector (a vector in the tangent space at q0). The horizontal lifts of these lines, starting at Q0, sweep out the section S of the Poincare\u0301 gauge",
            " In general, a geodesic on shape space is a trajectory q(t) of a system of free particles with zero angular momentum, as is fairly obvious by setting V = 0 and L = 0 in Eq. (2.12). The corresponding trajectory up in the bundle is of course a straight line with constant velocity, also with L = 0. The bundle trajectory is also the horizontal lift of the trajectory in shape space (since L = 0 is the condition for the horizontal lift). Thus, if Riemann normal coordinates are used to define the radial lines which when lifted produce the section for Poincare\u0301 gauge, that section will consist of all straight lines passing through a point Q0 (see Fig. 3.1) on the equilibrium fiber F0 which are orthogonal to F0 at Q0. The section itself is then simply the flat subspace of R3N\u22123 of dimension 3N \u2212 6 which is orthogonal to the equilibrium fiber F0 at Q0 (in fact, it passes through the origin and so is a vector subspace). But as explained in Littlejohn and [1997], this is precisely the geometrical description of the Eckart frame (or gauge). Therefore the Eckart frame is the same as Poincare\u0301 gauge, relative to Riemann normal coordinates on shape space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure1.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure1.7-1.png",
        "caption": "Fig. 1.7 Deformation of a composite under stress in the x-direction",
        "texts": [
            " Exx is composed of the invariants U1, U2 with a period of p and U3 with a period of p/2. It is clear that U2 = U3 = 0 is satisfied for an isotropic material, such as steel or aluminum. The material behaves in an isotropic manner if U1 is larger than U2 and U3 and in an anisotropic manner if U1 is smaller than U2 and U3. 1.3 Mechanics of a Composite 15 (1) Tensile modulus of a composite When only stress rxx is applied in the x-direction with orientation angle h measured from the principal L-axis of the orthotropic material as shown in Fig. 1.7, the stress vector is expressed by 16 1 Unidirectional Fiber-Reinforced Rubber The substitution of Eq. (1.53) into the first equation of Eq. (1.46) yields exx \u00bc Cxxrxx rxx=Ex eyy \u00bc Cxyrxx mxrxx=Ex cxy \u00bc Cxsrxx; \u00f01:54\u00de where we note that Ex is different from Exx in Eq. (1.45). Ex is determined with the zero transverse and shear stress boundary condition, while Exx is determined with the zero transverse and shear strain boundary condition. Figure 1.7 shows that, when stress is applied in the x-direction, there is not only tensile deformation in the x-direction and compressive deformation in the y-direction but also shear deformation. From Eq. (1.54), we obtain Ex \u00bc rxx=exx \u00bc 1=Cxx mx eyy=exx \u00bc Cxy=Cxx: \u00f01:55\u00de Calculating the inverse matrix [E]\u22121 of Eq. (1.39), Cxx and Cxy can be expressed using Eij. The substitution of Cxx and Cxy into Eq. (1.55) yields The direction in which Ex is maximized or minimized can be obtained by solving the relation dEx/dh = 0 in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure23-1.png",
        "caption": "Fig. 23. Whole gear drive finite element model.",
        "texts": [
            " The versions correspond to face-gear drives with conventional and rounded fillet, respectively (Fig. 4). The finite element mesh of five pair of teeth of version 2 is represented in Fig. 22. Elements C3D8I [5] of first order enhanced by incompatible modes to improve their bending behavior have been used to form the finite element mesh. The total number of elements is 67,240 with 84,880 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Fig. 23 shows the whole finite element model of the gear drive. Figs. 24 and 25 show the maximum contact and bending stresses obtained at the mean contact point for gear drives of two versions of fillet (see Fig. 4). It is confirmed that the bending stresses are reduced more than 10% for the face gear generated with a rounded-top shaper in comparison with the face gear generated with a edged-top shaper. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.101-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.101-1.png",
        "caption": "Fig. 10.101 Finite element tire model used for prediction of the external force [48]",
        "texts": [
            " (2) Prediction of the interior noise of a vehicle (air-borne noise and structure-borne noise) employing FEA and a BEM (2-1) Prediction of air-borne noise The interior noise of a vehicle consists of air-borne noise and structure-borne noise as shown in Fig. 10.30. Saguchi et al. [48] first developed a procedure with which to predict the interior noise of a vehicle. They followed Nakajima\u2019s procedure [16, 10.13 Tire Noise Prediction 681 17] of predicting air-borne noise except for the external force estimation. Instead of adopting the procedure of Fig. 10.45, the external force was calculated from the difference in contact pressures between patterned and smooth tires that were predicted by quasi-static rolling contact analysis in Fig. 10.101. A finely meshed finite element model of a tire must be used for prediction of the external force. The external force is then mapped from the fine finite element model to a relatively coarse mesh model for vibration analysis. Although the coarse mesh model lacks a precise reproduction of the tread pattern complexity, it has excellent prediction capabilities for tire vibration up to approximately 1 kHz including the cavity resonance response. The inertance (A0/F0) at the driving point (where the acceleration and input force are measured) is compared between the prediction and the experiment in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure11-1.png",
        "caption": "Fig. 11 Coordinate systems Sm and Sc",
        "texts": [
            " In order to mathematically describe the generation process, we reak down the relative motion elements of the kinematical model hown in Fig. 5 and attach a coordinate system to each of them. oordinate system Sm Fig. 9 , called the machine coordinate sysem, is connected to the machine frame and considered as the eference of the relative motions. System Sm defines the machine lane and the machine center. System Ss is connected to the sliding base element 11 and repesents its translating motion. System Sr Fig. 10 is connected to he machine element 10 and represents the machine root angle etting. System Sc Fig. 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter. System Sp is connected to the machine element 9 and represents he work head setting motion Fig. 12 . System So is connected to he machine element 8 and represents the work head offset setting ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 motion Fig. 13 . Sw is connected to the work 8 and represents the work rotation with angular parameter Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.9-1.png",
        "caption": "Fig. 7.9 Fig. 7.10",
        "texts": [
            " The roots are therefore the first approximate stationary solution (or periodic solution) of eq. (7.72) x = e;' cosrot + T]' sin rot (7.74) Let A = ~T]'2 + e;'2 be the amplitude of a stationary vibration, then A must satisfy the equation <1>( A 2, ro 2, F) == A 2 [~\u00a3 A 2 + (ro 2 - ro ~) J + 4n2 ro 2 A 2 - F2 = 0 (7.75) where F,n,ro are known. This is a cubic equation of A2 and usually there may be one or three periodic solutions. We can illustrate eq. (7.75) from a geometrical point of view. are controlling parameters. A is the state variable. A,F, are shown as curved surfaces in Fig. 7.9. In Fig. 7.9, the values of F,O,1,2,3,4 represent the relative sizes. Several solutions may be obtained only when F ~ 2. Of the three surfaces, the middle one is unstable. The dividing line between stability and instability is the curve ABCDE. If we make a projection of ABCDEonto the plane Fro, we get abcde. The bifurcation set looks sharp in shape. In the projection on plane c is the sharp point (projection of Application of the Averaging Method in Bifurcation Theory 249 all points in any curved surface can be classified into three kinds: non-singular point, folding point and sharp point)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000690_tie.2018.2889634-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000690_tie.2018.2889634-Figure1-1.png",
        "caption": "Fig. 1. A robotic arm system.",
        "texts": [
            " SIMULATION STUDY To validate the correctness and applicability of the proposed control design method, simulation results for the practical example introduced in Section II\u2013a robotic arm system are presented in this section. Considering robotic arm system (1), an adaptive controller and a disturbance observer will be designed under the control scheme proposed in Section III. System (1) can be expressed as x\u03071 = x2 x\u03072 = M\u22121(qd + x1)v + f(x) + d y = x1 (50) where v =\u03c4 d =M\u22121(qd + x1)\u03c4d f(x) =\u2212M\u22121(qd + x1)[C(qd + x1, q\u0307d + x2)(q\u0307d + x2) +G(qd + x1)]\u2212 q\u0308d. The control method can be applied to n degrees of freedom robotic arm, and the system dynamic is expressed in (1), see [30]. As shown in Fig. 1, taking four degrees of freedom manipulator as an example, the parameters have been chosen as m1 = 13(kg), m2 = 12(kg), m3 = 2.5(kg), m4 = 2.5(kg), I1 = 0.24(kgm2), I2 = 0.15(kgm2), I3 = 0.95(kgm2), I4 = 0.02(kgm2), L1 = 0.5(m), and L2 = 0.4(m), where mi is the mass of the ith link, and Ii is the moment of inertia of the ith link. For convenience of comparison, in this simulation, the simulation results for the first joint are discussed, and the other joints are locked at 0\u25e6. The correctness and applicability 0278-0046 (c) 2018 IEEE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000822_j.jmst.2020.05.080-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000822_j.jmst.2020.05.080-Figure11-1.png",
        "caption": "Fig. 11. Deformation distribution of different deposition patterns (unit: mm), (a) Z",
        "texts": [
            " For both e and 1, the S-pattern has the minimum values. In detail, the e,max and 1,max of S-pattern are 10.8 %\u201336.9 % and 9.5 %\u201332.7 % lower than those of the other five patterns, respectively. Warpage is another major challenge in the AM process, which can cause part distortion, loss of geometric tolerances, and cracks [46,47]. Moreover, residual stress and warpage often occur simultaneously because they interact with each other. Hence, in this work, the warpages under different patterns are also studied. Fig. 11 shows the warpage in Z-direction under the six patterns. For all patterns, the warpage at the starting deposition position is larger due to the higher temperature gradient between t w t T \u221a \u00a9 \u00a9 \u00a9 he deposition material and the substrate at the initial position. he warpage distribution of the zig-zag pattern and raster patern are similar and almost symmetric in the Y-direction. The arpage distribution of the out-in spiral and in-out spiral pattern re approximatively symmetric along the diagonal line of the subtrate",
            " For the out-in spiral pattern, the displacement of the center art is negative while the in-out spiral pattern leads to opposite esults. Smaller warpage can be found under the alternate-line attern, and positive and negative displacement are alternate coresponding to the pattern in the deposition area. For S pattern, he warpage of four corners and the first S contour is relatively igh. Among all patterns, the in-out spiral pattern can achieve the ost homogeneous warpage, since the heat is accumulated outard. In order to compare the deformation of the substrate in Fig. 11, he Uz along the diagonal direction is normalized by the thickness of he substrate (d) and the normalized warpage Uz/d is summarized n Fig. 12. For the center part, all the curves collapse. At the edge, t is observed that the in-out spiral pattern achieves the minimum ormalized warpage. The normalized warpages at both ends are added to obtain he maximum normalized warpage Uz,max/d of different patterns, hich are plotted in Fig. 13. The in-out spiral pattern can achieve he lowest warpage, while the raster pattern produces the highest"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003946_s0022112008003807-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003946_s0022112008003807-Figure2-1.png",
        "caption": "Figure 2. A sketch of the arrangement of a bottom-heavy squirmer. Gravity acts in the g direction, while the squirmer has orientation vector e and radius a, and its centre of mass is at distance h from its geometrical centre.",
        "texts": [
            " A gravitational torque and a repulsive force If squirmers are bottom-heavy, external gravitational torques are generated when they are not vertically oriented, and they tend to swim upwards on average. The fact that micro-organisms are generally somewhat denser than water, and therefore experience a net gravitational force, is neglected in this study because the sedimentation speed of dead cells is much less than the swimming speed of live cells (Kessler 1986). If the distance of the centre of mass is h from the centre of the squirmer, in the direction opposite to its swimming direction in undisturbed fluid (see figure 2), then there is an additional torque of Lbh = 4 3 \u03c0a3\u03c1he \u2227 g, (2.19) where \u03c1 is the cell density; g is the gravitational acceleration vector; and the gravitational direction is g/g. A non-hydrodynamic inter-particle repulsive force Frep is added to the system in order to avoid the prohibitively small time step needed to overcome the problem of overlapping particles. We will follow Brady & Bossis (1985) and Ishikawa & Pedley (2007a), and use the following function: Frep = \u03b11 \u03b12 exp(\u2212\u03b12\u03b5) 1 \u2212 exp(\u2212\u03b12\u03b5) r r , (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.37-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.37-1.png",
        "caption": "Fig. 5.37: Magnetostrictive cantilever",
        "texts": [
            " Magnetostrictive multilayered actuators are also becoming more and more of interest since they have been discovered as well suited converter elements for microsensors and actuators. Compared to conventional Terfenol-D rods, the devices which can be built are more light weight and offer a higher movement potential at low cost. Bimorphic magne tostrictive actuators play an important role since a relative change of length in one component of the bimorphic structure can be transformed into large cantilever and membrane movements, Fig. 5.37. E.g. a silicon cantilever can be used as the elastic substrate layer in a bimorphic structure. Compared to piezoelectric layers, magnetostrictive materials have a relatively large change of length and need no direct electrical contacts. actuators have not been implemented successfully in many products. The manufacturing methods for Terfenol-D are much too expensive. Improved mechanical material parameters to make other designs have not been found. Also good methods of integrating the microactuators into other systems and suitable control algorithms are missing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure23-1.png",
        "caption": "Fig. 23. Illustration of worm singularities: (a) regular points A of shaper that generate worm singularities; (b) singularities B on worm thread surface.",
        "texts": [
            " The approach for determination of worm singularities is the same as applied for determination of singularities of face-gear tooth surface R2 (Section 5.4). Fig. 22(a) and (b) show lines of tangency of the shaper with the worm that are determined for the existing and proposed design, respectively. Lines Q are the image of singular points on the plane of surface parameters of the shaper. Drawings of Fig. 22 enable us to determine the maximum angle of rotation of the shaper permissible for avoidance of worm singularities. Then, it becomes possible to determine the maximal number of threads of the worm. Fig. 23(a) shows lines A\u00f01\u00de and A\u00f02\u00de on the shaper tooth surface formed by regular points of the shaper. Points of lines A\u00f01\u00de and A\u00f02\u00de generate singular points on the worm surface. The worm surface Rw must be limited with two lines B to avoid undercutting of the worm. The worm dressing is based on generation of its surface Rw point by point by a plane or by a conical disk that has the same profile that the rack-cutter that generated the shaper. The execution of motions of the disk or the plane with respect to the worm is accomplished by application of a CNC machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000520_j.addma.2019.100808-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000520_j.addma.2019.100808-Figure10-1.png",
        "caption": "Fig. 10. Residual stresses along x-direction in the Ti-6Al-4V components fabricated using (a) long deposition pattern, (b) short deposition pattern and (c) spiral deposition pattern when the deposits cooled down to room temperature and the clamps were released. Residual stresses along x-direction in the Inconel 718 components deposited with (d) long deposition pattern, (e) short deposition pattern and (f) spiral deposition pattern when the deposits cooled down to room temperature and the clamps were released. The processing conditions are provided in Table 1.",
        "texts": [
            " 9 b and e) have the least residual stresses among the three deposition patterns. This is because more hatches needed to fabricate the deposits using short deposition pattern significantly alleviate the stresses due to the reheating effect. It can also be found that after clamp removal, high tensile stresses accumulate on the bottom of the substrates for both alloys due to the upward bending of the substrates. The x-component of the residual stresses for both alloys fabricated using three deposition patterns are shown in Fig. 10. For both alloys and all three deposition patterns, high x-direction tensile stresses originate perpendicular to the x-axis near the longer edge of the deposit due to the contraction during cooling. High compressive stresses can be found near the shorter edge of the deposit to balance the tensile stresses in the substrate. For both alloys, compressive stresses can be found on the surface of the deposit printed using short deposition pattern (Fig. 10 b and e) because x-direction is the primary contraction direction for that deposit. In addition, for both alloys, the deposits with spiral pattern (Fig. 10 c and f) have the highest stresses values compared to the other depositions. Delamination of the component mainly depends on the stresses (\u03c3) at the substrate-deposit interface and the yield stress (Y) of the alloy at room temperature. A delamination index, d*, is proposed here to evaluate the susceptibility to delamination of WAAM components and is expressed as: d* = \u03c3/Y (2) For both the alloys, two lines (line 3 and 4 as indicated in Fig. 1) are selected at the substrate-deposit interface to study the influence of different deposition patterns on delamination of the components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.13-1.png",
        "caption": "Fig. 3.13: Details of an Impact",
        "texts": [
            " All classical textbooks on mechanics and most current research concentrate on mechanical systems with a few degrees of freedom and with one impulsive or frictional contact. Books and papers on chaotical properties very often use as mechanical examples impact or stick-slip systems. In the following we shall discuss some ideas [148],[166],[158],[138]. Two bodies will collide if their relative distance becomes zero. This event is then a starting point for a process, which usually is assumed to have an extremely short duration. Nevertheless, deformation of the two bodies occurs, being composed of compression and expansion phases (Figure3.13). The forces governing this deformation depend on the initial dynamics and kinematics of the contacting bodies. The impulsive process ends when the normal force of contact vanishes and changes sign. The condition of zero relative distance cannot be used as an indicator for the end of an impact, because the bodies might separate in a deformed state. In the general case of impact with friction we must also consider a possible change from sliding to sticking, or vice versa, which includes frictional aspects as treated later"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.75-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.75-1.png",
        "caption": "Fig. 12.75 Coefficient of friction with respect to the tire temperature, sliding velocity and thermal conductivity of a tire [114]",
        "texts": [
            " The heat conduction Qi from the interface to ice per unit length of the track is given by12 Qi \u00bc B Tm T0\u00f0 \u00de=V1=2 s \u00bdJ=length B \u00bc 2kib l=\u00f0pai\u00def g1=2; \u00f012:102\u00de where ki is the thermal conductivity of ice, ai is the thermal diffusivity of ice, l is the contact length, and b is the contact width. Using Eqs. (12.101) and (12.102) and considering the heat required to melt ice, the friction coefficient on ice l is given by l \u00bc Qr \u00feQi \u00feQm\u00f0 \u00de=Fz lr \u00fe li \u00fe lm; \u00f012:103\u00de where Fz is the vertical load and Qm is the heat required to melt ice per unit length of the track. lr is proportional to 1/Vs while li is proportional to 1= ffiffiffiffiffi Vs p . As lm increases, l decreases as shown in Fig. 12.75a, b. This is because the layer of melted water is thick in the region of higher values of lm. l increases with the conductivity of the tread rubber k because the heat conduction from the interface to the tire Qr increases as shown in Fig. 12.75c. 12Note 12.6. 12.4 Traction on Ice 869 Giessler et al. [120] measured the temperature increase on the surface of a winter tire on a hard packed snow track by conducting a longitudinal traction test in the time domain. The maximum friction power for the tire is about 3 kW and the maximum difference in surface temperature over time is about 6 K. Although these data are for the temperature increase of a tire on snow, similar temperature increases may be observed on ice. (2) Hayhoe and Shapley\u2019s model (2-1) Changes in temperature and heat flux at the interface Hayhoe and Shapley [116] developed an analytical model of the friction coefficient of a sliding tire on ice by dividing the contact area into two distinct regions, namely a dry sliding region and viscous flow region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure27-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure27-1.png",
        "caption": "Fig. 27. Contact and bending stresses for proposed geometry of face-gear drive generated with rounded-top shaper.",
        "texts": [
            " 25 and 26 show the maximum contact and bending stresses obtained at the mean contact point for the existing and the proposed geometry, respectively. For such examples a traditional edged-top shaper has been applied. Comparison between Figs. 25 and 26 shows that: i(i) Edge contact can be avoided, reducing the magnitude of the maximum contact stress to 40%. (ii) For a considerable part of the cycle of meshing only one pair of teeth is in contact. The max- imum bending stress at the fillet of the existing geometry of face-gear is 43% lower. Fig. 27 confirms that application of a rounded-top shaper (Fig. 5) reduces the bending stresses of the face-gear from 6% to 12% during the cycle of meshing. This enables us to keep the increment of the bending stresses for the proposed geometry less than 40%. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs. 28 and 29). Figs. 28 and 29 illustrate the variation of bending and contact stresses of the face-gear and the pinion during the cycle of meshing for face-gear generated with an edged-top shaper and a rounded-top shaper, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.31-1.png",
        "caption": "Fig. 3.31: Principle of the Throwing Machine",
        "texts": [],
        "surrounding_texts": [
            "constraints that change some velocity reduces the kinetic energy. Hence, by the collision of inelastic bodies, some kinetic energy is always lost\u201d[180]."
        ]
    },
    {
        "image_filename": "designv10_2_0000742_aisy.202000185-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000742_aisy.202000185-Figure2-1.png",
        "caption": "Figure 2. Schematic diagram of several types of twisted-fiber artificial muscles. A) SEM images of twisting (left) and coiling structures (right) for fiberbased artificial muscles; Left: Reproduced with permission.[9] Copyright 2011, American Association for the Advancement of Science.; Right: Reproduced with permission.[22] Copyright 2012, American Association for the Advancement of Science. B) Schematic illustration of the carbon nanotube (i) and silk fiber artificial muscle (ii); (i): Reproduced with permission.[22] Copyright 2012, American Association for the Advancement of Science; (ii): Reproduced with permission.[26] Copyright 2019, Wiley-VCH. C) Actuation mechanism of the artificial muscle, which is based on water adsorption-induced swelling and untwisting of the helical yarns; Reproduced with permission.[27] Copyright 2016, Royal Society of Chemistry. D) Schematic illustration of the twisted graphene oxide (GO) artificial muscle. Reproduced with permission.[10] Copyright 2014, Wiley-VCH.",
        "texts": [
            " In 2011, the pioneer work of Spinks and co-workers found that twist insertion can further amplify the actuation performance Adv. Intell. Syst. 2020, 2000185 2000185 (2 of 13) \u00a9 2020 The Authors. Advanced Intelligent Systems published by Wiley-VCH GmbH metrics of artificial muscle fibers.[9] In recent years, much research progress has been made in the field of twisted-fiber artificial muscles based on fibrous materials, including torsional and tensile actuations, using twisting and coiling structures (Figure 2A). Upon volume expansion in response to environmental stimuli (including temperature, humidity, light, electricity, pH, etc.), these twisted-fiber artificial muscles generate a large-angle torsional actuation and a large stroke tensile actuation. By inserting twist into the fiber, torsional stress is generated in the fiber and a bias angle is observed on the fiber surface. In general, twist is inserted into a fiber loaded with a constant weight (isobaric), which is torsionally tethered and not allowed to rotate freely",
            " Advanced Intelligent Systems published by Wiley-VCH GmbH Such torsional artificial muscles can also be realized using other configurations. For example, the twisted fiber may be folded in the middle to allow it to ply together to form a selfbalanced structure (Figure 2Bii).[26] In this case, the fiber plying serves as the torsional balance spring to avoid twist release of the individual fibers. Volume expansion in individual fibers causes reversible untwisting of the individual fiber and twisting of fiber plying. Such torsional balancing may also be realized by a sheath-core structure (Figure 2C)[27] or during the formation of a twisted fiber by twisting a gel-spinning fiber (Figure 2D) .[10] By twist insertion, the fiber surface forms a bias angle with the fiber length direction, which is denoted by \u03b1. This angle shows that the fiber orientation is off the center axis, which can be calculated using the following formula: \u03b1\u00bc tan 1(2\u03c0rT ), where r is the radius of the fiber and T is the twist density (insert twist divided by the length of fiber, typically measured in units of turns per m). The volume expansion-induced torsional actuation stroke can be explained by n n0 \u00bc V0 V \u03bbL0L2S \u03bb3L30 L0L2S L30 1=2 (1) where V0, L0, and n0 are the fiber volume, fiber length, and number of inserted twists in the initial state, respectively; V, L, and n are the fiber volume, fiber length, and number of inserted twists for the actuated state, and \u03bb\u00bc L/L0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.19-1.png",
        "caption": "Fig. 8.19",
        "texts": [
            " When Il < 0, the Hamiltonian system is transformed into a positive dissipative system, and the center changes to a sink. See Fig. 8.18(b). When Il> 0, the Hamiltonian system is transformed into a negative dissipative system, and the centre changes to a source. See Fig. 8.18(c). We know from Fig. 8.18, when Il = 0, the phase structure of this orbit has undergone a change in nature, and hence a bifurcation occurs. We shall study an example of a heteroclinic orbit once again. Suppose (8.35) When Il = 0, let xi = xi = 0, so we can obtain two saddles. For the heteroclinic orbit, see Fig. 8.19. Brief Introduction to Chaos 285 The heteroclinic portrait is a stable manifold of a saddle point, but an unstable manifold of another saddle point. Here, what we called the manifold, generally speaking, means the curve or curved surface in Euclid space. To generalize, consider a two-dimensional system (8.36) Suppose that eq. (8.36) has a saddle point Po E ;e2, that is f(po) = 0, and the two eigenvalues of Df(po) are one positive and the other negative, and further suppose that there exists a homoclinic orbit q0(t), passing through Po and that when t ~ \u00b1oo, q0(t) ~ po"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.11-1.png",
        "caption": "Fig. 8.11: Foot Design",
        "texts": [
            "58) The Jacobian for this special coordinate definition and its time derivation results directly from the above relations. We get q\u0307R = (\u03b1\u0307 \u03d5\u03071 \u03d5\u03072)T = J\u22121 R \u03c9, J\u0307R = \u2212JR J\u0307\u22121 R JR (8.59) The stability and also the controllability of the walking machine depends to a large extent on the torques transmitted from the feet to the machine. They are directly proportional to the lenght and width of a foot characterized by its four corner points. The reference trajectory will be described by the inertial 8.3 Walking Trajectories 531 position of these four corner points, see Figure 8.11. The vector with respect to inertial coordinates to the four corner points is defined as xK11...xK14 for the right and xK21...xK24 for the left foot. The position of the complete foot is given with the middle point of the four corners xF,i = 1 4 (xKi1 + xKi2 + xKi3 + xKi4), i \u2208 1, 2. (8.60) The orientation of the feet can be calculated by the relative position of the corners to each other. We get \u03bai,1 = zKi1 + zKi2 \u2212 zKi3 \u2212 zKi4 xKi1 + xKi2 \u2212 xKi3 \u2212 xKi4 , \u03bai,2 = zKi1 \u2212 zKi2 + zKi3 \u2212 zKi4 xKi1 \u2212 xKi2 + xKi3 \u2212 xKi4 , \u03bai,3 = yKi1 + yKi2 \u2212 yKi3 \u2212 yKi4 xKi1 + xKi2 \u2212 xKi3 \u2212 xKi4 , (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.53-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.53-1.png",
        "caption": "Fig. 7.53 Tread pattern design and finite element model [38]",
        "texts": [
            " The subsequent \u201cpeel-off\u201d deformation at the edge reduces the area of real contact so that the friction coefficient of the block with a flat surface is smaller than that of the optimized block at a large amplitude of deformation. 7.5 Pressure Distribution of a Block and the Frictional Force 435 The shear force for wet conditions was measured by spraying water on a rough epoxy surface. Figure 7.52 shows that the friction coefficient on the wet surface of the optimized block is 5% larger than that of the block with a flat surface. (4) Application of the optimized block surface to tires and validation The optimized block surface was applied to a tire sized 225/55R16 with the practical pattern shown in Fig. 7.53. The pressure dependence of the friction coefficient for an asphalt surface was considered. The surfaces of the four blocks were separately optimized to make the contact pressure uniform by considering nine external forces. Tires having the same construction and material and differing only in terms of their block surfaces were made to validate the effectiveness of the proposed technology. In on-vehicle subjective testing at proving grounds, the vehicle maneuverability on dry and wet surfaces and the riding comfort were improved by the optimized block",
            " This decrease is due to the lower compressive strain in the shoulder area due to the lower contact pressure. The RR was improved without sacrificing other performances using the optimized crown shape; i.e., other performances, such as the maneuverability and braking distance, also improve. The only remaining problem is that the riding comfort was a little harsh. The surface of a block optimized to make the pressure distribution uniform was discussed in Chap. 7. Nakajima et al. [80] applied the optimized block surface to a tire sized 225/55R16 with a practical pattern as shown in Fig. 7.53. The RR of a tire 996 13 Rolling Resistance of Tires with the optimized block surface was measured on a drum tester and found to be 3% less than that of a tire with a flat block surface. This reduction is due to the contact pressure decreasing at the block edges, and the barrel deformation is also suppressed by the optimized block surface as shown in Fig. 13.60. RR is improved by the optimized block surface without sacrificing other performances; i.e., other performances also improve. (5) In search for a new design element to decrease RR using optimization technology Optimization technology sometimes provides us an unprecedented design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.10-1.png",
        "caption": "Fig. 5.10: Elastic Shaft Model",
        "texts": [
            "15) Elastic shafts represent the simplest possible case of an elastic multibody element, as far as rotational linear elasticity is concerned. Assuming only linear elastic deformations gives us two modeling alternatives, namely applying some Ritz approach according to chapter 3.3.4 on page 124 or just discretizing the shaft into a limited number of shaft elements. Anyway, the number of shape functions of a Ritz approach as well as the number of the shaft elements depend on the frequency range of the system under consideration. In our case we discretize into n elements interconnected by springs and dampers, see Figure 5.10. The equations of motion for such a chain of torsional elements with (n) equal bodies and (n-1) equal springs and dampers can be written in the form  J\u0304 0 \u00b7 \u00b7 \u00b7 0 0 J\u0304 \u00b7 \u00b7 \u00b7 0 ... ... . . . ... 0 0 \u00b7 \u00b7 \u00b7 J\u0304  \ufe38 \ufe37\ufe37 \ufe38 MEW  \u03d5\u03081 \u03d5\u03082 ... \u03d5\u0308n\u22121 \u03d5\u0308n  \ufe38 \ufe37\ufe37 \ufe38 q\u0308EW = =  (\u03d52 \u2212 \u03d51) c\u0304 + (\u03d5\u03072 \u2212 \u03d5\u03071) d\u0304 (\u03d53 \u2212 2\u03d52 + \u03d51) c\u0304 + (\u03d5\u03073 \u2212 2\u03d5\u03072 + \u03d5\u03071) d\u0304 ... (\u03d5n+1 \u2212 2\u03d5n + \u03d5n\u22121) c\u0304 + (\u03d5\u0307n+1 \u2212 2\u03d5\u0307n + \u03d5\u0307n\u22121) d\u0304 (\u03d5n\u22121 \u2212 \u03d5n) c\u0304 + (\u03d5\u0307n\u22121 \u2212 \u03d5\u0307n) d\u0304  \ufe38 \ufe37\ufe37 \ufe38 hEW +  ManS 0 ... 0 \u2212MabS  \ufe38 \ufe37\ufe37 \ufe38 hEWS . (5.16) 5.1 Automatic Transmissions 225 One-way clutches allow a relative rotational motion in one direction only, whereas the other direction is blocked"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure1.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure1.7-1.png",
        "caption": "Fig. 1.7: Goal of the MITI program- active micro machines a) medical catheter; b) industrial microrobots. According to [MITI91)",
        "texts": [
            " The latter has a patronage over three national research facilities: the Mecha  nical Engineering Laboratory (MEL), the Electrotechnical Laboratory (ETL) and the National Research Laboratory of Metrology (NRLM). All of them are more and more involved in MST projects. Within the framework of this program, fundamental research, component and system development will be done over a period of 10 years. The main goal is to manufacture very small machines and instruments which can operate with high accuracy in a tiny space. These machines can be used in medicine, bio technology and industry, Fig. 1.7. In medicine, the conceived microrobots should be able to independently carry out examinations, analyses and treat ments at otherwise inaccessible locations during minimal-invasive surgical operations. Many operations which now endanger the patient's health (due to anesthesia and blood loss) could be done by micromachines one day. In the long-term, robots having a diameter under 1 mm are to be developed which can also move inside a blood vessel. Small industrial microrobots should go into complex machines and locally repair defects",
            " a thin fiber cable with an integrated cold light-source and video camera (endoscope) can be inserted into a natural bodily orifice or a small incision to make the surgery environment visible to the surgeon. If necessary, other tiny incisions are made to insert other miniaturized instruments, such as clamps, needles, slings, scalpels and rinsing/suction tubes. MST will make it possible to integrate various instruments needed for an operation within an active en doscope. The design of such an endoscope was presented in Figure 1.7a. Minimal-invasive surgery is economical and will be very important to the fu ture development of medicine. Less pain and fewer scars, and with this faster recovery and briefer stay in hospital (many endoscopic operations can today be carried out as out-patient treatments) will reduce costs for health insu rance companies and employers. Endoscopic inspection with subsequent la paroscopic removal of the gall bladder, appendix and ovaries is a standard procedure now. Today, 80% of all gall bladders are removed with the help of minimal invasive surgery [Conra94]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure4.18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure4.18-1.png",
        "caption": "Fig. 4.18: Five-Stage Automatic Transmission 5HP24 (Zahnradfabrik Friedrichshafen ZF [284])",
        "texts": [
            " As a classical solution of such transmissions we have the automated gears, today with up to eight stages, and more recently the applications of CVTs, Continuous Variable Transmissions, which compete with the classical configurations. Modeling such components always means modeling the complete system, because the neglection of components might result in an only partly realistic output, though we may model the complete drive for example in a more rough way so-to-say around the automatic transmission. Figure 4.18 gives an impression of a fivestage transmission, and Figure 4.19 depicts the principal configuration of the 208 4 Dynamics of Hydraulic Systems p [b complete powertrain with the accompanying and necessary gear and motor management systems on an electronic basis. Automatic transmissions, as many other components in cars, are controlled by complicated hydraulic systems, which supply the switching elements with the necessary oil pressure [91]. Such hydraulic control units include hydraulic lines, pressure reducers, control valves, pilot valves, gate valves and dampers, all arranged within a die cast metal box with an extremely complicated topology, see Figure 4",
            " In the following we shall consider a standard automatic gear box, its Ravigneaux-component and two types of CVTs, the rocker pin and the push belt configurations. As already indicated, establishing a model of an important machine component means establishing a model of the complete machine. We can limit to a certain extent these models by considering the component we want to have in all details and by modeling the surrounding machine with a few degrees of freedom, which nevertheless have to cover all influential frequencies. Modeling the automatic transmission [91] of Figure 4.18 on page 208 therefore comprises the complete drive train as shown in Figure 4.19 on page 209, the representation of which is self-explaining. The hydraulic unit has already been considered in chapter 4.4.2. Clutch A B C D E F 1st Gear x - - - - - 2nd Gear x - - - x - 3rd Gear x - - x - - 4th Gear x x - - - - 5th Gear - x - x - - R-Gear - - x - - x called one-way clutch gear shifting. The case that the ratio change is performed only by engaging and disengaging wet clutches, is termed overlapping 5",
            " Hence, the driving torque in the drive train is not interrupted while changing the gear ratio. Some explanations with respect to Figure 5.1 have already been given in connection with the hydraulic unit of the automatic transmission (Figure 4.21 on page 210). Table 5.1 presents a scheme of the clutches, which have to be closed for establishing the various stages (character \u201dx\u201d for closed). Together with Figure 5.1 the possible combinations are obvious. To model the complete drive train we work on the following assumptions, which have been derived from the real system as shown in Figure 4.18 on page 208. A drive train with automatic transmission generally consists of five main components: engine, torque converter, gear box, output train and vehicle. Each component of the drive train can be considered as a rigid multibody system. The partitioning into single bodies is often given by their technical function. In case of an elastic shaft, a discretization of the body is performed using the stiffness and mass distribution as criteria. Thereby, only torsional degrees of freedom are considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.32-1.png",
        "caption": "Fig. 7.32 Hertz theory",
        "texts": [
            " The contact pressure decreases with an increase in the shear force Q and increases with an increase in the load F. The calculation made using Eq. (7.106) agrees well with the experimental results. Figure 7.31 shows the relation of the lift-off length x and the shear force Q/Qcr calculated using Eq. (7.121). The theory is in good agreement with the experimental results. 7.4 Pressure Dependence of the Friction Coefficient on a Dry Surface (1) Load dependence of the friction coefficient For contact problems without friction as shown in Fig. 7.32a, the normal displacement uz at point A resulting from stress pz(x0, y0) at point B is calculated by integrating the product of pz(x0, y0) and Green\u2019s function, which is the displacement due to a point loading [21]. The stresses and displacements in an elastic half-space due to a point loading were derived by Boussinesq. The displacement of Boussinesq\u2019s solution normal to the elastic half-space is shown in Fig. 7.33, where the displacement is infinity at the point of loading. Using the solution derived by Boussinesq, the normal displacement uz due to arbitrary stress pz(x0, y0) is expressed as F=1",
            " 412 7 Mechanics of the Tread Pattern where E and m are, respectively, Young\u2019s modulus and Poisson\u2019s ratio of a body. Suppose that rotationally symmetrical stress is applied to the body. The normal displacement at a point depends only on the radius r from the origin owing to the rotational symmetry. It is therefore sufficient to determine only the displacement at point A on the x-axis. The stress at point B also depends only on the distance t from the origin owing to the rotational symmetry. Referring to Fig. 7.32a, t is expressed as t2 \u00bc r2 \u00fe s2 \u00fe 2rs cos/: \u00f07:123\u00de 7.4 Pressure Dependence of the Friction Coefficient on a Dry \u2026 413 Referring to Fig. 7.32b, uz is approximately expressed as uz \u00bc d t2=\u00f02R\u00de: \u00f07:124\u00de We assume that the pressure distribution is expressed by the Hertz equation: pz \u00bc p0 1 t2 a2 1=2 : \u00f07:125\u00de The substitution of Eqs. (7.123) and (7.125) into Eq. (7.122) yields uz \u00bc 1 pE ZZ pz\u00f0x0; y0\u00de dx 0dy0 s \u00bc 1 pE p0 a Z2p 0 Zs1 0 a2 r2 s2 2rs cos/ 1=2 sdsd/ s \u00bc 1 pE p0 a Z2p 0 Zs1 0 a2 2bs s2 1=2 dsd/ a2 \u00bc a2 r2 b \u00bc r cos/: \u00f07:126\u00de The integral over ds is calculated as Zs1 0 a2 2bs s2 1=2 ds \u00bc 1 2 ab\u00fe 1 2 a2 \u00fe b2 p 2 tan 1 b a : \u00f07:127\u00de By integrating Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-62-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-62-1.png",
        "caption": "Figure 4-62. Torque reversal as in Figure 4-61, Figure 4-63. Inverter leg of a three-level topology tracking control disengaged.",
        "texts": [
            " Open Loop Schemes 173 ferent pulse numbers N; (b) resulting current trajectory with the pulse number changing from N = 5 to N = 4 at ; = /,. operation is intended. The situation turns worse at transient operation. The reference vector of the modulator then changes its magnitude and phase angle very rapidly. Sections of different optimal pulse patterns are pieced together to form a real-time pulse sequence in which the preoptimized balance of voltage-time area is lost. The dynamic modulation error accumulates, and overcurrents occur which may cause the inverter to trip. Figure 4-62 gives an example. Optimal Subcycle Method. This method considers the durations of switching subcycles as optimization variables, a subcycle being the time sequence of three consecutive switching-state vectors. The sequence is arranged such that the instantaneous distortion current equals zero at the beginning and at the end of the subcycle. This enables the composition of the switched waveforms from a precalculated set of optimal subcycles in any desired sequence without causing undesired current transients under dynamic operating conditions",
            " Here, the upper channel provides accuracy and undisturbed synchronous optimal pulse width modulation in the steady state. The high dynamic performance is contributed by the lower channel [54]. Figure 4-61 shows the dynamic response and the extracted fundamental current isl. The shape of the oscillographed harmonic pattern A in Figure 4-6lb gives proof of achieved synchronous optimal modulation before the step. The pattern B is optimal, although not steady state, since the machine starts accelerating after the step. With the trajectory control disengaged, shown in Figure 4-62 at C, the modulator fails to achieve optimal modulation even in the steady state. A high dynamic modulation error builds up after a step change, causing subsequently an overcurent trip of the inverter at D. 4.7. MULTILEVEL CONVERTERS Multilevel converters are fed from more than one source voltage on the DC side. This permits generating three or more different voltage levels on the AC side. The voltage potentials at the output of the inverter legs are no longer restricted to pure rectangular waveforms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure14.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.2-1.png",
        "caption": "Fig. 14.2 Abrasion pattern and tire wear. Reproduced from Ref. [1] with the permission of Tokyo Denki University Press",
        "texts": [
            " When rubber wears, a pattern is inscribed on the worn surface. This is called the abrasion pattern. The generation mechanism of the abrasion pattern in Fig. 14.1 is explained by the crack growth of rubber [2\u20134]. The abrasion pattern is generated during wear under a strong shear force, with the separation of adjacent patterns L and depth H being proportional to the applied shear force. The abrasion pattern is carved on the tread in the direction perpendicular to the shear force by a crack that has the cross-sectional shape shown in the right figure of Fig. 14.2. Meanwhile, the abrasion pattern is not clear if the shear force is weak. Wear without clear abrasion patterns may be governed by chemical factors as well as physical factors, because the shear force is weak and the wear speed is low [1]. 1020 14 Wear of Tires Tire wear has been analyzed considering the wear energy or frictional energy, Ew, which is the energy due to slippage per unit area and calculated as the dot product of the shear stress~s and slip S ! : Ew \u00bc Z l 0 ~s d S!\u00bc Z l 0 sxdSx \u00fe sydSy ; \u00f014:1\u00de where l is the contact length, sx and sy are, respectively, shear stresses in x- and ydirections, and Sx and Sy are, respectively, slip distances in x- and y-directions",
            "71 Cross-sectional tread wear profiles for the front left tire. Reproduced from Ref. [41] with the permission of Tire Sci. Technol. H ee l & to e pr of ile (m m ) inside outside Cross-sectional position (mm) 0.6 0.4 0.3 0.2 0.1 0 60 40 20 0 \u221260 \u221240 0.5 \u221220 80 V=105 km/h \u221280 indoor wear drum prediction 14.11 Indoor Wear Evaluation 1099 1100 14 Wear of Tires (1) Evaluation of the wear abradability of rubber The wear abradability of rubber is usually evaluated using an indoor apparatus. The abrasion pattern of Fig. 14.2 is usually observed on the surface of a rubber sample, especially when a strong external force is applied to the rubber sample. However, it is difficult to observe the abrasion pattern on the surface of a passenger-car radial tire, except for wear at the edge of a block or H&T wear. This may be because the wear severity or the magnitude of the external force becomes low owing to good road maintenance and the lower rolling resistance of tires. 14.11 Indoor Wear Evaluation 1101 Hence, there may be two wear mechanisms, one for abrasive wear that generates the abrasion pattern and another for wear without the abrasion pattern"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001407_jiee-1.1920.0064-Figure16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001407_jiee-1.1920.0064-Figure16-1.png",
        "caption": "FIG. 16.\u2014Example of predetermination: the magnetic system of a magneto generator.",
        "texts": [
            " Hence it was found possible to obtain an average energy for the leakage paths from one magnet limb to the other was first estimated in the ordinary way by the formula for parallel cylinders ; but as the substitution of a cylindrical cross section for the rectangular section of the magnet seemed of doubtful validity in the case of a rectangle differing so widely frcm a square, a second estimate was made by treating each individual bar of steel as a cylinder and assuming that each pair of cylinders utilized one half of the entire surrounding space. These alternative methods gave <7 = 2-io and q \u2014 2-og respectively, and the forecast was based on the first of these figures. It may be noted that a rough estimate made by drawing freehand lines of force between the limbs, a method which unavoidably omits the conductance of the remoter regions of space, gave the value 9 = 1-83. The third example, Fig. 16, is a novel type of magneto generator designed by the author ; and being the first machine of its kind it was of special interest to see how closely the estimated performance of the field-magnet system would be realized in practice. The output product for the whole magnet, not much less than the maximum product $e$e for the magnet steel which it was intended to use, and the magnet closely approached the economy of an ideal magnet. As a result of the inevitable mishaps which attend the construction of the first machine of a new pattern, the actual dimensions of the completed generator were found to differ from the drawings in one or two places, and the final forecast of the flux in the armature was therefore based on the measured dimensions in order to avoid confusing errors of workmanship with errors in predetermination",
            " In an ordinary magnet of uniform sectional area, whether designed for economy of steel or not, there is an unavoidable variation in flux density between the neutral section and the ends. The total external energy which TABLE 7. Total Possible External Energy which might be maintained by the Volume of Steel in a Magnet, compared with the Energy actually delivered at the Ends of the Magnet and the Energy utilized. Description of Magnet Bent magnet with pole-pieces, Fig. 14 Field magnets of Megger Testing Set, Fig- 15 Field magnets of magneto generator, Fig. 16 Ring magnet; air-gap 0-148 cm., Fig. 20 Effective Volume of Steel in the Magnet, cubic cm. I9-32 214 4OO 19-25 Total Possible External Energy W< v,\u2022^-r x Volume, ergs 264 OOO 2 8lO OOO 5 240 000 234 IOO Actual Energy deduced from the Observed Flux Delivered, ergs 204 000 2 481 OOO 4 740 000 67 000 Utilized, ergs 103 000 1 291 000 4 020 000 67 000 Proportion to M ' x volume 8TT Delivered, per cent 77 88 90 28 Utilized, per cent 39 46 77 28 magnet of the magneto generator (Fig. 16) is not entirely the result of increased size. Something must be credited to the essentially economical nature of the design, which by reducing leakage from the magnet limbs to a relatively insignificant amount, brought the unavoidable variation in flux density in the steel (above and below the economic value j8\u00ab&) within a very narrow range, and in that way a remarkably close approach to the economy of an ideal magnet has been reached. The little bent magnet (Fig. 14) was designed with equal care for economy of steel, but in this example the pole-pieces, which constitute the apparatus with which the magnet is used, waste in leakage nearly half the energy delivered by the magnet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure1-1.png",
        "caption": "Fig. 1 Concept of hypoid gear generation",
        "texts": [
            " Analogous to the generation of a air of mating cylindrical gears using two complementary rack utters, the basic concept of generation of a pair of mating hypoid ears uses two complementary crown gears to generate the pinion nd gear, respectively 1 . Traditional cradle-style hypoid generaors were invented and designed with this basic concept. On a radle-style hypoid generator, the generating crown gear is repreented by the machine cradle mechanism and the teeth of the enerating crown gear are represented by the rotating blades on utter heads shown in Fig. 1. There are two major processes called face milling and face obbing for cutting spiral bevel and hypoid gears, both of which re widely employed by the gear manufacturing industry 1,2 . wo basic motions, generating roll and indexing, are provided in utting hypoid gears. The way of indexing defines face milling nd face hobbing. In face hobbing, a timed continuous indexing is rovided between the work and the cutter. Whereas in face millng, the indexing is intermittently provided by rotating the work fter finishing a tooth space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.74-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.74-1.png",
        "caption": "Fig. 5.74: Contact Point Interpolation [249]",
        "texts": [
            " For linear elastic multibody systems the equations of motion in the form (5.116) include only linear elastic term of first order. The mass matrix consists only of 0-th order terms, while the minimal accelerations q\u0308i as well as the right hand side vector hi comprise also 1-th order terms. The corresponding integrals depend only on space and not on time and can be evaluated once only at the beginning of every simulation. One of the problems connected with the consideration of an elastic pulley set consists in the then necessary interpolation of the contact points. Figure 5.74 illustrates the situation. The discretization of the pulley sets in order to evaluate the eigenvectors leads also to a truncated description of the surface of the cone sheaves. These surfaces are the contact zones with the pins of the chain link. Hence, an exact description is inevitable to generate the correct contact forces. For this purpose we apply the following procedure. We know approximately the position and orientation of the chain within the pulley set, which allows us to select a data set of potential nodes situated near some possible contact point. We store these data together with the elastic node deformations. As we know also the position of the pin centerline we can determine the four nodes P1 to P4, which span a bilinearly defined plane including the point of intersection (Figure 5.74). The nodes P1 to P4 belong to the sheave surface. In a first step we then calculate the exact point of intersection of the pin center line and the bilinearly assumed area spanned by the four nodes P1 to P4. This is point L. It is not positioned on the sheave surface, but has a distance h to it. To evaluate this distance h we assume in a second step, that the value of h in the deformed is not so much different from its value in the undeformed state, which allows an analytical calculation of h on the basis of no deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.28-1.png",
        "caption": "Fig. 11.28 Relation between the fore\u2013aft force and side force and the relation between the fore\u2013aft force and self-aligning torque. Reproduced fromRef. [2] with the permission ofGuranpuri-Shuppan",
        "texts": [
            "104) is given by the condition tan2 a\u00fe s2 3lsFz=CFa\u00f0 \u00de2: \u00f011:106\u00de 13Problem 11.3. 14See Footnote 13, Note 11.11. 744 11 Cornering Properties of Tires Figure 11.26 shows the calculation of the fore\u2013aft force for various slip angles and slip ratios. Figure 11.27 shows the calculation of the side force and self-aligning torque for various slip angles and slip ratios. Combining the results of Figs. 11.26 and 11.27, the relation between the fore\u2013aft force and side force and the relation between the fore\u2013aft force and self-aligning torque are obtained as shown in Fig. 11.28. The calculations use parameters of the load (Fz = 4 kN), contact length (l = 243 mm), lateral spring rate of the tire (Ky = 2.5 kN/cm), braking and driving stiffness (CFs = CFa = 57.2 kN) and friction coefficient (ls = 1.0, ld = 0.7). According to Sakai [2], the results in Figs. 11.26, 11.27 and 11.28 agree well with the measurements of bias tires but not those of radial tires. A comparison of Eq. (11.103) with Eq. (11.104) reveals that the side force under the braking condition is stronger than that under the driving condition if the slip ratio and slip angle are small"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.37-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.37-1.png",
        "caption": "Fig. 6.37: Contact Kinematics for Link and Guide",
        "texts": [
            " To the next link with contact there are two spring elements of the two joints. In reality however the elasticity of the chain plate acts between each contact. To consider these effects, we suppose that each link has one contact to the sprocket. Because of the fact, that we do not deal with chain rollers, we define a contour circle with the diameter of a chain roller seated in the reference point HL of a link (Figure 6.36). Contact between a Link and a Guide Modeling the contact between a link and a guide the link plate is the contact partner (Figure 6.37). Some varieties of the contact configuration may appear, for example contact in the front or rear side of the link, or along the link plate, which must be considered separately, see [69]. Corresponding to the contact model above, a contour circle with the diameter of the plate width is used. The high rotation speed of combustion engines induces high relative velocities at the contact points between the links and the guides. Therefore stickslip processes do not appear. Regarding the contact of a link to a sprocket, there is an additional oilwhip between the roller and the bushing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure8.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure8.13-1.png",
        "caption": "Fig. 8.13: Manipulation principle with distributed magnet actuators. According to [Inoue95)",
        "texts": [
            " Therefore, the motion principle introduced above was replaced by cantilever shaped piezoactuators, Fig. 8.12. A prototype of this microrobot could move at a speed of 2 mm/s carrying a load of 2 g. Distributed magnet actuator In [Inoue95), a new drive principle was introduced, using several cylindrical permanent magnets to move an object about a work table. Under the work table electromagnets were mounted in a matrix arrangement. Objects can be moved and rotated by coordinating the action of the permanent magnets, e.g. they can be arranged to perform gripping operations, Fig. 8.13. The power of motion is provided by energizing selectively the solenoids to produce the desired magnetic field. The magnetic actuators can move various objects and can perform complex manipulations since they are not intercon nected, Fig. 8.14. By using this principle, objects can be moved across the work place or rotated about themselves. This manipulator does not have any singularities, which are always present in conventional robot arms. The pro totype of the device shown in Figure 8.14 has a 4",
            " The maximum force that could be applied was 7.4 mN. This principle has an unlimited motion potential and also allows performance of 3D manipulations. For a practical application, a four legged robot was built which holds a rod as an endeffector; each leg is fastened to the rod through a 8.4 Drive Principles for Microrobots: Ideas and Examples 323 flexible joint, Fig. 8.15. The legs are provided with permanent magnets, which allow the robot to position the endeffector using the motion principle dis cussed in Figure 8.13. This robot can carry the endeffector to different places, can rotate it and tilt it. The rod of the robot is 60 mm long and the length of the legs is 35 mm. The force which could be transmitted by the tip of the rod was 6.8 mN in the downward direction and 3.2 mN in the upward direction. ' Piezoelectric swimming microrobot A concept of a swimming microrobot was introduced in [Fuku95). The robot can be used as a mobile platform for an industrial application, e. g. to inspect pipelines or as a miniaturized device for medical purposes to inspect blood vessels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure6-1.png",
        "caption": "Fig. 6 Face hobbing tool and blades",
        "texts": [
            " The representation of dynamic machine settings can be applied to the sophisticated modification of the tooth surfaces and the optimization of contact characteristics, through which the higher order coefficients of the polynomials can be determined. Tool Geometry The Gleason face hobbing process uses TRI-AC\u00aeor PENTAC\u00aeface hobbing cutters. Face hobbing cutters are different from face milling cutters. The cutter heads accommodate blades in groups. Normally, each group of blades consists of an inside finishing blade and an outside finishing blade with mean point M located at a common reference circle see Fig. 6 . Basically, the tool geometry can be defined by the major parameters of the Table 1 Machine motion elements and axes of rotation No. Names of elements and related motion 1 Machine frame, motion reference 2 Cradle, rotation/cradle angle 3 Eccentric, radial setting 4 Swivel, swivel setting 5 Tilt mechanism, tilt setting 6 Tool/cutter head, rotation 7 Work, rotation 8 Work support, offset setting 9 Work head setting 10 Root angle setting 11 Sliding base setting a Cradle axis b Eccentric axis c Cutter head/tool spindle axis d Work spindle axis e Swivel pivot axis for root angle setting blades and their installation on the cutter heads",
            " Determination of transformation matrix Mtb is based on the geometric description of the rake, hook, and blade slot offset angles shown in Fig. 8 and can be defined as a multiplication of three homogeneous matrices as Mtb = M M M 17a where M , M , and M are represented as, M = cos sin 0 0 \u2212 sin cos 0 0 0 0 1 0 0 0 0 1 17b M = 1 0 0 0 0 cos sin 0 0 \u2212 sin cos 0 0 0 0 1 17c M = cos \u2212 sin 0 Rbcos sin cos 0 Rbsin 0 0 1 0 0 0 0 1 17d Coordinate system Si is used to represent the rotation of the cutter head with an angular displacement . From Fig. 6, one can obtain the transformation matrix Mit and ri = Mit rt u = ri u, 18 ti = Mit tt u = ti u, 19 Applied Coordinate Systems Up till now, no paper has been found regarding exact modeling of face hobbing process. Mathematical modeling of face milling process has been developed and well known 7\u20139 . Both face milling and face hobbing processes can be virtually modeled using the mechanical cradle-style hypoid generator shown in Fig. 5. In comparison with the existing description of the cradle-style hypoid generators, this paper describes the kinematics of a universal hypoid generator in several major different aspects: a two independent rotations related to the work axis, cutter-head axis and cradle axis are considered; b the machine tool settings are represented as functions of cradle increment angle , instead of etry of blades Transactions of the ASME 6 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.3-1.png",
        "caption": "Fig. 8.3 Vibration around one point of contact on the tire surface. Reproduced from Ref. [11] with the permission of Guranpuri-Shuppan",
        "texts": [
            " (1) Fore\u2013aft vibration around one point of contact on a tire surface We suppose that a wheel is fixed, and one point on the tire surface is in contact with the road. Furthermore, we assume the deformation of the contact area is small, because it is difficult to rigorously consider a largely deformed tire in contact with the road. The fore\u2013aft vibration mode around one point of contact on a tire surface is expressed by superposing translational vibration on rotational vibration around the tire axle, as shown in Fig. 8.3a. Suppose that point P is in contact with the road. Considering that triangle PQR is a right-angled triangle, the radius of the rotation of point Q around point P is given as r0 \u00bc 2rD cos\u00f0h=2\u00de; \u00f08:17\u00de where rD is the radius of the tire. When the tread ring rotates through a small angle Da around point P, point Q moves by r0Da in a direction perpendicular to the r0 axis. Forces in the radial and rotational directions per small length rDdh at point Q (fr and ft) are given by fr \u00bc r0Da sin\u00f0h=2\u00dekrrDdh ft \u00bc r0Da cos\u00f0h=2\u00dektrDdh: \u00f08:18\u00de Using Eq",
            "21) can be rewritten as f \u00bc 1 2p ffiffiffiffiffiffiffiffiffiffiffiffi 3kt \u00fe 2kr 4m0 q m0 \u00bc m\u00fe am0; \u00f08:22\u00de where a is the modification parameter used to define the equivalent mass m0 and is given by Eq. (8.5). (2) Lateral vibration around one point of contact on a tire surface The lateral vibration mode around one point of contact on a tire surface is expressed by superposing the translational mode with distance rDa on the rotational mode with the rotational angle Da around the fore\u2013aft axis that is perpendicular to the tire axle, as shown in Fig. 8.3b. The moment DMp around point P is expressed by DMp \u00bc Rsr2DDa\u00feRmzDa; \u00f08:23\u00de where Rs is the lateral spring rate of a tire expressed by Eq. (8.6) and Rmz is the out-of-plane torsional spring rate expressed by Eq. (8.9). The torsional spring rate Bxp around point P is given by 8.1 Vibration Properties of Tires 455 Rxp \u00bc DMp=Da \u00bc Rsr 2 D \u00feRmz: \u00f08:24\u00de The substitution of Eqs. (8.6) and (8.9) into Eq. (8.24) yields Rxp \u00bc pr3D 3ks \u00fe kr \u00fe kt\u00f0 \u00de b 2rD 2 ( ) : \u00f08:25\u00de The moment of inertia IPx around the fore\u2013aft axis (x-axis) at point P is given by5 IPx \u00bc 3mpr3D: \u00f08:26\u00de The fundamental frequency f of lateral vibration around point P is given by f \u00bc 1 2p ffiffiffiffiffiffi Rxp IPx s \u00bc 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 m ks \u00fe kr \u00fe kt 3 b 2rD 2 ( )vuut : \u00f08:27\u00de When the combined mass of the two sidewalls m0 per unit length in the circumferential direction is considered, Eq",
            "174) Suppose the cubic equation x3 \u00feA1x 2 \u00feA2x\u00feA3 \u00bc 0: Applying the transformation y \u00bc x\u00feA1=3 to the cubic equation, we obtain y3 \u00fe py\u00fe q \u00bc 0; where p \u00bc A2 3 A1 3 2 ; q \u00bc A3 2 A1A2 6 \u00fe A1 3 3 : The discriminant D of the cubic equation is given by D = q2 + p3. When D < 0 is satisfied, three real solutions are obtained. Problems 8:1 Show that the moment of inertia of the tread around the rotational axis Ip is given by Ip \u00bc 2p r3Dm of Eq. (8.14). 8:2 Derive Eq. (8.19). Show that the moment of inertia IPp around point P in Fig. 8.3a and the moment of inertia IPx around the x-axis (moving direction) in Fig. 8.3b are expressed by IPp \u00bc 4pmr3 of Eq. (8.20) and IPx \u00bc 3pmr3 of Eq. (8.26). 8:3 Derive Eq. (8.48). 8:4 Derive Eq. (8.54). 8:5 Derive Eq. (8.102). 536 8 Tire Vibration 8:6 Derive Eqs. (8.147) and (8.148). 8:7 Derive elements of the transfer function [T], Eq. (8.155a) to Eq. (8.155y) in Appendix 2. 1. JSAE (ed.) , Handbook of vehicle technology, Fundamentals and Theory (in Japanese) (JSAE, 2008), p. 325 2. J.T. Tielking, Plane Vibration Characteristics of A Pneumatic Tire Model (SAE Paper, No. 650492, 1965) 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003444_28.855958-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003444_28.855958-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a motor structure of the transverse-laminated type.",
        "texts": [
            " This can be obtained by both the axially laminated and the transverse-laminated types of rotor construction. The latter type (transverse) is preferable, in practice, because it is more suited to industrial manufacturing. In addition, the rotor can be easily skewed in this case, thus allowing for very low values of torque ripple [18]. The transverse-laminated rotor structure requires, in practice, that the various iron segments in the rotor be connected to each other by thin iron ribs, as schematically shown in Fig. 1. These ribs are magnetically saturated by the stator MMF, thus allowing the required anisotropy. On the other hand, these ribs enhance cross saturation, with reference to the magnetic model of the machine. This is in addition to the usual phenomenon, which is common to the other types of machines. As a consequence, an accurate modeling of the magnetic behavior is required, for both evaluation of the machine\u2019s performance in terms of torque and definition of the most suited control strategy. This, of course, is particularly needed in the applications for which high overload is required, as is the case of servomotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001114_j.jallcom.2021.158868-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001114_j.jallcom.2021.158868-Figure10-1.png",
        "caption": "Fig. 10. Schmid factor contours for (a) Perfect a/2 < 110 > dislocations, (b) Leading partial dislocations, (c) Trailing Shockley partial dislocations, and (d) for the difference mtrail \u2212 mLead. The Schmid factors of each dislocation for the < 100 > , < 110 > and < 111 > tensile directions are signaled. < 110 > and < 111 > directions are susceptible to deformation twinning, while < 100 > directions are not.",
        "texts": [
            " From studies on twinninginduced plasticity (TWIP) steels [59,60], it was noted that the forces applied on the leading and partial dislocations can be different depending on the crystallographic orientation, which causes the width deff of the stacking fault to change. Following Schmid\u2019s Law, where the resolved shear stress acting on the slip plane depends on the applied stress and Schmid factor such that \u03c4RSS = \u03c3m, an examination of the Schmid factor of the perfect and partial dislocations was performed. Fig. 10 displays the Schmid factor contours for slip of perfect dislocations (Fig. 10(a)), their leading (Fig. 10(b)), and trailing (Fig. 10(c)) Shockley partials. When evaluating the difference between the Schmid factor of the trailing and leading partials (Fig. 10(d)), one can clearly observe a division along the [311]-[210] boundary where the Schmid factors of both types of partial dislocations are the same (mlead = mtrail). To the right of this boundary, mlead > mtrail, meaning the Schmid factor of the leading partial is larger than that of the trailing partial, and so are the resolved shear stresses acting on them. The opposite happens to the left of this boundary, where mlead < mtrail. This will cause the distances between the leading and trailing partials to widen in the region to the right, and to constrict in the region to the left"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000081_j.microc.2019.103985-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000081_j.microc.2019.103985-Figure2-1.png",
        "caption": "Fig. 2. Influence of time on the peak current.",
        "texts": [
            " It is evidently detected that, the surface area of modified CPE is around 0.086 cm2 and which is significantly higher than the bare sample. = \u00d7I (2.69 10 ) n A D C *p 5 3/2 0 1/2 1/2 0 (1) Characterization of the electrode was studied by AFM. The AFM images of CPE, GO-CPE, and NC+GO-CPE are shown in Fig. 1 and morphology values are depicted in Table 1. The investigation of preconcentration time effect was performed in a range of 0\u201360 s and the utmost oxidation peak was reported at 0 s, and is presented in Fig. 2. This result specifies the achievement of drenched adsorption on the improved sensor without accumulation time. Thus, further studies were carried out with no accumulation of time. The construction of composite modified CPE was previously reported (Section 2.2). The voltammograms were recorded by changing the weight of the silica gel particles added through the sensor construction and variations in the peak potential and in peak current were observed. From this result, it is clearly noticed that the optimum usage of graphene oxide and NC particles were found to be 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003669_j.automatica.2004.05.017-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003669_j.automatica.2004.05.017-Figure6-1.png",
        "caption": "Fig. 6. Eigenvalue configurations of the system A\u0302(v).",
        "texts": [
            " The design of a specific control proceeds as follows: One assumes, without loss of generality, that the linear system (1) is in controllable standard form, where A=   0 1 0 \u00b7 \u00b7 \u00b7 0 0 0 1 \u00b7 \u00b7 \u00b7 0 ... ... . . . ... 0 0 0 1 \u2212a0 \u2212a1 \u2212a2 \u00b7 \u00b7 \u00b7 \u2212an\u22121   ,b=   0 0 ... 0 1   , (28) or have been transformed into the above. We now choose the control vector, k(v), of Eq. (23) such that the eigenvalues, i , of the plant (23) will be shifted onto rays, i (v)= i (1)v\u22121, that start at i (1) and proceed toward negative infinity with decreasing v, as illustrated in Fig. 6. Note that (C1) will now be satisfied. The above choice of k(v) leads to faster linear control subsystems (23), since v decreases during regulation cycles. As in the discontinuous case of Section 3.1, the aim here is achieving increasingly higher regulation rates during regulation cycles. In order to achieve these ray-like eigenvalue paths, i (v), we need to formulate the control vector, k(v), as follows: k(v) =   a\u03020v \u2212n \u2212 a0 a\u03021v \u2212(n\u22121) \u2212 a1 ... a\u0302n\u22121v \u22121 \u2212 an\u22121   , (29) where the a\u0302i are the coefficients of the characteristic polynomial of A\u0302(v = 1), as given by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000420_j.triboint.2020.106200-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000420_j.triboint.2020.106200-Figure10-1.png",
        "caption": "Fig. 10. Tool engagement with respect to the prior \u03b2 grains orientations for the 0deg sample (a), and zoomed picture showing the orientation angle of the \u03b1GB layers relative to the cutting tool registration angle \u03ba (b).",
        "texts": [
            " Since in the machining tests carried out in this work, all the above-mentioned characteristics were L. Lizzul et al. Tribology International 146 (2020) 106200 kept constant, the different tool wear trends can be attributable just to the workpiece material. Thus, to better correlate the tool wear with the AM-induced material anisotropy, microstructural considerations are mandatory. As already reported, after the heat treatment, an \u03b1GB layer developed along the prior \u03b2 grains, representing a discontinuity of the microstructure and a weak point along which cracks may develop [4,28, 29]. Fig. 10 (a) shows the direction of the cutting process with respect to the \u03b1GB layers for the 0deg sample, which showed the lowest tool wear. When the end mill rotates, it progressively engages the material with the so-called registration angle \u03ba, which, for the end mill utilized in this work, approaches 90\ufffd. The orientation angle of the \u03b1GB layers relative to the registration angle for the 0deg sample is shown in Fig. 10 (b) and, in this case, the two angles correspond. This facilitates the chip formation and thus the material removal, reducing the forces acting on the cutting edge and increasing the tool life. For the 90deg sample, the situation is opposite, since the prior \u03b2 grains, thus the weak \u03b1GB layers, are oriented horizontally with respect to the registration angle. Based on the same reasoning, for the 36deg and the 72deg samples, the situation is intermediate. The tool wear curves can be also explained considering the prior \u03b2 grains width discussed in x 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003397_s0020-7403(01)00084-4-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003397_s0020-7403(01)00084-4-Figure8-1.png",
        "caption": "Fig. 8. Physical interpretation of: (a) 1-D axisymmetric; and (b) 2-D GPS models.",
        "texts": [
            " However, as discussed shortly, only negligible global yielding occurs for the stainless steel=carbon steel combinations considered herein. The constrained residual stress state in a deposited layer is obtained herein using both 1-D axisymmetric and 2-D generalized plane strain (GPS) thermomechanical <nite element models. The models are designed to approximate the microcasting experiments previously described, where a single layer of 308 stainless steel is deposited onto a 1018 carbon steel substrate. As depicted in Fig. 8a, the 1-D models e8ectively represent an entire layer deposited at once. The 1-D models also approximate the maximum stresses at the centerline of a microcast droplet (Chin et al. [6\u20139]), so that the results can be used in predicting an upper bound on subsequent warping. The GPS models are used to approximate a single deposited layer composed of <ve successively deposited rows (Fig. 8b), which accounts for some of the thermomechanical interactions between rows, as well as inherent substrate pre-heating due to previously deposited material. In addition, the GPS models enable a comparison of the warping curvatures parallel and transverse to the deposition direction. The 1-D numerical modeling procedures used herein follow those described in detail by Chin et al. [6\u20139], although the dimensions and material properties were modi<ed to be in accordance with the warping experiments previously discussed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003281_s100510050283-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003281_s100510050283-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of the experimental setup (not to scale).",
        "texts": [
            " A tungsten carbide bead, 8 mm in diameter, is suspended at the end of a vertical brass tube inside which a partial vacuum is drawn by means of a pump. The bead has a tolerance of \u00b11 \u00b5m in diameter and \u00b10.8 \u00b5m in sphericity. The tube is fixed on a micrometric linear positioner allowing a precise adjustment of the height of the release. A quick opening valve relieves the vacuum and releases the bead above a PCB 200B02 piezoelectric force sensor which is screwed on a duralumin square flat plate. Each side of this latter is 30 cm long, and its thickness is 2 cm. As it is shown in Figure 2, the whole setup is fixed on a table with adjustable legs in order to ensure horizontality of the impact plane. The force sensor is connected to a digital oscilloscope performing single shot acquisition of 50 000 points with a sampling rate up to 10 ns/pt. The height of fall h0 is 2 mm in order to avoid the plastic limit of the sensor material. For such height of fall, the air friction force on the bead motion is negligible1. In order to have a satisfactory resolution on the oscilloscope, i.e., 5 \u00b5s/pt, only the last bounces are recorded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003948_978-3-642-48819-1-Figure2.12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003948_978-3-642-48819-1-Figure2.12-1.png",
        "caption": "Fig 2.12.1 Inversion of the worm-gear mechanism",
        "texts": [
            "13) 2 which has a unique solution if ~ and ~ do not have a common null space, for then, the sum of them becomes of full rank, i.e. in that case \u2022 2 rank(~+~ )=3, and hence this sum is nonsigular. In this case, then, one single point of the body, located by the position vector ~O' has a zero acceleration. This point is called an aeeet~on pole and its position vector is given as \u2022 2-1 Y =y - W+rl) a _0 _p - - -p (2.12.14) Example 2.12.1 For a rigid-circular cone rolling without slipping on a plane, its acceleration pole is its apex (prove it) Exercise 2.12.2 The system shown in Fig 2.12.1 is an inversion of the worm-gear mechanism and is composed of a rigid arm OA of lenght b that can rotate freely about .axis EE', this axis being normal to the plane of 161 motion of OA. A rigid wheel is coupled to OA at A in such a way that the wheel can rotate freely about axis FF' passing though A; this axis is perpendicular to both OA and EE'. If OA rotates at a constant rate p and the wheel rotates about FF' at a constant rate q, show that the point of the disk on OA, a distance d from 0, has zero acceleration, the distance d being given by 162 An extensive account of this topic is presented in (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.7-1.png",
        "caption": "Fig. 8.7: Foot Design [85]",
        "texts": [
            "23) J1q\u03081 = Tan \u2212 r1\u03bbG \u2212 s1\u03bbT J2q\u03082 = \u2212Tab + r2\u03bbG \u2212 s2\u03bbT (8.25) The friction forces are set-valued forces. For sliding and stiction we get accordingly ([137], [226]) \u03bbT = sign(q\u03071)\u00b5G(|\u03bbG|+ \u03bbG,0) for q\u03072 = 1 i q\u03071 = 0, |\u03bbT | \u2264 \u00b5G(|\u03bbG|+ \u03bbG,0) for q\u03072 = 1 i q\u03071 = 0. (8.26) The equations of motion will take into consideration this situation by applying the structures of section 3.4 on page 131. Walking stability depends mainly on the contacts between feet and ground. For JOHNNIE a foot consists of three separate bodies (see Figure 8.7). The two lower foot plates are connected by a rotational joint about the foot longitudinal axis ensuring that the ground contact situation is not overconstrained. The ground contact elements are rounded such that a smooth rolling motion of the foot can be realized during touch down and lift off. The upper foot plate is connected to the lower plates by a damping element which absorbes shocks and bridges the time gap between impact and the controller response. With respect to the foot contacts we have two possibilities, namely modeling the ground forces in a unilateral way, which means rigid body contacts and set-valued forces, or modeling the ground forces by smooth contact laws in the form of spring-damper characteristics",
            "1 is based on the text of [202] 8.4 The Concept of JOHNNIE 537 The design of the knee joint corresponds to that of the hip pitch joint. The actuation of the ankle joint is realized with two linear drives based on ball screws (see Figure 8.4 on page 514). Two motors drive the ballscrews via timing belt. A motion of the sliders in the same direction leads to a pitch motion of the foot, the roll motion is realized by moving the sliders in reverse direction. The foot consists of three separate bodies (see Figure 8.7 on page 520). The two lower foot plates are connected by a rotational joint about the foot longitudinal axis ensuring that the ground contact situation is not overconstrained. The ground contact elements are rounded such that a smooth rolling motion of the foot can be realized during touch down and lift off. The upper foot plate is connected to the lower plates by a damping element which absorbes shocks and bridges the time gap between impact and the controller response. The joint angles and joint angular velocities are measured by incremental encoders (HP 5550 HDSL) that are attached to the motor shafts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.10-1.png",
        "caption": "Fig. 8.10: Definition of the Trunk Angular Coordinates [137]",
        "texts": [
            " Such a case appears, if the maximum torques being transmitted by the feet to the machine, exceed their limits. Then controllability is lost, and we have to define, which of the coordinates may deviate from the reference trajectory. For example, this might be the inclination of the trunk. In addition to this situation we cannot assign to the angle coordinates of the classical representations inertial coordinate axes. For a description of the trunk of JOHNNIE we therefore develop an individual angular coordinate system. Figure 8.10 illustrates these new definitions [137]. The orientation of the coordinate system K (with primes) is defined by the angles \u03b1, \u03d51 and \u03d52. The angle \u03b1 describes a rotation around the z-axis of the inertial system. It is the angle between the e1-axis and the e\u20321-axis projected onto the inertial x-y-plane. By the angles \u03d51 and \u03d52 spanned between the e\u20321-, the e\u20322-axis and the z-axis we are able to define independently the inclinations of the trunk in the forward and sidewards directions. This is a very important issue"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.43-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.43-1.png",
        "caption": "Fig. 6.43: Configuration of the Chain Drive [69]",
        "texts": [
            "116) In a further step we can derive similar complementarity conditions as above on the velocity level and obtain thus finally the equations containing all active contacts. 6.4 Bush and Roller Chains 391 g\u0307+ n =Aimpact\u039b+ bimpact, g\u0307+ n,i \u22650, \u039bi \u2265 0, g\u0307+ n,i\u039bi = 0. (6.117) The solution of the above equations results in the necessary impact magnitudes, but also in an information of the passive or active contact state. Exchanging (G=guide and L=link) by the couple (S=sprocket and P=pin or B=bushing) we can apply the above equations for these combinations. Figure 6.43 illustrates the chain drive for the numerical simulation. \u2022 The chain consists of 120 links with altogether 360 degrees of freedom. \u2022 The crankshaft is excited by a time dependent rotation speed, resulting from measurements. Hence this sprocket has no degrees of freedom. \u2022 On the camshafts act angle dependent torques, so we have to apply at least one rotational degree of freedom. \u2022 One guide is inertially fixed. The contact contour of this body consists of three arcs. \u2022 The tension guide with the additional tension device act by rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000822_j.jmst.2020.05.080-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000822_j.jmst.2020.05.080-Figure2-1.png",
        "caption": "Fig. 2. Finite element model.",
        "texts": [
            " The main conclusions and future work are summarized in section 6. Numerical modeling is a good way to study the complex thermomechanical performance with relations to process [35]. In this work, the FE method was used to scrutinize the effect of deposition patterns on the transient temperature field, residual stress, and warpage. The model was one square deposition layer with the dimensions of 120 mm \u00d7 120 mm \u00d7 2.23 mm and a square substrate with the dimensions of 200 mm \u00d7 200 mm \u00d7 20 mm , as shown in Fig. 2. The deposition layer was divided into 36 \u00d7 36 \u00d7 2 elements and the average mesh size was 3.3 mm \u00d7 3.3 mm \u00d7 1.1175 mm. Relatively coarse mesh was assigned in the remaining part. Aluminum alloy 2319 was selected in this study. The melting range was 543\u2212643 \u25e6C, and the mass density was assumed to be 2823 kg/m3 and temperature independent. The temperature-dependent material properties of AA2319, such as the thermal conductivity coefficient, thermal expansion coefficient, temperature-dependent yield stress, are obtained from Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.31-1.png",
        "caption": "Fig. 6.31: Running-In of a Chain Element into a Sprocket Tooth",
        "texts": [
            " The above velocity oscillations decrease with increasing number of teeth, linearly in transverse and quadratically in longitudinal directions. The polygonal frequency itself is simply the sprocket velocity multiplied with the number of teeth: \u2126polygon = z\u2126 (6.38) We always get an impact with friction when a chain element enters or leaves the sprocket wheel. The directions of motion of chain and sprocket are different leading to a vector difference of the velocities, which can only be demounted by a shock between the chain and the sprocket tooth (see Figure 6.31). This vector difference between the element velocity vG and the sprocket velocity vR of the contact point writes \u2206v = 2R\u2126 sin( \u03a0 z ) cos( \u03a0 z ), (6.39) which is mainly a vector in transverse direction of the chain. The position of the inlet shock is very important, because it changes significantly the direction n and with n the direction of the relative velocity \u2206v. The shocks in the running-in area are a main source of noise and wear. Furtheron we know from observations, that especially for large rotational velocities the element already in contact with a sprocket tooth detaches again leading to additional shocks and noise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001172_j.triboint.2021.106856-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001172_j.triboint.2021.106856-Figure7-1.png",
        "caption": "Fig. 7. Model parameters extraction: (a) The parameters Rmax, Rmin, (b) the parameters KT , K\u221e, \u03d5m",
        "texts": [
            " In addition, by comparing the simulation results of medium hexahedral mesh and medium tetrahedral mesh, it can be found that when the number of meshes is basically the same, the Rmax extracted by the two methods are basically the same, but the hexahedral mesh has fewer nodes, so its solution time is shorter. In this paper, the finite element model is a simple single bolted joint, the accuracy of the extracted parameters is our concern, so the fine hexahedral mesh is used for subsequent analysis. After solving the load step 1, the pressure distribution at the joint surface are shown in Fig. 7(a), and the action radius Rmax, Rmin of pre- tightening force at the interface can be extracted from the pressure data. After solving the load step 2, by extracting the slip displacement of the upper and lower lap board in the direction of tangential force, the relative slip displacement of interface can be obtained by subtracting the lower board displacement from the upper board displacement. Combined with the applied tangential load, the force-displacement curve is shown in Fig. 7(b). The initial slope of the curve is KT, the slope of the curve in the macro slip stage is K\u221e, and the displacement at the transition from micro sliding to macro sliding is \u03d5m. Through the analysis of the finite element simulation data, the corresponding parameters of the improved stiffness model are obtained. In order to verify the effectiveness of the stiffness model and parameters identification method proposed in this paper, a slip experiment of bolted joint is designed. An overall view of the experimental device is in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000774_j.addma.2021.101884-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000774_j.addma.2021.101884-Figure3-1.png",
        "caption": "Fig. 3. (a) Diagram of underwater laser-material interaction process, (b) actual UDED process at a water depth of 150 mm, (c) surface appearance of UDED sample and (d) simulated local dry cavity by gas curtain nozzle at a water depth of 150 mm.",
        "texts": [
            " The laser cladding head with an annular stream powder feed module was used to deposit the metal material, while the gas curtain nozzle was employed to create the local dry cavity in an underwater environment. The compressed air supplied by the air compressor was used as the drainage gas for the gas curtain nozzle. The underwater manufacturing tool can be implemented to repair metallic parts on-site in underwater environments. Before UDED, the preprepared HSLA-100 steel plate was placed in the water tank (Fig. 2). The detailed description of the underwater laser-material processing can be seen in Fig. 3(a). During UDED, compressed air was introduced to the external channel of the nozzle to exclude the water around the Z.D. Wang et al. Additive Manufacturing 39 (2021) 101884 trapezoidal groove and block water from entering the local dry zone. The pressure of the compressed air was approximately 0.8 MPa and the gas flow rate was 210 L/min. It is noted that a buffer was added to the gas curtain nozzle to eliminate the impact of fluctuant water on the local dry cavity during the fast reciprocating scanning process",
            " After the water was excluded, the laser beam was irradiated on the trapezoidal groove to generate a melt pool. The HSLA-100 powder was simultaneously fed into the melt pool using the powder feeder. The flow rates of the carrier gas and shielding gas were 10 L/min. After all tracks were finished in one layer, the laser cladding head was moved upward along the z-axis to begin the metal deposition for the following layers. Eight-layer deposition experiments were implemented in an underwater environment to fill the trapezoidal groove completely. Fig. 3(b) presents the actual underwater laser processing with an underwater manufacturing tool at a water depth of 150 mm. Fig. 3(c) shows that the sample repaired by UDED has a good surface appearance. Fig. 3(d) exhibits an example of the local dry cavity generated upon the simulated groove of a transparent acrylic plate using the underwater manufacturing tool, which was captured from the bottom of the water tank. A circular local dry area with a diameter of 70 mm was formed around the laser-material processing region at a water depth of 150 mm. Several trial experiments were carried out to test processing parameter windows. Based on the trials, HSLA-100 steel plates were repaired using a series of systematically designed processing parameters, and the optimized processing parameters are presented in Table 2",
            "618 ml/100 g). With increasing water depth, the drainage effect of the same gas flow rate worsens, which might account for the increase in hydrogen in sample B5. The fast scanning speed (1000 mm/min) during UDED weakens the barrier capacity of the air curtain. Water can break the gas curtain and then interrupt the stability of the local dry cavity, leading to the interaction of the melt pool and water. In addition, although the water in the local dry cavity was drained by the gas curtain nozzle (Fig. 3(d)), there was still a thin film of water left in the processing area. During laser-material interactions in underwater environments, the temperature of the melt pool is extremely high, resulting in the splitting of water and the entrance of hydrogen into the melt pool. Generally, a large amount of hydrogen will escape and bubbles will be generated during the solidification process. However, the solidification rate of the melt pool is very high, restricting the gas overflow of hydrogen. Thus, the diffusible hydrogen content in the RZ increases due to the poor drainage quality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003932_1.2164467-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003932_1.2164467-Figure3-1.png",
        "caption": "Fig. 3 Generation of excitation force for radial vibration measurement",
        "texts": [
            " As discussed earlier, the excitation to the system is caused by the pulses generated due to the interaction of the defect with the mating elements. It is also assumed that only the particular element which is being struck by the defect gets excited. Thus, excitation force F1 results when the pulses are generated on the inner race or mass m1 and F2 is caused when the pulses are generated on the outer race or mass m2. Force F3 is always equal to zero because a localized defect on a bearing element cannot cause any force to be exerted on the mass m3. The generation of the excitation force for radial vibration is explained in Fig. 3. The generated pulse form, f t , will depend on Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F the severity, extent, and age of the damage. A typical rectangular pulse form is shown in Fig. 4. The pulse width, T, can be determined by dividing the defect width by the relative velocity between the mating elements. The load at the point of excitation, P , will certainly influence the excitation force, F t . It is assumed that F t depends linearly on both f t and P "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure9-1.png",
        "caption": "Fig. 9. Generation of profile-crowned tooth surfaces by application of rack-cutters: (a) for pinion generation by rack-cutter Rc; (b) for gear generation by rack-cutter Rt.",
        "texts": [
            " 19) m module m12, mwp gear ratios between pinion and gear and between worm and pinion, respectively Mij matrix of coordinate transformation from system Sj to system Si n \u00f0j\u00de i , N \u00f0j\u00de i unit normal and normal to surface Rj in coordinate system Si Ni number of teeth of pinion (i \u00bc 1; p), gear (i \u00bc 2) or worm (i \u00bc w) p1, p2 screw parameters of the pinion and the gear, respectively ri radius of pinion (i \u00bc p1; p), gear (i \u00bc p2) or worm (i \u00bc w) pitch cylinder rd1 dedendum radius of the pinion r i radius of pinion (i \u00bc p1) or gear (i \u00bc p2) operating circle (Fig. 12) ri position vector of a point in coordinate system Si sa parameter of pinion topland (Fig. 28) si displacement of pinion (i \u00bc c) or gear (i \u00bc t) rack-cutter during the generation of profile- crowned pinion or gear, respectively (Fig. 9) s1, s2 dimensions of pinion and gear rack-cutter teeth, respectively (Fig. 6) Si\u00f0Oi; xi; yi; zi\u00de coordinate systems (i \u00bc a; b; c; e; k; t;m; r; s; 1; 2; f ; q; h;D) \u00f0ui; hi\u00de parameters of surface Ri The existing design and manufacture of involute helical gears provide instantaneous contact of tooth surfaces along a line. The instantaneous line of contact of conjugated tooth surfaces is a straight line L0 that is the tangent to the helix on the base cylinder (Fig. 1). The normals to the tooth surface at any point of line L0 are collinear and they intersect in the process of meshing the instantaneous axis of relative motion that is the tangent to the pitch cylinders",
            " The locations of points Q and Q are denoted by jQP j \u00bc ld and jQ P j \u00bc lc where ld and lc are defined as ld \u00bc pm 1\u00fe b sin ad cos ad cos ac sin\u00f0ad \u00fe ac\u00de ; \u00f05\u00de lc \u00bc pm 1\u00fe b sin ac cos ac cos ad sin\u00f0ad \u00fe ac\u00de : \u00f06\u00de i(ii) Coordinate systems Sa\u00f0xa; ya\u00de and Sb\u00f0xb; yb\u00de are located in the plane of the normal section of the rackcutter (Fig. 6(b)). The normal profile is represented in Sb by the matrix equation rb\u00f0uc\u00de \u00bc Mbara\u00f0uc\u00de \u00bc Mba\u00bd acu2c uc 0 1 T: \u00f07\u00de (iii) The rack-cutter surface Rc is represented in coordinate system Sc (Fig. 8) wherein the normal profile performs translational motion along c\u2013c. Then we obtain that surface Rc is determined by vector function rc\u00f0uc; hc\u00de \u00bc Mcb\u00f0hc\u00derb\u00f0uc\u00de \u00bc Mcb\u00f0hc\u00deMbara\u00f0uc\u00de: \u00f08\u00de We apply coordinate systems Se and Sk (Fig. 6(c)) and coordinate system St (Fig. 9(b)). The straight-line profile of gear rack-cutter is represented in parametric form in coordinate system Se\u00f0xe; ye\u00de as: xe \u00bc 0; ye \u00bc ut: \u00f09\u00de The coordinate transformation from Sk to St is similar to transformation from Sb to Sc (Fig. 8) and the gear rack-cutter surface is represented by the following matrix equation: rt\u00f0ut; ht\u00de \u00bc Mtk\u00f0ht\u00deMkere\u00f0ut\u00de: \u00f010\u00de The profile-crowned pinion and gear tooth surfaces are designated as Rr and R2, respectively, wherein R1 indicates the pinion double-crowned surface. Profile-crowned pinion tooth surface Rr is generated as the envelope to the pinion rack-cutter surface Rc. The derivation of Rr is based on the following considerations: ii(i) Movable coordinate systems Sc\u00f0xc; yc\u00de and Sr\u00f0xr; yr\u00de are rigidly connected to the pinion rack-cutter and the pinion, respectively (Fig. 9(a)). The fixed coordinate system Sm is rigidly connected to the cutting machine. i(ii) The rack-cutter and the pinion perform related motions, as shown in Fig. 9(a), where sc \u00bc rp1wr is the displacement of the rack-cutter in its translational motion, and wr is the angle of rotation of the pinion. (iii) Using coordinate transformation from coordinate system Sc to coordinate system Sr we obtain a fam- ily of generating surfaces Rc represented in Sr by the following matrix equation: rr\u00f0uc; hc;wr\u00de \u00bc Mrc\u00f0wr\u00derc\u00f0uc; hc\u00de: \u00f011\u00de (iv) The pinion tooth surface Rr is determined as the envelope to the family of surfaces rr\u00f0uc; hc;wr\u00de and requires simultaneous application of vector function rr\u00f0uc; hc;wr\u00de and the equation of meshing represented as follows (see [7,8,16]): orr ouc orr ohc orr owr \u00bc fcr\u00f0uc; hc;wr\u00de \u00bc 0: \u00f012\u00de Equation fcr \u00bc 0 may be determined applying an alternative approach Nc v\u00f0cr\u00dec \u00bc 0: \u00f013\u00de Here: Nc is the normal to Rc represented in Sc; v\u00f0cr\u00dec is the relative velocity represented in Sc. The coordinate transformation discussed above is based on application of homogeneous coordinates and matrices 4 \u00b7 4 [6,7]. The schematic of generation of R2 is represented in Fig. 9(b). Surface R2 is represented by the following two equations considered simultaneously: r2\u00f0ut; ht;w2\u00de \u00bc M2t\u00f0w2\u00dert\u00f0ut; ht\u00de; \u00f014\u00de ft2\u00f0ut; ht;w2\u00de \u00bc 0: \u00f015\u00de Here: vector equation rt\u00f0ut; ht\u00de represents the gear rack-cutter surface Rt; \u00f0ut; ht\u00de are the surface parameters of Rt; matrixM2t\u00f0w2\u00de represents the coordinate transformation from St to S2; w2 is the generalized parameter of motion. It may be verified that the generated surface is a screw involute one. Eqs. (14) and (15) represent surface R2 by three related parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure24-1.png",
        "caption": "Fig. 24. Three-pairs-of-teeth face-gear drive model.",
        "texts": [
            " (d) Finite element models of three pairs of teeth are applied and therefore the boundary conditions are far enough from the loaded areas of the teeth. Finite element analysis has been performed for the two versions of face-gear drives represented in Tables 1 and 2. For the second version of face-gear drive, it has been also considered the application of a rounded top shaper (Fig. 5), in order to compare the bending stresses at the fillet of the generated face-gear. The finite element mesh of three pair of teeth of version 2 is represented in Fig. 24. Elements C3D8I [5] of first order, enhanced by incompatible nodes to improve their bending behavior, have been used to form the finite element mesh. The total number of elements is 44820 with 58327 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Figs. 25 and 26 show the maximum contact and bending stresses obtained at the mean contact point for the existing and the proposed geometry, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure1.16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure1.16-1.png",
        "caption": "Figure 1.16 compares the upper and lower bounds of Eq. (1.93) and measurements of cobalt composite reinforced with tungsten carbide. Young\u2019s moduli of the fiber and matrix are, respectively, Ef = 703 GPa (WC) and Em = 207 GPa (Co). The measurement is in the region between the upper and lower bounds.",
        "texts": [],
        "surrounding_texts": [
            "Halpin and Tsai [9] developed simple and generalized semiempirical equations to approximate the results of more exact micromechanics analyses. The prediction of these equations is reasonably accurate if the fiber volume fraction does not approach 1. The Halpin\u2013Tsai equations for composite modulus are EL \u00bc EfVf \u00feEmVm mL \u00bc mfVf \u00fe mmVm ET \u00bc Em 1\u00fe ngVf 1 gVf GLT \u00bc Gm 1\u00fe g0Vf 1 g0Vf mT \u00bc mL ET EL ; \u00f01:94\u00de 1.4 Micromechanics 27 where EL is Young\u2019s modulus in the fiber direction, ET is the modulus in the direction transverse to fiber, mL is Poisson\u2019s ratio in the fiber direction, mT is Poisson\u2019s ratio in the direction transverse to fiber, GLT is the shear modulus on the L\u2013T plane, Ef and Em are Young\u2019s moduli of the fiber and matrix, Gf and Gm are shear moduli of the fiber and matrix, Vf and Vm are the volume fractions of the fiber and matrix, and mf and mm are Poisson\u2019s ratios of the fiber and matrix. \u03b7 and g0 are expressed as g \u00bc Ef=Em\u00f0 \u00de 1 Ef=Em\u00f0 \u00de\u00fe n ; g0 \u00bc Gf=Gm\u00f0 \u00de 1 Gf=Gm\u00f0 \u00de\u00fe 1 ; \u00f01:95\u00de where n is a measure of reinforcement that depends on the fiber geometry, packing geometry and loading conditions. It is suggested that a value of n = 2 be used for fibers with a circular or square cross section. For fibers with a rectangular cross section, n is calculated as n \u00bc 2 a=b; \u00f01:96\u00de where a/b is the aspect ratio of the rectangular cross section with direction a taken in the direction of loading. Jones [10] showed that when the relation n = 0 is satisfied, the Halpin\u2013Tsai equation with respect to ET in Eq. (1.94) reduces to the inverse rule of mixtures given as Eq. (1.72), whereas a value of n = \u221e yields the rule of mixture given as Eq. (1.67). The interpretation of the curve-fitting parameter, n, as a measure of the degree of fiber reinforcement thus has a theoretical basis. The transverse composite modulus ET calculated using the Halpin\u2013Tsai equation is shown as a function of the fiber volume fraction for different constituent modulus ratios as shown in Fig. 1.17. Figure 1.18 shows the transverse modulus of a 28 1 Unidirectional Fiber-Reinforced Rubber composite as a function of the fiber volume fraction Vf calculated using the Halpin\u2013 Tsai equation (Eq. 1.94) and upper and lower bounds (Eq. 1.93). The value calculated using the Halpin\u2013Tsai equation is between the upper and lower bounds."
        ]
    },
    {
        "image_filename": "designv10_2_0000981_j.triboint.2021.106996-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000981_j.triboint.2021.106996-Figure13-1.png",
        "caption": "Fig. 13. The schematic summarizing the wear mechanisms of different as-SLMed Ti6Al4V alloys.",
        "texts": [
            " It can be seen the tribo-oxide layers are not found on the worn surfaces of all the tested Ti6Al4V samples, it means that the tribo-oxide layers with protection function has no positive effect on improving the wear resistance for the tested Ti6Al4V sample. However, from Fig. 12a, b and 12c, the severe deformation (the \u03b1\u2032 martensitic at the bottom of the groove bend to both sides) is observed under high applied loads (5 N and 10 N) in the as-built sample which contains high content of soft \u03b2 and low micro-hardness J. Ju et al. Tribology International 159 (2021) 106996 (<400 HV). but, it is not observed after wear under a load of 2 N. Combined with the worn surface morphology of wear scar, the physic model of wear can be established as shown in Fig. 13. For the as-built sample composed of a large amount of softer \u03b2 phase, the deformation of the softer \u03b2 is more severe than that of harder \u03b1\u2032 phase under the high load, and the softer \u03b2 phase is difficult to protect the harder \u03b1\u2032 phase, J. Ju et al. Tribology International 159 (2021) 106996 which will cause the fracture and spalling of \u03b1\u2032 phase and form the wear debris (Fig. 10a\u2013c). In addition, the concave-convex matrix and the high internal stress of oxide layer lead to the cracking and spalling of the oxide scale, as shown in Fig. 13a. The formed hard and large size debris under the tangentuial force from the Si3N4 ball increase the shear on the surface and the formation of the deep grooves. the SLM-860 sample contains highest amount of soft \u03b2 phase and deformation zone after wearing for 120 min can be observed under all applied loads. In comparison with the SLM sample, the high amounts of soft \u03b2 phase in SLM-860 sample further decrease the protection of \u03b1\u2032 phase and increase the initial deformation of microstructure. The formed oxide layer is completely peeled off, and forms the peeling pits and large-size debris. The large-size debris can aggravate to cut the soft matrix, forming the deeper furrows, as seen in Fig. 13c. When the microstructure of \u03b1\u2019+\u03b2 transforms into the almost complete \u03b1\u2032 microstructure, the deformation of microstructure disappeared in Fig. 12g\u2013i. For the SLM-1060 sample with high micro-hardness, the microstructure is composed of the hard \u03b1\u2032 phase which has lower plastic deformation at the initial wear. The wear debris become finer as shown in Fig. 13d, which can provide lubrication to effectively prevent the friction pair from contact with the fresh metals directly, and decreasing the wear rate. The effect of heat treatment on the microstructure, micro-hardness and tribological behavior of Selective Laser Melting Ti6Al4V alloy was investigated, and the applied load varied from 2 N to 10 N to study the effect. The wear mechanism was also discussed. The main conclusions can be summarized as follows: (1) The microstructure of as-built Ti6Al4V is mainly composed of \u03b1\u2032 lath martensite and \u03b2 phase, as the heat temperature increasing to 860 \u25e6C, the \u03b2 phase content increases and the \u03b1\u2032 lath martensite coarsens"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000968_j.addma.2021.102203-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000968_j.addma.2021.102203-Figure2-1.png",
        "caption": "Fig. 2. (a) Diagrammatic of laser-CMT hybrid additive manufacturing. (b) The fixture and substrate.",
        "texts": [
            " The residual stress of the thin-wall parts was measured with a Proto-iXRD XRD system using a chromium target, as stated in Fig. 1b, the measurement accuracy is \u00b1 8 MPa [30,31]. The deposition material chosen for the wire was ER2319 aluminum alloy (1.2 mm diameter), and the substrate was 2219 aluminum alloy. The substrate was machined and cleaned with acetone before the experiment. The chemical compositions of the substrate and wire are given in Table 1. The laser was defocused and aligned with the center of the welding wire. The relative positions of the laser output head and the CMT torch are indicated in Fig. 2a. The height of the bottom of the laser output head is 225 mm, and the angle between the laser output head and the substrate is 40\u25e6. As illustrated in Fig. 2b, a fixture is designed for mounting substrates where both ends of the substrate are clamped, and lateral movement on one side is restricted. During fabrication, the welding mode was CMT pulse advanced (CMT-PADV), and the process parameters of the laser-CMT process are shown in Table 2. Fig. 3 presents the geometric size of the thin-wall part and substrate. The two ends of the substrate have a footstep for clamping. In this R. Li et al. Additive Manufacturing 46 (2021) 102203 experiment, three types of path strategies viz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure15-1.png",
        "caption": "Fig. 15. Motion branch of evolved 6R mechanism. (a) Motion branch of 6R mechanism (b) Its prototype.",
        "texts": [
            " The above analyses demonstrate the mechanism varies the mobility from 2 to 5 without changing link-joint numbers and joint property. Hence, the mechanism is a member of reconfigurable mechanisms, or more precisely, kinematotropic mechanisms. Taking the concept of metamorphosis in the 8R mechanism, the motion of joints F and H are restricted when adjacent links FB 1 , FB 2, and HB 3 , HB 4 are partially overlapped, respectively, during structure reconfiguration. Consequently, a special overconstrained 6R linkage in Fig. 15 can be evolved from the 8R mechanism with renumbered new links B 1 B 2 and B 3 B 4 . The axes of each pair of adjacent joints B 1 , B 2, and B 3 , B 4 are perpendicular, respectively. The geometry of the remaining adjacent joints keeps unchanged in the reconfiguration. The dimensional conditions of the evolved 6R linkage in Fig. 15 are denoted as follows: a 12 = a 45 = a 34 = a 61 = a, a 23 = a 56 = 0 {\u2212\u03b112 = \u2212\u03b145 = \u03b134 = \u03b161 = \u03c0/ 2 \u03b123 = \u03b156 = \u03c0/ 2 { d 1 = d 4 = 0 d 2 = \u2212d 3 = d 5 = \u2212d 6 = R (17) where a > 0 and R > 0 based on the geometrical conditions. The DH parameters indicate that the evolved 6R linkage is a special Altmann linkage [63] , belonging to a special line and plane-symmetric Bricard linkage [26] . Given the symmetry, the Cartesian coordinate frame O-XYZ is attached to point O. To facilitate the analysis, screws are illustrated in Fig. 15 (a) to indicate joint axes. Hence, the screws of the mechanism can be written as follows: S l1 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S 1 = ( c \u03b1, 0 , s \u03b1, 0 , 0 , 0 ) T S 2 = ( \u2212c \u03b2s \u03b1, \u2212c \u03b1s \u03b2, c \u03b1c \u03b2, lp , \u2212lq , ln ) T S 4 = ( c \u03b2s \u03b1, \u2212c \u03b1s \u03b2, c \u03b1c \u03b2, lp , lq , \u2212ln ) T \u23ab \u23aa \u23ac \u23aa \u23ad S l2 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S 5 = ( \u2212c \u03b1, 0 , s \u03b1, 0 , 0 , 0 ) T S 6 = ( c \u03b2s \u03b1, c \u03b1s \u03b2, c \u03b1c \u03b2, \u2212lp , lq , ln ) T S 8 = ( \u2212c \u03b2s \u03b1, c \u03b1s \u03b2, c \u03b1c \u03b2, \u2212lp , \u2212lq , \u2212ln ) T \u23ab \u23aa \u23ac \u23aa \u23ad (18) where \u03b1 denotes the angle between the X-axis and line OE, \u03b2 is the angle between the Y-axis and line OF, e is the distance from the origin O to the axis of joint B 1 , l = e \u221a ( s \u03b1+ s \u03b2) 2 + c \u03b12 + c \u03b22 , p = c \u03b1( 1 + s \u03b1s \u03b2) , q = c \u03b2( 1 + s \u03b1s \u03b2) , n = s \u03b1c \u03b22 \u2212 c \u03b12 s \u03b2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003605_j.talanta.2003.11.021-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003605_j.talanta.2003.11.021-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of the modified NiHCNF carbon composite electrode prepared by (a) two-step and (b) one-step sol\u2013gel techniques in 0.1 M phosphate buffer (pH 7) containing 0.5 M NaCl, potential scan rate 10 mV s\u22121.",
        "texts": [
            " After 5 min potential cycling, the NiHCF modified carbon composite electrode presented stable electrochemical behavior. The bare carbon ceramic electrode was constructed by the same procedure without adding NiCl2 and Na3[Fe(CN)6]) to graphite powder. Electric contacts was made by a copper wire through the back of the electrodes. The electrochemical properties of the NiHCF modified carbon composite electrodes prepared with one and two-step sol\u2013gel technique were studied, using cyclic voltammetry. Fig. 1 shows typical cyclic voltammograms of the NiHCF modified electrodes that were prepared by one and two-step sol\u2013gel techniques in 0.5 M KCl solutions in phosphate buffer electrolyte solution (pH = 7) at scan rate 10 mV s\u22121. A single and well-defined redox couple with formal potential 0.46 V versus reference electrode, low background current and Ep = 60 mV (Fig. 1a) has found. For the modified CCE that was prepared by one-step sol\u2013gel method, after 5 min potential cycling scanning (\u22120.2 to 1 V), the NiHCF modified electrode shows reproducible cyclic voltamograms. As it has been shown in Fig. 1b, a defined redox wave with the formal potential 0.50 V, characteristic of NiHCF, was observed, but for this modified electrode the peak potential separations was high, Ep > 300 mV. Next the cyclic voltammograms of the modified CCE (prepared by two-step sol\u2013gel technique) were recorded in phosphate buffer solution (pH = 7) at various potential sweep rates. As it can be seen in Fig. 2, the voltammetric peaks corresponding to the [NiIIFeIII/II(CN)6]\u22121/\u22122 couple are typical of a surface immobilized redox couple",
            "446nFAD1/2 ( \u03bdF RT )1/2 CS (6) Where D and Cs are the diffusion coefficient (cm2 s\u22121) and the bulk concentration (mol cm\u22123) of substrate (hydrazine or hydroxylamine), respectively and other symbols have their usual meanings. Low value of kcat results in values of the coefficient lower than 0.496. For low scan rates (5\u201320 mV s\u22121) the average value of this coefficient was found to be 0.28 for a NiHCNF modified CCE, with a coverage of 5.35 \u00d7 10\u22128 mol cm\u22122 and a geometric area (A) of 0.0314 cm2 in 20 mM hydrazine at pH = 7. According to the approach of Andrieux and Sav\u00e9ant and using Fig. 1 [54], the average value of kcat for modified electrode prepared by two-step sol\u2013gel technique was found 8.8(\u00b10.2) \u00d7 103 M\u22121 s\u22121. For carbon composite ceramic electrode doped with NiHCNF prepared by one-step sol\u2013gel technique, the value of kcat was about 1.38(\u00b10.2) \u00d7 102 M\u22121 s\u22121 for hydrazine oxidation. For hydroxylamine oxidation the values of catalytic rate con- stants were 3.5(\u00b10.2) \u00d7 103 and 1.4(\u00b10.2) \u00d7 102 M\u22121 s\u22121 at the surface of CCE prepared by two and one-step sol\u2013gel technique. The catalytic rate constant of hydrazine and hydroxyl amine oxidation at the modified CCE prepared by two-step sol\u2013gel technique are higher than that obtained at the surface of CCE modified by one-step sol\u2013gel method suggesting that the monolayers adsorbed at CCEs prepared with two-step sol\u2013gel technique are more active than multilayers entrapped in the carbon composite lattice"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000887_j.mechmachtheory.2020.104055-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000887_j.mechmachtheory.2020.104055-Figure4-1.png",
        "caption": "Fig. 4. Model of a gear tooth considering TSW in Scenario 1.",
        "texts": [
            "5) where E refers to the Young\u2019s modulus, G refers to the shear modulus, k b , k s and k a denote the bending, shear, and axial compressive mesh stiffness, respectively, h refers to the distance from the mating point on gear to the tooth central line, d indicates the distance from the contact point on gear to the gear root, A x is the area of the tooth section, I x refers to the moment of inertia of the tooth section, and x is the distance from the tooth section to the tooth root. According to previous studies [3 , 14 , 28] , two scenarios shall be considered in calculation of the mesh stiffness of a stan- dard external spur gear with the addendum coefficient of 1, tip clearance coefficient of 0.5 and pressure angle of 20 \u25e6. Scenario 1 : GRC radius < GBC radius. When less than 42 teeth are present, GRC radius is smaller than GBC radius ( r r < r b , see Fig. 4 ). The total energy stored in the tooth includes two parts: the energy stored in the part between contact section and GBC and the energy stored in the part between GRC and GBC. In Fig. 4 , the dotted line along the involute profile represents the worn tooth profile, which varies from that of the perfect involute with the wear depths along the load line. As the contact points cannot reach the lowest point of involute profile and there is no wear on the tooth profile between the lowest point of the involute profile and the lowest point of tooth contact (LPTC), the energy stored in the part between contact section and GBC can be further divided into two parts considering TSW. Therefore, the three terms of mesh stiffness can be calculated with three components, respectively: 1 k \u2032 b = \u222b d 1 0 [ (d \u2032 \u2212 x ) cos \u03b11 \u2212 h \u2032 sin \u03b11 ]2 E I x dx + ( \u222b d s d 1 [ (d \u2032 \u2212 x ) cos \u03b11 \u2212 h \u2032 sin \u03b11 ]2 E I x dx + \u222b d \u2032 d s [ (d \u2032 \u2212 x \u2032 ) cos \u03b11 \u2212 h \u2032 sin \u03b11 ]2 E I \u2032 x dx \u2032 ) (3.6) 1 k \u2032 s = \u222b d 1 0 6 cos 2 \u03b11 5 G A x dx + (\u222b d s d 1 6 cos 2 \u03b11 5 G A x dx + \u222b d \u2032 d s 6 cos 2 \u03b11 5 G A \u2032 x dx \u2032 ) (3.7) 1 k \u2032 a = \u222b d 1 0 sin 2 \u03b11 E A x dx + (\u222b d s d 1 sin 2 \u03b11 E A x dx + \u222b d \u2032 d s sin 2 \u03b11 E A \u2032 x dx \u2032 ) (3.8) where symbol \u2018 \u2032 \u2019 means that the variables consider the effects of TSW and d s represents the distance from the LPTC to the gear root. In Eqs 3.6\u20133.8 , x \u2032 , d \u2032 , h \u2032 x , and h \u2032 are shown in Fig. 4 and have been derived as in Appendix B (Note: \u03b12 is defined as a negative value in this study): x \u2032 = r b [ (\u03b1 \u2212 \u03b12 ) sin \u03b1 + cos \u03b1] \u2212 r r cos \u03b13 \u2212 h w x sin \u03b1 (3.9) d \u2032 = r b [ ( \u03b11 \u2212 \u03b12 ) sin \u03b11 + cos \u03b11 ] \u2212 r r cos \u03b13 \u2212 h w sin \u03b11 (3.10) h \u2032 x = r b [ ( \u03b1 \u2212 \u03b12 ) cos \u03b1 \u2212 sin \u03b1] \u2212 h w x cos \u03b1 (3.11) h \u2032 = r b [ ( \u03b11 \u2212 \u03b12 ) cos \u03b11 \u2212 sin \u03b11 ] \u2212 h w cos \u03b11 (3.12) where r b and r r denote GBC radius and GRC radius, respectively, \u03b1 is the pressure angle of reference circle, h w and h w x respectively represent the wear depths of tooth contact section and the tooth section where the distance from the gear tooth root is x "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.4-1.png",
        "caption": "Fig. 8.4: Ankle Joint Actuation",
        "texts": [
            "4) From this we get the transformation matrix from the inertial system into the trunk coordinates by the expression The translational and rotational velocities of the trunk given in trunk coordinates then write: OvO =O AOI IvO, O\u03c9O =O A\u03d1\u03d5(\u03c8\u0307 \u03d1\u0307 \u03d5\u0307)T JO,R = (OA\u03d1\u03d5|03\u00d7(n\u22123)), JO,T = (03\u00d73|OAOI |03\u00d7(n\u22126)) J\u0302O,R = \u2202O\u03c9O \u2202q , J\u0302O,T = \u2202OvO \u2202q (8.6) with the transformation matrix OA\u03d1\u03d5 = ( sin\u03d1 sin\u03d5 cos\u03d5 0 sin \u03d1 cos\u03d5 \u2212 sin\u03d5 0 cos\u03d1 0 1 ) (8.7) According to section 2.2.4 on page 25 we evaluate the walking machine kinematics recursively. The ankle joint needs special modeling due to the fact that actuation is realized by a ball screw spindle, see Figure 8.4. Due to this mechanism we get a kinematical closed loop not consistent with the tree-like structure of the machine kinematics. Therefore we choose for the generalized coordinates OAOI = ( cos\u03c8 cos\u03d5\u2212 sin\u03c8 cos\u03d1 sin\u03d5 sin\u03c8 cos\u03d5 + cos\u03c8 cos\u03d1 cos\u03d5 sin\u03d1 sin\u03d5 \u2212 cos\u03c8 sin\u03d5\u2212 sin\u03c8 cos\u03d1 cos\u03d5 \u2212 sin\u03c8 sin\u03d5 + cos\u03c8 cos\u03d1 cos\u03d5 sin\u03d1 cos\u03d5 sin\u03c8 sin\u03d1 \u2212 cos\u03c8 sin\u03d1 cos\u03d1 ) (8.5) the two angles of the universal joint, from which we are able to calculate the position of the ball screw spindles. Figure 8.5 depicts the principle of the ankle joint kinematics",
            " The coresponding equations can only be solved iteratively, for example by the Newton-algorithm: qK,i+1 = qK,i \u2212 ( \u2202\u03c6i \u2202qK )\u22121 \u03c6i (8.12) In addition to that we need for the simulation the derivations of the generalized ankle coordinates with respect to the spindle coordinates. This writes \u2202qK \u2202s = ( \u2202\u03c6 \u2202qK )\u22121( \u2202\u03c6 \u2202s ) . (8.13) The time derivatives follow from that to q\u0307K = \u2202qK \u2202s s\u0307 q\u0308K = ( \u2202\u03c6 \u2202qK )\u22121( \u2202\u03c6 \u2202s s\u0308 + ( \u2202\u03c6 \u2202s )\u0307s\u0307 + ( \u2202\u03c6 \u2202qK )\u0307q\u0307K ) (8.14) The above formulas are necessary for the determination of the transmission ratios. According to Figure 8.4 the spindles are driven by an electrical motor, which are coupled to the spindles by a timing belt stage. The rotation of the spindles in combination with the ball nuts transform rotation into translation. The timing belt stage has a transmission ration of iZ = 15 11 , which gives together with the thread pitch of 5 mm a transmission ratio of iSP = iZ iS = 15 11 1 5 mm (8.15) for the special case of JOHNNIE. For the transmission from the motors to the ankle joints we have to consider the relation q\u0307K = \u2202qK \u2202s \u2202s \u2202qM q\u0307M = \u2202qK \u2202s ( 1 iSP 0 0 1 iSP ) q\u0307M = JSP q\u0307M (8",
            " Further, an aluminum Wave Generator with optimized shape is included. Its moment of inertia is 50% lower than that of the standard series. The shank includes the PWM-amplifiers for the knee joint actuation (PWM - pulse width modulation). The table on page 517 shows technical data of the joints. 2 Section 8.1 is based on the text of [202] 8.4 The Concept of JOHNNIE 537 The design of the knee joint corresponds to that of the hip pitch joint. The actuation of the ankle joint is realized with two linear drives based on ball screws (see Figure 8.4 on page 514). Two motors drive the ballscrews via timing belt. A motion of the sliders in the same direction leads to a pitch motion of the foot, the roll motion is realized by moving the sliders in reverse direction. The foot consists of three separate bodies (see Figure 8.7 on page 520). The two lower foot plates are connected by a rotational joint about the foot longitudinal axis ensuring that the ground contact situation is not overconstrained. The ground contact elements are rounded such that a smooth rolling motion of the foot can be realized during touch down and lift off"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.55-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.55-1.png",
        "caption": "Fig. 6.55 Location of the neutral plane in ks predicted by FEA",
        "texts": [
            "5 Modification of Yamazaki\u2019s Model 6.5.1 Modification of Yamazaki\u2019s Model Nagai et al. [19] modified Yamazaki\u2019s model by considering the location of the neutral plane for bending deformation of the sidewall, Young\u2019s modulus of the carcass and the location of point D in Fig. 6.41. Yamasaki assumed that the neutral plane for bending deformation was located on the inner carcass, but FEA shows that the neutral plane in the prediction of ks is located at the middle of the turnup ply and downward ply as shown in Fig. 6.55, where the red color indicates tensile stress in the radial direction and the blue color indicates compressive stress. When the R ad ia l s pr in g ra te k r( M N /m 2 ) theory experiment 175SR14 (5J-14) load: 3kN rB=192 mm rC=251 mm rD=296 mm \u03a6D=53.5\u00b0 Em=3.5 MPa 0.1 0.20 1 2 0 Inflation pressure (MPa) location of the neutral plane is changed to the middle of the turnup ply and downward ply, Eq. (6.108) becomes D/ \u00bc Em\u00f0r\u00deh3\u00f0r\u00de 12\u00f01 v2m\u00de : \u00f06:171\u00de Yamasaki [5] neglected Young\u2019s modulus of the carcass in the calculation of energies, but it is included in the modified theory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001118_j.msea.2021.140984-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001118_j.msea.2021.140984-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic diagram of hybrid manufacturing process. (b) Morphology of Ti\u20136Al\u20134V powder. (c) Hybrid manufacturing sample and the position of tensile sample. (d) Size of tensile sample.",
        "texts": [
            " In this study, to explore the microstructure and mechanical properties of forging-additive hybrid manufactured Ti\u20136Al\u20134V alloys, the powder feeding laser additive manufacturing is performed on a forged Ti\u20136Al\u20134V substrate. The microstructure evolution and formation mechanism of the bonding zone will be analyzed carefully, and the tensile mechanical properties and behaviors of stain evolution will be discussed. The hybrid manufactured Ti\u20136Al\u20134V samples were prepared with a LAM machine (LSF-VII, 6 kW semiconductor laser) under an argon atmosphere (oxygen content less than 50 ppm). A bulk deposit with dimensions of 60 \u00d7 20 \u00d7 60 mm3 was produced using the cross-hatching scanning strategy, as shown in Fig. 1a. The processing parameters for the LSF process are shown in Table 1. In our study, the processing parameters of additive manufacturing were optimized. In order to obtain high tensile properties, several processing parameters were tested initially, including P1 (laser power) = 1500 W, V1 (scanning speed) = 900 mm/ min; P2 = 2000W, V2 = 900 mm/min; and P3 = 2000W, V3 = 600 mm/ min. After checking the forming quality and the tensile performance, we chosen the processing parameters of P1 = 1500 W and V1 = 900 mm/ min as the optimized one. The Ti\u20136Al\u20134V powder was prepared by the plasma rotating electrode process (PREP). Fig. 1b shows that the diameter is about 80\u2013150 \u03bcm. A forged Ti\u20136Al\u20134V plate with dimensions of 100 \u00d7 90 \u00d7 55 mm3 was used as the substrate. Table 2 presents the chemical composition of the powder and the substrate materials. In order to determine the tensile properties of different zones, the wrought substrate zone sample (W), the bonding zone sample (W + L) and laser deposition zone sample (L) for uniaxial tensile testing were taken as shown in Fig. 1c. For each zone, three identical dog-boneshaped specimens with gauge dimensions of 15 \u00d7 5 \u00d7 2 mm3 (Fig. 1d) were subjected to room temperature tensile testing at a constant displacement rate of 0.9 mm/min on an Instron-3382 testing machine. Metallographic samples were obtained by wire electrical discharge machining. For metallographic observation, the tested specimens were prepared via conventional mechanical polishing and etched using Kroll\u2019s reagent (1% hydrofluoric acid and 3% nitric acid in distilled water) for optical microscopy (OM, OLYMPUS GX71) and scanning electron microscope (SEM, TESCAN MAIA3, the acceleration voltage is 15 kV) inspections",
            " The average microhardness is approximately 310, 335 and 322 HV for WSZ, HAZ, and LDZ, respectively. As discussed above, the high hardness in HAZ is attributed to the strengthening effect of the secondary \u03b1 phase (Fig. 3). In addition, the microhardness of LDZ was higher than that of WSZ because the basket-wave microstructures have more \u03b1/\u03b2 interfaces, which could hinder the slip of dislocations, resulting in a higher microhardness in LDZ. The tensile properties at room temperatures of the three different kinds of samples (W, W + L, and L as shown in Fig. 1c) of the hybridmanufactured Ti\u20136Al\u20134V alloys are shown in Fig. 12. The detailed values are also summarized in Table 3. The yield strength (~853 MPa) of the W + L sample is superior to those of the W and L samples, but its elongation (~14.1%) is the lowest. The yield strength of the L sample is higher than those of the W sample, however, the elongation is opposite. J. Ma et al. Materials Science & Engineering A 811 (2021) 140984 The yield strength of W, W + L, and L samples is consistent with that of the highest hardness in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000816_j.mechmachtheory.2020.103870-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000816_j.mechmachtheory.2020.103870-Figure2-1.png",
        "caption": "Fig. 2. Method for acquiring the global compliance matrix.",
        "texts": [
            " \u03bbp i 1 + \u03bbg i 1 \u03bbp i 2 + \u03bbg i 2 . . . \u03bbp i j + \u03bbg i j . . . \u03bbp in + \u03bbg in . . . . . . . . . . . . . . . . . . \u03bbp n 1 + \u03bbg n 1 \u03bbp n 2 + \u03bbg n 2 . . . \u03bbp n j + \u03bbg n j . . . \u03bbp nn + \u03bbg nn \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (1) where the subscripts i and j denote the extracted point and load point, respectively. The superscripts p and g represent the pinion and gear, respectively. In order to avoid the local deformation [29 , 34\u201335] , the extracted point is at the depth of 0.2 m beneath the tooth surface ( m is the module) (see Fig. 2 ). The expression of the contact compliance matrix is: \u03bbc = diag ( \u03bbc1 , \u03bbc2 , \u03bbc3 . . . \u03bbc i . . . \u03bbc n ) , \u03bbc i = 1 . 275 E 0 . 9 L 0 . 8 F 0 . 1 i (2) where L and E are the face width and the modulus of elasticity, respectively. F i denotes the contact force corresponding to contact point i . The equation of compatibility can be written as: [ \u2212( \u03bbc + \u03bbb ) I n \u00d71 I 1 \u00d7n 0 ][ F n ste ] = [ \u03b5 T / r b1 ] (3) where F n is the load distribution vector. \u03b5 is the clearance vector, which contains various kinds of profile errors",
            " Contact loss occurs on the tooth flank away from the web due to the low bearing capacity at those positions (see Fig. 6 ). The dynamic meshing force under different rotational speed is shown in Fig. 7 . Under 200 r/min, the difference between the dynamic meshing force and static meshing force is not very obvious. However, obvious deviation between and dynamic and quasi-static condition can be observed under 30 0 0 r/min. The load density under the dynamic condition is shown in Fig. 8 . The definition of r k can be found in Fig. 2 . Obvious partial load can be observed for the gear pair with asymmetric rim structure (rim structure B). Meanwhile, the dynamic force leads to the oscillation of the load density along the tooth profile direction. The load density under 30 0 0 r/min is quite different from that under quasi-static condition, which means that the effects of the dynamic load should be taken into the consideration under this condition. The accumulated wear depth (axial position z = 40 mm) is plotted in Fig. 9 , which shows the wear evolution along the tooth height direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.13-1.png",
        "caption": "Fig. 12.13 Pressure distribution of tires having different fore\u2013aft spring rates in braking",
        "texts": [
            " The tire size is 185/70R14 (wheel 5 J-14), and the inflation pressure is 200 kPa. Figure 12.11 compares the fore\u2013aft force between experiment and calculation. The slope with respect to the slip ratio is steeper for the driving condition than for the braking condition in the region of a small slip ratio. This is because the adhesion region in the driving condition is larger than that in the braking condition, because the pressure distribution in the driving condition is higher at the trailing edge as shown in Fig. 12.10. 816 12 Traction Performance of Tires Figure 12.13 presents conceptual figures for the pressure distribution of tires with different fore\u2013aft spring rates in the braking condition to clarify the mechanism. When the same torque is applied to tires with large and small fore\u2013aft spring rates, the fore\u2013aft displacement of the tire with a large fore\u2013aft spring rate is smaller than that of the tire with the small fore\u2013aft spring rate. Hence, the slope of the contact pressure distribution of the tire with the large fore\u2013aft spring rate is less steep than that of the tire with the small fore\u2013aft spring rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003948_978-3-642-48819-1-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003948_978-3-642-48819-1-Figure4-1.png",
        "caption": "Fig 4. 2.11 lin RSCR linkage",
        "texts": [
            " The main aim of this chapter is to establish the methods required to obtain a (usually implicit) relationship between the input and the output variables of single-degree of freedom linkages. 4.2 THE METHOD OF DENAVIT AND HARTENBERG (4.5). This method first appeared in (4.2) to (4.4) and is based on a closure relationship of successive affine transformations. An affine transformation is a change of coordinates involving a translation of the origin and a rotation of axes. Let X1 ' Y1 , Z1 and x2 ' Y2 , Z2 be two sets of coordinates related by an affine transformation, as appears in Fig 4.2.1 Fig 4.2.1 Translation and rotation of coordinate axes. 190 Thus, the position vector of any point P, referred to coordinates 1 and 2, can be expressed as (4.2.1 ) where e12 and ~12 are the translation vector and the rotation matrix, from axes 1 to axes 2. Eq. (4.2.1) indicates the general form of an affine trans formation. Symbolically, the transformation of (4.2.1) can be written as* (4.2.2) Affine transformations contitute a group under the composition operation defined as (4.2.3) ~23 is given through vector e23 and matrix ~23 as (4",
            " f) Let ui be the angle between Zi and Zi+1' measured along the positive direction of Xi +1 g) Let 9i be the angle between Xi and xi +1 ' measured along the positive direction of Z .\u2022 h) ~ construct the translation vectors (a .. 1)' and the rotation matrices -~,~+ ~ (Q .. 1)\" as is described next. -~,~+ . ~ i) Apply the closure conditions (4.2.20) and (4.2.21) and from them obtain the sought input-output relationship. In order to construct the translation vectors (a .. 1)\" it is necessary -~,~+ ~ first to construct the rotation matrices (Q .. 1)\" which is done next. -~,~+ ~ The relationship between coordinate systems i and i+1 is shown in Fig 4.2.', in agreement with the notation of f) and g). z. ~ ~~------- Y. X. ~ \\ \\ \\ \\ Xi+l ~ Fig 4.2.2. Relative position of coordinate systems i and i+1 Since Xi +1 is perpendicular to Zi (by definition), Xi and Xi +1 lie in a plane perpendicular to Zi. Thus, Xi can be made coincident with Xi +1 by means of a rotation through an angle 6i about Zi' as shown in Fig 4.2.3, where Xi, Yi, zi are the original axes Xi' Yi , Zi after the said rotation, so that Z! coincides with Z .\u2022 ~ ~ z. z~ ~ ~ \\ \\ ...... ...... 8. ~ Xi \\ Xi (=Xi+l) Y~ ~ Y. ~ Fig 4.2.3 ~tation through an angle ei about axis Zi. 195 196 Hence, from section 2.3, cosS. -sinS. 0 .~ ~ (Q .. f ).= sine. cosS. 0 -~~ ~ ~ ~ (4.2.23) 0 0 Next notice that Xi + 1 (i.e.Xi> is perpendicular to Yi' Yi+l' Zi (Le.zi) and Zi+l. Hence, Yi and Zi can be made coincident with Yi + 1 and Zi+1 by means of a rotation through an angle a i about Xi. The relative position of axes i' and i+l is shown in Fig 4.2.4. From Fig 4.2.4 and section 2.3, o 0 \\ \\ U. 1 Z'. 1 o o cosa. ~ sina. ~ U. 1 -sina. ~ cosa. ~ ~~------~~------- y~ 1 Xi (=Xi+l) Fig 4.2.4 Relative position of axes i' and axes i+l Finally, from eq. (4.2.18), the desired matrix is obtained as (4.2.24) (4.2.25) 197 cose. -sine.cosa. sine.sina. 1. 1. 1. 1. 1. {~i,i+1},i. sine. cosS.cosa. -cose.sina. (4.2.26) 1. 1. 1. 1. 1. 0 sina. cosa. 1. 1. Now it is possible to construct vectors (a. '+1)'. ~1.,1. 1. The relative configuration of three successive links appears in Fig 4.2.5, where the notation of a) to g) has been followed. Fig 4.2.5 Three successive links of a linkage From Fig 4.2.5, (4.2.27) with (4.2.28) and (o!6. 1)' 1\",(a. ,O,O)T 1. 1.+ 1.+ 1. . (4.2.29 ) 198 (~ .. 1)' be~ng as given by e~. (4.2.26l. ~;L(;L+ ;L Substituting (4.2.26), (4.2.28) and (4.2.29) into (4.2.27), (a .. 1}.=(a.cos6. ,a.sin6. ,s.}T ~;L,;L+;L ;L ;L;L ;L;L (4.2.30) Expressions (4.2.26) and (4.2.30) enable the analyst to systematically construct the affine transformations required to establish the closure condition (4.2.19). As is shown in Examples 4.2.1 and 4.2.2, it is not always necessary to apply both closure conditions (4.2.20) and (4.2.21) arising from (4.2.19), since only one suffices. Example 4.2.1. Analysis of the universal joint. The layout of a universal (or Hooke's) joint appears in Fig 4.2.6, where the DH notation has been used. The universal joint is a special class of RRRR spherical linkages. Obtain an input-output relationship of the form f(6 i ,64) = o. Fig 4.2.6 Universal Jo~nt Since all coordinate axes involved in this linkage have a common origin, the closure condition on the translation vectors is irrelevant and only that on the rotation matrices will be employed. The rotation matrices appearing in the present analysis are constructed from the fact that, in this case, 0. 1:=0.2:=0.3=90 0 Constructing the rotation matrices according to egs. (4.2.26) and (4.2.30), one obtains Thus, c8,C8 2c83+s8,s8 3 c8,s82 c8,C82S83-S8,c83 (~'2)1(~23)2(~34)3:= s8,c8 2c83-C8,s8 3 S8,S82 s8,c82S83+c8,c83 (4",
            "4 0 sa.4 ca.4 But, from (4.2.14a), (~14) 1:=(~41)! Hence, c84 sa 4 0 (~14) 1:= -s84c a.4 c84ca.4 sa.4 (4.2.32) s84s a.4 -c 84sa.4 ca.4 199 200 Equating the (',2)-and the (2,2)-entries of both forms of (Q14)' -eqs. (4.2.31) and (4.2.32) - one obtains cos6,sin6 2=sin64 sin61sin82=cos84cos~4 Eliminating 82 in the above expressions, which is the input-output relationship meant to be obtained. (4.2.33a) (4.2.33b) (4.2.34) Example 4.2.2. Analysis of an RSRC linkage. A typical RSCR linkage is shown in Fig 4.2.7, where the DH notation has also been used. The parameters and variables have the values 2:. 'IT a, a 1 a 2 a 2 a 3 a 4 = - 2 2 8, -\u00a2 82 62 8 3 83 84 84 a, = a a 2 b a 3 0 a 4 0 s, = c s2 = 0 s3 = 0 s4 -s For the analysis of this linkage, only the closure condition of the trans la- tion vectors will be needed. Since these vectors, as given by eq. (4.2.30), have to be expressed in one single coordinate system, the rotation matrices will also be constructed. Thus, c\u00a2 s\u00a2ca, -s\u00a2sa, (~'2)'= -s\u00a2 c\u00a2ca, -c\u00a2sa, (4",
            "39) can be reduced to 12 2 2 2 set) = asin~ + {b - c - a cos ~ (4.2.40) which explicity provides the set of values of s for each value of ~. A table of values for set) was obtained from a digital computer output, for the following values of mechanism parameters: a = 1.00 m, b = 3.00 m, c = 2.00 m for a value of ~ constantly equal to 1500 rpm. Similar tables for velocity and acceleration values were obtained via differentiation of set) by application of second central differences. Curves appearing in Fig 4.2.8 were obtained from the said tables. Notice that eq. (4.2.40) could have also been obtained from the geometry of the linkage of Fig 4.2.7, due to the simplicity of the linkage. In more general instances, however, the geometry is not so simple and the MDH becomes essential to perform the analysis. In addition to the digital-computer method previously outlined, to obtain the output set), set) and sCt) out of eq. (4.2.40), analog computer methods can also be applied. An analog computer is a (usually electrical) physical system whose behaviour is governed by the same mathematical model governing the system 203 4 Fig 4 . 2 . 7 Layout of an RSRC linkage 1 5 7 m /s ec 2 12 3 40 m /s ec 2 m / - .... .... .... \\ \\ / / I \\ \\ \\ \\ / 1 - ., .. . \" / - ' - .. .. - - - - - 1 \\ / . ~ \\ \\ / I . 10 0 \\ \\ I / \\ \\ / \\ I I \\ I / \\ \\/ \\ 1 / \\ I \\ / \\ / \"' --/ ' ,- . / 20 0 / / / 30 0 s - - - - s - - - - s F ig 4 .2 .8 D is p la ce m en t, v e lo c it y a n d a c c e le ra ti o n c u rv es o f an R SR C li n k a g e . '\" ~ \u00a2 (d eg re es ) 205 206 under analys~s. The elements constituting an analog computer perform the usual mathematical operations appearing in mathematical models, i.e., algebraic add~tion, multiplication, division, integration and differentiation. Besides these operations, the analog computer is also supplied with function generators. All these elements are symbolically represented as appearing in Fig 4.2.9. An analog computer representation of a mathematical model is usually called \"a realisation\" of the model, because via that representation the model is taken into physical reality. Equation (4.2.40) could readily be realized in an analog computer, and two differentiations would have to be performed to obtain the acceleration set). However, due to the noise present in every physical system, and the fact that a differentiator is a noise amplifier, it becomes undesirable to perform more than one differentiation. To avoid the second differentiation to obtain set), then, eq. (4.2.40) is first differentiated to obtain ds 5 S' (CP)= - = .. = dcp cp (4.2.41) which has to be integrated once, with initial conditions s=sO at cp =CPo' and differentiated only once to obtain set). The analog realization of eq. (4.2.41) appears in Fig 4.2.10 Details about analog simulation of linkages can be found in (4.6). Concerning simulation of mechanical systeresin general, the reader can see (4.7) . A digital computer-oriented algorithm, based on an iterative procedure, to obtain the history of all variables of a linkage is presented in (4.8). Exercise 4.2.10 Given the RSCR linkage of Fig 4.2.11, obtain an inputoutput relationship f(W,CP), an analog realization yielding cp,cp and cP and curves cp vs. t, cp vs. t and cp vs. t, for the following values: 207 ~=:I \u2022 )-~ x-J DIF )--x . X-j SIN )-SinX X-1 COS )- cos x X-4 SIN-1)- sin-1 x x-j COS-1)- cos-1 x Ixl ~ 1 Ixl ~ 1 t-l CFG )-f(t) X-l~ )--rx x~O ;=:1 X )-XY Fig 4.2.9. Elements for analog realisations 208 la=0.5m, b=1.0m, c=0.25m, d=0.75m, e=0.5m, ~=1200rpm(const) 4.3 AN ALTERNATE METHOD OF ANALYSIS. Using the MDH one does not necessarily obtain one single relationship for the input and the output variables, but usually a system of nonlinear algebraic equations involving all the different linkage variables which appear strongly coupled, as occurs with eqs. (4.2.39). If the system is not very complicated, then it can happen that, after introducing appropriate trigonometric identities, one can obtain a single inputoutput relationship where the only variables appearing are the input and the output",
            " The next example illustrates how to apply this method to spherical linkages. Example 4.3.1 Analysis of the general RRRR s2herical linkase. The MDH can be applied, of course, to general spherical linkages, following the same procedure applied to the universal joint. The fact that the MDH introduces other variables besides the input and the output, however, produces very cumbersome equations, algebraically difficult to handle. The alternate method proves, in this case, to be particulary helpful. Consider the RRRR spherical linkage appearing in Fig 4.3.1 210 Let ~O' ~O' SO' go and ~,p,g,g be the position vectors of points A, B, C and D in a reference configuration and in a time-varying configuration, respectively. Furthermore, let Q and ~ be the rotation matrices carruing links 2 and 4, respectively, from the reference to the current configurations. Thus, (4.3.4) and c=Rc - --0 (4.3.5) Clearly, ~=~O and g=gO\u00b7 The cosine of a 3 in both the reference and the current configurations is (4.3.6a) and ( ) bTc cosa3 cur = (4.3.6b) where Ilbo II and II Co II are assumed unity, without loss of generality. Since link 3 is rigid, u3 remains constant throughout the linkage motion and, since II~II = 11~011 and II~II lie II, one obtains -0 T T ~ ~ = ~o~o (4.3.7) or, substituting the relations (4.3.4) and (4.3.5) in the above equation, (4.3.8) which is the scalar input-output relationship meant to be obtained. The only variables appearing in eq. (4.3.8) are $ , contained in Q, and ~ , contained in R. Define the coordinate axes appearing in Fig 4.3.2, with Xi and Xo directed along the axes of R12 and R41 , respectively. z. ,z 1 9 Fig 4.3.2 Fixed coordinate axes containing the axes of R12 and R41 Matrices Q and ~, referred to i- and 0- axes respectively, are given as 0 0 0 0 1 (Q) . 0 cos1jJ -sin1jJ , (~)o 0 cos~ -sin~J (4.3.9) _ 1 0 sin1jJ cos1jJ 0 sincp coscp 211 212 vectors band c are shown in Figs 4.3.3a and 4.3.3b -0 -0 Hence, cosa2 COSCl4 (!?O) i sina2COSlj!0 (co)o sina4cosCPO (4.3.10) sina2sinwO sina4 sincpO In order to perform the products appearing in eq. (4.3.8) it is necessary to express all vectors and matrices in the same coordinate axes. The transformation matrix carrying the i-axis into the o-axes, referred to the i-axes, is given as X. l - Z. l cosa 1 -sinal 0 sinal cosa 1 o o o _}--BO Wo - - - -- (al (bl Fig 4.3.3 Reference configuration of points Band C. (4.3.11) /,h ..- ...... \"'0 / / ). / / / ,/ The product b T -0 T 9 ~ ~o needed in eq. (4,3.8) is next computed T T (g~o I ~ ~o~ ~~o ;= (4.3.12) which yiedls (4.3.13) When eq. (4.3.13) is substituted into eq. (4.3.8) one obtaines the desired input-output equation (4.3.13a) in which ~ and \u00a2 are measured from the reference values ~o and \u00a2o' respectively, as defined previously. If the said angles are measured from the plane of the axes of R12 and R41 , instead, then the latter equation becomes (4",
            "9) have generalized the notation of Denavit and Hartenberg, however, to overcome the aforementioned situation and furthermore, to extend the application of the MDH to the analysis of higher-pair mechanisms. * If a link is coupled to 2 other links, it is called binary; if it is coupled to 3, it is called ternary, and so on. 215 4.4 APPLICATIQNS TO QPEN KI~TIC CHAINS , The method of Denavit and Hartenberg, described in section 4.2, can also be applied to open kinematic chains. An example is next described, showing the applicati on o~ the method to the analysis of a 3-degree- of-freedom manipulator. Fig 4 . 4.1 Shows ~ 3-degree~f-freedom manipulator whose function is to position point \u00b04 , Of link numb.er 4, in an arbitrary position given by the three cartesian coordinates x,y,z, referred to frame X,-y,-z,. The manipulator is composed of 4 links and t~ee revolute pairs . The axes of pairs R'2 and R23 are perpendicular, whereas those of pairs R23 and R34 are parallel. Moreover, axis z4 is chosen parallel to these. Fig 4.4.' Three-degree-of-freedom manipulator. Following Denavit and Hartenberg's notation, one has 216 a =90 0 a =0 0 a =QO 1 ' 2 '3 The corresponding closure equation takes on the form (4.4.1) where r is the positon vector o~ 04 and the foregoing relation is assumed to be referred to f:reame X1-\u00a51-Z1' :From eq. (4.2.30), (4.4.2a) (4.4.2b) (4.4.2c) Since all vectors in eq. (4.4.1) should be described in the same reference frame,a change of coordinates should be introduced, namely (4.4.3a) (4.4.36) From eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure6.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure6.13-1.png",
        "caption": "Fig. 6.13",
        "texts": [
            " For saddle point (+1,0), we obtain a Hamilton constant from eq. (6.161): H(1,O) =~. 3 The contour line equation of the saddle point is v 2 u3 2 -+u--=2 3 3 (6.163) Now we determine the crossing points of v = 0 and contour line of eq. (6.163). Substituting v = 0 into the above equation, yields u3 -3u+2 = 0 or (u-1)(u2 + u- 2) = 0 I.e. u2 +u-2=(u-1)(u+2), :.u=1,-2. Therefore, u = and u = -2 are the crossing points of v = 0 and the contour line. According to the above discussion, we can draw the phase portrait of eq. (6.159), as shown in Fig. 6.13. Give a perturbation E to the global solution curve of eq. (6.159), and this can show the dynamical behaviour of system (6.148) when U 1 and U 2 are close to zero. ro in Fig. 6.13 corresponds to contour line H ( u, v) = 2 / 3, allowing rl = -1 to correspond to u 1 :::; O. In this case the Hamilton vector field of eq. (6.159) contains all behaviours of universal unfolding. To obtain the equation of saddle loop ro which passes through qo = (-2,0), we expand the right-hand side of eq. (6.162) at qo to a Taylor series: v~ = 3-4uo +u~ Deriving eq. (6.164a) and substituting (6. 164b) into it, we obtain (6. 164a) (6. 164b) 216 Bifurcation and Chaos in Engineering As d 2uO = ~(dUo) = duod (dUo) dt 2 dt dt dtduo dt If we suppose duo = u , dt then d2uO A du 2 -2-=u-=3-4uo +uo dt dt and integrating the above equation yields ( ) 2 A 2 duo 2 2 3 (U) = - =6uO -4uO +-UO +C dt 3 i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.4-1.png",
        "caption": "Fig. 7.4: Robot Relative Kinematics",
        "texts": [
            " In a similar way we describe also the motor position and orientation with respect to some predecessor motor. For the relevant coordinates we introduce the notation q\u0304 = ( q\u0304M q\u0304L ) \u2208 IRnf , with nf = nM + nL, (7.1) where L stands for link and M for motor. The number of robot degrees of freedom is nf composed by the link degrees of freedom nL and the motor degrees of freedom nM . Expressing the position and orientation of a link i by the center of mass vector ri regarding in addition the rotation matrix from the inertial system to link i, we come out with (see Figure 7.4) ri = ri\u22121+ri\u22121,i, ri\u22121,i = rSE,i\u22121+rES,i, Ai,0 = Ai,i\u22121Ai\u22121,0, (7.2) where the vector rSE,i\u22121 connects the mass center Si\u22121 with the joint between the bodies Bi\u22121 and Bi, and the vector rES,i connects the joint with the mass center Si of link i. From the above relations we get the velocities and the accelerations \u03c9i =\u03c9i\u22121 + \u03c9i\u22121,i, r\u0307i =r\u0307i\u22121 + \u03c9\u0303i\u22121rSE,i\u22121 + \u03c9\u0303irES,i + r\u0307ES,i, \u03c9\u0307i =\u03c9\u0307i\u22121 + \u03c9\u0303i\u22121\u03c9i\u22121,i + \u03c9\u0307i\u22121,i, r\u0308i =r\u0308i\u22121 + \u02d9\u0303\u03c9i\u22121rSE,i\u22121 + \u03c9\u0303i\u22121\u03c9\u0303i\u22121rSE,i\u22121+ + \u02d9\u0303\u03c9irES,i + \u03c9\u0303i\u03c9\u0303irES,i + 2\u03c9\u0303ir\u0307ES,i + r\u0308ES,i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003342_28.556642-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003342_28.556642-Figure5-1.png",
        "caption": "Fig. 5 Flux paths due to magnetizing current, z.::, in an unloaded closed rotor slot machine at steady state.",
        "texts": [
            " Since the high-frequency flux paths characterize the stator transient inductance, main flux path ND LORENZ: TRANSDUCERLESS FIELD ORIENTATION CONCEPTS EMPLOYING SATURATION-INDUCED SALIENCIES 1383 patial modulation aligned with the main flux flux in the stator, the fundamental and highonent fluxes share largely dissimilar paths in een the stator anld rotor fluxes, and the respective indicated in Fig. 3. Based upon the above saliency would be expected to be more leakage inductance (and thus the stator transient e) by a factor of two or more from the unsaturated is variation is substantially more than that obtained n in typical open and semiclosed slot machines. saturauon of the rotor slot bndge can be expected e main flux path due to a portion of the flux flowing the slot bridges as shlown in Fig. 5. A spatial modula- Under loaded operating conditions, rotor current will tend to drive the slot bridges much further into saturation. A larger saliency in the stator transient inductance would then be created that is aligned with the rotor current vector, rather than the main flux. As the space vector diagram in Fig. 6 indicates, the rotor current vector is orthogonal to the rotor flux at steady state. Thus the saliency created by load-induced saturation of the slot bridge will be orthogonal to the saliency created by main flux saturation of the slot bridge",
            " Heterodyning the high-frequency signal currents by sin w,t and cos w,t in the form (15) ,E? = z:~, sin wat + i&z cos w,t p = L o + L l COS[2(Q, - wzt)] . yields (16) Similar to (lo), I,, is isolated by low pass filtering (17) From f t 0 the inductance magnitude can be obtained by mapping. The approach is illustrated in Fig. 10. Similar to the saliency tracking, the magnitude information contained within 20 may more closely correlate to either the stator or rotor flux, JANSEh or in 1 stator design desirec C. Ma Sin( nitude (Fig. 5 oped t known utilizir This a by flu compe accura the ma this ai sluggi! The trackir vector VD LORENZ TRANSDUCEFILESS FIELD ORIENTATION CONCEPTS EMPLOYING SATURATION-INDUCED SALIENCIES 1387 4 heterodyning scheme with inductance mapping to provide flux magnitude information from the high-frequency signal injection. 1 closed-loop tracking scheme to obtain rotor flux position information given rotor flux magnitude and machine parameters, with the fundamental zitation angle, Bel, added to improve tracking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000128_j.procir.2017.03.073-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000128_j.procir.2017.03.073-Figure3-1.png",
        "caption": "Fig. 3. Direct material deposition: (a) coaxial powder; (b) lateral wire.",
        "texts": [
            " Adaptive toolpath deposition method has been developed to manufacture and repair turbine compressor airfoils [20]. In the last couple of years, a number of hybrid manufacturing systems have been announced with the combination of LAM and CNC milling or multi-wire heads or different energy sources such as laser and electron beam. These systems are gaining traction in hot-work applications such as the repair of tools, hard facing and other opportunities where it reduces cost of repair applications [21, 39]. Fig. 3 shows the working principle of two deposition techniques used for DMD. In Fig. 3(a), powder is fed coaxially, whereas in Fig 3(b), wire is delivered laterally to the molten pool caused by laser energy. In general, powderfed systems are more expensive than wire-fed systems because of the critical powder manufacturing process. Every deposition technique (wire or powder) has its pros and cons, and if combined together then gives new more advantages (Fig. 4). However, there is limited research done in order to combine both techniques for hot-work tool steel applications and push the LAM process a step ahead because of the complexity involved into the process",
            " Second application is for near-net shape fabrication based on DMD process. It is an evolving CAD/CAM technology that utilizes a laser beam to melt deposited wire and/or powder to form a functional component layer-by-layer. This laser based process does not need any molds or dies and hence provides the flexibility to quickly change the component design. This feature quietly suits to the industries\u2019 demand i.e. time to market. DMD is more effective compared to SLM in terms of development of FGMs like Inconel-steel FGM [14]. Fig. 3(a) shows the working principle of powderbased DMD, which has been used to build a freeform by using laser to consolidate H13 and CPM 9V tool steel (CPM: crucible particle metallurgy) [34]. However, powder-based DMD process has maximal defects compared to wire because the technology for wire is transferrable from mature welding consumable supply chain. Although the parts built using these LAM processes are metallurgically sound and free of cracks, concerns have been raised about surface finish and dimensional accuracy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure1-1.png",
        "caption": "Fig. 1. Profile of the grinding wheel.",
        "texts": [],
        "surrounding_texts": [
            "A fi d w o F d c \u00a9\nK\n1\ns s h s d g B t p s d m\nd p n\n0 d\nWear 262 (2007) 1281\u20131288\nGear tooth contact analysis and its application in the reduction of fatigue wear\nK. Mao \u2217 Mechanical Engineering, School of Engineering and Design, Brunel University, Uxbridge, Middlesex UB8 3PH, UK\nReceived 27 May 2005; received in revised form 7 June 2006; accepted 19 June 2006 Available online 25 July 2006\nbstract\nThe present paper will concentrate on the gear fatigue wear reduction through micro-geometry modification method. An accurate non-linear nite element method will be employed to provide a quantitative understanding of gear tooth contact behaviour. Shaft misalignment and assembly eflection effects on the gear surface wear damage will be investigated as well. To achieve high accuracy of the gear geometry, the tooth profile ill be mathematically generated though using Python script interfacing with the finite element analysis (FEA) software instead of importing from ther computer aided design (CAD) packages. Real rolling and sliding contact simulations have been achieved through using the latest non-linear EA techniques. An investigation has been carried out on automotive transmission gear surface failure due to shaft misalignment and assembly eformations. The solution for the wear is consequently proposed based on gear micro-geometry modification approach, i.e. tip relief, facewidth rowning and lead correction.\n2006 Elsevier B.V. All rights reserved.\nation;\nd f n i n l s c s i o e a a\np\neywords: Tooth contact analysis; Gear fatigue wear; Micro-geometry modific\n. Introduction\nHigh performance gears in automotive/motorsport transmision are required to operate at ever increasing high torque and peed whilst still remaining competitively spaced and priced and ighly reliable. The net consequence of increasing torque and peed is that the gears accumulate surface fatigue more rapidly ue to shaft misalignment and assembly deformation resulting ear surface high local contact. The existing methods [1\u20133] and ritish Standard [4] lead to over design and the gears end up oo large for the limited space available in the high performance owertrain transmission systems. It is very difficult to find a ubstantial solution from the existing design methods and stanards for the gear surface local pitting caused by the gear shaft isalignment and assembly deformation. Significant progress has been made in the past decades in the\nevelopment of a variety of surface engineering technologies, roducing engineered surfaces with thickness ranging from the anometer scale to the millimetre scale [5]. The ever increasing\n\u2217 Tel.: +44 1895 266700; fax: +44 1895 232806. E-mail address: ken.mao@brunel.ac.uk.\na i F e s t a\n043-1648/$ \u2013 see front matter \u00a9 2006 Elsevier B.V. All rights reserved. oi:10.1016/j.wear.2006.06.019\nNon-linear finite element method\nemands in combined properties for modern machinery have urther led to the recent development of duplex surface engieering technologies [6\u20138]. Many surface engineering systems, ncluding single, duplex and multi-layer systems [9,10], are ow available to combat various component degradation probems and to meet the requirements of new design of mechanical ystems operating under ever more severe conditions. Surface oatings, e.g. tungsten carbon carbide coating (WC/C), can ometimes provide significant increase in carburised gear scuffng resistance and wear resistance [11]. However, due to the lack f reliable mathematical models and design systems for surface ngineering, the requirements in the surface layer for specific pplications are usually determined on the basis of experience nd empirical formula.\nSeveral attempts have been made in the past to solve this comlex multi-layer contact problem, involving the removal of the ssumptions made in the Hertz theory. This approach mainly nvolves the application of the Sneddon\u2019s theory [12] and the ourier integral transform technique to formulate the considred contact problem and the use of numerical techniques to olve the model. For example, Gupta and Walowit [13] simulated he contact behaviour of an elastic layer on an elastic substrate, ssuming smooth and frictionless contact based on Sneddon\u2019s",
            "1 62 (2007) 1281\u20131288\nt t t p a a r e l h t b f b d R t [ r e p s t a o a m f\nf m f b m a m r f s b a w i u m b\n2 m\na i p d p p\nt a l d p a\nt C b o then read into the FEA software through using Python script interfacing with the solver. The full 2D gear geometry is then generated through rotation copying the one single tooth. Fig. 3\n282 K. Mao / Wear 2\nheory. They derived the mathematical formulation relating to he problems of a layered elastic surface indented by an elasic indenter. More recently, the smooth and frictionless contact roblem of multi-layer systems has been solved by Elsharkawy nd Hamrock [14]. Further development has been made by Cole nd Sayles [15] in considering the frictionless contact of real ough multi-layer systems. Attempts have been made by Mao t al. [16,17] to tackle the even more realistic real rough, multiayer contact problem where frictional forces are involved. It as been noticed that failure of coating systems under many ribological situations is seldom caused by conventional wear, ut by debonding of the coating from the substrate (adhesive ailure), or fracture of the coating (cohesive failure), or even y subsurface failure (substrate failure) [18]. All these degraation phenomena are facilitated by local plastic deformation. ecently, the finite element method (FEM) has been employed o analyse the deformation behaviour of several coating systems 19,20] to overcome the difficulties associated with the laboious numerical technique and the complex form of analytical quations. An FEM model has been developed to analyse the lastic deformation behaviour of various hard coating\u2013substrate ystems [21]. Particular attention has been paid to the initiaion and development of the plastic zone in the coating system, nd the influence of coating thickness and substrate properties n the deformation behaviour. Layer coated gear surface pitting nalysis [22,23] has been carried out by using 2D finite element ethod and crack growth rates have been evaluated by using racture mechanics method. Even though surface engineering will improve gear surface atigue problems, for local surface contact failures due to shaft isalignment and assembly deflection, thin coatings and subsurace treatments do not provide adequate solutions. One of the est solutions for this kind of surface local pitting is gear surface icro-geometry optimisation, i.e. tip relief, facewidth crowning nd lead correction. This is because this kind of local pitting is ainly caused by shaft misalignment and assembly deformation esulting very high localised contact. Existing design methods or gear surface micro-geometry modifications are either from implified finite element models using gap elements [24] or ased on experimental experiences. None of them could provide n accurate design guide for the gear surface local contact fatigue ear problems. These fatigue wear problems will be investigated n the current paper using micro-geometry modification method nder real operating conditions. Advanced non-linear finite eleent method will be employed to simulate gear surface contact\nehaviour using accurate three-dimensional gear tooth profiles.\n. Tooth profile generation and micro-geometry odifications\nThe existing methods [25\u201327] for gear geometry generation re based on the following procedure. Establish the mathematcal model of gear drives first according to the manufacturing\nrocess and gear meshing theory. Export the calculated surface ata points into a CAD package and construct the surface data oints into gear surface and trim the surface from the design arameters. The gear tooth solid models are then imported into\nhe FEA solver from the CAD package using IGES, DXF, ACIS nd STEP formats. The geometry importation tools may cause a ot of problems, primarily because of the disparity between stanard interpretation and level implementation. Analyst should ay special attention on the accuracy of the imported and therefter geometry clear up.\nThe present work will generate the required geometry within he FEA software (Abaqus [28]) instead of imported from other AD packages. The gear tooth profile data points are generated ased on the hob manufacturing process and gear meshing thery [29,30] as shown in Figs. 1 and 2. The calculated data are",
            "K. Mao / Wear 262 (2007) 1281\u20131288 1283\nal gears and their assembly.\ns t t g t d t t m\nt d g a\nt b t i t t\nf s o i p\n\u2022 \u2022\n\u2022\nhows an example of three full 3D helical gears\u2019 geometry and heir assembly. The 3D full helical gear geometry is obtained hrough extruding the 2D geometry. This method is of very high eometry accuracy with resolution of 10\u22126 mm and this may be he best way to obtain high accurate gear geometry to avoid the isparity between standard interpretation and level implementaion. This high accurate gear geometry makes researchers have he powerful tool to investigate the effects of gear tooth surface\nicro-geometry modifications. Gear surface micro-geometry modifications are tooth profile ip relief (Fig. 4), lead correction and crowning in facewidth irection. Those modifications are very important for proper ear mesh and engagement process, especially when shaft mislignment and assembly deflection are significant.\nFor the mating pair of teeth under load, it is not possible o have the next tip enter contact in the pure involute position ecause there would be sudden interference corresponding to he elastic deflection and the corner of the tooth tip would gouge nto the mating surface [31]. Manufacturing errors can add to his effect that is the reason to relieve the tooth tip to ensure that he corner does not dig in.\nThe gear profile functions with tip relief can be obtained rom the following approach. For a given rack O1a (with tandard pressure angle of \u03b11) and ab (with pressure angle f \u03b12 for tip relief) as shown in Fig. 5, the correspondng involute profiles can be obtained from the gear meshing rinciple.\ny\nn p t\nb\nx\nAssuming:\nglobal co-ordinate: OXY; rack local co-coordinate: O1X1Y1 (originally located at OXY); gear local co-coordinate: O2X2Y2.\nThe equation for O1a line is:\n1 = x1\ntan(\u03b11) (1)\nIf a point M1 in O1a line will contact with the gear, the rack eeds to be moved a distance b1 (O1O) to achieve the normal of oint M1 cross with point O according to the gear conjugating heory:\ny1\n1 = tan(\u03b11) + x1 (2)\nFor co-ordinate transformation from O1X1Y1 to OXY:\n= x1 \u2212 b1, y = y1"
        ]
    },
    {
        "image_filename": "designv10_2_0000228_j.matpr.2021.02.632-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000228_j.matpr.2021.02.632-Figure4-1.png",
        "caption": "Fig. 4. Tool Paths for any AM process (a) Raster, (b) Zig-Zag, (c) Contour, (d) Spiral, (e) Hybrid tool paths [26,28]",
        "texts": [
            " A complete robotic configuration for WAAM deposition is therefore required [27]. The improvement of an intricate route planning approach is another critical step in WAAM. Mathematical uncertainty affects route planning arrangements for AM steps that have rough estimated deposits. In addition, the properties of the deposited type could be impacted by the direction of the deposition course. Various tool path generation techniques are reported in literature to produce various sorts of deposition paths. Raster tool path: Fig. 4(a) shows the raster filling path depends on the projection of the planar beam along one line. In this method, a lot of scan lines with small width occupy 2-dimensional regions. Because of its simple implementation, it is frequently used in AM and is sufficient for any arbitrary boundary [28]. Zig-zag tool path: The zig-zag approach, as shown in Fig. 4(b), is the same as the raster path where the only difference is that separate parallel lines are combined by a single continuous pass reducing the number of tool path passes. The outer boundary accuracy for both raster and zig-zag methodologies is poor because of the discretization mistakes on any edge that isn\u2019t in flow to the direction of motion of the tool [29]. Table 3 Application of welding arc for AM of different metals and their alloys. Material Application area Welding technique used Remarks Citations Steels Die steel (H13 wire) Thin walled parts GMAW welding Well deposited welds with no strong delineations between layers were obtained",
            " [22] Al alloy Al 2219 Structural components, High strength weldments GMAW Tandem process When active cooling is applied, the overall forming efficiency has improved by more than 0.97 times, due to both increased maximum wire feed speed and reduced inter-layer dwelling time. [23] Al5Si Aluminium alloy Aerospace products, Lightweight structures Hybrid WAAM (WAAM + Milling) Both surface roughness and machining allowance were reduced when milling thickness is 0.4\u20131.2 mm. When after the WAAM procedure plane milling is done, melt flow slows down thus reducing the side profile of thin wall structure. [24] Contour tool path: Contour path, as shown in Fig. 4(c), actually follows the outer boundary of the deposition pattern which can resolve the outer boundary issue associated with rastar and zig- zag tool path planning. All the inner fillings are done according to the outer boundary structure simultaneously as shown in Fig. 4(c) [30]. Fig. 2. Steps in a WAAM system [8] Fig. 3. (a) Component with basic build direction (b) supports required (c) multidirectional slicing with build direction B1, B2 and B3 [25] Spiral tool path: Fig. 4(d) shows the spiral tool path, it is widely used while machining like pocket milling, but also can be used equally for AM process. This method of tool path generation can remove the shortcoming of zig-zag tool path, however, it is suitable for some special geometrical models only [31]. Hybrid tool path: As shown in Fig. 4(e), the hybrid tool path planning is well suited for AM processes as it incorporates several promising merits of different approaches. In order to meet both the mathematical precision and manufacture efficient product, a blend of contour and zig-zag tool path is normally created. There are many ways of hybrid tool path planning. Mixed tool path where zig-zag is used to fill the inside to increase performance while the contour is for the product boundary that provides a better surface and outer body finish is used [32,33]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure5-36-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure5-36-1.png",
        "caption": "Figure 5-36. Possible trajectories of current vector for the eight inverter states, and \\s qds (current command), is qds (stator current vector location) when the error bound \u00d9AS is reached.",
        "texts": [
            " Note, however, that only two multipliers are required for implementation beyond that needed for the ordinary stationary regulator. Reference 26 provides an in-depth study of the synchronous regulator and a detailed comparison with the stationary regulator. Predictive (optimal) current controllers are a relatively recent development. The control of stator current is seen as an optimization problem that can be described as choosing an optimal voltage vector to best move the current in the vector plane as shown in Figure 5-36. In this case, the future path of the current vector is predicted for all possible inverter output voltage vector states (inverter switch connections). Six active inverter output voltage vector states can be identified together with 2 null or zero voltage states in which the currents of the inverter \"coast\" in a similar manner as described previously. At each clock cycle the inverter switching state is chosen that best keeps the current vector within a prescribed circle on this plane, the radius of which denotes the tolerable current error band [23] while minimizing some cost function, such as rms current ripple",
            " Current Regulators for Motion Control 249 ing conditions) where the angle of the current error vector along with the angle of the equivalent voltage vector are the inputs and the optimal inverter state is the output. The equivalent voltage vector is defined as the sum of the unity voltage vector and the derivative of the reference current vector multiplied by the filter inductance, all of which can be readily measured. The switching action is executed whenever the current error vector exceeds defined boundaries in a similar manner to that illustrated in Figure 5-36. Another algorithm which approximates the optimal voltage vector solution is the method by Habetler, and colleagues [25]. This method switches nearly constantwidth output voltage pulses resulting from a high-frequency resonant link to produce a pulse density modulation of the inverter output voltage. This controller can be implemented in a very inexpensive set of hybrid hardware, which is shown in Figure 5-37. For this current regulator the decision of which voltage vector to select is simple digital logic. A voltage vector is preselected by a 3\u03c6 currentregulated delta modulator (CRzlM). Based on the present output vector, 250 5. Motion Control with Induction Motors Sa(k \u2014 1), Sb(k\u2014 1), SC(\u00c4:\u2014 1), no direct jumps between nonzero vectors are allowed, except for a jump to an adjacent voltage vector (such as from vector 2 to vector 3 or 1 in Figure 5-36). If the vector is not adjacent, the inverter is forced to select the zero vector for one pulse width before selecting the new nonzero voltage vector (such as from vector 2 to zero to vector 5 in Figure 5-36). The logic for this algorithm is contained in Table 5-1. In addition to this simple switching logic, this \"adjacent state\" controller has a simple bang-bang loop on the neutral voltage. This allows it to maintain a zero average neutral voltage. This controller is an approximation to the optimal controller in that the CRJM does not select \"optimal\" states. However, most of its decisions have been shown to be consistent with the optimal voltage vector selection [24]. Furthermore, the adjacent state algorithm does effectively reduce the rms ripple currents by never allowing the worst case switching to occur"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.46-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.46-1.png",
        "caption": "Fig. 6.46 Geodesic path of a circular ring and cord tension. Reproduced from Ref. [5] with the permission of Tire Sci. Technol.",
        "texts": [
            " To consider the nonlinearity of the rotational spring rate at a large twist angle, the formulation for a bias tire in Sect. 5.2.5 is used. The geodesic line path satisfies the relation r cos a \u00bc rD cos aD \u00bc q\u00f0const\u00de: \u00f06:139\u00de In the coordinate system with z(rD) = 0, Eq. (5.19) can be rewritten as z\u00f0r\u00de \u00bc ZrD r Affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p dr; \u00f06:140\u00de where9 A \u00bc r2 r2c sin/D r sin aDffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 q2 p : B \u00bc r2D r2c \u00f06:141\u00de Referring to Fig. 6.46, the twist angle dw is given as dw \u00bc dv=r \u00bc cot a ds=r: \u00f06:142\u00de Equation (6.139) can be rewritten as cot a \u00bc qffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 q2 p : \u00f06:143\u00de Using Eqs. (6.140), (6.142) and (6.143), the twist angle w and carcass length L are given as10,11 w \u00bc ZrD rB q r Bffiffiffiffi D p dr \u00bc ZrD rB rD cos aD r Bffiffiffiffi D p dr; \u00f06:144\u00de 9Problem 6.5. 10See Footnote 10. 11See Footnote 10. 6.4 Fundamental Spring Rates Based on the Equilibrium Shape \u2026 353 L \u00bc ZrD rB rBffiffiffiffi D p dr; \u00f06:145\u00de where D \u00bc B2 A2 r2 q2 \u00bc r2D r2c 2 r2 q2 r2 r2 r2c 2 sin2 /D sin2 aD: \u00f06:146\u00de Referring to Fig. 6.46, the cord tension tc, which is constant on the geodesic path as shown in Table 5.2, is expressed as tc \u00bc pp r2D r2c N sin/D sin aD : \u00f06:147\u00de Considering that a tire has two sidewalls, the cord tension in the circumferential direction is tccosaD and the arm length for the moment is rD, the torque due to the carcass tension T(c) is given as T\u00f0c\u00de \u00bc 2NrDtc cos aD \u00bc 2pprD r2D r2c sin/D cot aD; \u00f06:148\u00de where Ntc is eliminated by substituting Eq. (6.147) into Eq. (6.148). Considering that the variable parameters are rC, /D and aD, the inextensibility condition of the carcass from point B to point D (dL = 0) and the fixed condition at point B of the bead area (dzB = 0) are expressed as 354 6 Spring Properties of Tires @L @rc drc \u00fe @L @/D d/D \u00fe @L @aD daD \u00bc 0 @zB @rc drc \u00fe @zB @/D d/D \u00fe @zB @aD daD \u00bc 0: \u00f06:149\u00de It follows from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003522_b009539g-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003522_b009539g-Figure1-1.png",
        "caption": "Fig. 1 A schematic illustration of the construction of the 2H2/O2biofuel cell. A : an anode compartment with pH 7.0 phosphate bu\u2020er containing D. vulgaris (H) cells and MV2` bubbled with dihydrogen gas, C : a cathode compartment with pH 7.0 phosphate bu\u2020er containing BOD and ABTS2~ bubbled with dioxygen gas, E1 and E2: carbon felt sheets as an anode and a cathode, respectively, S : an anion exchange membrane, R : a resistor. Actual sizes of E1 and E2 and the thickness of S are given in the text.",
        "texts": [
            " The cell population in the suspension was determined using a hemacytometer ; the suspension at unit absorbance (A\\ 1 at 610 nm) contained 2.9] 108 cells per cm3. All common chemicals were obtained from commercial sources. Cyclic voltammetry was performed using a Bioanalytical Systems (BAS) CV-50 W electrochemical analyzer. A glassy carbon electrode with /\\ 3.0 mm (BAS, No. 11-2013) was used as the working electrode. A platinum disk and Ag oAgCl oKCl(saturated) were used as the counter and reference electrode, respectively. The construction of the biofuel cell is illustrated schematically in Fig. 1. A carbon felt sheet (Toray B0050 carbon felt mat, Toray Co.) was cut into sheets of size 1.5 cm height] 1.5 cm width ] 0.1 cm depth and the sheets were used for both anode E1 and cathode E2. An anion exchange membrane, 180 lm thick, Asahi Chemical Co.) was used for(ACIPLEX}-A501, the separator membrane S. The contact area of S with the electrolyte in each compartment was 12.5 cm2. Each compartment had 5 mL of electrolyte solution. The pH of the electrolyte solution was adjusted to pH 7.0 with andNaH2PO4at the total concentration of 50 mM phosphate, theNa2HPO4ionic strength of the solution being adjusted to 0.1 with KCl. The anode and cathode of the biofuel cell were connected through a resistor R (a Type 2786 Decade Resistance Box, Yokogawa Hokushin Electric Co., Tokyo) as illustrated in Fig. 1. The value of the resistance R was changed stepwise from 100 k) to 90 ), and the potentials and wereEa , Ecell Ecsimultaneously measured at each value of R using SC 7403 Digital Multimeters (Iwatsu Co.). Linear sweep voltammetry was carried out using the carbon felt sheet anode (or cathode) in the biofuel cell (Fig. 1) as the working electrode in a three-electrode system using the Ag oAgCl oKCl(saturated) immersed in the same compartment as the reference electrode and a platinum wire immersed in the opposite compartment as the counter electrode. The circuits to measure and were disconnected during the volt-Ecell , Ea Ecammetric measurements. All measurements were made at 25 \u00a1C, and all potentials are referred to Ag oAgCl oKCl(saturated) unless stated otherwise. Fig. 2a shows a cyclic voltammogram for the redox reaction of being the anion radical ofABTS~~/ABTS2~ (ABTS~~ ABTS2~) at pH 7",
            "61 V, and has a limiting current smaller than the cathodic limiting current,34 which is very similar to our result in Fig. 2c. The results indicate that D. vulgaris (H) exhibits catalytic activity as high as the isolated hydrogenases. This is a fortunate result, since whole cells of D. vulgaris (H) are more stable and easier to handle than isolated hydrogenases. 3.2 Potentials, and of the biofuel cell as aE cell , E a E c , function of current output, I The biofuel cell illustrated schematically in Fig. 1 was used as a prototype biofuel cell to evaluate the performance of the fuel cell composed of the biocathode (ABTS~~/ABTS2~-BODthe bioanode vulgaris (H)-O2/H2O), (MV2`/MV~`-D. 2H`/H2),and an anion exchange separator membrane in 50 mM phosphate bu\u2020er of pH 7.0. The biofuel cell was operated with and gas bubbling in the cathode and anode com-O2 H2partments, respectively, at atmospheric pressure at 25 \u00a1C. Closed circles in Fig. 3A plot against I, where I was cal-Ecellculated from the value at a given value of R"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure2-1.png",
        "caption": "Fig. 2 Tooth lengthwise curve of face milling",
        "texts": [
            " Manuscript received January 26, 006; final manuscript received April 6, 2006. Review conducted by David Dooner. ournal of Mechanical Design Copyright \u00a9 20 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 satisfy the required contact characteristics. The nongenerating method offers higher productivity than the generating method because the generating roll is eliminated in the former. The lengthwise tooth curve of face-milled bevel gears is a circular arc with the curvature radius equal to the radius of the tool Fig. 2 , while the lengthwise tooth curve of face hobbed gears is an extended epicycloid, which is kinematically formed during the relative indexing motion Fig. 3 . Therefore, the generating surfaces of face milling and face hobbing are totally different. In addition, facehobbing designs use a uniform tooth depth system, whereas most face-milling designs use tapered-tooth depth systems. Modern theory of gearing has been significantly enhanced with computerized approaches to the advanced design of gearings 3\u20136 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure13.52-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure13.52-1.png",
        "caption": "Fig. 13.52 Design variables for the optimized tire size",
        "texts": [
            " Considering that RR is proportional to the product of the strain energy and volume, there may be an optimized section width for the RR. However, it is difficult to experimentally search for the optimum tire size because we need to make many molds and trial tires. Nakajima [75, 76] has thus searched the optimized section width or optimized tire size for the RR using optimization technology. Both the tread width and tire shape are selected as design variables in which the tire shape is represented by multiple arcs, as shown in Fig. 13.52. The section width and rim width are redetermined by the tread width to maintain the ratio between the section width and the tread width and the ratio between the rim width and the tread width. The rim diameter, the overall diameter and vertical load are fixed. Not only the optimized tire shape but also the optimum tire size can be obtained by adding the tread width to the design variables. When the initial tire size is 165R13, the optimized tire size becomes 225/60R13. RR can be reduced by 25% in the prediction made employing FEA and Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.13-1.png",
        "caption": "Fig. 6.13: Gear System and Equivalent Mechanical Model for a 4-Stroke 12- Cylinder Diesel Engine",
        "texts": [
            "34) where a and n might be determined from the simulation results by using a least square fit. The magnitude H0 is the number of events of passing the nominal load. For hammering processes the nominal load is zero. Figure 6.12 gives an excellent comparison of formula (6.34) with simulated results. As an application of the theory presented, a four-stroke diesel engine with 12 cylinders and a power of about 3000 kW has been considered. The nonsymmetrical gear system driving the combined camshaft/injection pump shaft is shown in Fig. 6.13 on the left-hand side. On the right-hand side we see the corresponding mechanical model. All gears are spur gears; they will be modeled 6.1 Timing Gear of a Large Diesel Engine 343 as rigid bodies according to the section on body models. The camshaft will be described as an elastic body considering torsional elasticity only (see the coupling components section). As an additional option we regard a camshaft damper. The simulations focus on side A of the gear system due to the more complicated dynamical properties",
            " This mean value would be TCS = 430 Nm (Fig. 6.7). \u2022 The quasi-static extremum load is that one which would be generated by a static transmission of the maximum torque values for the camshaft (peak values in Fig. 6.7). This maximum torque is Tmax = 2520 Nm. \u2022 The dynamical maximum load is evaluated from the load distribution (see the section on evaluation of the simulations) under the assumption that these loads will be realized with a probability of 99%. The results for the three gear meshes of Fig. 6.13 are given in the Table. A systematic investigation of parameter tendencies allows the conclusions [217]: 6.1 Timing Gear of a Large Diesel Engine 345 Gear Loads [kN] Gear Static Quasi-static Dynamical Loads Mesh Mean Maximum (Fig. 11.13) Load Load Backlash = 0 Nom. Backlash 1/2 1.96 11.4 34.5 42.4 2/3 1.96 11.4 31.3 34.8 4/5 3.17 18.5 37.4 38.8 Table: Gear Loads in Gear Meshes \u2022 Excitation Sources \u2013 Crankshaft excitation is small. \u2013 Camshaft excitation dominates, especially due to the injection pump loads"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.32-1.png",
        "caption": "Fig. 5.32: The glass fiber alignment device. According to [Aosh92]",
        "texts": [
            " Manufacturing these grooves to micrometer exact dimensions is very difficult. The accuracy has to be very high because optical waveguides can have excentric cores which must be matched. The attenuation achieved with conventional aligners is about 0.1 dB for a 1.55 f.!m DSF (dispersion shifted fiber), which is significant for extremely long waveguides (e.g. in un derwater applications). A piezoelectrically driven microaligner was deve loped, which can position glass fibers independently of each other. Figure 5.32 shows the construction of the aligning device which was developed to handle several waveguides. The optical waveguides are placed in the parallel V -shaped grooves. The alignment is done by piezoelectric actuators which move the microarms up and down relative to their base. Each positioning unit consists of two piezo- elements which are attached to the base and arms with tapered tips fastened to each piezoelement. Each arm can be individually controlled by applying voltage to its piezoelement. This causes it to move accurately in the micro meter range"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure9.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure9.3-1.png",
        "caption": "Fig. 9.3 Deformation of the belt and sidewall",
        "texts": [
            "3, the radial distributed load of the unit length in the circumferential direction, fr, is given as fr \u00bc bp 2Q0 krw kTk; \u00f09:8\u00de where b is the width of the ring, p is the inflation pressure, Q0 is the load per unit length in the circumferential direction of one inflated sidewall, kr is the radial fundamental spring rate of the unit length in the circumferential direction of the sidewall, kT is the spring rate per unit length in the thickness direction of the tread spring, and k is the tread ring compression. To solve the contact problem, the tread spring kT was added to the tread ring as first proposed by Akasaka [43]. Referring to the left figure of Fig. 9.3 and neglecting the structural spring in Sect. 6.1.2, kr is simply expressed by the radial fundamental spring rate of a tire due to the tensile stiffness [44]3: rk \u03c4 aa p a a p \u03c4 p rk rk Tk Tk Tk bFig. 9.1 Side view and meridional section of an elastic ring model for tires. Reproduced from Ref. [2] with the permission of J. Appl. Mech. 2Same as Eq. (8.49). 3Same as Eq. (6.13). 542 9 Contact Properties of Tires kr \u00bc 2 dQ0 dw w\u00bc0 \u00bc p cos/s \u00fe/s sin/s sin/s /s cos/s : \u00f09:9\u00de Referring to Fig. 9.2, the tread ring compression k is geometrically expressed by k \u00bc w\u00fe d0 a 1 cos h\u00f0 \u00de; \u00f09:10\u00de where d0 is the displacement at the center of the contact patch and a is the radius of the tread ring. The circumferential tension T is decomposed into two parts: T \u00bc T0 \u00feDT ; \u00f09:11\u00de where T0 is the tension of the tread ring due to the inflation pressure p, while DT is the additional tension due to the deformation. Referring to the right figure of Fig. 9.3, the force equilibrium equation is 9.2 Contact Analysis of Tires Using an Elastic Ring Model 543 T0 \u00bc abp 2aQ0: \u00f09:12\u00de Suppose that h in Fig. 9.2 is the contact angle connecting the contact region and the free region. The continuity condition is applied to h as boundary condition. Using Eq. (9.10), the displacement d0 is determined by the condition that k is zero at h . d0 is expressed by d0 \u00bc w h \u00f0 \u00de\u00fe a 1 cos h \u00f0 \u00de; \u00f09:13\u00de where a \u00bc a\u00fe s and s is the thickness of the tread rubber. The contact pressure q is given by q \u00bc kTk \u00bc kT w\u00fe d0 a 1 cos h\u00f0 \u00def g: \u00f09:14\u00de The total load Fz is obtained by integrating the contact pressure over the contact region: Fz \u00bc 2b Zh 0 akT w\u00fe d0 a 1 cos h\u00f0 \u00def gdh: \u00f09:15\u00de Substituting Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure31-1.png",
        "caption": "Fig. 31. Whole gear drive finite element model.",
        "texts": [
            " The principal characteristics of the described approach are as follows: \u2022 Finite element models of the gear drive can be automatically obtained for any position of pinion and gear obtained from TCA. Stress convergence is assured because there is at least one point of contact be- tween the contacting surfaces. \u2022 Assumption of load distribution in the contact area is not required since the contact algorithm of the general computer program [3] is used to get the contact area and stresses by application of the torque to the pinion while the gear is considered at rest. \u2022 Finite element models of any number of teeth can be obtained. As an example, Fig. 31 shows a whole i(i) Boundary conditions are far enough from the loaded areas of the teeth. (ii) Simultaneous meshing of two pairs of teeth can occur due to the elasticity of surfaces. Therefore, the load transition at the beginning and at the end of the path of contact can be studied. The finite element analysis has been performed using the design parameters shown in Table 1. A finite element model of three pairs of contacting teeth has been applied for each chosen point of the path of contact. Elements C3D8I [3] of first order (enhanced by incompatible modes to improve their bending behavior) have been used to form the finite element mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.2-1.png",
        "caption": "Fig. 6.2: Rigid Body Model [217]",
        "texts": [
            " The dissertations [124] and [133] deepened the rattling theory and compared onestage rattling with laboratory tests. From the very beginning all theoretical research focused on general mechanical systems with an arbitrary number of degrees of freedom and with an arbitrary number of backlashes. Application fields are drivelines of large diesel engines, which, due to a large temperature operating range, are usually designed with large backlashes [217]. Rigid bodies are characterized by six degrees of freedom: three translational and three rotational ones. We combine these magnitudes in an IR6-vector (Figure 6.2 and [217]) p = ( \u03a6 rH ) \u2208 IR6 (6.1) with \u03a6 = (\u03d5x, \u03d5y, \u03d5z) T , rH = (\u2206xH , \u2206yH , \u2206zH)T \u2208 IR3 . (6.2) Accordingly, the velocities are v = ( \u03a6\u0307 v\u0307H ) = ( \u03c9 vH ) \u2208 IR6 . (6.3) Elastic bodies in gear or driveline units usually are shafts with torsional and/or flexural elasticity. In the following we consider only torsion by applying a Ritz approach (see section 3.3.4 on page 124) to the torsional deflection \u03d5 (Figure 6.3): \u03d5(z, t) = w(z)Tqel(t) with w, qel \u2208 IRnel (6.4) where the subscript el stands for \u201celastic",
            " It starts with d\u2019Alembert\u2019s principle, which states that passive forces produce no work or, according to Jourdain, generate no power, see chapter 3.3. This statement can be used to eliminate passive forces (constraint forces) and to generate a set of differential equations for the coupled machine system under consideration. We start with the equations of motion for a single rigid body. Combining the momentum and moment of momentum equations and considering the fact that the mass center S has a distance d from the body-fixed coordinate frame in H (Figure 6.2) we obtain Iv\u0307 = \u2212fK + fB + fE = fS(p,v, t) (6.11) where I = ( IH md\u0303 \u2212md\u0303 mE3 ) \u2208 IR6,6 d = (0, 0, d)T \u2208 IR3 IH = diag (A, A, C) \u2208 IR3,3 \u2212fK = [ (\u03c9\u0303IH\u2126e3) T , 0 ]T \u2208 IR6 fB = [( \u2212IH\u2126\u0307e3 )T ,0 ]T \u2208 IR6 fE = [(\u2211 MHk )T , (\u2211 F k )T ]T \u2208 IR6 . (6.12) The magnitudes A,C are moments of inertia; fK , fB and fE are gyroscopic, acceleration and applied forces, respectively, and \u2126, \u2126\u0307 are prescribed values of angular velocity and acceleration, respectively. The unit vector e3 is bodyfixed in H (Figure 6.2). By adding components with torsional elasticity we can influence the rigid body motion only with respect to the third equation of (6.11). Therefore torsional degrees of freedom can be included in a simple way. The equation of motion for a shaft with torsional flexibility is Ip(z) \u22022\u03d5 \u2202t2 \u2212 \u2202 \u2202z [ GIp(z) \u2202\u03d5 \u2202z ] \u2212Mk\u03b4(z \u2212 zk) = 0 . (6.13) ( density, Ip area moment of inertia, G shear modulus, Mk torque at location zk). The total angle \u03d5 has three parts: \u03d5(z, t) = \u222b \u2126(t)dt + \u03d5z(t) + \u03d5(z, t) , (6.14) where \u2126(t) is the angular velocity program, \u03d5z(t) is the z-component of \u03a6 (eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure4.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure4.3-1.png",
        "caption": "Fig. 4.3: Hydraulic junctions with constant and variable volume",
        "texts": [
            " In the case of relatively large volumes this assumption is reasonable whereas for very small volumes incompressible junctions, with unilateral or bilateral behavior, are a better approach. Complex components like control valves can be composed of elementary components like lines, check valves and so forth. In the following a selection of elementary components is considered. It is shown how the equations of motion are derived and how they are put together to form a network. Junctions are hydraulic volumes filled with oil. The volumes may be considered as constant volumes or variable volumes as show in Figure 4.3. Junctions with variable volume are commonly used for hydraulic cylinders. 4.2 Modeling Hydraulic Components 191 Assuming compressible fluid in such a volume leads to a nonlinear differential equation for the pressure p. Introducing the pressure-dependent bulk modulus E(p) = \u2212V dp dV (4.3) yields a differential equation for the pressure in a constant volume p\u0307 = E V \u2211 Qi (4.4) and p\u0307 = E V (Q1 \u2212AK x\u0307) (4.5) in a variable volume, respectively. A common assumption with respect to the fluid properties considers a mixture of linear elastic fluid with a low fraction of air"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003833_rspb.1998.0424-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003833_rspb.1998.0424-Figure7-1.png",
        "caption": "Figure 7. Experimental tracings of vertical (Fy) and horizontal (Fx) ground reaction force, expressed in body weight units (BW). Plus and minus labels represent acceleration and braking in the forward direction, while T and L refer to trail and leading limbs, respectively. (a) Typical Fy and Fx patterns for human running and skipping, obtained in our laboratory. (b) Fx tracings of each limb of a horse cantering at a speed of about 5.2m s\u00ff1 (Niki et al. 1984, adapted from their Fig. 2); hind- and forelimb signals have been aligned with respect to the time axis so as to maintain the real footfall sequence during the stride.",
        "texts": [
            " In addition, even more interestingly, the (compound) horizontal force pattern before the \u00a3ight shows an initial acceleration (\u00a2rst limb) and a successive deceleration (second limb), an opposite sequence to R.The main reason for this is the more vertical and anterior position (with respect to the body centre of mass) of the \u00a2rst and second limb, respectively, of the c\u0300ompound' step at touchdown. Experimental records of Fy and Fx in skipping adults, obtained in our laboratory, were consistent with the simulation (see \u00a2gure 7a). Figure 7b shows Fx records (Niki et al. 1984) from the four limbs of a galloping horse (mass 540 kg, speed 5.2m s\u00ff1) where the pattern for the hindlimbs resembles the one for skipping humans. (Actually, a paper by Bryant et al. (1976) shows that fore^ aft ground reaction forces in the galloping dog are di\u00a1erent from the ones measured in horses (Niki et al. 1984; Merkens et al. 1991), with the braking phase preceding the acceleration phase in all limbs. The authors, however, comment that the dog could be accelerating when galloping over the platforms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000419_j.ymssp.2019.106583-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000419_j.ymssp.2019.106583-Figure1-1.png",
        "caption": "Fig. 1. Interactions between the balls and the rings in (a) plane YOZ (b) plane XOZ.",
        "texts": [
            " Structural parameters such as the ball diameter tolerance, the arrangement of balls and the number of balls are also regarded to make impact on the loading condition, and the influence of the parameters are discussed at last. The uneven loading conditions can be recognized through the signal analysis, and the impact of the parameters can be compared by changes of features. In this paper, the outer ring is set fixed and the inner ring rotates with a horizontal shaft. The displacements of the elements are shown in multiple coordinates. Radial load and axial preload are both considered, and the contact model between the jth ball and inner ring is shown in Fig. 1. In Fig. 1, coordinate system {O; X, Y, Z} is the reference coordinate system of the outer ring, with the bearing axis in the OX direction. {Oi; Xi, Yi, Zi} shows the displacement of the inner ring, with Oi as the center of the inner ring. Tnij is the traction force from the inner ring, and Fe shows the centrifugal force with the eccentricity of e and eccentricity angle of /e. aij and aoj are the contact angles of the inner ring and outer ring, and Fa is the axial preload of the bearing. Coordinate system {Obj; Xbj, Ybj, Zbj} shows the positions of the jth ball, with ObjZbj along the direction of OiObj, and ObjXbj along the axial direction of the bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003836_012-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003836_012-Figure3-1.png",
        "caption": "Figure 3. The deposition head used for model illustration and verification.",
        "texts": [
            " A series of experiments were performed using a coaxial deposition head in use at The University of Manchester Laser Processing Research Centre. The head comprises Laserline collimating and focusing optics and a nozzle assembly made by DeBe Lasers Ltd (http://www.debe.co.uk/). The nozzle consists of a central laser passage with a gas stream to protect the optics, a single powder outlet annulus, with no second outlet for a focusing gas stream, and an annular water cooling passage. The nozzle is illustrated in figure 3. The laser beam was provided by a Laserline LDL160-1500 diode laser with dual wavelength output of 808 and 940 nm. It was conveyed to the head via an optical delivery cable of 1 mm internal diameter. Gas-atomized Inconel 718 powder was fed through the nozzle; this material is widely used for deposition, especially in the aerospace industry. The powder was examined under a scanning electron microscope (SEM) prior to the test. Particles were generally spherical or near spherical in shape although there was some adhesion of smaller and larger particles (\u2018satelliting\u2019)",
            " According to Mie theory, the average luminance of any scattering element within the stream is proportional to the concentration of powder within it [36] so images captured while powder was flowing from the nozzle were used directly to calculate the relative concentrations of reflective powder particles in the stream. The model described in section 2 was implemented using Wolfram Research Mathematica 5.2 software (http://www.wolfram.com/). The model integrals for intensity and powder heating were handled numerically within the code using the default adaptive Gauss\u2013Kronrod method [37]. Figure 6 compares modelled and measured powder concentrations in the axial plane for the nozzle shown in figure 3 and parameters quantified in table 1. Because the light sheet technique gives relative concentrations all values in the graphs are normalized to a maximum value of 100. The value of s0 in the model is set to 10.25. The two compare well, although images indicate that there is powder within the annulus created by the converging streams before the merge point that is not accounted for in this or any previous model. This can be attributed to Figure 5. Schematic diagram of equipment used for powder stream visualization and digital analysis (plan view). irregularities within the nozzle causing a small inward powder stream from one portion of the nozzle. It is clearly visible as an additional concentration peak in the measured graph of figure 5(b). The annular streams converge to form a single approximately Gaussian concentration distribution, which is in accordance with previous studies [11, 12, 20, 26, 31]. In order to experimentally verify the powder temperatures reached, an experiment using the nozzle shown in figure 3 was performed, as shown in figure 7. The laser beam focal plane was aligned with the powder consolidation plane, positioned 7.5 mm below the nozzle exit. Due to the speed of the particles and their rapidly changing temperatures they were measured pyrometrically using an Agema ThermaCAM 550 thermal camera with macro lens system to monitor radiation levels in the 3.6\u20135 \u00b5m wavelength band. During the experiment, data from the camera was conveyed to a microcomputer via a PCMCIA card interface and later analysed using the proprietary Thermacam Researcher software package",
            " Figure 10 shows how the attenuation increases on moving beyond the powder consolidation plane for the default conditions in table 1. The effect of the central Gaussian stream rapidly becomes significant near the axis and for distances beyond the merge point could lead to results similar to those of Dinez Neto et al [22] and Huang et al [23] in predicting laser light with an initially Gaussian distribution to reach the substrate surface with an annular intensity maximum. The powder temperatures predicted in the powder consolidation plane for the nozzle shown in figure 3 when used for deposition with a 1000 W laser beam of uniform intensity distribution and 2 mm radius is shown in figure 11. When modelling a larger radius beam of this type, powder temperature variations within the beam and at its periphery can be easily identified. At every position in the powder consolidation plane except the centre of the beam the powder consists of two components with distinctly different temperatures. For example with reference to figure 1, point C would receive unheated powder from point A and powder that had been heated by travelling across the full diameter of the beam from point B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003961_s11044-007-9088-9-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003961_s11044-007-9088-9-Figure7-1.png",
        "caption": "Fig. 7 RCCC linkage, R: Revolute pair, C: Cylindrical pair [14, 37]",
        "texts": [
            "1 Kinematic analysis of the RCCC spatial mechanism The following different numerical methods of solution are presented: \u2022 Method A: Iterative numerical solution of a dual nonlinear equation. \u2022 Method B: Iterative solution of system of dual nonlinear equations. \u2022 Method C: Iterative solution of a system of redundant nonlinear equations. Method A The following example is aimed to give a practical application of (37). In bibliographical Refs. [14, 37], it is demonstrated that position analysis of the RCCC linkage (see Fig. 7) reduces to the solution of the following nonlinear equation6 F\u0302 (\u03b8\u03024) \u2261 A\u0302 sin \u03b8\u03024 + B\u0302 cos \u03b8\u03024 + C\u0302 = 0, (40) where A\u0302 = sin \u03b1\u03021 sin \u03b1\u03023 sin \u03b8\u03021, (41) B\u0302 = \u2212 sin \u03b1\u03023(cos \u03b1\u03021 sin \u03b1\u03024 + sin \u03b1\u03021 cos \u03b1\u03024 cos \u03b8\u03021), (42) C\u0302 = cos \u03b1\u03023(cos \u03b1\u03021 cos \u03b1\u03024 \u2212 sin \u03b1\u03021 sin \u03b1\u03024 cos \u03b8\u03021) \u2212 cos \u03b1\u03022. (43) We acknowledge that (40) can be solved by substituting the sin \u03b8\u03024 and cos \u03b8\u03024 functions with their tan \u03b8\u03024 2 correspondent. However, the numerical solution of such equation is herein reported for demonstration purposes only"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000968_j.addma.2021.102203-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000968_j.addma.2021.102203-Figure5-1.png",
        "caption": "Fig. 5. Mesh model of thin-wall part and substrate.",
        "texts": [
            " Additive Manufacturing 46 (2021) 102203 the arc striking point and inclination at the arc extinguishing point compensate for each other. The upper surface appearance of the part is flat. For the SRM path strategy, the trajectory was divided into two segments and reciprocated. No defects were found at the joint of the two sections. The top layer has arc extinguishing points at both ends, so there is a slight tilt. In addition, the interpass cooling in the SRM path strategy is 9.3 s. Regardless of the path strategy, the total cooling time of each layer is consistent, which is 18.6 s As depicted in Fig. 5, 3D finite element meshes were established by ABAQUS with the same geometry as the experiment. The built-in code of ABAQUS is used to predict temperature, residual stress and deformation. A sparse grid cannot guarantee sufficient calculation accuracy, and a dense grid significantly increases the computational cost. Generally, the mesh size ranges between 1 mm and 2 mm, and the type of mesh is set as the eight nodes thermally coupled brick, trilinear displacement, and temperature (C3D8T) [12,19,35]",
            " Additive Manufacturing 46 (2021) 102203 directions that are perpendicular to each other. \u03b5p and \u03b5q can be calculated by the equation Eqs. (20)-(21) [47]: \u03d5(p, q,H\u03b1) = 0 (20) \u2206\u03b5p \u2202\u03d5 \u2202q +\u2206\u03b5q \u2202\u03d5 \u2202p = 0 (21) In the above equations, H\u03b1 is a set of hardening parameters, and p, qandH\u03b1 are defined by the following Eqs. (22)-(24) [47]: p = pel +K\u2206\u03b5p (22) q = qel + 3G\u2206\u03b5q (23) \u2206H\u03b1 = h\u03b1(\u2206\u03b5p,\u2206\u03b5q, p, q,H\u03b2) (24) where H\u03b2 is the hardening modulus with G and K being the shear and bulk modulus. In the mechanical analysis, the clamped area of the substrate is set to be fully constrained (Fig. 5). The y direction displacement constraint is applied to the lateral side. A rigid plane under the substrate is created to simulate the platform. The clamp constraints are released after cooling to room temperature. In this work, a calibration test of emissivity is carried out. Single bead deposition is performed by laser-CMT hybrid process in advance with the same materials and process parameters mentioned in Section 2. The temperature was captured simultaneously by IR thermography and thermocouple (K type), simultaneously"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000852_s11837-020-04291-5-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000852_s11837-020-04291-5-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the experimental setup coupling x-ray and IR imaging of the laser powder bed fusion process. Image not to scale. Reprinted with permission from Ref. 37 (Color figure online).",
        "texts": [
            "22,24\u201327,33\u201336 Zhao and Parab were the first to utilize the capabilities of this beamline to observe the high speed process of laser powder bed fusion in situ via imaging and diffraction.22,31 Within the current work, the authors further expound on the groundwork laid by Zhao and Parab by developing the ability to record simultaneous thermal and xray images. The schematic of the LPBF experiment Gould, Wolff, Parab, Zhao, Lorenzo-Martin, Fezzaa, Greco, and Sun as well as the IR and x-ray imaging are depicted in Fig. 1. Additionally, a photograph of the experimental setup is shown in Fig. 2. A polychromatic x-ray beam with the first harmonic energy of 25 keV was generated using an 18-mm period undulator with a gap set at 14 mm. The x-ray beam was allowed to pass through the samples in conjunction with the translation of the laser beam. The transmitted xrays were converted to visible light photons using a single-crystal LuAG:Ce scintillator (thickness 100 lm). The converted visible light images were then recorded using a commercial high-speed In Situ Analysis of Laser Powder Bed Fusion Using Simultaneous High-Speed Infrared and X-ray Imaging camera (Photron FastCam SA-Z)",
            " Plate samples were manufactured to the dimensions of 400 lm thick, 2.9 mm tall, and 50 mm long for the case of Ti-6Al-4V, and 300 lm thick, 2.9 mm tall, and 50 mm long for the case of tungsten. The experiments were performed with and without powder. In the experiments that utilized powder, miniature powder bed samples were created to mimic the commercial laser powder bed fusion process. These samples consisted of a metal base (same dimensions as the plate samples) sandwiched between two glassy carbon plates (1 mm thick, 3 mm tall, and 50 mm long), as shown in Fig. 1. The difference in height between the glassy carbon plates and the metal plate created a 100- to 150-lm-tall channel that was filled with powder (particle size: 15\u201345 lm) for printing. In the experiments that did not utilize powder, the glassy carbon plates were omitted to better view the IR signature of the metal plate. To reduce the variation in sample emissivity and also enhance the x-ray image quality, all the samples used in the current work were polished to a mirror finish using series of polishing steps ending in 4000-grit sand paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.2-1.png",
        "caption": "Fig. 5.2 Coordinate system of the tire cross section",
        "texts": [
            " As previously mentioned, three important theories have been developed in the study of tire shape; natural equilibrium theory for a bias tire [2], natural equilibrium theory for a radial tire [15, 17] and ultimate optimized tire shape theory [22]. The cross-sectional shape of a bias tire is defined using parameters in Fig. 5.1. The carcass tension T is expressed by T \u00bc pR; \u00f05:1\u00de where p is the inflation pressure and R is the radius of curvature along the cord direction. Because the tension is supported using only cords in netting theory, the tension of one cord tc is given by tc \u00bc T=nr \u00bc pR=nr; \u00f05:2\u00de where nr is the multiplicative product of the number of cords in one ply per unit width and the number of plies. Figure 5.2 shows the small element of a tire that is expressed by two radii of curvature, the smallest radius r1 and largest radius r2 called the principal radius. r1 and r2, respectively, are the radii in the meridian (cross-sectional) and circumferential directions. The vectors tangent to the principal 5.1 Studies on Tire Shape 243 radii are orthogonal to each other. b is the orientation angle of a ply measured from the circumferential direction. In Fig. 5.1, Euler\u2019s theorem in differential geometry gives the radius of curvature R: 1=R \u00bc sin2 a=r1 \u00fe cos2 a=r2: \u00f05:3\u00de Referring to Fig. 5.2, the substitution of the relation r2 = r/sin / into Eq. (5.3) yields 1=R \u00bc sin2 a=r1 \u00fe cos2 a sin/=r: \u00f05:4\u00de Substituting Eq. (5.4) into Eq. (5.2), we obtain p tc nr \u00bc sin2 a r1 \u00fe cos2 a r sin/: \u00f05:5\u00de Referring to Fig. 5.3, the force equilibrium in the z-direction between the pressure p on a circular ring from rC to r and the tensile force tcsin a is expressed by z z 244 5 Theory of Tire Shape pp\u00f0r2 r2C\u00de \u00bc tcN sin a sin/; \u00f05:6\u00de where N is the number of cords in a tire and is given by N \u00bc 2prnr sin a: \u00f05:7\u00de Eliminating tc and nr in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003227_s100510170283-Figure19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003227_s100510170283-Figure19-1.png",
        "caption": "Fig. 19. (a) Magnetic charges with surface densities \u03c3 = +M and \u03c3 = \u2212M on the end faces of a longitudinally magnetized cylinder (M \u2016 x\u0302). (b) The angles for the calculation of the stray field generated by an infinite transversally magnetized cylinder (M in the y \u2212 z plane).",
        "texts": [
            " Analytical expressions for the z component of the stray field generated by a uniformly magnetized straight cylinder of radius R and the revolution axis of which is parallel to the x\u0302 direction can be obtained in two particular cases which are relevant in the present study. (i) We first consider the case of a longitudinally magnetized cylinder (magnetization M parallel to x\u0302) of finite length L. For such a cylinder, the stray field can be regarded as the superposition of the magnetic fields created by two discs having \u03c3 = +M and \u03c3 = \u2212M as surface pole densities, which correspond to the two circular end faces of the cylinder (Fig. 19a). According to literature [35], the z or radial component of the field from a disc with diameter R, perpendicular to the x\u0302 direction, centred at x = x0 and having a uniform surface pole density of \u03c3 is hz = \u03c3 \u221a R \u03c0k \u221a z [( 1\u2212 k2 2 ) K(k)\u2212E(k) ] with k2 = 4Rz (R + z)2 + (x\u2212 x0)2 (B.3) where K(k) and E(k) are the complete elliptic integrals of first and second kind respectively, which may be differentiated to give dK dk = E k (1\u2212 k2) \u2212 K k dE dk = E k \u2212 K k \u00b7 (B.4) Using equations (B.4), the second derivative of hz with respect to z can be calculated and expressed in terms of elliptic integrals as \u22022hz \u2202z2 = ( \u03c3 4\u03c0 ) [AKK(k) +AEE(k)] (B",
            " Then, one may show that it is also equivalent to the field created by two parallel infinite lines of pole densities \u03c1 = \u00b1SM/\u03b4 per unit length (S = \u03c0R2 being the cylinder sectional area) separated by a distance \u03b4 along the transverse direction t\u0302 = M/M , in the limit \u03b4 \u2192 0. Starting from the well-known expression of the scalar potential for such two lines, V = 2|\u03c1| log(r/r\u2032) with r\u2032 = r\u2032 + \u03b4t\u0302, and working out the limit \u03b4 \u2192 0, as is done in reference [37], leads to the following expressions for the components of h = \u2212\u2207V respectively parallel (radial component) and perpendicular to r (tangential component), hr = 2\u03c0R2M cos\u03c9 r2 e\u0302r, hn = \u22122\u03c0R2M sin\u03c9 r2 e\u0302n (B.8) where, referring to Figure 19b, \u03c9 is the angle between the magnetization M and the position vector r normal to the cylinder axis. From these relations, one can easily derive that the z component of the stray field and its second derivative with respect to z are respectively hz = 2\u03c0R2M [ z2 \u2212 y2 (y2 + z2)2 cos\u03d5+ 2yz (y2 + z2)2 sin\u03d5 ] (B.9) and \u22022hz \u2202z2 = 12\u03c0R2M \u00d7 [ y4 + z4 \u2212 6y2z2 (y2 + z2)4 cos\u03d5+ yz3 \u2212 y3z (y2 + z2)4 sin\u03d5 ] (B.10) where \u03d5 is the angle between the cylinder magnetization M and the z\u0302 axis, \u03d5 being chosen as clockwise positive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.15-1.png",
        "caption": "Fig. 6.15: Measurement principle of the sensor. According to [Kato91]",
        "texts": [
            " Many of these devices need inclination sensors to calculate the exact tilting of the robot with respect to a reference plane. A very novel inclination sensor and its components are shown in Figure 6.14. The sensor system consists of an LED and a semi-spherical glass cup, which is mounted on a photodiode matrix array. The glass cup is filled with liquid and has an enclosed air bubble. The LED sends light through the cup which casts shadows on the four photodiodes underneath. If the sensor is tilted in one direction, the shadow moves across the diode matrix, Fig. 6.15. The out put currents of the photodiodes are transformed into voltages and are ampli fied, and from this information the inclination angle and tilt direction can be determined. The sensor system was tested in two applications. The first application was the determination of the position of a small moving vehicle in a pipe system. The measuring principle made it necessary that the speed be kept as con stant as possible, since sudden acceleration or deceleration would falsify the results by an unpredictable movement of the air bubble"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000897_j.oceaneng.2021.108903-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000897_j.oceaneng.2021.108903-Figure5-1.png",
        "caption": "Fig. 5. 3-D trajectories.",
        "texts": [
            " Formation parameters are l = [0,5, 5], \u03b8 = [0,\u03c0 /6, \u2212 \u03c0 /6], \u03c8 = [0,\u03c0 /3, \u2212 \u03c0 /3], \u03b3 = [1, 1, 1,1], \u03b11 = 1,\u03b21 = 1,\u03b1 = 1,\u03b2 = 4ky = 1,kv = 20,\u03c1 = [1,1],\u03d6 = diag(1, 1,1.5).For the neural network, the Gaussian RBF neural network with the centers ci evenly spaced on [0,1] and the width bi = 0.8. The hidden layer contains 5 neurons. The weight update rule from the hidden layer to the output layer is given by formula \u02d9\u0302W = \u03b34svh(x). For the conditional integrator, the control gain matrices areK = diag(5, 1,1)\u03bc = diag(10,2,2)G = diag(0.5,0.5,0.1). The simulation results of scenario 1 are shown in Figs. 5\u201313. In Fig. 5, the green line is the desired trajectory of the virtual leader, the red line is the AUV1\u2019s trajectory. The blue lines represent the trajectories of AUV2 and AUV3, respectively. Orange arrows denote external disturbances. In the simulation results, two aspects can be observed clearly: 1. Although G. Xia et al. Ocean Engineering 233 (2021) 108903 G. Xia et al. Ocean Engineering 233 (2021) 108903 there is an initial error between AUVs and desired trajectory, each follower AUV can converge to the desired trajectory in finite time; 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure13.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure13.3-1.png",
        "caption": "Fig. 13.3 Energy loss and stress/strain",
        "texts": [
            " The stress/strain curve follows the same path in loading and unloading for an elastic material, while it follows different paths for a viscoelastic material. The area enclosed by the paths in loading and unloading is related to the energy loss. Although the viscoelastic properties of rubber vary with temperature, strain velocity (frequency) and strain amplitude, rubber is often modeled as a linear viscoelastic material. When stress r is applied to rubber in the form of a sinusoidal function, the response of strain e to the stress has a time lag. As shown in Fig. 13.3, the stress and the strain are expressed by e \u00bc e0 sinxt r \u00bc r0 sin xt\u00fe d\u00f0 \u00de: \u00f013:1\u00de 13.1 RR of Tires 933 Instead of the second equation of Eq. (13.1), the stress can be expressed by r \u00bc E0 sinxt\u00feE00 cosxt\u00f0 \u00dee0; \u00f013:2\u00de where E0 is the storage modulus and E00 is the loss modulus. Comparing Eq. (13.1) with Eq. (13.2), E0 and E00 are defined as E0 \u00bc r0=e0 cos d E00 \u00bc r0=e0 sin d : \u00f013:3\u00de The ratio of E00 to E0 is the loss tangent tan d defined by E00=E0 \u00bc tan d: \u00f013:4\u00de The strain energy loss per unit volume in a cycle, wloss, is expressed by wloss \u00bc Z2p 0 rde \u00bc Z2p=x 0 r_edt \u00bc pe20E 00 \u00bc pe20E 0 tan d: \u00f013:5\u00de wloss is equal to the area of the ellipse as shown in Fig. 13.3. Dividing Eq. (13.5) by one cycle 2p, we obtain e20E 0 tan d=2, which shows that the energy loss is equal to the product of the strain energy related to the storage modulus and tan d. (1) Phase lag model The stress/strain curve of parts in a rolling tire is usually a simple loop as shown in Fig. 13.3. The simplest method of calculating the strain energy loss of a tire is to apply Fourier series expansion to the stress and strain in the circumferential direction: e \u00bcP n ens sin nh\u00fe enc cos nh\u00f0 \u00de r \u00bcP n rns sin nh\u00fe rnc cos nh\u00f0 \u00de ; \u00f013:6\u00de where h is the angle in the circumferential direction. Figure 13.4 compares stresses between the calculation and the approximation of Fourier series expansion. The Fourier series expansion gives a good approximation of the stress/strain of a tire. Considering the phase lag of stress d in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure4.36-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure4.36-1.png",
        "caption": "Fig. 4.36: A bistable fluidic switch made by the LIGA technique a) schematic design; b) a 500 f.A.m high prototype made of PMMA with a nozzle width of 30 f.A.m. Courtesy of the Karlsruhe Research Center, IMT",
        "texts": [
            " The valve opens and the medium inside is pushed out. At the same time, the inlet valve is closed since the polyimide membrane contacts the titanium membrane. If the pump membrane is moved upwards, the pressure and valve states reverse and the medium flows into the pump. The device can transport 70 f.d/min of water or The LIGA technique can also be used to realize components for microfluidic controllers which are mostly used in biomedicine. A bistable switch for mic rofluid flow control was presented in literature [Menz93a], Fig. 4.36. adheres to one of the two switch walls due to the Coanda effect. It is stable 4.2 LIGA Technology 107 as long as there are only small disturbances. This condition denotes a state 1 and in our figure the fluid flows through Output 1. When a control signal is applied to Control port 1 in form of a pressure increase, the fluid jet flips over to Output 2, changing the state of the switch to state 2. The switch does not need any movable parts. LIGA structures have very smooth walls and are suitable for microoptics",
            "2 mm, the gap between the piston and the chamber walls is only 1-3 f..tm. The friction of the piston is reduced by the lubrication effect of the driving fluid. This microactuator will be integrated in an active heart catheter (Chapter 2.2) to drive a linear cutting tool for removing deposits in blood vessels mechanically. In this case, the device consists of two symmetric actuators (of the type described above) having an opposed piston between them. The cutting tool is fastened to the piston which is driven by an oscillating fluid jet: a fluidic micro switch (Figure 4.36) alternately directs the fluid into one of the two actuator chambers with a frequency of several 100 Hz. The attainable stroke of the piston is several 100 ~-tm; a force of 5 mN can be reached with a fluid pressure of 0.54 bar. Chemical actuators are based on different chemical processes taking place in fluid or gaseous media. E.g. many chemical reactions produce gases which can be used to create a high pressure in a chamber [Jend93a]. Substances of interest for chemical actuators are polymer gels"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000878_j.matchar.2020.110358-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000878_j.matchar.2020.110358-Figure2-1.png",
        "caption": "Fig. 2. Illustration of Ti64 processing methods: (a) HP, (b) SPS, (c) SLM.",
        "texts": [
            " The relationship of processing parameters, microstructures and mechanical properties will be discussed. In this work, the commercially available gas atomized Ti64 powders (53\u2013103 \u03bcm supplied by Sino-Euro Materials Technologies of Xi'an Co., LTD.) were used as the raw material (Fig. 1) for hot pressing (HP), spark plasma sintering (SPS) and selective laser melting (SLM). In the HP process, 45 g powders were poured into a graphite die with external diameter of 100 mm and internal diameter of 30 mm (Fig. 2a). Then the Ti64 powders was sintered in HP (a maximum load of 3 \u00d7 104 kg) at sintering temperature of 1195 K for 1 h at a pressure of 30 MPa and a vacuum of 4.3 \u00d7 10\u22122 Pa. In the SPS process, the raw powder, 127 g Ti64 powders was first loaded into a graphite die with external diameter of 76 mm and internal diameter of 30 mm (Fig. 2b). After that, the raw powder was prepressed and put into the SPS (LABOX-330, Japan) sintering room with a vacuum of ~0.5 Pa. The sintering temperature was 1273 K and keeping time was 30 min (50 K\u00b7s\u22121 heated to 773 K, 30 K\u00b7s\u22121 heated to 1073 K, and then 20 K\u00b7s\u22121 heated to 1213 K, finally 10 K\u00b7s\u22121 heated into 1273 K). During sintering, the vacuum was lowered to be< 0.1 Pa. The sample was cooled down in the furnace for about 4 h. The applied pressure during SPS was constantly held on 30 MPa. In the SLM process, the SLM machine AM250 supplied by RENISHAW Co. UK was used. It was equipped with a SPI laser system with a wavelength of 1070 nm, a maximum power of 200 W in continuous laser mode as well as a spot size of 70 \u03bcm. At first, the raw Ti64 powders of 5 kg were loaded into a container. And then, the chamber temperature was heated up to 373 K with a vacuum of ~1 Pa in the building room. Finally, the sample was produced with a laser power of 200 W, a scanning speed v of 1000 mm\u00b7s\u22121, a thickness of 30 \u03bcm layer, a hatch spacing (h) of 105 \u03bcm (Fig. 2c). Each layer scanning trace that followed a zigzag pattern was rotate 67\u00b0 one by one with an alternate continuous laser mode. The as-fabricated Ti64 alloy samples were machined by electric spark cutting to designed bulks for a series of tests including density measurements, microstructural characterization and mechanical testing. The density was measured by the Archimedes method for more than three times and an average value was achieved. Bulk samples were polished and then etched by a solution of 5 ml of HF, 10 ml HNO3 and 85 ml HF [15]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.60-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.60-1.png",
        "caption": "Fig. 16.60 Moment in a tire due to compressive deformation of the inclined void",
        "texts": [
            " Because the shear force of the block with the dented surface is weaker than that of other regions as shown in the right figure of Fig. 16.59, a positive moment is generated in this block pattern. Note that the signs of Mz in Fig. 16.59 are the same even though the directions of arcs are opposite, because the z-axis is directed toward to the road. When the slot angles of a tire are circumferentially inclined in the same direction at both edges of a block, there are fore\u2013aft shear forces owing to the equilibrium of moments in the block as shown in the left figure of Fig. 16.60. When the same block with inclined slot angles is used in the shoulder of the tire pattern with point symmetry, the direction of the fore\u2013aft shear force in one shoulder region is opposite that in the other shoulder region. The coupling forces generate a moment in the tire contact patch [27]. (3) Contributions of the tire pattern and construction to vehicle pull The contributions of the tire pattern and construction to vehicle pull are estimated by experiment. Figure 16.61 shows the effect of the lug angle on PRCF of tires having opposing belt angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000952_j.cma.2021.113707-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000952_j.cma.2021.113707-Figure11-1.png",
        "caption": "Fig. 11. Schematic diagram for SLM [36].",
        "texts": [
            " Reducing the hatch distance to the same size of laser diameter can help eliminate the sticking particles ut discontinuity due to balling effect can be still found (Fig. 10b). With a 25% overlapping, both defects can be ffectively reduced (Fig. 10c). .4. Simulation of multi-layer SLM SLM is commonly based on a layered manufacturing process where a single layer of molten track is formed rom the metallic powders and is bonded to previous layers until the final object is completed [156], as illustrated n Fig. 11. This section further demonstrates the capacity of our proposed method in modeling multi-layer SLM rocess. The same set of model parameters as listed in Table 4 are used. We follow four steps to model the preparation for the next powder layer after melting the former layer. (1) emove the suspended portion (Fig. 12(a)) of the molten track due to the extremely high viscosity and Darcy\u2019s e s C ffects (Fig. 12(b)) that may adversely affect the subsequent layering process. These suspended parts refer to the patters observed in experiments which would cause the denudation zone if left uncleared [98]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure7-17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure7-17-1.png",
        "caption": "Figure 7-17. Phasor diagram.",
        "texts": [
            "37) \"0 = 1/3 ( Mcyc a + \"eye b + \"eye c) ( 7 . 3 8 ) To understand the way the drive system works, it is useful to regard the cycloconverter and the excitation rectifier as current sources which impress their currents onto the motor by means of their controls. The excitation DC current ie = Ie generates a magnetic field in the stator which is turning with the rotor. The angular frequency of the rotor is \u03c9 = 2\u03c0 \u00b7 n \u25a0 zp, where n is the speed and zp the number of pole pairs. The flux linkage of this field is represented in Figure 7-17 as a rotating phasor IeMeJU1' given by the current Ie and the stator-rotor coupling inductance M. The phasor is in line with the excitation field axis. 7.8. The Cycloconverter-Fed Synchronous Motor 371 The three-phase currents iabc also form a magnetic field in the stator, which turns synchronously at the same angular frequency \u03c9. The flux linkage of this field is represented in Figure 7-17 as a rotating phasor ILeiwl with / = \u0399\u03b2]\u03c8\". It is determined by the amplitude / of the stator current multiplied with the stator inductance L and has a phase shift tpie to the excitation field axis. The triangle formed by the flux linkage phasors L,Mejut and ILeiu' and of their resultant phasor ^_eJU\" (Figure 7-17 and equation 7.39) encloses an area, which is proportional to the electromagnetic torque. That means, the torque Te can be influenced by the currents /, Ie, and the phase angle \u03c6-\u03ba. The relation between the resultant flux linkage and the stator voltage is given by the steady-state phasor equation 7.40 in which the stator resistors are neglected. \u03a6 = IL + IeM (7.39) \u03af\u0396=7^\u03a6 (7.40) To obtain good magnetic utilization of the motor and to work under all load conditions with the lowest possible current in converter and motor, the currents / and Ie and the phase angle \u03c8-\u03ba should be combined in such a way, that \u2022 The resultant magnetic field (\u03a6) is always kept constant at its nominal value. \u2022 The stator current / = \u0399^\u03c8\" is a purely active current, the phasor of which is in line with the voltage phasor U= Ue**\u00ab (U: amplitude). See Figure 7-17. neglected.) P = P-- (7-40) _ * \u25a0* e ~ -\\u, = \u2014 \u03c4 z e = z - /\u03a6 372 7. High-Power Industrial Drives (7.41) (7.42) (7.43) Controls. The main objective of the controls is speed control by means of torque control. This has to be achieved with rated stator flux and a purely active stator current in order to keep converter and motor as small as possible at the given power and speed ratings. The simplified basic control structure shown in Figure 7-16 should be regarded rather as an illustration of the control tasks than as a real control structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000691_j.rinp.2019.01.002-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000691_j.rinp.2019.01.002-Figure7-1.png",
        "caption": "Fig. 7. Principal stress profile at different laser power (a) 50W (b) 100W (c) 150W and (d) 200W for a scan speed of 100mm/S.",
        "texts": [
            " From the graph, it is observed that there is a significant agreement between the simulated and analytical results with an error less than 5%. Effect of laser power on thermal residual stress The successful fabrication of components in direct metal laser sintering process mainly depends on the input heat supplied and appropriate control of the processing conditions. Also, the sintering rate is influenced by the process parameters which manipulate the required energy for melting and consolidation of the powders. Fig. 7 illustrates the principal stress profile of the powder bed with varying laser power at 50W, 100W, 150W and 200W while keeping the laser scan speed 100mm/S constant in all the cases. From the principal stress profile, it is found that there is an enhancement of the principal stress in the build part with increasing laser power. At laser power 50W, the average maximum stress in the powder bed is approximately 85.68MPa. When the laser power is increased from 50W to 200W, the average stress is changed from 85"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.63-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.63-1.png",
        "caption": "Fig. 6.63 Tire model and tire deformation for the line spring rate. Reproduced from Ref. [14] with the permission of Tire Sci. Technol.",
        "texts": [
            "5 0.6 180 200 220 240 260 280 300 320 C on tri bu tio n of e xt en si on to ra di al fu nd am en ta l s pr in g: k r ( M Pa /m m ) Radius(mm) total bead filler tread side wall side wallbead filler gum-chafer tread gum-chafer Fig. 6.61 Contribution of extensional deformation to kr(r) 368 6 Spring Properties of Tires The line spring rate is related to the tire harshness when the tire rolls over bumps and is defined by the ratio of the reaction to the displacement on a rectangular cleat as shown in Fig. 6.63. The characteristic of enveloping a protrusion on a rough road is called the envelope property of a tire. The envelope property can be improved by decreasing the line spring rate. Walter [20] reported that the envelope property corresponds to the out-of-plane flexural rigidity in the circumferential direction calculated using CLT, which will be 0 0.5 1 1.5 2 2.5 180 200 220 240 260 280 300 320 C on tri bu tio n of e xt en si on a nd be nd in g to k r( M Pa /m m ) Radius(mm) total bending extension side wallbead filler gum-chafer tread Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000697_j.jallcom.2019.04.287-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000697_j.jallcom.2019.04.287-Figure2-1.png",
        "caption": "Fig. 2. Schematic illustration showing laser additive manufacturing assisted by highfrequency micro-vibration.",
        "texts": [
            " Before laser scanning, the substrate was cut into sheets of 55 50 5mm by machining. In addition, it was polished by abrasive paper to remove the oxide layer. Then the substrate was cleaned with ultrasonic cleaner in the absolute ethanol (purity 99%). The experiment was conducted on the laser manufacturing system including an IPG-YLS-5000 fiber laser, KUKA six-axis robot, M-PF22 double barrel powder feeder and high-frequency microvibration platform. The laser manufacturing system equipped with the high-frequency micro-vibration platform is shown in Fig. 2. The platform is designed by the principle of the super-magnetic expansion, which is able to change the vibration field by control the vibration frequency of the exciter. The vibration direction is perpendicular to the vibration platform. The vibration amplitude is 10 mm. The vibration acceleration of the vibration system was measured before selecting the resonance vibration frequencies corresponding to the peak values of the vibration acceleration. Based on the measurement, the selected vibration frequencies used in this study were 546, 969 and 1387 Hz in the range of 0e1600Hz"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.11-1.png",
        "caption": "Fig. 5.11: Model of a One-Way Clutch [91]",
        "texts": [
            " (\u03d5n+1 \u2212 2\u03d5n + \u03d5n\u22121) c\u0304 + (\u03d5\u0307n+1 \u2212 2\u03d5\u0307n + \u03d5\u0307n\u22121) d\u0304 (\u03d5n\u22121 \u2212 \u03d5n) c\u0304 + (\u03d5\u0307n\u22121 \u2212 \u03d5\u0307n) d\u0304  \ufe38 \ufe37\ufe37 \ufe38 hEW +  ManS 0 ... 0 \u2212MabS  \ufe38 \ufe37\ufe37 \ufe38 hEWS . (5.16) 5.1 Automatic Transmissions 225 One-way clutches allow a relative rotational motion in one direction only, whereas the other direction is blocked. They are passive components, which connect shafts with shafts or shafts with the housing. Within an automatic power transmission one-way clutches allow shifting without an interruption of the traction forces and without an influence on the shifting quality itself, and that with a really simple technology. Figure 5.11 depicts a model of such a one-way clutch, which includes some inertias of the input and output parts and in addition unilateral constraints. The state of the clutch is given by its relative rotational speed g\u0307FL = \u03d5\u0307an \u2212 \u03d5\u0307ab, (5.17) with non-negative values in the free direction. The one-way clutch possesses two states, which exclude each other. If we have the same speed on both sides, input and output, the clutch is blocked and transmits a positive constraint torque MFL > 0 from input to output"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001287_tie.2021.3076719-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001287_tie.2021.3076719-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the bearing angle in the multi-USV system.",
        "texts": [
            " Consider a multi-USV system consisting of n USVs, of which each is described by the kinematics in the Cartesian coordinates [37], x\u0307i = ui cos\u03c8i \u2212 vi sin\u03c8i, y\u0307i = ui sin\u03c8i \u2212 vi cos\u03c8i, \u03c8\u0307i = ri, (1) where qi(t) = [xi(t), yi(t)] T \u2208 R2 denotes the position, \u03c8i(t) \u2208 R the yaw angle of USV i, respectively, and ui(t), vi(t), ri(t) \u2208 R the surge, the sway and the yaw velocities of USV i in the USV coordinate, respectively. The dynamics of USV i generally follow a practical model (see e.g., [17]) as u\u0307i = k1ui + k2viri + k3\u03c4i,1, r\u0307i = k4ri + k5\u03c4i,2, v\u0307i = k6vi + k7uiri, (2) where k1, k2, k3, k4, k5, k6, k7 \u2208 R are the identified parameters via zig-zag experiments afterwards, and \u03c4i,1, \u03c4i,2 \u2208 R the actuator inputs of USV i. A motional target represented by qd(t) = [xd(t), yd(t)] T \u2208 R2 satisfies q\u0307d = pd (3) with a constant velocity pd = [vdx, v d y ]T \u2208 R2. As is shown in Fig. 1, it is assumed that only the relative bearing angle \u03b1i is measured between the i-th USV and the target in the i-th USV\u2019s coordination frame, which is not necessarily aligned to the frames of the other USVs, but not the position qd or the velocity pd of the target vessel. Combined with the yaw angle \u03c8i, one has \u03c3i := qd,i \u2016qd,i\u2016 (4) as a unit vector with \u2220\u03c3i := \u03c8i + \u03b1i and qd,i := qd \u2212 qi in Eq. (21). In a multi-USV system, define the communication topology as G(V, E), where V := {1, 2, . . . , n} is the node set and E := {(i, j), j \u2208 Ni, i \u2208 V} the edge set",
            " Note that there might be more than two neighbors in Ni, where the preneighbor i+ and next-neighbor i\u2212 of USV i can be selected randomly from Ni, respectively. Let the relative distance \u03c1i and the bearing angle \u03b8i between the USV i and the target vessel be \u03c1i = \u221a (xi \u2212 xd)2 + (yi \u2212 yd)2, \u03b8i = arctan2(yi \u2212 yd, xi \u2212 xd) + 2\u03ba\u03c0 \u2208 [0, 2\u03c0) (5) with an appropriately selected integer \u03ba to make sure that \u03b8 \u2208 [0, 2\u03c0). arctan2(y, x) denotes a two-argument arctangent function retuning the angle of vector (x, y) as a numeric value between \u2212\u03c0 and \u03c0 radians. Then, one has \u03b8i = \u03c8i + \u03b1i + \u03c0 (6) with \u03b1i, \u03c8i illustrated in Fig. 1. Define the separation angle \u03c2i between USV i and its pre-neighbor i+ with respect to the target vessel as \u03c2i := \u03b8i+ \u2212 \u03b8i + \u03bei (7) with \u03bei = { 0, \u03b8i+ \u2212 \u03b8i \u2265 0, 2\u03c0, \u03b8i+ \u2212 \u03b8i < 0. With the target and neighboring information above, the following assumptions are necessary for afterwards derivation. Assumption 1. The velocity pd \u2208 R2 of the target in (3) has an upper bound p\u2217d \u2208 R+, i.e., \u2016pd\u2016 \u2264 p\u2217d. Assumption 1 is reasonable since the energy of the target vessel is always limited in practice, which implies that the velocity of target has an upper bound",
            " Then, one has lim t\u2192\u221e x(t) = 0, if the nominal system x\u0307 = A(t, d(t))x is uniformly globally exponentially stable and h(t) is bounded which satisfies limt\u2192\u221e h(t) = 0. Lemma 2. [38] For a connected and symmetric matrix L \u2208 Rn\u00d7n, the following property holds: min 1Tx=0,x6=0 xTLx \u2016x\u20162 \u2265 \u03bb2(L) > 0. (25) Lemma 3. [35] For a nominal system governed by \u02d9\u0303qd,i = \u2212\u03c3\u0304i\u03c3\u0304T i q\u0303d,i, (26) where q\u0303d,i := q\u0302d,i \u2212 qd,i \u2208 R2 is the estimated error given in (29), and \u03c3\u0304i, i \u2208 V , denotes a unit vector perpendicular to \u03c3i with angle \u2220\u03c3\u0304i = \u03c8i +\u03b1i\u2212\u03c0/2 in Fig. 1. Then, it derives that lim t\u2192\u221e q\u0303d,i(t) = 0, i.e., \u03c3\u0304i(t), i \u2208 V , is persistently exciting [39], if \u03b2 in (23) satisfies \u03b2 > 2\u03c0c4 + p\u2217d + \u03b2\u2217 (27) with a constant \u03b2\u2217 \u2208 R+ and the control gain c4 \u2208 R+ in the controller (23). Lemma 4. For the estimator of the state qd,i, pd governed by (1), (3), (21), (22), one has lim t\u2192\u221e q\u0302d,i(t) = qd,i, lim t\u2192\u221e p\u0302d,i(t) = pd, (28) if \u03b2 in (23) satisfies the condition (27) in Lemma 3. Proof. Let q\u0303d,i, p\u0303d be the estimated errors as q\u0303d,i :=q\u0302d,i \u2212 qd,i, p\u0303d,i := p\u0302d,i \u2212 pd",
            " Then, one has \u02d9\u0303qd,i =\u02d9\u0302qd,i \u2212 q\u0307d,i, \u02d9\u0303pd,i = \u02d9\u0302pd,i. (30) Substituting Eqs. (3), (22) into Eq. (30) yields \u02d9\u0303qd,i =\u2212 c1(I \u2212 \u03c3i\u03c3T i)(q\u0303d,i + qd,i) + p\u0303d,i, \u02d9\u0303pd,i =\u2212 c2(I \u2212 \u03c3i\u03c3T i)(q\u0303d,i + qd,i). (31) Bearing in mind of the fact that (I \u2212 \u03c3i\u03c3 T i)qd,i = qd,i \u2212 qd,i \u2016qd,i\u2016 qT d,i \u2016qd,i\u2016qd,i = 0 and \u03c3\u0304i\u03c3\u0304T i = I \u2212 \u03c3i\u03c3T i , one has[ \u02d9\u0303qd,i \u02d9\u0303pd ] =A [ \u02d9\u0303qd,i \u02d9\u0303pd ] (32) with A = [ \u2212c1\u03c3\u0304i\u03c3\u0304T i I \u2212c2\u03c3\u0304i\u03c3\u0304T i 0 ] . (33) Here, \u03c3\u0304i denotes the unit vector perpendicular to \u03c3i with angle \u2220\u03c3\u0304i = \u03c8i + \u03b1i \u2212 \u03c0 2 in Fig. 1. It is clear that the error dynamic (32) converges if the matrix A is Hurwitz, which is equivalent to proving that \u03c3\u0304i, i \u2208 V , is persistently exciting [39]. In accordance to Lemma 3, one concludes that \u03c3\u0304i is persistently exciting with a properly chosen \u03b2 in (27). Accordingly, the estimated errors q\u0303d,i, p\u0303d,i converge, i.e., lim t\u2192\u221e q\u0303d,i(t) = 0, lim t\u2192\u221e p\u0303d,i(t) = 0, (34) the proof is thus completed. Remark 2. The condition \u03b2 > 2\u03c0c4 + p\u2217d + \u03b2\u2217 in Eq. (27) explicitly shows that all the USVs everlastingly rotate around a motional target vessel under the proposed bearing-only protocol (23), which guarantees that \u03c3\u0304i(t), i \u2208 V in (32) is persistently exciting and thus forms a necessary condition for the convergence of the estimator (22) in Lemma 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003824_027836499701600505-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003824_027836499701600505-Figure3-1.png",
        "caption": "Fig. 3. A &dquo;catastrophic&dquo; jump.",
        "texts": [
            " Also, from the diagram in Figure 2, we can expect the occurrence of a catastrophic jump dynamics (Jackson 1991 }, produced by a slight change of kp. This phenomenon can appear when the bifurcation parameter 1~~ is increased across bifurcation points. Note that any change that is made in the bifurcation parameter kp must be &dquo;slow&dquo; or adiabatic with respect to the equation of motion, for otherwise the equation must be treated as nonautonomous. The resulting behavior of position error 4 and velocity ~ is illustrated in Figure 3, where kv = 0.1, and kp varies &dquo;slowly&dquo; as 1~~ = O.OIt + 1.8 and the initial conditions are q(0) = 4 rad and 4(0) = 0. When l~p is increased past 0.21723 mgl - 2.1288, the stable equilibrium [~ 4] = [ 1.43030~r 0] disappears, and the system &dquo;jumps&dquo; to the only distant available stable equilibrium: the origin of the state space. ~ at NORTHERN ILLINOIS UNIV on September 7, 2014ijr.sagepub.comDownloaded from 669 10. The Adaptive Version One of the important applications of strict Lyapunov functions is in adaptive control design (Wen 1990)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure13.69-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure13.69-1.png",
        "caption": "Fig. 13.69 Downsized tire [87]",
        "texts": [
            " Maneuverability may be improved by control technology, such as electric stability control or autonomous driving. If the design elements of a tire are used to improve only the suitable performances of mobility and the remaining performances are improved through the design of the vehicle and road, all performances of mobility will be good. Kuwayama et al. [59, 60] proposed a downsized tire with high inflation pressure and large radius to ensure the compatibility of RR and other performances as shown in Fig. 13.69. They compared the performances of an ordinary tire and a downsized tire with high pressure and large diameter. The size and air pressure were 175/ a larger diameter. The void ratio was 18% for 155/55R19 and 30% for other sizes. 13.7 Future Tires 1003 The RR of 155/55R19 tires was 30% less than that of 175/65R15 tires owing to the high pressure and small rubber volume. The cornering stiffness of 155/55R19 tires was 17% greater than that of 175/65R15 tires owing to the long contact length and small void ratio"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure1-1.png",
        "caption": "Fig. 1 Basic concept of bevel gear generation",
        "texts": [
            " However, the generated method offers more freedoms of controlling tooth surface geometries; 2 the lengthwise tooth curve of face milled bevel gears is a circular arc with a curvature radius equal to the cutter radius while the lengthwise tooth curve of face hobbed gears is an extended epicycloid which is kinematically generated by the indexing motion; and 3 face hobbing gear designs use the uniform tooth depth system while face milling gear designs use the tapered tooth depth system. Theoretically, the face hobbing process is based on the generalized concept of bevel gear generation in which the mating gear and pinion can be considered respectively, generated by the complementary generating crown gears as shown in Fig. 1. The tooth surfaces of the generating crown gears are kinematically formed by the traces of the cutting edges of the tool blades as shown in Fig. 2. The generating crown gear can be considered as a special case of a bevel gear with 90 deg pitch angle. Therefore, a generic term \u201cgenerating gear\u201d is used. The concept of complementary generating crown gear is considered when the generated mating tooth surfaces of the pinion and the gear are conjugate. In practice, in order to introduce mismatch of the mating tooth surfaces, the generating gears for the pinion and the gear may not be NOVEMBER 2006, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.14-1.png",
        "caption": "Fig. 6.14: Inclination sensor. According to [Kato91]",
        "texts": [
            " The prototype is about 4 mm long and can measure the rotational angle with an accuracy of 0.028 degrees at temperatures between -10\u00b0C and +80 \u00b0C. Inclination sensor There is a trend to develop small inspection robots for various applications (Section 1.4.2). E.g. they are missioned to go into complex machinery or in accessible pipes to locate and repair defects. Many of these devices need inclination sensors to calculate the exact tilting of the robot with respect to a reference plane. A very novel inclination sensor and its components are shown in Figure 6.14. The sensor system consists of an LED and a semi-spherical glass cup, which is mounted on a photodiode matrix array. The glass cup is filled with liquid and has an enclosed air bubble. The LED sends light through the cup which casts shadows on the four photodiodes underneath. If the sensor is tilted in one direction, the shadow moves across the diode matrix, Fig. 6.15. The out put currents of the photodiodes are transformed into voltages and are ampli fied, and from this information the inclination angle and tilt direction can be determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003228_a:1008914201877-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003228_a:1008914201877-Figure3-1.png",
        "caption": "Figure 3. Two axis scanning sensor configuration.",
        "texts": [
            " 2) to sense the dig face, truck, and obstacles in the workspace. Two scanners are needed for full coverage of the workspace and to enable concurrent sensing operations. Each sensor has a sample rate of 12 kHz, and a motorized mirror sweeps the beam circularly in a vertical plane. The mirror spins at approximately 1800 rpm providing 30 circles of sensor data per second. Additionally, each scanner can pan at a rate of up to 120 degrees per second, enabling this circle to be rotated about the azimuth, as shown in Fig. 3. The lasers have an effective range of 200 m and are eye-safe when the mirror is spinning. The scanner positioned over the operator\u2019s cab is called the \u201cleft scanner\u201d, and it is responsible for sensing the workspace on the left hand side of the excavator. The \u201cright scanner\u201d, which is located at a symmetric position on the right, is responsible for sensing the workspace on the right hand side of the excavator. The excavator uses its scanners in the following fashion when loading a truck (Fig. 4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.37-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.37-1.png",
        "caption": "Fig. 3.37: An Example of Reality and Model",
        "texts": [
            " The first point concerns the requirement, that a mechanical picture representing for example a large machine must be consistent, and it must be a clear picture of the real world. These pictures must be correct in an unambiguous sense, not least because of their property of being the starting point for the mathematical models. Finally mechanical models should be simple, which relates to the efforts needed to solve such problems. My own experience tells me, that models should be as complicated as necessary to achieve a good relation to reality, but as simple as possible to keep expenditure small. Figure 3.37 illustrates a typical case. On the left side we see an artist\u2019s impression of a roller coaster system, called the \u201dwild mouse\u201d, which is in operation on many German fairs. The loads on the wheel packages and the strength of the wheels caused some problems. Therefore we had to model the contacts of the wheels with the track to evaluate the contact forces. Each car possesses four wheel packages with six wheels each. Driving along the track, a rather exciting track as partly indicated in the Figure, puts on the wheels a quickly varying set of load cycles, which led to wheel damages. The model should focus on the wheel loads but also consider the overall dynamics of the car going along the track. Therefore we modeled all four wheel packages with all details, especially with all contact details according to the right side of Figure 3.37. The model went along the track finally providing us with the necessary information to suggest a better wheel design [253]. The example illustrates that model complexity can be reduced sometimes by focussing on the most problematic components, in this case the wheels, and modeling the other system parts around that in a more or less rough and simplified way. All methods presented in this book generate mathematically a set of ordinary second order differential equations together with certain sets of linear or non-linear, smooth or non-smooth side conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.35-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.35-1.png",
        "caption": "Fig. 6.35: Tension Guide",
        "texts": [
            " It is a premise to the contact model to make this effects apparent. The direction of the contour parameter s is given by the contour coordinate system (t,n) with the condition that the normal vector n directs to the inner part of the guide. The behavior of the tension device, acting on the tension guide, leads at this point with many simplifications to a description of a force element with a matched damping characteristic. This force element is composed of a spring with the very low spring coefficient cTD and the damping coefficient dTD (Figure 6.35). Depending on the relative velocity in the normal direction nTD we assume for negative values a high damping coefficient, for positive values a low damping coefficient. We shall discuss these tension devices in a separate chapter. Contact between a Link and a Sprocket To describe the contact between a link and a sprocket we have to distinguish the two types of links. For a roller chain the contact is realized by the rollers rotating around the pin of the roller chain (Figure 6.29), for a bush chain the bush comes directly into contact with the sprocket"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003240_02640410050082297-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003240_02640410050082297-Figure6-1.png",
        "caption": "Fig. 6. Relationship between the ground reaction force and the development of angular momentum about the Y-axis of rotation. Location of the centre of mass is represented by the symbol d .",
        "texts": [
            " As a result of this motion, the centre of mass of the back leg rotated clockwise relative to the centre of mass of the whole body, thus acquiring a large amount of negative Y-axis angular momentum ( - 2.8 \u00b1 0.5 kg \u00b4m2 \u00b4s - 1). The negative angular momentum about the Y-axis acquired by the body is the result of the o\u00fe -centre vertical impulse produced by the back leg (right leg) about the Y-axis as it pushed against the ground. This o\u00fe - centre impulse produced clockwise angular momentum (viewed from the front of the players) and elevated the racket-side of the body and lowered the opposite side (see Fig. 6). These actions are the beginning of the leg drive and are important in the transfer of angular momentum from the lower limbs to the upper limb (Elliott, 1988). From the time of maximum elbow \u00af exion to the racket\u2019 s lowest point, the angular momentum about the 588 Bahamonde D ow nl oa de d by [ A us tr al ia n N at io na l U ni ve rs ity ] at 2 2: 35 1 6 Ja nu ar y 20 15 Y-axis decreased to an average of - 3.7 \u00b1 3.2 kg \u00b4m2 \u00b4s - 1. The trunk contributed the largest amount of this angular momentum as it continued to rotate clockwise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-41-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-41-1.png",
        "caption": "Figure 4-41. Dead-time effect: (a) location of the polarity vector sig(i'); (b) trajectory of the distorted average voltage uav.",
        "texts": [
            " The error magnitude Au is proportional to the actual safety time margin Td - Tsl; its direction changes in discrete steps, depending on the respective polarities of the three phase currents. This is expressed in equation 4.34 by a polarity vector of constant magnitude sigfo) = f [sign(/a) + a sign(/6) + a2 \u25a0 sign(ic)] (4.36) where a = \u03b5\u03c7\u03c1(/2\u03c0/3), and is is the current vector. The notation sig(/i) was chosen to indicate that this complex nonlinear function exhibits properties of a sign function. The graph sig(/s) is shown in Figure 4-41a for all possible values of the current vector is. The space vector s\\g(is) is of constant magnitude; it always resides in the center of that 60\u00b0 sector in which the current space vector is located. The three phase currents are denoted as ia, ib, and ic. The dead-time effect described by equations 4.34 through 4.36 produces a nonlinear distortion of the average voltage vector trajectory uav. Figure 4-41 b shows an example. The distortion does not depend on the magnitude u* of the fundamental voltage and hence its relative influence is very strong in the lower-speed range where 4.5. Open Loop Schemes 177 u is small. Since the fundamental frequency is low in this range, the smoothing action of the load circuit inductance has little effect on the current waveforms, and the sudden voltage changes become clearly visible, Figure 4-42a. As a reduction of the average voltage occurs according to equation 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003717_robot.1999.769929-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003717_robot.1999.769929-Figure4-1.png",
        "caption": "Figure 4: Two simple examples to compare and contrast the COP (P), GCoM (C), and FRI point (F). In the top figure the foot is in static equilibrium since F is within the support line (although C is outside). P is coincident with F. At bottom, the foot is starting to rotate since F is outside the support line (although C is inside). P is at the tip about which the foot rotates.",
        "texts": [
            " The stability margin of a robot against foot rotation may be quantified by the minimum distance of the support polygon boundary from the current location of the FRI point within the footprint. Conversely, when the FRI point is outside the footprint, this minimum distance is a measure of instability of the robot. An imminent foot rotation will be indicated by a motion of the FRI point towards the support polygon boundary. 2.2 Examples The difference between the COP, GCoM, and the FRI point will be analytically explored in Section 3. Here we provide two examples to aid our intuitive understanding. Fig. 4 depicts a planar inverted pendulum connected by an \u201cankle\u201d joint to a massless3 triangular foot. In the first example (top) the pendulum configuration corresponds to a GCoM position denoted by C, outside the support polygon. The foot is however prevented from rotating by the ankle torque (mZ2e - mZgcos0) and the FRI point F is situated within the support line. Note that in order to stop the robot from tipping over [5] used a scheme to accelerate forward the heavy robot body. This generates a supplementary backward inertia force - similar to this example - which shifts the FRI point backward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001217_j.icheatmasstransfer.2021.105325-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001217_j.icheatmasstransfer.2021.105325-Figure4-1.png",
        "caption": "Fig. 4. Schematics of (a) substrate with powder layer and (b) computational domain.",
        "texts": [
            " (19) with the latent heat of vaporization [30\u201332], which yields q\u02dd evap = Ji\u0394Hevap (20) where qevap \u2032\u2032 is the evaporative heat flux from the metal (W/m2), and \u0394Hevap is the latent heat during the vaporization (J/kg-K). In the computational domain, the temperatures at the bottom, left, front, and rear boundaries do not change over time. Therefore, the heat fluxes across these boundaries are neglected in the study. The right boundary is a symmetrical condition. \u2212 keff \u2202T \u2202z \u20d2 \u20d2 \u20d2 \u20d2 z=0 = 0 (21) Fig. 4 demonstrates the physical model developed in the present study. The substrate shown in Fig. 4(a) has lall = 10 cm of the length, wall = 10 cm of the width, and tall = 1.5 cm of the thickness. The layer thickness of the metal powder on the substrate is 40 \u03bcm. As depicted in Fig. 4(b), the SS316L substrate of the length, width, and height are 650 \u03bcm, 250 \u03bcm, and 400 \u03bcm, respectively. Half region of the molten pool as the computational zone can reduce the cost of time in calculation. To calculate the detailed development of the molten pool, a fine mesh is Y.-H. Siao and C.-D. Wen International Communications in Heat and Mass Transfer 125 (2021) 105325 used in the strong variation of the melting area. The coordinates of the initial position of the laser are (0 \u03bcm, 400 \u03bcm, 250 \u03bcm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000159_j.ijfatigue.2020.105946-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000159_j.ijfatigue.2020.105946-Figure2-1.png",
        "caption": "Fig. 2. Representative cellular specimen used for mechanical testing: (a) 3D view of the entire specimen, with uvw reference system; (b) view of specimen cross-section; (c) specimen longitudinal section, showing transition regions. i.e. bell shape and thicker struts close to the flange, between solid flanges and inner cellular portion.",
        "texts": [
            " The treatment is known to be sufficient in order to relieve residual stresses generated during the powder bed fusion process and to transform the martensitic as-built microstructure into a stable \u03b1 + \u03b2 one [56]. Neither sandblasting nor other surface treatments were applied. To reduce the border effects to a reasonable level, the specimens were designed according to the guidelines provided by the ISO14333 standard: the cellular part is cylindrical, made of 12 unit cells along the height and 11 along the diameter (Fig. 2a and 2b). During half of the fully reversed fatigue cycle the specimen is in traction, therefore the specimen must be appropriately connected to the testing machine, a condition ensured by adding bolted flanges directly printed with the specimen. To indicate the printing orientation of the specimen an XYZ reference system is used: the printing direction is indicated by Z, while the build plane is the XY plane. The as-built/as-designed mismatch issue in L-PBF lattices can be addressed via a procedure known as compensation [29]",
            " Batches from A to D were designed with the parameters of the nominal geometry listed in Table 1 (L = 4000 \u00b5m, t0 = 670 \u00b5m, R = 600 \u00b5m); for batch E the unit cell size L is 3000 \u00b5m, and the t0/L and R/L ratios are identical to the other batches, hence t0 = 500 \u00b5m and R = 450 \u00b5m. The nominal geometry of the specimens was determined with the procedure described in a previous work [48], requesting the nominal elastic modulus to be 3 GPa. Table 1 summarizes nominal and compensated parameters of the cell geometry. Table 2 lists the size of the specimens (parameters in Fig. 2), which depends on the unit cell size L. To guarantee the validity of the fatigue tests, two requirements should be met: failure should occur away from the flanges and the internal load distribution should be uniform within the cross-section of the cellular specimen. These conditions are not trivial to fulfill, given the geometric characteristics of the specimen, which is cellular as opposed to the standard sample of solid material. Fig. 5 shows the computational result of an iterative design process using FE (Ansys\u00ae Release 18",
            " In this article only a brief description of the design process is given, while a more detailed account of the procedure is planned for a future publication. The strategy devised to avoid failure close to the flanges consists of thickening both the vertical struts and fillets of the unit cells in the planes interfacing the flanges. The compliance of the flange causes the external annulus of the cellular specimen to carry a higher fraction of the load, unless the thickness of the flange is increased at its center. The simplest expedient was to design the flange shaped as a bell (Fig. 2c). Fig. 5 shows a plot of the normalized load in the struts (defined as the ratio between the force calculated from the FE simulations and the force calculated as if the traction was carried uniformly by all the struts) for two sections along the w axis of the specimen (see Fig. 2c). The results confirm that an increase of the flange thickness at its center improves the load distribution so as to make it more uniform. The difference in loading between the center and the external annulus decreases from roughly 30% to 10%. This difference further increases if no transition zone is added between the solid flange and the cellular sample, leading to failure in the external annulus, at the region attached to the flange. For the metrological characterization of the specimens, we adopt a procedure previously developed [31]. Four specimens were randomly selected from each batch, and the Nikon SMZ25 stereomicroscope was used to take photographs of 8\u201312 unit cells along the directions perpendicular and parallel to the printing direction. Specimens of type A, D and E had to be cut in the uv plane of the specimen (Fig. 2a) to obtain pictures perpendicular to the printing direction. The mean value and the standard deviation of the geometrical parameters for each batch are calculated using all the measurements obtained from the different pictures. Metallographic specimens were prepared to investigate the microstructure and assess the effect of the heat treatment. For each batch, two specimens were prepared, one parallel and one perpendicular to the printing direction. The sectioned samples were then mounted, ground with SiC abrasive papers (with 120, 180, 320, 400, 600, 1000, 1500 grit sizes), and polished with a 3-\u00b5m diamond paste followed by a 1-\u00b5m paste",
            " The S-N curve of the base material was also constructed using 12 fully dense specimens (gauge section diameter and length of 4 mm and 12 mm, respectively) printed along their loading direction with same machine parameters and powder as the cellular specimens, tested under identical loading conditions. The data on fatigue are fitted with an asymptotic curve, given by: = +c c Na f m1 2 (2a) where a is the homogeneous axial stress amplitude (the ratio between the load on the unit cell and the nominal circular area of diameter Dlattice of the lattice part, as in Fig. 2 and Table 2), Nf is the number of cycles to failure and the remaining quantities are fitting constants. The scatter of the fatigue data is assessed by computing the estimated regression variance assumed to be uniform for the whole fatigue life range and expressed by: = =S n p ( )i n a i a i2 1 , , 2 (2b) where a i, is the i.th fatigue amplitude data point, a i, is its estimator, n is the number of data elements, and p is the number of parameters in the regression (p = 3 in this specific case). The fatigue notch factor K f was calculated from the experimental fatigue results by dividing the fatigue strength of the fully dense specimens and by the fatigue strength of the cellular specimens normalized by the nominal cross-section area of the specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003870_tia.2006.872930-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003870_tia.2006.872930-Figure1-1.png",
        "caption": "Fig. 1. Open-circuit field distributions with four-pole rotor at peak coggingtorque position. (a) One slot. (b) Six slots.",
        "texts": [
            " The cogging-torque waveforms and harmonic spectra, which result when the stator has only one slot, and two, three, four, five, and six uniformly distributed slots are analyzed and analytically synthesized, and then compared with finite-element predicted results and measurements. The Maxwell stress integration method is employed in the finiteelement calculation of both the cogging torque due to a single slot and the resultant cogging torque, with particular attention being paid to the discretization so as to achieve the required accuracy. Fig. 1 shows open-circuit magnetic-field distributions for the one-slot and six-slot motors, while Fig. 2 shows the cogging torque of the one-slot motor, for which 2p = 4, Ns = 1, Nc = 4, and C = 1. Thus, its cogging-torque waveform has a periodicity of 90\u25e6 mechanical, and Tcog1 = \u221e\u2211 i=1,2,3,... Tsci sin(4i\u03b8) (12) where Tsci is the amplitude of the ith harmonic of the cogging torque. The least common multiple Nc, the goodness factor C, the harmonic order, and the amplitude of the cogging torque, which result in the two-slot, three-slot, four-slot, five-slot, and six-slot four-pole motors, are given in Table I",
            " Given that the cogging torque due to a single slot is calculated from finite-element analysis, and, therefore, accounts for the actual slot geometry and local magnetic saturation in the adjacent teeth, the high level of agreement is not TABLE I Nc AND C FOR FOUR-POLE MOTORS Fig. 3. Cogging torque for one-slot and three-slot four-pole motors. (a) Waveforms. (b) Harmonics. surprising; the main assumption in synthesizing the resultant cogging torque being the magnetic field distribution in the region of a single slot is not affected by the presence of adjacent slots. This is likely to be the case for most machines, and certainly the case for the prototype machines. Further, from Fig. 1, it will be seen that although the flux distribution in the single slot and six-slot stators is different, the level of magnetic saturation in the stator back iron is similar. Thus, the synthesized and resultant finite-element calculated coggingtorque waveforms are almost identical. It will be evident that for the two-slot and four-slot motors, 2p/Ns is an integer, and that they have the same value of Nc as the one-slot motor. Hence, the periodicity of the coggingtorque waveform is identical for all three motors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.12-1.png",
        "caption": "Fig. 6.12 Simplified tire model",
        "texts": [
            "10 Rotation of a sidewall Because /s is larger for a tire with a lower aspect ratio and larger rim diameter, Kp and ks will be smaller for a tire with a lower aspect ratio. This explains why tires with a low aspect ratio are reinforced by large and stiff bead fillers. The effects of the rim width, tire height and tire width on the radial fundamental spring rate of a tire due to the tensile stiffness Kp and the lateral fundamental spring rate ks are evaluated using Eqs. (6.13) and (6.17). The simplified tire model is used as shown in Fig. 6.12, where Wr, Ws, H and r are, respectively, the rim width, side width, tire height and radius of the sidewall. Assuming that the rim width is equal to the tread width, r is given as 0 0.5 1 1.5 2 2.5 3 40 50 60 70 80 Angle: \u03c6s (deg) Sp rin g ra te (M N /m 2 ) p=0.25MPa Kp ks Fig. 6.11 Radial fundamental spring rate of a tire due to the tensile stiffness Kp and lateral fundamental spring rate ks of a tire versus the tire shape 316 6 Spring Properties of Tires Rotta [1] derived an equation for the circumferential fundamental spring rate of a bias tire per unit circumferential length"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000848_j.mechmat.2020.103499-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000848_j.mechmat.2020.103499-Figure1-1.png",
        "caption": "Fig. 1. Rotational bending fatigue samples and microstructures (the black dotted lines are molten pool boundaries) of selective laser melting (SLM) AlSi10Mg alloy: (a), (d) 90\u00b0 sample; (b), (e) 45\u00b0 sample; (c), (f) 0\u00b0 sample; and (g) dimensions of RBF bar samples.",
        "texts": [
            " Aluminum alloys Si Mg Fe Cu Pb Ti Mn Al AM AlSi10Mg 9.70 0.45 0.25 0.000 0.20 0.15 0.100 Bal. Table 2 Mechanical properties of SLM AlSi10Mg alloys (standard deviations in brackets). E, GPa \u03c30.2, MPa \u03c3b, MPa \u03b4 HV Ns 0\u00b0 sample 73.1 (5.1) 232.6 (8.2) 328.2 (7.7) 7.6% (2.1) 88.0 (6.1) 5 45\u00b0 sample 71.2 (3.5) 219.3 (10.1) 312.5 (8.4) 6.9% (1.1) 82.8 (5.0) 5 90\u00b0 sample 71.5 (4.2) 221.4 (12.6) 310.4 (9.5) 6.7% (1.3) 81.4 (7.1) 5 The AlSi10Mg samples produced by SLM processes in different building directions (0\u00b0, 45\u00b0 and 90\u00b0) are shown in Fig. 1. The rotational bending fatigue (RBF) samples, as shown in Fig. 1g, can be obtained by machining work. In addition, abrasive papers (2000 #) were used to achieve a uniform and high surface roughness (the maximum height of the profile Ry, the distance between the profile peak line and valley line, was approximately 2 \u00b5m), which is far smaller than the size of the AlSi10Mg powders. Therefore, the effect of sample surface roughness on the fatigue properties of the SLM AlSi10Mg alloy can be ignored. The RBF bar specimens were tested on a YAMAMOTO (Japan) testing system to obtain the fatigue data of the SLM AlSi10Mg alloy",
            " Results and discussion Considering the different building directions, the typical microstructures of the three kinds of SLM AlSi10Mg samples were analysed by the OM. Fish-scale molten pools caused by SLM processes can be identified on the 45\u00b0 and 90\u00b0 samples, as shown in Figs. 1d and e. The shape and dimensions of the molten pools were inhomogeneous for the SLM AlSi10Mg samples. The molten pool depth and width ranged from 60 to 120 \u03bcm and 80 to 250 \u03bcm, respectively. In addition, the microstructures of the 0\u00b0 samples are presented in Fig. 1f. The molten pools along the different laser scanning directions and with a rotation of 67\u00b0 between two adjacent layers can be observed. Additional microstructure information of the SLM AlSi10Mg specimens can be obtained by SEM. The primary \u03b1-Al phase exhibited a dark contrast and the Al-Si eutectic exhibited a light contrast in the SEM images (Uzan et al., 2017; Bagherifard et al., 2018). For the as-built SLM specimens, a fine cellular eutectic morphology was resulted from a high SLM process temperature, large temperature gradient and fast cooling rate",
            " The influence of building direction on the fatigue crack propagation behavior of Ti6Al4V alloy produced by selective laser melting. Mater. Sci. Eng. A 767, 138409. Xu, Z.W., Wu, S.C., Wang, X.S., 2019b. Fatigue evaluation for high-speed railway axles with surface scratch. Int. J. Fatigue 123, 79-86. Yang, H.H., Wang, X.S., Wang, Y.M., Wang, Y.L., Zhang, Z.H., 2017. Microarc oxidation coating combined with surface sealing pores treatment enhanced corrosion fatigue performance of 7075-T7351 Al alloy in different media. Materials 10(6), 609. Figure Captions Figure 1 Rotational bending fatigue samples and microstructures (the black dotted lines are molten pool boundaries) of selective laser melting (SLM) AlSi10Mg alloy: (a), (d) 90\u00b0 sample; (b), (e) 45\u00b0 sample; (c), (f) 0\u00b0 sample; and (g) dimensions of RBF bar samples. Figure 2 Typical microstructures of selective laser melting (SLM) AlSi10Mg alloy after a 520\u2103 SRA for 2 hours: (a), (b) molten pool boundaries; (c) partial separation of continuous silicon networks; and (d) lack of fusion (LOF) defect and the growth direction of Al-Si eutectic structures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000047_iet-cta.2016.0231-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000047_iet-cta.2016.0231-Figure1-1.png",
        "caption": "Fig. 1. Truck-trailer model diagram.",
        "texts": [
            " (29) Therefore, all signals are UUB based on Definition 2 and (28), which implies the sliding motion enters a neighborhood of equilibrium in limited time and keeps within it. As discussed in [55], this completes the proof. This section provides a truck-trailer model system and a ball and beam system to demonstrate the effectiveness of the proposed results. First, we consider the following example. Example 1: In this example, we will make a comparison between the actuator normal case and actuator faulty case via the truck-trailer model shown in Fig. 1. The state space equation of the truck-trailer model [52] is  x\u03071 = \u2212 vt\u0304 Lt0 x1 + vt\u0304 lt0 u, x\u03072 = vt\u0304 Lt0 x1, x\u03073 = vt\u0304 t0 sin ( vt\u0304 2L x1 + x2 ) , (30) where L = 5.5 m, l = 2.8 m, v = \u22121.0 m/s, t\u0304 = 2.0 s and t0 = 0.5 s. We use the following two-rule T-S fuzzy system in s-domain to represent the dynamics of system (30) as follows: Plant Rule 1: IF \u03b8 (t) = x2 + vt\u0304 2L x1 is about 0, THEN x\u0307 (t) = As1x (t) +Bs1u (t) , Plant Rule 2: IF \u03b8 (t) is about \u03c0 or \u2212\u03c0, THEN x\u0307 (t) = As2x (t) +Bs2u (t) , where x (tk) = [ x1 (tk) x2 (tk) x3 (tk) ]T and As1 =  \u2212 vt\u0304 Lt0 0 0 vt\u0304 Lt0 0 0 v2 t\u03042 2Lt0 vt\u0304 t0 0  , As2 =  \u2212 vt\u0304 Lt0 0 0 vt\u0304 Lt0 0 0 b0v2 t\u03042 2Lt0 b0vt\u0304 t0 0  , Bs1 = Bs2 =  0 0 vt\u0304 lt0  , and b0 = 10t0/\u03c0 with the membership functions h1 (\u03b8 (t)) = ( 1\u2212 1 1 + e(\u22123(\u03b8(t)\u22120"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000772_j.precisioneng.2021.01.007-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000772_j.precisioneng.2021.01.007-Figure3-1.png",
        "caption": "Fig. 3. The vectors of joint axes.",
        "texts": [
            " The parasitic motion \u03c8 can be obtained as \u03c8 = arcsin \u239b \u239c \u239d k3 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 k2 1 + k2 2 \u221a \u239e \u239f \u23a0 \u2212 \u03be (7) B. Mei et al. Precision Engineering 69 (2021) 48\u201361 where k1 = vbh1vr1 + vbh2vr2, k2 = vbh2vr1 \u2212 vbh1vr2, k3 = aT 1vr\u2212 vbh3vr3 and \u03be = arctan ( k1 k2 ) . Combining Eqs. (2) and (7), li is acquired as li = |Rai + h \u2212 bi| (8) The actuation variable of motor in the i-th chain can be expressed as \u03b1si = 2\u03c0 li hs + \u03b1sri (9) where hs = 10 mm/r is thread pitch of the ball screw and \u03b1sri is the selfrotation angle of the ball screw in the i-th chain. As shown in Fig. 3, ubi1 and ubi2 are unit vectors of the axes of universal joints connected to the base in the i-th chain (i = 1, \u2026,5). uai1 and uai2 are unit vectors of the axes of universal joints connected to the spindle in the i-th chain (i = 2,3,4,5). ua12 is the unit vector of the axis of revolute joint connected to the spindle in the 1st chain. \u03b1sri can be acquired by calculating the angle between uai2 and ubi2. In the base reference frame, ubi1 can be expressed as ubi1 = [cos \u03d5bi sin \u03b8bi, sin \u03d5bi sin \u03b8bi, cos \u03b8bi] T (10) where \u03b8bi is the angle between ubi1 and z axis, and \u03d5bi is the angle between x axis and the projection vector of ubi1 on the plane O-xy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.29-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.29-1.png",
        "caption": "Fig. 6.29: Bush and Roller Chain Elements (left), Corresponding Model (lower element of the left side and right)",
        "texts": [
            " Therefore chains, inspite of their larger mass and thus of their larger inertial forces, get a chance. The Figures 6.27 and 6.28 give an impression of two German timing chain systems for high performance cars. Obviously the design and the arrangement of the chains have to follow very restricted space considerations. Widely distributed chains are the bush and roller chains, which we shall consider in this chapter, and with respect to the inverted tooth chains we refer to [111]. The first configurations are applied more in Europe, the second ones in the US. Figure 6.29 depicts a roller chain and a bush chain together with their models we shall use. In the case of the bush chains the teeth of the sprocket contact directly the pins fixed in the tab plates, whereas in the case of roller chains we have an additional rolling element reducing the friction in the toothroller-contact by rolling without sliding, at least approximately. The external elements comprising two tab plates and two pins do not have contact with the sprocket teeth. Typical chain pitches are 7 mm, 8 mm and 9",
            " This force element is composed of a spring with the very low spring coefficient cTD and the damping coefficient dTD (Figure 6.35). Depending on the relative velocity in the normal direction nTD we assume for negative values a high damping coefficient, for positive values a low damping coefficient. We shall discuss these tension devices in a separate chapter. Contact between a Link and a Sprocket To describe the contact between a link and a sprocket we have to distinguish the two types of links. For a roller chain the contact is realized by the rollers rotating around the pin of the roller chain (Figure 6.29), for a bush chain the bush comes directly into contact with the sprocket. Keeping in mind that a link is modeled as a rigid body, we have no elasticity between the two contact points of a bushing link. To the next link with contact there are two spring elements of the two joints. In reality however the elasticity of the chain plate acts between each contact. To consider these effects, we suppose that each link has one contact to the sprocket. Because of the fact, that we do not deal with chain rollers, we define a contour circle with the diameter of a chain roller seated in the reference point HL of a link (Figure 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.14-1.png",
        "caption": "Fig. 7.14: Time-Optimal Topology with Forces at the Gripper for a Circular Path [185]",
        "texts": [
            "46) The magnitudes are: s path coordinate, s\u0307 path velocity, M \u2208 IRf,f mass matrix, Mi the i-th row of M, q = qr \u2208 IRf generalized coordinates of the \u201drigid\u201d manipulator, \u2202V\u2202qi mainly gravitaional forces, FG0 forces at the gripper, JTi Jacobian from workspace into configuration (joint) space, FC0 friction force along the path, n surface normal, vrel relative tangential velocity along the path (|vrel| = s\u0307), Ti(s) torque in joint (i). The relations (7.46) represent a basis for time-optimization according to the preceding sections, but now for given trajectories with prescribed forces at the gripper. Such forces posses a considerable influence on the time-optimal 7.2 Trajectory Planning 437 results. Figure 7.14 gives an example for a circular path parallel to the y-zplane, being tracked by a manipulator with five revolute joints. The numerical results come from [117] and [223]. The zero force solution (F=0) includes three critical points (saddle points). The maximum velocity as well the timeoptimal curves are symmetrical with respect to the s=0.5 point. Applying a negative force, which means pushing down the gripper, results in a very slow starting movement of the manipulator due to the negative retarding force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000025_j.jmsy.2020.06.019-Figure23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000025_j.jmsy.2020.06.019-Figure23-1.png",
        "caption": "Fig. 23. Workpiece of exhaust-driven turbocharger.",
        "texts": [
            "28 % higher due to cutting heat, machine tool precision [52] and cutting tool angles. The relevant parameters should be adjusted according to the test result. In order to evaluate and compare the aerodynamic performance of various CI workpieces, CI_FFSB and CI_DRSB, an exhaust-driven turbocharger is designed and assembled for performance test, which consists of compressor housing, turbine housing, a rotor system and other components. Furtherly, the rotor system is comprised of a CI and a turbine. The workpiece of exhaust-driven turbocharger is demonstrated as Fig. 23. Fig. 17. Comparison of entropy distribution of S2 section in meridian plane. Experimental setup As shown in Fig. 24, the hot gas test stand accommodates the exhaust-driven [53] turbocharger at Weifu Tianli Turbocharging Technology Co. Ltd. Lab [54,55]. The test instrumentation consists of two thermocouple sensors distributed in the compressor inlet and outlet, a pair of orthogonally positioned speed sensors [56] attached to the specific nut at the compressor end to measure rotor speed. The pressure and temperature at the air inlet/outlet of the turbine and compressor are displayed to better monitor the test operation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.6-1.png",
        "caption": "Fig. 6.6: Capacitive force sensor made of silicon. According to [Desp93]",
        "texts": [
            " By applying cyclically thermal energy to the device, the mem brane starts to resonate. The main advantage of this measurement principle is that the transmission of the measured value in form of a frequency is prac tically noiseless and the signals can be digitally processed. In the next sec tions we will introduce some interesting prototypes and construction concepts of miniaturized pressure sensors. The order in which they are brought does not suggest a rating. Capacitive pressure sensor A capacitive sensor is shown in Figure 6.6. The electrodes are made up of a planar comb structure. Here, the applied force is exerted parallel to the sen sor surface. In force sensors which use membranes, the force is usually applied perpendicular to the sensor surface. Here, nonlinearity and cross-sen sitivity may cause problems. In the device described here, the sensor element mainly consists of two parts: first, a movable elastic structure which trans forms a force into a displacement, and second, a transformation unit con sisting of the electrodes which transform the displacement into a measurable change of capacitance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure24-1.png",
        "caption": "Fig. 24. Contact and bending stresses for version 1 of face-gear drive, generated by an edged-top shaper.",
        "texts": [],
        "surrounding_texts": [
            "The finite element analysis has been performed for two versions of face-gear drives of common design parameters represented in Table 3. The versions correspond to face-gear drives with conventional and rounded fillet, respectively (Fig. 4). The finite element mesh of five pair of teeth of version 2 is represented in Fig. 22. Elements C3D8I [5] of first order enhanced by incompatible modes to improve their bending behavior have been used to form the finite element mesh. The total number of elements is 67,240 with 84,880 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Fig. 23 shows the whole finite element model of the gear drive. Figs. 24 and 25 show the maximum contact and bending stresses obtained at the mean contact point for gear drives of two versions of fillet (see Fig. 4). It is confirmed that the bending stresses are reduced more than 10% for the face gear generated with a rounded-top shaper in comparison with the face gear generated with a edged-top shaper. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs. 24 and 25). The obtained results show the possibility of an edge contact in face-gear drives by application of involute pinion. Avoidance of edge contact requires the changing of the shape of the pinion profiles. Fig. 26 illustrates the variation of bending and contact stresses of the gear and the pinion during the cycle of meshing. The stresses are represented as functions of unitless parameter / represented as / \u00bc /P /in /fin /in ; 06/6 1: \u00f032\u00de Here /P is the pinion rotation angle; /in and /fin are the magnitudes of the pinion angular positions in the beginning and the end of the cycle of meshing. The unitless stress coefficient r (Fig. 26) is defined as r \u00bc rP rPmax ; jrj6 1: \u00f033\u00de Here rP is the variable of function of stresses, and rPmax is the magnitude of maximal stress. The increase of contact stresses during the cycle of meshing is caused by the edge contact."
        ]
    },
    {
        "image_filename": "designv10_2_0000784_bf02288899-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000784_bf02288899-Figure2-1.png",
        "caption": "FIG. 2",
        "texts": [
            " The plotting of centroid axes is simply accomplished by laying a sheet of paper on the board and locating the points by means of the grids on the underlying graph paper, which can be seen plainly. The two axes so plotted may be rotated by turn ing the sheet until the horizontal and vertical graph lines which intersect at the origin are located in the desired positions relative to the plot on the sheet. The next axes are then drawn using the T square and triangle. When a rotation is planned with two factors, each of which has already been plotted, e.g., 1st and IlI2 in Figure 2, the procedure is as follows: (1) In the lower left-hand portion of the board adjust the sheet of paper on which the last rotated plot for one of the factors appeared. I t does not matter , of course, wha t other factor is plotted on the same * This method of holding the papers in place was suggested by Sg~ J. Booty. I S represents the fifth rotation of centroid axis I. sheet. The sheet is so adjusted that the rotated axis of the factor is parallel to the vertical lines on the graph paper beneath. See factor III~, in Figure 2. (2) Then, in the upper r ight-hand portion of the board, adjus t the sheet on which the last rotated plot for the second 'factor appears so tha t the axis of the factor is parallel to the horizontal lines in the graph paper. See Fac to r 15, in Figure 2. (3) Next adjust a new sheet so that all the test loadings projected horizontally to the r ight from the lower plot, and projected vertically downward from the upper plot will fall on the paper. See :Figure 2. (4) Using the T square and triangle, draw horizontal and vertical axis lines on the new sheet a s continuations of the desired axes on the two previous plots. Draw these lines lightly to facilitate the perceptual discrimination between the plotted axes and the rotated axes which wilt later be drawn with heavier lines. (5) Now plot the position of each test on the new sheet. F i rs t ad jus t the hairline on the T square so that it passes through the point representing the test number which is farthest upward on the lower plot, e.g., variable 9 in Figure 2. Then adjust the vertical hairline of the triangle so that it passes through the point representing the same number on the upper plot. (6) Inser t a pencil in the hole in the triangle and mark the position of the test on the new plot. Record the number of the test. (7) Move the T square hairline downward until it passes through the next test point on the lower plot, e.g., variable 1 in Figure 2. (8) Then adjust the vertical hairline of the triangle to pass through the corresponding point on the upper plot. (9) Mark the position of this test on the new plot and record its number. (10) Continue in this manner until all test loadings have been projected to the new sheet. (11} When the rotation has been determined, draw the new axes with a heavier line than those for the original axes. (12) Label the new axes. On the old sheets indicate by a cross or a check mark the axes which have now been rotated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000751_s00170-021-07807-8-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000751_s00170-021-07807-8-Figure8-1.png",
        "caption": "Fig. 8. The typical parts manufactured by HDMR system [144, 145, 148, 151\u2013153]",
        "texts": [
            " Support vector vachines [138] It uses an optimal linear separating hyperplane to discriminate training samples in a multidimensional feature space. Cluster analysis [132] (1) Sample data is selected and define the set of variables or features that characterize the entities. (2) Computation of the similarities among the data. (3) The cluster analysis method is used to create groups of similar objects based on data similarities. (4) Validation of the resulting cluster solution. the same time, the system has been successfully applied to the manufacturing of the parts in Fig. 8. For a Ti-6Al-4V component, this HDMR system consumes only 35% of the energy of conventional approaches. The micro-rolling technology increases the energy efficiency of traditional forging by more than 150 times [151]. At the same time, the columnar to equiaxed transition (CET) of HDMR processing shows superior performance in tensile strength and plasticity [16, 152]. The demand of the integrated, and lightweight metal parts with complex structures gradually increase in various industrial sectors like aerospace, nuclear power, marine, and others"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.14-1.png",
        "caption": "Fig. 3.14: Sliding and Static Friction",
        "texts": [],
        "surrounding_texts": [
            "being composed of compression and expansion phases (Figure3.13). The forces governing this deformation depend on the initial dynamics and kinematics of the contacting bodies. The impulsive process ends when the normal force of contact vanishes and changes sign. The condition of zero relative distance cannot be used as an indicator for the end of an impact, because the bodies might separate in a deformed state. In the general case of impact with friction we must also consider a possible change from sliding to sticking, or vice versa, which includes frictional aspects as treated later. In the simple case of only normal velocities we sometimes can idealize impacts according to Newton\u2019s impact laws, which relate the relative velocity after an impact with that before an impact. Such an idealization can only be performed if the force budget allows it. In the case of impacts by hard loaded bodies we must analyze the deformation in detail. Gear hammering taking place under heavy loads and gear rattling taking place under no load are typical examples [200]. As in all other contact dynamical problems, impacts possess complementarity properties. For ideal classical inelastic impacts either the relative velocity is zero and the accompanying normal constraint impulse is not zero, or vice versa. The scalar product of relative velocity and normal impulse is thus always zero. For the more complicated case of an impact with friction we shall find such a complementarity in each phase of the impact. A collision with friction in one contact only is characterized by a contact condition of vanishing relative distance and by two frictional conditions, either sliding or sticking (Figure (3.14)). From the contact constraint rD = 0 we get a normal constraint force FN which, according to Coulomb\u2019s laws, generates friction forces. For sliding FTS = \u2212\u00b5FNsgn(vrel), and for stiction FT0 = \u00b50FN , where \u00b5 and \u00b50 are the coefficients of sliding and static friction, respectively. Stiction is indicated by vrel = 0 and by a reserve of the static friction force over the constraint force, which means \u00b50|FN | \u2212 |FTC | \u2265 0. If this friction reserve becomes zero, the stiction situation will end, and sliding will start again with a nonzero relative acceleration arel. Again we find here a complementary behavior: Either the 3.4 Multibody Systems with Unilateral Constraints 133 relative velocity (acceleration) is zero and the friction reserve is not zero, or vice versa. The product of relative acceleration and friction reserve is always zero. Things become more complicated if we consider multiple contacts for a multibody system with n bodies and f degrees of freedom. In addition we have nG unilateral contacts where impacts and friction may occur. Each contact event is indicated by some indicator, for example, the beginning by a relative distance or a relative velocity and the end by a relevant constraint force condition. The constraint equation itself is always a kinematical relationship. If a constraint is active, it generates a constraint force; if it is passive, no constraint force appears. In multibody systems with multiple contacts these contacts may be decoupled by springs or any other force law, or they may not. In the last case a change of the contact situation in only one contact results in a modified contact situation in all other contacts. If we characterize these situations by the combination of all active and passive constraint equations in all existing contacts, we get a huge combinatorial problem by any change in the unilateral and coupled contacts. Let us consider this problem in more detail [200]. Figure (3.15) shows ten masses which may stick or slide on each other. The little mass tower is excited by a periodically vibrating table. Gravity forces and friction forces act on each mass, and each mass can move to the left with v\u2212, to the right with v+, or not move at all. Each type of motion is connected with some passive or active constraint situation. Combining all ten masses, each of which has three possibilities of motion, results in 310 = 59, 049 possible combinations of constraints. But only one is the correct constraint configuration. To find this one configuration is a crucial task by combinatorial"
        ]
    },
    {
        "image_filename": "designv10_2_0000895_j.addma.2021.102019-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000895_j.addma.2021.102019-Figure14-1.png",
        "caption": "Fig. 14. The contour plot of stress (X-component and Y-component) at 23% and 42% hot rolled for the WAAM AA2196 Al\u2013Li plate: 23% hot deformation (a,b); 42% hot deformation (c,d).",
        "texts": [
            " At a lower L/H ratio, the larger deformation is concentrated in the surface area of the plate, the smaller deformation occurs in the central area of the plate, and the central area of the plate may be subjected to tensile stress, which results in longer microporosities in the central area. In the case of a high L/H ratio, although the pressure in the surface area of the sheet is higher than in the center area, the higher compressive stress can also be transferred to the center area of the sheet, resulting in the closure of the microporosity in the center area [49]. When the deformation is 23% in Fig. 14(a) and (b), the tensile stress at the surface area in the X-axis of the specimen is 500\u2013600 MPa, and the tensile stress in the center area is very small, only 0\u2013100 MPa, the central area is pulled by the larger stress in the former area, resulting in the elongation of the microporosities in the central area, and the compressive stress in the central area in the Y-axis is relatively small compared to the sample with 42% hot deformation. As a result, the central region microporosities are elongated in the X-axis and cannot be closed in the Y-axis, which is consistent with the experimental observations. As the number of deformation increases to 42% (Fig. 14(c) and (d)), the central region of the specimen is subjected to large tensile stress (100\u2013200 MPa) in the X-axis direction, while relative to 23% hot deformation, a large deformation occurs in the Y-axis direction and the central region compressive stress reaches 800 MPa, which leads to the closure of most of the microporosities, the large microporosities flatten out due to the large compressive stress at 42% hot deformation, and if the microporosities are completely closed, the amount of rolling C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-8-1.png",
        "caption": "Figure 2-8. Typical power factor for four-pole and eight-pole induction motors over a range of power ratings.",
        "texts": [
            " Inductance parameters, being proportional to area over length, will increase by the factor k, while the winding resistances being proportional to length over area will be divided by k [14]. Thus, in larger motors, the leakage inductance will be increased. From equation 2.7, this increase in inductance tends to decrease the maximum available torque and also combines with the decrease in resistance to decrease the slip frequency at which this maximum torque occurs. The magnetizing inductance will be increased in larger motors, and the magnetizing current will therefore be a smaller component of the supply current. The power factor of the motor increases with rating as shown in Figure 2-8. Note also the reduction in power factor as pole number is increased. Induction motors are simpler in structure than commutator motors. They are more robust and more reliable. They require little maintenance. They can be designed with totally enclosed rotors to operate in dirty and explosive environments. Their initial cost is substantially less than for commutator motors and their efficiency is comparable. All these features make them attractive for use in industrial drives. The majority of induction motors currently in use are in essentially constant speed applications",
            " The eddy current iron loss can be minimized by appropriate choice of the iron lamination material and also by designing with a smaller number of wider teeth per pole. In addition, the rate of change of tooth flux density can be reduced by beveling the magnet edges. Typically, the PM motor core loss may be in the range 1.25-2.0 times that of a machine with near-sinusoidal flux distribution. The PM motor can be operated at unity power factor, while the induction motor will always have a lagging power factor, typically in the range 0.8-0.9 for four-pole motors and lower for larger numbers of poles (Figure 2-8). For the same input power rating, the ratio of the stator currents of the PM and induction motors will be this power factor. Thus, the ratio of the stator winding losses for the PM and induction motors will be the induction motor power factor squared. For the same power ratings, the total losses in the PM motor will typically be about 50-60% of those of the induction motor [28]. Predicted values of PM motor efficiency are about 95-97% for ratings in the range 10-100 kW as compared with 90-94% for induction motors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure7.22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure7.22-1.png",
        "caption": "Fig. 7.22: Control of a rod balancer. According to [Rojas93]",
        "texts": [],
        "surrounding_texts": [
            "\"responsible\" for one subarea. Figure 7.21 shows the spread of a 2-dimensio nal Kohonen network after 0, 20, 100, 1000, 5000 and 100,000 training cycles ."
        ]
    },
    {
        "image_filename": "designv10_2_0003391_j.fss.2004.05.008-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003391_j.fss.2004.05.008-Figure1-1.png",
        "caption": "Fig. 1. Two inverted pendulums on carts.",
        "texts": [
            " However, controller (36) for the much more general nonlinear system (1) is obtained via recursive design, and the resulting closed-loop control system can only achieve the uniform ultimate bound performance. 5. A simulation example We consider two inverted pendulums connected by a moving spring mounted on two carts [13]. We assume that the pivot position of the moving spring is a function of time that can change along the length l of the pendulums. The motion of the carts is specified. For this example we specify this motion as sinusoidal trajectories. The input to each pendulum is the torque ui applied at the pivot point. See Fig. 1 for illustration. The dynamic equations of the inverted double pendulums on carts can be described as \u03081 = g cl 1 + 1 cml2 u1 + N21( 1, \u03071) + [ k(a(t) \u2212 cl) cml2 (\u2212a(t) 1 + a(t) 2 \u2212 y1 + y2) ] , (52) \u03082 = g cl 2 + 1 cml2 u2 + N22( 2, \u03072) + [ k(a(t) \u2212 cl) cml2 (\u2212a(t) 2 + a(t) 1 \u2212 y1 + y2) ] , (53) where i and \u0307i are the angles and angular velocities of the pendulums, respectively, with respect to vertical axes, u1 and u2 are the control torques applied to the pendulums, c = m/(M + m), k and g are spring and gravity constants, respectively, N21( 1, \u03071) and N22( 2, \u03072) are uncertain terms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000831_physrevlett.126.108002-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000831_physrevlett.126.108002-Figure1-1.png",
        "caption": "FIG. 1. Robots and the interactive LED light board environment. (a) Each robot has one microcontroller. A robot base, of diameter of 65 mm, has four RGB sensors for detection of light color from the LED light board. The movement of each robot is controlled by two independent pulse-width modulated gear motors. (b) The four RGB sensors are used to codetect gradient vectors from the underneath resource landscape. (c) The LED light board of dimension 4.0 \u00d7 4.0 m2 and 2.5 mm pitch supplies complex and dynamic environment for the robot communities. (d) The rules and parameters that control landscape resource and agents consumption property.",
        "texts": [
            " We present here a robot swarm that emulates natural collective ensembles in that they change their environment by their very presence, and observe collective state changes as a consequence of their ability to self-modify their environment and respond to that self-modification. Two of the innovations that distinguish our biological ecology based robot swarms from more conventional active matter systems [15] are the dynamic resource landscape and how the robots self-modify the landscape. They move over a 4.0 \u00d7 4.0 m2 light-emitting diode (LED) light board. Each robot has four downward facing single pixel RGB sensors in the base, which determine local light intensities and the gradient of the resource (Fig. 1). The sensors are at opposing quadrants on the base of the robot and detect corresponding intensities from a 2.5 mm LED pitch. Positions of the robots are observed by an overhead infrared CCD camera with resolution of 800 \u00d7 800 pixels. Each pixel of the camera sees a single 2.5 mm LED element of the light board; thus, positions in this Letter are given PHYSICAL REVIEW LETTERS 126, 108002 (2021) Editors' Suggestion Featured in Physics 0031-9007=21=126(10)=108002(5) 108002-1 \u00a9 2021 American Physical Society conveniently in terms of pixel coordinates and speeds are given in pixels/s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000604_j.mechmachtheory.2019.103627-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000604_j.mechmachtheory.2019.103627-Figure4-1.png",
        "caption": "Fig. 4. The modeling of an arbitrary real bearing fault: (a) the general view of defect, (b) the specific shape of defect, (c) the defect shape fitted by spline curve.",
        "texts": [
            " Through a large number of statistical studies, it is found that the peaks and troughs of the fault points satisfy the normal distribution. Assume that there is no contact deformation in the fault region, and the heights of fault points at the peaks are randomly produced via the normal distribution in simulation, given the maximum height. Then a spline curve fitting method for the peak points is proposed to approximate the profile of damage, and an additional displacement excitation is applied to characterize the excitation of the rolling element. The modeling of an arbitrary real bearing fault is illustrated in Fig. 4 . In Fig. 4 (a), the fault area boundary is denoted by the damage length L , damage width B , and damage depth H . In Fig. 4 (b), L is the fault length along the bearing rolling direction; H max is the maximum fault height; A denotes the starting point of the fault region; B denotes the end point of the fault region; \u03b8d represents the effective angle region of the fault in the circumferential direction; h k represents the additional displacement excitation of the rolling element caused by the local fault. In this paper, cubic spline is used to fit the peak points in the fault area, and then the fitting function is defined as: f ( l ) = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 f 1 ( l ) , l \u2208 [ l 0 , l 3 ] f 2 ( l ) , l \u2208 [ l 3 , l 7 ] . . . f i ( l ) , l \u2208 [ l 4 i \u22125 , l 4 i \u22121 ] . . . f n ( l ) , l \u2208 [ l n \u22123 , l n ] (15) where f i (l) = A i + B i (l \u2212 l i ) + C i (l \u2212 l i ) 2 + D i (l \u2212 l i ) 3 , (i = 1 , 2 , ..., n \u2212 1) ; l i (i = 0 , 1 , ..., n ) is peak point of the fault contour ( l 0 is the first peak point while l n is the last peak point); A i , B i , C i , D i is the fitting parameter; l is the arc length of the rolling element movement. For the damage shown in Fig. 4 (b), its contour obtained by fitting is shown in Fig. 4 (c). For the convenience of derivation, a coordinate system is built up in Fig. 5 . In this figure, \u03d5d represents the angle between the failure position and the X-axis, \u03b81 is the initial angle between the first rolling element and the X-axis, \u03b8 k is the real-time angle position of the kth rolling element, and \u03d5\u03b8 is the angle between the first roller and the fault position. When there is a local damage in the inner ring or out ring, the impulsive effect will occur when the rolling element passes through the damaged area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003961_s11044-007-9088-9-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003961_s11044-007-9088-9-Figure2-1.png",
        "caption": "Fig. 2 Computation of dual angle between two line vectors",
        "texts": [
            " (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 \u03b8 s + 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. Table 1 Computational cost of operations with dual numbers Line vector A\u0302 \u00b7 B\u0302 A\u0302 \u00d7 B\u0302 Skew ab cos \u03b8\u0302 abS\u0302 sin \u03b8\u0302 Incident (s = 0) ab cos \u03b8 abS\u0302 Parallel (\u03b8 = 0) ab \u03b5ab s Coaxial (\u03b8 = s = 0) ab 0 5.2 Dual angle between 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 \u2016A\u0302i\u2016 (i = 1,2). (8) 2. Compute their cross product E\u03023 = E\u03021 \u00d7 E\u03022 \u2016E\u03021 \u00d7 E\u03022\u2016 . (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. 5.3 Sum of two dual vectors With reference to the geometry of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.16-1.png",
        "caption": "Fig. 7.16: Elastic Manipulator in Contact with a Surface",
        "texts": [
            "15), defined originally in the element-fixed coordinates (E) by Er can be written in the body-fixed system (R) by the relation Rrtotal = R(r0 + x + re) + ARE \u00b7 Er (7.47) with the transformation matrix ARE from (E) to (R). Considering only small elastic deformations the transformation ARE can be approximated by (see section 2.2.8 on page 47) ARE \u2248(E + \u03d5\u0303e) + O(2) \u2208 IR3,3, ARE \u2248  1 \u2212\u03b4 \u03b2 \u03b4 1 \u2212\u03b1 \u2212\u03b2 \u03b1 1  \u2248  1 \u2212v\u2032 \u2212w\u2032 v\u2032 1 \u2212\u03b1 w\u2032 \u03b1 1 + O(2) (7.48) with the following magnitudes: E the identity matrix and (\u00b7)\u2032 derivation with respect to x, for example v\u2032 = dv dx . Considering in a first step manipulators with tree-like structure and altogether j joints (Figure 7.16), the position vector rp from the inertial frame to the contact point can be written in the form (see equations (7.4)) rp = j\u2211 i=1 { i\u220f k=1 [E + \u03d5\u0303e]k\u22121 \u00b7AEk\u22121Rk } Lk\u22121 \u00b7 (xi + rei)Li , (7.49) 7.2 Trajectory Planning 439 where Li refers to the total lenght ofthe link i and AEk\u22121Rk is the transformation from Rk to Ek\u22121, which for revolute joints is the usual elementary rotation matrix. With the help of the vectors defined in Figure 7.15 the absolute translational and rotational velocities of a mass element come out with vEi =v0i + r\u0307ei + \u03c9\u03030i(xi + rei), \u03c9Ei =\u03c90i + \u03d5\u0307ei, } Ri - frame (7",
            " In the last case the additional joint equations of motion write IM \u00b7 q\u0308MI = T0\u2212 Kgear igear ( qMI igear \u2212 qME ) . (7.57) Figure 7.17 illustrates the corresponding model, see also Figure 7.3. The magnitudes Kgear and igear denote the joint stiffness and the gear transmission ratio, respectively, qMI and qME are the internal and external joint coordinates, IM is the motor moment of inertia and T0 the actuating motor torque. A manipulator coming into contact with its environment forms a closed kinematical loop with special properties (see Figure 7.16). Considering for example manufacturing processes usually requires also the inclusion of some given forces or torques at the end-effector. Let us first consider the holonomic constraint accompanying such a configuration in the form \u03a6(q, t) = 0 \u2208 IRm. For later convenience we differentiate this constraint twice with respect to time and come out with \u03a6\u0308 = ( \u2202\u03a6 \u2202q ) q\u0308 + d dt ( \u2202\u03a6 \u2202q ) q\u0307 + d dt ( \u2202\u03a6 \u2202t ) = 0. (7.58) Substituting ( \u2202\u03a6 \u2202q ) = (w1,w2, \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7wm)T we arrive at the general constraint equation on the velocity level wT k (q)q\u0308 + \u03b6k(q, q\u0307) = 0, wk \u2208 IRf , (k \u2208 (1, 2, \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7m)), (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003217_70.833196-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003217_70.833196-Figure3-1.png",
        "caption": "Fig. 3. The platform.",
        "texts": [
            "i ui]: (14) According to the (5), the dynamic equation for a leg of the Gough\u2013Stewart platform manipulator can be written as Ai _yi = Di (15) where Ai = 2 k=1 mi;kvi;k T vi;k + wi T Ji;kwi Di = fi biyi and fi = 2 k=1 vi;k T Fi;k bi = 2 k=1 mi;kvi;k T _vi;k + wi T !iJi;kwi: In (15), mi;k is the mass of each part. Fi;k including gravity, actuator forces, friction forces, and so on, is the resultant force acting on each part. Ji;k is the inertia dyadic matrix of two parts relative to the center of mass in local frames. B. Dynamics of the Platform The platform is shown in the Fig. 3. The local frame of the platform is denoted as xpypzp with its origin located at pointOp: The platform and legs are connected at pointPi (i = 1; 2; ; 6): Let rp;i be the position vector of Pi in xpypzp; and rG be the position vector of the gravity center G of platform (including the payload) in xpypzp: Components of the angular and linear velocities of platform in X0Y0Z0 are used as generalized speeds yp = [!p;x !p;y !p;z p;x p;y p;x] T : (16) Because the platform is a single rigid body, its dynamic equations can be written as follows, directly: Ap _yp = Dp (17) where Ap = 0Jp mp 0rG 0rG mp 0rG mp 0rG mp13 3 Dp = Mp mp 0rG a\u0302 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.31-1.png",
        "caption": "Fig. 11.31 Cornering properties and friction ellipse [35]",
        "texts": [
            " When the cornering force reaches the maximum Fy max at slip angle amax, Fy max is given by Fmax y \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lFz\u00f0 \u00de2 F2 x q : \u00f011:108\u00de Assume that the cornering force decreases at the same rate for all slip angles as shown in the left figure of Fig. 11.30. When the fore\u2013aft force Fx is applied to a tire, Eq. (11.108) can be rewritten as 11.4 Cornering Properties for a Large \u2026 747 Fy Fy0 \u00bc A A0 \u00bc Fmax y lFz \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lFz\u00f0 \u00de2 F2 x q lFz ; \u00f011:109\u00de Furthermore, Eq. (11.109) can be rewritten as Fx lFz 2 \u00fe Fy Fy0 2 \u00bc 1: \u00f011:110\u00de The relationship between the cornering force Fy and fore\u2013aft force Fx at slip angle a0 can be expressed by the ellipse shown in Fig. 11.31a, which is called the friction ellipse. At the slip angle amax where the cornering force is a maximum, the friction ellipse becomes the friction circle. Figure 11.31b shows that cornering properties with the combined slip can be estimated from only data of the friction circle. Comparing Fig. 11.31b with the measurements in Fig. 11.29, the cornering 748 11 Cornering Properties of Tires properties can be expressed by the friction ellipse except in the region of a high slip ratio. The drawback of the friction ellipse is that it cannot express the cornering properties at a high slip ratio. 11.4.2 Sakai\u2019s Model (1) Fundamental equations Sakai [2] developed a tire model for cornering properties under the combined slip condition with a large slip angle and large slip ratio by applying the same revisions used in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003350_tra.2003.808865-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003350_tra.2003.808865-Figure1-1.png",
        "caption": "Fig. 1. ODIN. (a) ODIN in a test pool. (b) Positioning of thrusters and a manipulator of ODIN from a top view.",
        "texts": [
            " The proposed control scheme and the structure and learning algorithm of R-SANFIS are presented in Section III. In Section IV, computer simulations of the proposed control scheme with recurrent neuro-fuzzy control and the PD control are conducted and its performance is compared with an adaptive controller to validate the effectiveness of the proposed approach. Finally, conclusions are summarized in the last section. ODIN is an autonomous underwater vehicle developed at the Autonomous Systems Laboratory of the University of Hawaii [6], [24], see Fig. 1(a). It is a closed-framed sphere with eight thrusters and one manipulator, see Fig. 1(b). ODIN is capable of maneuvering with six-DOF motion: sway, surge, heave, roll, pitch, and yaw. ODIN\u2019s on-board assembly is a compact and efficient unit located on the upper mounting dish within the spherical hull. The overall architecture was designed for easy expansion to include additional components. Its on-board computer is a Motorola 68 040 CPU running at 32 MHz clock speed with VxWorks real time operating system. Four vertical thrusters and four horizontal thrusters, as shown in Fig. 1(b), are used for the omni-directional motion. The vertical thrusters allow instantaneous coupled motion of pitch, roll, and heave. Because of the thruster configuration, ODIN possesses inherent thruster redundancy. Vertical motion is possible using all vertical thrusters or just two thrusters. Similarly, the four horizontal thruster configuration possesses the capabilities of providing the , and yaw motion. Also, all six DOF motion is possible with all eight thrusters or just six thrusters (three horizontal thrusters and three vertical thrusters)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000625_j.rcim.2020.102084-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000625_j.rcim.2020.102084-Figure5-1.png",
        "caption": "Fig. 5. The six different unoptimised configurations and the optimised configuration. The optimal configuration was slightly different among ten subjects, therefore the joint angle values are reported as: mean \u00b1 std.",
        "texts": [
            " During the experiment we assumed that the task execution movement is within a close proximity of the optimised solution and that these deviation are small. However, if considerable deviations are necessary to perform the task, re-optimisation is required. The experimental procedure was divided into two stages (as shown in the right of the Fig. 4). In the first stage, the subjects had to perform the given task in six different configurations of the arm, following the outline of the range of risk in the shoulder and elbow on Rapid Entire Body Assessment (REBA) [59]. See Fig. 5 for details and illustrations of the selected configurations. In the second stage, the proposed method was used to select the optimal working configuration in terms of overloading joint torques and given constraints (manipulability capacity, etc.). The on-line acquisition of the human body position data was performed using the MVN Biomech system. This data was then used to calculate vector x0 and matrix Bthat were necessary for real-time calculation of CoP in (2) and the human overloading joint torque vector in (8)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000709_s10439-019-02388-w-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000709_s10439-019-02388-w-Figure1-1.png",
        "caption": "FIGURE 1. (a) Designed structure of the proposed force sensor and the fiber arrangement configuration. (b) Sarrus linkage produces a linear motion from a hinged mechanism.",
        "texts": [
            " The structural optimization design enabled by the simulation has been conducted to further improve the sensor\u2019s sensitivity. The optimized sensor design has been prototyped and calibrated by static calibration experiments. Further dynamic force stimulation experiments, in vitro phantom experiments and ex vivo experiments have validated the effectiveness and capacity of the presented sensor design during tissue palpation. The detailed mechanical structure design and assembly drawing of the proposed palpation sensor have been illustrated in Fig. 1a. This sensor is mainly composed of a force-sensitive flexure and one suspended optical fiber inscribed with an FBG element, a threaded contact head and a sensor holder connector. The force-sensing flexure uses a miniature and modified parallel mechanism configuration, and arranges four flexure hinges along its circumference with a uniform interval of 90 to form a symmetrical structure. It is designed with a length of 4.9 mm, and has an inner and outer diameter of 3.8 mm and 5 mm respectively. The optical fiber has been tightly suspended, and its two ends are firmly glued inside the small grooves which are made at the central axis of the designed flexure",
            " The FBG element is located at the neutral axis of the sensor, therefore avoids cross-talk interferences from radial directions. The flexure design has been proposed and prototyped through the configuration synthesis of Sarrus linkage by using a rigid-body replacement method.25 The adopted Sarrus linkage mechanism typically involves using spatial multiple-bar linkages with rotation joints, and converts the constrained circular motion to generate a straight-line motion without using any reference guideways,3,5 as shown in Fig. 1b. Such advantages enable the movable connection upper plate to produce the translational movement with a large travel range and an excellent linearity due to the special constraints of the mechanism.3,5 This presented approach aims to replace the kinematic pairs of the rigid Sarrus linkage in a large size by using the miniature flexure hinges. The designed flexure based on modification and improvement of the large Sarrus linkage can effectuate the equivalent functions with a miniature size. The detailed flexure design is labeled in the blue rectangle, as illustrated in Fig. 1a. The corresponding structural parameters include 0.5 mm for the circular cutting diameter of flexure hinges, 35 for the angle between the flexure linkage and the horizontal plane, and 0.45 mm for the flexure hinge\u2019s BIOMEDICAL ENGINEERING SOCIETY width. Such design preserves the inherent properties of Sarrus linkage and thus possesses remarkable superiorities in terms of large axial deformation capacity, and an excellent linear force\u2013deformation relationship. When the axial direction force Fz is exerted on the distal tip, the embedded FBG element experiences the force-caused strain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.4-1.png",
        "caption": "Fig. 6.4: Elastic Coupling",
        "texts": [
            " The spatial possible motion of the joint can be described by (\u03a6iqJi ) with relative displacements qJi in the nonconstrained directions of the joint i. A complementary matrix \u03a6ci \u2208 IR6,6\u2212fi exists for the constrained directions of the joint. Always \u03a6Ti \u03a6 c i = 0, and the constraint forces are written as fJi = \u03a6ci\u03bbi , \u03bbi \u2208 IR6\u2212fi . (6.5) The Lagrange multipliers \u03bb follows from d\u2018Alembert\u2018s principle and a Lagrangian treatment of the equations of motion. Elastic couplings in drivelines are characterized by some force law in a given direction between two bodies (Figure 6.4). The relative displacement and displacement velocity may be expressed by \u03b3k = \u03c8Tk ( \u2212Ckipi +Ckjpj ) , \u03b3\u0307k = \u03c8Tk (\u2212Ckivi +Ckjvj) (6.6) Cki = ( E 0 c\u0303Tki E ) \u2208 IR6,6 . The vector cki follows from Figure 6.4, and c\u0303ki is the relevant skewsymmetric tensor (a\u0303b \u2261 a\u00d7 b). The vector \u03c8k \u2208 IR6 represents a unit vector in the direction of relative displacement. In that direction we have a scalar force magnitude \u03b6k according to the given force law. It can be expressed in the body coordinate frames Hi, Hj (Figure 6.4) by the generalized forces (see section 3.3.5 on page 128) f i = CT ki\u03c8k\u03b6k , f j = \u2212CT kj\u03c8k\u03b6k . (6.7) 6.1 Timing Gear of a Large Diesel Engine 333 As a simple example a linear force law would be written as \u03b6k = c\u03b3k + d\u03b3\u0307k (6.8) Of course, any nonlinear relationship might be applied as well, such as the force law with backlash according to Figure 6.5. Gear meshes with backlash are modeled with the characteristic of Figure 6.5. In this case care has to be taken with respect to the two possibilities of flank contact on both sides of each tooth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.107-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.107-1.png",
        "caption": "Fig. 10.107 Mesh used for the WFEM and BEM calculation. Reproduced from Ref. [59] with the permission of J. Sound Vib.",
        "texts": [
            " [59] analyzed noise radiated from a rolling tire using the WFEM, contact model and BEM to investigate the effect of road roughness on tire/road noise. Figure 10.106 shows a schematic view of Kropp\u2019s tire/road noise model. They employed WFEM (an axisymmetric FEA) for tire vibration, analytical contact model for the external force and BEM for sound radiation. In the beginning, they used a two-dimensional contact model and two-dimensional BEM for the radiation model and then extended the models to three-dimensional models. Figure 10.107 shows the meshes used for the WFEM and BEM calculations where the tire mesh comprises 46 shell elements (for the tire structure) and 20 solid elements (for the tire tread). 10.13 Tire Noise Prediction 685 It was found that tire noise is mainly generated by cross-sectional and circumferential modes (Fig. 10.20) of lower order and that the breathing mode (zeroth circumferential mode) especially has a strong effect around 300\u2013600 Hz. Waki et al. [57] identified noise-radiating parts by considering the sound radiation efficiency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003614_b97525-Figure4.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003614_b97525-Figure4.7-1.png",
        "caption": "Figure 4.7. Z2-symmetric periodic attractors for d = 0, \u03b1 = 0.1, \u039b = 2/9 and (a) \u00b5 = 1.41, R0R1-symmetry; (b) \u00b5 = 1.64, R1-symmetry; (c) \u00b5 = 1.875, R0-symmetry. Courtesy M. Higuera and J. Porter.",
        "texts": [
            " We use this \u039b value to investigate further the dynamics associated with this bifurcation. Along this path the first Hopf bifurcation (at \u00b5 1.106) occurs almost immediately after the birth of the NU branch (see Fig. 4.5). Between this Hopf bifurcation and the leftmost saddle-node bifurcation on the NU branch at \u00b5 2.674 there are no stable fixed points; in this region one can easily find chaotic attractors, such as those shown in Fig. 4.6, as well as a variety of interesting periodic solutions (see Fig. 4.7). 6. Nearly Inviscid Faraday Waves 209 Notice that the periodic orbits in Fig. 4.7 have Z2 symmetry, i.e., they are invariant under one of the reflections: R0, R1, R0R1. Although these particular periodic orbits are somewhat exotic (in the sense that they do not belong to one of the basic families of periodic solutions analyzed below but resemble something like the \u2018multi-pulse\u2019 orbits identified in perturbations of the Hamiltonian problem) there are also sequences of simpler periodic orbits which come close to both O and U . These orbits, characterized by their symmetry (or lack thereof) and by the number of oscillations they experience near O, are related in a fundamental way to the heteroclinic connection U \u2192 O \u2192 U ",
            "8), while they oscillate \u201cout of phase\u201d in the threedimensional case with inversion symmetry. These differences between the standard situation and ours are a direct consequence of the fact that our two-mode truncation is four-dimensional, allowing new types of connection that are not possible in three dimensions. Note that in Fig. 4.8 we have only investigated the first two of the main heteroclinic bifurcations (recall that there are four such bifurcations when \u039b = 2/9) and that there are many periodic solutions (e.g., those of Fig. 4.7) which have not been shown; these may form isolas or terminate at other, subsidiary, connections. In short, the full situation is extremely complex. Since it is the dynamics of the PDE (4.2)\u2013(4.3) that are of ultimate interest, one would like to understand how faithfully their behavior is represented by a truncated set of ordinary differential equations (ODEs). While there is no a priori reason to assume that a finite number of modes can accurately capture the effect of the nonlinear terms, it turns out that in many problems they do (Knobloch, Proctor, and Weiss [1993]; Doelman [1991]; Rucklidge and Matthews [1996])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001205_j.addma.2021.101890-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001205_j.addma.2021.101890-Figure2-1.png",
        "caption": "Fig. 2. (a) Computer aided design of the PBS platform: (b) Cross-section view of the recoater module and the attached CIS unit. The recoater module can mount 2 types of recoater blade: (b1) a metal blade that mimic the design of the EOS DMLS and (b2) a rubber blade from the SLM500 (SLM Solutions). (c) An example of a R powder layer scan at 4800 DPI. Individual powder particles are visible by digital zoom of the raw scan. Since the CIS unit acquires coloured scans, oxidized powders appear in orange/red/blue colour. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " Additive Manufacturing 39 (2021) 101890 are the length and width of an elongated particle, respectively) is indicative of particle elongation, while the circularity factor (denoted by fcirc = 4\u03c0A p2 , where A is the cross-sectional area and p is the perimeter of the particle) is related to the level of irregularity of the particles (including satellites). The micrographs in Fig. 1 shows examples of these morphologies. To perform the recoating experiments, we used a custom-made PBF platform consisting of three main modules: a powder recoater; a contact image sensor (CIS) unit taken from a Canon LiDE 220 flatbed scanner attached to the recoater; and a substrate, whose height and tilt can be adjusted manually. An illustration of the PBF platform is shown in Fig. 2 (a). We first dispensed the powder batch onto the substrate through an open slot-reservoir on the recoater arm (Fig. 2(b)). Subsequently, we triggered the motion of the recoater arm, which is driven by a planetary geared stepper motor (OMC Stepper 17HS15-1684S-PG5) through a timing-belt-driven mechanism. The spreading speed can be adjusted from 0.2 mm/s to 150 mm/s via a programmable electronic circuit board. Since the recoater is driven by a timing belt and a stepper motor, it reaches the targeted velocity instantaneously, without any acceleration or deceleration. Such abrupt motion of the recoater arm had some minor effects on the quality of the powder layer, which we discuss in greater details in Section 4",
            " In this work, we employed the highest resolution allowed by the CIS (4800DPI or 5.3 \u00b5m/pixel), which corresponds to an image acquisition rate of approximately 25 msec/line and a translational speed of 0.2 mm/s. Since the powder layer is stationary when imaged by the CIS, and since the recoater speed is synchronized with the image acquisition rate (i.e., the recoater only moves to the next line when the previous line scan is completed), the acquired images are free from motion blur and distortion. Fig. 2(c) displays an example scan at such resolution where digital zoom into the scan reveals the individual powder particles. Because the recoater speed was fixed at 0.2 mm/s during scanning, it was not possible to spread and scan powder layers simultaneously at Table 2 Powder moisture content, flow behaviour, size and morphology. Powder batch Moisture content (%MC) Flow rate FR (s/50 g) Mean diameter (\u00b5m) Aspect ratio (Ar) Circularity ( f circ) V 0.07 \u00b1 0.002 14.93 \u00b1 0.13 29.86 0.85 \u00b1 0.124 0.927 \u00b1 0",
            " (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) T.-P. Le et al. Additive Manufacturing 39 (2021) 101890 higher recoating velocities. Therefore, we first spread the powder layer at the targeted velocity on the way forward, and then acquired the scan at 0.2 mm/s on the way back. As the recoater blade positions behind the CIS during scan acquisition, it does not disturb the powder layer topography formed during the recoating. We set the powder layer thickness by adjusting the gap between the recoater blade and the substrate (shown in Fig. 2(b)) using a manual zstage with micrometre precision at the centre of the PBF platform substrate (Fig. 2(a)). To ensure that the re-coater arm translation is always parallel to the substrate, we manually adjusted the tilt of the substrate using three screws that connect it to the z-stage. In this work, we used a black anodized Aluminium plate with a surface roughness of 2 \u00b5m as the substrate for powder spreading. The black colour and low reflectivity of the substrate helped minimize spurious light reflections and enhanced the image quality of the captured scans. The recoating experiments in this work included the use of two types of recoater blade: a metal blade made of SS316L (Fig. 2(b1)) and a hard rubber blade (Fig. 2(b2)). The metal blade geometry was inspired by the one used in EOS Direct Metal Laser Sintering (DMLS) systems, while the rubber blade was taken from the recoater module of a SLM500 (SLM Solutions) and attached to our recoater through an adapter. To ensure that the acquired scans are in focus, we mounted the blade to the recoater arm such that the blade edge tip lays within the CIS focal plane. To achieve this configuration, we varied the substrate height to bring it into focus using the adjustable z-stage (Fig. 2(a)) and then fixed the recoater blade to the recoater arm after placing the blade in contact with the substrate surface. Due to the cantilever beam design of the recoater arm, mechanical vibrations are enhanced at the free end of the recoater arm. Throughout our experiments, we noticed that these vibrations generate surface ripples in the regions of the powder layer which lay directly beneath this free end, and that this phenomenon is especially noticeable at high recoating velocities. For this reason, we limit the powder layer analysis to an area (26 mm wide and 130 mm long) that is close to the supported end of the recoater arm (highlighted with red-dash line in Fig. 2(a)), which is less susceptible to mechanical vibrations. To investigate the effects of powder feedstock conditions and recoating strategy on the powder layer quality, we performed a full factorial design of recoating experiments based on three main factors: T.-P. Le et al. Additive Manufacturing 39 (2021) 101890 [A] powder condition, [B] recoater blade type, and [C] recoating velocity. Here, [A] is a three-level factor, [B] is a two-level factor, and [C] is a four-level factor, as detailed in Table 3",
            " By contrast, the rubber blade produces high layer thickness variations at a recoating velocity of 0.2 mm/s (green profile in Fig. 5(e, f)). While the different blades\u2019 materials could play a role on powder spreadability, we found no report in the literature suggesting that it would be the major contribution to the trends seen in Fig. 5. Following the simulation work by Haeri et al. [33, 47], we propose that the different response of powders to the type of recoater blade are instead related to the blade geometry. We suspect that the thin and sharp edge of the metal blade (Fig. 2(b1)) might be the reason why powder flow instabilities are amplified at high recoating velocities, resulting in a more heterogeneous layer thickness along the recoating direction. This effect is more pronounced when using batch RH, which suggests a higher sensitivity of metal blade to powder moisture content. By contrast, the slanted opening, dual-edge and large contact surface area of the rubber blade (Fig. 2(b2)) may provide the combined effect of compressing the powder particles into the powder bed and removing ripples on the layer surface that may originate from powder flow instabilities. This geometry, however, is not beneficial when recoating powders at the lowest velocity (0.2 mm/s), which yields layers with progressively decreasing thickness. Despite being less pronounced, this progressive thickness reduction is visible even in the other experiments at different recoating velocities. We believe this phenomenon to be related to the progressive reduction of the total mass of the powder pile ahead of the recoater blade as the recoating operation proceeds"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.32-1.png",
        "caption": "Fig. 5.32: Geometrical Derivation of the Phase Shift",
        "texts": [
            " The force \u03bbT in radial direction is computed employing the viscous friction coefficient \u00b5v and the relative velocity g\u0307T : \u03bbT (g\u0307T ) = \u00b5vg\u0307T . (5.67) Phase shift is the offset \u2206x of the varying tooth stiffness along the transverse path of contact of a gear train as pictured in figure 5.31. It is of high importance for the parameter excitation in multistage or planetary gears. The curve of the tooth stiffness is always specified for a special point, in this case for the (A) marked position of the first contact point on the line of action as shown in Figure 5.32. Depending on the number of teeth and the geometrical config- uration, which means the tilt of a gear train respective to the antecedent one, the contact point of two engaging tooth profiles will normally not be placed in point A for the starting position. The quotient of the phase shift s12 of Figure 5.32 and the base pitch pt leads to the phase shift \u2206x used for the calculation of the current tooth stiffness. The following equations show the derivation of the phase shift for a single gear train and can be transferred to single stage and Ravigneaux planetary gears. The location of the pitch point C of a mesh can be determined by the pitch circle diameter dw which is depending on axle base and the number of teeth of both gear wheels: rC = r1 + dw1 2 e12 (5.68) Several geometrical characteristics of the toothing define the length gf of the line from the pitch point C to the point of action A rA = rC \u2212 gf n . (5.69) The initial rotation angle \u03d501 in figure 5.32 provides the position of the first tooth of the driving gear 1 versus the y-axis and follows from the prior meshing and the resulting status of the gear wheel. In combination with the position \u03d5A of point A, the following equation calculates the angle \u03d5U1 of the root point of the first tooth within the transverse path of action from A to E \u03d5U1 = 2\u03c0 z1 floor(z1 \u2206\u03d5 2\u03c0 + 1) + \u03d501, \u2206\u03d5 = { \u03d5A \u2212 \u03d501 , \u03d5A \u2265 \u03d501 2\u03c0 + \u03d5A \u2212 \u03d501 , \u03d5A < \u03d501 . (5.70) The function floor(\u2022) rounds the argument down toward the next smaller integer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.14-1.png",
        "caption": "Fig. 5.14 Tire shape and bead tension",
        "texts": [
            "3 Effects of the Tire Shape on Tire Properties 259 The maximum value of cord tension is related to the durability of the cord. The cord tension of the pantograph path tmax c is a maximum at the crown center (r = rA): tmax c \u00bc pp N r2A r2C sin aA : \u00f05:59\u00de The safety factor of the cord is defined by the ratio of the static failure stress and the maximum stress of the cord calculated using the maximum cord tension. The cord density or the number of cords N and the failure stress of a cord are important design parameters in tire design in terms of realizing the target safety factor. Referring to Fig. 5.14, cord tension at the bead tB in the r-direction is given by tBcos/B sinaB. The force per unit length at the bead q is expressed by q \u00bc NtB cos/B sin aB=\u00f02prB\u00de: \u00f05:60\u00de Referring to the right figure of Fig. 5.16, the force equilibrium between q and the tension of the bead core TB yields TB \u00bc qrB \u00bc NtB cos/B sin aB=\u00f02p\u00de: \u00f05:61\u00de 260 5 Theory of Tire Shape Substituting r = rB into Eq. (5.6), cord tension at the bead tB is expressed as tB \u00bc pp\u00f0r2C r2B\u00de N sin aB sin/B : \u00f05:62\u00de The substitution of Eq. (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003342_28.556642-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003342_28.556642-Figure3-1.png",
        "caption": "Fig. 3. Illustrahon of instantaneous fundamental currents and flux paths over one pole of an induction machine with semiclosed rotor slots under loaded operating conditions.",
        "texts": [
            " The extent to which each affects the stator transient inductance is strongly influenced by the type of rotor slotting; i.e., open and semiclosed, or closed rotor slots. A. Open and Semiclosed Rotor Slot Machines Induction machines are commonly designed such that the main flux path is at least partially saturated under rated operation. The stator teeth are typically the most saturated. With open and semiclosed rotor slots, localized saturation near the slot openings is often not significant, particularly in smaller machines. Fig. 3 illustrates the fundamental component currents and flux paths in an induction machine at one instant of time under loaded operating conditions. Fig. 4 illustrates the currents and flux paths for high (slip) frequency excitation in the same machine. Due to rotor conductor skin effects, the highfrequency flux does not penetrate as deeply into the rotor as does the fundamental component flux. The high-frequency flux and the fundamental component main flux are seen to share similar paths within the stator core and teeth. Saturation of the main flux path clearly impacts the highfrequency flux path. Since the high-frequency flux paths characterize the stator transient inductance, main flux path ND LORENZ: TRANSDUCERLESS FIELD ORIENTATION CONCEPTS EMPLOYING SATURATION-INDUCED SALIENCIES 1383 patial modulation aligned with the main flux flux in the stator, the fundamental and highonent fluxes share largely dissimilar paths in een the stator anld rotor fluxes, and the respective indicated in Fig. 3. Based upon the above saliency would be expected to be more leakage inductance (and thus the stator transient e) by a factor of two or more from the unsaturated is variation is substantially more than that obtained n in typical open and semiclosed slot machines. saturauon of the rotor slot bndge can be expected e main flux path due to a portion of the flux flowing the slot bridges as shlown in Fig. 5. A spatial modula- Under loaded operating conditions, rotor current will tend to drive the slot bridges much further into saturation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000897_j.oceaneng.2021.108903-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000897_j.oceaneng.2021.108903-Figure1-1.png",
        "caption": "Fig. 1. Geodetic coordinate system and body coordinate system.",
        "texts": [
            " (Qiao and Zhang, 2019) (Li Shihua and Yu-Ping, 2007): The cascaded system (1) is uniformly finite-time stable if the following conditions hold. (1) Each subsystem satisfies locally finite time stability respectively. (2) The derivative of \u0398(t, x1) satisfies \u0398\u0307(t, x1)\u2264\u03a9[\u0398(t, x1)], \u2200t\u2265 t0 \u2265 0 (3) Where \u03a9 : \u211d\u22650\u2192\u211d\u22650is a nonsubtractive function satisfying the following conditions for some constant \u03c9 > 0 \u03a9(\u03c9)\u2265 0, \u222b \u221e \u03c9 dc/\u03a9(c) = \u221e (4) The AUV dynamic model can be described as 6-DOF model in the earth-fixed coordinate systemE \u2212 \u03be\u03b7\u03b6 and the body-fixed coordinate systemO \u2212 xyz. As shown in Fig. 1. Inspired by (Do, 2009) (Shojaei and Arefi, 2015), (Xia et al., 2020), consider the above underactuated 5-DOF AUVs. Its dynamics and kinematics model can be presented as follows: \u03b7\u0307i = J(\u03b7i)vi Miv\u0307i +Ci(vi)vi + Di(vi)vi + g(\u03b7i) = \u03c4i + \u03c4id (5) The expression of the main parameters is as follows, and the detailed G. Xia et al. Ocean Engineering 233 (2021) 108903 meaning of each parameter is the same as that of references (Do, 2009), (Shojaei and Arefi, 2015) and (Xia et al., 2020). Miis the inertia matrix, Ci(vi) is the Coriolis and centripetal matrix, Di(vi) is the hydrodynamic damping matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.47-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.47-1.png",
        "caption": "Fig. 5.47: Pump/Motor Model",
        "texts": [
            " It is coupled to the drive flange and to the piston drum by a kind of three \u201dfeet\u201d, which allow relative motion in axial and radial but not in circumferential tangential direction. These three feet consist of three pins perpendicular to the tripod axis and three rings with a spherical outer surface moving in corresponding bushings in the flange or the drum, which allow axial and radial motion, but which can transmit the full torsional torques. Therefore the tripod joint is a really critical part, which has to be designed properly. Figure 5.47 depicts a tripod model with the relative kinematics of the tripod axis, the position and orientation of which we need to know. As a first step we state, that the contact points of the six tripod feet in the drum and in the flange can be described twice, using the body coordinates of the flange and the drum on the one and using the body coordinates of the tripod itself on the other side. Putting rdrum,flange = rtripod results altogether in (6x3 = 18) algebraic equations, because everyone of the six r possesses of course three components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.25-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.25-1.png",
        "caption": "Fig. 6.25 Tire deformation when a fore\u2013aft force is applied to the tire crown",
        "texts": [
            "50) in the circumferential direction, we obtain the overall force Fz in the z-direction as 326 6 Spring Properties of Tires Fz \u00bc 2 Zp 0 fzrAda \u00bc 2 Zp 0 \u00f0krz sin2 a\u00fe ktz cos2 a\u00derAda \u00bc pzrA\u00f0kr \u00fe kt\u00de: \u00f06:51\u00de The eccentric spring rate Rd of rigid ring model is given by Rd \u00bc Fz=Z \u00bc prA\u00f0kr \u00fe kt\u00de: \u00f06:52\u00de When the tire tread rotates around the wheel axle through the small angle a as shown in Fig. 6.24, the torque My is given by cosz x sinz z The in-plane rotational spring rate Rt is given by Rt \u00bc My=a \u00bc 2pr3Akt: \u00f06:54\u00de When the fore\u2013aft force is applied to a tire as shown in the third figure from the left in Fig. 6.1, the tire deformation of the rigid ring model can be separated into translational displacement d1 and rotational displacement d1 as shown in Fig. 6.25. Using Eqs. (6.52) and (6.54), the overall displacement x is given as x \u00bc d1 \u00fe d2 \u00bc Fx Rd \u00fe r2AFx Rt \u00bc Fx prA kr \u00fe kt\u00f0 \u00de \u00fe Fx 2prAkt : \u00f06:55\u00de The fore\u2013aft spring rate Rx of the rigid ring model is expressed as Rx \u00bc Fx x \u00bc 2prA\u00f0kr \u00fe kt\u00dekt 3kt \u00fe kr : \u00f06:56\u00de The fundamental spring rates are measured using an apparatus such as that shown in Fig. 6.26, where the whole tire tread is clamped. Because the tire tread cannot be completely clamped by the apparatus owing to the cross-sectional crown shape, the tire tread does not behave as a rigid ring in general"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000339_j.jmapro.2019.06.013-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000339_j.jmapro.2019.06.013-Figure4-1.png",
        "caption": "Fig. 4. Schematic view of molten pool geometry and dimensions in SLM [11].",
        "texts": [
            " A similar practice was used to calculate the temperature drop due to heat loss from convection and radiation at the part boundary, where the air was served as the ambient environment at room temperature (constant heat convection coefficient and constant radiation emissivity). The laser absorption was adopted from the literature as 0.818 [21], which was approximated based on the heat transfer model proposed by Gusarov et al. [31] The absorption was used as a fractional coefficient for laser power in the presented model. The molten pool geometry was obtained by comparing to the material melting temperature. The molten pool dimensions, including melting length (L), melting width (W), and melting depth (D) were determined as illustrated in Fig. 4. The molten pool volume was calculated with determined molten pool dimensions as =Vol DLW 6 (15) To test the proposed model, temperature distributions were predicted under various process conditions when the laser traveled to the center of the uppermost layer. Molten pool dimensions were obtained from the predicted temperature distribution and validated with experimental measurements adopted from literature [11], in which the melting width and melting depth were measured using an optical microscope based on the solidified microstructure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000697_j.jallcom.2019.04.287-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000697_j.jallcom.2019.04.287-Figure9-1.png",
        "caption": "Fig. 9. Evolutionary process of fine microstructure obtained under high-frequency micro-vibration: (a) molten liquid phase before solidification; (b) fracture of the eutectic Si under high-frequency micro-vibration; (c) fine eutectic Si obtained by high-frequency micro-vibration; (d) fine-grained and compact structure in the alloy.",
        "texts": [
            " It grows along the normal direction at the edge of the molten pool (indicated by arrows in Fig. 8c). The evolution of fine microstructure produced by high- Table 3 The EDAX analysis results of the TiC/AlSi10Mg alloys (Points shown in Fig. 7). Points Al Si Mg Ti C S1 Wt% 97.95 01.49 00.56 e e At% 97.95 01.43 00.62 e e S2 Wt% 88.20 10.86 00.94 e e At% 88.49 10.47 01.04 e e S3 Wt% 76.44 19.00 00.70 3.10 0.76 At% 78.00 18.62 00.79 1.79 1.80 S4 Wt% 94.61 04.07 01.31 e e At% 94.63 03.91 01.46 e e S5 Wt% 85.70 11.55 02.75 e e At% 85.83 11.11 03.06 e e frequency micro-vibration is shown in Fig. 9. The eutectic temperature of Al-Si is 577 C [50], while the melting point of AlSi10Mg and TiC is about 620 C [51] and 3140 C [20], respectively. Primarily, the TiC/AlSi10Mg alloy powders are rapidly melted by laser heating during the laser deposition process assisted by highfrequency micro-vibration. The eutectic Al-Si structure could be firstly formed due to relatively lower eutectic temperature of the Al-Si system. The phase of Si (indicated by arrow) would precipitate upon solidification (Fig. 9a). Then, with the help of the highfrequency micro-vibration, the long strip of eutectic Si is gradually broken and fractured into fine particles by the intensified melt flow (Fig. 9b). The fine particles are distributed homogeneously with the flow of the molten pool (Fig. 9c) and finally the compact and fine-grained net structures are formed owing to the relatively high cooling rate during the process (Fig. 9d). The net structure are closely bondedwith the a-Al (indicated by arrow), providing a good compactness of the alloy. Five samples produced using the same vibration frequency were measured by Archimedes method in order to obtain a statistical error. The effects of the high-frequency micro-vibration on the densities and surface morphologies of the TiC/AlSi10Mg alloys obtained by laser additive manufacturing are shown in Fig. 10. When the vibration frequency is 969Hz, the maximum density reaches to 99"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001121_j.matdes.2021.109685-Figure24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001121_j.matdes.2021.109685-Figure24-1.png",
        "caption": "Fig. 24. The arches built with and without support have significantly different temperature distribution trends. The support structure has the effect of not only providing physical anchoring of the part, but also is a pathway to conduct heat away. In the arches built without support the heat accumulates in the top most portions, while in the part without support the heat is rapidly conducted away.",
        "texts": [
            " This is because, following a recoater crash and breakage of the arch A10, the laser can only scan and melt powder without any solidified part underneath. Since, the unconsolidated metal powder is a relatively poor conductor of heat compared to a solidified part, the powder bed surface of a broken part tends to retain heat. Heat retention is consistently observed subsequent the crash of arch A05 in layer 556, and A20 and A25 in layer 574. Indeed, the debris from the crash of arch A10 is discerned in the thermal images at layer 574. The qualitative difference in the layer-by-layer temperature distribution of two types of arches is shown in Fig. 24. The arches without supports tended to accumulate heat which led to superelevation (Fig. 2), ultimately causing a recoater crash. Since supports conduct heat away from the thin cross-section of the arch, the arches built with supports avoid deformation and subsequent recoater crash. In Fig. 25, the surface temperature, predicted using graph theory, are overlaid on the experimental for the arches observations. These results are reported in Table 7. All the unsupported arches except the one with 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.5-1.png",
        "caption": "Fig. 8.5 Two coordinate systems for the tread ring element and displacement of an element at r [16]",
        "texts": [
            " One is the space-fixed (nonrotating) coordinate system, and the other is the rotating coordinate system. The translational displacement of the center of a wheel is described in terms of Cartesian coordinates (x, z) in the nonrotating coordinate system, or \u00f0x ; z \u00de in the rotating coordinate system. The location of an infinitesimal element of a tread ring is described in terms of cylindrical coordinates (r, /) in the nonrotating coordinate system, or (r, h) in the rotating coordinate system, as shown in Fig. 8.5a. The position of point A on the middle surface of the tread ring is determined from (i) the rotation of the system, (ii) rigid body displacement of the system due to translational motion of the wheel, and (iii) deformation of the tread ring. In the rotating coordinate system, the first part of the displacement can be disregarded. z 458 8 Tire Vibration The rigid body displacement is represented by x and z in the rotating coordinate system (or x and z in the nonrotating coordinate system). The displacement components on the middle surface of the tread ring in the rotating coordinate system due to the ring deformation are described by wr in the radial direction and vr in the tangential direction",
            " 8.2 Elastic Ring Model Without a Tread Spring 459 (3) Strain\u2013displacement relations of a tread ring The strain\u2013displacement relations of a tread ring are expressed by6 er \u00bc @W @r eh \u00bc 1 r W \u00fe @V @h \u00fe 1 2r2 @W @h V 2 erh \u00bc @V @r \u00fe 1 r @W @h V ; \u00f08:32\u00de where er and eh are, respectively, the normal strains in radial and tangential directions, erh is the in-plane shear strain, and W and V are the total displacement at radius r (r = a + y), where y is measured from the middle plane of a tread ring (Fig. 8.5b). W and V can be considered the displacements measured from the middle plane because the rigid body displacements do not produce strains. The second-order nonlinear term in eh is retained to consider the pretension effect of the tread ring. Note that w and v are displacements in the middle plane of the tread ring, while W and V are the displacements located a distance y measured from the middle plane of the tread ring. According to Note 8.3, the normal strain in the tangential direction eh is expressed by7 eh \u00bc 1 a w\u00fe @v @h \u00fe y a2 @v @h @2w @h2 \u00fe 1 2a2 @w @h v 2 : \u00f08:33\u00de The first and third terms represent the extensional deformation of the middle surface of a tread ring, while the second term represents the bending of a tread ring. (4) Kinetic and potential energy of tread ring As shown in Fig. 8.5,~p denotes the position vector of a tread ring with mass dm in the rotating coordinate system, while the dot in _~p denotes the time derivative. The time derivative of the position vector of a tread ring in the nonrotating coordinate system, _~r, can be expressed as8 _~r \u00bc _~p\u00fe X ! ~p \u00bc _w Xv\u00f0 \u00de~er \u00fe _v\u00feX\u00f0a\u00few\u00def g~eh; \u00f08:34\u00de where indicates the cross product and X ! is the angular velocity vector. 6Note 8.2. 7See Footnote 6. 8Note 8.3. 460 8 Tire Vibration The kinetic energy of a tread ring T1 is expressed by9 T1 \u00bc Z 1 2 _~r _~rdm \u00bc 1 2 qabh Z2p 0 _w Xv\u00f0 \u00de2 \u00fe _v\u00feX\u00f0a\u00few\u00def g2 h i dh \u00bc 1 2 qAa Z2p 0 _w Xv\u00f0 \u00de2 \u00fe _v\u00feX\u00f0a\u00few\u00def g2 h i dh; \u00f08:35\u00de where q is the density of the ring material, h is the thickness of the tread ring, b is the width of the tread ring, and A = bh. The kinetic energy of the wheel is expressed by T2 \u00bc m _x2 \u00fe _z2 \u00fe Ir X\u00fe _hr 2 =2; \u00f08:36\u00de where m is the wheel mass, Ir is the moment of inertia of a wheel around the axle, _hr is the angular speed variation from the mean value X. The substitution of Eq. (8.30) into Eq. (8.36) yields T2 \u00bc m _x Xz \u00f0 \u00de2 \u00fe _z \u00feXx \u00f0 \u00de2 n o \u00fe Ir X\u00fe _hr 2 =2: \u00f08:37\u00de Referring to Fig. 8.5a and using Eq. (8.29), the potential energy of the elastic springs (i.e., radial and tangential fundamental springs) V1 is expressed by V1 \u00bc 1 2 a Z2p 0 kt v\u00fe x sin h z cos h ahr\u00f0 \u00de2 \u00fe kr w x cos h z sin h\u00f0 \u00de2 n o dh; \u00f08:38\u00de where kr and kt are the radial and tangential fundamental spring rates per the circumferential unit length of the ring. hr is the angular displacement of a wheel due to the variation in rotating speed _hr. Suppose that a tread ring is in equilibrium under the inflation pressure and the centrifugal force that induces the prestress in the tread ring",
            "208), we obtain F \u00bc m0 3 \u20aczD 1\u00fe rD rD \u00fe rB : \u00f08:209\u00de When the combined mass of the two sidewalls is located on the tread, using the correction parameter a for the equivalent mass, the inertia force is expressed by F \u00bc am0\u20aczD \u00f08:210\u00de Comparing Eqs. (8.209) and (8.210), a is given as a \u00bc 1 3 1\u00fe rD rD \u00fe rB : \u00f08:211\u00de Lecomte [48] reported that a tire with rD = 346 mm and rB = 236 mm has the value a = 0.92 in his model. However, a = 0.66 is appropriate to fit experimental results. For this tire, Sakai\u2019s model gives a = 0.33, Eq. (8.205) gives a = 0.20 and Eq. (8.211) gives a = 0.53. Note 8.2 Eqs. (8.32) and (8.33) [7] Figure 8.5b shows the locations of an infinitesimal element AB on the ring before deformation and an element A\u2032B\u2032 after deformation in a polar coordinate system. The location of point A before deformation is defined by the polar coordinates Notes 527 (r, h), while the location of point B is defined by (r + dr, h + dh). The infinitesimal length of element AB is given by ds2 \u00bc dr2 \u00fe rdh\u00f0 \u00de2: \u00f08:212\u00de After ring deformation, point A moves to point A\u2032 with displacements W and V in the radial and tangential directions, respectively, and point B moves to point B\u2032. The position of point A\u2032 is defined by (r + fr, h + fh). The positions of points A and B change to those of points A\u2032 and B\u2032: A\u00f0r; h\u00de ! A0\u00f0r\u00fe fr; h\u00fe fh\u00de B\u00f0r\u00fe dr; h\u00fe dh\u00de ! B0\u00f0r\u00fe fr \u00fe dr\u00fe dfr; h\u00fe fh \u00fe dh\u00fe dfh\u00de: \u00f08:213\u00de Referring to Fig. 8.5b, we obtain fh ffi sin fh ffi V=\u00f0r\u00feW\u00de; fr ffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r\u00feW\u00f0 \u00de2 \u00feV2 q r ffi W : \u00f08:214\u00de The infinitesimal length ds\u2032 of an element A\u2032B\u2032 is expressed by ds02 \u00bc dr\u00fe dfr\u00f0 \u00de2 \u00fe r\u00fe fr\u00f0 \u00de2 dh\u00fe dfh\u00f0 \u00de2; \u00f08:215\u00de where dfh \u00bc @fh=@h dh\u00fe @fh=@r dr dfr \u00bc @fr=@h dh\u00fe @fr=@r dr: \u00f08:216\u00de The substitution of Eq. (8.216) into Eq. (8.215) yields ds02 \u00bc Grrdr2 \u00fe 2Grhdrdh\u00feGhhdh 2; \u00f08:217\u00de where Grr \u00bc r\u00fe fr\u00f0 \u00de2 @fh=@r\u00f0 \u00de2 \u00fe 1\u00fe @fr=@r\u00f0 \u00de2 Grh \u00bc r\u00fe fr\u00f0 \u00de2 1\u00fe @fh=@h\u00f0 \u00de@fh=@r\u00fe @fr=@h 1\u00fe @fr=@r\u00f0 \u00de Ghh \u00bc r\u00fe fr\u00f0 \u00de2 1\u00fe @fh=@h\u00f0 \u00de2 \u00fe @fr=@h\u00f0 \u00de2: \u00f08:218\u00de Referring to Fig",
            " The in-plane shear strain is then small and can be neglected. The only appreciable strain is therefore that in the tangential direction. The radial displacement W can be approximated by that of the middle surface, and the tangential displacement varies linearly across the ring thickness. The radial and tangential displacements W and V can be expressed as W w; V y; h; t\u00f0 \u00de \u00bc v\u00f0h; t\u00de\u00fe yb\u00f0h; t\u00de; \u00f08:226\u00de where b is the rotation angle of the ring cross section and y is the distance from the middle surface (Fig. 8.5b). The substitution of Eq. (8.226) into Eq. (8.225) yields eh \u00bc 1 a\u00fe y w\u00fe @v @h \u00fe y @b @h \u00fe 1 2 a\u00fe y\u00f0 \u00de2 w\u00fe @v @h \u00fe y @b @h 2 \u00fe 1 2 a\u00fe y\u00f0 \u00de2 @w @h v yb 2 erh \u00bc 1 a\u00fe y @w @h v\u00fe ab : \u00f08:227\u00de Because the ring is thin \u00f0h a\u00de, a + y can be replaced by a and the shear strain erh in Eq. (8.227) is zero according to Bernoulli\u2013Euler theory. Hence, b is given by b \u00bc 1 a v @w @h : \u00f08:228\u00de The substitution of Eq. (8.228) into the first equation of Eq. (8.226) yields eh \u00bc 1 a w\u00fe @v @h \u00fe y a2 @v @h @2w @h2 \u00fe 1 2a2 w\u00fe @v @h 2 \u00fe 1 2a2 @w @h v 2 : \u00f08:229\u00de 530 8 Tire Vibration Gong [16] omitted the third term in Eq",
            " dydh V2 \u00bc 1 2 Z2p 0 2r0hA w\u00fe @v @h \u00fe r0hA a v @w @h 2 ( ) \u00fe E a A w\u00fe @v @h 2 \u00fe I a2 @v @h @2w @h2 2 ( )\" # dh Equation (8.42) Wei [19] added the work of the moment on the tread qb to Eq. (8.42): dE1 \u00bc Z2p 0 qwdw\u00fe qvdv\u00fe qbd v0 w a adh\u00fe fx dx \u00fe fz dz \u00fe Tdhr: \u00f08:238\u00de Equation (8.43) The work done by the inner pressure can be derived as dE2 \u00bc dp0b Z2p 0 dA a2 2 dh ; \u00f08:239\u00de where A is the deformed ring area expressed by A \u00bc 1 2 Z2p 0 ~r d~r \u00bc 1 2 Z2p 0 x dz z dx \u00f0 \u00de: \u00f08:240\u00de Here,~r is the vector of the deformed ring. x and z are positions of the ring in the rotating coordinate system as shown in Fig. 8.5 and expressed by x \u00bc a\u00few\u00f0 \u00de cos h v sin h; z \u00bc a\u00few\u00f0 \u00de sin h\u00fe v cos h: \u00f08:241\u00de The substitution of Eq. (8.241) into Eq. (8.240) and then Eq. (8.239) gives Notes 533 dE2 \u00bc p0b Z2p 0 1\u00fe 1 a w\u00fe @v @h dw 1 a @w @h v dv adh: \u00f08:242\u00de Note 8.5 Eq. (8.46) I \u00bc Zt2 t1 Z L\u00f0w; _w;w0;w00; v; _v; v0\u00dedhdt; dI \u00bc Zt2 t1 Z L;wdw\u00fe L; _wd _w\u00fe L;w0dw0 \u00fe L;w00dw00 \u00fe L;vdv\u00fe L;_vd _v\u00fe L;v0dv 0 dhdt Integration by parts of the above equation yields Rt2 t1 L; _wd _wdt \u00bc L; _wd _w t2 t1 Rt2 t1 @L; _w @t dwdt R2p 0 L;v0dv0dh \u00bc L;v0dv 2p 0 R2p 0 @L;v0 @h dvdh:: dI is expressed by dI \u00bc Z2p 0 L; _wd _w t2 t1 dh\u00fe Zt2 t1 L;w0dw 2p 0 dt Zt2 t1 @L;w00 @h dw 2p 0 dt\u00fe Z2p 0 L; _vdv t2 t1 dh\u00fe Zt2 t1 L;v0dv 2p 0 dt \u00fe Zt2 t1 Z L;w @ @t L; _w @ @h L;w0 \u00fe @2 @h2 L;w00 dw\u00fe L;v @ @t L; _v @ @h L;v0 dv dhdt \u00bc 0: Note 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure8.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure8.8-1.png",
        "caption": "Fig. 8.8: Schematic design of a bristle actuated microrobot. According to [Fuku93a]",
        "texts": [
            " For an operating frequency of 400 Hz, the platform speed can reach up to 1 mm/s. The platform can reach the same positioning accuracy of 10 nm, as the first micro-crawling machine, but for this motion principle the navigation control problems are more difficult. Bristle-based motion principle Another example of a mobile platform is a bristle actuated device (Fur Driven Micro-mobile-mechanism, FDM), which can serve as an electromagnetically driven transport unit for microrobots [Fuku92], [Fuku93a]. Two different de signs were built, Fig. 8.8. Unit 1 can only move forwards, while Unit 2 can additionally turn left and right. The motion principle is the same for both devices and therefore will only be described for the simpler Unit 1. The robot consists of a body made from aluminum, a solenoid coil, a leg part with a permanent magnet, an L-shaped sheet metal leg to the bottom of which a nylon cloth with bristles is attached, and a stopper made from cop per. The magnetic coil is made from an iron core and an enamel coated wire coil having 600 windings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003228_a:1008914201877-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003228_a:1008914201877-Figure4-1.png",
        "caption": "Figure 4. Top view of sensor configuration.",
        "texts": [
            " Additionally, each scanner can pan at a rate of up to 120 degrees per second, enabling this circle to be rotated about the azimuth, as shown in Fig. 3. The lasers have an effective range of 200 m and are eye-safe when the mirror is spinning. The scanner positioned over the operator\u2019s cab is called the \u201cleft scanner\u201d, and it is responsible for sensing the workspace on the left hand side of the excavator. The \u201cright scanner\u201d, which is located at a symmetric position on the right, is responsible for sensing the workspace on the right hand side of the excavator. The excavator uses its scanners in the following fashion when loading a truck (Fig. 4). While the excavator digs its first bucket, the left scanner pans left from the dig face across the truck both to detect obstacles and to recognize, localize, and measure the dimensions of the truck. Using this information, a desired location in the truck to dump the material is planned, and the bucket swings toward the truck. During this swing motion, the right scanner pans left across the dig face to measure its new surface, and the next location to dig is calculated. The right scanner continues to pan toward the truck"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003791_3477.662755-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003791_3477.662755-Figure2-1.png",
        "caption": "Fig. 2. Unit line vectors and the D\u2013H kinematic parameters.",
        "texts": [
            " This formula will be used to transform the position vector, which points to the origin of a link frame with respect to its previous frame, to the base frame in order to determine the position of the end-effector. Algorithm 2: Formulation of the kinematic equations of a -link robot based on Lie algebra representation. 1) Assignment of a local coordinate system to every link and to the base of the robot (identical procedure as in step 1 of the Algorithm 1). 2) Determination of kinematic parameters for the links 1 to (see Table I and Fig. 2). 3) Determination of the vectors representing the orientation of the th frame with respect to the frame (14) (see analytic comments on the determination of this vector at the end of the algorithm) 4) Computation of the orientation vector for to of every link coordinate system to the base system, using (15) where the operation is defined in (12). 5) Transformation of the position vector repre- senting the position of the frame with respect to frame , for to into the base coordinate system, given by using (13)",
            " 6) Computation of the position vector of the gripper by the sum (16) where is the fourth column of the matrix given by (6) if the index is replaced by the . The core of this algorithm is the determination of the vector given by (14). In order to determine this vector, the 3 3 orientation matrix of the transformation matrix can be replaced in (11), however the geometrical meaning of the determination is obscured. The following way gives an intuitive explanation of the geometrical significance of the involved parameters. As it is shown in Fig. 2, the orientation of the frame with respect to the frame is composed by two simple rotations: 1) one rotation around the axis of the frame by an angle (17) 2) one rotation around the axis of the frame by an angle (18) Using the group composition law the formula of (14) is obtained. The algorithm offers a compact way to represent the orientation of the end-effector of a manipulator with respect to the base frame. However, the position of the end-effector has to be calculated through the formula given by (16), borrowing the determination of the position vector from the first method based on the homogeneous transformation",
            " To show that the axis has been translated along the axis by , the vector from the origin of the coordinate system vertical to the line in the new location is calculated by Transformation equations (24) and (25) are mainly used in the solution of the direct kinematic problem. The exact procedure for solving this problem is described in the following algorithm. Algorithm 3: Solution of the direct kinematic problem for a -link robot arm using screw transformation by dual quaternions. 1) Assignment of a coordinate system to every link and to the base (same procedure as in step 1 of the Algorithm 1). 2) Determination of the kinematic parameters for the links 1 to (see Table I and Fig. 2). 3) Definition of as the unit line vector which is coincident with the common normal between the th and th axis and as the unit line vector along the axis of the th joint (see Fig. 2). Compute these unit vectors successively from to using the transformations (28) and (29) Begin with the base frame unit vectors (30) The transformation operators (quaternions), are (31) and (32) where the dual angle between and is defined as (33) and , the dual angle between and is defined as (34) in terms of the four D\u2013H kinematic parameters. 4) Computation of the position vector of the end-effector by (35) 5) Determination of the orientation matrix of the end effector coordinate system by the three vectors (36) By following the steps of the presented algorithm the kinematic equations of any spatial manipulator can be formulated. However, some explanations on the derivation of the equations used in this algorithm are necessary. In Fig. 2, the unit line vectors are drawn. The unit line vector defines the axis of the joint and defines the common perpendicular to the axes of the and joints. The dual quaternion transforms the unit line vector to . In other words translates the axis of frame along the axis of joint by and rotates the axis of frame about the axis of joint by an angle . The operation of the dual quaternion is similar: it translates and rotates the joint axis along and about the common perpendicular to this joint axis and the next one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.20-1.png",
        "caption": "Fig. 2.20: Orientation of two Bodies",
        "texts": [
            " For that purpose we consider the corresponding velocities in the form vn = nTvC , vt = tTvC , (2.98) with their time derivatives v\u0307n = n\u0307TvC + nT v\u0307C , v\u0307t = t\u0307TvC + tT v\u0307C . (2.99) With n\u0307, t\u0307 from equation 2.92, v\u0307C = aC from equation 2.97 and noting the relations nT \u2126\u0303t = bT\u2126 and tT \u2126\u0303t = 0 we derive v\u0307n =nT (aQ \u2212 \u2126\u0303vC)\u2212 \u03bas\u0307tTvC + s\u0307bT\u2126, (2.100) v\u0307t =tT (aQ \u2212 \u2126\u0303vC) + \u03bas\u0307nTvC . (2.101) With these fundamental equations for one body we are able to consider in a next step two contacting bodies. We are still in a plane. Figure 2.20 gives the nomenclature and the directions. The sense of the contour parameters s1 and s2 are chosen in such a way that the binormals of both moving trihedrals are the same, b1 = b2. The origins of the two trihedrals are connected with the relative distance vector rD. To determine this distance vector we orient the trihedrals in such a manner, that they are mutually perpendicular, which is always possible and gives the conditions: nT1 (s1) \u00b7 t2(s2) = 0, \u21d4 nT2 (s2) \u00b7 t1(s1) = 0. (2.102) These conditions require that both, normals and tangents, are parallel (see Figure 2.20). For an evaluation of these equations we need of course only one, because the two are equivalent. The next requirement consists in putting the relative distance rD unidirectional with the two normals and thus perpendicular to the two tangent vectors. This gives rTD(s1, s2) \u00b7 t1(s1) = 0, \u21d4 rTD(s1, s2) \u00b7 t2(s2) = 0. (2.103) From the four equations 2.102 and 2.103 we need only two, for example the first ones. The solution (s1, s2) of these two conditions as nonlinear functions of (s1, s2) results in a configuration indicated in Figure 2.20: normal and tangent vectors are antiparallel to each other, and the relative distance vector rD is perpendicular to the two surfaces, which at the same time is the shortest possible distance between the two bodies. The values (s1, s2) are the \u201ccontact parameters\u201d of our problem, and the accompanying points (C1, C2) the \u201ccontact points\u201d. The axes of the two trihedrals are given by n1 = \u2212n2, t1 = \u2212t2, b12 = b1 = b2. (2.104) From this we get easily the distance between the two bodies gN (q, t) = rTDn2 = \u2212rTDn1",
            " Therefore relative kinematics of contacts include the whole set of position and orientation, of velocities and of accelerations. Some of these magnitudes we get by differentiation. In that case we should not forget the original state of the relative kinematic magnitudes for the special contact event under consideration, for example, in normal direction of a contact the event contact is indicated by the relative distance becoming then a constraint. In tangential direction the relative tangential velocity indicates the stick or slip situation. We shall come back to these properties later. We consider Figure 2.20 and assume for a while that the equations 2.102 and 2.103 have not yet been fulfilled. The relative distance rD is then not perpendicular to the two surfaces \u03a31 and \u03a32, but it represents some straight connection between the future contact points C1 and C2. The absolute change of rD with time writes r\u0307D = v\u03a32 \u2212 v\u03a31, (2.106) where the contour velocities v\u03a3 come from the equations 2.95. For evaluating the relative velocities we need in a further step the contour velocities s\u0307. For this purpose we differentiate the equations 2",
            " After some elementary calculations (see [200]) we come out with s\u03071 = \u03ba2tT1 (vC2 \u2212 vC1)\u2212 \u03ba2gNbT12\u21261 + bT12(\u21262 \u2212\u21261) \u03ba1 + \u03ba2 + gN\u03ba1\u03ba2 , s\u03072 = \u03ba1tT1 (vC2 \u2212 vC1)\u2212 \u03ba1gNbT12\u21262 \u2212 bT12(\u21262 \u2212\u21261) \u03ba1 + \u03ba2 + gN\u03ba1\u03ba2 , (2.109) with the \u201cbinormal\u201d b12 = \u2212t2 \u00d7 n1 to the vectors n1 and t2. The relative distance gN is defined by equation 2.105. With the above equations we can now evaluate the relative velocities and the relative accelerations of two bodies coming into contact or sliding on each other. Starting with the relative velocities we write (see Figure 2.20 and [200]) g\u0307N = nT1 vC1 + nT2 vC2, g\u0307T = tT1 vC1 + tT2 vC2, (2.110) where vC1 and vC2 are the absolute velocities of the potential contact points C1 and C2. These velocities might be expressed by the generalized, or minimal, velocities q\u0307 using the Jacobians JC1 and JC2 (see [27], [200]) vC1 = JC1q\u0307 + j\u0303C1, vC2 = JC2q\u0307 + j\u0303C2. (2.111) Combining the last two equations results in g\u0307N = wT N q\u0307 + w\u0303N , g\u0307T = wT T q\u0307 + w\u0303T , (2.112) with wN =JTC1n1 + JTC2n2, wT = JTC1t1 + JTC2t2, w\u0303N =j\u0303TC1n1 + j\u0303TC2n2, w\u0303T = j\u0303TC1t1 + j\u0303TC2t2, (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003217_70.833196-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003217_70.833196-Figure1-1.png",
        "caption": "Fig. 1. Stewart platform manipulator.",
        "texts": [
            " v and w denote the partial velocity and partial angular velocity of body k in inertial reference frame <; respectively. Jkmn is the component of the inertia matrix of body k relative to its mass center in <: ersm is the permutation symbol. Fkm and Mkm are the components of the resultant force acting at the mass center of body k in <: The explicit form of(5) was first developed by Huston and was called the Huston form of Kane\u2019s equation. The mechanism model of the Gough\u2013Stewart platform manipulator shown in Fig. 1 has a base and a platform. They are connected by six extensible legs with spherical joints at the platform end and universal joint at the base end. Since the legs of the Gough\u2013Stewart platform manipulator are identical, we only need to derive the dynamic equations of the platform and one leg. S1042\u2013296X/00$10.00 \u00a9 2000 IEEE A. Dynamics of the Legs Fig. 2 illustrates one leg of a general Gough\u2013Stewart platform. Let X0Y0Z0 denote the inertial frame fixed at the base. xiyizi (i = 1; 2; ; 6) is parallel to X0Y0Z0 and its origin coincident with Bi: The origins of local frames are attached to each part and labeled as Oi;1 and Oi;2: These two local frames are parallel and their x-axis point to the joint point Pi: si is the position vector from Oi;1 to Oi;2 in the local frame Oi; 1 and qi is the position vector from Oi;2 to Pi in the local frame Oi;2: Let ri;k be the position vector of the mass centers Gi;k in local frames",
            "p;z p;x p;y p;x] T : (16) Because the platform is a single rigid body, its dynamic equations can be written as follows, directly: Ap _yp = Dp (17) where Ap = 0Jp mp 0rG 0rG mp 0rG mp 0rG mp13 3 Dp = Mp mp 0rG a\u0302 !p 0Jp!p Fp mpa\u0302 and a\u0302 = 0 ag + !p (!p 0 rG): In the above equations, 0rG = 0RprG and 0Jp = 0RpJp( 0Rp) T where Jp is the inertia dyadic matrix of platform in xpypzp: 0Rp is the transformation matrix from xpypzp to X0Y0Z0: 0ag is gravity acceleration in X0Y0Z0: Fp and Mp are the resultant force and moment acting on the platform, respectively. Considering the platform given by Fig. 1, six legs are connected to platform by spherical joint at points Pi (i = 1; 2; ; 6): Because the velocities of leg i and platform at points Pi are the same, the velocity, partial velocity, and its derivative of point Pi in the ith leg can be written as follows: i p = [Ri(si + qi)] !i +Ri _si (18) i vp = [ Ri(si + qi) ui] (19) i _vp = [Ri(si + qi) !i +Ri _si !iui]: (20) Similarly, the velocity, partial velocity, and its derivative of point Pi in the platform are given by 0 p;i = 0 !p (0Rirp;i) + 0 p (21) 0 p;i = [ 0Rprp;i j 13 3] (22) 0 _vp;i = [ (0Rprp;i) 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003604_mssp.2002.1479-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003604_mssp.2002.1479-Figure1-1.png",
        "caption": "Figure 1. Experimental set-up.",
        "texts": [
            " A single-layer perceptron network was trained by means of the perceptron-learning rule within a finite number of iterations, which endorses the fact that the data are linearly separated between load conditions by the normalisation approach to vibration waveforms. The trained network can distinguish between the fault severities of a load condition, which were not presented during the training of the network. The experimental set-up consisted of a single-stage gearbox, driven by a 5 hp Dodge Silicon Controlled Rectifier motor. A 5.5 kVAMecc alte spa three-phase alternator was used for applying the load. Figure 1 illustrates the test rig. The gears were manufactured in accordance with DIN3961, Quality 3. The gears in the pair each had 69 teeth. The gearbox casing was machined from a steel billet to minimise the probability of resonant frequencies within the experimental frequency bandwidth, as such frequencies might distort the amplitude and the phase of the vibration source signal caused by the fluctuating gear mesh stiffness. This precaution was taken to ensure a reliable and representative signal from the gear mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.18-1.png",
        "caption": "Fig. 4.18 Finite element model of a two-ply bias laminate and magnified view. Reproduced from Ref. [2] with the permission of Tire Sci. Technol.",
        "texts": [
            "17 is similar to that of Fig. 3.22 obtained using MLT. Comparing the bending rigidity for the cord pace d = 3 mm with that for the cord pace of 10 mm, it is interesting to note that the flexural rigidity increases only a little when decreasing the cord pace by about two-thirds. McGinty et al. [2] studied a two-ply bias laminate without out-of-plane coupling deformation employing a finite element model of a laminate. The entire finite element model and a magnified view of the model are shown in Fig. 4.18. The control model was 60 mm wide and 180 mm long and had a cord diameter of 0.56 mm, cord pace of 1.6 mm, thickness of the adhesive rubber layer of 0.9 mm and bias angle of 25\u00b0. 230 4 Discrete Lamination Theory Similar to DLT in Sect. 4.1, the finite element model allows us to observe the distribution of interlaminar shear strain between cords. Figure 4.19 shows the distribution of strain at the ply edge along the two paths of the control model. The interlaminar shear strain is low in the middle plane of point (a) and is a maximum at the interface of the cord of the point (b) in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.8-1.png",
        "caption": "Fig. 6.8: Mesh of Gears with Backlash and Relevant Force Laws",
        "texts": [
            "19) describe a multibody system with n bodies and a maximum number of (f = 6n) rigid degrees of freedom and, according to the Ritz Ansatz (eq. 6.4) a certain number of elastic degrees of freedom (number of shape functions per body times number of elastic bodies). In practical applications, however, the number of degrees of freedom might be reduced drastically. For example, driveline units with straight-tooth bevels may be sufficiently modeled by rotational degrees of freedom only. To include backlashes we have to implement an algorithm which controls the contact events (Fig. 6.8), by considering contact kinematics and contact forces. 6.1 Timing Gear of a Large Diesel Engine 339 A contact at a tooth flank occurs if the relative distance in contact k becomes zero (eq. 6.7): \u03b3k ( pi, pj , \u03c8k ) = 0 . (6.31) The subsequent deflection of both teeth follows the force laws of the Figs. 6.5 and 6.6, but the end of the contact is not reached, when we again get \u03b3k = 0. The correct condition consists of the requirement that the normal force (\u03b6keki, i = 1, 2) (Fig. 6.8) vanish. As we have a unilateral contact problem, separation takes place when the normal force changes sign, which is not the case if \u03b3k = 0. Due to the dynamics of the contacting bodies and to the damping influence of the contact oil model (Fig. 6.6), the normal force changes sign before \u03b3k = 0, which means the tooth separation takes place when the teeth are still deflected. For separation we therefore must interpolate the force condition (Fig. 6.8) \u03b6kn = \u2212eki\u03b6k = \u2212eki (ck\u03b3k + \u03b6kD (\u03b3k, \u03b3\u0307k)) = 0 (i = 1, 2) , (6.32) where \u03b6kn is the normal force vector and \u03b6kD the damping force law due to oil and structural damping. Considering several backlashes we need an additional algorithm to determine the shortest time step to the next contact or separation event. This means formally that we have to evaluate in all existing backlashes the following equations: 340 6 Timing Equipment \u2206tFC = min k \u2208 np {\u2206tk| \u03b3k(pi,pj , \u03c8k) = 0 \u2227 \u03b6kn(\u03b3k, \u03b3\u0307k, en) < 0 } , \u2206tCF = min k \u2208 np {\u2206tk| \u03b6kn(\u03b3k, \u03b3\u0307k, en) \u2265 0} , (6",
            " The jerky ignition pressure course as well as the irregularities of the crankshaft excite the system to produce vibrations, which are characterized by impulsive contacts between the meshing gears at the front and at the rear flanks thus generating a hammering effect. Hammering consists 6.2 Timing Gear of a 5-Cylinder Diesel Engine 349 in contact and detachment under load and results in very large load peaks. Consequently, this load is also influenced by the backlash itself, it increases with increasing backlashes due to larger kinetic energy in large plays. Therefore we must choose a force law based on two-sided force elements with play, see Figure 6.18 and see also Figure 6.8. The gear construction of this figure is well-known (see for example [170]), and according to that the tooth forces act in the directions of the lines of contact, which are the connecting tangential lines to the two base circles. Assuming a linear spring damper force law we may write for the contact forces Fmesh = (c \u00b7 g + d \u00b7 g\u0307)e1,2, where (g, g\u0307) are the deformation and deformation velocity in the contact. The spring and damper coefficients must be evaluated by a FEM-model or by the standard model of Ziegler [285], which due to its excellent approximations is still in use in industry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000589_tsmc.2021.3062206-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000589_tsmc.2021.3062206-Figure4-1.png",
        "caption": "Fig. 4. Chaotic attractor of system (41).",
        "texts": [
            " evolutions of solutions for system (40) with different initial values are provided in Fig. 3, from which we can see that the chattering is suppressed when the sign function is replaced by the saturation function. Example 3: Consider the following controlled three-cell cellular neural network y\u0307(t) = Ly(t)+ Pg(y(t))+ u(t) (41) where L = \u2212I3, g(y) = (g1(y1), g2(y2), g3(y3)) T , and gi(v) = 0.5(|v + 1| \u2212 |v \u2212 1|) and P = \u239b \u239d 1.25 \u22123.2 \u22123.2 \u22123.2 1.1 \u22124.4 \u22123.2 4.4 1.0 \u239e \u23a0. It has been proved in [57] that neural network (41) exists a chaotic attractor, which is presented in Fig. 4 with initial value y(0) = (0.1, 0.1, 0.1)T . First, we consider the fixed-time stabilization of system (41) under controller (30). By using LMI toolbox in MATLAB and condition (31), when \u03c9 = (1/7), one can obtain that K = \u239b \u239d 5.1998 0.1644 \u22120.6258 0.1644 5.4147 0.3126 \u22120.6258 0.3126 5.4653 \u239e \u23a0. Select \u03b1 = 2, \u03c3 = 0.6, \u03b4 = 1.9, and\u03b8 = 0.1 in controller (30). It follows from Theorem 2 that the origin is fixed-time stabilized within the time T7 = 2.04, which is demonstrated in Fig. 5 and 6, where each initial value y(0) is selected randomly on [\u22125, 5]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure19-1.png",
        "caption": "Fig. 19. Switch process of main configurations.",
        "texts": [
            " As shown in Table 2 , the mechanism evolves into overconstrained 6R and 4R linkages resorting to link annexing. It is the intersection of metamorphic mechanisms and kinematotropic mechanisms. For illustrating the motion sequence more clearly, the switch process of several main configurations will be described as follows. According to the mobility analyses in Sections 3 and 4 , the mechanism has at most five degrees of freedom. Hence, joints F , G , H , B 1 , and B 4 are selected to actuate the mechanism. Further, the switch process of main configurations is seen at a glance as displayed in Fig. 19 . As shown in Fig. 19 (a), the mechanism lies in primary configuration with two DOFs. Due to the symmetry, we choose to actuate the joints G and B 1 . Subsequently, when the axes of joints E, G and F , H are collinear, respectively, the mechanism moves to a singular configuration with three DOFs as seen in Fig. 19 (b). Further, two motion branches are shown in Figs. 19 (c) and (e). When we only actuate the joints F , H until adjacent links FB 1 , FB 2 , and HB 3 , HB 4 are partially overlapped, respectively, then the motion of joints F and H are restricted, a special overconstrained 6R linkage in Fig. 19 (c) can be obtained. Similarly, when the adjacent links EB 1 , EB 4 , and GB 2 , GB 3 are further partially overlapped, an overconstrained 4R linkage in Fig. 19 (d) can be unveiled. On the other way, when the joints F and H are actuated until the joints E, G are coincident as shown in Fig. 19 (e), the configuration of the mechanism is singular with 4 DOFs. Following this, Figs. 19 (f) and (g) display two branches. When the joints B 1 , B 4 are driven until the joints E, G , F , and H are coincident, the mobility of the singular configuration as shown in Fig. 19 (f) is 5. On the other branch, the joint B 1 is actuated until the axis of joint F and axes of joints E, G are parallel, the mobility under the configuration as seen in Fig. 19 (g) changes from 4 to 3. Furthermore, Fig. 19 (h) illustrates that the joint B 4 is actuated until axis of H and axes of joints E, G are parallel, the mobility of the mechanism increases from 3 to 4 again. Finally, Fig. 19 (i) shows that deployable configuration of the mechanism is obtained when the joints F , G are driven until the axes of joints B 1 , B 3 and B 2 , B 4 are collinear, respectively. In addition, by using the kinematotropic metamorphic 8R mechanism as the reconfigurable trunk, a novel quadruped robot is fabricated and assembled with four legs. The actuation scheme of the robot trunk is shown in Fig. 20 . Five motors are assembled in joints F , G , H , B 1 , and B 4 . Further investigation of the quadruped robot with a reconfigurable trunk, such as workspace, gait planning and the control algorithm with additional sensors will be the subject of the future research"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.6-1.png",
        "caption": "Fig. 7.6: Prescribed Trajectory for a Robot",
        "texts": [
            " Considering the classical methods of nonlinear, smooth dynamics (see for example [148], [27], [125], [187]) we may express these kinematical magnitudes by a parameter s in the following way: q\u0307j = q\u2032j s\u0307, q\u0308j = q\u2032j s\u0308 + q\u2032\u2032j s\u0307 2, with q\u0307j = dqj dt , q\u2032j = dqj ds , s\u0307 = ds dt . (7.28) This form of parameterization can easily be interpreted as the path coordinate of a prescribed trajectory, which, together with the, certainly idealized, assumption, that the end effector of the robot should track the given path in an ideal and perfect manner, results in a system with one degree of freedom only, namly this path coordinate, independent of the number of joints and the structure of the robot [117], [186]. Figure 7.6 illustrates the situation. A given path starts at s = 0 and runs with the path coordinate s to the end point s = sF . The joint coordinates qj of the robot have to be adapted to the path in a way, so that the end effector coordinate system is exactly located on the trajectory. Applying now the formulas (7.28) to the equations of motion we come out with Ti =Ai(s)(s\u03072)\u2032 + Bi(s)(s\u03072) + Ci(s), (i = 1, 2, \u00b7 \u00b7 \u00b7 , f) Ai(s) = 1 2 \u2211 j Mijq \u2032 j , Bi(s) = \u2211 j Mijq \u2032\u2032 j + \u2211 j \u2211 k [ j k i ] qjqk, Ci(s) = \u2202V \u2202qi , (7",
            "29) would be preserved if we add any addional forces or torques depending only on s. A formal integration of equation 7.29 yields s\u03072(s) = s\u03072(s0) + s\u222b s0 exp  v\u222b s0 ( Bi Ai )du  \u00b7 (Ti \u2212 Ci Ai )dv  exp  s\u222b s0 ( Bi Ai )du  . (7.30) For achieving optimal solutions for the path planning problem we have more elegant ways than using the relation (7.30), though it might be helpful for special cases. We represent the given path by a vector r originating from an inertial system and ending in some path point (Figure 7.6). Such a trajectory point depends on the joint coordinates qT = (q1, q2, \u00b7 \u00b7 \u00b7 , qf ) or r = r(q), so that the derivatives with respect to s result in q\u2032 =  ( \u2202r \u2202q )T [( \u2202r \u2202q )( \u2202r \u2202q )T]\u22121  \u00b7 r\u2032 q\u2032\u2032 =  ( \u2202r \u2202q )T [( \u2202r \u2202q )( \u2202r \u2202q )T]\u22121  \u00b7 [ r\u2032\u2032 \u2212 ( \u2202r \u2202q ) q\u2032 ] . (7.31) The above equations anticipate the fact that in the following we consider motion along the trajectory only and do not take into account the attitude behaviour of the hand, for example. The latter case would demand inclusion of directional terms into equation(7",
            " The most important constraints are the following: \u2022 The joint torques or forces are limited, which means Ti,min \u2264 [Ai(s)(s\u03072)\u2032 + Bi(s)(s\u03072) + Ci(s)] \u2264 Ti,max. (7.34) For many applications we shall assume Ti,min = \u2212Ti,max. \u2022 The joint angular or translational velocities may be limited due to some maximum speeds of the drive train components, q\u0307i,min \u2264 [q\u2032is\u0307] \u2264 q\u0307i,max. (7.35) Again, we shall assume q\u0307i,min = \u2212q\u0307i,max. \u2022 The path velocity itself might become constrained by some manufacturing process \u2212vmax \u2264 |r\u2032|s\u0307 \u2264 +vmax, (7.36) with the vector r from Figure 7.6. The relations (7.35) and (7.36) define together a maximum velocity s\u0307G along the path which must not be exceeded: 0 \u2264 (s\u03072) \u2264 (s\u03072)G, with (s\u03072)G = min [ ( q\u0307i,max q\u2032i )2, ( vmax |r\u2032| )2 ] . (7.37) The solution of the time-optimal problem given with the relations (7.33) to (7.37) may be constructed in the following manner: We look at the equations (7.34) for the limiting cases (Ti,min, Ti,max) stating, that minimum time can only be achieved by applying in a maximum number of joints the limiting torques or forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003685_022-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003685_022-Figure2-1.png",
        "caption": "Figure 2. Melt pool surface modelling.",
        "texts": [
            " Therefore, the problem of predicting the melt pool depth and dilution reduces to a heat conduction problem where the heat source is placed on the melt pool top surface. As mentioned before, the main goal of this modelling is to develop a model predicting the dilution in real time applications. Since the height and width of the melt pool can be measured by a vision system, it is assumed that they are given parameters. By knowing these values and considering a parabolic equation for the borders of the melt pool shown in figure 2, the following equations can be derived. According to figure 2(a), the upper melt pool surface can be modelled as z = h(x)|y=0 = h0 [ 1 \u2212 (x + L2) 2 (L1 + L2)2 ] , (1) where h(x)|y=0 is the melt pool height at the centre line of the clad (i.e. y = 0 and at point x), h0 is the clad height (m), and L1 and L2 are dimensional parameters as shown in figure 2(a). It is assumed that the clad height has a parabolic cross section (see figure 2(d)), and hence, the melt pool height at each point of (x, y) is obtained as h(x, y) = h(x)|y=0 [ 1 \u2212 y2 w(x)2 ] , (2) where w(x) is the melt pool width at section x. By considering a circular shape for the top view of the melt pool in x > 0 and a constant width for x < 0 , w(x) is obtained as w(x) = w0 [ sign(\u2212x) + ( 1 \u2212 x2 (w0/2)2 )1/2 sign(x) ] , \u2212L2 x L1 (3) where w0 is the clad width (m) and sign is defined as sign(x) = { 1 x 0 0 x 0. (4) Figure 3 shows a schematic view of the heat conduction problem in a LPD process",
            " (25) Since zm is not an explicit function with respect to V , the critical scanning speed can be obtained by taking the differential from equations (21) and (23) with respect to V which yields d\u03c6Tm1 dV = \u2202\u03c6Tm1 \u2202V + \u2202\u03c6Tm1 \u2202xm dxm dV + \u2202\u03c6Tm1 \u2202zm dzm dV + \u2202\u03c6Tm1 \u2202h0 dh0 dV = 0, (26) d\u03c6Tm2 dV = \u2202\u03c6Tm2 \u2202V + \u2202\u03c6Tm2 \u2202xm dxm dV + \u2202\u03c6Tm2 \u2202zm dzm dV + \u2202\u03c6Tm2 \u2202h0 dh0 dV = 0. (27) In the LPD process the clad height and scanning speed are related to each other. By considering a parabolic shape for the clad (see figure 2) and applying the mass balance rule, the clad height is obtained by h0 = 3\u03b1powderm\u0307 2\u03c1powderw0V , (28) where \u03b1powder is powder catchment efficiency, m\u0307 is powder flow rate (kg s\u22121) and \u03c1powder is powder density (kg m\u22123). By taking the differential from the above equation with respect to scanning speed, it yields dh0 dV = \u2212 3\u03b1powderm\u0307 2\u03c1powderw0V 2 . (29) By considering equations (25)\u2013(28), the critical scanning speed can be obtained as Vcr = \u221a 3\u03b1powderm\u0307 2\u03c1powderw0 \u00d7 J2 J1 , (30) where J1 and J2 are the Jacobians as follows: J1 = \u2223\u2223\u2223\u2223\u2202(\u03c6Tm1 , \u03c6Tm2) \u2202(x, V ) \u2223\u2223\u2223\u2223 , (31) J2 = \u2223\u2223\u2223\u2223\u2202(\u03c6Tm1 , \u03c6Tm2) \u2202(x, h0) \u2223\u2223\u2223\u2223 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000630_tro.2021.3060969-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000630_tro.2021.3060969-Figure2-1.png",
        "caption": "Fig. 2. Modular design of the gripper. (a) Diagram of a single module of the modular gripper. (b) Cross section of the module. (c) Whole modular gripper.",
        "texts": [
            " 1) Large grasping range: the gripper can grasp objects of different sizes that cover most of the daily supplies. 2) Sufficient stiffness: the gripper can grasp heavy objects without unwanted deformation. 3) Compact structure and light weight. 4) No adding of extra energy sources other than pneumatics. Our gripper is symmetrically structured and is composed of four identical modules (see Fig. 1). The four modules are arranged as two pairs, and within one pair, one module is placed opposite the other. Each module [see Fig. 2(a)] contains three pneumatic actuators: a distance-adjusting actuator, an angleadjusting actuator, and a finger actuator, along with several pieces of 3-D printed rigid components (e.g., connectors and sliders). We designed the distance-adjusting actuators as linear actuators for adjusting the distances between modules on the side direction, and angle-adjusting actuators as bending actuators for adjusting the angle between modules within a pair. We chose a serial configuration for the distance-adjusting actuator, angle-adjusting actuators, and finger actuator arrangement in each module to simplify the construction process as well as the control algorithm. Yet a serial configuration, compared with its parallel counterpart, usually suffers from the problem of low stiffness, thus, we pay particular attention to guarantee sufficient stiffness in the actuator design. The distance-adjusting actuator is composed of an inner soft actuator and an outer rigid exoskeleton to enhance its stiffness in both the axial and the bending directions [see Fig. 2(b)]. The inner soft actuator possesses a circumferentially symmetrical bellow structure and when inflated, it expands axially. However, a pure soft actuator would suffer from buckling when a critical axial compressive force is exerted. In addition, pure soft Authorized licensed use limited to: Dalhousie University. Downloaded on May 25,2021 at 12:16:37 UTC from IEEE Xplore. Restrictions apply. actuators have bending stiffness far from enough to bear loads from side directions. To overcome the aforementioned problems with pure soft actuators, a rigid exoskeleton, including an inner slider and an outer slider [see Fig. 2(b)], is designed to house the soft actuator. When compressed air is fed into the inner soft actuator, it expands and causes relative linear motion between the inner slider and the outer slider. For the angle-adjusting actuator, we used a fabric-reinforced bending elastomer actuator with relatively thick walls, also to guarantee its bending stiffness. When inflated, the angleadjusting actuators bend outward, increasing the angle between opposite actuator. For the finger actuator, we optimized the \u201cfast-pneu-net\u201d actuator [19] design by adopting a decreasing width design, so as to further improve the gripper\u2019s grasping performance by increasing the contact area with various objects being gripped. When inflated, the finger actuators bend inward and execute an action of prehension. Modular design facilitates easy maintenance and replacement of the gripper components. In order to make the gripper compact and easy to install on a robotic arm, we 3-D printed a single piece of fixing structure to replace the four separate outer sliders, as shown in Fig. 2(c). 1) Soft-Rigid Hybrid Distance-Adjusting Actuator: Distance-adjusting actuators are used to adjust the distance between modules to increase the gripper\u2019s ability for grasping long objects. The distance adjusting actuators are located at the root of the gripper, bearing loads from all the left part as well as the grasped objects, so they must have enough axial stiffness, bending stiffness, and torsional stiffness. Considering the gravity and inertial force of objects being grasped by the gripper, we estimated that the axial stiffness of the distance-adjusting actuators should be greater than 750 N/m, and should be able to resist a bending moment of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure3-28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure3-28-1.png",
        "caption": "Figure 3-28. Resonant DC link inverter. Figure 3-29. Resonant pole inverter.",
        "texts": [
            " Now that most resonant principles and topologies have been established, the challenge for the next decade will be to reduce the number of components and simplify the construction of resonant converters. Operation of the DC resonant link (RL) and resonant pole (RP) inverters are complementary in many respects, and both introduce more than double stresses on the semiconductor switches. In case of the RL circuit the voltage stresses are in the order of 2-2.5 per unit (p.u.). Under steady-state conditions the average voltage across the inductor needs to be zero and the link voltage (Flink) has to reach zero to ensure soft switching. As indicated in Figure 3-28, the steady-state condition requires area 1 = area 2 which implies a voltage stress larger than 2 p.u. Similarly, in the case of the RP inverter, steady state requires that the average of voltage at the output should not change and charge balance can only be achieved if area 1 = area 2 for the inductor current (IL), Figure 3-29, which implies larger than 2 p.u. current stresses on the switches. The 2-2.5 p.u. stresses on the switches in the RL and RP inverters demand that the installed rating of semiconductors needs to be doubled"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure15.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure15.3-1.png",
        "caption": "Fig. 15.3 Analytical tire model",
        "texts": [
            "1 summarizes studies on standing waves in tires. Analytical models are classified according to the dimensions for analysis, the types of parameters and the modeling strategy, such as the wave propagation approach or resonance approach. A one-dimensional model considers only the circumferential direction, while the two-dimensional model considers both circumferential and width directions. As Pacejka [12] mentioned, the equations of these models are different but the results are not greatly different. In Table 15.1 and Fig. 15.3, EI is the flexural rigidity of the tread band, Ex is the extensional stiffness of the tread band in the circumferential direction, Tx and Ty are, respectively, the tensions of the tread band in the circumferential and width directions, kr is the fundamental radial spring rate of the 15.1 Studies on Standing Waves in Tires 1131 T ab le 15 .1 Su m m ar y of st ud ie s on st an di ng w av es in tir es R es ea rc he rs B el t st iff ne ss T en si on St iff ne ss (c ar ca ss , et c. ) D am pi ng (c ar ca ss , et c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.1-1.png",
        "caption": "Fig. 5.1: Five-Speed Automatic Transmission, Example 1. Stage,[91]",
        "texts": [
            " Clutch A B C D E F 1st Gear x - - - - - 2nd Gear x - - - x - 3rd Gear x - - x - - 4th Gear x x - - - - 5th Gear - x - x - - R-Gear - - x - - x called one-way clutch gear shifting. The case that the ratio change is performed only by engaging and disengaging wet clutches, is termed overlapping 5.1 Automatic Transmissions 215 gear shifting. In both cases engagement and disengagement of shift elements are performed simultaneously. Hence, the driving torque in the drive train is not interrupted while changing the gear ratio. Some explanations with respect to Figure 5.1 have already been given in connection with the hydraulic unit of the automatic transmission (Figure 4.21 on page 210). Table 5.1 presents a scheme of the clutches, which have to be closed for establishing the various stages (character \u201dx\u201d for closed). Together with Figure 5.1 the possible combinations are obvious. To model the complete drive train we work on the following assumptions, which have been derived from the real system as shown in Figure 4.18 on page 208. A drive train with automatic transmission generally consists of five main components: engine, torque converter, gear box, output train and vehicle. Each component of the drive train can be considered as a rigid multibody system. The partitioning into single bodies is often given by their technical function",
            " The differential gear is used to divert the rotating motion from the drive shaft longitudinal axis to the output shaft longitudinal axis. The vehicle model takes into account the vehicle mass, the rolling friction, the driving resistance, the tire elasticity and damping. In the following we shall derive in a first step the component models and then in a second step the system model. The section closes with some typical results and with comparisons with measurements. With respect to the engine model we rely on performance maps and approximate motor dynamics by two degrees of freedom. Figure 5.1.2 depicts the basic model. With the help of a measured performance map, for example Figure 5.3, we determine a drive torque MKF depending on the accelerator position \u03b1DK of the driver and on the engine speed \u03c6\u0307M . This torque MKF may be reduced during switching by the motor engagement angle \u03b2 by using the digital engine electronics (DME), which works in connection with the gear control electronics (EGS). The measure of reduction depends on the engine speed and the torque MKF itself. Due to delays in connection with changes of the throttle valve position, of the motor control and of the motor speed the engine generates the engine torque MM also in a delayed manner, an effect, which can be approximated by a first order delay element with delay time TM , see Figure 5.1.2. This effect is important especially with respect to starting and shifting processes. The engine losses comprise friction in bearings and the drive losses of all auxiliary equipment. They are expressed by the loss torque MV and of course indirectly included in the performance characteristics of Figure 5.3. As a final result we have the torque (MM \u2212MV ) which represents one part of the engine shaft load, the other part being the torque of cut MMS to the adjacent components. The moment of inertia of the engine shaft includes the inertia of the shaft itself, but also in a summarized way the projected inertias of the crankshaft, the pistons and the piston rods and of all relevant auxiliary equipment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure25-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure25-1.png",
        "caption": "Fig. 25. Contact and bending stresses for version 2 of face-gear drive, generated by a rounded-top shaper.",
        "texts": [],
        "surrounding_texts": [
            "The finite element analysis has been performed for two versions of face-gear drives of common design parameters represented in Table 3. The versions correspond to face-gear drives with conventional and rounded fillet, respectively (Fig. 4). The finite element mesh of five pair of teeth of version 2 is represented in Fig. 22. Elements C3D8I [5] of first order enhanced by incompatible modes to improve their bending behavior have been used to form the finite element mesh. The total number of elements is 67,240 with 84,880 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Fig. 23 shows the whole finite element model of the gear drive. Figs. 24 and 25 show the maximum contact and bending stresses obtained at the mean contact point for gear drives of two versions of fillet (see Fig. 4). It is confirmed that the bending stresses are reduced more than 10% for the face gear generated with a rounded-top shaper in comparison with the face gear generated with a edged-top shaper. The performed stress analysis has been complemented with investigation of formation of the bearing contact (Figs. 24 and 25). The obtained results show the possibility of an edge contact in face-gear drives by application of involute pinion. Avoidance of edge contact requires the changing of the shape of the pinion profiles. Fig. 26 illustrates the variation of bending and contact stresses of the gear and the pinion during the cycle of meshing. The stresses are represented as functions of unitless parameter / represented as / \u00bc /P /in /fin /in ; 06/6 1: \u00f032\u00de Here /P is the pinion rotation angle; /in and /fin are the magnitudes of the pinion angular positions in the beginning and the end of the cycle of meshing. The unitless stress coefficient r (Fig. 26) is defined as r \u00bc rP rPmax ; jrj6 1: \u00f033\u00de Here rP is the variable of function of stresses, and rPmax is the magnitude of maximal stress. The increase of contact stresses during the cycle of meshing is caused by the edge contact."
        ]
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.17-1.png",
        "caption": "Fig. 7.17",
        "texts": [],
        "surrounding_texts": [
            "By comparing the corresponding phase diagrams in Fig. 7.12 and Fig. 7.13, we find that the original homoclinic orbits H and H' break into two curves respectively. They divide plane e; into two regions (Fig. 7.14). They are two stable singular points, and are also attractor regions. For the original vibration system, the motion finally tends to S or S' , depending upon the initial conditions. These two regions are twinned to each other. The proper change of the initial condition will cause great variation in the final stationary states. 252 Bifurcation and Chaos in Engineering The twinning of the two-attractor regions, however, is not the whole of the problem. Fig. 7.13 is the phase diagram of the averaging equation on the rotating plane. Let us discuss again the phase diagram of the averaging equation and the real equation as shown in Fig. 7.8 and Fig. 7.7. Can we guess the type of Fig. 7.7 from Fig. 7.8 ? It is possible in linear systems, because there is only one equilibrium point A. However, it is rather complicated if we guess the real c; plane curves from Fig. 7.13. Roughly speaking, the periodic wave added to the track line in Fig. 7.13 will not be large if the amplitude is not large. So even if the shape of the dividing line is not as smooth as that in Fig. 7.14, we can still divide the plane into two parallel bands, that is to say, there exist two attractor regions. But, if the amplitude of the disturbing force is large enough, then the amplitude of the wave to be added is large. Furthermore, as the c; system is not autonomous, a track line may intersect itself or track each other. Besides, there is a certain kind of motion that approaches neither S nor S', but wanders between S and S'. This is what we call \"non-periodic motion\", and even damping exists. It is different in property from the curve Fig. 7.14 c3 where damping does not exist (Fig. 7.11), which is the process of chaos that we are going to discuss. Chaos depends upon the initial conditions. The dependence is extremely sensitive. The above statement is only a guess or an estimation. It indicates that the averaging method (together with other methods of approximation, such as the method of perturbation, the asymptotic method and so on) may fail, because its results are not qualitatively correct in comparison with practice. This was not recognized until the middle of the 1970s. It is necessary to take this into acount in future so as to determine the range of utility. 7.4.3 The Sub harmonic Solution of the Duffing Equation One third subharmonic resonant vibration may occur when the disturbing frequency satisfies ro = 3roo. The amplitude of the subharmonic solution can be obtained by the use of the averaging method on the rotating plane, except that now the rotating angular velocity is } , instead of ro. So, the fixed point on the rotating plane equals the subharmonic solution, and the disturbing force turns one circle when the plane rotates three turns. Assuming 1 . 1 x = c; cos-rot + 11 sm -rot 3 3 (7.81) x' 1 . 1 Y = -- = -c;cos-rot + 11 sm-rot ro/3 3 3 (7.82) the amplitude can be solved by the equation \u00b7 M th d in Bifurcation Theory Application of the A veragmg e 0 253 254 Bifurcation and Chaos in Engineering (7.83) so, the solution is (7.84) The subharmonic solution can be obtained only when the value of damping is small; ro is a little bit larger than 3roo' when E > O. As shown in Fig. 7.15, there are possibly three solutions when ro = ro'. CD x = A~I) coJ!.ro '( +pC.,I\u00bb) + AI(l) cos(ro '( +p~I\u00bb+ ... i \\3 i The first harmonic solution has already been obtained. The second solution is unstable. The third subharmonic solution is what we want to determine. We can see, therefore, that the component of the harmonic wave is somewhat weaker, i.e. A?) < A?), when harmonic solution exists. When ro = ro', the occurrence of subharmonic solutions is determined by the initial conditions. The phase diagram of the averaging equation on the rotating plane is shown in Fig. 7.16. There are seven singular points on plane S . The origin gives out a harmonic solution; of the three saddle points two give out an unstable subharmonic solution; three focus points give out a stable subharmonic solution. Part of the curves pass through two boundary lines, which divide the S plane into the attractive regions of a harmonic wave solution and the attractive regions of a subharmonic solution respectively. 7.4.4 The Present State ofthe Art ofthe Duffing Equation Study"
        ]
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure18-1.png",
        "caption": "Fig. 18. Determination of disk surface RD: (a) and (b) installment of grinding disk; (c) line LrD of tangency of surfaces Rr and RD; (d) illustration of generation of surface Rs by disk surface RD.",
        "texts": [
            " 0045-7825/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0045-7825(03)00367-0 Nomenclature ai (i \u00bc d; c) normal pressure angle for the driving profile (i \u00bc d) or the coast profile (i \u00bc c) at the point of tangency of mismatched rack-cutters (Fig. 6) b helix angle (Figs. 5 and 8) cDp crossing angle between the disk and the pinion (Figs. 18 and 19) cwp crossing angle between the worm and the pinion (Fig. 21) ki (i \u00bc p;w) lead angle of the pinion (i \u00bc p) or of the worm (i \u00bc w) (Fig. 21) qD radius of generating disk (Fig. 18) /i (i \u00bc 1; 2) angle of rotation of the pinion (i \u00bc 1) or the gear (i \u00bc 2) in the process of meshing wi (i \u00bc r; 1; 2) angle of rotation of the profile-crowned pinion (i \u00bc r), the double-crowned pinion (i \u00bc 1), or the profile-crowned gear (i \u00bc 2) in the process of generation Dc shaft angle error (Fig. 14) Dk lead angle error Dki (i \u00bc 1; 2) correction of lead angle of the pinion (i \u00bc 1) or the gear (i \u00bc 2) D/2\u00f0/1\u00de function of transmission errors Dwp additional rotational motion of the pinion during the feed motion (Fig",
            " The contents of this section cover longitudinal crowning of the pinion by application of a plunging generating disk. The same goal (double-crowning) may be achieved by application of a generating worm (see Section 6). The approach is based on the following ideas: ii(i) The profile-crowned surface Rr of the pinion is considered as given. i(ii) A disk-shaped tool RD that is conjugated to Rr is determined (Fig. 17). The axes of the disk and pinion tooth surface Rr are crossed and the crossing angle cDp is equal to the lead angle on the pinion pitch cylinder (Fig. 18(b)). The center distance EDp (Fig. 18(a)) is defined as EDp \u00bc rd1 \u00fe qD; \u00f029\u00de where rd1 is the dedendum radius of the pinion and qD is the grinding disk radius. (iii) Determination of disk surface RD is based on the following procedure [6,7]. Step 1. Disk surface RD is a surface of revolution. Therefore, there is such a line LrD (Fig. 18(c)) of tan- gency of Rr and RD that the common normal to Rr and RD at each point of LrD passes through the axis of rotation of the disk [6,7]. Fig. 18(c) shows line LrD obtained on surface RD. Rotation of LrD about the axis of RD enables representation of surface RD as the family of lines LrD. Step 2. It is obvious that screw motion of disk RD about the axis of pinion tooth surface Rr provides surface Rs that coincides with Rr (Fig. 18(d)). (iv) The goal to obtain a double-crowned surface R1 of the pinion is accomplished by providing of a com- bination of screw and plunging motions of the disk and the pinion. The generation of double-crowned pinion tooth surface is illustrated in Fig. 19 and is accomplished as follows: (1) Fig. 19(a) and (b) shows two positions of the generated double-crowned pinion with respect to the disk. One of the two positions with center distance E\u00f00\u00de Dp is the initial one, the other with EDp\u00f0w1\u00de is the current position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure4.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure4.2-1.png",
        "caption": "Fig. 4.2: The basic lithographic exposure methods. According to [Mokw93]",
        "texts": [
            " Ultraviolet light with a wavelength bet ween 250 nm and 450 nm is mainly used for the silicon process. The mask is made of a light-transparent substrate, usually glass of a few mm thickness and a light-blocking layer deposited onto it. This so-called absorber layer, in general made of chromium, masks up the resist which is to remain unexpo sed. It is only a few 100 nm thick and is deposited onto the glass substrate, using a sputtering technique. In practice, three basic lithographic methods are used, Fig. 4.2: \u2022 Contact lithography means pressing the mask directly onto the substrate. A very precise structural resolution of better than 1 ~-tm can be reached. However, contact lithography is not suitable for mass-production, since the mask is exposed to a high mechanical load during exposure and it can be easily damaged by dust particles deposited on it from the surrounding. \u2022 In proximity lithography, there is an air gap of 20 to 50 ~-tm between the mask and the wafer. This reduces the wear on the mask, but due to the Fresnel diffraction of light, the resolution is limited to 2 ~-tm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure14-1.png",
        "caption": "Fig. 14. Illustration of installment of coordinate systems for simulation of misalignment.",
        "texts": [
            " 5 and 8) cDp crossing angle between the disk and the pinion (Figs. 18 and 19) cwp crossing angle between the worm and the pinion (Fig. 21) ki (i \u00bc p;w) lead angle of the pinion (i \u00bc p) or of the worm (i \u00bc w) (Fig. 21) qD radius of generating disk (Fig. 18) /i (i \u00bc 1; 2) angle of rotation of the pinion (i \u00bc 1) or the gear (i \u00bc 2) in the process of meshing wi (i \u00bc r; 1; 2) angle of rotation of the profile-crowned pinion (i \u00bc r), the double-crowned pinion (i \u00bc 1), or the profile-crowned gear (i \u00bc 2) in the process of generation Dc shaft angle error (Fig. 14) Dk lead angle error Dki (i \u00bc 1; 2) correction of lead angle of the pinion (i \u00bc 1) or the gear (i \u00bc 2) D/2\u00f0/1\u00de function of transmission errors Dwp additional rotational motion of the pinion during the feed motion (Fig. 24) Dsw translational motion of the grinding worm during the feed motion (Fig. 24) DE center distance error (Figs. 12 and 14) Ri surfaces (i \u00bc c; t; r; s; 1; 2;w;D) ac parabola coefficient of profiles of pinion rack-cutter in its normal section (Fig. 7) amr parabola coefficient of the parabolic function for the modified roll of feed motion apl parabola coefficient of plunging by grinding disk or by grinding worm b parameter of relative tooth thickness of pinion and gear rack-cutters EDp shortest center distance between the disk and the pinion (Figs",
            " The normals to the tooth surface at any point of line L0 are collinear and they intersect in the process of meshing the instantaneous axis of relative motion that is the tangent to the pitch cylinders. The concept of pitch cylinders is discussed in Section 2. The involute gearing is sensitive to the following errors of assembly and manufacture: (i) the change Dc of the shaft angle, and (ii) the variation of the screw parameter (of one of the mating gears). Angle Dc is formed by the axes of the gears when they are crossed, but not parallel, due to misalignment (see Fig. 14). Such errors cause discontinuous linear functions of transmission errors which result in vibration and noise, and may cause as well edge contact wherein meshing of a curve and a surface occurs instead of surface-to- surface contact (see Section 9). In a misaligned gear drive, the transmission function varies in each cycle of meshing (a cycle for each pair of meshing teeth). Therefore the function of transmission errors is interrupted at the transfer of meshing between two pairs of teeth (see Fig",
            " The meshing and contact are simulated in the paper for two cases: (i) the pinion of the gear drive is profile-crowned, and (ii) the pinion is double-crowned (see Sections 5\u20137). Comparison of the output for both cases (Sections 4 and 7) shows that double-crowning of the pinion enables to reduce the transmission errors and noise and vibration of the gear drive. Drawings of Fig. 13 illustrate instantaneous tangency of surface Rr and R2 in a fixed coordinate system Sf . The surfaces have to be represented in Sf taking into account the errors of alignment (see Fig. 14). Knowing the representation of tooth surfaces Rr and R2 in coordinate systems Sr and S2 that are rigidly connected to the pinion and the gear, we may represent surfaces Rr and R2 in fixed coordinate system Sf . We use for this purpose the coordinate transformation from Sr and S2 to Sf . It is supposed that Rr and R2 are profile-crowned and therefore they are in point tangency. Tangency of Rr and R2 at common point M means that they have at M the same position vector and the surface normals are collinear",
            " In accordance to the theorem of implicit function system existence [4], observation of inequality D 6\u00bc 0 enables to solve the system of Eqs. (23)\u2013(26) by functions fuc\u00f0/r\u00de; hc\u00f0/r\u00de;wr\u00f0/r\u00de; ut\u00f0/r\u00de; ht\u00f0/r\u00de;w2\u00f0/r\u00de;/2\u00f0/r\u00deg 2 C1: \u00f027\u00de Solution of system of nonlinear Eqs. (23)\u2013(26) is an iterative computerized process based on application of Newton\u2013Raphson method [15]. The computational procedure provides the paths of contact on pinion and gear tooth surfaces and the function of transmission errors. We have applied for the simulation of meshing the following coordinate systems (Fig. 14): ii(i) Movable coordinate systems Sr and S2 that are rigidly connected to the pinion and the gear, respec- tively (Fig. 14(a) and (c)). i(ii) The fixed coordinate system Sf where the meshing of tooth surfaces Rr and R2 of the pinion and gear is considered. (iii) All errors of assembly are referred to the gear. An additional fixed coordinate system Sc (Fig. 14(c) and (b)) is applied to simulate the errors of installment DE and Dc as parameters of installment of coordinate system Sc with respect to Sf . Rotation of the gear is considered as rotation of coordinate system S2 with respect to Sc. (iv) Errors of DE and Dc are illustrated in Fig. 14(b). Parameter L shown in Fig. 14(b) is applied to simulate such an error Dc of the shaft angle wherein the shortest distance between the crossed axes zr and z2 does not coincide with yf . An example of meshing of profile-crowned pinion and gear tooth surfaces has been investigated for the following data: N1 \u00bc 21, N2 \u00bc 77, m \u00bc 5:08 mm, b \u00bc 1, b \u00bc 30 , ad \u00bc ac \u00bc 25 , the parabola coefficient ac \u00bc 0:002 mm 1. The following errors of alignment have been simulated: (i) change of center distance DE \u00bc 1 mm; (ii) error Dk \u00bc 30 of the lead angle; (iii) change of shaft angle Dc \u00bc 30 and L \u00bc 0; (iv) change of Dc \u00bc 150 and L \u00bc 15 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.79-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.79-1.png",
        "caption": "Fig. 10.79 Ray of multiple reflections in a wedge having angle a [70]",
        "texts": [
            " The amplification of the sound radiated by sources due to the horn effect was almost 20 dB at around 1 kHz on the plane of a tire and around 5 dB by the side of the tire. Graf et al. [32] studied the horn effect using a three-dimensional BEM to identify the width of the effect of the cylinder and the directivity of amplification. The horn effect was illustrated using Ronneberger\u2019s wedge model [69], and Kuo et al. [70] applied ray theory to analyze the horn effect. The geometrical configuration of the wedge is sketched in Fig. 10.79, where a is the wedge angle. A point source of sound S is located at a distance d0 from the apex of the wedge, and the 10.11 Horn Effect 657 observer position is at a distance L and angle / relative to the road. The incident angle hn is defined as the angle between the incident ray and the normal to the road or wedge surface. The subscript n refers to the n-th reflection at reflection point Pn, which is at a distance dn from the apex of the wedge. The traveling distance between the n-th and (n + 1)-th reflection points is denoted ln"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure3-1.png",
        "caption": "Fig. 3 Tooth lengthwise curve of face hobbing",
        "texts": [
            "asmedigitalcollection.asme.org/ on 01/27/201 satisfy the required contact characteristics. The nongenerating method offers higher productivity than the generating method because the generating roll is eliminated in the former. The lengthwise tooth curve of face-milled bevel gears is a circular arc with the curvature radius equal to the radius of the tool Fig. 2 , while the lengthwise tooth curve of face hobbed gears is an extended epicycloid, which is kinematically formed during the relative indexing motion Fig. 3 . Therefore, the generating surfaces of face milling and face hobbing are totally different. In addition, facehobbing designs use a uniform tooth depth system, whereas most face-milling designs use tapered-tooth depth systems. Modern theory of gearing has been significantly enhanced with computerized approaches to the advanced design of gearings 3\u20136 . Computerized modeling and simulation of contact of spiral bevel and hypoid gears has been a major subject of interest of gear researchers. Most of published works were related to the facemilling process where a conical generating surface was considered 7\u201312 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.70-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.70-1.png",
        "caption": "Fig. 10.70 Finite cylindrical cavity",
        "texts": [
            "96) predicts two natural frequencies for the deflected tire, fl and fh corresponding to modes 1 and 2 are expressed by fl \u00bc c Lc\u00fe\u00f01 m\u00delcp fh \u00bc c Lc \u00f01 m\u00delcp : \u00f010:97\u00de The lower frequency, mode 1, for the deflected tire is lower than the undeflected resonant frequency. The higher frequency, mode 2, is higher than the undeflected frequency. (2) Wave resonance in a cylindrical cavity for undeformed tires Molisani et al. [74] applied the closed-form analytical model for a cylindrical cavity as shown in Fig. 10.70. The acoustic natural frequency of the undeformed cylinder is expressed by 10.10 Acoustic Cavity Noise of Tires 649 flqp \u00bc c ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pp a b 2 \u00fe 2l a\u00fe b 2 \u00fe qp L 2s b[ 0:5a \u00f010:98\u00de and the mode acoustic shape is given by wlqp\u00f0r; h; x\u00de \u00bc qc2Gpl\u00f0r\u00de cos\u00f0ph\u00de cos\u00f0kxqx\u00de with q; p; l \u00bc 0; 1; 2; . . .; \u00f010:99\u00de where Gpl\u00f0r\u00de \u00bc Y 0 p\u00f0kpl\u00deJp kpl r a J 0p\u00f0kpl\u00deYp kpl r a : \u00f010:100\u00de Jp is the Bessel function of the first kind, and Yp is the Bessel function of the second kind"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000231_tie.2021.3073313-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000231_tie.2021.3073313-Figure2-1.png",
        "caption": "Fig. 2. The structural design of the 2-DOF needle insertion device. All parts are shown in different colors.",
        "texts": [
            " From tb to tc, the relative sliding happens in the fast-backward motion phase, the shaft will move backward with a smaller step distance due to its inertia. The alternation of stick and slip gives rise to the step motion output of the shaft, on the end of which an arched needle is installed. The movement direction can be reversed by swapping the stick and slip phase orders and the step size can be controlled by scaling the movement range of the driving foot. The overall structural design of the 2-DOF needle insertion device is shown in Fig. 2. The axially unsymmetrical needle is installed on the shaft using a custom-made instrument Authorized licensed use limited to: Carleton University. Downloaded on June 04,2021 at 12:01:14 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 3 connector. A pair of linear motion bearings is mounted in bearing chocks of the connecting frame, on which the longitudinal-flexural composite piezoelectric actuator is connected",
            " The locating block and device cases were made by stereo lithography appearance 3D printer. The piezoelectric stack with a sphere header glued was placed on the slot of the locating block that was on the bottom of the case. Additional thin copper pads were placed under the locating block in order to adjust the preload force applied on the stack. The piezoelectric slates were glued on the side faces of the T shape beam. The flange of the flexure beam was connected to the case using bolts. The actuator was also mounted on the framework using blots as depicted in Fig. 2. The diameters of the holes on the framework were slightly larger than those of the bolts. In this way, the relative position between the actuation and the shaft could be adjusted to compensate the manufacturing errors. The insertion device performs stepper translational and rotary movements. As an open-loop control system, it is critical to output high resolution and consistent incremental step displacement, allowing for the needle insertion operation. The movement responses of the needle insertion device under driving pulses were characterized by laser displacement measurement system, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.4-1.png",
        "caption": "Fig. 5.4: Torque Converter and Model, P=pump wheel, T=turbine wheel, L=impeller, FL=one-way clutch (free wheel), TL=torque converter lock-up, [91]",
        "texts": [
            " We may go now two ways for modeling the torque converter, either applying a known theory based on a stream tube approach [97], which is quite frequently used in industry, or applying performance maps based on measurements. We shall go both ways. The first model according to [97] considers a stream tube for all three wheels and averages the partial differential equations for the fluid motion over the relevant cross-sections. The result of such a one-dimensional stream tube theory consists in a model with four degrees of freedom, which are indicated in Figure 5.4. The dynamics approximated by the pump speed \u03c6\u0307P , the turbine speed \u03c6\u0307T , the impeller speed \u03c6\u0307L and the oil volume flow V\u0307 can be described by the following set of equations 218 5 Power Transmission  a11 0 0 a13 0 a22 0 a23 0 0 a38 a33 a41 a42 a50 a43  \ufe38 \ufe37\ufe37 \ufe38 MW  \u03d5\u0308P \u03d5\u0308T \u03d5\u0308L V\u0308  \ufe38 \ufe37\ufe37 \ufe38 q\u0308W = =  \u2212a14V\u0307 \u03d5\u0307P \u2212 a17V\u0307 \u03d5\u0307L \u2212 a16V\u0307 2 \u2212MPV \u2212a24V\u0307 \u03d5\u0307P \u2212 a25V\u0307 \u03d5\u0307T \u2212 a26V\u0307 2 \u2212a35V\u0307 \u03d5\u0307T \u2212 a37V\u0307 \u03d5\u03072 L \u2212 a36V\u0307 2 hV  \ufe38 \ufe37\ufe37 \ufe38 hW +  MPS \u2212MTS \u2212MLS 0  \ufe38 \ufe37\ufe37 \ufe38 hWS (5.2) with the abbreviation hV = \u2212a44V\u0307 \u03d5\u0307P \u2212 a45V\u0307 \u03d5\u0307T \u2212 a46V\u0307 2 \u2212 a47\u03d5\u0307 2 P \u2212 a48\u03d5\u0307 2 T \u2212a48\u03d5\u0307P \u03d5\u0307T \u2212 a51V\u0307 \u03d5\u0307L \u2212 a52\u03d5\u0307P \u03d5\u0307L \u2212 a53\u03d5\u0307T \u03d5\u0307L \u2212 a54\u03d5\u0307 2 L "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure10-1.png",
        "caption": "Fig. 10 Coordinate systems Ss and Sr",
        "texts": [
            " In order to mathematically describe the generation process, we reak down the relative motion elements of the kinematical model hown in Fig. 5 and attach a coordinate system to each of them. oordinate system Sm Fig. 9 , called the machine coordinate sysem, is connected to the machine frame and considered as the eference of the relative motions. System Sm defines the machine lane and the machine center. System Ss is connected to the sliding base element 11 and repesents its translating motion. System Sr Fig. 10 is connected to he machine element 10 and represents the machine root angle etting. System Sc Fig. 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter. System Sp is connected to the machine element 9 and represents he work head setting motion Fig. 12 . System So is connected to he machine element 8 and represents the work head offset setting ournal of Mechanical Design om: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000628_j.mechmachtheory.2021.104262-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000628_j.mechmachtheory.2021.104262-Figure1-1.png",
        "caption": "Fig. 1. Elastic force on an external gear tooth.",
        "texts": [
            " In some engineering applications, gears are designed with addendum modifications to improve the load capacity and smoothness of the gear transmission. In previous works [6\u201310] , mesh stiffness calculations for standard gears were studied using the potential energy method. Based on the works of Refs. [10\u201312] , the bending stiffness, axial compressive stiffness, and shear stiffness of the external and internal addendum modified gear teeth are determined in this section. An external gear tooth model is shown in Fig. 1 . Based on the potential energy method, the bending stiffness, axial compressive stiffness, and shear stiffness are given in Eqs. (5\u20137) [10\u201312] . 1 K b = \u222b \u03b12 \u2212\u03b11 { 3 { 1 + cos \u03b11 [ ( \u03b12 \u2212 \u03b1) sin\u03b1 \u2212 cos \u03b1] } 2 \u00d7 ( \u03b12 \u2212 \u03b1) cos\u03b1 } 2 EL [ sin \u03b1 + ( \u03b12 \u2212 \u03b1) cos \u03b1] 3 d\u03b1 (5) 1 K a = \u222b \u03b12 \u2212\u03b11 ( \u03b12 \u2212 \u03b1) cos \u03b1sin 2 \u03b11 2 EL [ sin \u03b1 + ( \u03b12 \u2212 \u03b1) cos \u03b1] d\u03b1 (6) 1 K s = \u222b \u03b12 \u2212\u03b11 1 . 2(1 + v )( \u03b12 \u2212 \u03b1) cos \u03b1cos 2 \u03b11 EL [ sin \u03b1 + ( \u03b12 \u2212 \u03b1) cos \u03b1] d\u03b1 (7) The expressions for \u03b11 and \u03b12 of the external standard gear tooth have been given in Refs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.33-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.33-1.png",
        "caption": "Fig. 7.33 Displacement normal to the elastic half-space due to point loading [22]",
        "texts": [
            "4 Pressure Dependence of the Friction Coefficient on a Dry Surface (1) Load dependence of the friction coefficient For contact problems without friction as shown in Fig. 7.32a, the normal displacement uz at point A resulting from stress pz(x0, y0) at point B is calculated by integrating the product of pz(x0, y0) and Green\u2019s function, which is the displacement due to a point loading [21]. The stresses and displacements in an elastic half-space due to a point loading were derived by Boussinesq. The displacement of Boussinesq\u2019s solution normal to the elastic half-space is shown in Fig. 7.33, where the displacement is infinity at the point of loading. Using the solution derived by Boussinesq, the normal displacement uz due to arbitrary stress pz(x0, y0) is expressed as F=1.25 kN F=1.00 kN F=0.75 kN Li -off length x (cm) Q /Q cr experiment 2 0 theory 0.5 1 3 7/3 1.51.0 2.05/3 Fig. 7.31 Relationship between the rated shear force Q/Qcr and the lift-off length x. Reproduced from Ref. [18] with the permission of Tire Sci. Technol. 412 7 Mechanics of the Tread Pattern where E and m are, respectively, Young\u2019s modulus and Poisson\u2019s ratio of a body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure11-1.png",
        "caption": "Fig. 11. Original design analysis.",
        "texts": [
            " Gear micro-geometry design against pitting failure The current approach to the gear surface fatigue wear probem is gear surface micro-geometry optimisation as described in ection 2. The optimisation will be under real operating condiions, i.e. gear contact deformation, shaft deflection, interference hrink fit effect and dynamic loadings. All the micro-geometry odifications have been achieved through Python and Abaqus 28] interface. Python script software has been developed for odifying the gear micro-geometry and its running time is only bout 10 min CPU time. The first analysis has been carried out for the original design s shown in Fig. 11 and it clearly shows the high concentrated ontact in the one side near the edge. This high stress concenration is corresponding well with the local contact fatigue wear howing in Fig. 10. The gear specifications can be found in ection 2, the shaft misalignment and assembly deflection have een measured in the experimental tests and its maximum vales are summarized in Table 1 (coordination system as shown in ig. 9). The first micro-geometry modification is lead correction. ig. 12 shows a significant contact improvement compared to hat shown in Fig. 11. The concentrated contact area is moved rom one side toward the centre of the facewidth and the highest ontact pressure is reduced as well. The modified lead correction s 37 m instead of the original designed 8 m. The second micro-geometry modification is the gear tooth rofile tip relief. Fig. 13 shows the result from the original esign, 61 m and it shows the second gear tooth started in ontact. This tip relief is over relieved resulting in tip contact pitting failure. K. Mao / Wear 262 (20 c s t t o w t p t o a r u r 6 c m m s o o p b s m T a ontribution too late, contact ratio low and concentrated contact tress at the lowest point of single tooth contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000833_acsami.1c03572-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000833_acsami.1c03572-Figure5-1.png",
        "caption": "Figure 5. Assembly of 3D table structure by selective heating of 4D printed active hinges. (a\u2212c) Superimposed time-lapse images of each strip of the table base before and after the thermal activation of the respective hinge area. (d) Assembled table structure capable of standing stably on the table base and bearing the load from a 500 g dead weight.",
        "texts": [
            " The value of \u0394R/R0 reached about 15% under a uniaxial, nominal strain of 20% on the SMP sheet and did not significantly affect the temperature distribution according to the IR images, thus ensuring a good consistency in the thermomechanical properties of the SMP material throughout the stretching. \u25a0 DEMONSTRATIONS In this section, we demonstrate how complex 3D structures can be generated by locally programming printed flat structural elements via heating with fractal-based stretchable circuits. Table with Foldable Active Hinges Programmed by Uniaxial Stretching. Figure 5 illustrates the application of 4D printed active hinges to the facile assembly of furniture pieces, exemplified here by a small table structure. 4D printing of structural elements in initially planar shapes offers the interesting advantages to save fabrication time, avoid material wastage, and allow for compact storage during the transportation.18,20 Nonetheless, the activation of the shape morphing process still relies on a high environmental temperature. The table structure shown in Figure 5 is an assembly of a table top and a base composed of three bilayer strips, each with an active hinge that is thermally activated by an embedded heating circuit. The working principle of the 3D printed bilayer strips is the same as that of the structure shown in Figure 1e. A single fifth-order Hilbert curve-based circuit with a side length of 25 mm was patterned using the EFD microscale 3D printing technology and embedded in an SMP strip of 1.8 mm in thickness. After performing a uniaxial stretching of 5 mm along the longitudinal direction of the strip under steady-state heating, similar to the process depicted in Figure 4b, the SMP strip was subsequently cooled down to lock the programmed geometry and then bonded to an unstretched elastomer strip of 0.3 mm in thickness. The asfabricated bilayer strips remained flat before being assembled into a table, thus occupying a minimal vertical space. https://doi.org/10.1021/acsami.1c03572 ACS Appl. Mater. Interfaces XXXX, XXX, XXX\u2212XXX F During the assembly, the hinge area in each of the bilayer strips was selectively activated by the embedded, stretchable heating circuit (see Video S1). The shape morphing step from flat strips into 3D structural elements of the table base is presented in Figure 5a\u2212c, where time-lapse images of each strip before and after the thermal activation of the SMP material in the hinge area are superimposed in the respective subfigures. As shown in Video S1, the hinges in the three strips were heated with different input power values. For the first strip (Figure 5a), with an applied input power of 4 W, the deformation of hinge was triggered after about 15 s of heating and completed within 40 s. For the second strip (Figure 5b), the deformation of hinge was triggered after 10 s and completed within 33 s with an input power of 4.25 W. For the third one (Figure 5c), the deformation was triggered in 7.5 s and completed within 20 s with an input power of 4.5 W. Figure 5d depicts the assembled table structure after cooling which is capable of standing stably on the table base formed by the three 4D printed strips with active hinges and bearing the load from a 500 g dead weight. The similar shape morphing results for the three strips suggest a good repeatability of the proposed 4D printing paradigm to uniaxially stretch and program SMP components assisted by heating with embedded, stretchable circuits. Structure with Double Curvature Programmed by Biaxial Stretching"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.2-1.png",
        "caption": "Fig. 16.2 Three cases of wandering. Reproduced from Ref. [1] with the permission of Tire Sci. Technol.",
        "texts": [
            " Nakajima, Advanced Tire Mechanics, https://doi.org/10.1007/978-981-13-5799-2_16 1159 dynamics. Kobayashi et al. [7] investigated the relationship between the yaw rate and the subjective feeling considering vehicle dynamics, when a passenger vehicle travels along a rutted road under the condition of a fixed steer angle. Sasaki et al. [8] analyzed the wandering phenomenon of trucks using commercial software for multi-body dynamics (ADAMS). Yamashita and Shiraishi [1] categorized the wandering phenomenon into three cases. In the first case (Fig. 16.2a), when a vehicle enters a rut in the road, the slope at the rut edge may cause the vehicle to fall into the bottom of the rut, resulting in large accelerations in both the yawing and lateral directions. In the second case (Fig. 16.2b), when a vehicle runs on a rut, large steering adjustments may be required to run on the rut, also resulting in large accelerations in both lateral and yawing directions. In the third case (Fig. 16.2c), when a vehicle exits a rut, a large steering angle may be required to prevent the vehicle from falling into the bottom of the rut. This results in a strong lateral force, and there is oscillatory yawing of the 1160 16 Tire Properties for Wandering and Vehicle Pull vehicle after the vehicle exits the rut. This oscillatory does not decay rapidly enough to prevent wandering. The mechanism underlying the three cases is discussed in the following section. (1) Force equilibrium of a tire on a rut where h is the angle of the road slope, c is the camber angle, c0 is the initial camber angle and CFc is the camber stiffness. For simplicity, assuming the relation c0 = 0, Eq. (16.1) is rewritten as Fy \u00bc CF\u00feFzh 1 CFc=Fz : \u00f016:2\u00de Yamashita and Shiraishi [1] discussed the effect of tire properties on wandering in the three cases of Fig. 16.2. In the first case (Fig. 16.2a), when a tire enters a rut of the road, the strong unbalanced force f causes the rapid fall of the tire to the bottom of the rut as shown in Fig. 16.4a. f is generated by the difference between the lateral force due to the slope Fzh and the camber thrust CT. High camber stiffness thus improves the wandering phenomenon. In the second case (Fig. 16.2b), when a tire travels on a rut of the road, steering adjustments may be insufficient to follow changes in the road. The unbalanced force f thus arises from the continuous change in the road slope h as shown in Fig. 16.4b. 16.1 Wandering Due to Ruts 1161 To decrease f, the lateral force Fy needs to be stronger. If the cornering force CF and camber thrust CT are strengthened by the large camber stiffness and the large cornering stiffness, the wandering phenomenon is improved and the frequency of adjustments of the steering angle is reduced. In the third case (Fig. 16.2c), when a tire exits a rut, the road slope changes from h to zero. As shown in Fig. 16.4c, an initial unbalanced force f0 is generated when the tire exits the rut. Because the unbalanced force f oscillates after the tire exits the rut, the steering needs to be adjusted. Hence, the third case relates to vehicle stability, which is theorized using the stability factor discussed in Note 11.20. To improve the wandering phenomenon, the resonance frequency of yawing and the stability factor are increased and the initial unbalanced force f0 is reduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000002_j.engfailanal.2018.04.050-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000002_j.engfailanal.2018.04.050-Figure1-1.png",
        "caption": "Fig. 1. Diagram for illustrating the ACBB with a localized defect.(Note: the plane polar coordinate system given in the lower left corner is used to express the angular position of balls in following analysis.)",
        "texts": [
            " [26] is adopted in this study and it can be described as follows = \u23a7 \u23a8 \u23aa \u23a9 \u23aa \u2212 \u2212 \u2212 + \u2212 \u2264 \u2264 \u2212 \u2212 \u2212 + + < \u2264 +d \u03c8 hR R r \u03c8 \u03c8 \u03c8 \u03c8 \u03c8 \u03c8 \u03c8 hR R r \u03c8 \u03c8 \u03c8 \u03c8 \u03c8 \u03c8 \u03c8( ) min( 0.25 ( 0.5\u0394 ) ) if 0.5\u0394 min( 0.25 ( 0.5\u0394 ) ) if 0.5\u0394 0 if others j o j j o j j 2 2 f f 2 f f f 2 2 f f 2 f f f (3) where d(\u03c8j) is the depth profile at azimuth angle \u03c8j of jth ball, R is the radius of ball, and ro is the radius of outer raceway. The diagram of ACBB with a localized defect on outer raceway as well as the magnification when a ball passes over the localized defect area is shown in Fig. 1. Assuming that the groove curvature center of outer raceway of bearing O is fixed, the groove curvature center of inner raceway B and the central position of jth ball C are varying with external force and moment acted on the inner raceway. The geometry relations between jth ball center and inner/outer raceway groove curvature centers are shown in Fig. 2. The geometrical constraint equations of jth ball can be represented as follows \u2212 + \u2212 \u2212 \u2212 + =A X A X f D \u03b4( ) ( ) [( 0.5) ] 0,j j j j j1 1 2 2 2 2 i i 2 (4) + \u2212 \u2212 + =X X f D \u03b4[( 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003608_pime_proc_1986_200_135_02-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003608_pime_proc_1986_200_135_02-Figure12-1.png",
        "caption": "Fig. 12 Combined shear of fluid and solid surfaces in a n EHD contact",
        "texts": [
            " The effect of temperature on traction in elastohydrodynamic lubrication. Phil. Trans. R. SOC., 1980, Ser. A, 298(1438), 183-208. 17 Johnson, K. L. Contact mechanics, 1985, p. 275 (Cambridge University Press). 18 Roelands, C. J. A., Vlugter, J. C. and Waterman, H. I. The viscosity-temperature-pressure relationship of lubricating oils and its correlation with chemical constitution. Trans. ASME, J. Basic Engng, 1963, Ser. D, 85,601-607. APPENDIX 1 Allowance for elasticity of the discs in the viscoelastic and elasticplastic regimes Referring to Fig. 12, the relative tangential displacement between the two rollers, 2u, at any position x in the nip, is made up of two components: shear in the film 2u, and tangential compliance of the rollers 224,. Clearly u = u1 + u, so that the sliding speed AU = U , - U , = 2U = 2ir1 + 2U2 (29) Shear in the film is given by equation (l), that is Compliance of the rollers may be analysed approximately by modelling the rollers as an elastic foundation [see Johnson (17)], whereupon 2u -4 , - K where K is the tangential stiffness of the foundation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000691_j.rinp.2019.01.002-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000691_j.rinp.2019.01.002-Figure3-1.png",
        "caption": "Fig. 3. Computational domain used for simulation.",
        "texts": [
            " Thermal strain can be represented as [28,23] = = \u2212\u03b5 \u03b1 T \u03b1 T T\u0394 ( )th e e ref (11) where Tref is the reference temperature at t= 0. \u03b1 is the coefficient of thermal expansion which is a function of temperature and can be written as, = \u222b\u03b5 \u03b1 T T( )dth T T ref (12) So, effective stress can be written as = + + + + +\u03c3 \u03c3 \u03c3 \u03c3 \u03c5 \u03c3 \u03c3 \u03c3 \u03c3 \u03c3 \u03c32 ( )eff 1 2 2 2 3 2 1 2 1 3 2 3 (13) where \u03c3 \u03c3 \u03c3, , and1 2 3 are the three principal stresses. The governing equations for thermal and mechanical analysis were discretized and solved by finite element method using ANSYS 17.0. Fig. 3 shows the computational domain used for simulation. The dimension of the computational domain is 10\u00d7 1.5\u00d7 1mm3 for powder bed and for the substrate is 12.5\u00d73\u00d72mm3. Considering the calculation efficiency and computational precision, tetrahedral mesh structure was obtained for powder bed with fine meshing and hexahedral mesh for substrate was obtained with medium mesh. The computational domain meshed into 20,535 numbers of elements and 47,500 numbers of nodes respectively for transient thermal and mechanical analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000429_j.eml.2021.101180-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000429_j.eml.2021.101180-Figure7-1.png",
        "caption": "Fig. 7. Illustration of the folding angle of the BBF element and its geometrical parameters. (a) Folded BBF element. (b) Three BBF elements with different geometrical parameters and their corresponding folding angles.",
        "texts": [
            " (9) The BBF element can then be considered as a parallel combination of the kirigami unit and the elastomer layer. As a result, the relationship between the force F of the BBF element and stretching can be expressed as F = Fk + Fe. (10) redictions of Eq. (10) are included in Fig. 6 for the force\u2013 isplacement responses of BBF elements with different geometical parameters, showing that the theoretical model is in good greement with FE simulations. A simple model can be developed to estimate the dependence f the folding angle upon the geometrical parameters of the BBF lement and is shown in Fig. 7a where the thickness is t = + t1 and we have assumed that the residual strain in the lastomeric layer is negligible and hence the length of the layer s approximately 2a after folding. The relationship between the olding angle \u03d5 and the geometrical parameters a, L, t1 and t2 can then be obtained as \u03d5 = \u03c0 \u22122\u03b1 = \u03c0 \u22122 arcsin ( a \u221a a2 + t2 ) +2 arcsin ( a \u2212 L \u221a a2 + t2 ) . (11) Three samples of BBF elements with different sizes are manufactured and are shown in Fig. 7b, together with their corresponding folding angles. It can be seen that the experimental and theoretical results of the folding angles agree with each other very well. The agreement indicates that the folding angle can be accurately controlled through the quantitative design of geometry and, thus, provides great potential for the programmability of the BBF element for advanced applications, e.g., mechanical logic gates shown below. I F w T b d r c w l r d s s a t w Although mechanical logic gates cannot compete with the electronic counterparts in terms of calculation speed and volume capacity, they can be less vulnerable to extreme in-service conditions (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003254_3-540-45000-9_8-Figure2.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003254_3-540-45000-9_8-Figure2.1-1.png",
        "caption": "Figure 2.1. Basic motion tasks for a WMR: (a) point-to-point motion; (b) trajectory following",
        "texts": [
            " Results on forward and parallel parking experiments are reported. Finally, in Section 7 the obtained results are summarised and compared in terms of performance, ease of control parameters tuning, sensitivity to nonidealities, and generalisability to other WMRs. In this way, some guidelines are proposed to end-users interested in implementing control laws for WRMs. Open problems for further research are pointed out. The basic motion tasks that we consider for a WMR in an obstacle-free environment are (see Figure 2.1): \u2013 Point-to-point motion: The robot must reach a desired goal configuration starting from a given initial configuration. \u2013 Trajectory following: A reference point on the robot must follow a trajectory in the Cartesian space (i.e. a geometric path with an associated timing law) starting from a given initial configuration. (a) start goal Execution of these tasks can be achieved using either feedforward commands, or feedback control, or a combination of the two. Indeed, feedback solutions exhibit an intrinsic degree of robustness",
            " When using a feedback strategy, the point-to-point motion task leads to a state regulation control problem for a point in the robot state space \u2014 posture stabilization is another frequently used term. Without loss of generality, the goal can be taken as the origin of the n-dimensional robot configuration space. As for trajectory following, in the presence of an initial error (i.e. an off-trajectory start for the vehicle) the asymptotic tracking control problem consists in the stabilization to zero of ep = (ex, ey), the two-dimensional Cartesian error with respect to the position of a moving reference robot (see Figure 2.1b). Contrary to the usual situation, tracking is easier than regulation for a nonholonomic WMR. An intuitive explanation of this can be given in terms of a comparison between the number of controlled variables (outputs) and the number of control inputs. For the unicycle-like vehicle of Section 3, two input commands are available while three variables (x, y, and the orientation \u03b8) are needed to determine its configuration. Thus, regulation of the WMR posture to a desired configuration implies zeroing three independent configuration errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003253_cdc.1991.261510-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003253_cdc.1991.261510-Figure1-1.png",
        "caption": "Figure 1: A graphical representation of the deadzone.",
        "texts": [
            " Section 5 contains simulation results for a first-order nonlinear plant. Finally, Section 6 gives some concluding remarks. 2 Problem Setup and Assumptions In this section, some preliminary assumptions are made. The first assumption limits where the deadzone may appear in the plant. Assumption 1 The deadzone is in the span of the control. By this we mean that the systems under consideration are described by x = f (.I + g(.)u(t) (2.1) where u( t ) is the output of an unknown deadzone graphically described in Figure 1 and mathematically defined as follows: m , v ( t ) - m,b, for v ( t ) 2 b, m , v ( t ) - mrbr for v ( t ) 5 6,. for bl < v ( t ) < b, (2.2) We also make some assumptions on the deadzone parameters. Assumption 2 The following bounds on the deadzone parameters are known: m, 2 a > 0, mi 2 a > 0, b, > 0 , and bl < 0 where an a as known. CH3076-7/91/0000-2111$01 .OO 0 1991 IEEE 2111 The first two inequalities are roughly equivalent to knowing the sign of the high frequency gain coefficient, a common assumption for adaptive control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003716_70.795786-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003716_70.795786-Figure14-1.png",
        "caption": "Fig. 14. Configuration of a straight-arm robot.",
        "texts": [
            " We use the proposed control law in (42) to control the state of the system to track the reference signal . Figs. 10 and 11 show that the curves of the states and of the closed system, respectively. The control input is shown in Fig. 12 and the transient response shown in Fig. 13. The simulation results in Figs. 10 and 11 indicate the effect of all the unmodeled dynamics, BMF modeling errors and external disturbances on the tracking error is attenuated efficiently by the proposed controller. Example 3: We consider a straight-arm robot shown in Fig. 14. The single link is assumed to be a thin homogeneous rod of mass and the length . Also, it is assumed that a load carried by the robot can be modeled as a point mass at the end of the arm. The dynamic equations of this robot system [17] are where is the mass of the load, m sec is the acceleration due to gravity, is the torque input, and is the external disturbance and is assumed to be a square wave with the amplitude 0.1 and the period 2 . We assume that 4 kg, 2 m, and 0 2 kg. The bounds on dictate that the straight-arm robot can be operating anywhere from a no load condition ( 0) to a full load condition ( 2 kg)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000932_j.jii.2021.100218-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000932_j.jii.2021.100218-Figure14-1.png",
        "caption": "Fig. 14. The welding sequence of one layer. (a) the innermost circle is welded first, (b) the outermost circle is welded second, (c) then weld the remaining circles from inside to outside, (d) finish welding for one layer.",
        "texts": [
            " 13(b). After slicing the part, the 3D model of each layer was taken out for path planning. Based on the outer diameter of each layer, the number of paths and OD for each layer was determined, targeted at minimizing the overbuild volume. Table 3 presents the calculated OD for each layer. The information about OD and layer height was input to the proposed SVR system. As presented in Table 3, a set of welding process parameters can be obtained by our software. The deposition process is illustrated in Fig. 14(a)-(d), the outside and inside bead were deposited first to avoid collapse at the edge and then the rest of the weld beads were deposited successively. It is worth mentioning that the start point of each weld path is randomly designated so that the irregular bead shape can be spread out. After each weld path D. Ding et al. Journal of Industrial Information Integration 23 (2021) 100218 deposition, the pryrometer was controlled to measure the temperatures of the five randomly distributed points on the deposited path surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003486_robot.1996.509284-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003486_robot.1996.509284-Figure6-1.png",
        "caption": "Figure 6: The 3-type 3 mechanism",
        "texts": [
            " We may write two equations that indicate that points Bz, B3 slide along the given lines: (A + r cos(8) - x,)wY - ( ~ s i n ( 8 ) - ya)wU, = 0 (1) (A + s cos(8 + a ) - xb)uy - (2) (s sin(8 + a ) - y b ) u , = 0 Any of these two equations can be used to calculate X which is then substituted into the remaining equation. This leads to an equation of the type A cos(B)+B sin(8) = C which admit two solutions in 6. As there is an unique value of X for a given 8 the direct kinematics of this mechanism may have two solutions. The geometrical interpretation is that as Bz, B3 move on their lines point B1 lie on an ellipse: the possible locations of B1 are therefore the intersection of a line and an ellipse. 2.2.3 3-type 3 mechanism This mechanism is described in figure 6: the posture of the robot can be computed using the length r of link AIBl and 8 the angle between link AlBl and the x axis. The angles ai denote constant angles between the platform and the prismatic joint axis. The coordinates of Bz and the components of the unit vector v2 of the axis of the prismatic joint (link 2) are: B2 = { rs inO+csin(O+a1) v 2 = { sin(8 + crz ) Similarly the coordinates of B3 and the components of the unit vector v3 of the axis of the prismatic joint (link 3) are: cos(e + cr2 ) rcos8 + C C O S ( ~ + cy1) cos e + a cos(o + c y 3 ) cos(8 + a3) sin(8 + a3) We may now write two equations which indicate that the vectors ( A 3 B 3 , ~ 3 ) have the same direction as have the vectors (A2B2, v2): ( r cos 6 + c cos(8 + cy1) - U) sin(8 + a ~ ) - ( r sin 8 + csin(8 + a1)) cos(8 + 0 2 ) = 0 (3) (T cos8 + ccos(8 + a3) - ul ) sin(8 + aq) - ( r sin 8 + c sin(8 + a1) - w1) cos(8 + aq) = 0 (4) Using the first equation we can compute r as a function of 6 and substitute its value in the second equation",
            " The solution of the direct kinematics are obtained by intersecting the coupler curve with the line described by B2 as member of chain 2: consequently there is at most 4 intersection points. 2.3.5 This mechanism is presented in figure 11. If we con- 2-type 3 and 1 type 1 sider the mechanism A I B ~ B ~ B ~ A ~ it can be shown that B3 describes a coupler curve of order 4 with full circularity (i.e. 2). Consequently as the solutions of the direct kinematics problem for B3 are obtained by intersection this curve with the circle centered at A3 the number of real intersection points will be at most 4. Using the notation of figure 6 we write first that A2 belongs to the line coming from the platform: ( rcose + ccos(8 + al) - u)sin(8 + a2) - ( r s in6 + csin(8 + al)) cos(@ + ag) = 0 (12) Then we write that point B3 should be at distance 1-3 from A3: (Tcos8 + acos(8 + a3) - + (T sin 8 + a sin(8 + a3) - = ri (13) We use the linear equation (12) to compute r which is then back substituted in equation (13), now an equation in the sine and cosine of 8. We get then a fourthorder polynomial in T = tan(f?/2). 2.3.6 This mechanism is presented in figure 12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000556_j.mechmachtheory.2021.104265-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000556_j.mechmachtheory.2021.104265-Figure3-1.png",
        "caption": "Fig. 3. The coordinate system of joint i .",
        "texts": [
            " At this point, as long as the above conditions are satisfied, the four equations without \u03b8 i and \u03b8 i + 1 can be found, thus obtaining the IK solutions of the other four joints variable. Next, consider setting the attitude at the cut point so that one of the axes is collinear with the joint\u2019s corresponding axis. The attitude setting at the first cut point needs to consider the value of the included angle \u03b2 [52] . Since the standard D-H method is adopted in this paper to establish each joint\u2019s coordinate system, the i th joint\u2019s coordinate system is actually at the origin of the ( i + 1)th joint, as shown in Fig. 3 . When point P is taken as the separation point, the corresponding two sub-chains\u2019 terminal attitude in Eq. (2) will be consistent with the coordinate system { i }. Meanwhile, z R of sub-chain R\u2019s terminal attitude axis is always collinear with the (i + 1)th joint axis. At this moment, the value of \u03b2 affects the complexity of the sub-chain L\u2019s attitude equations. Case 1: \u03b2= 0, \u03c0 . The axes of the two joints are collinear, and the terminal attitude of the two sub-chains has z L = z R . This design usually does not come up in practice, so it is not considered in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.18-1.png",
        "caption": "Fig. 6.18: R5 - Gear Mesh with Backlash and Model",
        "texts": [
            " The jerky ignition pressure course as well as the irregularities of the crankshaft excite the system to produce vibrations, which are characterized by impulsive contacts between the meshing gears at the front and at the rear flanks thus generating a hammering effect. Hammering consists 6.2 Timing Gear of a 5-Cylinder Diesel Engine 349 in contact and detachment under load and results in very large load peaks. Consequently, this load is also influenced by the backlash itself, it increases with increasing backlashes due to larger kinetic energy in large plays. Therefore we must choose a force law based on two-sided force elements with play, see Figure 6.18 and see also Figure 6.8. The gear construction of this figure is well-known (see for example [170]), and according to that the tooth forces act in the directions of the lines of contact, which are the connecting tangential lines to the two base circles. Assuming a linear spring damper force law we may write for the contact forces Fmesh = (c \u00b7 g + d \u00b7 g\u0307)e1,2, where (g, g\u0307) are the deformation and deformation velocity in the contact. The spring and damper coefficients must be evaluated by a FEM-model or by the standard model of Ziegler [285], which due to its excellent approximations is still in use in industry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure15.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure15.9-1.png",
        "caption": "Fig. 15.9 Wave pattern on an expanded tire. Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [
            "39) are obtained as A \u00bc n0 k 1 a \u00fe 1 RD \u00bc 2l0 cot a np n0 1 a \u00fe 1 RD ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V Vc 2 1 r \u00bc a1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V Vc 2 1 r a1 \u00bc 2l0 cot a np n0 1 a \u00fe 1 RD L \u00bc 2p k \u00bc 4l0 cot a n ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V Vc 2 1 r f \u00bc V L \u00bc n tan a 4l0 VVcffiffiffiffiffiffiffiffiffiffi V2 V2 c p ; \u00f015:40\u00de where a1 is a constant determined by the tire construction, tire size and drum radius. (4) Wave pattern on an expanded tire If the tire speed is lower than the critical speed of the standing wave Vc, the radial displacement exponentially decays in the circumferential direction as shown in Eq. (15.35) and the left figure of Fig. 15.9. Meanwhile, if the tire speed is higher than the critical speed of the standing wave Vc, the standing wave forms outside the trailing edge of the contact patch as shown in the right figure of Fig. 15.9. The standing wave with a harmonic number n = 1 usually occurs, but the standing wave with n = 3 may occur in tires with a thin tread and large cross-sectional radius. When the inflation pressure increases, n0 decreases owing to the decrease in h0. Hence, on the basis of Eq. (15.40), the amplitude of the standing wave A decreases with increasing inflation pressure. When the load increases, n0 increases owing to the increase in h0. The amplitude of the standing wave A thus increases with the load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000628_j.mechmachtheory.2021.104262-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000628_j.mechmachtheory.2021.104262-Figure5-1.png",
        "caption": "Fig. 5. Contact deflection of two cylinders: (a) cylinder on a cylinder and (b) cylinder in a cylindrical socket.",
        "texts": [
            " Hertz used the following assumptions [22] : ( \u2170 ) the bodies in contact are isotropic, ( \u2171 ) the proportional limit of materials is not exceeded, ( \u2172 ) the loading acts perpendicular to the surface, ( \u2173 ) the dimensions of the compressed area are small when compared with the whole surface of the bodies pressed together. The pressure distribution on the surface of two cylinders p ( x ) and half contact width a is defined by the expressions in Ref. [22] . p(x ) = 2 P \u03c0a \u221a 1 \u2212 x 2 a 2 (24) a = \u221a 4 P R \u03c0E \u2217 (25) where 1 / E \u2217 = (1 \u2212 v 2 1 ) / E 1 +( 1 \u2212 v 2 2 ) / E 2 , P is the load per unit length F/L, E 1 and v 1 are the elastic modulus and Poisson\u2019s ratio of the upper cylinder, and E 2 and v 2 are the elastic modulus and Poisson\u2019s ratio of the lower cylinder. As shown in Fig. 5 , for a cylinder on a cylinder, R is defined as R = R 1 R 2 /( R 1 + R 2 ), and for a cylinder in a cylindrical socket, R is defined as R = R 1 R 2 /( R 2 - R 1 ) . Johnson [22] noted that in the case of two-dimensional contact, the elastic compressions \u03b41 and \u03b42 are not proportional to the local indentations but depend upon the arbitrarily chosen datum for the elastic displacements. An expression for elastic compression similar to \u03b4 = (9 P 2 / 16 R E \u22172 ) 1 / 3 (elastic compression formula for three-dimensional contact) cannot be found in this case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000525_j.robot.2019.103309-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000525_j.robot.2019.103309-Figure9-1.png",
        "caption": "Fig. 9: Misalignment between a human upper arm and the exoskeletal upper arm when the upper arm is raised (marked by number 2) starting from the downward posture (marked by number 1) on the coronal plane; \u2206\u03b8 and \u2206D indicate this misalignment",
        "texts": [
            " Furthermore, in the coronal plane, a solution is required for the shoulder movement which is accompanied with up/down translation of the center of the GH (CGH) joint when having flexion/extension of the upper arm due to the intervention of the other joints [36]. This translational movement of the CGH especially when the upper arm is raised higher can cause larger misalignment between the exoskeleton and the upper arm. Therefore, in order to effectively mitigate this misalignment described by a translational mismatch \u2206D and a rotational mismatch \u2206\u03b8 in Fig. 9, we adopted a simple mechanism: the armrest was mounted on the upper arm cover 1https://sizekorea.kr/ Jo ur na l P re -p ro of frame via a free revolute joint with a \u00b115 degree rotational range with respect to LAN . Fig. 9 including blue and red links corresponding to human and exoskeletal upper arms shows how the misalignments such as \u2206\u03b8 & \u2206D are represented when the upper arm is raised-up. In order to accommodate \u2206\u03b8, the armrest mounted on the exoskeletal upper arm is designed to freely rotate, which leads to alignment with a wearer\u2019s upper arm. A similar approach was implemented on other vest exoskeletons mentioned earlier and the thigh cuff of the lower-extremity exoskeleton is similar as well [37]. According to the shoulder kinematic analysis in [24], there certainly exists a translational mismatch \u2206D, with consideration of the maximum angle of 70 degree of the exoskeletal upper arm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003513_s003590050245-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003513_s003590050245-Figure1-1.png",
        "caption": "Fig. 1 Schematic drawing of the mechanical structure of a windreceptor hair. Hair shaft with inertia moment I is supported by a circular diaphragm of joint membrane with spring sti ness S. The hair is driven by torque N t due to drag force from moving air and causes angular de\u00afection h t . Mechanical energy of hair motion is consumed by resistance R of wet tissue within hair base. y: distance variable along hair shaft from hair base, arm length of torque generation. a y : hair shape. L0; a0: length and base radius of hair. JM joint membrane acting as hair supporting spring. Es exoskeletal substrate. Cr center of rotation for hair motion. Hair thickness is extremely exaggerated. Actual ratio of diameter/length is less than 1/100 in 1000-lm hairs. Realistic drawings and scanning electron micrographs have appeared in Shimozawa and Kanou (1984a, b)",
        "texts": [
            " The model they proposed was an inverted pendulum with a cone-shaped solid shaft supported by a spring at the base. The pendulum shaft which protrudes into the air is driven by the viscous force applied by the moving air. The inverted pendulum is a typical second-order mechanical system, which consists of a moment of inertia that represents the mass distribution along the hair shaft, a spring that provides the restoring torque towards a resting position of the hair, and a torsional resistance within the hair base (Fig. 1). The moment of inertia depends on the geometrical con\u00aeguration of each hair. The moment of inertia is proportional to both the second power of the base diameter and the third power of the length, and therefore to the \u00aefth power of hair length if length and diameter vary in isometric fashion (Shimozawa and Kanou 1984b; Humphrey et al. 1993; Kumagai et al. 1998b). T. Shimozawa (&) \u00e1 T. Kumagai1 \u00e1 Y. Baba Neuro-Cybernetics Laboratory, Research Institute for Electronic Science, Hokkaido University, Sapporo, 060 Japan Fax: +81-11 706-4971, e-mail: tateo@ncp8",
            " The mobility data are given in the frequency-domain expression, pairs of the de\u00afection amplitude and phase shift in response to the air motion of 1 mm s\u00ff1 peak velocity at several di erent frequencies. The mobility data of 27 hairs with lengths which ranged from 160 to 1500 lm are analyzed. Least-square error sum determination of the intrinsic mechanical parameters The three intrinsic mechanical parameters of the wind-receptor hair \u00b1 I : moment of inertia of hair shaft, R: torsional resistance within hair base, and S: spring sti ness of hair supporting base \u00b1 were estimated by the least-square error sum method for the fundamental equation of motion of an inverted pendulum model (Fig. 1). For the conservation of angular momentum, I d 2h t dt2 R dh t dt S h t N t Nm : 1 The left-hand side represents the inertial, frictional, and restoring momentum due to the angular motion of the hair shaft. The external torque N t on the right-hand side should balance the sum of the angular momenta for every form of motion and at every instant in time. We have a set of data of hair mobility, pairs of de\u00afection magnitude Hm and phase shift um in response to the sinusoidal stimulus air motion of known velocity 1mm s\u00ff1 at several frequencies fm (Kumagai et al",
            " Although the shapes of the substrate are quite di erent, the boundary layers have similar forms (see Discussion). The amount of phase advancement in the close vicinity of the surface is smaller in the case of the cylindrical substrate. See Appendix B for the details of the boundary layer on the cylindrical substrate. The forest of hairs may a ect the pro\u00aeles of velocity amplitude and phase shift of the boundary layer if hair density is high (see Discussion). Torque calculation The drag force acting on a section of the hair shaft at a distance from the hair base produces a turning torque (Fig. 1). The total torque N t that turns the hair shaft around its base is given by the integrated sum of the small torques, each generated on an in\u00aenitesimally thin disc of hair shaft at the arm length of rotation y. Thus, N t Z L0 0 F y; t y dy Nm ; 5 where F y; t represents the drag force per unit length acting on the hair shaft at height y, at time t, and L0 is the hair length. The drag force is a function of the shaft radius and the velocity of air relative to the shaft. Two theories of \u00afuid dynamics were used for the drag force evaluation",
            " For the long hairs, the reconstructed de\u00afections at higher frequencies were 50% those in the original data, although the slopes were similar (Fig. 6, C1, D1). This may correspond to the 30% over-estimation of the moment of inertia (Fig. 3). Oseen's drag force gave a similar reconstruction of de\u00afection amplitude, but the reconstructed phase curves were not of the typical sigmoid form (not shown). Moment of inertia I and spring sti ness S obviously re\u00afect the cuticular structures of the hair shaft and the circular diaphragm of joint membrane at hair base (Fig. 1). These two mechanical parameters are the result of the cytological programs of cuticular secretion during morphogenesis achieved by the trichogen and the tormogen cells (Gnatzy 1978). The geometrical con\u00aegurations of the hair shaft and the spring diaphragm constrain the two parameters. Torsional resistance R estimated within the hair base represents the absorption of mechanical energy of hair motion by the sensory cell, or energy dissipation by a viscous \u00afow of the internal wet tissue. The combination of the trichogen, the tormogen, and the sensory cells determines the content of sensory information transmitted by the sensillum",
            " It is ideal, for a band-pass \u00aelter array designed to cover a wide frequency range, that the best frequency of each \u00aelter varies sensitively with a parameter while the \u00aelter gain does not. The length dependency of L1:670 of the spring sti ness seems to have a functional role designed to realize the weak length dependency on the best sen- sitivity, while giving an adequate length dependency on the best frequency (Table 1). Scaling in biological design and isometric physics The hair is supported by a circular diaphragm of joint membrane (Fig. 1, Gnatzy and Tautz 1980). If the hair support is a rectangular leaf springmade of elastic cuticle, the spring sti ness is given by S E bh3= 4l , where E is Young's modulus of the cuticle, b; l and h are, respectively, the width, length and thickness of the leaf (Ohashi 1976). Therefore, the size dependence of the spring sti - ness would be L2, if both the thickness and the length vary in an isometric fashion. If we extend this consideration to the isometric design of the wind-receptor hair, we obtain a list of size dependencies of other mechanical quantities (Table 1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000630_tro.2021.3060969-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000630_tro.2021.3060969-Figure4-1.png",
        "caption": "Fig. 4. Design of the distance-adjusting actuator. (a) Axial and radial expansion of the soft inner actuators. (b) Assembly process of the distance adjusting actuator by combining the soft actuator and the rigid exoskeleton. (c) State before the actuator assembly. (d) State after the actuator assembly. (e) State of the actuator at inflation.",
        "texts": [
            " 3(f) and (g)] as one single piece using silicone rubber (Dragon Skin 30 from Smooth-On, Inc.). Finally, we seal the two ends of the actuator. One end is directly sealed with the same silicone rubber and the other end is inserted into a rubber tube and sealed [see Fig. 3(h)]. So far, we have completed the fabrication of the inner actuator for the distance-adjusting actuator [see Fig. 3(i) and (j) shows its structural dimensions]. The inner soft actuator exhibits large axial elongation (112% at 65 kPa) and small radial expansion (15% at 65 kPa), as shown in Fig. 4(a). This characteristic of unidirectional deformation makes the actuator an appropriate one to serve as the inner part Authorized licensed use limited to: Dalhousie University. Downloaded on May 25,2021 at 12:16:37 UTC from IEEE Xplore. Restrictions apply. of the final rigid-soft linear actuator, as radial expansion would cause excessive friction between the soft actuator and the rigid case and, thus, energy loss. The rigid exoskeleton has an inner slider and an outer slider with four slide rails, which make the inner slider slide axially in the out slider, without rotation [see Fig. 4(b)]. The two sliders are 3-D printed with glossy surfaces to reduce friction and no extra lubricants are applied, thus a small friction between the sliders still exits, which causes the actuator unable to fully recover. We design the inner actuator shorter than the sliders [there is an axial gap between inner soft actuator and inner slider in Fig. 4(c)], slightly preinflate the inner actuator before bonding to sliders, and deflate it afterward, thus, there is a pretension (20%) in the actuator. This pretension will overcome the friction between the sliders and drag them back to the initial positions, and the penalty is, there is no elongation at low inflating pressures. At the same time, we intentionally leave a radial gap (2 mm) between inner soft actuator and the inner slider, so as to provide some space for the radial expansion of the actuator [see Fig. 4(c)]. One end of the actuator is bonded with the inner rigid slider and the other is bonded with the outer one [see Fig. 4(d)], so that when the inner actuator is inflated, the outer slider and the inner slider slides relatively, and when deflated, the elastomeric force stored in the soft actuator drag the sliders back to initial positions. Fig. 4(e) shows the state of the inflated actuator. 2) Fabric-Reinforced Angle-Adjusting Actuator: The angleadjusting actuator is used to adjust the angle between the facing modules to increase the gripper\u2019s ability to grasp objects with large diameters. The angle-adjusting actuators are placed in series with the distance adjusting actuator and the finger actuator, bearing loads from the fingers and grasped objects, so they must have enough bending stiffness to stay at the required postures. Considering the gravity of the finger actuator connected to one end of the angle-adjusting actuator, we estimated that the bending stiffness of the angle-adjusting actuators should be greater than 0",
            " This critical pressure is the same as the inflating pressure at the assembly process. When the pressure exceeds 10 kPa, the extension of the actuator increases monotonically with the pressure, and almost linearly until pressure reached about 80 kPa, and this is consistent with our theoretical predictions as in (6). The maximum effective elongation of the distance-adjusting actuator is 32.2 mm at pressure of 90 kPa, which is smaller than the elongation of the inner soft actuator at pressure of 65 kPa [see Fig. 4(a)]. This is because there is friction between the inner slider and the outer slider, as well as between the inner slider and the inner soft actuator. When contracts, the actuator\u2019s elongation is slightly larger than that during the extension at the same pressure. This is due to the change of static friction direction during extension and contraction process. In addition, because of the relatively low driving pressure (maximum 90 kPa) required Authorized licensed use limited to: Dalhousie University"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.7-1.png",
        "caption": "Fig. 4.7 Interlaminar shear strain Wx0",
        "texts": [
            " The displacements in the middle plane u0 and v0 are expressed by u0 \u00bc u00 \u00fe Du\u00feDu 2 \u00bc e0x e0 X1 n\u00bc1 Cn sin 2pnn a \u00fe sin 2pnn a 2 \u00bc e0x e0 X1 n\u00bc1 Cn sin 2pnx a sin 2pny b0 v0 \u00bc v00 \u00fe Dv\u00feDv 2 \u00bc h/\u00f0y\u00de f0\u00f0s\u00de X1 n\u00bc1 Cn sin 2pnn a sin 2pnn a 2 \u00bc h/\u00f0y\u00de f0\u00f0s\u00de X1 n\u00bc1 Cn cos 2pnx a sin 2pny b0 : \u00f04:10\u00de Referring to Fig. 4.6, b0 is expressed as b0 \u00bc a tan a: \u00f04:11\u00de Note that the periodic displacement is generated even in the middle plane as shown in Eq. (4.10). (2) Displacements of the cord and rubber of lamination Referring to the deformation of the cord and rubber of a laminate in Fig. 4.7, the nonperiodic interlaminar shear strains wx0 and wy0 are expressed by 194 4 Discrete Lamination Theory Note that Eq. (4.12) is similar to Eqs. (3.75) and (3.77) in MLT. Rearranging Eq. (4.12), the displacements u and v are given by u \u00bc u0 \u00fe hwx0 Hw;x v \u00bc v0 \u00fe hwy0 Hw;y ; \u00f04:13\u00de where H \u00bc h\u00fe h0=2: \u00f04:14\u00de The nonperiodic displacements in Eq. (4.13), denoted u10 and v10, are obtained by adding u00 and v00 to the displacements caused by the interlaminar shear strain: u10 \u00bc u00 \u00fe hwx0 Hw;x v10 \u00bc v00 \u00fe hwy0 Hw;y : \u00f04:15\u00de In the case of uniaxial tensile loading, the interlaminar shear strain wy0 in the width direction periodically becomes zero at the mid-point between cords in the x-direction",
            "31) The strain energy in the plane strain state is expressed by Uplane stress \u00bc 1 2 rxex \u00fe ryey \u00fe sxycxy \u00bc 1 2 Em 1 m2m e2x \u00fe e2y \u00fe 2mmexey \u00fe 1 mm 2 c2xy : The strain energy of bending deformation is expressed by Ubending \u00bc 1 2 Mxjx \u00feMyjy \u00fe 2Mxyjxy \u00bc D 2 w;xx w;xx \u00fe mmw;yy \u00few;yy w;yy \u00fe mmw;xx \u00fe 2 1 mm\u00f0 \u00dew2 ;xy n o \u00bc D 2 w2 ;xx \u00few2 ;yy \u00fe 2mmw;xxw;yy \u00fe 2 1 mm\u00f0 \u00dew2 ;xy n o \u00bc D 2 r2w 2 2 1 mm\u00f0 \u00de w;xxw;yy w2 ;xy n o ; where w is the displacement normal to a plate, jx and jy are curvatures, and jxy is twisting curvature. The bending rigidity D is given by D \u00bc Emh30 12 1 m2m : 238 4 Discrete Lamination Theory Note 4.3 Eq. (4.36) In Note 4.2, the strain energy of bending deformation is expressed by Ubending \u00bc 1 2 Mxjx \u00feMyjy \u00fe 2Mxyjxy \u00bc D 2 w;xx w;xx \u00fe mmw;yy \u00few;yy w;yy \u00fe mmw;xx \u00fe 2 1 mm\u00f0 \u00dew2 ;xy n o : If the rotation in Fig. 4.7 is considered, w,x and w,y in the above equation must be replaced using the correspondences w;x , wx w;x w;y , wy w;y : Furthermore, considering the relation jxy \u00bc \u00f0wx w;x\u00de;y \u00fe wy w;y ;x n o = 2, the strain energy of an adhesive rubber layer is given as Ubending \u00bc 1 2 Mxjx \u00feMyjy \u00fe 2Mxyjxy \u00bc D 2 wx w;x ;x wx w;x ;x \u00fe mm wy w;y ;y n o \u00fe wy w;y ;y wy w;y ;y \u00fe mm wx w;x ;x n o \u00fe 2 1 mm\u00f0 \u00de wx w;x\u00f0 \u00de ;y \u00fe wy w;y\u00f0 \u00de ;x 2 2 2 666664 3 777775 \u00bc Em 2h\u00f0 \u00de3 24 1 m2m w2 ;xx \u00few2 ;yy \u00fe 2mmw;xxw;yy \u00fe 2 1 mm\u00f0 \u00dew2 ;xy n o \u00bc Emh3 3 1 m2m wx;x w;xx 2 \u00fe wy;y w;yy 2 \u00fe 2mm wx;x w;xx wy;y w;yy \u00fe 1 mm\u00f0 \u00de 2 wx;y \u00fewy;x 2w;xy 2 8>< >: 9>= >;: When we only consider half of the laminate, the energy will be half that given above: Ubending 2 \u00bc Emh3 6 1 m2m wx;x w;xx 2 \u00fe wy;y w;yy 2 \u00fe 2mm wx;x w;xx wy;y w;yy \u00fe 1 mm\u00f0 \u00de 2 wx;y \u00fewy;x 2w;xy 2 8>>< >>: 9>>= >>; : Appendix 2: Parameters in Equations \u2026 239 Note 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure17-1.png",
        "caption": "Fig. 17 Coordinate systems Sj and Si",
        "texts": [
            "org/ on 01/29/201 motion Fig. 13 . Sw is connected to the work 8 and represents the work rotation with angular parameter Fig. 14 . System Se is connected to the eccentric setting element and represents the radial setting Fig. 15 . System Sj is connected to the tilt wedge base element which performs rotation relatively to the eccentric element to set the swivel angle j Fig. 16 . System Si is connected to the cutter-head carrier which performs rotation relatively to the tilt wedge base element to set the tool tilt angle i Fig. 17 . Through the coordinate transformation from Si to Sw, the position vector and the unit tangent at the current cutting blade point P can be represented in the coordinate system Sw, namely rw = Mwiri u, 20 tw = Mwiti u, 21 where Mwi is a resultant coordinate transformation matrix and is formulated by the multiplication of the following matrices representing the sequential coordinate transformations from Si to Sw, Mwi = MwoMopMprMrsMsmMmcMceMejM ji 22 where matrices Mwo , Mop Em , Mpr Xp , Mrs m , Msm Xb , Mmc , Mce s , Mej j and M ji i can be obtained directly from Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003940_physreve.60.1847-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003940_physreve.60.1847-Figure3-1.png",
        "caption": "FIG. 3. Nematic elastomer structure in two neighboring domains: ~a! no external stress, ~b! at the transition point. Note the uniaxial extension turning into shear with opposite directions in neighboring domains and the domain wall localization.",
        "texts": [
            " Nevertheless, when an external stress is applied, the system would minimize the elastic energy if the director field and elastic network deformations are separated in space. Namely, by localizing the director distortions in narrow domain walls, the system will make the domains free of director undulations and allow them to be deformed softly. Such domain walls localization causes transformation of uniaxial extension of the whole sample into shear deformation of single domains with shear direction alternating between different domains ~see Fig. 3 and @18#!. Localizing the deformation inside the domain walls will cost some additional energy and will be energetically favorable only above certain threshold. This energy and related deformations can be estimated using the following scaling argument. Let us consider two neighboring domains with initially perpendicular director orientations, shown schematically in Fig. 4~a!. Under the extension \u00ab , the domain B will generate the elastic energy of the order of m 2 \u00ab2j3, in proportion to its volume j3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000520_j.addma.2019.100808-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000520_j.addma.2019.100808-Figure9-1.png",
        "caption": "Fig. 9. Residual stresses along y-direction in the Ti-6Al-4V components fabricated using (a) long deposition pattern, (b) short deposition pattern and (c) spiral deposition pattern when the deposits cooled down to room temperature and the clamps were released. Residual stresses along y-direction in the Inconel 718 components deposited with (d) long deposition pattern, (e) short deposition pattern and (f) spiral deposition pattern when the deposits cooled down to room temperature and the clamps were released. The processing conditions are provided in Table 1.",
        "texts": [
            " It is evident from the figure that along the same line the residual stresses can be significantly different depending on the deposition pattern used. These differences can be more pronounced for various alloy systems with different thermo-physical and mechanical properties. To investigate the simultaneous effects of deposition patterns and alloys, the stresses and deformation of the components made using three different deposition patterns are calculated for Ti-6Al-4V and IN 718 as explained below. Fig. 9 shows the y-component of the residual stresses in both alloys fabricated with three deposition patterns after releasing the clamps. Cutaway isometric views are used to show the accumulations of residual stresses inside the component. For both alloys, the y-direction stress distributions in the substrate are the same with high tensile stress near the shorter edge of the deposit and high compressive stress near the longer edge of the substrate. Y-direction stresses mainly originate from the expansion along this direction during heating and shrinkage during cooling. During the cooling time, all deposits shrink resulting in high tensile stresses near the shorter edge of the deposit. For the region near the longer edge of the substrate, compressive stresses originate due to the upward bending of shorter edges of the substrate after releasing the clamps. For the components fabricated with long deposition pattern (Fig. 9 a and d), compressive stresses are observed on the top surface of the deposits because y-direction is the primary contraction direction for the deposit with long deposition pattern. For both alloys, high tensile stresses can be found in the center of the deposit with spiral deposition pattern (as shown in Fig. 9 c and f) since the last hatch is deposited at that location. For both alloys, the deposits made using short deposition pattern (Fig. 9 b and e) have the least residual stresses among the three deposition patterns. This is because more hatches needed to fabricate the deposits using short deposition pattern significantly alleviate the stresses due to the reheating effect. It can also be found that after clamp removal, high tensile stresses accumulate on the bottom of the substrates for both alloys due to the upward bending of the substrates. The x-component of the residual stresses for both alloys fabricated using three deposition patterns are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-73-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-73-1.png",
        "caption": "Figure 4-73. Three-level synchronous optimal PWM, steady-state trajectories: (a) stationary coordinates; (b) synchronous coordinates.",
        "texts": [],
        "surrounding_texts": [
            "The design of pulse width modulators for multilevel topologies follows the same principles as discussed before for the special case of the three-level topology. Suboscillation Method. In principle, any PWM method that is suited for controlling a two-level inverter can be adapted for three-level inverter control. Special care must be taken with carrier-based methods, for example, the suboscillation method. It is important to observe the polarity consistency rule (Section 4.7), which, in the case of a three-level inverter, implies that switching between low voltage levels must occur around a zero crossing of the phase voltages. An example of a well-designed pulse pattern is shown in Figure 4-72b. When applying the suboscillation technique, a reduction of the harmonic distortion can be achieved by adding adequate zero-sequence waveforms to the sinusoidal reference signal. A viable example of a zero-sequence signal is the triangular wave in Figure 4-68b [58]. The amplitude of this signal varies in proportion to the modulation index m. It is added to each of the signals ua', ub , and uj in Figure 4-68a. These signals represent a set of balanced, sinusoidal three-phase voltages having their amplitudes adjusted in proportion to the modulation index. The resulting signals form the set of reference voltages, two of which are shown in Figure 4-68c and e. The carrier signals are synchronized with the reference waveforms to avoid the generation of subharmonic components. Note that each of the carrier signals has a defined phase relationship with respect to its particular reference signal to ensure minimum harmonic distortion of the modulation process. There is a positive carrier ucrb+, the intersections of which with the reference signal ub determine the switching instants of the positive voltage pulses at the phase terminal L2, Figure 4-64; similarly the negative carrier ucr b_ generates the negative voltage pulses. Different carriers are used for the other phases, see Figure 4-68e. The resulting loss factor is displayed in Figure 4-69a as function of the modulation index m and the pulse number N. The performance of an ill-designed three-level pulse width modulator shall be derived for comparison. Figure 4-70 characterizes a suboscillation modulator that uses sinusoidal reference signals and a common synchronized carriers for all three 198 4. Pulse Width Modulation for Electronic Power Conversion phases. Figure 4-69b shows that the harmonic distortion is poor as compared with Figure 4-69a. Space Vector Modulation. Also the space vector modulation method is well applicable for the control of three-level inverters. The location of the reference vector u*(ts) at a given sampling instant ts determines those three switching-state vectors from the pattern in Figure 4-67 that are in closest distance from the reference vector. The three switching-state vectors that form the modulation subcycle are named \u00aba, \u00ab\u00bf, and uc. The on-durations ta, tb, and tc of the pertaining switching-state vectors ua, ub, and uc are obtained from the solution of Vs \u25a0 {taUa + tbUb + tcUc) = U*(ts) tc 2/, t\u201e h (4.39a) (4.39b) 4.7. Multilevel Converters 199 sinusoidal reference signals and common carriers. ui 2 4* '\u03af II. I Ub.Uc -jUd Figure 4-70. Three-level suboscillation method, N = 3; sinusoidal reference voltages and common carrier: (a) reference signals and carrier signals; (b) phase potential uL2. uL2\\ -\u00a1ud 1 I W \u039b W \u039b \\/2\u03c0 \"er - t\" hnn I UUL2* (a) (b) < o f - The sequence in time of the switching-state vectors is determined such that the number of commutations of the converter bridges is minimum. The selection exploits also the redundancy of switching-states. Optimal Pulse Width Modulation. In high-power applications, the larger number of power switches in a three-level inverter is well utilized since the power output increases approximately in proportion to the number of switches. Since highpower switches generally require operation at low-switching frequency, an optimal PWM method is a good choice. The same optimization methods apply as described in Sections 4.5.4, 4.6.2, and 4.6.3. The optimization using the d -> min criterion yields the set of switching angles ak that is shown in Figure 4-7la as a function of the modulation index. The resulting distortion factor d is displayed in Figure 4-7lb in comparison with two other syn- 200 4. Pulse Width Modulation for Electronic Power Conversion \u03c0/2 \u03c0/4 - chronous PWM methods. Two decisive advantages of the optimal method can be observed: 202 4. Pulse Width Modulation for Electronic Power Conversion 0.1o' 0.05 Fundamental current oU\u00fcilii 111) nu. ..Ill, 0 0.5 1.0 1.5 2.0 2.5 kHz Figure 4-74. Three-level synchronous optimal PWM, harmonic spectrum of the waveform in Figure 4-72(c) Superimposing a fast current control scheme around a synchronous optimal pulse width modulator requires trajectory tracking control. This method eliminates the dynamic modulation error. It is described in Section 4.6.3. Alternatively, the current controller must operate slowly enough so as to maintain quasi-steady-state conditions for pulse width modulation. Extension. Multilevel converters having more than three voltage levels are less common. Their switching-state vectors are arranged similar to those in Figure 4-67, with each additional voltage level defining another hexagon. The switching-state vectors pointing to the most outward hexagon are unique. The redundancy of switching-state vectors increases stepwise by one for any next inner hexagon. The set of zero vectors is reached after the last step. For instance, there are five different zero vectors in a five-level converter. 4.8. CURRENT SOURCE INVERTER The preceding discussions on pulse width modulation techniques made reference to a power circuit configuration as in Figure 4-6, in which the DC power is delivered by a voltage source U\u00bf. Rectangular voltage waveforms are impressed on the load circuit, from which current waveforms result that depend on the actual load impedances. Another approach, dual to the aforementioned principle of power conversion, is the current source inverter. A switched rectangular current waveform is injected into the load, and it is the voltage waveforms which develop under the influence of the load impedances. The fundamental frequency is determined by the switching sequence, exactly as in the case of a voltage source inverter. There are two different principles employed to control the fundamental current amplitude in a current sourve inverter. Most frequently the DC current source is varied in magnitude, which eliminates the need for fundamental current control on the AC side, and pulse width modulation is not required. An alternative, although not very frequently applied, consists controlling the fundamental current by pulse 4.9. Conclusion 203 width modulation [59]. There is a strong similarity to PWM techniques for voltage source inverters, although minor differences exist. The majority of applications are based on the voltage source principle, which is owed in the first place to favoring properties of the available power semiconductor switches. 4.9. CONCLUSION Pulse width modulation for the control of three-phase power converters can be performed using a large variety of different methods. Their respective properties are discussed and compared based on mathematical analyses and on measured results obtained from controlled drive systems in operation. Performance criteria assist in the selection of a PWM scheme for a particular application. An important design parameter is the switching frequency since it determines the system losses. These are hardly a constraint at low power levels, permitting high-frequency switching combined with straightforward modulation methods. The important selection factors in this range are cost of implementation and dynamic performance. As the losses force the switching frequency to be low at higher power, elaborate techniques are preferred including off-line and on-line optimization. These permit that the contradicting requirements of slow switching and fast response can be satisfied. 204 4. Pulse Width Modulation for Electronic Power Conversion Nomenclature a unity vector d distortion factor S loss factor f\\ fundamental frequency fs switching frequency hd amplitude density spectrum h\u00a1 discrete current spectrum ih harmonic current is stator current vector ilr transient current //, mutual inductance ls stator inductance lsa stator leakage inductance \u0399\u03c3 total leakage inductance L inductance per phase m modulation index N pulse number P set of pulse patterns P sig(is) polarity vector T mechanical torque Td lock-out time Ton on-time of a switch /0 constant subcycle duration Ts variable subcycle duration Ts, storage time \u03930 constant subcycle duration ua voltage of phase a ud normalized DC link voltage Ud DC link voltage w/, harmonic voltage \u00ab, back-EMF voltage \u00abi discrete sequence of switching state vectors uL phase to neutral voltage u\u201ep neutral point potential uph phase voltage us stator voltage vec- tor U\\ ... ue switching state vectors a* reference voltage vector Greek Symbols a switching angle \u03b4 dynamic modulation error \u03c3 total leakage factor 7> rotor time constant TJ transient time constant \u03c95 stator frequency <jjs ss steady-state stator frequency \u03a8 flux linkage vector Indices a, b, c phases av average value 1 fundamental quantity max maximum value min minimum value r rotor R rated value s stator ss steady-state value (...) bracket encloses on-duration estimated value References 205"
        ]
    },
    {
        "image_filename": "designv10_2_0003589_63.662844-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003589_63.662844-Figure3-1.png",
        "caption": "Fig. 3. Space vectors and voltage components of the VSI: (a) space vectors and (b) voltage components.",
        "texts": [
            " The switching function for switch is defined as when switch is on when switch is off. In the PWM inverter with voltage link, either or ( or , , or ) is conducting, and only one of them is allowed to conduct in any moment, i.e., (5) (6) (7) In the PWM inverter, the space vector is represented as follows: (8) Substituting switching function, one or zero, of each phase into (8), the following discrete space vectors are obtained: (9) (10) The available space voltage vectors according to eight switch states are shown in Fig. 3(a). Among these space voltage vectors, is the zero voltage vector, and it has two switching patterns (0 0 0) and (1 1 1). To obtain the required output space vector , the conduction times of the selected six switches are modulated according to the amplitude and angle of . and are the peak voltage and angular frequency of the output voltage vector , respectively. The angle of determines a region among six regions in the complex plane. The reference space vector in Fig. 3(b) is modulated as follows: (11) which is called the space-vector modulation. Then, the duty cycles and of two space vectors and adjacent to in a given region and the duty cycle of the zero vector are given by (12) where the modulation index is defined as (13) Thus, the SVM technique utilizes three space vectors , , and to generate the output voltage vector in the specified region. On the other hand, the following equation is obtained from Fig. 2: (14) where is the output-line-current vector, is the counter emf vector of the induction motor, and and are the equivalent stator resistance and inductance, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001033_j.jmapro.2021.01.012-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001033_j.jmapro.2021.01.012-Figure2-1.png",
        "caption": "Fig. 2. Utilized ADDILAN V0.1 wire arc additive manufacturing machine, the machine structure representation determining its parts and scheme of the measuring devices installed on the torch head.",
        "texts": [
            " The principal contribution relies on a definition of a unique fingerprinting of additive parts, as a baseline for in process defect detection and a presentation of a matrix-manufacturing strategy to ensure more efficient production. The development and the industrialization of WAAM metal additive manufacturing technologies for aeronautical applications is at present a central challenge for equipment manufacturers, turning this technology into a competitive alternative to traditional manufacturing methods. The main experimental configuration for this work is based on an ADDILAN platform, shown in Fig. 2. The AM machine operates a 4-axis printer head and a tilt table with Cartesian coordinates in an inert build chamber. All the main process parameters and variables may be accessed through its dedicated computer numerical control unit. The working area of the ADDILAN V0.1 machine (see Fig. 2) is 1300 mm x 900 mm x 500 mm with a maximum weight of 300 kg, a set-up previously used by the authors in their previous work [20]. Within this working area a single or as many as nine aeronautical fittings may be manufactured using the matrix-manufacturing strategy. The AM machine can integrate different WAAM technologies, mainly PAW, GTAW or GMAW, depending on the material and the desired metallic properties. In this paper, the selected technologies are PAW, for Titanium-6Al4V and Stainless-Steel-316 LSi parts, and GMAW, for Inconel-718 and Aluminum 5356 parts. The AM machine was powered by a Tetrix 552 AC / DC Synergic Plasma arc (EWM) welding system supplying up to 420 A. It generates a direct plasma flow through the plasma torch used in PAW mode and uses Titan XQ 400 AC pulse (EWM) welding equipment in GMAW mode. The geometry of each deposited layer is measured with a geometric laser scanner (Laser Scanner Q4 Series) located on the manufacturing head (Fig. 2). In addition, a pyrometer (Optris CT) was also installed to monitor the temperature during the wall manufacturing processes, for determination of the inter-pass cooling time. Finally, a Rapidox R2100 Oxygen Analyzer was also used to measure the oxygen level. A key task, prior to the initiation of WAAM manufacturing and industrialization, is the definition of the parameters required to produce acceptable 3D parts in each material. Characterization walls are initially produced, by joining the material, layer by layer, in order to build geometrically and mechanically functional pieces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003980_jmbr.39.5.369-380-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003980_jmbr.39.5.369-380-Figure3-1.png",
        "caption": "FIGURE 3. Schematic of experimental setup in Phase 2 for the coupled response mode. 3D = three dimensional.",
        "texts": [
            " The laser pointer was positioned pointing downward in a vertical line over the photocell at a height of 180 cm. When the bat was swung across home plate, the laser bean was interrupted, causing a voltage change in the photocell. We attached a three-dimensional (3D) accelerometer (Entran Devices, Fairfield, NJ) to the bat at a distance of 65 cm from the handle. For the uncoupled response mode, we used a voice-activated switch to record the time of the batter\u2019s response. A schematic of the experimental setup is shown in Figure 3. We produced six visual conditions by manipulating the visual information available to the batter. The conditions ranged from visual availability of only 100 ms of ball flight (B100) to availability of full visual information, including the pitcher\u2019s motion and complete ball flight (FULL). A complete description of the conditions is provided in Table 1. D ow nl oa de d by [ U ni ve rs ity o f N or th T ex as ] at 1 1: 20 2 6 N ov em be r 20 14 374 Journal of Motor Behavior For the B100 condition, we initially displayed the ball in red at the release position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure3.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure3.4-1.png",
        "caption": "Fig. 3.4 Laminate with two kinds of boundary conditions [4] a Laminate under uniform displacement and stress b Laminate with constrained displacement at x = \u00b1a",
        "texts": [
            " 102 3 Modified Lamination Theory E\u00f02\u00de xx @2 @x2 \u00fe 2E\u00f02\u00de xs @2 @x@y \u00feE\u00f02\u00de ss @2 @y2 u2 \u00fe E\u00f02\u00de xs @2 @x2 \u00fe E\u00f02\u00de xy \u00feE\u00f02\u00de ss @2 @x@y \u00feE\u00f02\u00de ys @2 @y2 v2 G hh2 u2 u1\u00f0 \u00de \u00bc 0 E\u00f02\u00de xs @2 @x2 \u00fe E\u00f02\u00de xy \u00feE\u00f02\u00de ss @2 @x@y \u00feE\u00f02\u00de ys @2 @y2 u2 \u00fe E\u00f02\u00de ss @2 @x2 \u00fe 2E\u00f02\u00de ys @2 @x@y \u00feE\u00f02\u00de yy @2 @y2 v2 G hh2 v2 v1\u00f0 \u00de \u00bc 0: \u00f03:6\u00de (1) Superposition of solutions for two boundary conditions Suppose that the relation a b is satisfied. If regions near the edges x = \u00b1a are not included in the analysis, the solution is given by the superposition of corresponding solutions to Fig. 3.4a, b. (2) Solutions under uniform displacement and stress The displacement is constrained at y = \u00b1b in the width direction, and a uniform displacement u0 is applied at x = \u00b1a in the longitudinal direction of a laminate, as shown in Fig. 3.4a. The boundary conditions are expressed by 3.2 MLT of a Two-Ply Laminate Without Out-of-Plane \u2026 103 u1 \u00bc u2 \u00bc u0 at x \u00bc a v1 \u00bc v2 \u00bc 0 at y \u00bc b: \u00f03:8\u00de The displacements ui and vi are expressed by u1 \u00bc u2 \u00bc u0=a x v1 \u00bc v2 \u00bc 0: \u00f03:9\u00de The substitution of Eq. (3.9) into Eq. (3.3) yields the uniform strain field: e\u00f0i\u00dex \u00bc u0=a e\u00f0i\u00dey \u00bc 0 \u00f0i \u00bc 1; 2\u00de c\u00f0i\u00dexy \u00bc 0: \u00f03:10\u00de 104 3 Modified Lamination Theory Equation (3.9) satisfies equilibrium equations of Eq. (3.6) and the boundary conditions of Eq. (3.8), and Eq",
            "4) yields the stresses: r\u00f0i\u00dex \u00bc E\u00f0i\u00de xx u0=a r\u00f0i\u00dey \u00bc E\u00f0i\u00de xy u0=a s\u00f0i\u00dexy \u00bc E\u00f0i\u00de xs u0=a: \u00f03:11\u00de The substitution of Eq. (3.7) into Eq. (3.11) yields r\u00f01\u00dex \u00bc r\u00f02\u00dex \u00bc Exx u0=a r\u00f01\u00dey \u00bc r\u00f02\u00dey \u00bc Exy u0=a s\u00f01\u00dexy \u00bc s\u00f02\u00dexy \u00bc Exs u0=a: \u00f03:12\u00de The stress relates to only the displacement u0/a, and the interlaminar shear stresses szx and szy are zero, but reactions r i\u00f0 \u00de y and s i\u00f0 \u00de xy are generated by the constraints at y = \u00b1b. (3) Solutions with constrained displacement The stresses are applied to both sides at y = \u00b1b in Fig. 3.4b, to cancel out the reactions of Fig. 3.4a. The boundary conditions at y = \u00b1b are expressed by4 r\u00f01\u00dey \u00bc r\u00f02\u00dey \u00bc Exyu0=a s\u00f01\u00dexy \u00bc s\u00f02\u00dexy \u00bc Exsu0=a at y \u00bc b: \u00f03:13\u00de The symmetry condition leads to the relations5 u1 \u00bc u2 \u00bc 0 v1 \u00bc v2 \u00bc 0 at y \u00bc 0: \u00f03:14\u00de Owing to the relation a b, the solution is only a function of y and independent of x except in the region near x = \u00b1a, according to the Saint-Venant principle. Considering that terms with \u2202/\u2202x can be eliminated under the above assumptions, Eq. (3.6) can be simplified as 4Note 3.1. 5See Footnote 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000202_anie.201907466-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000202_anie.201907466-Figure4-1.png",
        "caption": "Figure 4. Schematic representation of voltage-dependent HPTS assays, showing generation of membrane potentials of 0, 118 and -118 mV using valinomycin and a K+ gradient.",
        "texts": [
            " In addition to indicating a mobile carrier mechanism, the lack of uniport also suggests that the transmembrane diffusion of free transporter is forbidden for compound 1, as this step (box in Figure 3) is required for Cl\u2212 uniport but not for H+/Cl\u2212 symport or anion exchange. The identical behaviour has been reported for prodigiosin.[11c] However, we next show different behaviours of 1 and prodigiosin when their voltage-dependent H+/Cl\u2212 symport properties were examined. We conducted voltage-dependent HPTS pH-discharge assays by using the K+-selective ionophore valinomycin and varying transmembrane K+ concentration gradients to generate membrane potentials ranging from 177 to -118 mV (Figure 4). No voltage dependence was found for prodigiosin (Figure 5a left). However, H+/Cl \u2212 symport mediated by 1 was found to be \u201cswitched-off\u201c by applying a positive membrane potential while also attenuated by a negative potential (Figure 5b left). Therefore compound 1 but not prodigiosin displays the voltage-switchable transport property reminiscent of the voltage-gated ion channels in biological systems.[20] The different voltage-sensitivity of 1 and prodigiosin can be readily understood by examining the species involved in their 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure2-1.png",
        "caption": "Fig. 2. Crowning of pinion tooth surface.",
        "texts": [
            " The tooth surface of the gear is a conventional screw involute surface. (iii) Profile crowning provides localization of bearing contact and the path of contact on the tooth surface of the pinion or the gear is oriented longitudinally (see Section 4). (iv) Longitudinal crowning enables to provide a parabolic function of transmission errors of the gear drive. Such a function absorbs discontinuous linear functions caused by misalignment and reduce there- fore noise and vibration (see Section 7). Fig. 2(a) and (b) illustrate the profile-crowned and double- crowned pinion tooth surface. i(v) Profile crowning of pinion tooth surface is achieved by deviation of the generating tool surface in pro- file direction (see Section 2). Longitudinal crowning of pinion tooth surface can be achieved by: (i) plunging of the tool or (ii) application of modified roll (see Sections 5 and 6). (vi) The effectiveness of the procedure of stress analysis is enhanced by automatization of development of The concept of generation of pinion and gear tooth surfaces is based on application of rack-cutters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.30-1.png",
        "caption": "Fig. 16.30 Effect of block rigidity on the shear force distribution [13]",
        "texts": [
            " The zigzag pattern has a smaller peak-to-peak value (Fpp) of the shear force than the straight pattern. Furthermore, Fpp decreases as the zigzag amplitude increases from 4 to 8 mm. The shear stress distribution changes when the shear spring rate of the block changes. When the value of aw is reduced by using soft rubber or by adding sipes to straight groove zigzag grooveFig. 16.28 Local coordinate system and rain grooves [13] 16.2 Rain Groove Wandering 1177 the block pattern, the conceptual figure of the shear stress distribution is that shown in Fig. 16.30. The residual lateral force variations of a tire with stiff and soft rubber are shown in Fig. 16.31. Young\u2019s modulus of soft rubber is a quarter that of stiff rubber. Fpp is decreased by adding sipes or softening tread rubber. (4) Validation of the analytical model of rain groove wandering The following statements have been concluded for rain groove wandering from the subjective feeling test. (i) Rain groove wandering becomes worse when the pitch of a rain groove is almost the same as the circumferential groove of a tire"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.40-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.40-1.png",
        "caption": "Fig. 12.40 Hydroplaning simulation of a rolling tire [42]",
        "texts": [
            ", the patent of which was granted for Bridgestone in 2002 [46], studies were conducted on the critical hydroplaning speed [47, 48], the effect of the tire pattern on hydroplaning [49] and the braking distance on a wet road [50, 51]. Osawa and Nakajima of Bridgestone [52] developed the riblet wall technology that suppresses the turbulence inside the main groove by CFD and validated to improve the hydroplaning of a tire. (2) Validation of hydroplaning simulation The hydroplaning simulation of a rolling tire with a practical tread pattern is shown in Fig. 12.40, where water drains into the two circumferential grooves and lateral grooves. The velocity of the tire is 60 km/h, the tire size is 205/55R16, the inflation pressure is 220 kPa, and the load is 4.5 kN. Prescribed velocities are applied to the tire model in the horizontal and rotational directions. The coefficient of friction between the tire and road is zero. The depth of water is 10 mm, and flow boundaries around the water pool are wall boundaries through which no water can flow. An explicit FEA/FVM scheme is applied in this simulation, and water flow is evaluated after the hydrodynamic force becomes stable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000628_j.mechmachtheory.2021.104262-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000628_j.mechmachtheory.2021.104262-Figure4-1.png",
        "caption": "Fig. 4. Meshing line of the external-internal gear pair: (a) standard gears, (b) gears with addendum modification (total modification coefficient x > 0 ).",
        "texts": [
            " [11\u201312] , 1 K b = \u222b \u03b21 \u03c6 { 3 { 1 + cos \u03b21 [ ( \u03b22 \u2212 \u03b2) sin\u03b2 \u2212 cos \u03b2] } 2 \u00d7 ( \u03b22 \u2212 \u03b2) cos\u03b2 } 2 EL [ sin \u03b2 + ( \u03b22 \u2212 \u03b2) cos \u03b2] 3 d\u03b2 (14) 1 K a = \u222b \u03b21 \u03c6 ( \u03b22 \u2212 \u03b2) cos \u03b2sin 2 \u03b21 2 EL [ sin \u03b2 + ( \u03b22 \u2212 \u03b2) cos \u03b2] d\u03b2 (15) 1 K s = \u222b \u03b22 \u03c6 1 . 2(1 + v )( \u03b22 \u2212 \u03b2) cos \u03b2cos 2 \u03b21 EL [ sin \u03b2 + ( \u03b22 \u2212 \u03b2) cos \u03b2] d\u03b2 (16) The expressions for \u03b21 , \u03c6, and \u03b22 of the internal standard gear tooth have been given in Refs. [11\u201312] . For gears with addendum modifications, when the total modification x = 0 , the expressions for \u03b21 , \u03c6, and \u03b22 are consistent with the results in Refs. [11\u201312] . As shown in Fig. 4 , when the total modification coefficient x = 0 , the reference circle of the external gear is tangent to the reference circle of the internal gear. When the total modification coefficient x > 0 , the reference circle of the external gear is disjoint from the reference circle of the internal gear; N 1 N 2 is the theoretical mesh line; B 1 B 2 is the actual mesh line; and P is the pitch point. Consider B 1 as the reference point, which corresponds to the initial mesh point of the first pair of mesh teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000630_tro.2021.3060969-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000630_tro.2021.3060969-Figure14-1.png",
        "caption": "Fig. 14. Grasping and picking process of a full 2-L Coca Cola bottle using the proposed gripper and a robotic arm. (P1: inflating pressure of all four distanceadjusting actuators; P2: inflating pressure of all four angle-adjusting actuators; and P3: inflating pressure of all four finger actuators).",
        "texts": [
            " 4) Lift the item up and stay for 5 s. Authorized licensed use limited to: Dalhousie University. Downloaded on May 25,2021 at 12:16:37 UTC from IEEE Xplore. Restrictions apply. 5) Move the gripper horizontally for 30 cm and stay for 5 s. 6) Lower the gripper and place the item. If such an attempt of grasp is finished without dropping off the item, then this attempt is considered as successful, otherwise, failed. For each object, we adopt a specific strategy for grasping by adjusting its initial postures. Fig. 14 shows the process of picking a full 2-L Coca Cola bottle (weight: 2.1 kg, diameter: 100 mm, length 325 mm) using our gripper. The grasping strategy is as follows: first, move the gripper to the top of the coke bottle [see Fig. 14(a)]; next, expand the distance and angle between fingers by inflating the distance- and angle- adjusting actuators, so that it is able to envelop the bottle [see Fig. 14(b)]; then move gripper down so that the object touches the root of the fingers [see Fig. 14(c)]; inflate the finger actuators to envelop the object [see Fig. 14(d)], followed by deflating the angle-adjusting actuator partially, to make the finger fit tighter with the object [see Fig. 14(e)]; finally, grasp the object by moving the gripper up [see Fig. 14(f)]. Fig. 15(a) gives the objects we have included in our grasping tests. Through adjusting the initial grasping postures, the gripper can grasp from very small objects, such as needle, washer, screw, to large and heavy objects, such as the full filled large coke bottle, electric drill, soccer, etc. Grasping testing experiments (Supplementary Movie S2, S3, and S4) show that the proposed gripper successfully picked and placed 58 items in Fig. 15(a), and failed in just one item\u2014a 400-g-cuboid acrylic box [circled in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000664_j.triboint.2020.106277-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000664_j.triboint.2020.106277-Figure3-1.png",
        "caption": "Figure 3 Schematic diagram of the gear contact model",
        "texts": [
            " A classic wear equation was chosen to realize this purpose as illustrated in the following sections. Subsequently, the damage accumulation was predicted based upon the stress-strain history during specific loading cycles, where the multiaxial fatigue criterion and the damage accumulation rule were applied. Figure 2 illustrates the technical flow chart of this work. Figure 2 Flow chart of competition model In the present work, the analyzed gear pair was selected from a 2 MW wind turbine gearbox, operating as the intermediate parallel stage. As displayed in figure 3, if the plain strain condition is assumed, the contact process of a gear pair at any instantaneous contact point is able to be equivalently regarded as two elastic circles with individual radius of curvature ( , ) meshing with each other [33]. The gear contact starts from the engage-in point (E), passing through the lowest point of single tooth contact (LPSTC), the pitch point (P), the highest point of single tooth contact (HPSTC), then finally reaching the recess point (R). Table 1 lists the main gear pair parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000484_j.matdes.2019.107792-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000484_j.matdes.2019.107792-Figure2-1.png",
        "caption": "Fig. 2. SEBM samples showing: (a) 7 can-shaped samples (a side-view inset shows an example of a high-preheat can-shaped sample) and a block sample, and (b) a CAD drawing and a X-Z cross-sectional view of the can-shaped sample. Note: X/Y is the lateral direction and Z is the build direction.",
        "texts": [
            " During the melting process, the preheating temperature at the top layer is calculated from the EBM software algorithm (ARCAM A2XX EBM control software ver. 3.2). Lastly, a post-heating stage is applied to the powder bed,maintaining it at high temperature, slowing down the rapid cooling effect, see details in ref. [33]. According to the log file, the electron beam stays on in all processing stages except for powder raking. In this study, we produced 3 separate SEBM builds; each comprising seven can-shaped samples and a block sample (Fig. 2a) using either 2, 4 or 8 scan repetitions in base sinter (referred to as low, standard and high preheat, respectively). The standard preheating is based on ARCAM A2XX EBM control software ver. 3.2 with the 70 \u03bcm themewhereas the others are user modified preheating schemes. The can-shaped sample has an outer diameter of 3 mm, a height of 3 mm and a wall thickness of 1 mm (Fig. 2b). It was designed to preserve the sintered powder (only subjected to the two-stage preheating) from damage during sample handling. Its diameter was set to achieve a high-resolution X-ray computed tomographic analysis. The block sample was 90 mm long (X), 14 mm wide (Y), and 17 mm tall (Z). the can-shaped sample, and then separated into (b) individual powder particles by the ) Closing applied on (c) to form the sintered powder image. The sintered neck image and (f) powder size; (g) illustrates the sintered necks (coloured) connected with the The SEBM process parameters are summarised in Table 1, wherein the line energy (Eline) was calculated by Eline \u00bc Ue Ib Vsc , indicating the ap- plied heat input in SEBM, i",
            " To simplify our results, we determined the characteristic tau factor (\u03c4c) by averaging \u03c4 values from all axes, and then calculated the tau factor anisotropy (\u03c3\u03c4) by averaging the sum of squared differences between \u03c4c and \u03c4 per orthogonal axis, see details in previous work [41]. The effective thermal diffusivity (\u03b1eff) could then be calculated by: \u03b1eff \u00bc \u03b10 \u03b5\u03c4 \u00f02\u00de where \u03b10 is the bulk thermal diffusivity and \u03b5 is the porosity. Next, we deduced the \u03bbeff by substituting \u03b1eff into [26]: \u03bbeff = \u03b1eff \u03c1 Cp. At room temperature, the bulk thermal diffusivity (\u03b10), density (\u03c1) and heat capacity (Cp) of Ti-6Al-4V are 2.9 \u00d7 10\u22126 m2 s\u22121 [42], 4420 Kg m\u22123 [43], and 546 J Kg\u22121 K\u22121 [43], respectively. The block samples were sectioned into two halves in the X-Z direction (Fig. 2a) and polished using SiC discs (P400 to P2400 grits) followed by a 9 \u03bcmdiamond suspension and then a 0.05 \u03bcmsilica dioxide suspension, etched by a Kroll reagent for 10 s, and then rinsed in water. They were cleanedwith ethanol and dried before SEM imaging. A 2Dporosity analysis was performed on the SEM-BS images (0.7 \u03bcm per pixel) using ImageJ version 1.51s [44]. We measured the Vickers microhardness (HV 0.5) on the polished surface of the block sample for each preheat condition along the build direction (Z) and the transverse direction (Y) (denoted in Fig. 2a) using a Buehler MicroMet 6030 hardness tester equipped with a diamond indenter. The microhardness test was performed 2 mm away from the sample edges, covering an area of 10 \u00d7 14 mm with 25 indentations. The gas atomised Ti-6Al-4V powder is mostly spherical, with a few particles exhibiting open pores and satellites on their surface (Fig. 4a). The powder size distribution (PSD) is in the range of 31\u2013127 \u03bcm (Fig. 4b), in which the D10, D50, and D90 are given by 45, 62, and 85 \u03bcm, respectively. The size and morphology of the Ti-6Al-4V powder match well with a typical powder used in SEBM [19]",
            " Given that all the samples were held at, or above, the preheat temperature during preheating and melting, we speculate that all samples cool slowly, resulting in Widmanst\u00e4tten lath-like \u03b1 phase within a of the indentation position of the block sample wherein the orange region shows that the ows the corresponding microhardness plot along the Z distance. matrix of \u03b2 and limiting the possibility of forming \u03b1\u2033-martensite [49] (Fig. 8d\u2013f). We performed microhardness tests on one fully consolidated block sample for each preheat condition to investigate the effects of preheating on their local mechanical properties in the Y-Z plane, denoted by Fig. 2a. Fig. 9a illustrates the indentation positions on the Y-Z plane of the block sample. The mean and standard deviation of the microhardness values of the Ti-6Al-4V block samples are calculated along the Y direction (highlighted in orange - Fig. 9a) and then plotted against with various Z height (Fig. 9b). The low, standard, and high preheat samples have a microhardness of 330 \u00b1 7, 332 \u00b1 5, and 315 \u00b1 11 Hv0.5, respectively. Fig. 9b shows that the high preheat samples exhibit anisotropic mechanical properties and their microhardness is ca"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003221_s0094-114x(98)00081-0-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003221_s0094-114x(98)00081-0-Figure2-1.png",
        "caption": "Fig. 2. Five-bar with revolute actuations.",
        "texts": [
            " s?sT and U mus g muW 2s ru \u00ffmuW 2L 2muW _L ru s L s 1 L muru g mdrd g 2a1W _L L \u00ffmuW 2L ru s 2muW _Ls ru s? in which a1 mur2u mdr2d Iu Id To arrive at the \u00aenal equations of motion, we consider the force balance at the output platform (which, in this case, is a point) and, using the leg index i as subscript for i-th leg, get the equation X2 i 1 Fi RExt 0 or, M t Z Hf RExt 15 where M P2 i 1 Qi; Z P2 i 1 Ui; H s1 s2 and f f1 f2 T: The \u00aeve-bar 2-DOF manipulator with revolute actuations is shown in Fig. 2 (leg details shown in only one leg). With the previous notation for the leg vector and denoting the lengths of the lower and upper links by l and u respectively, the position kinematics of a single leg gives S t\u00ff b; L kSk; s S=L c tan\u00ff1 Sy=Sx ; b cos\u00ff1 l 2 L2 \u00ff u2 2lL ; y c2b unit vectors c and d along the lower and upper links obtained from c cos y sin y ; j b lc; d t\u00ff j =u and f tan\u00ff1 dy=dx Angular velocities of the lower and upper links are given by\" _y _f # A\u00ff11 _t where A1 \u00ffl sin y \u00ffu sin f l cos y u cos f and the linear velocity of the intermediate joint is _j lc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-30-1.png",
        "caption": "Figure 4-30. Overmodulation mode II. Sequence at equidistant time intervals showing the locations of the reference voltage vector and the average voltage vector.",
        "texts": [
            " In this mode, the average voltage moves along the linear trajectories that form the outer hexagon. Its velocity is controlled by varying the duty cycle of the two switching-state vectors adjacent to uav. As m increases beyond wmax3, the velocity becomes gradually higher in the center portion of the hexagon side, and lower near the corners. Eventually the velocity in the corners reduces to zero. The average voltage vector remains then fixed to the respective hexagon corner for a time duration that increases as the modulation index m increases. Such operation is illustrated in Figure 4-30 showing the locations of the reference vector u and the average voltage vector uav in an equidistant time sequence that covers one-sixth of a fundamental period. As m gradually approaches unity, uav tends to get locked at the corners for an increasing time duration. The lock-in time finally reaches one-sixth of the fundamental period. Overmodulation mode II has then smoothly converged into six-step operation, and the velocity along the edges has become infinite. Throughout mode II, and partially in mode I, a subcycle is made up by only two switching-state vectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000816_j.mechmachtheory.2020.103870-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000816_j.mechmachtheory.2020.103870-Figure5-1.png",
        "caption": "Fig. 5. Geometry of the thin-rimmed gear pair: (a) tooth pair A; (b) tooth pair B.",
        "texts": [
            " The mean contact stress in the Hertzian contact half width can be expressed as [8] : \u03c3 H = 3 f d 2 \u03c0( L/n L ) a H (10) Based on the quasi-static load distribution mode, geared rotor dynamic model and Archard\u2019s wear model, the accumulated wear depth can be calculated (see Fig. 4 and [29] ). There is no need to update the worn tooth profile after each wear cycle until the accumulated wear depth exceeds the wear threshold \u03b5 W ( \u03b5 W = 2 \u03bcm). When N (wear cycle) > N max (maximum wear cycle), the iteration of the wear calculation can be stopped. Gear parameters from [42] are listed in Table 1 . Two types of rim structure are involved in this paper (see Fig. 5 ). Initial load distribution (before wear process) has a strong impact on the gear surface wear. The contact pattern (contact pressure over the meshing process) without wear or tooth modification is shown in Fig. 6 . The simulated contact pattern is very close to the measured results in [42] , which verified the proposed load distribution model. Symmetrical load distribution along the face width can be found for rim structure A. But for the rim structure B, obvious stress concentrations can be observed at the location corresponding to the web"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.1-1.png",
        "caption": "Fig. 6.1: Typical Diesel Engine Driveline System and Forces in a Mesh Meshes of Gears",
        "texts": [
            " A typical example can be found in gear systems of diesel engines, which usually must be designed with large backlashes due to the operating temperature range of such engines, and which are highly loaded with the oscillating torques of the injection pump shafts and of the camshafts. Therefore, the power transmission from the crankshaft to the camshaft and the injection pump shaft takes place discontinuously by an impulsive hammering process in all transmission elements [217], [71]. We shall start this chapter with such an example, which was also presented in [200]. Figure 6.1 indicates how the process works. A typical gear unit contains several meshes with backlashes, in the case shown two meshes with backlashes between crankshaft and injection pump shaft and three meshes with backlashes between crankshaft and camshafts. Due to periodical excitations mainly from the injection pumps and subordinately from the crankshaft and the camshaft, the tooth flanks separate, generating a free-flight period within the backlash which is interrupted by impacts with subsequent penetration. The driven flank (working flank) usually receives more impacts than the non- working flank (Figure 6.1). Additionally, in all other backlashes of the gear unit similar processes take place, where the state and the impacts in one mesh with backlash influence considerably the state in all other meshes. This behavior must be accounted for by the mathematical model. As a definition we use the word \u201chammering\u201d for separation processes within backlashes where high loads cause large impact forces with deformation. Motion within backlashes without loads is called \u201crattling.\u201d This represents a noise problem without load problems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003895_002-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003895_002-Figure1-1.png",
        "caption": "Figure 1. Essential components of a biosensor. The transducer is in intimate contact with a biomolecule that interacts specifically with the analyte present in the sample. Physicochemical changes derived from this interaction are amplified and converted into quantifiable and processable electrical signals. According to the nature of the biological sensing element we can distinguish between two large groups of biosensors: catalytic biosensors and affinity based biosensors.",
        "texts": [
            " Because of the different approaches accomplished by different research groups the term biosensor has been applied to many kinds of configurations. A precise definition of what we call a biosensor is: a miniaturized device integrating a biologic sensing element (antibody, enzyme, receptor, cell, etc) on intimate contact with an appropriate transducer (optic, electrochemical, piezoelectric, etc) for conversion of the recognition success to a primary signal (optical or electrical) that can be amplified and subsequently processed eventually to take automatic remediation actions (see figure 1). The sensor should respond directly, selectively and continuously to the presence of one or various analytes when in contact with untreated uncollected samples. Consequently the biological reaction should be highly reversible to provide on-site, real (or near-real) time accurate measurements. Although the proposed definition corresponds to the operational features of an ideal biosensor, in practice most of the devices meet only some of these requisites. For example, most of the immunosensors reported to date do not give a direct answer to the presence of a contaminant but measure a secondary signal product of an enzymatic reaction or a fluorescent compound; some devices do not work under fully reversible conditions (disposable (or single-use) and reusable sensors) and some are difficult to miniaturize or do not have the appropriate electronical configuration to be used on-site"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000587_jestpe.2021.3057665-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000587_jestpe.2021.3057665-Figure15-1.png",
        "caption": "Fig. 15. Prototype parts. (a) Stator, (b) HIR, (c) Modulating ring, (d) LOR.",
        "texts": [
            "3N\u00b7m and its amplitude is 15A. When overload occurs at 0.2s, the MG-IPMBM plays its self-protection function, the three-phase winding current amplitude does not exceed the safety value, and the output electromagnetic torque oscillates near zero. In order to verify the effectiveness and accuracy of the above simulation and analysis, the MG-IPMBM is designed and manufactured, the test bench is built and the experiments are carried out. The main components and test bench of the MG-IPMBM are shown in Fig. 15 and 16, respectively. Authorized licensed use limited to: Carleton University. Downloaded on May 27,2021 at 18:09:13 UTC from IEEE Xplore. Restrictions apply. 2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Fig. 17 shows the waveform of no-load back EMF. Fig. 17(a) shows the calculated waveform, and Fig. 17(b) shows the test waveform. It can be seen that there are some errors between the two waveforms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001088_j.jallcom.2021.158613-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001088_j.jallcom.2021.158613-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of the tensile samples. (a) Schematic diagram of forming position of tensile sample. (b) Two-dimensional schematic diagram of tensile sample.",
        "texts": [
            " Thus, the yield strength, tensile strength, elongation and other parameters were obtained. Moreover, considering that the placement of tensile samples will have a significant effect on the mechanical properties of the fabricated parts (that is, when the tensile axis of the tensile samples is parallel to the fabricated direction, its mechanical properties are lower than those of the tensile axis perpendicular to the fabricated direction), combined with the S-type orthogonal scanning method in this paper (as shown in Fig. 3(a)), the tensile samples with the tensile axis direction parallel to the X-Y plane are prepared and the angle between the tensile parts and the X and Y axis is maintained at 45\u00ba (as shown in Fig. 3(a)), and the design structure follows the ISO 6892\u2013201 standard (as shown in Fig. 3(b)) to avoid interference from stress concentration on the measurement of mechanical properties. Under the low-magnification environment (OM), the Inconel 718 fabricated parts show different microscopic forming characteristics in different fabrication positions; that is, an S-type orthogonal molten channels distribution mode with consistently staggered interlayers with the laser source scanning mode is observed on the fabricated top surface/fabricated bottom surface (as shown in Fig. 4(a)). Additionally, remelted wire is formed in the repeated sintering zone at the boundary of adjacent molten channels, and its compact and parallel arrangement ensures good metallurgical bonding characteristics; on the fabricated side surface (as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003397_s0020-7403(01)00084-4-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003397_s0020-7403(01)00084-4-Figure5-1.png",
        "caption": "Fig. 5. Welding deposition paths: (a) raster; (b) outside-in spiral; and (c) inside-out spiral.",
        "texts": [
            " For all welded specimens, both the <nal deposit and substrate thicknesses were the same as those used for the microcast specimens. As a result, the de9ections and curvatures measured over a 102 \u00d7 102 mm2 region can still be used in comparing microcasting and welding with respect to warping in a single deposited layer. Several welded specimens were manufactured in an e8ort to compare warping in microcasting and welding. In addition, welding was used to investigate the e8ects of various deposition paths, including the raster path used for microcasting (Fig. 5a), an outside-in spiral path (Fig. 5b) and an inside-out spiral path (Fig. 5c). The outside-in path began in the positive x\u2013y corner and continued in a spiral fashion until ending in the center, while the inside-out path began in the center and ended in the positive x\u2013y corner. A summary of the average (n = 2) curvatures obtained for <ve welded specimens is contained in Table 2, where the deposition path used for each specimen is indicated beneath the specimen number. As was the case for microcasting, the average (n=2) curvatures for the raster path specimens in Table 2 are greater in the x direction (parallel to the deposition direction) than in the y direction (transverse to the deposition direction)",
            " These results might be expected in light of the closer proximity of the torch during welding, which results in an increase in inherent substrate pre-heating (or a reduction in thermal mismatch) during material deposition. Table 2 Average (n= 2) curvature results for <ve welded specimens\u2217 Specimen # 1 2 3 4 5 (Path) (Raster) (Raster) (Outside-in) (Inside-out) (Inside-out) w;xx = max 0.0933 0.0948 0.151 0.302 0.300 w;yy = max 0.0784 0.0734 0.197 0.270 0.283 \u2217Note: max = 0:328 m\u22121. Fig. 6. Measured and least square (n= 3) welded results for the raster path of Fig. 5a. In an e8ort to obtain more uniform warping, the spiral deposition paths of Figs. 5b and c were also considered. The measured and n=3 results for a representative inside-out specimen (specimen #4 in Table 2) are shown in Fig. 7. Indeed, the inside-out spiral path resulted in nearly spherical warping, so that the curvatures w;xx and w;yy were nearly equal and essentially uniform. Similar results were obtained for specimen #5. While the outside-in path of Fig. 5b was also considered (specimen #3 in Table 2), the n = 3 results indicated somewhat less uniform warping than that obtained for the inside-out path [18]. This result can be attributed to less uniform initial substrate heating associated with the outside-in path, for which the substrate remains comparatively cold while the torch initially traverses the outside perimeter. It should <nally be noted that compared to the raster path results, both the inside-out and outside-in deposition paths result in substantially greater average warping (see Table 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.17-1.png",
        "caption": "Fig. 2.17: Moving trihedron",
        "texts": [
            " The matrix W(z, t) will be of course completely different for the two constraint types, a Jacobian derived above for the holonomic case, and a Jacobian given by the system configuration for the non-holonomic case. The upcoming fields of robotics and of contact dynamics are accompanied by more frequent applications of curvilinear coordinate systems either for robot trajectories or for contact surfaces ([208],[152]). Let us first discuss the idea to project a mechanism with many degrees of freedom like a manipulator or a gear-mechanism onto one suitable degree of freedom connected with a prescribed trajectory or the like. Considering figure 2.17 and borrowing from the theory of spatial curves (see [51]) the most important relationships we introduce the path coordinate s = s(t) as a parameter and write r(t) = r[s(t)] with v(t) = r\u0307(t) = d r d s \u00b7 d s d t = r\u2032 \u00b7 s\u0307. (2.72) The derivation r\u0307 of the radius vector r(t) with respect to time divided by the path velocity s\u0307 represents the tangent unit vector t to the point trajectory: t(t) = r\u0307 s\u0307 = r\u2032 = d r d s . (2.73) From the velocity vector of equation 2.72 we derive the acceleration vector by a differentiation with respect to time and get a(t) = r\u0308(t) = d (r\u2032 \u00b7 s\u0307) d t = d (r\u2032 \u00b7 s\u0307) d s \u00b7 d s d t = r\u2032\u2032 \u00b7 s\u03072 + r\u2032 \u00b7 s\u0308, (2",
            " It should be noted that this parameterization of spatial curves must not be carried out by using the time t. Instead we may take any general parameter u, which of course must be selected according to the requirements coming from the dynamical system. For certain applications it makes sense to supplement the path coordinate s(t) and its corresponding unit vector t(t) by the normal and binormal vectors resulting in an orthogonal trihedron connected with the spatial path 2.2 Kinematics 33 curve (see figure 2.17). As pointed out above the principal normal vector n(t) is perpendicular to the tangent vector t(t), these two vectors forming the osculating plane for the spatial curve at the point P, and the bi-normal vector is perpendicular to this plane, which means b(t) = [t(t)]\u00d7 [n(t)]. These properties can be used to evaluate the well-known Frenet-equations, which are a basis for all applications connected with spatial trajectories. They write [51] d t d s = +\u03ba \u00b7 n, dn d s = \u2212\u03ba \u00b7 t + \u03c4 \u00b7 b, db d s = \u2212\u03c4 \u00b7 b"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.114-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.114-1.png",
        "caption": "Fig. 12.114 Physical meaning of the Mohr\u2013Coulomb failure criterion",
        "texts": [
            " 914 12 Traction Performance of Tires Equation (12.87) (Fig. 12.113) h\u00f0x\u00de \u00bc j\u00fe t w x h2 \u00bc 1 w Zw 0 h2\u00f0x\u00dedx \u00bc 1 w Zw 0 j\u00fe t w x 2 dx \u00bc j2 \u00fe j t\u00fe t2=3 Note 12.5 Eq. (12.99) The Mohr\u2013Coulomb failure criterion can be determined in shear tests for various normal stresses r. The Mohr\u2013Coulomb failure criterion is that when Mohr circle comes into contact with the line of Eq. (12.99), with plastic deformation occurring at this point. Suppose that the Mohr circle comes into contact with the Mohr\u2013 Coulomb failure criterion at point A of Fig. 12.114a and the angle between the raxis and the line connecting point A with the center of the Mohr circle is 2h (where the counterclockwise direction is positive). A(r, s) in Fig. 12.114a expresses the stress field in the coordinate system at angle h (clockwise direction) measured from the direction of the maximum stress r1. Hence, the shear stress s is applied on plane A\u2013A in Fig. 12.114b. Considering similarly at point A\u2032 expressed by A\u2032(r, \u2212 s) in Fig. 12.114a, the shear stress \u2212s is applied on plane A\u2032\u2013A\u2032 with an angle p/2 \u2212 h measured from the direction of the maximum stress r1 in Fig. 12.114b. According to internal friction theory, planes A\u2013A and A\u2032\u2013A\u2032 will become sliding planes. Note 12.6 Eqs. (12.102), (12.113) and (12.121) for the Heat Flow of a Semi-infinite Solid [160] The governing equation for the heat conduction of a semi-infinite solid is @T @t \u00bc a @2T @z2 0 z\\1; t 0; T \u00bc T0 0 z\\1; t \u00bc 0: \u00f012:222\u00de h(x) w j x t The solution to Eq. (12.222) is T\u00f0z; t\u00de \u00bc T0erf z 2 ffiffiffiffi at p ; \u00f012:223\u00de where erf(z) is defined by erf z\u00f0 \u00de \u00bc 2ffiffiffi p p Zz 0 e n2dn: \u00f012:224\u00de Suppose that initial condition and boundary condition are given by T \u00bc T0 0 t l=V ; T \u00bc Tm z \u00bc 0: \u00f012:225\u00de The solution to Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure13-1.png",
        "caption": "Fig. 13. Tip relief for the original design.",
        "texts": [
            " The gear specifications can be found in ection 2, the shaft misalignment and assembly deflection have een measured in the experimental tests and its maximum vales are summarized in Table 1 (coordination system as shown in ig. 9). The first micro-geometry modification is lead correction. ig. 12 shows a significant contact improvement compared to hat shown in Fig. 11. The concentrated contact area is moved rom one side toward the centre of the facewidth and the highest ontact pressure is reduced as well. The modified lead correction s 37 m instead of the original designed 8 m. The second micro-geometry modification is the gear tooth rofile tip relief. Fig. 13 shows the result from the original esign, 61 m and it shows the second gear tooth started in ontact. This tip relief is over relieved resulting in tip contact pitting failure. K. Mao / Wear 262 (20 c s t t o w t p t o a r u r 6 c m m s o o p b s m T a ontribution too late, contact ratio low and concentrated contact tress at the lowest point of single tooth contact. Fig. 14 shows he modified design with 36 m tip relief and it can be seen from he figure that the tip contact contribution started earlier than the riginal design in Fig. 13. More contact ratio and load sharing ill be achieved from the modified design without causing high ip local contact. R [ [ [ [ [ 07) 1281\u20131288 1287 Crowning of 10 m on pinion and 8 m on wheel gear is roducing even contact stress between the centre of the gear and he edges at the required torque and it can be concluded that the riginal design of crowning is adequate. The recommendations for the gear micro-geometry design re then made based on the modeling results as above. The ecommendations have been used for the gear redesign and manfacturing, the gear contact fatigue wear has been significantly educed and final designed life has been achieved successfully"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000042_c6cs00242k-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000042_c6cs00242k-Figure4-1.png",
        "caption": "Fig. 4 Scheme illustrating the sequence of events leading to the emergence of surface flows in Sugawara\u2019s system. Figure adapted with permission from ref. 45. Copyright 2007 by American Chemical Society.",
        "texts": [
            ", 2016, 45, 4766--4796 | 4769 \u2018\u2018strengths\u2019\u2019 were different at the low- and the high-pH sides, eventually \u2018\u2018pulling\u2019\u2019 the droplet towards low-pH regions and the maze\u2019s exit. Another simple system supporting movement of single droplets was reported by Sugawara et al.45 and was based on fatty acid chemistry. It comprised an oleate surfactant (oleic acid in pH = 11 alkaline water) and an oil (oleic anhydride in nitrobenzene) droplet. After immersion of the oil droplet in the surfactant medium it was initially covered by the oleate surfactant and no movement was observed (Fig. 4, \u2018\u2018stage 1\u2019\u2019). Subsequently, however, the symmetry of the surface was broken and discrete structures accumulated within the droplet\u2019s oil phase. These structures were performing oscillatory-type movements, periodically exposing the oil to the surrounding alkaline water and enabling the hydrolysis of oleic anhydride to oleate. This hydrolysis reaction, in turn, affected the surface tension of the system and lowered the pH near the droplet\u2019s surface (Fig. 4, \u2018\u2018stage 2,\u2019\u2019 red circles). The interfacial motions and flows caused by the local surface-tension gradients ultimately synchronized into a droplet-wide flow pattern, in which the oleate surfactant was being pushed towards the anterior pole of the droplet (Fig. 4, \u2018\u2018stage 3,\u2019\u2019 blue arrows) where it desorbed from the droplet\u2019s surface. Conversely, the hydrolysis reaction localized to the surfactant-poor, \u2018\u2018front\u2019\u2019 pole. The pH gradient over the droplet\u2019s surface then gave rise to two counter-rotating vortices within the droplet that propelled it \u2018\u2018forward\u2019\u2019 (Fig. 4, \u2018\u2018stage 3\u2019\u2019). In their subsequent publication, the same team46 used a different surfactant to act as a chemical \u2018\u2018fuel\u2019\u2019 powering the moving droplets\u2014namely, (N-(4-[3-[trimethylammonio]ethoxy]benzylidene)-4-octylaniline bromide) (Fig. 5a, 1) mixed with 4-octylaniline (Fig. 5a, 2). A fluorescent catalyst (Fig. 5a, 4) present in 4-octylaniline droplets was used to drive the hydrolysis of surfactant 1 back into aniline derivative 2 and benzaldehyde derivative 3. Of these two species, the former was lipophilic and accumulated inside of the droplets, while the latter was hydrophilic and migrated into the aqueous phase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000968_j.addma.2021.102203-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000968_j.addma.2021.102203-Figure14-1.png",
        "caption": "Fig. 14. Von Mises stress distributions in different path strategies. (a) SDM path strategy. (b) RM path strategy. (c) SRM path strategy.",
        "texts": [
            " The characteristic parameters of the heat source are constant in the simulation process, but they are changed in the experiment. The thermophysical properties of the material and the number of meshes in the model affect the accuracy of the simulated results [19]. Additionally, the residual stress measured by XRD is influenced by measuring the parameters and state of the sample surface [18]. In general, it can be proven that the model provides R. Li et al. Additive Manufacturing 46 (2021) 102203 a reliable prediction for the residual stress distribution of thin-walled parts with arc and line features. Fig. 14 illustrates Von Mises stress distributions in different path strategies after parts are cooled to room temperature, and clamps are released. More considerable stress appears at the junction of the wall and the substrate. The von Mises stress of the substrate in the SDM path strategy presents an asymmetric distribution, and the stress near the arc extinguishing point is slightly greater than that near the arc striking point. The heat accumulation at the arc extinguishing position is more significant than that at the arc striking position, resulting in greater thermal expansion and plastic deformation of the surrounding materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000604_j.mechmachtheory.2019.103627-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000604_j.mechmachtheory.2019.103627-Figure2-1.png",
        "caption": "Fig. 2. Force condition of rolling element.",
        "texts": [
            " 5 ) D (3) According to the relative axial displacement \u03b4a , the relative radial displacement \u03b4r and relative angular displacement \u03b8 between the inner and outer rings, the radius i of the curvature center track of the inner raceway and the initial contact angle \u03b10 of the bearing, the axial and radial distance of the groove curvature center between the inner and outer rings can be obtained: { A 1 k = BD sin \u03b10 + \u03b4a + i \u03b8 cos \u03b8k A 2 k = BD cos \u03b10 + \u03b4r cos \u03b8k (4) If the \u201couter raceway control\u201d is approximately true, it can be assumed that the gyroscopic moment of the rolling element is completely balanced by the friction moment between the rolling element and the outer raceway, which has little influence on the calculation accuracy. If not, it is reasonable to distribute the gyroscopic moment equally between the rolling element and the raceway contact area. Fig. 2 shows the force condition of one rolling element when a rolling bearing is running. If outer raceway control is considered, the gyroscopic moment distribution coefficient of inner ring is \u03bbik = 0 , and the gyroscopic moment distribution coefficient of outer ring \u03bbok = 2 ; Otherwise we let \u03bbik = \u03bbok = 1 . The equations of force balance in both directions are given by: { Q ik sin \u03b1ik \u2212 Q ok sin \u03b1ok \u2212 M gk D ( \u03bbik cos \u03b1ik \u2212 \u03bbok cos \u03b1ok ) = 0 Q ik cos \u03b1ik \u2212 Q ok cos \u03b1ok + M gk D ( \u03bbik sin \u03b1ik \u2212 \u03bbok sin \u03b1ok ) + F ck = 0 (5) By the use of Hertz contact theory, the relationship between normal load and normal contact deformation of rolling element is defined as: { Q ok = K ok \u03b4 3 / 2 ok Q ik = K ik \u03b4 3 / 2 ik (6) where K ik represents the contact stiffness between the rolling element and the inner ring, and K ok represents the contact stiffness between the rolling element and the outer ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003961_s11044-007-9088-9-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003961_s11044-007-9088-9-Figure5-1.png",
        "caption": "Fig. 5 Adjacent links in a spherical mechanism (left) and spatial mechanism (right)",
        "texts": [
            " (31) It can be demonstrated [48, 72] that the resultant spherical motion is defined by the following vector \u03c43 = \u03c41 + \u03c42 \u2212 \u03c41 \u00d7 \u03c42 1 \u2212 \u03c41 \u00b7 \u03c42 . (32) Consider two finite screw motions about the axes located by the unit line dual vector E\u0302i (i = 1,2). The rotation angle and the displacement along the axis are denoted with \u03b8i and hi (i = 1,2), respectively. The formula for the composition of these finite motions is obtained by changing the vectors into dual vectors T\u03023 = T\u03021 + T\u03022 \u2212 T\u03021 \u00d7 T\u03022 1 \u2212 T\u03021 \u00b7 T\u03022 , (33) where T\u0302i = E\u0302i tan \u03b8\u0302i 2 (i = 1,2, . . . ). (34) With reference to Fig. 5, the formulas obtained for the kinematic analysis of spherical mechanisms can be extended to the general spatial mechanism with skew links by substituting: \u2022 the relative position angles \u03b8i between adjacent links with the dual angles \u03b8\u0302i = \u03b8i + \u03b5si \u2022 the angular length \u03b1i with the dual angle \u03b1\u0302i = \u03b1i + \u03b5ai . It is worth observing that \u03b8i , si , \u03b1i and ai form a set of Denavit\u2013Hartenberg (DH) parameters. The dual transform matrix from coordinates system Oi+1 \u2212 Xi+1Yi+1Zi+1 to Oi \u2212 XiYiZi has the following expression [37] [A\u0302i] = [\u0398\u0302i][\u039b\u0302i] (35) where [\u0398\u0302i] = \u23a1 \u23a3 cos \u03b8\u0302i \u2212 sin \u03b8\u0302i 0 sin \u03b8\u0302i cos \u03b8\u0302i 0 0 0 1 \u23a4 \u23a6 , [\u039b\u0302i] = \u23a1 \u23a3 0 0 1 cos \u03b1\u0302i \u2212 sin \u03b1\u0302i 0 sin \u03b1\u0302i cos \u03b1\u0302i 0 \u23a4 \u23a6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001018_j.jmapro.2021.01.027-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001018_j.jmapro.2021.01.027-Figure6-1.png",
        "caption": "Fig. 6. a) Transverse cutting of horizontal and vertical tensile samples from the \u201cgrip section\u201d. b and c) Optical micrographs of etched transverse sections of horizontal and vertical samples, respectively, and d) Schematic 3D model of microstructure architecture, according to the applied tensile load direction.",
        "texts": [
            " Fig. 1. a) Ti64 particle diameter distribution of new powder and used powder, b) Typical SEM image of used Ti64 powder particles after being sieved. Table 2 SLM process parameters to fabricate Ti64 samples. Laser Power, P (W) Scanning velocity, v (mm/s) Layer thickness, t (\u03bcm) hatch spacing, h (\u03bcm) Laser beam spot size, w0 (\u03bcm) 270 1800 30 85 70 1 ImageJ is a trademark; (https://imagej.net/Welcome) A. Dareh Baghi et al. Journal of Manufacturing Processes 64 (2021) 140\u2013152 the vertical samples, Fig. 6a. Optical microscopy of polished samples reveals that the morphology of the pores appears to vary: semi-equiaxed in the horizontal samples and generally elongated in the vertical test pieces. The pores\u2019 morphologies are easily recognizable after the polished samples are etched (see Fig. 6b and c). The elongated pores shown in Fig. 6c have the same direction as the laser vector strategy, i.e., \u00b145\u25e6 criss-cross, perhaps suggesting that there is a minor lack of fusion in the solidifying molten pool with its adjacent solidified track or with the previously-solidified layers, i.e., inter-track pores or inter-layer pores. Some of the semi-equiaxed pores observed in the horizontal samples could be the same elongated pores appearing in the vertical samples, given that sectioning the architecture and viewing the samples from a different angle could have altered their morphology",
            " The porosity content of the transverse sections of the horizontal and vertical samples are summarised in Table 3. The very low content of porosity of 0.14 %, confirms the selection of appropriate process parameters to render SLM fabricated Ti64 parts with nearly full density (99.86 %). The magnitude of the standard deviation may also suggest the distribution of pores examined by 2D image analysis is nearly the same in two directions. The microstructure of the etched transverse section of the horizontal sample, Fig. 6b, exhibits a columnar pattern; whereas the transverse section of the vertical sample, Fig. 6c, shows a chessboard pattern, which is the consequence of criss-cross alternating layering. The chessboard side length of 85 \u03bcm and diagonal length of 120 \u03bcm displayed in Fig. 6c or the ~120 \u03bcm of columnar grain width in Fig. 6b, all correspond with the laser hatch spacing of 85 \u03bcm, Table 2. The columnar architecture of the microstructure parallel to the build direction and the formation of a chessboard pattern perpendicular to the build direction are consistent with other studies [3,22,35]. Fig. 6.d illustrates a schematic representation of the 3D architecture of the SLM fabricated Ti64 parts according to the criss-cross alternating layering and with respect to the direction of applied tensile load for horizontal and vertical samples. It could be expected that this architecture, with respect to the applied loading direction, results in an anisotropy of the mechanical properties. The boundaries separating the individual columnar grains are believed to be the grain boundaries of the prior \u03b2 phase upon solidification of the Ti64 [36]. The martensitic lath structure in the columnar or chessboard grains in Fig. 6b and c are due to the steep thermal gradient experienced during the SLM process, i.e., cooling rates of 104-106 [37\u201339], by which the \u03b2 phase directly transforms to a martensitic \u03b1\u2019 phase. The SEM micrographs in Fig. 7 show the lath morphology of the martensitic phase (\u03b1\u2019) is almost similar for both vertical and horizontal samples. The XRD spectrum in Fig. 8 confirms there is no trace of the bcc structure \u03b2-titanium phase in the SLM fabricated part, or, at least, it is below the detection limit of the XRD method",
            " 9d shows that the machined verticals and horizontals are very similar in their strengths but the strain at fracture of the machined verticals is still nearly half that of the horizontal samples, which will be discussed later in this section. The variation of Young\u2019s modulus for all samples, according to Fig. 9e, is approximately 4 %. This means the build direction and associated surface condition of the samples does not have any significant effect on the elasticity (stiffness), which is not the case for YS and UTS. As explained in the section on microstructural characterisation, the direction of tensile loading with respect to the columnar architecture (Fig. 6d) can result in anisotropy of the mechanical properties but there are other factors affecting the mechanical properties, especially in the as-built vertical. The different behaviour of vertical samples under two conditions of as-built and machined, Fig. 9b, may suggest that the interrelationship between the surface topography of the test pieces and the loading axis needs to be examined closely to verify if the build direction has any effect on the directionality of the valleys and hills of the roughness profile with respect to the loading axis",
            " 9e shows that, by removing the surface layer of the vertical samples via machining, a considerable improvement in the mechanical properties could be achieved. Further investigation is required to show whether the surface characteristics (the sharp notches on the surface) of the as-built vertical samples alone are responsible for the premature failure or the residual stresses, or both. The observed lower ductility of machined vertical samples with respect to their horizontal counterparts could partially be attributed to the sharp angles of inter-layered pores, appearing perpendicular to the applied tensile load, Fig. 6c. In other words, anisotropy of pores with respect to the direction of applied load could be a potential cause of anisotropy of A. Dareh Baghi et al. Journal of Manufacturing Processes 64 (2021) 140\u2013152 A. Dareh Baghi et al. Journal of Manufacturing Processes 64 (2021) 140\u2013152 the mechanical properties. Porosities, which are inevitable SLM-induced defects [11,44], often limit the ductility of Ti64 parts [45]. In some studies [12,20], it is shown that these thin flattened pores, which are due to the lack of fusion between layers, may act as local stress risers, with some role played in the early fracture of the vertical samples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.50-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.50-1.png",
        "caption": "Fig. 5.50: Piston Kinematics",
        "texts": [
            " The influence of these characteristics on the dynamics of the tripod itself is not very large, which corresponds to experience. Therefore a detailed analysis will be only necessary for special evaluations required for the tripod joint. The hydrostat piston kinematics produces oil flow and oil pressure. The pistons perform a stroke motion within the drum cylinders, while rotating around the tripod joint. This motion depends on the displacement angle \u03b1, which at the same time represents a control quantity for flow and pressure. According to Figure 5.50 we get the following vector chain rTF = h+ rK + lK , (5.94) which can be decomposed to the three equations for the unknowns (h, \u03b2, \u03b3) \u03b3 = arcsin ( rTF lK (sin\u03d5TF cos\u03d5K \u2212 cos\u03d5TF sin\u03d5K cos\u03b1) ) \u03b2 = arcsin ( rK \u2212 rTF (sin\u03d5TF sin\u03d5K + cos\u03d5TF cos\u03d5K cos\u03b1) lK cos \u03b3 ) h =rTF cos\u03d5TF sin\u03b1 + lK cos\u03b2 cos \u03b3 (5.95) The results of these equations are illustrated in Figure 5.3.2. To get an idea of the forces resulting from the above kinematical consideration we investigate a simplified case with no rotational speed difference, \u03d5T \u2212\u03d5K = 0, and a piston pressure according to Figure 5",
            "99) were linearized around a stationary operation point, which gives for our case a reasonable approximation of the real dynamic behaviour including nonlinearities. With Mq\u0308 + Kq = 0 we are able to evaluate eigenforms and eigenfrequencies, which has been done for 20 eigenfrequencies up to \u2248 2000 Hz. We shall consider only a few of them. The matrix K contains all linearized stiffnesses of the system, which are of particular interest for the hydrostat, because its stiffness depends on the inclination angles \u03b1 and \u03b2 (Figure 5.50) and thus on the speed ratio is = ncollectingshaft/nengine = 1/i. As a consequence all eigenforms and eigenfrequencies resulting from an analysis of Mq\u0308 + Kq = 0 depend also on the ratio is. Figure 5.3.3 depicts the depencies of some typical eigenfrequencies on the speed ratio. With the exception of hydropump and hydromotor themselves the influence on all other components is very small. For system design one need to know the topological vibration behaviour, that means what components vibrate with respect to other ones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000931_j.matdes.2021.109605-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000931_j.matdes.2021.109605-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of our 4Dprintingmethodwith a hybrid hinge fabricated using the The hinge after 3D printing consists of two hinges with 4D printing capabilities and an elastom elastomer layer and the shrinkable SMP layer. The hybrid hinge is composed of 4D printed hin applying an external force to the 4D printed sample below the glass transition temperature o and unfolding deformation.",
        "texts": [
            " As non-shrinkable SMPs and elastomers do not shrink on heating, the thermal expansion coefficients of thesematerials were set to 0/K in all the directions. The shrinkage of SMP was shrunk by raising the atmospheric temperature by 1 K. The boundary conditions in the simulationwere fixed at the edge of the panel parts of the sidewalls. For calculating the self-folding angle during the simulation, the values of the coordinates at two points of the panel were used. A schematic illustration of our proposed 4D printing method with the hybrid hinge is shown in Fig. 1. In this study, the polymers in a glassy state at room temperature and capable of retaining internal stresses during 3D printing are called SMPs, while the polymers in a rubbery state at room temperature are called elastomers. The initial 3D printed structure consists of panels and a hybrid hinge. The panel is a sandwich structure comprising non-shrinkable SMP layers and anelastomer layer. The hybrid hinge consists of two rigid hingeswith a 4Dprinting function FDM3Dprinter. (a) Transformation from3Dprinted shape to 4Dprinted shape by heating",
            " er hinge. The shape transformation occurs because of the shrinkingmismatch between the ges and an elastomer hinge. (b) Folding and unfolding deformation after 4D printing. By f the SMP, elastic bending deformation occurs at the elastomer hinge, resulting in folding for self-folding and a soft elastomer hinge capable of bending after the 4D printing. A hybrid hinge with two 4D printing hinges at both ends and one elastomer hinge in the center of the hinge was designed for this study, as shown in Fig. 1. The 4D printing hinge consists of a shrinkable SMP layer and an elastomer layer, and an elastomer hinge consisting only of an elastomer layer. When an external stimulus causes the SMP layer to shrink, the shrinkage mismatch between the SMP and elastomer layers causes bending deformation referred to as 4D printing (Fig. 1(a)).When an external force is applied after 4D printing, deformation occurs at the elastomer hinge, which is less rigid than the 4D printed hinges and can be transformed into a folded or an unfolded shape even below the glass transition temperature of the SMP (Fig. 1(b)). First, a 4D printed sample with the proposed hybrid hinge was fabricated. Fig. 2(a) shows the fabrication process of the sample. Furthermore, as seen from the results of the shrinkage of the SMP as a function of the printing temperature shown in Figs. S1(a) and (b), SMPs printed at 200 \u00b0C and 240 \u00b0C were found to shrink by 30% and 1%, respectively, when heated to 90 \u00b0C for 2 mins. Hence, the shrinkable SMP to form the 4D printing hinge was printed at 200 \u00b0C, and the nonshrinkable SMP to form the panel was printed at 240 \u00b0C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.34-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.34-1.png",
        "caption": "Fig. 5.34: Functional principle of a piezoelectric cycloid motor. According to [Haya91]",
        "texts": [
            " The disadvantage, however, is the short lifetime due to the wear on the stator and rotor from friction. In Japan, a new concept was developed for these motors, which contains a piezoelectric drive. In the so-called cycloid motor, the lifetime is prolonged by reducing friction. This is realized by transmitting forces via a special geardrive. The inner part of the disc-like stator and the outer part of the rotor have gear teeth and engage with one another. The four piezoelectric drive elements are equally spaced at 90\u00b0 along the outside of the stator, Fig. 5.34. If an alternating voltage is app- lied to oppositely located piezoelements with a phase difference of 90\u00b0, an os cillation is induced in the freely floating stator. The oscillation causes the rotor to move in the opposite direction due to the force transmission by the gears. The first prototype of the cycloid motor had piezo actuators with a dimension of 5 x 5 x 20 mm3. The piezo elements have a maximum expansion of 16 J.lm under a voltage of 150 V. The motor's dimensions are mainly determined by the size of the piezoactuators"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.13-1.png",
        "caption": "Fig. 11.13 Fiala model. Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [
            " The total moment Mz is given by 11.1 Tire Models for Cornering Properties 721 Mz \u00bc M0 z \u00feM z : \u00f011:35\u00de Suppose that the lateral displacement of the string in the contact patch v can be expressed by a straight line at a given slip angle a. Neglecting the circumferential displacement u, v is given by v \u00bc a a x\u00fe r\u00f0 \u00de: \u00f011:36\u00de The substitution of Eq. (11.36) into Eqs. (11.32) and (11.33) yields Fy \u00bc CFaa Mz \u00bc CMaa CFa \u00bc 2ks r\u00fe a\u00f0 \u00de2 CMa \u00bc 2ksa r r\u00fe a\u00f0 \u00de\u00fe a2=3 : \u00f011:37\u00de (1) Beam model and Fiala model Figure 11.13 shows the Fiala model [3], where D is the rigid wheel, B is the circular beam acting as the belt of a radial tire, C is the springs acting as the carcass, and T is the tread rubber. The circular beam has in-plane flexural rigidity EIz, where Iz is the moment of inertia of area, and E is Young\u2019s modulus of the belt in the circumferential direction. ks is the lateral fundamental spring rate per unit length in the circumferential direction discussed in Sects. 6.1.3 and 6.4.2. When the side force Fy is applied to the circular beam, the deformation of the circular beam can be solved as a bending problem of the beam on an elastic foundation as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001018_j.jmapro.2021.01.027-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001018_j.jmapro.2021.01.027-Figure3-1.png",
        "caption": "Fig. 3. Typical sample of the first batch of the horizontally-built parts after being removed from the substrate.",
        "texts": [
            " 2 shows the schematic of the first batch of the horizontal samples used to measure the deflection after support removal, immediately after deposition. The coloured arrows in Fig. 2 show the laser path in alternating layers employed for the horizontal samples. The build direction is perpendicular to the plane of this page and the laser path has an alternating angle of \u00b145\u25e6 with respect to the tensile axis of the test pieces. The deflection of the first batch of the horizontal samples were measured, by a dial gauge, on the centre axis of both ends to the centre of test piece. That was approximately 1 mm as depicted in Fig. 3. The deflection distribution of the individual points along the tensile axis of two typical horizontal samples is shown in Fig. 4. Once the deflection values of the fabricated samples (length = 126 mm) was determined (Fig. 4), a reversed design was considered to fabricate the samples with a maximum length of 80 mm. The selection of this length, 80 mm, was based on the maximum allowable height of the vertical parts to be built by the ProX-200 3D printing machine. As demonstrated in Fig. 4, a deflection of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.3-1.png",
        "caption": "Fig. 7.3: Robot Example and Drive Models",
        "texts": [
            " The basic idea consists in the assumption, that the manipulator end effector follows perfectly and in an ideal way a prescribed trajectory, the path coordinate of which is used as the only degree of freedom whatever the robot configuration might be. To realize that we must project all kinematics and all kinetics onto this one degree of freedom resulting in a structure of the equations of motion, which then allows an analytic-topological solution for the time-optimum problem. These ideas were persued nearly at the same time in the US and in Europe, see [21], [48], [109], [243], [204], [186]. We consider any robot configuration and establish in a first step the kinematics of such a robot. Figure 7.3 gives an example [219], [152]. We refer to chapter 2.2 on page 12, and there especially to the sections 2.2.2 to 2.2.5. It should be noted that for the description of robots also Denavit-Hartenberg coordinates are frequently applied. We did not discuss them in chapter 2.2, but there is a lot of literature dealing with this type of coordinates [42], [3], [208]. We describe the position and orientation of a robot link with respect to its predecessor link (see for example Figures 2.15 on page 26 and 2",
            " To provide the equations of motion (7.11) with the forces and torques on the right hand side we consider in the following the motor and gear forces, the control forces and the contact forces (and/or torques). For motors and gears we shall regard rigid and elastic models. In the first case the drive has no additional degree of freedom, but is connected to the link by a simple transmission ratio acting as an additional condition between drive and link. In the second case elesticity requires an additional degree of freedom (see Figure 7.3) connected to the link by a spring/damper force element. The corresponding torque writes \u03c4L,j = cj ( q\u0304M,j iG,j \u2212 q\u0304L,j ) + dj ( \u02d9\u0304qM,j iG,j \u2212 \u02d9\u0304qL,j ) , (7.12) Where q\u0304M,j is the additional degree of freedom of the j-th joint drive, iG,j is the gear transmission ratio, q\u0304L,j is the j-th link degree of freedom, and cj, dj are the spring and damper coefficients. The torque acting on the motor shaft is the drive torque \u03c4j reduced by the spring/damper torque \u03c4L,j iG,j and a friction torque \u03c4R,j . We get \u03c4M,j = \u03c4j \u2212 \u03c4L,j iG,j \u2212 \u03c4R,j (7",
            "56) where j is the number of the manipulator joints, M its mass matrix, g a vector with all gyroscopical and gravitational forces, B the actuator matrix, T includes the actuators forces and torques, FG and TG are forces and torques at the gripper and the matrices JT ,JR the Jacobians of translation and rotation at the gripper. qMI \u03d5 qME Kgear Fig. 7.17: Elastic Joint Model From this we conclude, that without elasticities in the joints we get fr = j and with joint elasticities fr = 2j considering only one degree of freedom for each joint. It might be more, of course. In the last case the additional joint equations of motion write IM \u00b7 q\u0308MI = T0\u2212 Kgear igear ( qMI igear \u2212 qME ) . (7.57) Figure 7.17 illustrates the corresponding model, see also Figure 7.3. The magnitudes Kgear and igear denote the joint stiffness and the gear transmission ratio, respectively, qMI and qME are the internal and external joint coordinates, IM is the motor moment of inertia and T0 the actuating motor torque. A manipulator coming into contact with its environment forms a closed kinematical loop with special properties (see Figure 7.16). Considering for example manufacturing processes usually requires also the inclusion of some given forces or torques at the end-effector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.44-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.44-1.png",
        "caption": "Fig. 6.44: Principle design of a biosensor (the sensor is shown in an open position). According to [Xie94]",
        "texts": [
            "4) were used to make the Ti/Pt electrodes. Each electrode consists of 70 fingers, each of them is 900 ~tm long and between 1 ~tm and 3.2 ~tm wide. The gap between neighboring fingers is between 186 and 800 nm. Single channel metabolism sensors Several thermal metabolism sensors can be installed in one sensor system to simultaneously detect various substances using different enzymes. For this purpose, many transducers must be integrated in the sensor system. Here microproduction techniques offer ideal solutions. Figure 6.44 shows such a microsystem; here: T x - thermistor, Ex - enzyme reaction range. The sensor consists of a quartz transformer chip (21 x 9 x 0.57 inm3), a layered silicon structure (17.5 x 0.8 x 0.32 mm3), which also serves as a spacer and flow channel, and a plexiglass cover to seal the microchannel; the latter contains inlet and outlet tubes made of steel. Several thermistors are arranged at a spacing of 3.5 mm along the flow channel; they are made by doping and etching the quartz chip at specified locations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001207_tec.2021.3056557-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001207_tec.2021.3056557-Figure1-1.png",
        "caption": "Fig. 1. Phasor diagrams of positive and negative sequence stator harmonics as viewed in the rotor reference frame: (a) hth harmonics in negative sequence; and (b) mth harmonics in positive sequence, where \u03b8neg h and \u03b8pos m are respective phase angles.",
        "texts": [
            " To express the harmonics in RRF, the stator harmonics in negative and positive sequence are both transformed from the abc coordinates to the RRF using Park\u2019s transformation matrix K, as ( ), , r dqs neg r abc neg\u03b8= \u22c5f K f , ( ), , r dqs pos r abc pos\u03b8= \u22c5f K f , (4) [6] [7] [8] [9] [10] [11] [12] [13] [14]- [15] [16]- [21] [22] [23] [24] [25] Proposed method Harmonic current reference calculation Torque model based method PM flux harmonics \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a Inductance harmonics \u221a Cogging torque \u221a \u221a \u221a \u221a \u221a \u221a Speed based method \u221a \u221a \u221a \u221a \u221a High-speed application \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a Minimal loss \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a Computation efficiency \u221a \u221a \u221a \u221a \u221a \u221a \u221a Harmonic current control Harmonic current feedback loop \u221a \u221a \u221a \u221a \u221a \u221a \u221a Width bandwidth \u221a \u221a \u221a \u221a \u221a Computation efficiency \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a Reference frame abc coordinate \u221a \u221a Multiple reference frame \u221a \u221a \u221a Rotor reference frame \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a \u221a Authorized licensed use limited to: Robert Gordon University. Downloaded on May 28,2021 at 02:43:27 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. in abc coordinates are transformed into RRF as the nth harmonics (n=6j), as shown in Fig. 1(a). Moreover, the speed of their rotation in the RRF becomes n\u03c9r (where \u03c9r represents rotor electrical speed). Thus, the hth harmonics in abc coordinates are viewed as the nth harmonics in RRF. The nth harmonic components in RRF can be obtained by projecting fabc,neg onto the dr and qr axes, respectively, which is expressed as ( ) ( ) ( ) ( ) , , ,, , , , , cos sin sin cos r n cos ds neg r r neg hr n dqs neg r n sin qs neg r r neg h f n n f f n n f \u03b8 \u03b8 \u03b8 \u03b8      = =    \u2212     f , (6) where the superscript \u201cr, n\u201d represents the nth order harmonics expressed in RRF. Similarly, the positive sequence mth harmonics in abc coordinates are also transformed into RRF as nth harmonics (n=6j), as shown in Fig. 1(b). The nth harmonic components in RRF can be obtained by projecting the fabc,pos onto the dr and qr axes, respectively, which is expressed as ( ) ( ) ( ) ( ) , , ,, , , , , cos sin sin cos r n cos ds pos r r pos mr n dqs pos r n sin qs pos r r pos m f n n f f n n f \u03b8 \u03b8 \u03b8 \u03b8      = =    \u2212     f . (7) Therefore, the total nth harmonics in RRF are the combination of the harmonics from the negative sequence (6) and the positive sequence (7), which is expressed as ( ) ( ) ( ) ( ) , ,, , , , , , , cos sin cos sin cos sin ds n r ds n rr n r n r n dqs dqs neg dqs pos cos sin qs n r qs n r f n f n f n f n \u03b8 \u03b8 \u03b8 \u03b8 +  = + =  +  f f f , (8) where fds,n cos = fneg,h cos + fpos,m cos , fds,n sin = fneg,h sin \u2212 fpos,m sin , fqs,n cos = fneg,h sin + fpos,m sin , and fqs,n sin = \u2212fneg,h cos + fpos,m cos are the magnitudes of nth harmonics, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-21-1.png",
        "caption": "Figure 4-21. Linearized trajectories of the harmonic current for two voltage references wt and \u00ab2: (a) suboscillation method; (b) space vector modulation; (c) modified space vector modulation.",
        "texts": [
            " The choice between the two switching sequences (4.28) and (4.29) should depend on the value of the reference vector. The decision is based on the analysis of the resulting harmonic current. Considering the equivalent circuit Figure 4-10, the differential equation dis 1 \u00ab,) (4.30) can be used to compute the trajectory in space of the current space vector is. In equation 4.30, us is the actual switching-state vector. If the trajectories dis{us)/dt are approximated as linear, the closed patterns of Figure 4-21 will result. The patterns are shown in this graph for the switching-state sequences in equations 4.28 and 4.29, and two different magnitude values, u\\* and u2*, of the reference vector are considered. The harmonic content of the trajectories is determined using 4.18. The result can be confirmed just by a visual inspection of the patterns in Figure 4-21: the harmonic content is lower at high-modulation index with the modified switching sequence 4.29; it is lower at low-modulation index when the sequence 4.28 is applied. Figure 4-23 shows the corresponding characteristics of the loss factor d1: curve svm corresponds to the sequence 4.28, and curve c to sequence 4.29. The maximum modulation index extends in either case up to wmax2 = 0.907. Synchronized Carrier Modulation. The aforementioned methods operate at constant carrier frequency, while the fundamental frequency is permitted to vary",
            " Performance of Carrier-Based PWM. The loss factor S of suboscillation PWM depends on the zero-sequence components added to the reference signal. A comparison is made in Figure 4-23 at 2 kHz switching frequency. Letters \"a\" through \"d\" refer to the respective reference waveforms in Figure 4-17. The space vector modulation exhibits a better loss factor characteristic at m > 0.4 as the suboscillation method with sinusoidal reference waveforms. The reason becomes obvious when comparing the harmonic trajectories in Figure 4-21. The zero vector appears twice during two subsequent subcycles, and there is a shorter and a subsequent larger portion of it in a complete harmonic pattern of the suboscillation method. Figure 4-15 shows how the two different on-durations of the zero vector are generated. Against that, the on-durations of two subsequent zero vectors Figure 4-2lb are almost equal in the case of space vector modulation. The contours of the harmonic pattern come closer to the origin in this case, which reduces the harmonic content",
            " \u2022 The modulation process generates subharmonic components. The amplitude density spectrum hd(f), shown in the Figure 4-46, includes also discrete components h\\{k-f\\) at subharmonic frequencies; the spectrum is almost independent of the modulation index. The switching frequency of a hysteresis current controller is strongly dependent on the modulation index, having a similar tendency as curve a in Figure 4-51 if the aforementioned special effects are not considered. This effect can be explained with reference to Figure 4-21. It is illustrated there that the current distortions reduce when the reference vector u reaches proximity to one of the seven switching-state vectors, u is in permanent proximity to the zero vector at low modulation index and in temporary proximity to an active switchingstate vector at high modulation index. Consequently, the constant harmonic current amplitude of a hysteresis current controller lets the switching frequency drop to near zero at m \u00ab 0, and toward a higher minimum value a t m - > mmax"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000888_ffe.13361-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000888_ffe.13361-Figure2-1.png",
        "caption": "FIGURE 2 Shape and dimensions (mm) of tested specimens: (A) for tensile tests, and (B) for ultrasonic fatigue tests",
        "texts": [
            " In addition, the porosity or defects was also characterized by 2D image observations of optical microscopy (OM) in both horizontal and longitudinal cross sections, that is, perpendicular and parallel to the SLM building direction, respectively. For OM examinations, the samples were ground by using SiC grinding papers down to 2000 grit size and then polished with SiO2\u2013H2O2 polishing compound. Monotonic tensile tests for the nine group specimens were conducted in a hydraulic servo testing machine with each group containing four specimens. The loading rate of the monotonic tension was 0.1 mm min\u22121. The geometry with the dimensions of the tensile specimen is shown in Figure 2A. Ultrasonic fatigue tests were performed at room temperature on a Lasur GF20-TC device, with a resonance frequency of 20 kHz, which requires that the resonant frequency of the specimen be equal to the input incitation frequency (20 kHz \u00b1 500 Hz) of the ultrasonic piezoelectric ceramic resonator. The stress ratio R was \u22121 for all fatigue tests. During the ultrasonic fatigue testing, compressive air was used to cool the specimen to eliminate the temperature rise of the specimen during testing. When a specimen was loaded beyond 1 \u00d7 109 cycles without failure, the test would be terminated and the unbroken specimen would be labelled as a run-out case. The specimens for ultrasonic fatigue testing are hourglass shape and the geometry with the dimensions of the specimen is shown in Figure 2B. Fracture surfaces of all failed specimens were examined via a high-resolution fieldemission SEM (FEI QUANTA 200 FEG). The results of the measured porosity RD for the nine groups of specimens are listed in Table 2. According to the extremum difference analysis,34 the value of the extremum difference can reflect the influence of each factor on the porosity, that is, the larger the extremum difference, the more remarkable the influence significance of a factor. The values of extremum difference for each concerned factor are obtained as 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure4.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure4.3-1.png",
        "caption": "Fig. 4.3",
        "texts": [
            " In other words, a sudden change in quality occurs at Il = 0 in the topological structure, and bifurcation of equilibrium branches appears at that point (such a bifurcation is called a pitchfork bifurcation). Example 3 Consider a planar system { x'=-Y+X[Il-(X2 +/)] y'= x + Y[Il-(x2 + i)] where Il E ~ is a bifurcating parameter. (x,y) E~2 r' = r(ll- r2) 8'= 1 (4.3) (4.4) From the above formulae we know that when Il ~ 0, eq. (4.3) has a unique asymptotically stable focus (0,0). When Il > 0, the focus (0,0) becomes the unstable focus of eq. (4.3). At this point there is also a stable limit cycle r = ~. On the transversal section perpendicular to the Il-axis Fig. 4.3 shows the phase portrait of system (4.3) when Il is fixed. Moreover, Fig. 4.3 also shows the bifurcation diagram-the change in position of stable points and the limit cycle of eq. (4.3) with the change of Il. From the figure, we know that a sudden change occurs at Il = 0 in the topological structure of system (4.3), when a bifurcation appears at this point (such a bifurcation is called a Hopfbifurcation). The existence of bifurcations implies that a small change in parameter near the bifurcation value will lead to a change in quality of the topological structure of the system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000915_admt.202000093-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000915_admt.202000093-Figure13-1.png",
        "caption": "Figure 13. Droplet bouncing and slippage behavior on curved surface and typical applications with suitable ink formulas. a) Droplets on slopes. Left parts and right bottom part: Reproduced with permission.[200] Copyright 2002, Elsevier. Right upper part: Reproduced with permission.[202] Copyright 2013, Cambridge University Press. b) Droplets on surfaces of different materials. Reproduced with permission.[199] Copyright 2015, AIP Publishing. c) The influence of the droplet hydrophilicity on the surface. Reproduced with permission.[203] Copyright 2015, Royal Society of Chemistry. d) Declining with the suitable ink formula. Reproduced with permission.[131] Copyright 2005, IEEE. e) Manufacturing process of multilayer tactile sensor. Reproduced with permission.[205] Copyright 2015, Elsevier. f) 3D-printed conformal array patch antenna. Reproduced with permission.[207] Copyright 2017, Springer Nature.",
        "texts": [
            " However, different from planar printing, conformal printing faces three new problems: droplet bouncing and slippage behavior on curved surfaces, 3D motion platforms and systems, and the formation of 3D structures and patterns. Since the droplets are in total different status on curved surfaces from those in planar surfaces, the quality of printed structures suffers from low viscosity inks, which inevitably streaming on steep surfaces in conformal manufacturing of curved electronics. In some complex motion status, droplets will slip or even roll,[193\u2013196] as shown in Figure\u00a013c, which will seriously affect the accuracy and quality of the printing pattern. So it can be said that the droplet behavior on curved substrates plays the most significant role, and the final deposition location is affected by the bouncing of the droplet on the curved surface[197] and the slippage caused by gravity on the curved surface.[198] Besides, electronic miniaturization and array of electronic devices are also required, so it is important to meet the resolution requirements of printed patterns",
            " The first aspect can be explained by printing mechanism, which has been relatively mature to control the droplets volume. While the second aspect Adv. Mater. Technol. 2020, 2000093 www.advancedsciencenews.com \u00a9 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim2000093 (19 of 29) www.advmattechnol.de requires in-depth study and accurate modeling due to the complexity of droplet dynamics on irregular substrate,[200\u2013202] where the shape and profile of the droplets greatly changes under different inclinations (Figure\u00a013a) or materials of substrates (Figure\u00a013b). In order to avoid above behavior in the process of conformal printing, surface treatment and ink modification are required. More importantly, it is not only necessary to obtain a higher ink viscosity to keep the liquid ink from flowing,[193] but also to enhance the adhesive force between droplets and curved surfaces in case of rolling droplets.[203] In addition, it is necessary to plan and compensate its motion so that the droplet rolling or slip does not affect the print pattern at the maximum acceleration or speed of the base motion. Therefore, as for printing of metallic nanoparticle inks, the most important thing is to control the concentration size and distribution of nanoparticles. When the formula is in the most appropriate state, the simplest declining inkjet printing could fabricate an antenna patterned on the inner surface of bugle cup (Figure\u00a0 13d).[131] Based on a quantity of experiments and analyses, concentrated nanoparticle inks with high solid content (weight over 70%) are preferred for printing. At the same time, ensuring good electrical performance is also extremely critical. Two different formulations of \u201capproximately-particle-free\u201d conductive liquid which has good electrical conductivities were proposed in order to acquire better performance. One is a novel aqueous solution, which exhibits excellent adhesion to glass and polymers, and has a resistivity close to bulk silver",
            " This microstructure can be seen as \u201cparticle free\u201d because of the close-packed statement after Adv. Mater. Technol. 2020, 2000093 www.advancedsciencenews.com \u00a9 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim2000093 (20 of 29) www.advmattechnol.de thermolysis and subsequent annealing.[204] Besides, there is another printing technique using suitable ink formula, which combine a developed piezoresistive polymer/nanocomposites with layer-by-layer soft molding process for compliant and multilayer tactile sensors, as shown in Figure\u00a013e. All the sensing elements were evenly printed in conformal skin structure.[205] Owing to desirable formulations, conformal printing of metallic nanoparticle inks offers an attractive alternative for meeting the demanding printing requirements on curved surface, and is developed to a promising tool for fabricating conformal, compliant antennas, sensors, or other electronics within extensible elastomeric matrices. Jennifer A. Lewis\u2019 research group first demonstrated the conformal printing of silver nanoparticle inks on the convex and concave surfaces of hemispherical glass substrates to fabricate ESAs.[16] Besides, conformal inkjet printed 2-bit four-element phased-array antenna was presented too, which exhibits an on\u2013off ratio of over 1000 and current of 3.6\u00a0mA at a low source\u2013drain bias of 0.8\u00a0V.[206] Moreover, Huang and coworkers also designed and fabricated a new kind of conformal 2 \u00d7 4 array patch antenna,[207] as shown in Figure\u00a013f. As the capabilities of curved electronics become more and more advanced, the requirements for manufacturing accuracy are extremely increasing. When the droplets leave the nozzle and fall onto the substrate, \u201cflight errors\u201d occur frequently that droplet deviates from its preset position. Therefore, the motion systems play a more significant role of conformal printing accuracy, which requires improvement in positioning accuracy of the moving axis, as well as the droplet resolution. At this stage, the most straightforward approach for conformal 3D fabrication is using printers, capable of omni-axis movement, for digital printing of functional ink on uneven surface, polyhedron surface, and sometimes very complex topography"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure4.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure4.9-1.png",
        "caption": "Fig. 4.9: Combination of smooth and non-smooth components",
        "texts": [
            " The pressure drop curve of a prestressed check valve can be split into an ideal unilateral part \u2206p1 and a smooth curve \u2206p2 considering the spring tension and pressure losses, see Figure 4.8 Many hydraulic standard components are combinations of basic elements. Since the combination of unilateral and smooth characteristics yields either non-smooth or smooth behavior it is worth to consider such components with 4.2 Modeling Hydraulic Components 195 a smooth characteristic separately. As an example we consider a typical combination of a throttle and a check valve. Figure 4.9 shows the symbol and the characteristics of both components. Since the flow rate of the combined component is the sum of the flows in the check valve and the throttle, the sum of the flow rates is a smooth curve. In such cases it is convenient to model the combined component as a smooth component (in the mechanical sense as a smooth force law). As an example for a servovalve we consider a one-stage 4-way-valve. It is a good example for the complexity of the networks representing such components like valves, pressure control valves, flow control valves and related valve systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.41-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.41-1.png",
        "caption": "Fig. 8.41",
        "texts": [
            " The cross-line in the normal direction plane is called a KAM curve. For an integrable Hamilton, such as a pendulum, the phase portrait consists of elliptic points and hyperbolic points alternatively. The phase plane is divided continuously by saddle points. The motions of all parts in the phase space do not cross one another. In the case of an non-integrable small disturbance, a change appears near the saddle point. The connecting line for saddle breaks and violent oscillations takes place near the saddles. (Fig. 8.41) 308 Bifurcation and Chaos in Engineering This kind of oscillation leads to structure similar to the Smale horseshoe, and hence to chaos. The relevant region is called the chaos layer. Here, this marks an important difference between systems with two degrees of freedom and multi degrees of freedom. See Fig. 8.1. The KAM torus in the system with two degrees of freedom is the two-dimensional torus in a three-dimensional phase space. Therefore, the motion in a random layer is confined to a certain region, and cannot depart much from it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000169_j.snb.2016.02.113-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000169_j.snb.2016.02.113-Figure1-1.png",
        "caption": "Fig. 1. Schematic of an aerosol jet micro-additive printer.",
        "texts": [
            " The sensitivity and accuracy of etection was determined as a function of the printed MEA strucure geometry. The potential applications of this method for other ypes of electrochemical sensors are also discussed. . Experimental .1. Micro-electrode array fabrication The MEAs were fabricated using aerosol jet (AJ) based irect-write technology that allows deposition of solvent based anoparticles with solution viscosity ranging from 1 to 1000 cP. schematic of the AJ system (AJ 300, Optomec Inc., Albuquerque, M, USA) is shown in Fig. 1 and includes two atomizers (ultrasonic nd pneumatic), a programmable XY motion stage, and a deposiion head. Solvent based nanoparticle ink is placed in the atomizer hich creates a continuous and dense mist of nanoparticles with a roplet size of 1\u20135 m which is then transferred to the deposition ead with the help of a carrier gas N2. The mist or dense vapor is hen focused and driven towards the nozzle with the help of a secndary gas (also N2) to form a micro-jet. A UV apparatus (UJ35 V cure subsystem, Panasonic Corporation, Osaka, Japan) conected to the machine can instantaneously cure the (UV curable) olymer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure5-1.png",
        "caption": "Fig. 5. Axodes of pinion, gear and rack-cutter: (a) axodes; (b) tooth surfaces of two skew rack-cutters.",
        "texts": [
            " Longitudinal crowning of pinion tooth surface can be achieved by: (i) plunging of the tool or (ii) application of modified roll (see Sections 5 and 6). (vi) The effectiveness of the procedure of stress analysis is enhanced by automatization of development of The concept of generation of pinion and gear tooth surfaces is based on application of rack-cutters. The idea of the rack-cutters is the basis for design of such generating tools as disks and worms. The concept of axodes is applied wherein meshing and generation of helical gears are considered. Fig. 5(a) shows that gears 1 and 2 perform rotation about parallel axes with angular velocities x\u00f01\u00de and x\u00f02\u00de with the ratio x\u00f01\u00de=x\u00f02\u00de \u00bc m12 where m12 is the gear ratio. The axodes of the gears are two cylinders of radii rp1 and rp2 and the line of tangency of the cylinders designated as P1\u2013P2 is the instantaneous axis of rotation [7]. The axodes roll over each other without sliding. The rack-cutter and the gear being generated perform related motions: i(i) translational motion with velocity v \u00bc x\u00f01\u00de O1P \u00bc x\u00f02\u00de O2P ; \u00f01\u00de where P belongs to P1\u2013P2",
            " (ii) rotation with angular velocity x\u00f0i\u00de (i \u00bc 1; 2) about the axis of the gear. The axode of the rack-cutter in meshing with gear i is plane P that is tangent to gear axodes. In the existing design, one rack-cutter with straight-line profile is applied for the generation of the pinion and gear tooth surfaces. Then, the tooth surfaces contact each other along a line and edge contact in a misaligned gear drive is inevitable. Point contact in the proposed design (instead of line contact) is provided by application of two mis- matched rack-cutters as shown in Fig. 5(b), one of a straight-line profile for the generation of the gear and the other one of a parabolic profile for the generation of the pinion. Such method of generation provides a profile-crowned pinion. It will be shown below (see Sections 5 and 6) that the pinion in the proposed new design is double-crowned (longitudinal crowning is provided in addition to profile crowning). Double-crowning of the pinion (pro- posed in [9]) enables to avoid edge contact and provides a favorable function of transmission errors. The normal section a\u2013a of the rack-cutter is obtained by a plane that is perpendicular to plane P and which orientation is determined by angle b (Fig. 5(b)). The transverse section of the rack-cutter is determined as a section by a plane that has the orientation of b\u2013b (Fig. 5(b)). Fig. 6(a) shows the profiles of the normal sections of the mismatched rack-cutters. The profiles of the pinion and gear rack-cutters are shown in Fig. 6(b) and (c), respectively. Dimensions s1 and s2 are related by module m and parameter b as follows: s1 \u00fe s2 \u00bc pm; \u00f02\u00de b \u00bc s1 s2 : \u00f03\u00de Parameter b, that is chosen in the process of optimization, relates pinion and gear tooth thicknesses and it can be varied to modify the relative rigidity. In a conventional case of design, we choose b \u00bc 1. The rack-cutter for the gear generation is a conventional one and has a straight-line profile in the normal section. The rack-cutter for the pinion is provided with a parabolic profile. The profiles of the rack-cutters are in tangency at points Q and Q (Fig. 6(a)) that belong to the normal profiles of driving and coast sides of the teeth, respectively. The common normal to the profiles passes through point P that belongs to the instantaneous axis of rotation P1\u2013P2 (Fig. 5(a)). The parabolic profile of pinion rack-cutter is represented in parametric form in an auxiliary coordinate system Sa\u00f0xa; ya\u00de as follows (Fig. 7): xa \u00bc acu2c ; ya \u00bc uc; \u00f04\u00de where ac is the parabola coefficient. The origin of Sa coincides with Q. The surface of the rack-cutter is denoted by Rc and is derived as follows: ii(i) The mismatched profiles of pinion and gear rack-cutters are represented in Fig. 6(a). The pressure angles are ad for the driving profile and ac for the coast profile. The locations of points Q and Q are denoted by jQP j \u00bc ld and jQ P j \u00bc lc where ld and lc are defined as ld \u00bc pm 1\u00fe b sin ad cos ad cos ac sin\u00f0ad \u00fe ac\u00de ; \u00f05\u00de lc \u00bc pm 1\u00fe b sin ac cos ac cos ad sin\u00f0ad \u00fe ac\u00de : \u00f06\u00de i(ii) Coordinate systems Sa\u00f0xa; ya\u00de and Sb\u00f0xb; yb\u00de are located in the plane of the normal section of the rackcutter (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000632_j.jsamd.2021.03.006-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000632_j.jsamd.2021.03.006-Figure8-1.png",
        "caption": "Fig. 8. 3D folding structures of a USPS shipping box: (a) a sequence of folding the USPS shipping box, (b) 3D printed self-folding box with different materials assigned at different hinges (cef) the design details at the hinges, and (gej) the self-locking mechanism upon heating [97].",
        "texts": [
            " One of the more widely known, studied, and developed multi-materials used in 4DP is polyurethane-based SMPs and their carbon nanotube composites (SMP/CNT). When voltage deviations were examined and measured, results showed that SMP/CNT sample recovery times were considerably reduced as the stimulus temperature exceeds the Tg of the samples [33]. Because 3D printing is dependent on the use of various Tgmaterials, adaptive designs with self-folding capabilities were created that quickly react to temperature-based stimulus and, subsequently, change its shape in response to the stimulus as shown in Fig. 8 [97]. On the other hand, a higher degree of deformationwith an increase in strength of the composite can be achieved by using graphene nanocomposite-based SMP systems [98]. These kinds of materials are promising for the expansion of self-morphing aircraft parts [14]. In addition, graphene-based smart materials have been explored and used for many applications due to their excellent thermal and electrical properties [99]. An in-depth review of other multimaterial structures that display a shape-changing effect can be found in [100]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001172_j.triboint.2021.106856-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001172_j.triboint.2021.106856-Figure6-1.png",
        "caption": "Fig. 6. The simulated bolted joint model: (a) FEA model, (b) the dimensions of bolted joint.",
        "texts": [
            " Due to the experimental process is easy to be disturbed by the external factors, and the relevant physical parameters such as sliding area and critical displacement value are difficult to extract accurately, with the development of numerical analysis technology, the interface sliding process can be accurately simulated by the finite element method, and the required physical parameters can be easily extracted. Therefore, this section introduced a FEA method to identify the parameters. The simulation model is a single bolt lap structure which has been widely studied, as shown in Fig. 6(a), it needs to be indicated that the FEA model is consistent with the experimental specimens in terms of joint dimensions and materials, the dimension parameters of bolted joint are shown in Fig. 6(b), and the corresponding material parameters are shown in Table 1. The FEA model was constructed by the commercial software Ansys 15.0\u00ae, and the simulations were conducted on the author\u2019s desktop computer (Computer computing environment: Windows 10 operating system, 2.80 GHz Intel core i5-8400 CPU and 16.00 GB RAM). the research [32] shows that there is no appreciable slip behavior occurs between the threaded fasteners and lap board, and the thread structure has little effect on these calculation results, thus, the bolt-nut structure is modeled as a solid piece, as shown in in Fig",
            " Tribology International 156 (2021) 106856 Through the designed experiment of bolted joint, the validity of the proposed stiffness model and parameters extraction method has been verified. In this section, the simulation of the bolted joint under different pre-tightening forces and friction coefficients is carried out systematically, and the influence of these factors on the tangential stiffness model is analyzed. In addition, the proposed model is compared with the existing Iwan model, and the stiffness softening is further explained from the perspective of slip area evolution. For the FEA model shown in Fig. 6, the pre-tightening force Ni is set to 5000 N, 10000 N, 15000 N, 20000 N, 25000 N and 30000 N respectively, and the friction coefficient is set to 0.15. In order to ensure that the FEA model appears macro slip, the corresponding tangential force is set to 0.2Ni. After the FEA model is solved, we extract the surface pressure data from mating surface, and then determine the maximum radius of the non-zero pressure region. The simulated pressure distribution nephograms are shown in Fig. 11. From the nephograms, the pressure distribution shapes under the different pre-tightening force is basically the same, only the maximum pressure value is different, which is consistent with the experimental result in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.14-1.png",
        "caption": "Fig. 2.14: Point Trajectory",
        "texts": [
            "21) which immediately confirms equation 2.8 and its properties AIBABI = E ABI = A\u22121 IB = AT IB (2.22) Before going to a derivation of the velocities we make a detour by considering the velocity of a point trajectory. It represents for example the case of a robot hand following a prescribed trajectory ([208]). The velocity of a point P along that trajectory is defined as v = lim \u2206t\u21920 r(t + \u2206t)\u2212 r(t) \u2206t = d r d t (2.23) 2.2 Kinematics 21 The velocity vector v has the direction of the tangent line to the point trajectory of Figure 2.14. If we consider the above defined velocity in an inertial frame as shown in Figure 2.14, we come out with Ivabs = d Ir d t = I r\u0307, (2.24) which means the following: The absolute velocity of a moving point P is the derivation with respect to time of a vector r(t) = Ir(t) represented in a coordinate frame I, which is assumed to be an inertial system. Note that this vector or any other mechanical object can be represented in any coordinate frame without changing its physical properties, for example the magnitude of the vector is always the same. We only look at this vector from another point of view leading to different coordinates, but the vector itself or the object itself remains the same. Going for example from an inertial system to a body-fixed frame in Figure (2.7) or to a point fixed frame in form of the moving trihedral in Figure 2.14 (see [51]) we must transform the corresponding vectors from one frame to the other one applying the equation 2.21, which yields Ivabs = I r\u0307, (2.25) Bvabs = ABI I r\u0307. (2.26) With these transformations we write the equation 2.20 IrOP = IrOQ + IrQP = IrOQ + AIB \u00b7 BrQP . (2.27) The main reason for doing that lies in two facts, firstly that principally all time derivations in dynamics have to be performed in an inertial frame, which requires the appropriate transformations, and secondly that in many multibody applications it is much more convenient to define some points, some mass elements for example, in body-fixed coordinates than in inertial ones",
            " The first three terms are applied accelerations, the fourth term the Coriolis- and the last term the relative acceleration due to some relative motion within the moving system. Transforming the expression 2.41 into a body-fixed coordinate system we come out with the well-known formula BaP,abs = ABI IaQ,abs + B \u02d9\u0303\u03c9Br + B\u03c9\u0303B\u03c9\u0303Br + 2B\u03c9\u0303B r\u0307 + B r\u0308. (2.42) The explanations with regard to the individual terms of this expression are the same as above, all these terms are now written in a body-fixed frame. Coming back again to the point trajectory of figure 2.14 we represent the vector r(t) in cylinder coordinates and derive from equations 2.23 and 2.24 2.2 Kinematics 25 the corresponding accelerations. We get with (x, y, z)T = (r cos\u03d5, r sin\u03d5, z)T the following expressions IvP = I r\u0307P =  r\u0307 cos\u03d5\u2212 r\u03d5\u0307 sin\u03d5 r\u0307 sin\u03d5 + r\u03d5\u0307 cos\u03d5 z\u0307  , IaP = I r\u0308P =  r\u0308 cos\u03d5\u2212 2r\u0307\u03d5\u0307 sin\u03d5\u2212 r\u03d5\u0308 sin\u03d5\u2212 r\u03d5\u03072 cos\u03d5 r\u0308 sin\u03d5 + 2r\u0307\u03d5\u0307 cos\u03d5 + r\u03d5\u0308 cos\u03d5\u2212 r\u03d5\u03072 sin\u03d5 z\u0308  . (2.43) For the evaluation of these formulas in a body-fixed frame we have to multiply the last equation with the transformation matrix from I to B, which results in BaP = ABI \u00b7 I r\u0307P =  r\u0308 \u2212 r\u03d5\u03072 2r\u0307\u03d5\u0307 + r\u03d5\u0308 z\u0308  , with ABI =  cos\u03d5 sin\u03d5 0 \u2212 sin\u03d5 cos\u03d5 0 0 0 1  "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001767_t-aiee.1918.4765578-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001767_t-aiee.1918.4765578-Figure14-1.png",
        "caption": "FIG. 14 FIG. 15",
        "texts": [
            " Bipolar Salient-Pole Machines. In multipolar machines the flux leaving the field at a place where the air gap is reduced by the eccentricity, also returns into the field in a place where the air g'ap is reduced. The sum total of all the fluxes taken over one-half of the machine will therefore be greater than the sum total of all the fluxes taken over the other half of the machine. The same possibility exists in a two-pole machine, if the eccentric displacement is at right angles to the field axis. In Fig. 14 this case is shown. A rotor is assumed with salient poles built in the manner of the Siemens H armature, with one exciting ROSENBERG: MAGNETIC PULL 1447 coil, the pole face covering a greater arc than is usual in actual machines, but presenting a distinct neutral zone. The field axis A A1 has a distance x from the stator center. It is clear that in this machine, lines of force leaving the left corner of the upper pole, marked 1, will after passing through the armature, re-encer the field at the left corner of the lower pole, marked 4, while lines leaving the field at the right hand corner 2 of the upper pole will re-enter at the right hand corner 3 of the lower pole",
            " 7 x respectively. Within the sector 5. 0 6 shown in Fig. 15 the flux density will be greater, and in the corner parts 3 and 4 smaller than the average. In the opposite sector 7. 0 8 the flux density will be smaller, and in the corner parts 1 and 2 greater than the average. The sectors mentioned will contribute an unbalanced pull directed to the left, the corner parts a smaller component directed to the right. It is clear that the total unbalanced pull in this case is smaller than in the case of Fig. 14. A two-pole rotating field will therefore*, if its center is displaced with regard to the stator center, experience an unbalanced pull which changes twice during a revolution from a maximum to a minimum value. In practise, a salient-pole of a two-pole machine, covers about 120 deg. In the case corresponding to Fig, 14 (displacement parallel to the neutral diameter) the limits for 0 from 1 to A are 30 deg. and 90 deg. or ir/6 and 7r/2. An element of the surface covering an infinitely small angle d 0 has an area 12 DL - d 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure35-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure35-1.png",
        "caption": "Fig. 35. Contact and bending stresses in the middle point of the path of contact on conventional involute helical pinion with error Dc \u00bc 30: edge contact with high stresses occurs.",
        "texts": [
            " A torque of 500 Nm has been applied to the pinion. Fig. 32 shows the contact and bending stresses obtained at the mean contact point for the pinion. The variation of contact and bending stresses along the path of contact has been also studied. Figs. 33 and 34 illustrate the variation of contact and bending stresses for the pinion and the gear, respectively. The stress analysis has been performed as well for the example of a conventional helical involute drive with an error of the shaft angle of Dc \u00bc 30 (Fig. 35). We remind that the tooth surfaces of an aligned conventional helical gear drive are in line contact, but they are in point contact with error Dc. The results of computation show that error Dc causes an edge contact and an area of severe contact stresses. Fig. 36 shows the results of finite element analysis for the pinion of a modified involute helical gear drive wherein an error Dc \u00bc 30 occurs. As shown in Fig. 36, a helical gear drive with modified geometry is free indeed of edge contact and areas of severe contact stresses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure9-1.png",
        "caption": "Fig. 9 Determination of the length of contact lines",
        "texts": [
            " And, the second-order approximation may not reflect the actual surface nature in such a large area. Based on these considerations, we developed a numerical approach to the determination of the instant contact lines of the contact pattern. The new approach is described in the following steps: Step 1. A local coordinate system is introduced by using the surface unit tangent and unit normal that have been determined after solving Eq. 22 or 23 . Let unit vectors u1= t1f, u2=n1f t1f, and u3=n2f represent the axes of the local coordinate system with origin at the current contact point P shown in Fig. 9 a . Vectors u1 and u2 lie in the tangent plane T. Fig. 10 TCA output of design A Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use i s s l s t c e i r s 7 c d i d o 8 c f F h t w t f i p w p g d a J Downloaded Fr Step 2. A cylindrical surface with radius r0 and its axis coincidng with the common normal u3 is introduced to cut the tooth urfaces 1 and 2. Iteration is conducted to determine the cross ection , where the minimum gap hmin between the two surfaces ocates Fig. 9 b and 9 c . Step 3. In the minimum-gap cross section , given a surface eparation , another iteration process is carried out to determine he contact length c1 and c2 normally, c1 c2 . The total length of ontact line is c=c1+c2, shown in Fig. 9 d . The advantage of this algorithm is that only the tooth surface quations are needed and the calculation of the surface curvatures s avoided. Meanwhile, the determined length of the contact lines epresents the actual surface condition because the second-order urface approximation is not used. Two Numerical Examples The developed algorithms are implemented with computer odes integrated into Gleason CAGE\u21224Windows Software. Two esign examples, face hobbing with a Formate gear and face millng with a generated gear, are illustrated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000295_tcst.2019.2963017-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000295_tcst.2019.2963017-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the Sawyer manipulator.",
        "texts": [
            " ILLUSTRATIVE SIMULATION RESULT In this section, we conduct multiple simulation experiments on Sawyer manipulator employing the data-driven CMG scheme (13) aided with DNN (14) to carry out the CMG task. The following simulation experiments all have the same parameter settings as follows: initial angular state \u03c60 = [0, \u22120.5, \u22120.5, \u22121.5, 2, \u22120.5, 0] rad; \u03be = \u03b4 = 500; \u03b3 = 1; n0 = 0.005 rad/s; initial state of J\u0303 = 0 \u2208 R b\u00d7a; the given task is tracking a tricuspid valve path. With seven degrees of freedom, the Sawyer manipulator, which is employed in the simulations, can drive seven joints to approach any position in the workspace, as shown in Fig. 2. The detailed structure parameters are presented in Table I. It is worth noting that the structure of the manipulator is not involved in the proposed method. Primarily, in the absence of additive noises, i.e., n = 0, we carry out computer simulations on Sawyer manipulator executing the data-driven CMG scheme (13) with the aid of DNN (14) with = 106. As analyzed in Section III, the generated angle in Fig. 3 does not change and stays at the original state, which indicates the failure of the given task without manipulator motions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.28-1.png",
        "caption": "Figure 7.28 is a conceptual representation of qu in which the compressive force F and extensional force R are applied to the upper surface. The values of qu at the left and right edges are, respectively, denoted q0 and q1.",
        "texts": [
            " This phenomenon reduces aspects of tire performance, such as the maneuverability and wear of a tire. Akasaka et al. [18] thus studied the lift-off of a block due to a shear force making two assumptions. Q/F=0.5 0.33 2 \uff10 1.67 1 1 0\u22121 q/ \u03c3 0 \u03be Fig. 7.26 Contact pressure distribution of a block with shape factor S = 1 for a loading ratio Q/F = 0.5. Reproduced from Ref. [18] with the permission of Tire Sci. Technol. 408 7 Mechanics of the Tread Pattern Equation (7.110) gives F \u00bc q0 2 a x\u00f0 \u00de q1 2 x R \u00bc q0 2 x2 a x R F \u00bc x2 a a 2x\u00f0 \u00de : \u00f07:111\u00de The moment equilibrium at point O\u2032 in Fig. 7.28 yields F y \u00bc 2=3 F a x\u00f0 \u00de\u00feRaf g; \u00f07:112\u00de where y is the length from point O\u2032 to the point at which the equivalent force F is applied. The substitution of the third equation of Eq. (7.111) into Eq. (7.112) yields y \u00bc 2 3 a x\u00fe x2 a 2x : \u00f07:113\u00de F q1 O\u2019 F+R R y a-x x q0 7.3 Properties of the Block in Contact with the Road 409 Suppose that the force F is applied at position y measured from the right edge of the block. y is given by y \u00bc y\u00fe x \u00bc 2 3 a a 3 2 x a 2x : \u00f07:114\u00de From Eq. (7.114), the length d in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000155_j.jmatprotec.2020.116701-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000155_j.jmatprotec.2020.116701-Figure2-1.png",
        "caption": "Fig. 2 (a) Schematic diagram of laser scanning strategy; (b) schematic diagram of dimensions and combination types: (\u2170) horizontal combination, (\u2171) vertical combination; (c) density variation three-dimensional diagram of CuSn10 specimens; (d) 316L/CuSn10 multi-material parts formed by SLM.",
        "texts": [
            " The key step in this experiment is to select the nine parameter combinations centered on the optimal parameters of CuSn10 to form the CuSn10 parts respectively (Parameters of all the nine groups were the same when fabricating 316L part). Finally, the further optimized parameter group of CuSn10 were selected to fabricate the test specimens taking the multi-material interface bonding strength into consideration, so as to ensure the good interface bonding without losing the overall mechanical properties of the composite. Both SLM single alloys and 316L/CuSn10 specimens were processed using the scanning strategy shown in Fig. 2a with a 67\u00b0 rotation between the layers towards building direction. Fig. 2b shows two types of tensile specimen with the same size. It combines the form of horizontal bonding (Type (\u2170)) with vertical bonding (Type (\u2171)), Jo ur na l P re -p ro of which was used to quantitatively obtain the interfacial bonding strength of the 316L/CuSn10 specimens. Table 4 lists the optimal parameter groups with the highest density when forming 316L and CuSn10 parts, respectively. Fig. 2c shows a threedimensional histogram of CuSn10 alloy density variation corresponding to laser powder and scanning speed. Fig. 2d shows the 316L/CuSn10 specimens formed by SLM with a well-bonded interface on a stainless steel substrate. Jo ur 10 / 36 Scanning space (mm) 0.14 0.12 Layer thickness (mm) 0.05 0.05 Relative density (%) 99.7 99.1 The microscopic morphology of the raw material powders was observed by a field emission scanning electron microscope (SEM, JSM-7600F, JEOL, Japan). The interface of composite specimen was ground with silicon carbide sandpaper. Finally, a diamond suspension with a particle size of 2.5 \u03bcm (Lab Testing Technology Co",
            " For type \u2161, the interfacial junction regions of Sample 1 and Sample 2 were severely cracked and there were over melting on the upper surfaces. There were different cracking degrees at the interfacial junction region of Sample 4, Sample 7 and Sample 8 in Type \u2162, but the upper surfaces were well fused. As for the sample 5 and sample 6 in type \u2160, the interfacial junction regions of the samples were slightly cracked, and moreover, a slight over-burning occurred on the upper surfaces of both samples. Density of CuSn10 specimens at the laser power of 400 W and scanning speed of 500 mm/s was 99.1% (Fig.2c), and the 316L/CuSn10 multimaterial composite had a strong interfacial bonding under this condition. Fig. 3 Process optimization of the 316L/CuSn10 specimens. A preliminary understanding of the fusion zone range, microscopic defects and Jo ur na l P re -p ro of 13 / 36 main element distribution of the SLM 316L/CuSn10 composite interfacial regions was obtained by means of optical microscopy and EDS spectroscopy. Fig.5a demonstrates the entire fusion zone with a range of approximately 600 \u03bcm, which can be divided into Region \u2160, Region \u2161 and Region \u2162 depending on the dominant matrix elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure3.10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure3.10-1.png",
        "caption": "Fig. 3.10 Composite structure of the bias belt. Reproduced from Ref. [5] with the permission of Tire Sci. Technol.",
        "texts": [
            "5% owing to the incompressibility of rubber. The width of a bias laminate becomes narrower under the extensional external force, if the orientation angle is relatively small as used in tires. The interlaminar rubber layer constrained above and below by two laminae will be in compression in the ydirection. Because the net internal force of the composite is zero, the compression of the interlaminar rubber layer generates tension in the two laminae. The composite structure of the bias belt is shown in Fig. 3.10. Hook\u2019s law for plane stress in isotropic materials is expressed by ry \u00bc Em 1 m2m ey\u00fe mmex ; \u00f03:34\u00de where Em and mm are, respectively, Young\u2019s modulus and Poisson\u2019s ratio of rubber. The equilibrium equation of internal lateral forces in two belt layers yields 2h0 ry;belt \u00fe h ry;rubber layer \u00bc 0: \u00f03:35\u00de Solving Eq. (3.35), the lateral stress of belt is given by ry;belt \u00bc 1 2 h h0 ry;rubber layer: \u00f03:36\u00de Note that the strains ex and ey of belts and the rubber layer of a tire must be the same to form a deformation-compatible laminate",
            "53) is explicitly rewritten as ex ey cxy 8< : 9= ; \u00bc 1 ET sin2 a 1\u00fe 3 cos2 a\u00f0 \u00de 3 sin2 a cos2 a sin 2a 2 cos2 a sin2 a cos2 a 1\u00fe 3 sin2 a sin 2a 2 sin2 a cos2 a symmetric 1\u00fe 3 cos2 2a 2 4 3 5 rx ry sxy 8< : 9= ;; \u00f03:54\u00de where ET = 4/3 Em/Vm, Vm is the volume fraction of rubber in the belt layer, Em is Young\u2019s modulus of rubber, and a is the orientation angle of belt cords. Note that the relation of Poisson\u2019s ratio of rubber, mm = 1/2, is used in deriving Eq. (3.54). Vm is expressed by Vm \u00bc dh0 p h0 2 2 dh0 ; \u00f03:55\u00de where d is the cord pace in Fig. 3.10, i.e., the distance between cords in the direction perpendicular to the direction of the cords. Using the second equation of Eq. (1.22), the relation eL \u00bc T\u00bd ex is obtained. The inextensibility of the belt cord is expressed by the strain in the cord direction being zero (eL = 0). The inextensibility of the belt cord is expressed by ex cos2 a\u00fe ey sin2 a\u00fe cxy sin a cos a \u00bc 0: \u00f03:56\u00de 116 3 Modified Lamination Theory In conclusion, this problem can be formulated using the six equations of Eqs. (3.51), (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.2-1.png",
        "caption": "Fig. 4.2 Coordinate system and dimensions of a discrete cord\u2013rubber system",
        "texts": [
            " (iv) The extensional rigidity of the cord Ef is much larger than that of the rubber Em\u00f0Ef Em\u00de. (v) The adhesive rubber layer is modeled by a plate where shear deformation is allowed. The interlaminar shear strain of the adhesive rubber layer is uniformly distributed in the thickness direction. (vi) The thickness of a cord is h0, the thickness of the adhesive rubber layer is 2h, the belt width is 2b, the orientation angle is a and the tensile force T is applied to a bias belt. The coordinate system for a composite is defined in Fig. 4.2, where s and t, respectively, indicate the cord direction and the transverse direction at the cord center, and \u03b7 and f are the displacements in oblique coordinates. The oblique coordinates are defined by s and t. uf, vf and wf are the displacements at the cord center in Cartesian coordinates, tf is the cord width, d is the cord distance in the t-direction, and a is the cord distance in the x-direction. When the tensile force is applied to a two-ply bias laminate in the x-direction, periodic displacement Dv with a period a is generated at the cord surface in the y-direction owing to the bending of the cord, as shown in Fig",
            "21) yields Dwx \u00bc Du Du 2h \u00bc e0 X1 n\u00bc1 Cn sin\u00f02pnn=a\u00de sin\u00f02pnn=a\u00de 2h \u00bc e0 h X1 n\u00bc1 Cn cos 2pnx a sin 2pny b0 Dwy \u00bc Dv Dv 2h \u00bc f0\u00f0s\u00de X1 n\u00bc1 Cn sin\u00f02pnn=a\u00de\u00fe sin\u00f02pnn=a\u00de 2h \u00bc f0\u00f0s\u00de h X1 n\u00bc1 Cn sin 2pnx a cos 2pny b0 : \u00f04:22\u00de 196 4 Discrete Lamination Theory Finally, the interlaminar shear strains are expressed by wx \u00bc u u 2h \u00bc w\u00f0y\u00de\u00fe e0 h P1 n\u00bc1 Cn cos 2pnxa sin 2pny b0 wy \u00bc v v 2h \u00bc f0\u00f0s\u00de h P1 n\u00bc1 Cn sin 2pnx a cos 2pnyb0 : \u00f04:23\u00de (3) Displacements at the cord center The displacements at the cord center are denoted \u03b7(s) and f(s) in the oblique coordinate system shown in Fig. 4.2. Figure 4.4 shows that the periodic term disappears at n = 0 or n \u00bc 0. The periodic terms are thus not included in displacements at the cord center \u03b7(s) and f(s). Because uf and vf correspond to u10 and v10 of Eq. (4.18), using the relation x = s cosa and y = s sina, \u03b7(s) and f(s) can be expressed as g\u00f0s\u00de \u00bc u\u00f0s\u00de cos a\u00fe v\u00f0s\u00de sin a \u00bc u10 cos a\u00fe v10 sin a \u00bc e0 cos2 a XH sin 2a s\u00fe h / sin a\u00few cos a\u00f0 \u00de f\u00f0s\u00de \u00bc u\u00f0s\u00de sin a\u00fe v\u00f0s\u00de cos a \u00bc u10 sin a\u00fe v10 cos a \u00bc e0 sin 2a=2\u00feXH cos 2a\u00f0 \u00des\u00fe h / cos a w sin a\u00f0 \u00de: \u00f04:24\u00de (1) Strain energy of the cord The strain energy of the cord Uf consists of energies related to extensional deformation, bending and torsional deformation: Uf \u00bc 1 2 Z l 0 Ef g 2 ;s \u00feDf f2;ss \u00few2 ;ss \u00feCf h 2 n o ds; \u00f04:25\u00de where Ef is the tensile rigidity of the cord, Df is the flexural rigidity of the cord, Cf is the torsional rigidity of the cord and h is the twist angle",
            " (4) Total strain energy of a two-ply bias laminate The total strain energy of a two-ply bias laminate U is defined by the volume of the reference area S and the half thickness of the two plies h + h0: U \u00bc Uf \u00feUr \u00feU0: \u00f04:39\u00de The total strain energy of the two-ply bias laminate U is expressed by U \u00bc Ema 2 e20K0 \u00fex2K1 \u00fe 2e0xK2 \u00fe 2e0/\u00f0b\u00deK3 \u00fe 2e0w\u00f0b\u00deK4 \u00fe 2x/\u00f0b\u00deK5 \u00fe 2xw\u00f0b\u00deK6 \u00feK7 Rb 0 w2dy\u00feK8 Rb 0 /02dy\u00feK9 Rb 0 w02dy\u00fe 2K10 Rb 0 /0w0dy \u00feK11 Rb 0 /00 cos a w00 sin a\u00f0 \u00de2dy 8>>>>< >>>>: 9>>>>= >>>>; ; \u00f04:40\u00de where XH \u00bc x Em \u00bc Emhb=\u00f01 m2m\u00de: \u00f04:41\u00de The constants Ki (i = 0,\u2026,11) can be calculated if the belt structure and material properties are given. These equations for Ki (i = 0,\u2026,11) can be easily implemented in Mathematica or MATLAB.6 6Appendix 1. 202 4 Discrete Lamination Theory Suppose that the tensile external force T is applied to a two-ply bias laminate. The volume V with half-width b, half thickness of the laminate h + h0 in Fig. 4.1 and length a in Fig. 4.2 is expressed by V \u00bc Tae0=4: \u00f04:42\u00de The stationary condition of the potential P for the entire system is given by dP \u00bc d U V\u00f0 \u00de \u00bc Ema de0 e0K0 \u00fexK2 \u00fe/\u00f0b\u00deK3 \u00few\u00f0b\u00deK4 T 4Em n o \u00fe dx xK1 \u00fe e0K2/\u00f0b\u00deK5 \u00few\u00f0b\u00deK6f g \u00fe d/\u00f0b\u00de e0K3 \u00fexK5\u00f0 \u00de\u00fe dw\u00f0b\u00de e0K4\u00fexK6\u00f0 \u00de \u00feK7 Rb 0 wdwdy\u00feK8 Rb 0 /0d/0dy\u00feK9 Rb 0 w0dw0dy\u00feK10 Rb 0 /0dw0dy \u00feK10 Rb 0 w0d/0dy\u00feK11 Rb 0 /00 cos a w00 sin a\u00f0 \u00de d/00 cos a dw00 sin a\u00f0 \u00dedy 2 6666666666664 3 7777777777775 \u00bc 0: \u00f04:43\u00de Applying integration by parts to Eq. (4.43) and considering that /(y) and w(y) are odd functions with respect to y, we obtain de0 e0K0 \u00fexK2 \u00fe/\u00f0b\u00deK3 \u00few\u00f0b\u00deK4 T 4Cm \u00fe dx xK1\u00fe e0K2 \u00fe/\u00f0b\u00deK5 \u00few\u00f0b\u00deK6f g \u00fe d/\u00f0b\u00de e0K3 \u00fexK5\u00fe/0\u00f0b\u00deK8 \u00few0\u00f0b\u00deK10 /000\u00f0b\u00de cos a w000\u00f0b\u00de sin af g cos aK11\u00bd \u00fe dw\u00f0b\u00de e0K4 \u00fexK6\u00few0\u00f0b\u00deK9 \u00fe/0\u00f0b\u00deK10 \u00fe /000\u00f0b\u00de cos a w000\u00f0b\u00de sin af g sin aK11\u00bd \u00fe d/0\u00f0b\u00de /00\u00f0b\u00de cos a w00\u00f0b\u00de sin af g cos aK11\u00bd dw0\u00f0b\u00de /00\u00f0b\u00de cos a w00\u00f0b\u00de sin af g sin aK11\u00bd : \u00fe Zb 0 K11 cos a /\u00f0IV\u00de cos a w\u00f0IV\u00de sin a K8/ 00 K10w 00 n o d/dy \u00fe Zb 0 K11 sin a /\u00f0IV\u00de cos a w\u00f0IV\u00de sin a K9w 00 K10/ 00 \u00feK7w n o dwdy \u00bc 0 \u00f04:44\u00de Euler equations are derived from Eq",
            "1 DLT of a Two-Ply Bias Belt with Out-of-Plane \u2026 217 Referring to Eq. (4.10), the displacements in the middle plane u0 and v0 are given by u0 \u00bc jxy\u00fe jy P1 n\u00bc1 Cn sin 2pnx a sin 2pny b0 v0 \u00bc 1 2 jx 2 \u00fe h/\u00f0y\u00de f0\u00f0s\u00de P1 n\u00bc1 Cn cos 2pnxa sin 2pny b0 : \u00f04:100\u00de Furthermore, referring to Eq. (4.23), the interlaminar shear strains are expressed by wx \u00bc w\u00f0y\u00de jy h P1 n\u00bc1 Cn cos 2pnxa sin 2pny b0 wy \u00bc f0\u00f0s\u00de h P1 n\u00bc1 Cn sin 2pnx a cos 2pnyb0 : \u00f04:101\u00de Taking the limit f(n) ! 0 in Eq. (4.99), the displacements of the cord \u03b7(s) and f(s) in the oblique coordinates of Fig. 4.2 are given by g\u00f0s\u00de \u00bc u\u00f0s\u00de cos a\u00fe v\u00f0s\u00de sin a \u00bc 1 2 js2 sin2 a cos2 a\u00fe h / sin a\u00few cos a\u00f0 \u00de f\u00f0s\u00de \u00bc u\u00f0s\u00de sin a\u00fe v\u00f0s\u00de cos a \u00bc 1 2 js2 cos a 1\u00fe sin2 a \u00fe h / cos a w sin a\u00f0 \u00de: \u00f04:102\u00de Considering that the displacement of a laminate in the thickness direction is constrained, the strain energy of the cord with extension and bending deformation, Uf, can be expressed by Uf \u00bc 1 2 Z l 0 Ef g 2 ;s \u00feDf f 2 ;ss n o ds; \u00f04:103\u00de 218 4 Discrete Lamination Theory where, using Eq. (4.102), the derivatives of \u03b7(s) and f(s) are given as g;s \u00bc js sin2 a cos2 a\u00fe h /0 sin a\u00few0 cos a\u00f0 \u00de sin a f;ss \u00bc j cos a 1\u00fe sin2 a \u00fe h /00 cos a w00 sin a\u00f0 \u00de sin2 a; \u00f04:104\u00de with the prime denoting the partial derivative with respect to y",
            "2 DLT of a Two-Ply Bias Belt Without Out-of-Plane \u2026 223 U \u00bc Ema 2 j2K0 2j K1 w0\u00f0b\u00de sin a /0\u00f0b\u00de cos af g\u00bd \u00feK2 Rb 0 yw0dy\u00feK0 2 Rb 0 y/0dy \u00feK3 Rb 0 /02dy \u00feK4 Rb 0 w2dy\u00feK5 Rb 0 w02dy\u00fe 2K6 Rb 0 /0w0dy \u00feK7 Rb 0 /00 cos a w00 sin a\u00f0 \u00de2dy 8>>>>>< >>>>>: 9>>>>>= >>>>>; ; \u00f04:117\u00de where Em is defined by the second equation of Eq. (4.41). The constants Ki (i = 0, \u2026,7) can be calculated using the given belt structure and material properties. These equations forKi (i = 0,\u2026,7) can be easily obtained usingMathematica orMATLAB.8 4.2.3 Stationary Condition and Natural Boundary Conditions (1) Stationary condition When the bending moment M0 is applied to a two-ply bias laminate, the volume Fig. 4.2 is expressed by V \u00bc M0ja=4; \u00f04:118\u00de where j is the curvature of bending deformation. Using Eqs. (4.117) and (4.118), the stationary condition of the potential P in the total system is obtained as dP \u00bc d U V\u00f0 \u00de \u00bc Ema dj jK0 K1 w0\u00f0b\u00de sin a\u00fe/0\u00f0b\u00de cos af gf \u00feK2 Rb 0 y/0dy\u00feK0 2 Rb 0 yw0dy M0=\u00f04Em\u00de \u00fe d/\u00f0b\u00de jbK2 \u00fe/0\u00f0b\u00deK3 \u00few0\u00f0b\u00deK6f \u00feK7 cos a w000\u00f0b\u00de sin a /000\u00f0b\u00de cos af gg \u00fe dw\u00f0b\u00de jbK0 2 \u00few0\u00f0b\u00deK5 \u00fe/0\u00f0b\u00deK6 K7 sin a w000\u00f0b\u00de sin a /000\u00f0b\u00de cos af gg \u00fe d/0\u00f0b\u00de jK1 cos a\u00feK7 cos a w00\u00f0b\u00de sin a\u00fe/00\u00f0b\u00de cos af gf g \u00fe dw0\u00f0b\u00de jK1 sin a K7 sin a w00\u00f0b\u00de sin a\u00fe/00\u00f0b\u00de cos af gf g Rb 0 jK2\u00feK3/ 00 \u00feK6w 00 \u00feK7 cos a w0000 sin a /0000 cos a\u00f0 \u00def gd/dy Rb 0 jK0 2 \u00feK5w 00 \u00feK6/ 00 K7 sin a w0000 sin a /0000 cos a\u00f0 \u00de dwdy 2 666666666666666666666666664 3 777777777777777777777777775 \u00bc 0; \u00f04:119\u00de 8Appendix 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000629_j.conengprac.2021.104763-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000629_j.conengprac.2021.104763-Figure6-1.png",
        "caption": "Fig. 6. A view of the quadcopter used in the flight experiments.",
        "texts": [
            " Similar results were obtained for stimating the function g. It is very important to note that in this imulation, due to the change in total mass of the quadcopter, function ang g were time-variant. Nevertheless, the approximation was well one. The main goal of the presented method in this paper is to control he quadcopter, not to estimate the functions f and g. Therefore, the ounded estimation error is considered. . Experimental results The proposed AFTSMC was evaluated in-flight experiments using a mall quadrotor (Fig. 6) built at the Biocontrol Laboratory of Shahid ajaee University. The flight control was implemented on a HiFive1 ev B board. An MPU6050 IMU, an HMC5883L compass sensor and a BLOX6 GPS were also applied. To reduce the effect of rotor vibration on the sensors inside the IMU, it was mounted on a passive mechanical suspension. Euler angles are calculated by solving the integral of the inverse of (8). Rate gyroscopes of the IMU measure the vector \ud835\udefa. A second-order low-pass filter was used to eliminate the gyroscope noise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.34-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.34-1.png",
        "caption": "Fig. 6.34: Sprocket Toothing",
        "texts": [
            " In this case we only have to consider the forces due to the oil displacements, produced by the translational motion of the pin towards the bushing. In combination with the material damping of the chain, which can be regarded as constant, we get the damping characteristic shown in Figure 6.33 ([217]). The elasticity of a chain link is concentrated in the joint and behaves like a radial spring with the constant spring coefficient cL. Hence, if pin and bushing are in contact, additional spring forces act on the links. Sprockets A sprocket, shown in Figure 6.34, is modeled as a rigid body. With the selection matrix QS for the sprocket \u2013 like QL in equation (6.40) \u2013 we can regard optional degrees of freedom zS = QS qS , zS = ( rS \u03d5S ) . (6.41) For a detailed description of the contact configuration between a link and a sprocket, we have to consider the exact tooth contour. Figure 6.34 illustrates the toothing of a sprocket due to DIN 8196 with the contact areas tooth 6.4 Bush and Roller Chains 371 profile and seating curve. These contact contours are defined by circles. Using a toothing fixed coordinate system the centers of these circles can easily be determined. Regarding a chain drive in a combustion engine, we have to consider various external excitations from the crankshaft (\u03d5Ext) and from the camshafts (MExt). One Sided and Double Sided Guides One sided and double sided guides are applied to reduce the vibrations of the chain strands",
            "82) For the evaluation of the tensioner\u2019s forces we need to know its relative displacements, which can be determined in a similar way as in the case of the joint bearings. The direction of the active force is nT . We get \u03b3 = nTTAIRJT0qR, \u03b3\u0307 = nTTAIR(JT0q\u0307R + \u2126J\u2217 T0qR). (6.83) The contribution to the equations of motion results from that in the form hR = . . . + JTT0ARInT \u03b6, (6.84) where \u03b6 must be calculated from the detailed tensioner analysis [69], [111]. In a preceding chapter we have already discussed the model properties of the sprocket. We shall consider here in a bit more detail the kinematics of the toothing contour following Figure 6.40 (see also Figure 6.34). Starting with the reference point H of the shaft at the sprocket position we calculate the position of a contour point K by considering the eccentricity \u03c1, if any, the vector rV Z to the origin of the toothing system and the vector rK(s) to the contour point. This writes in disc-fixed coordinates rHK = + rV Z + rK(s) (6.85) The absolute position and the kinematics follow from these equations in the form (O = center of inertial coordinate system) IrOK =AIR[rOH +ARKrHK ], vK =AIR[JTK q\u0307R + j\u0302TK ], v\u0307KG = AIR[JTK q\u0308R + jTK ], with JTK =JT \u2212ARK r\u0303HKJR j\u0302TK =j\u0302T \u2212ARK r\u0303HK j\u0302R jTK =jT \u2212ARK r\u0303HKjR +ARK \u03c9\u0303K0\u03c9\u0303K0rHK (6",
            " J\u2217 G = ( E3\u00d73,\u2212r\u0303K ) , J\u2217 L = ( E3\u00d73,\u2212Rrollerplaten\u0303 ) wG\u03bb = QT GJ \u2217T G ( n\u2212 vrel |vrel| \u00b5t ) \u03bb, wL\u03bb =\u2212QT LJ \u2217T L ( n\u2212 vrel |vrel| \u00b5t ) \u03bb. (6.102) Contact between a Sprocket and a Link Regarding the contact between a sprocket and a link we achieve very simplified relations for the normal velocity and acceleration. Due to the fact that the toothing contour is composed of circles, it is sufficient to consider the center of these contour circles. For this purpose we use the vector d from the reference point HL to the contour center MK (Figure 6.42). Applying the radius RK of the contour in the contact areas, according to Figure 6.34 with RK,toothprofile = RTP and RK,seatingcurve = \u2212RSC , the distance vector rD results in rD =d\u2212 nRK , r\u0307D =d\u0307+ RKtb T\u2126S , r\u0308D =d\u0308+ RKn(bT\u2126S)2 + RKtb T \u2126\u0307S (6.103) After some transformations the equations (6.98), (6.99) and (6.100) can be written as gn = nTd\u2212RK , g\u0307n = nT d\u0307, g\u0308n = nT d\u0308+ ( tT d\u0307 )2 nTd . (6.104) Contact Configuration For establishing the complementarities we have to evaluate forces and accelerations, which characterize the relevant contact configuration. In order to combine the kinematic constraint (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000193_j.msea.2018.12.078-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000193_j.msea.2018.12.078-Figure2-1.png",
        "caption": "FIGURE 2",
        "texts": [
            " 1c, (Case 4) orthogonal scan for five parts (compositions of each part are same with Case 3), which is firstly scanned with vector along x and secondly along y starting from the same location among layers, Fig. 1d, and (Case 5) island scans in five parts (compositions of each part are same with Case 3), Fig. - 7 - 1e. The island size of 5 x 5 mm 2 was deposited by the orthogonal manner without shifts or rotations between layers to eliminate any possible geometric complexity on residual stresses. Three samples were fabricated in each case using identical processing conditions and provided for residual stress measurements using ND, CM, and DHD (ICHD), respectively, Fig. 2. Microstructural characterization was performed on cross-sections of each specimen. The specimens for optical microscopy (OM) were prepared by cutting with electrical discharging machining (EDM) and electrolytically etching them with the etchant of 10% perchloric acid and 90% acetic acid. A field-emission scanning electron microscope (JSM-7100F) equipped with electron backscatter diffraction (EBSD) system was utilized to analyze grain structure on the cross-section (y-z plane) with the step sizes of 0",
            " Thus, higher spatial resolution were utilized with the gauge volume of 2(x) \u00d7 2(y) \u00d7 2(z) mm 3 (mode II). The Si (220) monochromators at take-off angles 45 o produced neutrons with the wavelength of 1.46 \u00c5 for the diffraction planes (311) in fcc and (211) in bcc at scattering angles of 84.4 o and 76.2 o , respectively. A total of 12 points were measured through the thickness of the DED FGM specimens starting from 2 to 18.5 mm from the top surface with 1.5 mm steps along the centerline as shown in Fig. 2. Mostly, the measurement period was about 20 minutes for each strain component achieving a strain uncertainty of about \u00b1100 . Comb-like \u201cstress free\u201d reference samples were extracted along the centerline of the specimens by EDM and cut along the z direction. Thus, the comb consists of 5 mm long (x), 10 mm wide (y), and 5 mm deep (z) coupons. The stress-free lattice spacing (do) was carefully measured at the same locations of the bulk specimen with the scattering volume of 2(x) \u00d7 2(y) \u00d7 2(z) mm 3 ",
            " The residual stresses are computed by applying the measured displacements inversely to an assumed flat surface contour using an elastic finite element model. One stress component normal to the cut surface can be reconstructed from a cut. The main experimental procedures include: (1) specimen cutting, (2) highly accurate surface displacement measurements, and (3) data reduction and analysis. More detailed description could be found in ref. 33. Each DED FGM specimen was cut in half at the mid-length position as shown Fig. 2. This was done by using EDM with a 100 \u03bcm diameter brass wire. To minimize cutting induced stresses, the specimen was submerged into the temperature-controlled de-ionized - 12 - water and performed the \u2018\u2018skim cut\u2019\u2019 with the cutting speed of 0.15 mm/min. After cutting, the normal direction (x) displacements on the cut surfaces were measured using a scanning confocal laser probe with an accuracy of \u00b10.02 \u03bcm. The maximum peak-to-valley range of the contour was about \u00b130 \u03bcm and fitted to a smooth analytical surface for stress calculation",
            " The main difference of the iDHD is that the core (diameter of 5 mm) is extracted in incremental machining steps and the diameter of the reference hole (diameter of 1.5 mm) is measured between each increment. The iDHD technique was used for a longitudinal (\u03c3x) and transverse stress (\u03c3y) measurements with 2 mm depth step (total of 12 points) though the thickness of the DED FGM specimens in Cases 1, 3, and 5. Besides, a DHD experiment was performed through the side surface at 5 mm from the top surface at Case 4 in Fig. 2 in order to confirm the a longitudinal (\u03c3x) and normal stress (\u03c3z) components between DHD and ND. The elastic moduli (E) and Poisson\u2019s ratio (\u03bd) are same with the contour method. Incremental center-hole drilling (ICHD) method is a semi-invasive, mechanical strain relief technique to determine stresses near surface [36]. The ICHD procedure involves - 13 - surface preparation, gauge bonding, and circuit connections. The surface firstly degreases and neutralized to remove any oxides and oils. The strain gauge rosettes of type EA-06-031RE120 adhered with gauge elements aligned to the x and y directions",
            " The extracted by CM stress profiles show that the difference of stress values (\u0394\u03c3) in Cases 1, 2, and 3 clearly decreases when the DED scanning strategies are adopted by the orthogonal (Case 4) or island (Case 5) scans as shown in Fig. 7d-e, respectively. For example, the maximum-to- - 16 - minimum difference of the stress (\u0394\u03c3x) decreases from 770 MPa in Case 3 (bidirectional scan) to 450 MPa in Case 4 as marked in Fig. 7c-d Finally, Fig. 8 shows the residual stress profiles obtained from the DHD measurements along the centerline (Fig. 2) through sample thickness in Cases 1, 3, and 5. It shows fine (0.2 mm) through-depth resolution. Owing to no severe plastic relaxation of the stressed region in the whole thickness of the specimen, the iDHD results were similar to DHD results. Fig. 8 shows that the range of stress values (\u0394\u03c3) is relatively decreased in Case 5 when compared to Cases 1 and 3 in both x and y DHD profiles. Besides, the DHD results elucidate the maximum stress location near top surface and the minimum at 8 mm depth in the mixture parts of Cases 3 and 5 in Fig",
            " Pasang, Reducing lack of fusion during selective laser melting of CoCrMo alloy: Effect of laser power on geometrical features of tracks, Mater. Des. 112 (2016) 357-366. Fig. 1. Schematic of the sample dimension and scanning strategies in additive manufactured functionally graded material (FGM) structures: (a) Case 1, bidirectional scan in two parts, (b) Case 2, bidirectional scan in three parts, (c) Case 3, bidirectional scan in five parts, (d) Case 4, orthogonal scan in five parts, and (e) Case 5, island scan in five parts. Fig. 2. Measurement locations. Contour in the cut surface, macroscopic stress-free coupon, and the reference core were shown for the contour method (CM), neutron diffraction (ND), and deep hole drilling (DHD), respectively. Fig. 3. Cross-sectional macrostructure of the direct energy deposition (DED) functionally graded material (FGM) specimens: (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4, and (e) Case 5. Fig. 4. Optical macrographs taken at the cross-section (top), electron backscatter diffraction (EBSD) images at the interfaces marked as squares in the macrographs (middle), and - 28 - microhardness profiles along the centerline (dot line) and hardness mapping at the crosssection (dot square) in each case (bottom)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure4-1.png",
        "caption": "Fig. 4 shows a modified helical gear drive in 3D space.",
        "texts": [],
        "surrounding_texts": [
            "The existing design and manufacture of involute helical gears provide instantaneous contact of tooth surfaces along a line. The instantaneous line of contact of conjugated tooth surfaces is a straight line L0 that is the tangent to the helix on the base cylinder (Fig. 1). The normals to the tooth surface at any point of line L0 are collinear and they intersect in the process of meshing the instantaneous axis of relative motion that is the tangent to the pitch cylinders. The concept of pitch cylinders is discussed in Section 2.\nThe involute gearing is sensitive to the following errors of assembly and manufacture: (i) the change Dc of the shaft angle, and (ii) the variation of the screw parameter (of one of the mating gears). Angle Dc is\nformed by the axes of the gears when they are crossed, but not parallel, due to misalignment (see Fig. 14).\nSuch errors cause discontinuous linear functions of transmission errors which result in vibration and noise,\nand may cause as well edge contact wherein meshing of a curve and a surface occurs instead of surface-to-\nsurface contact (see Section 9).\nIn a misaligned gear drive, the transmission function varies in each cycle of meshing (a cycle for each pair\nof meshing teeth). Therefore the function of transmission errors is interrupted at the transfer of meshing\nbetween two pairs of teeth (see Fig. 16(a)). New approaches for computerized design, generation and application of the finite element method for\nstress analysis of modified involute helical gears are proposed.\nThe basic ideas proposed in the developed approaches are as follows:\nii(i) Line contact of tooth surfaces is substituted by instantaneous point contact.\ni(ii) The point contact of tooth surfaces is achieved by crowning of the pinion in profile and longitudinal\ndirections. The tooth surface of the gear is a conventional screw involute surface.\n(iii) Profile crowning provides localization of bearing contact and the path of contact on the tooth surface of the pinion or the gear is oriented longitudinally (see Section 4).\n(iv) Longitudinal crowning enables to provide a parabolic function of transmission errors of the gear drive.\nSuch a function absorbs discontinuous linear functions caused by misalignment and reduce there-\nfore noise and vibration (see Section 7). Fig. 2(a) and (b) illustrate the profile-crowned and double-\ncrowned pinion tooth surface.",
            "i(v) Profile crowning of pinion tooth surface is achieved by deviation of the generating tool surface in pro-\nfile direction (see Section 2). Longitudinal crowning of pinion tooth surface can be achieved by: (i)\nplunging of the tool or (ii) application of modified roll (see Sections 5 and 6).\n(vi) The effectiveness of the procedure of stress analysis is enhanced by automatization of development of\nThe concept of generation of pinion and gear tooth surfaces is based on application of rack-cutters. The\nidea of the rack-cutters is the basis for design of such generating tools as disks and worms.",
            "The concept of axodes is applied wherein meshing and generation of helical gears are considered. Fig. 5(a) shows that gears 1 and 2 perform rotation about parallel axes with angular velocities x\u00f01\u00de and x\u00f02\u00de with the ratio x\u00f01\u00de=x\u00f02\u00de \u00bc m12 where m12 is the gear ratio. The axodes of the gears are two cylinders of radii rp1 and rp2 and the line of tangency of the cylinders designated as P1\u2013P2 is the instantaneous axis of rotation [7]. The axodes roll over each other without sliding."
        ]
    },
    {
        "image_filename": "designv10_2_0003734_s0022112007007835-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003734_s0022112007007835-Figure13-1.png",
        "caption": "Figure 13. Squirmer-averaged velocity vectors relative to the background flow field with Gbh = 3, 10, 30 and 100 (g/g = \u2212 x, c = 0.1, Sq = 1 and \u03b2 =5).",
        "texts": [
            " Gravity is taken parallel to \u2212x In this case the shear flow is directed vertically, as in Kessler\u2019s (1986a) experiments using vertical pipe flow. The three-dimensional movement of 64 identical bottomheavy squirmers in a simple shear flow field is computed for various Gbh . The other parameters are set as c = 0.1, Sq = 1 and \u03b2 = 5. The velocity vectors of each squirmer relative to the background flow field are averaged over all squirmers in the computational cell during t =20 \u2212 100, and the results are shown in figure 13. We see that the length of the squirmer-averaged velocity vector increases with increasing Gbh and its direction approaches to the x-direction with increasing Gbh . This is because the more bottom-heavy the squirmers are, the more rapidly their swimming direction returns towards the vertical after an interaction; disturbances to this direction due to the background vorticity are also suppressed by the strong bottom-heaviness. Similar phenomena have been observed in experiments using real micro-organisms, such as Kessler\u2019s (1986a) pipe flow experiments. When the flow is directed downwards, the cells swim towards the pipe axis, forming a concentrated focused beam. When the flow is upwards, the cells swim towards its periphery, away from the fastest upflow. These tendencies are consistent with figure 13: the fact that the average velocity vector has a negative y-component means the squirmers are moving towards lower values of the upflow velocity. We will show squirmer-averaged velocity vectors under different conditions, and all of these results are consistent with the discussion in Pedley & Kessler (1992). It may be helpful in understanding the squirmers\u2019 motion to introduce a normalized angular probability density function, defined as p\u2032(\u03b8i) = 2 nV sin(\u03b8i) \u222b \u222b \u03b8i=const P (r, e) dAe dV, (4.1) where P (r, e) dAe is the probability that there is a squirmer centred at r with orientation vector e within the solid angle dAe, and \u03b8i is the angle from the i-axis",
            " P (r, e) satisfies the following equation:\u222b \u222b P (r, e) dAe dV = N. (4.2) If one assumes isotropic orientation of squirmers, then p\u2032(\u03b8i) = 1 for all \u03b8i . The results for p\u2032(\u03b8x) with various Gbh are shown in figure 14. When Gbh = 3 the p\u2032(\u03b8x) distribution is almost isotropic, and the squirmers only gradually show a preferred direction as Gbh increases. Their average orientation vectors shift towards the x-axis with increasing Gbh , and the peak of p\u2032(\u03b8x) increases with increasing Gbh . These results are consistent with the average velocity vectors shown in figure 13. The stresslet of a solitary squirmer is given by (1.4), and it is a function of the orientation vector e. The stresslet generated by a solitary squirmer has an order-c effect on the bulk stress, which is therefore strongly dependent on the squirmer orientations. The effect of Gbh on the particle stress component Hxy is shown in figure 15 (c = 0.1, Sq = 1 and \u03b2 = 5). The symmetric part of Hxy is defined as (Hxy + Hyx )/2, and the antisymmetric part of Hxy is defined as (Hxy \u2212 Hyx )/2. In figure 15, we also show three kinds of contributions to the total stress: (i) the stress due to the background shearing motion (including the repulsive interactive force contribution), (ii) the stress due to the squirming motion, and (iii) the stress due to the bottom-heaviness",
            " If Gbh is so large that a solitary squirmer swims in the x-direction even in a shear flow, the (x,y)-component of the stresslet given by (1.4) is zero. If Gbh is so small that a solitary squirmer swims with the constant background vorticity, the (x,y)-component of the time-averaged stresslet is again zero because it is isotropic. The (x,y)-component of the stresslet for a solitary squirmer is negative when exey is negative, and it has its minimum value when e =(\u00b11/ \u221a 2, \u22131/ \u221a 2, 0), which corresponds to \u03b8x = \u03c0/4. It is found from figure 13 that the squirmer-averaged velocity vectors are in the region x > 0, y < 0. This is why the symmetric part of Hxy becomes smaller than in the inert sphere case. We see from the p\u2032(\u03b8x) distribution in figure 14 that the Gbh =30 case has its large peak around \u03b8x = \u03c0/8. This is the reason why the symmetric part of Hxy is at its most negative then. The asymmetric part of Hxy is generated by torques due to the bottom-heaviness. The rheological properties of a dilute suspension of dipolar spheres have been calculated by Brenner (1969), and the contribution of the torques due to bottomheaviness to the (x,y)-component of the particle bulk stress \u03a3 (p) xy can be deduced to be \u03a3 (p) xy = \u00b5\u03b3\u0307 ( 5 2 c + 3 2 c ) , G\u2032 bh 4\u03c0, \u03a3 (p) xy = \u00b5\u03b3\u0307 ( 5 2 c ) , 1 G\u2032 bh, } (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.57-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.57-1.png",
        "caption": "Fig. 5.57 Tire shape near the center of the tire crown",
        "texts": [],
        "surrounding_texts": [
            "z1 \u00bc r1A sin g1; r \u00bc rA \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r21A z2 q r1A 0 z z1: Note 5.4 Geodesic Line The geodesic line is a curve that connects two points with the shortest length. Suppose that the shape of an axisymmetrical object is expressed by (Fig. 5.58) 302 5 Theory of Tire Shape The length of a line element dL is given by dL2 \u00bc r2dh2 \u00fe dr2 \u00feH0\u00f0r\u00de2dr2: \u00f05:136\u00de The geodesic line is thus obtained by minimizing the functional L \u00bc Z F r; dh dr dr; \u00f05:137\u00de where F r; dh dr 1\u00feH0\u00f0r\u00de2 \u00fe r2 dh dr 2 \" #1=2 \u00bc 1\u00feH0\u00f0r\u00de2 \u00fe r2h0 2 h i1=2 : \u00f05:138\u00de The Euler\u2013Lagrange equation is d dr @F @h0 @F @h \u00bc 0: \u00f05:139\u00de"
        ]
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure22-1.png",
        "caption": "Fig. 22 Condition of tooth surface contact",
        "texts": [
            "org/about-asme/terms-of-use e r t b o M b f t o es J Downloaded Fr ters G=0 and P=0 are assumed. Denoting 1 and 2 as the otational motion parameters of the pinion and the gear respecively shown in Fig. 21, we can obtain for the pinion r f 1 = r f 1 u1, 1, 1, 1 n f 1 = n f 1 u1, 1, 1, 1 t f 1 = t f 1 u1, 1, 1, 1 f1 u1, 1, 1 = 0 35 for generated gear r f 2 = r f 2 u2, 2, 2, 2 n f 2 = n f 2 u2, 2, 2, 2 t f 2 = t f 2 u2, 2, 2, 2 f2 u2, 2, 2 = 0 36 for non-generated gear r f 2 = r f 2 u2, 2, 2 n f 2 = n f 2 u2, 2, 2 t f 2 = t f 2 u2, 2, 2 37 The basic condition of two tooth surfaces 1 and 2 Fig. 22 eing in contact at a common point P is that the position vectors f the pinion and the gear coincide and their normals are collinear. athematically, the following equations are satisfied, r f 1 = r f 2 n f 1 = \u00b1 n f 2 38 However, it is difficult to computationally implement Eq. 38 ecause of changing of the normal directions on the tooth suraces. Therefore, the following equivalent equations are proposed o replace Eq. 38 for the iteration process, r f 1 \u2212 r f 2 = 0 n f 2 t f 2 \u00b7 n f 1 = 0 t f 2 \u00b7 n f 1 = 0 39 r Fig",
            "org/ on 01/29/201 r f 1 \u2212 r f 2 = 0 n f 1 t f 1 \u00b7 n f 2 = 0 t f 1 \u00b7 n f 2 = 0 40 Geometrically, vector n f i t f i and t f i i=1,2 are two orthogonal vectors that lie in the tangent planes of the pinion tooth surface 1 i=1 and gear tooth surface 2 i=2 . To avoid divergence of TCA iteration, a similar modified approach has also been proposed, which uses the tangents of the curvilinear coordinates of the mating tooth surfaces to formulate the TCA iteration 23 . When the two surfaces contact at point P, the tangent planes coincide and become a common tangent plane Fig. 22 . Considering the equations of meshing, Eq. 39 or Eq. 40 generally yields five independent equations. Given a motion parameter, say 1, which physically means an angular displacement increment of the driving member, Eq. 39 or Eq. 40 can be solved for the rest of the parameters if the related Jacobian differs from zero 11,12 . And, consequently, a serial of contact points and the corresponding transmission errors can be determined, which formulate the TCA output as the bearing contact patterns and the diagrams of transmission error"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000531_s11661-019-05505-5-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000531_s11661-019-05505-5-Figure1-1.png",
        "caption": "Fig. 1\u2014(a) Optical micrograph of a cross-sectional view of AlSi10Mg powder starting stock and (b) the printed sample with schematic representation of scanning strategy.",
        "texts": [
            " Furthermore, through analytical simulation of rapid solidification phenomenon, in the context of LPBF processing conditions, we shed light on underlying mechanisms controlling the phase evolution. Finally, the nano-hardness variations across the microstructure will be explained in relation to the evolution of the strengthening agents. An AlSi10Mg powder starting stock with a size range of 20 to 63 lm and an Mg content of approximately 0.3 wt pct was used in this study. An optical micrograph of the cross-sectional view of the powder particles is shown in Figure 1(a). The powders were printed into a rectilinear sample (100 mm 9 20 mm 9 10 mm) on a support structure of 3 mm in height, as shown in Figure 1(b). The sample was printed in an Ar atmosphere using a Renishaw AM400 (equipped with a Y fiber laser operated in pulse mode) run with the machine\u2019s default parameters listed in Table I. The build plate was heated to a temperature of 35 C during printing and a hatching angle of 67 deg, counter-clockwise (see Figure 1(b)), was employed between consecutive layers to enhance the densification of the finished part, as explained in Reference 2. Samples for metallographic analysis were prepared in the front-view cross section (in the vicinity of the XZ plane in Figure 1(b)) by sectioning along the building direction (Z) of the as-fabricated part. The samples were ground to #2000 SiC paper and then mechanically polished with 3 lm diamond suspension followed by a final fine-polishing using 0.6 lm colloidal silica slurry. All samples were ion-milled using a PECS II system before performing Scanning Electron Microscopy (SEM). Melt track morphology and cellular/dendritic structure were characterized using a FEG-SEM (FEI Nova NanoSEM 400) at 20 kV, operated in secondary electron imaging mode. For nano-hardness measurements across, a specimen was prepared in the top-view cross section (in the vicinity of the XY plane in Figure 1(b)) and then polished and ion-milled with the same procedure as described above. The nano-hardness was measured using NanoTest Vantage system with a Berkovich indenter under depth-control mode. In order to reveal the hardness evolution across the solidified melt pool, 6 (rows) 9 6 indents (totaling 36) with a loading and unloading rate of 2.0 mN/s and a depth of 1500 nm were applied. For Transmission Electron Microscopy (TEM) experiments, 3-mm-diameter discs from the front-view section (in the vicinity of the XZ plane in Figure 1(b)) were ground down to ~ 70 lm which were then ion-milled using a PIPS II system. A fully digital 200 kV FEI Tecnai Osiris (Scanning) Transmission Electron Microscope (S/TEM) was used for a comprehensive microstructural, crystal structure/orientation, and chemical composition analysis in nano-to-atomic scale. The four Super-X windowless Energy Dispersion X-ray (EDX) detectors incorporated in the TEM allowed for fast acquisition of X-ray spectrum and a high sensitivity for low-energy counts, and also enabled nano-scale mapping of elemental distribution using Chemi-STEM EDX technology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003217_70.833196-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003217_70.833196-Figure2-1.png",
        "caption": "Fig. 2. One leg of the Stewart platform.",
        "texts": [
            " Fkm and Mkm are the components of the resultant force acting at the mass center of body k in <: The explicit form of(5) was first developed by Huston and was called the Huston form of Kane\u2019s equation. The mechanism model of the Gough\u2013Stewart platform manipulator shown in Fig. 1 has a base and a platform. They are connected by six extensible legs with spherical joints at the platform end and universal joint at the base end. Since the legs of the Gough\u2013Stewart platform manipulator are identical, we only need to derive the dynamic equations of the platform and one leg. S1042\u2013296X/00$10.00 \u00a9 2000 IEEE A. Dynamics of the Legs Fig. 2 illustrates one leg of a general Gough\u2013Stewart platform. Let X0Y0Z0 denote the inertial frame fixed at the base. xiyizi (i = 1; 2; ; 6) is parallel to X0Y0Z0 and its origin coincident with Bi: The origins of local frames are attached to each part and labeled as Oi;1 and Oi;2: These two local frames are parallel and their x-axis point to the joint point Pi: si is the position vector from Oi;1 to Oi;2 in the local frame Oi; 1 and qi is the position vector from Oi;2 to Pi in the local frame Oi;2: Let ri;k be the position vector of the mass centers Gi;k in local frames",
            " In order to derive the dynamic equations of leg i in xiyizi; the components of angular velocity of leg i and the relative sliding velocity between two parts are used as generalized speeds. yi = [!i;x !i;y !i;z _si;x] T : (6) The angular velocity of leg i is given by !i = [!i;x !i;y !i;z] T : (7) Based on(6) and (7), the partial angular velocity and the time derivative of partial angular velocity of leg i can be determined as follows, respectively: wi = [13 3 03 1] (8a) _wi = 03 4 (8b) where 13 3 is a 3 3 unit matrix and 03 4 is a 3 4 zero matrix. Referring to Fig. 2, the mass center velocities of two parts can be obtained as i;1 = (Riri;1) !i (9) i;2 = [Ri(ri;2 + si)] !i +Ri _si (10) where Ri is the transformation matrix from local frame to xiyizi: The relative translational velocity between two parts is _si = [ _si;x 0 0]T : According to !i = wiyi; we can obtain the partial velocities of two parts. vi;1 = [ Riri;1 03 1] (11) vi;2 = [ Ri(ri;2 + si) ui] (12) where ui is the unit vector along the leg i: The overbar denote the skew-symmetric matrix of a vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.72-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.72-1.png",
        "caption": "Fig. 5.72: Contact Rocker Pin - Sheave [249]",
        "texts": [
            " In the meantime the prox-algorithm makes such an approach unnecessary. For the tangential situation we might choose a model on the basis of unilateral multibody systems on the basis of chapter 3.4 on the pages 131, or we might choose a regularized force law approximating Coulomb\u2019s law. In the first case we are able to describe stick-slip effects, in the second case not. For the planar case Srnik [250] developed both models, unilateral and regularized ones and compared the two with much success. The contact situation as a whole is pictured by Figure 5.72. Neglecting its eigendynamics the pair of rocker pins can be modeled as one single massless spring acting only perpendicular to the model plane, which is identical with the pulley-chain plane. Figure 5.73 shows the model and the forces acting in the contact plane. The oblique contact planes are symmetrical with respect to the two pulley sheaves. The pin danamics can be neglected thus allowing a quasi-static investigation. The normal contact force FN acts perpendicular to the contact plane, and the frictional forces FT,r and FT,c are parallel to this plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.46-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.46-1.png",
        "caption": "Fig. 5.46: Pump/Motor Configuration of the Hydrostat",
        "texts": [
            " For an angle \u03b1 = 10\u25e6 the difference of minmal and maximum stiffness is 6%, for \u03b1 = 20\u25e6 about 10% and for \u03b1 = 30\u25e6 already 30%. The parameter excitation influences as a matter of fact the whole power transmission system of the tractor. The heart of the VARIO power drive is the hydrostatic system with its hydraulic pumps and motors operating on the basis of a piston type machine. They are heavily loaded, especially for processes like ploughing and mulching. Therefore it makes sense to know these loads already during the design phase to find the correct lay-out. Figure 5.46 shows a drawing of the pump/motor 5.3 Tractor Drive Train System 265 configuration as used in the VARIO system. The piston drum is rotationally displaced with respect to the shaft axis by an angle \u03b1, the magnitude of which determines the oil fluid flow. The translational motion of the nine pistons within the corresponding cylinder liners increase with increasing pivot angle. Drive flange, pistons and piston drum can be modeled as rigid bodies. The tripod joint is an elastic part, it transmits the rotational motion of the drive flange to the piston drum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000431_j.cirpj.2020.12.004-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000431_j.cirpj.2020.12.004-Figure13-1.png",
        "caption": "Fig. 13. Copper coated on high refractory materials. (a) and (b) Copper coated on tantalum. (c) and (d) Copper coated on niobium [190].",
        "texts": [
            " Despite the difference in various properties of the substrate and deposited material, good metallurgical bonding can be achieved since it is a thermomechanical process. AFSD is not just limited to additive manufacturing, it can also be applicable for coating applications, repair, joining, and composite fabrication. AFSD can be used for repairing operations locally, which can eliminate damage, crack, wear, etc. Coating operation can be very effective using AFSD as this results in an excellent metallurgical bond between the coating and the part. Fig. 13 shows the prototypes of tantalum and niobium coated with copper. It was reported that coating was performed on a flat sample and then it was bent into U shape with no crack or delamination [177]. Applications of AFSD can also be extended to add features like rib stiffeners (Fig. 14), flanges and so on that cannot be effortlessly incorporated in casting or extrusion operations. This ability to add able 4 uild rate of AM techniques for different materials. Technique Build rate (cm3/hr) Aluminum Steel Nickel Titanium AFSD 1020 622 81"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000100_taes.2020.3040519-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000100_taes.2020.3040519-Figure1-1.png",
        "caption": "Fig. 1. Diagram of FAHV.",
        "texts": [
            " The remainder of this article is arranged as follows. In Section II, problem formulation is stated. Design process is developed in Section III. In Section IV, stability analysis is given. Simulations are performed in Section V. Finally, Section VI concludes this article. II. PROBLEM FORMULATION A. FAHV Dynamics Derived from the longitudinal model established in [26] and [27], the FAHV dynamics can be rewritten as the following strict-feedback form for the sake of hierarchical controller design, while the FAHV geometry is shown in Fig. 1. \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 V\u0307 = gV + fV + dV h\u0307 \u2248 V \u03b3 \u03b3\u0307 = g\u03b3 \u03b1 + f\u03b3 + d\u03b3 \u03b1\u0307 = g\u03b1Q + f\u03b1 + d\u03b1 Q\u0307 = gQ\u03b4e + fQ + dQ \u03b7\u0308i = \u22122\u03b6i\u03c9i\u03b7\u0307i \u2212 \u03c92 i \u03b7i + Ni, i= 1, 2, 3. (1) Model in (1) is described via six differential equations with respect to rigid-body states and flexible states, while the velocity V , altitude h, fight path angle (FPA) \u03b3 , angle of attack (AoA) \u03b1, and pitch rate (PR) Q contribute to the rigid-body states, and \u03b7 = [\u03b71, \u03b7\u03071, \u03b72, \u03b7\u03072, \u03b73, \u03b7\u03073]T represent flexible states. \u03b4e, are the actual control inputs of FAHV, which represent elevator deflection and FER, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure27-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure27-1.png",
        "caption": "Fig. 27. Contact lines Lcr and limiting line L: (a) in plane \u00f0uc; hc\u00de; (b) on surface Rc.",
        "texts": [
            " Singularities of the pinion may be avoided by limitation of the rack-cutter surface Rc that generates the pinion by line L. The determination of L is based on the following procedure: (1) Using equation of meshing f \u00f0uc; hc;wr\u00de \u00bc 0, we may obtain in plane of parameters \u00f0uc; hc\u00de the family of contact lines of the rack-cutter and the pinion. Each contact line is determined for a fixed parameter of motion wr. (2) The sought for limiting line L is determined in the space of parameters \u00f0uc; hc\u00de by simultaneous consideration of equations f \u00bc 0 and F \u00bc 0 (Fig. 27(a)). Then, we can obtain the limiting line L on the surface of the rack-cutter (Fig. 27(b)). The limiting line L on the rack-cutter surface is formed by regular points of the rack-cutter, but these points will generate singular points on the pinion tooth surface. Limitations of the rack-cutter surface by L enable to avoid singular points on the pinion tooth surface. Singular points on the pinion tooth surface can be obtained by coordinate transformation of line L on rack-cutter surface Rc to surface Rr. Pointing of the pinion means that the width of the topland becomes equal to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.43-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.43-1.png",
        "caption": "Fig. 12.43 Shape of a sloped block [42]",
        "texts": [
            " Because the local model is independent of the global model, the effect of a small change in the tread pattern design on hydroplaning can be analyzed by changing only the local model. The computational time can thus be reduced in this global\u2013local analysis. 12.2 Hydroplaning 845 (4) Development of a new pattern design through hydroplaning simulation Global\u2013local hydroplaning simulation is conducted to develop new pattern technology. To control water flow around the tread pattern, the three-dimensional design of the block shape is studied. The water flow around the block tip can be made smooth by a sloped block tip, which is shown in Fig. 12.43. Typical dimensions of the block tip are given in the figure, and the depth of the tread pattern is 8 mm. Two rolling tires are simulated with and without the sloped block to study the effect on hydroplaning. The water flow of the tire with the sloped block becomes smoother than that of the tire without the sloped block as shown in Fig. 12.44, indicating that the sloped block avoids an increase in the hydrodynamic pressure around the block tip. The measurement of the tire hydroplaning velocity shows a 1-km/h improvement due to the sloped block, demonstrating that the sloped block is effective in improving the hydroplaning performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003775_13552540510573383-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003775_13552540510573383-Figure2-1.png",
        "caption": "Figure 2 Schematic of the laser engineered net shape (LENS) process Plate 1 Wall-shaped build in progress using the LENS process",
        "texts": [
            " Laser direct metal deposition consolidates deposited metal powder using a high energy laser beam. Flat wire welding is a pulsed laser based method of joining sequential layers of metallic wire. Ultrasonic consolidation is a solid state process that consolidates foil layers by application of frictional energy under load. Laser direct metal deposition trials were conducted with the Laser Engineered Net Shape (LENS) process developed at Sandia National Laboratories (Atwood et al., 1998). The LENS process, shown schematically in Figure 2, is a layer additive powder deposition process that consolidates powder layers with a laser operated in continuous beam mode. The LENS process employs multiple nozzles to feed elemental and pre-alloyed powders to produce nearly continuous composition gradients. A wall-shaped build in progress is shown in Plate 1. The deposits for this study were produced on Ti-6-4 base plates from powders of Ti-6-4 and/ or Inconel 718. The chemistries for the supplied powders are provided in Table I. Deposits were produced from Ti-6-4 and Inconel 718 in order to establish deposition parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000536_978-3-030-11981-2-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000536_978-3-030-11981-2-Figure10-1.png",
        "caption": "Fig. 10 Gear conjugated profiles, in which ML is a line segment passing through a pitch point",
        "texts": [
            " In Zone 2, permissible size defects (pores and slag inclusions) in the weld were detected. The graph of the location of AE sources in Fig. 7 is one of many elements of the analysis of AE data. Sources of AE are evaluated by the energy characteristics of the generated signals, by the trends of these characteristics, by the connection of the time of registration of signals with the stages of application of the load, and by the characteristics of location clusters and other parameters. For example, Fig. 10 shows a graph of the correlation for two energy characteristics of AE signals (Amplitude and Counts) which associated with the registration of localized events on the shell of the column to a height of approximately 14,000 cm for channels ##1\u201312, 16\u201324. Triangles are signals on channels 3 and 5. In the ellipse area in the right corner of the graph, there are signals registered on channels 3 and 5, associated with the registration of defects in Zone 4 and Zone 5. Signals from the cluster formed by the ellipse, registered on other channels, also considered as signs of registration of defects",
            " 13): \u03d510 = \u2212 x0 O1a (11) \u03b3i = asin ( xi rK1 ) (12) \u03c8 = \u03d51i \u2212 \u03d510 \u2212 \u03b3i (13) 5. Coordinates of KL in X* 1Y * 1 (and of K1 in X1Y 1): x1i = \u2212rK1 \u00b7 sin\u03c8 (14) y1i = rK1 \u00b7 cos\u03c8 \u2212 rw1 (15) Algorithm for calculating coordinates of points Mi on the rack tooth profile is demonstrated in Fig. 9. The figure also shows all initial data and calculation results. Formulae for determination of coordinates of the points on 2 in system X2O2Y 2 (Fig. 7) are similar to formulae (7\u201315) for 1. These formulae are universal, as they can be used for any 0. Figure 10 shows the fragment of three gearings (the analog of Fig. 7) created by one of the key procedures while testing and debugging optimization design system for cylindrical gears. Calculations were made for the involute gear with following parameters: z1 = 14, z2 = 29,m = 6 mm, x1 = 0.3, x2 = 0.4, \u03b1 = 20\u00b0, h*a = 1, h*l = 1 ppi aw = 106.219 mm. An example of linear ML is chosen to compare the obtained working sections of all three profiles with profiles determined in accordance with existing reliable programs for involute gears. Figure 10 shows the four meshing links ( , 0, 1, 2) and OY axes for 1 and 2 in two positions: initial i = 0 (profiles are marked with a dotted line) and current i = 3 (profiles are marked with a solid line). All the lines and point are obtained with the help of the computer program; the text is typed in the graphic editor by one of the authors. The image is an \u201caction\u201d image: Now it allows to observe only current contact position of reference points in motion. Figure 11 demonstrates the rack profile obtained for the meshing line in the form of an arc of a circle. Red lines correspond to normal lines to profile. In a contact point, the normal line passes through the pitch point\u2014it represents the accuracy of obtained formulae and algorithms. Figure 12 shows the fragment of three gearings made for ML in the form of an arc of a circle. Figure 12 is obtained with the help of the program used for Fig. 10. Figure 13 represents the rack (Figs. 11, 12) profile radii of curvature diagram. Further planes include setting ML in the form of an involute section and deter- mining rack, pinion, and gearwheel teeth profiles. Calculation accuracy of rack profile coordinates depends on real rack profile approximation errors; the approximation is realized by the set of arcs. Teeth profiles opti- 104 D. T. Babichev et al. Determination of Conjugated Profiles of Teeth \u2026 105 mization synthesis requires iterations",
            " Figure 8c shows a model of PC19 centrifuge with a swinging rotor, manufactured by Deltamec (RF). Two schemes of balancing devices with mobile counterweights and swinging rotors are shown in Fig. 9 [6]. The scheme shown in Fig. 9a, in addition to automatic static balancing, allows you to additionally limit the dynamic imbalance (Fig. 9b), since during rotation of a dynamically unbalanced rotor, the former declines from its horizontal position, which is fixed by the position switch. HPC-4-7-600 centrifuge, manufactured by Acuitas (Switzerland), with automatic balancing, is shown in Fig. 10 [13]. One of the tasks in the development of centrifugal benches is a casing design. As a rule, in centrifuges of small radius (for example, up to 1 m, Fig. 11a), the casing design is technological and relatively easy to manufacture. Therefore, it is quite reasonable that such a centrifuge has a casing, and a designing engineer always has a desire to locate a rapidly rotating element of a machine, the rotor, inside a protective screen (Fig. 11). with ergonomics rules in relation to heightH of the rotor servicing area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.8-1.png",
        "caption": "Fig. 4.8 Stiffness of a twisted steel cord",
        "texts": [
            "18), using the relation x = s cosa and y = s sina, \u03b7(s) and f(s) can be expressed as g\u00f0s\u00de \u00bc u\u00f0s\u00de cos a\u00fe v\u00f0s\u00de sin a \u00bc u10 cos a\u00fe v10 sin a \u00bc e0 cos2 a XH sin 2a s\u00fe h / sin a\u00few cos a\u00f0 \u00de f\u00f0s\u00de \u00bc u\u00f0s\u00de sin a\u00fe v\u00f0s\u00de cos a \u00bc u10 sin a\u00fe v10 cos a \u00bc e0 sin 2a=2\u00feXH cos 2a\u00f0 \u00des\u00fe h / cos a w sin a\u00f0 \u00de: \u00f04:24\u00de (1) Strain energy of the cord The strain energy of the cord Uf consists of energies related to extensional deformation, bending and torsional deformation: Uf \u00bc 1 2 Z l 0 Ef g 2 ;s \u00feDf f2;ss \u00few2 ;ss \u00feCf h 2 n o ds; \u00f04:25\u00de where Ef is the tensile rigidity of the cord, Df is the flexural rigidity of the cord, Cf is the torsional rigidity of the cord and h is the twist angle. Uf can easily be calculated using the orthogonality of trigonometric functions and the basic curve for periodic displacement f(n). The other parameters in Eq. (4.25) are expressed by 4.1 DLT of a Two-Ply Bias Belt with Out-of-Plane \u2026 197 g;s \u00bc e0 cos2 a XH sin 2a\u00f0 \u00de\u00fe h /0 sin a\u00few0 cos a\u00f0 \u00de sin a f;ss \u00bc h /00 cos a w00 sin a\u00f0 \u00de sin2 a w;ss \u00bc X sin 2a h \u00bc w;st \u00bc X cos 2a; \u00f04:26\u00de where the prime denotes the partial derivative with respect to y. Referring to Fig. 4.8 for the twisted steel cord, we have e \u00bc d\u00f0k cos a\u00de ds \u00bc dk dx dx ds cos a \u00bc dk dx cos 2 a \u00bc e0 cos2 a Q \u00bc EAe \u00bc EAe0 cos2 a P \u00bc Q cos a \u00bc EAe0 cos3 a; \u00f04:27\u00de where P is the force applied to a twisted cord, Q is the force applied along a wire in the cord, k is the stretch of the cord, a is the braiding angle, E is Young\u2019s modulus of the wire, A is the sectional area of the wire, s is the length along the cord and e0 is the strain of a cord. The tensile rigidity of cord Ef is expressed by Ef \u00bc nP=e0 \u00bc nEA cos3 a A \u00bc pd2wire=4; \u00f04:28\u00de where dwire is the diameter of the wire and n is the number of cords"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003783_s0022112007007847-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003783_s0022112007007847-Figure1-1.png",
        "caption": "Figure 1. A sketch of the arrangement of a bottom-heavy squirmer. Gravity acts in the g-direction, while the squirmer has orientation vector e, radius a and its centre of mass is at distance h from its geometrical centre.",
        "texts": [
            " Fsq is the force\u2013torque due to the squirming motion, which is calculated from superposition of the pairwise interactions between squirmers (Ishikawa et al. 2006). We should note that Fsq includes the effect of high multipoles, because they are captured in the computation using a boundary element method. Ftor represents the external torques due to the bottom-heaviness. If the distance of the centre of gravity is h from the centre of the squirmer, in the opposite direction to its swimming direction in undisturbed fluid (see figure 1), then there is an additional torque of Ftor = 4 3 \u03c0a3\u03c1he \u2227 g, (2.2) where \u03c1 is the density of the cell, e is the unit orientation vector of a cell, g is the gravitational acceleration vector, and the gravitational direction is g/g. Frep represents the non-hydrodynamic interparticle repulsive force that is added to the system in order to avoid the prohibitively small time step needed to overcome the problem of overlapping particles: Frep = \u03b11 \u03b12 exp(\u2212\u03b12\u03b5) 1 \u2212 exp(\u2212\u03b12\u03b5) r r , (2.3) where \u03b11 is a dimensional coefficient, \u03b12 is a dimensionless coefficient and \u03b5 is the gap between squirmer surfaces non-dimensionalized by their radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003530_j.jmatprotec.2004.01.058-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003530_j.jmatprotec.2004.01.058-Figure1-1.png",
        "caption": "Fig. 1. Experimental set-up.",
        "texts": [
            " The brazing process is proposed to deposit the masking material at the edge of each layer in order to allow the formation of an overhang [11]. Previous rapid prototyping techniques have produced either steel parts or non-metallic physical models that do not have the properties of functional parts. Because many important parts are made of aluminum alloys, the development of a rapid prototyping technique that can produce functional parts of aluminum alloys is an important research goal. Rapid prototyping of the 4043 Al-alloy was carried out using VP-GTAW equipment with a tungsten electrode 3.2 mm in diameter, as shown in Fig. 1. The Z\u2032-axis holding the weld torch was fixed to the Z-axis. The traveling Table 1 Experimental condition for rapid prototyping of 4043 Al-alloy Welding speed (mm/s) 60\u2013100 Arc current (A) 110\u2013180 Arc length (mm) 3 Electrode material Tungsten Electrode diameter (mm) 3.2 Diameter of welding wire (mm) 1.2 Gas flow of argon (l/min) 10 Type of torch Straight torch, water cooled speed of the Z-axis depended on the height of the deposited layer and the rotational speed of a substrate. The motion along the Z\u2032-axis was monitored and controlled to provide a constant arc length during the deposition process according to the acquired arc-length signal. A 6061-T6 Al-alloy plate fixed on a rotating R-axis was used as the substrate to build up three-dimensional parts, as shown in Fig. 1. Three key factors are substrate preheating, arc length monitoring and controlling, and heat input controlling [11]. The relevant experimental conditions were selected as shown in Table 1. The following analyses are performed to compare the specimens resulting from different studies: microhardness testing for selected samples, microstructure and porosity evaluation for all samples, surface roughness for selected samples, and deposit width and height for selected samples. The microhardness testing is performed using a Vickers microhardness tester and a 200 g load for 10 s duration on polished specimens"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure6-1.png",
        "caption": "Fig. 6. Limitation of length face-gear tooth.",
        "texts": [
            " This means that the product of principal curvatures at the surface point is negative. The fillet of the face-gear tooth surface of a conventional design (Fig. 3) is generated by the edge of the shaper. The authors have proposed to generate the fillet by a rounded edge of the shaper as shown in Fig. 4 that allows the bending stresses to be reduced approximately in 10%. The shape of the modified fillet of the face gear is shown in Fig. 5. The length of the face-gear teeth has to be limited by dimensions L1 and L2 (Fig. 6) to avoid [8]: (i) undercutting in plane A, and (ii) tooth pointing in plane B. The permissible length of the face-gear tooth is determined by the unitless coefficient c represented as c \u00bc \u00f0L2 L1\u00dePd \u00bc L2 L1 m \u00f01\u00de where Pd and m are the diametral pitch and the module, respectively. The magnitude of coefficient c depends mainly on the gear ratio m12 \u00bc N2=N1 and is usually in the range 8 < c < 15. TCA is designated for simulation of meshing and contact of surfaces R1 and R2 and enables us to investigate the influence of errors of alignment on transmission errors and shift of bearing contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000630_tro.2021.3060969-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000630_tro.2021.3060969-Figure6-1.png",
        "caption": "Fig. 6. Assembly and components. (a) Assembly diagram of one module. (b) Structure of the inner slider. (c) Structure of the connector. (d) 3-D model of the fixing structure.",
        "texts": [
            " 1) It increases the dexterity of the gripper due to the smaller fingertip as it can grasp small targets. 2) It increases the gripper\u2019s capability to grasp large and heavy objects as the curvature gradually decreases from the root to the tip so that contact area with object is increased. 3) The actuation speed of the finger is improved due to the decreasing chamber volume. Its fabrication process is similar with that of the distance-adjusting actuator\u2019s inner part. The assembly process of one module for the gripper is shown in Fig. 6(a). To meet the system\u2019s compactness and stiffness requirements, we design a cylindrical groove on the inner slider of the distance-adjusting actuator for connecting with the angleadjusting actuator, as shown in Fig. 6(b). The small hole at the bottom of the cylindrical groove is used to pass through the air tubes. The small holes on both sides of the cylindrical groove are used to limit the position of the angle-adjusting actuator. The 3-D printed slider and the angle-adjusting actuator (made of soft elastomers) are bonded with instant adhesive (F409 from MNglue). To connect the angle-adjusting actuator and the finger actuator, we 3-D print a rigid connector, as shown in Fig. 6(c). Each side of the connector has a groove, with one of them used to connect with the angle-adjusting actuator, and the other for the finger actuator. In addition, there are two small holes on both sides of the groove, which are used to limit the position of the angle-adjusting actuator and the finger actuators, through small rods. There is also a larger hole for passing through the air tubes on the connector. Finally, we assemble the whole gripper using a 3-D printed fixing structure [see Fig. 6(d)]. There are two sliding channels on each side of the fixing device (four in total), which are used to connect with the inner sliders of each module. At the bottom of each slider, there is a small hole for passing through the air tubes. On top of the fixing structure, there is an interface for connecting with the outside. Now we have finished the construction of the gripper. After the design, fabrication, and assembly of the gripper were completed, we tested various performances of both the components and the whole gripper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003707_9.280779-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003707_9.280779-Figure1-1.png",
        "caption": "Fig. 1. A 3R spatial open chain.",
        "texts": [
            " Then wt is a unit vector in the direction of joint axis i , expressed in inertial (tip) frame coordinates; uz is a vector, also described in inertial (tip) frame coordinates, such that the pitch of the screw motion generated by joint i is wTv,. Note that for revolute joints the pitch is zero; for prismatic joints w 2 = 0 and U , is in the direction of movement. In both cases wz x ut is required to be a point lying on the joint axis. Example 1: Let the forward kinematics for the 3R open chain of Fig. 1 be of the form f(z1, 2 2 , x3) = eA1x1eA2x2eA3x3M. Setting the joint axes to zero, the tip frame M = (0, b ) relative to the base frame is given by 0 = I, b = (LI + Lz, 0, 0). Joint 1 has a screw axis in the direction w1 = (0, 0, 1); since w1 x v1 is a point lying on the joint axis, with vl normal to w1, it follows that v1 = (0, 0, 0). Similarly, for joints 2 and 3 we have w2 = (0, -1, 0), 212 = (0, 0, 0), and w3 = (0, -1, 0), As the above example illustrates, the POE formula is a global description of an open kinematic chain that can be obtained independently of the DH parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure6.12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure6.12-1.png",
        "caption": "Fig. 6.12",
        "texts": [
            " Therefore there is a limit circle in (3a), and there is no limit circle in (3b), so there must be another transition set between (3a) and (3b). The topological structure of both the saddle (x+O) and sink (x_,O) in the whole domain of a> does not vary; as the phase portraits change in nature outside the local domain of those two changing points, so a global bifurcation must occur. The disappearance of the limit circle from the loop may be due to the appearance of the saddle node loop. The stable manifold crosses the unstable manifold at the saddle point. In other words, this bifurcation is a bifurcation of an infinite period (see Fig. 6.12). To prove our guess that transition set (3c) is a saddle loop (or bifurcation with infinite period), we shall discuss eq. (6.148) again, using singular transformation and . 2 3 4 2 1_ rescalmg eq. (6.148): x = E u,y = E v,u) = E Y p u 2 = E Y2 and (= -( , where E > 0 E is small. Substituting every transformation into eq. (6.148) yields (6.157) System (6.157) becomes a Hamilton system when E = 0, so we have Hamilton function: v 2 u3 H(u,v)=2- y )u- 3 (6.158) and aH aH 2 av-=v=u', -a;;=Y) +u =v' (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003346_j.bbrc.2003.10.031-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003346_j.bbrc.2003.10.031-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the MWNT-based biosensor for glucose detection.",
        "texts": [
            " When the electrode background current was stable, the addition of glucose was carried out in a 0.1M phosphate buffer solution (pH 7.4). All measurements were performed at room temperature of 25 C. The scanning electron microscope (SEM) and the transmission electron microscope (TEM) images were taken using a field emission scanning electron microscope (the FE-SEM 6340F) and a transmission electron microscope (the JEM-2010 Electron Microscope), respectively, Fourier transform infrared (FTIR) spectra were measured using a Perkin\u2013Elmer FT-IR spectrometer (SPECTRUM 2000). Fig. 1 schematically depicts the proposed reaction mechanism of enzymatic amperometric MWNT-based biosensor for the electro-enzymatic detection of glucose. Different from other groups\u2019 samples in which the nanotubes were commonly cast or pasted on the electrode surfaces, our self-assembled MWNT layer has good adhesion. In addition, our samples are capable of preventing the binding of undesirable species from the sample surfaces. The immobilization of the enzyme GOD into the MWNTs would allow the mediated direct electron to transfer to the gold transducer and produce the response current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003919_978-94-015-9064-8_5-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003919_978-94-015-9064-8_5-Figure1-1.png",
        "caption": "Figure 1. Tsai manipulator Figure 2. 3-(RRPRR) parallel manipulator",
        "texts": [],
        "surrounding_texts": [
            "The growing variety of fully parallel mechanism applications has led researchers also to study parallel mechanisms with only three degrees of freedom (dot). The basic topology of three dof parallel mechanisms is constituted by two rigid bodies (base and platform) connected to each other by a number of open and/or closed chains (legs), where only some kinematic pairs are actuated to provide three dof to the platform (movable) with respect to the base (fixed). Different architectures of three dof parallel manipulators have been presented in the literature. Some of them provide a pure relative rotation of the platform about a fixed point (Alizade et aI, 1994 Asada and Cro Granito, 1985; Gosselin and Angeles, 1989; Innocenti and Parenti-Castelli, 1993) and are used as wrists of manipulators, mechanisms for antenna orientation, and pointing devices. Others (Clavel, 1988; Herve and Sparacino, 1991; Herve, 1992; Tsai 1996, Tsai and Stamper, 1996) provide the platform with a pure translational motion and are of interest in automated assembly, especially for pick and place operations, and in machine tools as alternative structure to the serial positioning devices. Moreover, also three dof parallel manipulators that provide coupled position and orientation have been presented (Jason and Sun-Lai, 1992; Lee and Shah, 1987; Po-hua et aI, 1996; Waldron et aI, 1989; Padmanabhan,"
        ]
    },
    {
        "image_filename": "designv10_2_0003717_robot.1999.769929-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003717_robot.1999.769929-Figure2-1.png",
        "caption": "Figure 2: Biped robot foot artificially disconnected to show the intervening forces. The COP and the FRI point are denoted by P and F , respectively.",
        "texts": [
            " We review the physics behind both the concepts and show that COP and ZMP are identical. 2 FRI point of a biped robot In order to formally introduce the FRI point, we first treat the entire biped robot - a general n-segment extended rigid-body kinematic chain (sketch shown for example purpose in Fig. 1) - as a system and determine its response to the external force/torque. We may employ Newton or d\u2019Alembert\u2019s principles for this purpose. The external forces acting on the robot are the resultant ground reaction force/torque, R and M , acting at the COP (denoted by point P , see Fig. 2), and the gravity. The equation for rotational dynamic equilibrium is obtained by noting that the sum of the external moments on the robot, computed either at its CoM or at any stationary reference point is equal to the sum of the rates of change of angular momentum of the individual segments about the same point. Taking moments at the origin 0, we have M + O P x R + x O G ; x m;g = where mi is the mass, Gi is the CoM location, ai is the CoM linear acceleration, and HG, is the angular momentum about CoM, of the i th segment. M is the frictional ground reaction moment (tangential) I An important aspect of our approach is to treat the stance foot as the focus of attention. Indeed, as the only robot segment interacting with the ground, the stance foot is a \u201cspecial\u201d segment subjected to joint forces, gravity forces and the ground reaction forces. Viewing from the stance foot, the dynamics of the rest of the robot may be completely represented by the ankle force/torque -RI and - 7 1 (negative signs for convention). Fig. 2 artificially disconnects t8he ankle joint to clearly show the forces in action at that joint. The dynamic equilibrium equation of the foot (segment#l) is: M+OPxR+OG1xmlg-r1-001xR1= E i G l + O G ~ x mlal. (2) The equations for static equilibrium of the foot are obtained by setting the dynamic terms (RHS) in Eq. 2 to zero: M+OPxR+OG1xmlg-r1-001xR1=0 (3) Recall that to derive Eq. 3 we could compute the moments at any other stationary reference point. Out of these the COP represents a special point where Eq",
            " 8 may be rewritten as O F x m;(ai - g ) - OF x m l g Carrying out the operation, we may finally obtain: NUM1 NUM2 (10) and OF, = - D E N D E N ' ' O F , = - 2.1 Properties of FRI point Some useful properties of the FRI point which may be exploited in gait planning are listed below: The FRI point indicates the occurrence of foot rotation as already described. The location of the FRI point indicates the magnitude of the unbalanced moment on the foot. The total moment Mfi due to the impressed forces about a point A on the support polygon boundary (Fig. 2) is: M A = AF x ( m l g - R ~ ) (11) which is proportional to the distance between A and F . If F is situated inside the support polygon M i is counter-acted by the moment due to R and is precisely compensated, see Fig. 3, top, for a planar example. Otherwise, Mfi is the uncompensated moment which causes the foot to rotate (Fig. 3, bottom). The FRI point indicates the direction of foot rotation. This we derive from Eq.11 assuming that m l g - RI is directed downwards. The FRI point indicates the stability margin of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.9-1.png",
        "caption": "Fig 6.9: Pressure sensor waveguide. According to [Hill94]",
        "texts": [
            " The measurement range of the device can be influenced by a change of the membrane thickness. The interferometer is made from silicon. When building such a device, particular attention must be paid to the optical properties of the waveguide. The production of this pressure sensor was reported in [Fisch91] and [Hill94]. Here, the CVD and Plasma-CVD methods were used (Section 3.1.1.1). The device consisted of three layers placed on a silicon substrate, the light guiding layer had a high index of refraction to allow the passage of light, Fig. 6.9. First, a 2 to 3 f..tm thick silicon dioxide layer with an index of refraction of 1.46 was applied to a (100) silicon wafer to keep the laser beam from being ab sorbed by the silicon substrate. Second, a 0.5 f..tm thick light guiding layer made of SiON was deposited; it had an index of refraction of 1.52. Third, a 0.6 f..tm thick silicon dioxide layer was added and structured using a dry etch ing process. By this design, the light is guided in the middle of the SiON layer to avoid parasitic modulation from changes in the surroundings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000691_j.rinp.2019.01.002-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000691_j.rinp.2019.01.002-Figure4-1.png",
        "caption": "Fig. 4. (a) Transient temperature profile of AlSi10Mg and (b) principal stress profile of AlSi10Mg build part.",
        "texts": [
            " 100mm/S and then varying the laser power from 100mm/S to 400mm/S by keeping the laser power constant i.e. 100W. The laser beam scans in the positive X-direction of the powder bed. Predicting the thermal distribution in direct metal laser sintering of powders involving several modes of heat transfer and numerous processing conditions has been a challenge to researchers in the subject area. The temperature distribution with respect to time plays a vital role in determining the thermal residual stresses in the build part. Fig. 4 represents the three-dimensional transient temperature profile and stress profile for 1mm thickness of AlSi10Mg powder layer during direct metal laser sintering. The simulations are carried out at 100W laser power and 100mm/S scan speed. The temperature distribution on the top surface of the powder bed is shown by different color gradient as shown in Fig. 4(a) and the middle region of the ellipse represents the molten pool on powder bed. Thus, the magnitude of the temperature line located at the edge of red color region stands for the liquid temperature of AlSi10Mg alloy (600 \u00b0C). The temperature contours are looks like series of ellipses around the laser irradiated regions on the top surface of the powder bed and the ellipses are more intensive in the laser scan direction. Along the laser scan direction, an elongated shape of the elliptical temperature distribution is observed behind the moving heat source",
            " Under the interaction of input laser energy with the powder bed, the temperature of the powder particles raised suddenly, causing a molten pool and heat affected zone in the adjacent loose powder. The substrate also plays a significant role for the heat dissipation. The cyclic heating and cooling of the powder bed during direct metal laser sintering process occurs within few milliseconds i.e. 5\u201325ms, which suggests that the laser illuminated regions are subjected to rapid thermal cycles. This repetitive heating and cooling in the build part lead to commensurate thermal stresses in the build part. Fig. 4(b) depicts the distribution of thermal residual stresses obtained by finite element model when the laser beam scans in a single track. It is observed that there is a significant variation of thermal residual stresses in the sintered track dependent on the temperature gradients. It is found that maximum stress is obtained at the interaction zone of the laser beam and powder bed and decline towards the surrounding region. This is because of the existence of large temperature gradient on the powder bed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000520_j.addma.2019.100808-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000520_j.addma.2019.100808-Figure5-1.png",
        "caption": "Fig. 5. The temperature distribution of Ti-6Al-4V part (a) at the beginning of cooling, (b) at the cooling time of 100 s, (c) at the cooling time of 500 s and (d) when the components have cooled down to room temperature and the clamps are released and the corresponding y-component of stress distribution (longitudinal stress) of Ti6Al-4V part (e) at the beginning of cooling, (f) at the cooling time of 100 s, (g) at the cooling time of 500 s and (h) when the components have cooled down to room temperature and the clamps are released. The results are for long deposition pattern using the processing conditions provided in Table 1.",
        "texts": [
            " Since the temperature fields reach steady state after the third layer, the stress distribution (tensile or compressive) remains the same but the magnitudes of the stresses continue to increase as shown in Fig. 4 (e) and (f). The stress that originate during the deposition as shown in Fig. 4 significantly contribute to the final residual stresses fields. In other words, the evolution of stresses fields during cooling starts from the stress distributions that have already originated during deposition as explained below. During the cooling process, the temperatures of the substrate and deposit continue to decrease as shown in Fig. 5 (a\u2013c). At the end of the cooling, the deposit cools down to the room temperature and the clamps are released as shown in Fig. 5 (d). The deposit continues to shrink along y-direction during the whole cooling process. This contraction generates high tensile stresses in the substrate because the substrate is constrained by the clamps. This contraction also results in high compressive stress in the substrate near the longer edge of the component as shown in Fig. 5 (e). Magnitudes of these stresses continuously increase during the cooling process as shown in Fig. 5 (e\u2013g). The last hatch of the 5th layer cools down at the end. Therefore, high tensile stresses are accumulated in this region as shown in Fig. 5 (f\u2013g). This can be attributed to the fact that there is no subsequent heating operation on the last hatch to partially alleviate the stresses. In contrast, the stress values in the previously deposited hatches are partially alleviated due to reheating during the deposition of subsequent hatches. Similar observation was also made by Mughal et al. [8] during multilayer WAAM of a mild steel component. Since the clamps constraint the substrate to contract, the substrate largely suffers from tensile stress, especially in the region close to the clamps and the region near the edge of the shorter side of the deposit, as shown in Fig. 5 (g). After releasing the clamps, the shorter edges of the substrate deform upward and thus the high tensile stresses near the clamps are relieved as shown in Fig. 5 (h). Upward deformation results in high compressive stress on the top surface of the substrate near the longer side of the deposit as shown in Fig. 5 (h). From Figs. 4 and 5 it is evident that the residual stresses and distortion evolve depending on the transient temperature field and are largely controlled by the deposition pattern. Therefore, the stresses of Ti-6Al-4V components printed using three different deposition patterns are compared below. To compare the x-component of residual stresses for three deposition patterns, variations in temperature and resulting stress evolutions have been investigated during the cooling process. Fig. 6 (a\u2013f) show the variations in temperature and x-component of stresses along line 1 (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.58-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.58-1.png",
        "caption": "Fig. 11.58 Cornering coefficient and aligning torque coefficient. Reproduced from Ref. [51] with the permission of SAE",
        "texts": [
            " 782 11 Cornering Properties of Tires 11.9.2 TPC Specification System General Motors [51] proposed the TPC specification system in 1974. The TPC have parameters of the cornering coefficient (f-function), aligning torque coefficient, load sensitivity (h-function) and load transfer sensitivity (g-function) for evaluation of the cornering properties of a tire. The cornering coefficient (f-function) is defined as the side force produced at a slip angle of 1\u00b0 and 100% of the 24-psi rated load, divided by the rated load Fz (Fig. 11.58a). This tire parameter is the most influential tire parameter affecting the linear directional control performance of the tire/vehicle system. Similarly, the aligning torque coefficient is defined as the aligning torque at a slip angle of 1\u00b0 and 100% of the 24-psi rated load, divided by the rated load Fz (Fig. 11.58b). The amount of aligning torque generated by the tire, in conjunction with the desired amount of vehicle front-suspension aligning torque compliance, controls the directional behavior of the vehicle. In addition, the aligning torque generated is important in determining the force fed back through the steering wheel to the driver during any vehicle maneuvering. The load sensitivity (h-function) is a measure of howmuch a tire is able to increase the side force produced at a slip angle of 1\u00b0 as the load increases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.44-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.44-1.png",
        "caption": "Fig. 6.44 In-plane shear strain c and circumferential displacement v",
        "texts": [
            "91) for the cord tension tc, the membrane forces of a radial tire in the meridian direction N/(c) and in the circumferential direction Nh(c) are expressed as N/\u00f0c\u00de \u00bc Ntc 2pr \u00bc p r2D r2c 2r sin/D Nh\u00f0c\u00de \u00bc 0: \u00f06:122\u00de Using the relation GLT Gm/Vm in Eq. (1.114), the shear membrane force due to structural stiffness of the sidewall N/h(r) can be expressed as N/h\u00f0r\u00de \u00bc GLThc \u00bc Gmhc=Vm; \u00f06:123\u00de where c is the shear strain of the sidewall, Gm is the shear modulus of the sidewall rubber, Vm is the volume fraction of the sidewall rubber, and h is the thickness of the sidewall. Note that these parameters change with position r. T Referring to Fig. 6.44, the in-plane shear strain c of Fig. 6.45 is given as c \u00bc c1 \u00fe c2\u00f0 \u00de \u00bc u\u00fe @u @h dh u rdh v\u00fe @v @s ds v r\u00fedr r ds \u00bc 1 r @u @h dv ds \u00fe v r @r @s ; \u00f06:124\u00de where u is the displacement along the meridian line, v is the circumferential displacement and s is the position along the sidewall. Recall the relation dr=ds \u00bc cos/: \u00f06:125\u00de Because the displacement u is uniform in the circumferential direction under the torsional deformation in Fig. 6.43, the term \u2202u/\u2202h will be zero in Eq. (6.124). The substitution of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.30-1.png",
        "caption": "Fig. 8.30 Fig. 8.31",
        "texts": [
            "28 we obtain a portion of the result of the global dynamical behaviour of the system. When the initial point is outside the region enclosed by the two invariant manifolds of point A, the iteration result will diffuse rapidly. When the initial point is in these regions, which are netted by the two invariant manifolds after many iterations, it will go to infinity finally. The points in the domain of 0(0, 0) will be in these regions forever in the course of iteration. We generalize the above results in Fig. 8.30. We term those original value regions that will dissipate eventually (it may take a long time) chaos seas (here it is actually a divergent region). The points that cannot dissipate are on the island of the regular solution. We have seen that the rotation angle at the fixed point 0 is cp = arccos(0.6/ 2) = 72.540 ; away from 0, the rotation angle will decrease, and when it decreases to 720 , we obtain the period-5 solutions. In linear systems, there are infinite groups of period-5 solutions; they form many ellipses",
            " If 11l1> 2, they are 296 Bifurcation and Chaos in Engineering hyperbolic points, and if I J..l1 < 2 they are elliptic points. From the numerical computation, for the period-5 solutions, SI'S2,S3' S4,S5' the value of J..l is 1.9999<2. They are elliptic periodic points. On the other hand, the five period-5 points Up U2 , U3 ' U4 , Us are hyperbolic periodic points. The value of J..l is 2.00172. Near every hyperbolic point there is also a Poincare bar. The difference is that it is formed by heteroclinic structure instead of homoclinic structure; for example, U1 , according to Fig. 8.30(a). These four lines, the unstable and stable manifolds which go from US forward or backward to the vicinity of U1 , and the two invariant manifolds from U2 , build the bar at U1\u2022 If the initial value is in these bars and the four invariant manifolds of U1 (it has not been drawn), after accumulative iterations of <p5, these points will drift in these regions. Such regions constitute the chaotic river network. Just as in Fig. 8.32(b), the width of the river is amplified by a few orders of magnitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.30-1.png",
        "caption": "Fig. 6.30: Polygon Effect for Roller Chains",
        "texts": [
            " The link model follows the dissertation [69] of Fritz, who was the first one to present a detailed simulation model of roller chain systems. In the following we shall give some more details (see also [70], [111] and [201]). Chains are loaded by internal and external excitations [69]. The structure comprising plates and pins generates polygonal effects with their frictional 6.4 Bush and Roller Chains 367 impact behaviour in the inlet and outlet of the sprocket wheels. In contrast to belts the chains form a polygonal structure contacting the teeth of the sprocket wheels in one point only (see Figure 6.30). To get an estimate for the velocities and the polygonal frequency we assume that the joint centers are positioned on the generated pitch circle. If then the sprocket wheel with z teeth and a pitch circle radius R rotates with the constant velocity \u2126 we get the following velocity variations with respect to the free strand transverse \u2206vt = R\u2126 sin(\u2126\u03b1), longitudinal \u2206vl = R\u2126[cos(\u2126\u03b1)\u2212 ( sin \u03a0 z \u03a0 z )], (\u2212\u03a0 z \u2264 \u03b1 < \u03a0 z ). (6.37) where the second term in the longitudinal equation represents the averaged velocity in longitudinal direction (see section 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001127_j.oceaneng.2021.109164-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001127_j.oceaneng.2021.109164-Figure1-1.png",
        "caption": "Fig. 1. References frames of an UUV. Earth-fixed frame (\ud835\udc42\ud835\udc3c ) and the body-fixed frame (\ud835\udc42\ud835\udc35 ).",
        "texts": [
            " Section 2 describes mathematical model of the UUV and Section 3 presents the main contribution of this paper, which is the design of controller, as well as the stability analysis based on Lyapunov theory. Next, Section 4 describes the underwater vehicle and Section 5 presents a set of simulation test. Then, Section 6 exposes the results of experimental tests in real-time, based on the results, the performance of the closed-loop system is demonstrated. Finally, Section 7 provides conclusions. The mathematical model of an UUV is analyzed in two coordinate frames: a body-fixed frame \ud835\udc42\ud835\udc35 and an earth-fixed frame \ud835\udc42\ud835\udc3c , see Fig. 1. In the literature, several works proposed different approaches to obtain the mathematical model (Graver, 2005; Bailey, 1997; Fossen, 1999). The representation proposed by Fossen (1999) is adopted in this work to describe the non-linear model of an UUV and using the notation for underwater vehicles described by the SNAME (SNAME, 1950). The matrix representation of the dynamic model is defined by the follow equations: \ud835\udc40?\u0307? + \ud835\udc36(\ud835\udf08)\ud835\udf08 +\ud835\udc37(\ud835\udf08)\ud835\udf08 + \ud835\udc54(\ud835\udf02) = \ud835\udf0f + \ud835\udf14 (1) ?\u0307? = \ud835\udc3d (\ud835\udf02)\ud835\udf08, where \ud835\udf08 = [\ud835\udc62, \ud835\udc63,\ud835\udc64, \ud835\udc5d, \ud835\udc5e, \ud835\udc5f]\ud835\udc47 is the state vector of velocity relative to the body-fixed frame, \ud835\udf02 = [\ud835\udc65, \ud835\udc66, \ud835\udc67, \ud835\udf19, \ud835\udf03, \ud835\udf13]\ud835\udc47 represents the vector of position and orientation relative to the earth-fixed frame, \ud835\udc40 \u2208 R6\u00d76 is the inertial matrix, \ud835\udc36(\ud835\udf08) \u2208 R6\u00d76 describes Coriolis matrix, \ud835\udc37(\ud835\udf08) \u2208 R6\u00d76 defines the hydrodynamic damping matrix, \ud835\udc54(\ud835\udf02) \u2208 R6 is the vector of hydrostatic forces, \ud835\udf0f = [\ud835\udf0f1, \ud835\udf0f2]\ud835\udc47 = [\ud835\udc4b, \ud835\udc4c ,\ud835\udc4d,\ud835\udc3e,\ud835\udc40,\ud835\udc41]\ud835\udc47 \u2208 R6 represents the vector of forces and moments in the body-fixed frame, \ud835\udf14 \u2208 R6 denotes the disturbance vector and \ud835\udc3d (\ud835\udf02) \u2208 R6\u00d76 is the kinematic transformation between the body frame and the inertial frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003775_13552540510573383-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003775_13552540510573383-Figure1-1.png",
        "caption": "Figure 1 Concept drawing of a metallic thermal protection system employing attachment clips to join a hot Inconel 718 aeroshell to a Ti-6-4 integrally stiffened tank structure",
        "texts": [
            " The test case for application of such material is an attachment bracket that joins nickel-based metallic thermal protection systems to titanium-based launch vehicle structure. The goal of the current study was to evaluate the compatibility of each method with the materials selected, examine the resulting microstructures and chemistries, and characterize any reaction products. Metallic thermal protection systems (TPS) under development offer potentially greater durability than ceramic tile systems. One design, shown in Figure 1, employs attachment brackets to join a hot service aeroshell to an integrally stiffened tank structure (Blosser, 2000; Blosser et al., 2004). In this concept the attachment bracket is made from Inconel 718 strip approximately 4 in. long, 1 in. wide, and 0.020 in. thick, with 0.5 in. long flanges at each end to facilitate brazing to the Inconel 718 aeroshell and the Ti-6-4 tank structure. Thermal analysis indicates that temperatures at the Inconel end would reach 1,8008F and be in the range of 400-5008F at the Ti end"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.26-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.26-1.png",
        "caption": "Fig. 5.26: Components of a Ravigneaux Planetary Gear",
        "texts": [
            " As pictured in figure 5.25, detail 3 or 6, the damping coefficient d attains the constant value d0 for two gear wheels in contact. Within the limits of the clearance s the damping coefficient d is approximated by an exponential curve which leads to a steady transition into the contact area. Ravigneaux type planetary gears are often used in passenger cars since they offer a multitude of gear-stage combinations and are at the same time very 5.2 Ravigneaux Gear System 245 compact requiring only small space. Figure 5.26 illustrates the basic design of such a planetary gear, the main components and their function for the first gear respectively: \u2022 Small and large sun gear S1 and S2 \u2022 Ring gear R \u2022 Planet carrier PC \u2022 Inner (short) planets P1 and outer (long) planets P2 \u2022 Input shaft A \u2022 Free coupling shaft F A Ravigneaux planetary gear is designed using two conventional planetary gears whereby the two planet carriers are combined, and one ring gear is omitted. In the first gear, which is treated in this paper, the shaft A drives the sun wheel S1 which is meshing the short planets P1",
            " The planets P1 are in gear with the long planets P2 and both are pivoted in the planet carrier PC that is inertially fixed by a rotational force element which approximately substitutes the effect of a multiple disk clutch. The ring gear is engaged with the planets P2 and transmits the load by the coupling described later. Other transmissions can be selected by changing the input shaft and the fixation of shafts and the planet carrier respectively. The connection between the components abovementioned is performed by the force elements pictured on the right side of figure 5.26. The toothing is modeled according to the equations given in the section \u201dToothing\u201d, where the geometrically caused phase shifts between the curves of the tooth stiffnesses of the single gear trains have to be taken into account. The vector of the generalized coordinates may contains either 4 or 6 degrees of freedom depending on the pitch motion under consideration. Due to the stiffness of the shafts and the small clearance in the bearings the 4 degrees of freedom qT = (x, y, z, \u03b1) were selected in this case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.26-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.26-1.png",
        "caption": "Fig. 6.26 Apparatus for measuring fundamental spring rates. Reproduced from Ref. [18] with the permission of Tokyo Denki University Press",
        "texts": [
            "24, the torque My is given by cosz x sinz z The in-plane rotational spring rate Rt is given by Rt \u00bc My=a \u00bc 2pr3Akt: \u00f06:54\u00de When the fore\u2013aft force is applied to a tire as shown in the third figure from the left in Fig. 6.1, the tire deformation of the rigid ring model can be separated into translational displacement d1 and rotational displacement d1 as shown in Fig. 6.25. Using Eqs. (6.52) and (6.54), the overall displacement x is given as x \u00bc d1 \u00fe d2 \u00bc Fx Rd \u00fe r2AFx Rt \u00bc Fx prA kr \u00fe kt\u00f0 \u00de \u00fe Fx 2prAkt : \u00f06:55\u00de The fore\u2013aft spring rate Rx of the rigid ring model is expressed as Rx \u00bc Fx x \u00bc 2prA\u00f0kr \u00fe kt\u00dekt 3kt \u00fe kr : \u00f06:56\u00de The fundamental spring rates are measured using an apparatus such as that shown in Fig. 6.26, where the whole tire tread is clamped. Because the tire tread cannot be completely clamped by the apparatus owing to the cross-sectional crown shape, the tire tread does not behave as a rigid ring in general. However, the stiffness at the tread is much greater than that of the sidewall, and the apparatus can therefore 328 6 Spring Properties of Tires measure tire spring rates within the required precision. Applying the four types of deformation shown in Fig. 6.27, the eccentric spring rate Rd, lateral spring rate Rs, in-plane rotational spring rate Rt and torsional spring rate Rmz can be measured",
            "120) through \u03b7 and f can be explicitly expressed as @j @rc \u00bc 4rrc sin/D B2 @j @/D \u00bc 2r cos/D B @l @rc \u00bc 2rc sin2 /D ZrP rB r2 r2c r2D r2 G3=2 dr @l @/D \u00bc B sin/D cos/D ZrP rB r2 r2c 2 G3=2 dr @l @rP \u00bc Bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 sin2 /D r2P r2c 2q G \u00bc B2 A2 A \u00bc r2 r2c sin/D B \u00bc r2D r2c ; \u00f06:121\u00de where rP is an intermediate variable that is replaced with r in the integration of Eq. (6.119). (4) Comparison of calculation and experimental results Yamazaki [5] compared calculation and experimental results for the lateral fundamental spring rate. An experiment was performed for a passenger-car belted radial tire sized 175SR14 (wheel: 5J-14) using an apparatus similar to that shown in Fig. 6.26. A cut section of the tire is drawn in Fig. 6.41, and the calculation used the values rB = 192 mm, rC = 251 mm, rD = 296 mm, /D = 53.5 deg, r B \u00bc 230mm, r D \u00bc 275mm, h1 = 12 mm, h2 = 6 mm, h3 = 11 mm, Em = 3.5 MPa, EmB = 28.7 MPa, EmD = 5 MPa, where Em and h2 are Young\u2019s modulus and thickness of the sidewall, EmB and h1 are Young\u2019s modulus and thickness of the bead filler, and EmD and h3 are Young\u2019s modulus and thickness of the tread rubber. Because Young\u2019s modulus and thickness vary with position r, the integration of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003943_tmag.2004.825185-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003943_tmag.2004.825185-Figure1-1.png",
        "caption": "Fig. 1. Two alternative solutions for skewing of the magnets. (a) Continuous. (b) Discrete.",
        "texts": [
            " Among various approaches, skewing is known to be the most effective method for reducing of the cogging torque in permanent magnet (PM) machines [1], [6], [7]. There are two alternative solutions, in which skewing of either the stator sheet pack (laminated core) or the rotor permanent magnets is applied. The latter method is a cost-effective solution recommended for the machines with short stack length [3]. This paper demonstrates how the cogging torque can be reduced when replacing continuous skew angle of PMs with a discrete one along the machine length (see Fig. 1). Such a construction of the magnetic circuit leads to a great reduction of the cogging torque and its optimization procedure is shown in this paper to be less complicated than that for the magnets with continuous skew angle. For optimization of skew angle of PMs, a genetic algorithm (GA) is applied. The skewed magnets need to be analyzed using three-dimensional (3-D) field models [3], [4]. However, the application of a 3-D field model in the optimization process would make the analysis time expensive [3]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.35-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.35-1.png",
        "caption": "Fig. 11.35 Self-aligning torque in a combined slip. Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [],
        "surrounding_texts": [
            "In the case of driving (s < 0), s1 = s + 1 and s2 = 1. 17Note 11.13. 18See Footnote 17. 11.4 Cornering Properties for a Large \u2026 753 Fx \u00bc Cxbl2h 2 s\u00fe n\u00fe 1 n 2nFzld ln\u00fe 1 l 2 n l lh\u00f0 \u00de 1 n\u00fe 1 l 2 n\u00fe 1 lh l 2 n\u00fe 1 ( )\" # cos h Fy \u00bc bCyl2h s1 2 tan a d Cy \u00fe l2 3r2Ky Fy s2 l 1 2 s2lh 3l \u00fe n\u00fe 1 n 2nFzld ln\u00fe 1 l 2 n l lh\u00f0 \u00de 1 n\u00fe 1 l 2 n\u00fe 1 lh l 2 n\u00fe 1 ( )\" # sin h Mz \u00bc FxFy K 0 y \u00fe bCys1l2h lh 3 l 4 tan a bCy d Cy \u00fe l2 3r2Ky Fys2 l2h l lh 3 s2l2h 4l l 4 \u00fe s2lh 6 \u00fe n\u00fe 1 n 2nFzld ln\u00fe 1 l 2 n\u00fe 1 l lh\u00f0 \u00de\u00fe l 2 n l2 l2h 2 1 n\u00fe 2 l 2 n\u00fe 2 lh l 2 n\u00fe 2 ( )\" # sin h \u00f011:130\u00de where sh is determined according to n\u00fe 1 n 2nFzls ln\u00fe 1b l 2 n lh l 2 n \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cxslh\u00f0 \u00de2 \u00feC2 y lhs1 tan a d Cy \u00fe l2 3r2Ky Fys2 lh l 1 s2 lh l 2 s : \u00f011:131\u00de Note that lh = 0 is used in the case that lh < 0. The effective slip angle a is smaller than the slip angle of the wheel a0 owing to the torsional deformation of the tire caused due to the self-aligning torque. The effective slip angle a is given by Eq. (11.68). (2) Example calculations The computational flow when calculating the side force, fore\u2013aft force and self-aligning torque is the same as that in Sect. 11.2. Sakai [2] calculated the side force and self-aligning torque with lateral and fore\u2013aft forces as shown in Figs. 11.34 and 11.35. The parameters used in the calculation are the contact length (l = 100 mm), contact width (b = 120 mm), radius of the tire (r = 270 mm), shear spring rate of the tread (Cx = Cy = 100 MPa/m), inflation pressure (Fz = 3 kN), velocity (V = 60 km/h), fundamental lateral spring rate of the sidewall (ks = 158 kN/m2), lateral spring rate of the tire (Ky = 50 kN/m), bending rigidity (EIz = 2.5 kNm2), torsional spring rate of the tire (Rmz = 10 kNm/rad), friction coefficient (ls = 1.1, ld = 0.8), friction decreasing constant (aV = 0.005) and inflation pressure (200 kPa) related to the lateral fundamental spring rate of the carcass. The drawback of the friction ellipse (i.e., that the ellipse cannot express cornering properties at a large slip ratio) can be solved using Sakai\u2019s theory. 754 11 Cornering Properties of Tires However, Sakai\u2019s theory for a large slip angle and large slip ratio still predicts that the cornering force in the braking condition is stronger than that in the driving condition. Measurements presented in Fig. 11.29 show the opposite relation. This may be because Sakai\u2019s model assumes that the contact pressure distribution does not change even under the fore\u2013aft forces. 11.4 Cornering Properties for a Large \u2026 755"
        ]
    },
    {
        "image_filename": "designv10_2_0000208_tvt.2019.2955020-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000208_tvt.2019.2955020-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed and body-fixed coordinate systems.",
        "texts": [
            " Section V is the fixed-time disturbance observer and discussion of the influence of disturbance on the sway. Numerical simulations and discussions are given in Section VI. II. System modeling and objective A. Kinematic model The configuration of a USV (i.e., the position and orientation) can be described by six independent coordinates, or six degree of freedoms (DOFs), i.e., surge, sway, heave, roll, pitch and yaw. For such USVs, an inertial frame {OG} and a body-fixed frame {OE} are used as depicted in Figure 1. It is common to reduce the six-DOFs (degree of freedom) model to a three-DOF one with the surge, sway and yaw, neglecting the heave, roll, and pitch, which is open loop stable for most USVs. Let u, v and r be the velocities in the surge, sway and yaw, respectively, and \u03b7 = [x, y, \u03c8]T , where [x, y] \u2208 R2 is the position of the vehicle in the inertial frame, and \u03c8 \u2208 [\u2212\u03c0, \u03c0] is the yaw angle of the USV relative to the geographic north. Then the model of the USV with nonholonomic constraints can be described as follows [6], x\u0307 = u cos\u03c8 \u2212 v sin\u03c8, y\u0307 = u sin\u03c8 + v cos\u03c8, \u03c8\u0307 = r, (1a)  u\u0307 = \u2212 d11 m11 u + m22 m11 vr + \u03c41[$1(t)] m11 + \u03be1, v\u0307 = \u2212 d22 m22 v \u2212 m11 m22 ur, r\u0307 = \u2212 d33 m33 r \u2212 m22 \u2212 m11 m33 uv + \u03c42[$2(t)] m33 + \u03be2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.44-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.44-1.png",
        "caption": "Fig. 7.44 Pressure dependence of friction",
        "texts": [
            "171) yields dQ \u00bc @ l\u00f0p\u00depf g @p p1 dp1s1 \u00fe @ l\u00f0p\u00depf g @p p2 dp2s2 0 \u00bc dp1s1 \u00fe dp2s2 : \u00f07:172\u00de Substituting the second equation of Eq. (7.172) into the first equation of Eq. (7.172), we obtain dQ \u00bc @ l\u00f0p\u00depf g @p p1 @ l\u00f0p\u00depf g @p p2 \" # dp1s1: \u00f07:173\u00de To maximize the frictional force Q, dQ should be positive. To make dQ positive, the sign of dp1 will be determined by the sign inside the parentheses [ ]. If \u2202{l(p)p}/ \u2202p monotonically decreases or l(p)p is convex with respect to p, the sign inside the parentheses [ ] is positive when p1 is smaller than p2 as shown in Fig. 7.44. In this case, dp1 must be positive to make dF positive. Because the signs of dp1 and dp2 are opposite according to the second equation of Eq. (7.172), dp1 is positive and dp2 is negative. In other words, if the value of p1 increases and the value of p2 decreases, Q increases. If we continue these iterations, p1 equals p2 andQ becomes a maximum. When the level of convexity of l(p)p is higher, the increase in the frictional force due to the uniform pressure distribution is larger judging from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure1-1.png",
        "caption": "Fig. 1. Application of face-gear drive in helicopter transmission.",
        "texts": [
            " Tooth contact analysis and stress analysis have been performed for both versions of geometry for their comparison. The following new advantages of the new design have been confirmed: (i) existence of a longitudinal bearing contact, (ii) avoidance of edge contact, and (iii) reduction of contact stresses. Numerical examples illustrate the developed theory. 2002 Elsevier Science Ltd. All rights reserved. A face-gear drive with a spur pinion wherein their axes are intersected is considered. Face-gear drives have been successfully applied in helicopter transmissions. The advantages of such application (Fig. 1) are the possibility of the split of the torque and reduction of weight. Two versions of geometry are considered: (i) version 1 that is based on application of a spur involute pinion, and (ii) version 2 based on application of a pinion with non-involute profiles (see Sections 2 and 3). The second version is proposed for the purpose of reduction of contact stresses and improvement of bearing contact. A substantial step in the technology of face-gear drives is the development of grinding (and hobbing) of face-gears by a grinding worm (a hob, respectively) [10]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000854_tfuzz.2020.3022570-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000854_tfuzz.2020.3022570-Figure11-1.png",
        "caption": "Fig. 11. Tripled inverted pendulums.",
        "texts": [
            " In addition, we can also see that the developed control algorithm has less energy consumption and fast convergence rates. Authorized licensed use limited to: Carleton University. Downloaded on September 13,2020 at 08:22:00 UTC from IEEE Xplore. Restrictions apply. 1063-6706 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Example 2 [13]: To further explain the feasibility of the developed control method, consider the tripled inverted pendulums from [13] given in Fig. 11. The dynamic equations are described as follows: \u03b8\u03081 = g L sin \u03b81 + u1 + K1\u03c3 2 M1L2 (sin \u03b82 cos \u03b82 \u2212 sin \u03b81 cos \u03b81) ; (81) \u03b8\u03082 = g L sin \u03b82 + 0.7u2 + K1\u03c3 2 M2L2 (sin \u03b81 cos \u03b81 \u2212 sin \u03b82 cos \u03b82) + K2\u03c3 2 M2L2 (sin \u03b83 cos \u03b83 \u2212 sin \u03b82 cos \u03b82) ; (82) \u03b8\u03083 = g L sin \u03b83 + 1.2u3 + K2\u03c3 2 M3L2 (sin \u03b82 cos \u03b82 \u2212 sin \u03b83 cos \u03b83) , (83) where \u03b8i(i = 1, 2, 3) are the angles of the ith pendulum, Mi = 5kg are the mass of the ith rod, g = 9.81m/s2 is the gravitational acceleration, \u03c3 = 0.25m is the distance from the pivot to the center of gravity of the rod, L = 1m is the length of each rod, ui are the inputs of the systems, Ki = 1N/m3 are the spring constants"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure10.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure10.1-1.png",
        "caption": "Fig. 10.1S(a) Invariant torus of coupled van dec Pol oscillators b=O, E = O. 1 Viewpoint (1.4,-2.6,-1.8)",
        "texts": [
            "63) in polar co-ordinates is expressed as follows: YI = rcosS, Y2 = rsinS f = Er( A-jr2) S = 1 + 31': r2 S The coefficients of the intermediate co-ordinate transformations are 31': -I': -31': -I': clO = COl =0,C21 =C12 =8' dlO = dOl =4\u00b7d21 =-S-\u00b7dI2 =g (10.65) respectively. The asymptotic solution of eq. (10.65) could also be obtained if we trace back all the nearly identity co-ordinate transformations x = I':a(-A + l....-a 2) cosS + ~al cos3S + (-a + 9E a l) sinS + ~al sin3S 32 32 32 32 (10.66) where the constant a denotes the amplitude defined by the initial condition. Further discussion of the normal-form amplitude eq. of(11.56) reveals the Hopfbifurcation of the Duffing-van der Pol equation on the parametric plane r-A.. As shown in Fig. 10.1, a spiral sink exists at (0,0) +\" 12 \" ~r, Source Sink Centre LimitCyc!e ).,<0 ).,=0 ).,>0 Computational Methods 359 for /<0 and a source at (0,0) surrounded by a limit cycle for 1.>0. The limit cycle evolves continuously from the centre at (0,0) for J...=O. The Hopf bifurcation is of importance in situations where a flow-induced oscillator is subjected to flutters or self-exciting movements. In such circumstances, the orbits of the steady-state periodic solutions stay on the surface of the parabola rotated by A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003625_mssp.2002.1483-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003625_mssp.2002.1483-Figure4-1.png",
        "caption": "Figure 4. Schematic of the test system.",
        "texts": [
            " It can be seen from the figure that most of the fatigue life is consumed by the period of material damage, i.e. the crack initiation phase. It is also observed that the time period associated with crack propagation and spalling is relatively short. Over this period, the signature of vibration response shows an abrupt and intense change. This conclusion agrees with the experimental results presented by [22, 23, 42, 43]. 3.2. MODELVERIFICATION WITH EXPERIMENTAL INVESTIGATION Bearing life tests were performed to validate the proposed methodology. The experimental set-up, as shown in Fig. 4, had three sub-systems: a test housing system, an oil circulation system, and a data acquisition and processing system. The radial load was provided by a hydraulic hand-pump (Power Team P59) that pressurised the load cylinder on the housing. The shaft was driven by a vector motor with a speed controller. The oil circulation system regulated the flow and temperature of the lubricant (ISO VG 32mineral oil). The bearing tested was Timken LM501310 cup (outer race) and LM501349 cone (inner race). It was a tapered roller bearing with a bore diameter of 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.72-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.72-1.png",
        "caption": "Fig. 10.72 Mode of tire cavity resonance. Reproduced from Ref. [71] with the permission of Tire Sci. Technol.",
        "texts": [
            " The transfer function between the axle force at the fixed wheel Fz and the excitation force at the tread ring Pw is obtained by substituting Z = 0 into Eq. (8.156): Fz=Pw \u00bc H52=H55: \u00f08:157\u00de Figure 8.15 shows the transfer function of Fz/Pw. Only the force generated by the first mode of the tread ring vibration will be transmitted to the wheel because the zeroth mode only causes the rotational motion of the wheel and the force generated 494 8 Tire Vibration by the high-frequency modes for n > 2 is not transmitted to the wheel owing to symmetry, which is a phenomenon similar to that shown in Fig. 10.72. Note that this is only true for the freely suspended tire\u2013wheel system because the loaded tire\u2013 wheel system loses its axisymmetry owing to the deformation of the contact region and the vibration modes of the tread ring for n > 2 will be transmitted to the wheel. Figure 8.16 shows transfer functions H22 (i.e., the radial displacement response of the tread ring to the radial force excitation of the tread ring) for a freely suspended tire\u2013wheel system. Because this is the transfer function of the force on the tread ring to the displacement on the tread ring, the vibration modes for n > 2 are transmitted",
            "101) and employing the Rayleigh\u2013Ritz method, the natural frequency f of a loaded tire is obtained as f \u00bc 1 2pr ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E q R 2p 0 \u00f0A\u00feDA\u00de\u00f0 r\u00feDr\u00de @U\u00f0h\u00de @h 2 dhR 2p 0 \u00f0A\u00feDA\u00de\u00f0 r\u00feDr\u00de3U\u00f0h\u00de2dh vuuut ; \u00f010:104\u00de where U is the natural mode shape of an angular displacement and a function of h. We are interested in only the first mode of U expressed by sin h or cos h, because the modes higher than the first mode do not contribute to the force on the wheel axis as shown in Fig. 10.72. Phases marked with a plus sign have forces that act radially inward; those marked with a negative sign have forces that act radially outward. The directions of the force vectors show that the wheel is excited vertically in the first mode of vibration, but the force vectors cancel out in the second and third modes, so no excitation is applied to the wheel. Therefore, only the first cavity mode resonance affects road noise. Substituting Eq. (10.103) into Eq. (10.104), ignoring terms of rank higher than the second power and using the orthogonality of a trigonometric function, the natural frequency for sin h mode is obtained as 10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000025_j.jmsy.2020.06.019-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000025_j.jmsy.2020.06.019-Figure2-1.png",
        "caption": "Fig. 2. CI parameters transferred among various sub-functional modules.",
        "texts": [
            " With the change of parameters, the models in the three modules are adaptively updated and optimized, which are considered as the core driving force for the operation of the DT system. E Connection Model The above four parts are connected in pairs to conduct efficient data transmission, so as to realize real-time interaction to ensure consistency among various models and accelerate iterative optimization. 3. Machinability improvement for five-axis flank milling CI parametric model is pretty significant for the DT model due to not only the connected various sub-modules in the virtual model, but also the vector of DT data. MS, SGV and SSL are taken as parameters (as shown in Fig. 2) to set up a parametric geometric modeling platform. The presented parametric platform facilitates the presented parameters to be transferred among various functional modules rapidly and effectively based on the previous researches of our group [39]. An integrated acquisition, together with contact and non-contact methods is employed. SGVs are identified and their boundary points are defined. After the uniform partition of SGV segments, the sequent equant-points along spanwise direction are packaged to fit SSL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003254_3-540-45000-9_8-Figure3.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003254_3-540-45000-9_8-Figure3.1-1.png",
        "caption": "Figure 3.1. Relevant variables for the unicycle (top view)",
        "texts": [
            "2) where the columns gi, i = 1, . . . ,m, of the n\u00d7m matrix G(q) are chosen so as to span the null space of matrix A(q). Different choices are possible for G, according to the physical interpretation that can be given to the \u2018weights\u2019 w1, . . . , wm. Equation (3.2), which is called the (first-order) kinematic model of the system, represents a driftless nonlinear system. The simplest model of a nonholonomic WMR is that of the unicycle, which corresponds to a single upright wheel rolling on the plane (top view in Figure 3.1). The generalised coordinates are q = (x, y, \u03b8) \u2208 Q = IR2 \u00d7 SO1 (n = 3). The constraint that the wheel cannot slip in the lateral direction is given in the form (3.1) as x\u0307 sin \u03b8 \u2212 y\u0307 cos \u03b8 = 0. A kinematic model is thus  x\u0307 y\u0307 \u03b8\u0307   = g1(q)v + g2(q)\u03c9 =   cos \u03b8 sin \u03b8 0   v +   0 0 1  \u03c9, (3.3) where v and \u03c9 (respectively, the linear velocity of the wheel and its angular velocity around the vertical axis) are assumed as available control inputs (m = 2). As we will show in Section 4, this model is equivalent to that of SuperMARIO",
            " However, when matrixG(q) in (3.2) has full column rank,m equations can always be transformed via feedback into simple integrators (input-output linearisation and decoupling). The choice of the linearising outputs is not unique and can be accommodated for special purposes. An interesting example is the following. Define the two outputs as y1 = x+ b cos \u03b8 y2 = y + b sin \u03b8, with b 6= 0, i.e. the Cartesian coordinates of a point B displaced at a distance b along the main axis of the unicycle (see Figure 3.1). Using the globally defined state feedback[ v \u03c9 ] = [ cos \u03b8 sin \u03b8 \u2212 sin \u03b8/b cos \u03b8/b ][ u1 u2 ] , the unicycle is equivalent to y\u03071 = u1 y\u03072 = u2 \u03b8\u0307 = u2 cos \u03b8 \u2212 u1 sin \u03b8 b . As a consequence, a linear feedback controller for u = (u1, u2) will make the point B track any reference trajectory, even with discontinuous tangent to the path (e.g. a square without stopping at corners). Moreover, it is easy to show that the internal state evolution \u03b8(t) is bounded. This approach, however, will not be pursued in this chapter because of its limited interest for more general kinematics",
            " It has been shown that a two-input driftless nonholonomic system with up to n = 4 generalised coordinates can always be transformed in chained form by static feedback transformation [23]. As a matter of fact, most (but not all) WMRs can be transformed in chained form. For the kinematic model (3.3) of the unicycle, we introduce the following globally defined coordinate transformation z1 = \u03b8 z2 = x cos \u03b8 + y sin \u03b8 z3 = x sin \u03b8 \u2212 y cos \u03b8 and static state feedback v = u2 + z3u1 \u03c9 = u1, (3.8) obtaining z\u03071 = u1 z\u03072 = u2 z\u03073 = z2u1. (3.9) Note that (z2, z3) is the position of the unicycle in a rotating left-handed frame having the z2 axis aligned with the vehicle orientation (see Figure 3.1). Equation (3.9) is another example of static input-output linearisation, with z1 and z2 as linearising outputs. We note also that the transformation in chained form is not unique (see, e.g. [9]). The experimental comparison of the control methods to be reviewed in this chapter has been performed on the mobile robot SuperMARIO, built in the Robotics Laboratory of our Department (Figure 4.1). SuperMARIO is a two-wheel differentially-driven vehicle, a mobility configuration found in many wheeled mobile robots"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.18-1.png",
        "caption": "Fig. 8.18 Transfer function under the axle\u2013free condition determined by two frequency response functions. Reproduced from Ref. [25] with the permission of Tire Sci. Technol",
        "texts": [
            " It is therefore important to include the DOFs of the wheel mass using the so-called free\u2013 free condition in theoretical analysis or laboratory tests on tire vibrations. A comparison of Fig. 8.17b with Fig. 8.15 reveals that the vibration modes of a tread ring for n > 2 will be transmitted to the wheel in Fig. 8.17b owing to the contact boundary condition or the prescribed displacement. The easiest way to identify the transfer function under the axle\u2013free condition is to measure two frequency response functions [25]. The transfer function between the wheel axle and the contact patch is given by (left figure of Fig. 8.18) 498 8 Tire Vibration Fz FFP1 .. . FFPN 8>< >>: 9>= >>; \u00bc G\u00f0x\u00de H1\u00f0x\u00de HN\u00f0x\u00de H21 H22 H2N .. . .. . .. . .. . HN1 HN2 HNN 2 6664 3 7775 Z W1 .. . WN 8>< >>: 9>= >>;; \u00f08:164\u00de where Fz is the axle force, FFPi is the contact force at the i-th node, Z is the axle displacement in the vertical direction, Wi is the vertical displacement of the i-th node in the contact area, Hi(x) denotes the transfer functions between the vertical force response on the wheel and the vertical displacement excitation on the contact patch with frequency x for the fixed wheel (Z = 0), G(x) is the transfer function between the vertical force response on the wheel and the vertical displacement excitation on the wheel with frequency x for the fixed contact area (Wi = 0), and Hij denotes other transfer functions",
            " These transfer functions can be determined by conducting two experiments. One experiment involves the tread surface excitation of a tire with a fixed axis, while the other involves the wheel axis excitation of a tire with a fixed contact area. Once the transfer functions are determined, the axle force under the axle\u2013free condition Fz can be expressed as the summation of the force F 1\u00f0 \u00de z due to road unevenness with the fixed wheel and the force F 2\u00f0 \u00de z due to the motion of a wheel without excitation from the road (right figure of Fig. 8.18): Fz \u00bc F\u00f01\u00de z \u00feF\u00f02\u00de z F\u00f01\u00de z \u00bcP i Hi\u00f0x\u00deWi F\u00f02\u00de z \u00bc G\u00f0x\u00deZ: \u00f08:165\u00de Using Eq. (8.165), the transfer function of Fz/Wi under the axle\u2013free condition can be easily obtained. 8.3 Frequency Response Function of Tires 499 The properties of a tire rolling over cleats are related to the ride harshness of a vehicle. In early studies, ride harshness was analyzed using the envelope properties of a tire, which were calculated from the mechanics of the composite material [26] and the line stiffness discussed in Chap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003838_s0301-679x(03)00094-x-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003838_s0301-679x(03)00094-x-Figure5-1.png",
        "caption": "Fig. 5. Ball bearings with grooved rings similar to modern deepgroove ball bearings.",
        "texts": [
            " When decreasing the speed from 1150 rpm, Stri- beck noticed that the friction was lower than during the speed increase despite almost constant temperature. He assumed that the friction decrease was due to running in of the surfaces, as this phenomenon was much stronger for rough surfaces than for polished surfaces, where the friction was not changed by running in. Stribeck ran tests with five different types of contact geometry for ball bearings and found that a deep-groove ball bearing with open osculation had the lowest coefficient of friction, 0.0015, of the tested types, see Fig. 5. For that bearing the largest allowable ball load was 11\u00b7d2 kg where d was the ball diameter in eighths of an inch. That shows the material development the last 100 years. The maximum load to avoid plastic deformation then was 3100 N on a diameter 17 mm ball. Today, the ball load is 10,000 N for infinite life. Stribeck also ran endurance tests and detected that also small variations in material hardness had a large influence on life. As soon as a plastically deformed rolling track was visible, the bearing life was short"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure12-1.png",
        "caption": "Fig. 12. The configuration with an intersection and four parallel axes. (a) The configuration (b) Its prototype.",
        "texts": [
            " To sum up, when the constraint screw has no meaning, the constraints emerge mutations and then these specific configurations need to be emphasized. Whether the mechanism occurs constraint singularity is further determined by the rank of the constraint-screw system [60\u201362] . When the wrench space spanned by the constraint wrenches of all limbs loses rank, the mechanism lies in singular configurations. It is noted that constraint singularity often provides furcation points [39] . In this section, motion characteristics of various special positions with distinct parametric constraints are explored. Fig. 12 shows the configuration with parametric constraints \u03b1 = 0 , \u03b2 = 0 , which point O is the intersection of joints E, F, G, and H, the axes of joints B 1 , B 2 , B 3 and B 4 are parallel with each other. A global coordinate frame O-XYZ is attached at point O. Screws are illustrated in Fig. 12 (a) to indicate joint axes. Similarly, the corresponding constraint-screw multiset \u3008 S r \u3009 can be derived as follows: S r l1 = { S r 11 = ( \u2212 c \u03b8+ s \u03b8 c \u03b8\u2212s \u03b8 , 1 , 0 , 0 , 0 , b c \u03b8\u2212s \u03b8 )T S r 12 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T } S r l2 = { S r 21 = ( \u2212 c \u03b8+ s \u03b8 c \u03b8\u2212s \u03b8 , 1 , 0 , 0 , 0 , \u2212 b c \u03b8\u2212s \u03b8 )T S r 22 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T } (14) where b is the distance from the origin O to the axis of joint B 1 , \u03b8 denotes the angle between the X-axis and axis of joint B . 1 Apparently, the number of independent loops l is 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003314_tia.2003.821816-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003314_tia.2003.821816-Figure15-1.png",
        "caption": "Fig. 15. Drive system of a bearingless switched reluctance motor.",
        "texts": [
            " The length of magnetic paths of the axial permeance is very long in comparison with the gap permeance . Thus, the derivative of with respect to the rotor displacement can be ignored. Therefore, the radial force , and the total torque produced by the phase can be derived by substituting (27), (32)\u2013(35), and (38) into (5)\u2013(7), respectively, as (39) (40) (41) Although it is necessary to carry out (39)\u2013(41) with a branching method based on the approximate lines I V, the radial force and the torque operating in a region of magnetic saturation can be calculated in real time by (39)\u2013(41). Fig. 15 shows the drive system of a bearingless switched reluctance motor controlling average torque with square-wave currents in the motor main windings [10]. The rotor displacements , are detected by the gap sensors, respectively. These displacements are compared to the displacement commands and . The radial force commands and are generated magnetomotive forceM = 280 At of rated value. by the proportional\u2013integral\u2013derivative (PID) controllers. In the controller of the radial force winding currents, the radial force commands and are transformed into the magnetomotive force commands of the radial force windings by means of the inverse functions of (39) and (40)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.71-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.71-1.png",
        "caption": "Fig. 12.71 Pattern of a studless tire [103]",
        "texts": [
            " After the use of studded tires was prohibited in Japan in 1990, winter tires without studs but with many sipes, called studless tires, were developed in Japan. The sedimentation of dust decreased but the winter-specific accidents increased as studless Temperature (\u00b0C) D ep th o f q ua si -li qu id la ye r ( \u212b) 20 40 60 0 0 \u22121 \u22123 \u22124 \u22125 \u22126 \u22127 \u22122 Fig. 12.67 Depth of the quasi-liquid layer versus temperature (reproduced from Ref. [94] with the permission of Hokkaido University Press) 12.4 Traction on Ice 863 tires were increasingly adopted as shown in Fig. 12.70. An example of a studless tire is shown in Fig. 12.71. Because studded tires have been prohibited in many countries, studies on friction on ice have been conducted in northeast Asia and Europe. Japanese research has concentrated on increasing the friction coefficient on ice rather than the tire performance on snow because it is difficult to drive a vehicle on ice. Additionally, the interaction between ice and the tire surface can be observed through ice using an indoor apparatus. Such observation is not possible for the interaction of a tire and snow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.104-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.104-1.png",
        "caption": "Fig. 5.104: Contact Configuration of Push Belt Elements",
        "texts": [
            "0 about 3000 elements enter and leave the pulleys in every second thus generating a polygonal frequency of 3 kHz. The lowest \u201ceigenfrequency\u201d is around 120 Hz for the overall system. In the following we shall consider only the plane case, the spatial case is still a matter of ongoing research. For establishing a realistic model we need multibody system theory including rigid and elastic components together with bilateral and unilateral constraints. The contacts of push belts are numerous and more complicated than chain contacts, see Figure 5.104. We have a uni- lateral spatial contact between the element and the pulley, a plane unilateral contact between the element and the ring and five contacts between the elements themselves. The last ones are covered by an empirical nonlinear force law. All other contacts are unilateral contacts described by complementarities, then converted and solved by prox-functions [82], [81]. The push belt CVT consists of a force transmitting push belt and two pulleys (primary and secondary pulley). The pulleys are pairs of sheaves, where one sheave is fixed onto the shaft and the second sheave can be shifted hydraulically in axial direction. Figure 5.104 shows the functionality of the CVT for two extreme transmission ratios, where \u03c9 denotes the angular velocity, M the torque and Q the hydraulic force. Power is induced into the CVT from the combustion engine over a torque converter. Within the CVT, power is transmitted from the primary to the secondary pulley in the following way: at the primary pulley, power is conveyed by friction in the contact pulley - push belt. Next a transformation by tension and push forces within the push belt itself takes place",
            " The elastic pulley model follows more or less the same ideas as those used for the rocker pin chain. Pulley deformations and the contacts with the belt elements are similar. The pulley sheaves are modeled by rigid cones. For both cones we approximate the deformation by quasistatic force laws given by the Maxwell numbers. External excitations coming from the CVT environment and acting on the pulleys are taken into account. At the primary pulley a kinematic excitation is given by an angular velocity \u03c9prim (see Fig. 5.104). Accordingly, this pulley has no degree of freedom. At the secondary pulley a kinetic excitation is applied in form of an external torque Msec. Accordingly, this pulley has one degree of freedom qp = (\u03b1sec) T , which is an angle of rotation. The pulley equations of motion write Mpu\u0307p = hp +W p \u03bb (5.148) with the positive definite, constant and diagonal mass matrixMp. The vector hp is only depending on the time t: hp = hp(t). Thus the matrices \u2202 hp \u2202 qp and \u2202 hp \u2202 up used for the numerical integration are zero matrices [81]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000880_j.addma.2020.101324-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000880_j.addma.2020.101324-Figure1-1.png",
        "caption": "Fig. 1. Test bench setup for recording acoustic emissions in the L-PBF process.",
        "texts": [
            "3 focuses on the data processing of the raw acoustic signal. Reference measurements for evaluating the density of each cube are performed and explained in Section 3.4 to obtain a data set for a supervised learning approach. An introduction to the ANN design itself is given in Section 3.5. It is necessary to integrate a sensor as close as possible to the process zone in order to test the abilities of an SBAE approach in the L-PBF process. For this purpose, a test setup was built for this work and introduced by Eschner et al. [56]. Fig. 1 shows a view across sections of the test setup. The following section describes the setup and relevant components. A continuous wave (CW) laser system provided by OR LASER with a wave length of 1064 nm and a peak power of 250 W, Gaussian beam profile and Raylase scan optics is used in the optical setup. The inert gas flow over the process zone is realized with the help of additive manufactured outlets and inlets (marked green in Fig. 1). A system provided by ULT AG filters particles from the inert gas and allows the inert gas to circulate via a controllable pump. An O2 sensor (Microx Oxygen Analyzer) is integrated into the inert gas flow to measure the O2 level. In the build chamber (see sketch in Fig. 1), a simple recoater system wipes the powder from the reservoir to the built platform with a metalsupported rubber lip (marked dark red in Fig. 1). Stepper motors in the micro-stepping mode control the movement of all parts (a lip, coating, powder reservoir, built platform). All parts are placed in a sealed chamber, which guarantees inert process conditions. The whole system (motors, scanner, and laser) is controlled by LabView, which offers a high degree of freedom for adjusting the process parameters. Regarding the material, 316 L (1.4404) is employed as it is a commonly used stainless steel alloy for L-PBF, but having a high demand for monitoring techniques, since it is more challenging to make post process CT scans due to the high material density. The powder is supplied in one batch by the company M4P. The powder is not reused in order to avoid contamination from spatters and to ensure consistent powder parameters throughout all experiments. Below the build platform (marked yellow in Fig. 1) of the process zone, an acoustic sensor (marked blue in Fig. 1) is mounted with a bolt. Glycerine is used as a coupling agent in order to guarantee a reproducible coupling. The sensor used is a massless piezoceramic sensor provided by QASS (model number: Q-WT-19 0232). A sampling rate of 4 MHz is used for the performed experiments. Preliminary tests showed that there are no relevant signals above 2 MHz, which also is in accordance with the findings mentioned in Section 2.1. Specimens with different density levels are built to find out if the monitoring system is capable of evaluating different densities"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.16-1.png",
        "caption": "Fig. 8.16: Hip Joint Design [85]",
        "texts": [
            " Therefore, encoders and tachometers, six-component-force-torque-sensors and an inertial platform are needed. Quantities like friction, which are not measured, can be estimated by observers. Altogether the most important requirements are as follows: size 1.80 m weight < 50 kg max. speed 0.5 \u2013 1.0 m/s configuration humanlike degrees of freedom leg 6 DOF foot (internal) 4 \u2013 8 DOF sensors encoders force-torque-sensors inertial platform actuators Neodym-Bor-DC-Motors Harmonic Drives Gears Ball Screws In the following we shall consider some more details concerning the hardware selection. Figure 8.16 shows a sectional view of the final version of the hip joint. The actuation for the yaw and roll axis are arranged coaxially with the joint axis and are integrated in the aluminum structure. The yaw joint is inclined 15 degrees with respect to the pelvis. This leads to a better power distribution among the four hip motors. The pitch joint is actuated with two motors via a timing belt. The employed gear has a modified Circular Spline, which is T-shaped in order to reduce weight. Further, an aluminum Wave Generator with optimized shape is included"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003486_robot.1996.509284-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003486_robot.1996.509284-Figure12-1.png",
        "caption": "Figure 12: The 2-type 3-1-type 2 mechanism",
        "texts": [
            " Using the notation of figure 6 we write first that A2 belongs to the line coming from the platform: ( rcose + ccos(8 + al) - u)sin(8 + a2) - ( r s in6 + csin(8 + al)) cos(@ + ag) = 0 (12) Then we write that point B3 should be at distance 1-3 from A3: (Tcos8 + acos(8 + a3) - + (T sin 8 + a sin(8 + a3) - = ri (13) We use the linear equation (12) to compute r which is then back substituted in equation (13), now an equation in the sine and cosine of 8. We get then a fourthorder polynomial in T = tan(f?/2). 2.3.6 This mechanism is presented in figure 12. As the pos- 2-type 3 and 1 type 2 sible positions for B3 are obtained as the intersection of the coupler curve of A1 B1 B3BgA2 with the line going through A3 from chain 3 we will clearly get at most four intersection points. Equation (12) is still valid. We write now that point B3 belongs to the line: ( r cos8 + acos(8 + a3) - ul)uy - ( r s in8 + asin(0 + a3) - w1)2r, = 0 (14) We use the linear equation (12) to compute r which is then back substituted in equation (13), now an equation in the sine and cosine of 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.8-1.png",
        "caption": "Fig. 6.8: Mach-Zehnder interferometer. According to [Fisch91]",
        "texts": [
            " The following dimensions and performance data were re ported: a diaphragm diameter of 1.2 mm and a thickness of 3 ~-tm; a resonator length of 100 ~-tm and a thickness of 0.5 ~-tm; a maximum diaphragm lift of 0.7 ~-tm; a pressure range of up to 1000 Pa; an accuracy of 0.01 Pa and a slight non-linearity of 0.1 %. Mach-Zehnder interferometer Many physical quantities can be measured by optical sensors, making use of the change of light which is sent through fiber optical cables, Fig. 6.2. A so called Mach-Zehnder interferometer is proposed as a pressure sensor, Fig. 6.8. Laser light is brought into the device by a fiber optical cable. The light is split and channeled via two waveguides to a photodiode. One of the light branches crosses a microstructured membrane which can be exposed to external pressure. The light beam in the other branch remains unchanged and serves as a reference signal. The two light beams are brought back together again to the photodiode. When the sensor membrane is actuated by pressure, the waveguide deforms and changes the properties of the light beam",
            " Attempts have been made to produce the pellistor micromechanically from silicon, but the high working tempera tures of up to 700\u00b0C caused serious problems [Gal191 ]. Optical sensor principle As already mentioned earlier, microoptics play an important role in many microsensors. Chemical sensors can also make use of various optical prin ciples. These sensors have several advantages, they are inexpensive, easy to sterilize, can accomodate small samples and are highly sensitive. In general, planar integrated microoptical chips in the form of an interferometer or a coupling grid are used. An optical interferometer was described in Section 6.2 (Fig. 6.8). Figure 6.31 shows the function of a coupling grid detector. Coupling grid Detector Fig. 6.31: Function of a coupling grid structure. According to [Krull93] photodiode sensor. The substance to be analyzed has direct contact with the waveguide, which changes its index of refraction . The amount of light striking the sensor is proportional to the concentration of the substance. Field effect transistor sensor principle Ion-sensitive field effect transistors are used to measure the concentration of ions of various elements such as hydrogen, sodium, potassium or calcium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.32-1.png",
        "caption": "Fig. 8.32",
        "texts": [
            " The difference is that it is formed by heteroclinic structure instead of homoclinic structure; for example, U1 , according to Fig. 8.30(a). These four lines, the unstable and stable manifolds which go from US forward or backward to the vicinity of U1 , and the two invariant manifolds from U2 , build the bar at U1\u2022 If the initial value is in these bars and the four invariant manifolds of U1 (it has not been drawn), after accumulative iterations of <p5, these points will drift in these regions. Such regions constitute the chaotic river network. Just as in Fig. 8.32(b), the width of the river is amplified by a few orders of magnitude. Actually, it is very difficult to locate the point exactly in the chaotic river because the value of J..l is close to 2. An important fact is that these river networks form five small islands around the stable periodic points. on this island. These rivers do not connect with the chaos sea outside. They are the internal rivers on the central large island, see Fig. 8.31. Even if the solution drifts in the chaos river, it is still bounded on the whole and in some sense it can be said to be stable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure12-1.png",
        "caption": "Fig. 12 Coordinate systems Sr and Sp",
        "texts": [
            " System Sm defines the machine lane and the machine center. System Ss is connected to the sliding base element 11 and repesents its translating motion. System Sr Fig. 10 is connected to he machine element 10 and represents the machine root angle etting. System Sc Fig. 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter. System Sp is connected to the machine element 9 and represents he work head setting motion Fig. 12 . System So is connected to he machine element 8 and represents the work head offset setting ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 motion Fig. 13 . Sw is connected to the work 8 and represents the work rotation with angular parameter Fig. 14 . System Se is connected to the eccentric setting element and represents the radial setting Fig. 15 . System Sj is connected to the tilt wedge base element which performs rotation relatively to the eccentric element to set the swivel angle j Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003943_tmag.2004.825185-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003943_tmag.2004.825185-Figure4-1.png",
        "caption": "Fig. 4. Finite-element mesh of the motor used in calculations.",
        "texts": [
            " Define a vector including angular displacements of consecutive slices: . Due to cross linkage fluxes, the torque density is not constant along the motor axis. It can be assumed that the th PM slice, where generates the cogging torque , which can be approximated as (1) where area under the th segment of the torque density curve along the direction; total area under the torque density curve along the direction; weighting coefficient (see Fig. 3); angular variation of cogging torque determined from 3-D model (see Fig. 4). The quantities and are determined from the standard 3-D finite-element field model by integration of an appropriate component of the Maxwell stress tensor over the surface of each 0018-9464/04$20.00 \u00a9 2004 IEEE pole slice for the basic configuration of PM poles (all slices in aligned position) [2]. In addition, the cogging torque variation is determined by integration of Maxwell stresses over the rotor surface for the same case. In this paper, a new two-phase outer-rotor brushless dc motor with the geometry shown in Fig. 3 is considered, whereas Fig. 4 presents the finite-element mesh of the machine used in calculations. The generalized scalar potential (GSP) formulation was used for determining of magnetic field distribution. Variation of the quantity versus motor length is dependent on machine geometry. In general, it can be approximated with a stairs-like function. For the considered motor, the weighting coefficient as well as the angular variation of cogging torque are plotted in Figs. 5 and 6, respectively. According to the earlier assumptions, for any configuration of PM poles, the overall cogging torque is composed of elementary torques produced by each pole slice shifted by the angle (2) Although the cogging torque values obtained from this model are not very accurate, they are useful to indicate a direction of change in the cogging torque while rearranging pole shape in the optimization process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure13-1.png",
        "caption": "Fig. 13. The configuration with a set of parallel axes and two collinear axes.",
        "texts": [
            " Similarly, the corresponding constraint-screw multiset \u3008 S r \u3009 can be derived as follows: S r l1 = { S r 11 = ( \u2212 c \u03b8+ s \u03b8 c \u03b8\u2212s \u03b8 , 1 , 0 , 0 , 0 , b c \u03b8\u2212s \u03b8 )T S r 12 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T } S r l2 = { S r 21 = ( \u2212 c \u03b8+ s \u03b8 c \u03b8\u2212s \u03b8 , 1 , 0 , 0 , 0 , \u2212 b c \u03b8\u2212s \u03b8 )T S r 22 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T } (14) where b is the distance from the origin O to the axis of joint B 1 , \u03b8 denotes the angle between the X-axis and axis of joint B . 1 Apparently, the number of independent loops l is 1. According to Eqs. (9) and (10) , the cardinal number of the constraintscrew multiset card \u3008 S r \u3009 is 4, the dimension of the constraint-screw system dim S r is 3. Thus, the rank is changed, and the configuration with parametric constraints \u03b1 = 0 , \u03b2 = 0 is singular. Further, the mobility is m = 8 \u2212 6 \u00d7 1 + 4 \u2212 3 = 3 . In this singular configuration, the mechanism has three DOFs. Fig. 13 illustrates the geometrical relationship between the joints. The axes of joints E (G), F, and H are parallel, while axes of joints B 1 , B 2, and B 3 , B 4 are collinear, respectively. A global coordinate frame O-XYZ is established at point O. In order to utilize the extended mobility criterion [57\u201359] , an assumption is introduced. It means that the same number of individual joints exists where several axes of joints are collinear. Thus, the number of independent loops l is 1. The two sub-chains constraint-screw systems can be derived as follows: S r l1 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 11 = ( 0 , 0 , 0 , 0 , 1 , 0 ) T S r 12 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 13 = ( 0 , 0 , 1 , c, 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 21 = ( 0 , 0 , 0 , 0 , 1 , 0 ) T S r 22 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 23 = ( 0 , 0 , 1 , \u2212c, 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad (15) where c is the length of OO 1 in the Y-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001018_j.jmapro.2021.01.027-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001018_j.jmapro.2021.01.027-Figure10-1.png",
        "caption": "Fig. 10. a) Longitudinal cutting direction for outer surface morphology, b) Optical microscopy of an as-built horizontal sample, and c) an as-built vertical sample.",
        "texts": [
            " 6d) can result in anisotropy of the mechanical properties but there are other factors affecting the mechanical properties, especially in the as-built vertical. The different behaviour of vertical samples under two conditions of as-built and machined, Fig. 9b, may suggest that the interrelationship between the surface topography of the test pieces and the loading axis needs to be examined closely to verify if the build direction has any effect on the directionality of the valleys and hills of the roughness profile with respect to the loading axis. Fig. 10 shows the surface topography of the as-built horizontal and vertical samples prepared longitudinally with respect to the applied tensile load. The peaks to valleys patterns on the outer surface of the horizontal sample in Fig. 10b is completely different from those observed in the vertical samples, Fig. 10c. The wavelength (peak to peak distance) on the outer surface of horizontal samples is greater compared with that of the as-built vertical. The short wavelength of the asperities on the outer surface of an as-built vertical sample is mainly correlated to the 30 \u03bcm layer thickness. This short wavelength, beside the unfused layers near the outer surface of the as-built vertical sample, leads to sharp, deep valleys (notches), as can be seen from Fig. 10c. The sharp valleys on the surface of the as-built vertical sample could act as stress concentration points, magnifying the applied stress at the surface and thus encouraging crack initiation. The high level of stress may then guide the crack towards the centre at a faster rate, causing premature fracture. It is also possible that the induced residual stress along the build direction, which is the tension on the edge of sample [15,43], may contribute to the stress concentration at the sharp notches"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000952_j.cma.2021.113707-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000952_j.cma.2021.113707-Figure12-1.png",
        "caption": "Fig. 12. Steps of preparation for next particle layer for SLM.",
        "texts": [
            " Simulation of multi-layer SLM SLM is commonly based on a layered manufacturing process where a single layer of molten track is formed rom the metallic powders and is bonded to previous layers until the final object is completed [156], as illustrated n Fig. 11. This section further demonstrates the capacity of our proposed method in modeling multi-layer SLM rocess. The same set of model parameters as listed in Table 4 are used. We follow four steps to model the preparation for the next powder layer after melting the former layer. (1) emove the suspended portion (Fig. 12(a)) of the molten track due to the extremely high viscosity and Darcy\u2019s e s C ffects (Fig. 12(b)) that may adversely affect the subsequent layering process. These suspended parts refer to the patters observed in experiments which would cause the denudation zone if left uncleared [98]. The unresolved FD\u2013DEM with a large grid size (150 \u00b5m) as described in Section 2.1 is used in this step. (a) Replace the molten track in the CFD by fixed particles with the same diameter as the grid size to ensure accurate transformation of complex molten surfaces, as shown in Fig. 12(c). The replacement only applies to cells with a volume fraction1 larger than 0.5 where particles are in the center of cells. In doing so, the interaction between the powders and the solidified metal can be simplified as the collision between particles in the DEM. (3) Perform DEM simulation to bring all moving particles into an static equilibrium state (Fig. 12(d)), and use a roller to press and push the standby particles from the left side to the work area in the fourth step (Fig. 12(d)), finishing the layering process. (4) Apply laser beam and melt this new particle layer. The above four steps are repeated to simulate a multi-layer SLM process to finish a design product. Significant surface roughness along the edge of multi-layer molten tracks and apparent ripples are found in both our simulation results and SEM images of experimental tests [157] (Fig. 13). The surface roughness is composed of sticking powders, partially melted powders and discontinuities caused by balling effect [155]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.47-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.47-1.png",
        "caption": "Fig. 6.47: Tensioners of the Timing Chain of the Porsche 996 Engine",
        "texts": [
            " These factors decide amongst others a good design of a timing system, which has been shown in many examples from industry, for example those of the Figures 6.27 and 6.28, where significant design improvements could be achieved. 6.5 Hydraulic Tensioner Dynamics 395 As indicated already in the preceeding chapter, all timing chains of modern combustion engines are tensioned by certain hydraulic tensioners, which are applied at the chain guides. By providing these guides with some rotational joint the tensioner can act on the guide, and via the guide it can tighten the chain. Figure 6.47 illustrates a typical application, and it depicts also the curvature of the guides. These curvatures are useful for a space-adapted design, but moreover for a good contact of all chain links along the guide and thus for a good efficacy of the tensioners with regard to the chain vibrations. The larger influence on wear can be counterbalanced by suitable materials of the guides. The action principle of a hydraulic tensioner comes from the combination of a spring-loaded piston in combination with an oil-hydraulic system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003337_j.asd.2004.05.004-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003337_j.asd.2004.05.004-Figure1-1.png",
        "caption": "Fig. 1. A simple model of a stick insect leg. A stick insect leg consists of four functional segments: the coxa (cx), the femur (fe, which is fused to a very short segment, the trochanter), the tibia (ti) and the foot (or tarsus, ta). When the joint of the foot and the foot itself are neglected for simplicity, a stick insect leg can be modelled as a manipulator with three hinge joints, resulting in three degrees of freedom. From the body towards the foot, the joints are called the thorax\u2013coxa joint (TC), coxa\u2013trochanter joint (CT) and femur\u2013tibia joint (FT). The joint axes (solid arrows) account for protraction/retraction of the coxa (Pro/Re), depression/levation of the trochanter and femur (Dep/Lev), and flexion/extension of the tibia (Flx/Ext), respectively. Each step cycle can be divided into two states, the stance movement on the ground (dashed arrow) and swing movement through the air (dotted arrow). The state transitions occur at the anterior extreme position (AEP) and posterior extreme position (PEP).",
        "texts": [
            " Thus, two important aspects of biological motor control are \u2019embodiment\u2019 of the controller, and \u2019situatedness\u2019 of the body in its environment (e.g. Brooks, 1991; Pfeifer and Scheier, 2001). Whereas embodiment refers to the significance of the physical properties of the body for the controller, i.e. the central nervous system, situatedness refers to the significance of a feedback loop via the real world, e.g. the impact that the body-substrate interaction has on the performance of the walking animal. In a walking insect, at least three joints per leg have to be controlled (Fig. 1): the thorax\u2013coxa joint (TC-joint), the coxa\u2013trochanter joint (CT-joint) and femur\u2013tibia-joint (FT-joint). The CT- and FT-joints are simple hinge joints with one degree of freedom corresponding to levation/ depression of the femur and extension/flexion of the tibia, respectively, (Fig. 1). The TC-joint, which connects the leg to the body, is more complex, but most of its movement can be modelled by rotation around a slanted axis. In the stick insect the two Euler angles that define the axis of protraction/retraction of the leg vary only little during normal walking (Cruse and Bartling, 1995) and are typically assumed constant (e.g. in Cruse et al., 1995a,b, 1998). Thus, an insect has to control 18 joints in total, which, due to their simplicity, result in an equal number of degrees of freedom",
            " WALKNET is based on behavioural rules that have been derived from experimental studies on walking stick insects and crayfish (Cruse, 1990). It consists of a set of six single-leg controllers, each of which is built by a number of distinct modules, which are responsible for solving particular subtasks. Some of these modules might be regarded as being responsible for the control of special \u2019microbe- haviours\u2019: for example, a walking leg can be regarded as being in one of two mutually exclusive states, namely performing a swing movement or a stance movement (Fig. 1). During stance (or power stroke), the leg maintains ground contact and is retracted to propel the body forward, while supporting the weight of the body. During swing (or return stroke), the leg is lifted off the ground and moved in the direction of walking, to touch down at the location where the next stance should begin. Due to the rhythmicity of insect gaits (e.g. Wilson, 1966) and the alternating activation of antagonistic motoneuron groups in reduced preparations (e.g. Bu\u0308schges et al., 1995), the two states of the step cycle of each leg are often treated as two phases of the same central motor pattern",
            " This is possible because swing duration is constant in the animal (Graham, 1985), and velocity-control has no impact on the swing module of WALKNET. Controlling a swing movement is easier than controlling stance movement because a leg in swing is mechanically uncoupled from the environment and, due to its small mass, essentially uncoupled from the movement of the other legs. Therefore, whatever a leg does during a swing movement, it has virtually no impact on the movements of the other legs. According to Fig. 1, each stick insect leg can be modelled as a manipulator with three degrees of freedom of rotation. As physiological experiments have revealed that each one of these degrees of freedom may show only weak neural coupling to the two others (Ba\u0308ssler and Bu\u0308schges, 1998), the neural control network must have at least three pairs of motor outputs, one for each pair of antagonistic muscles per leg joint. For simplicity, each pair of these motor outputs is modelled in WALKNET as a single floating point variable, allowing both negative and positive output"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003884_robot.1990.126246-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003884_robot.1990.126246-Figure1-1.png",
        "caption": "Figure 1. The biped model.",
        "texts": [
            " In practice, implementation requires a feedback control law at the lower level to track the trajectory and to stabilize the walking trajectory, a topic which is beyond the scope of this study and will be treated elsewhere. The analysis described in this paper is based on a biped model consisting of a body (torso) and two legs. Each leg has three segments: thigh, shank, and sole, and has 6 degrees-of-freedom: 3 degrees-of-freedom (actuators) in the hip joint, 1 in the knee joint, and 2 in the ankle joint. Fig. 1 shows a schematic representation of this model where the center of mass (COM) of each segment, (Bi, i=l,..,7), is marked by a dot. The sequence and range of the joint movements for both legs are tabulated in Table I. The mass and geometric data of each segment are shown in Table II(a) and 0). In the rest of this paper, the origin 0 of the fixed reference coordinate B is located under the support leg on the ground as shown in Fig. 1. The X axis points to the forward direction, and Z axis points upward, and Y axis is cross product of the Z and X axis. The X-Z plane is the sagittal plane and X-Y plane is the horizontal plane. 2. Zero Moment Point When the biped is walking, forces acting on the mechanism are gravity, reaction force, and inertial forces. According to D'Alembert's Principle, if all forces are balanced, the motion of the biped is physically realizable. In this section, those forces and the torques acting on the ground and caused by the motions of the biped will be derived",
            " The trajectory of t t e hip in the supporting leg, denoted by (Xl, yl, Zl), is (12) T (13) yl(t) = A, cos(2~ 1) T Zl(t) = H (14) Xl(t) = s 1 where T = 4 T1 and -TI + T2 < t < TI- T4 . Because the supporting foot is located at the origin 0, x l , y1, and z l can be represented by the last three joints of the supporting leg. From Eq. (12), (13), and (14), it is sufficient to solve for these three joints of the supporting leg. From the kinematic relation, we obtain xf(t) + (zl(t)-d)'+~(t)- 1: - 1; 2 11 12 9fi(t) = cos -1 (15) ( 1 6 ) e:(t) = sin -1 - llsin(h)) - tan-l . J x m + (z(t)-d)2+yT,(t) .J (zi(t)-d)2+yf(t) (17) where d, 11, and 12 are defined in Fig. 1. Let the body rotate about the X-axis, its rolling angle be a shifted cosine function with magnitude & and be represented by (18) pitch and yaw angles remain zero. Then, we a(t) = %(t) = - A, (i+cos(47t1)) Both obtain the following equality of rotation matrices, T . where R x ( ~ ) , Ry(e), and RZ@) are rotation matrix with respect to X-axis, Y-axis, and Z-axis, respectively. From the equality of two matrices in Eq. (191, we obtain e:(t) = 0 (20) ekt) = - e!&) - &t) e: (t) = - a(t) - &t) . (21) (22) Then the motion of the hip at the swing leg, denoted by (Xr, yr, Zr), can be represented by xr(t) = XlO) y,(t) = A, cos(2d) - 2w cos(a(t)) T q( t ) = H - 2w sin(a(t)) ",
            " Choosing e;, e;, e;, and 9: as free variables and assuming their time functions are linear, we obtain (25) (26) (27) = (1- e h ) + h e h d . (28) 9'l(t) = (1- h) e h ) + h e'l(t1) e;(t) = (1- h) e;(to) + h e;(tl) 9',(t) = (1- h) &(to) + h 9'3(tl) From the kinematic relation between the COM of the swing leg in the Cartesian space and joint space, &(t) and 9kt) can be represented by e;(t) + &(t) = c o s - 1 w + tan-1: Ju2+v2 (29) Pi, P2, and P3 are ratios of the masses of the upper leg, lower leg, and the foot to the total mass of the swing leg, respectwely. ri, rz, r3, and p3 are defined in Fig. 1. A typical proposed walking pattern in the saggital plane is shown in Fig. 3(a). The trajectories of 6 joints for the left and right legs are shown in Fig. 3cb) and Fig. 3(c), respectively. 4. Analysis of ZMP Trajectories In this section, we qualitatively analyze the ZMP trajectory of the walking pattern described in the previous section. In the case that the ZMP trajectory does not lie completely inside the stable region, we present a strategy to adjust the trajectory of the ZMP through modification of the pattern parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.106-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.106-1.png",
        "caption": "Fig. 12.106 Effect of the lug pattern on the tractive force [131]",
        "texts": [
            "20 0.6 0.8 1.00.4 0.2 0 0.2 0.4 0.6 0.8 0.4 Fig. 12.105 Effects of tire design elements on traction on soil [140] 906 12 Traction Performance of Tires The maximum coefficient of the tire traction increases and the motion resistance decreases with increasing tire diameter r and wheel width b. These experimental results qualitatively agree with Eq. (12.203). (4) Effect of the lug pattern on the tractive force The effect of the lug pattern on the tractive force can be estimated for the two modes of Fig. 12.106, where hl is the lug height, d is the diameter of the bottom of the lug, r is the tire diameter, pt is the contact pressure on the top of the lug, pca is the contact pressure on the bottom of the lug, and k is the ratio of the area of the top of the lug to the total area of the tread. When sinkage on the top of the lug zr or ze is smaller than the lug height hl, the carcass does not make contact with the road and pca = 0 is satisfied. In the rigid mode, pt is applied to the ratio k of the contact area while pca is applied to the ratio (1 \u2212 k) of the contact area",
            "4-(1)-(1-1), and pt and pca can be determined using the obtained zr. Substituting these values into Eq. (12.220), the effective critical pressure pecr is obtained. When pecr is less than the average contact pressure pg of Eq. (12.206), which can be calculated using a generalized deflection chart, a tire with lugs must be in rigid mode. The traction on the top and bottom of the lug (st and sca) can then be determined following the same procedure described in Sect. 12.6.4-(2)-(2-1). In the elastic mode of Fig. 12.106, the sinkage of the top of the lug ze and sinkage of the carcass ze \u2212 hl are obtained from the average contact pressure pav: 12.6 Traction on Soil 907 pav \u00bc kpt \u00fe 1 k\u00f0 \u00depca; \u00f012:221\u00de where pt is a function of ze while pca is a function of ze \u2212 hl. If ze is determined following the procedure described in Sect. 12.6.4-(1)-(1-2), pt and pca can be determined using the obtained ze. The traction on the top and bottom of the lug (st and sca) can then be determined following the same procedure described in Sect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure2-1.png",
        "caption": "Fig. 2 Generation of extended epicycloids",
        "texts": [
            " However, the generated method offers more freedoms of controlling tooth surface geometries; 2 the lengthwise tooth curve of face milled bevel gears is a circular arc with a curvature radius equal to the cutter radius while the lengthwise tooth curve of face hobbed gears is an extended epicycloid which is kinematically generated by the indexing motion; and 3 face hobbing gear designs use the uniform tooth depth system while face milling gear designs use the tapered tooth depth system. Theoretically, the face hobbing process is based on the generalized concept of bevel gear generation in which the mating gear and pinion can be considered respectively, generated by the complementary generating crown gears as shown in Fig. 1. The tooth surfaces of the generating crown gears are kinematically formed by the traces of the cutting edges of the tool blades as shown in Fig. 2. The generating crown gear can be considered as a special case of a bevel gear with 90 deg pitch angle. Therefore, a generic term \u201cgenerating gear\u201d is used. The concept of complementary generating crown gear is considered when the generated mating tooth surfaces of the pinion and the gear are conjugate. In practice, in order to introduce mismatch of the mating tooth surfaces, the generating gears for the pinion and the gear may not be NOVEMBER 2006, Vol. 128 / 131506 by ASME 6 Terms of Use: http://www",
            " This related motion proides the continuous indexing between the tool and the work. The ndexing relationship can also be represented by the rotation of the ool and the generating gear as, t c = Nc Nt 2 here c and Nc denote the angular velocity of the generating ear and the tooth number of the generating gear, respectively. eanwhile, the indexing motion between the tool and the generting gear kinematically forms the tooth surface of the generating ear with an extended epicycloid lengthwise tooth curve as shown n Fig. 2. The radii of the rolling circles of the generating gear and he tool are determined, respectively, by 316 / Vol. 128, NOVEMBER 2006 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 Rc = Nc Nt + Nc \u00b7 s 3 and Rt = Nt Nt + Nc \u00b7 s 4 where s is the machine radial setting. The second set of related motion is the rotation of the generating gear and rotation of the work. Such a related motion is called rolling or generating motion and is represented as, w c = Nc Nw = Ra 5 where Ra is called the ratio of roll"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure1.35-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure1.35-1.png",
        "caption": "Fig. 1.35 Incompressibility of rubber",
        "texts": [
            " Integrating De in the volume of the structure, the energy loss in a period DE and the initial strain energy E0 are expressed by DE \u00bc p Z V erf gT E00\u00bd erf gdV E0 \u00bc 1 2 Z V erf gT E0\u00bd erf gdV : \u00f01:173\u00de Equations (1.171) and (1.173) give the modal damping ratio fr expressed by 54 1 Unidirectional Fiber-Reinforced Rubber fr \u00bc 1 2 R V erf gT E00\u00bd erf gdVR V erf gT E0\u00bd erf gdV : \u00f01:174\u00de Hence, if the complex elastic matrix \u00bdE is known, fr can be calculated from the strain energy distribution of the mode corresponding to the real eigenvector. Notes Note 1.1 Incompressibility of Rubber Rubber has specific properties that the volume is maintained under external forces. Referring to Fig. 1.35a, the incompressibility is expressed by 1\u00fe ex\u00f0 \u00delx 1\u00fe ey ly 1\u00fe ez\u00f0 \u00delz \u00bc lxlylz: The low-strain assumptions ex, ey, ez 1 yield ex \u00fe ey \u00fe ez \u00bc 0: Figure 1.35b shows the deformation of the element where the external force is applied in the z-direction. When the strain along the z-axis is e, strains along the xand y-axes can be expressed by e and Poisson\u2019s ratio m. Referring to Fig. 1.35b, the incompressibility can be expressed by 1 me\u00f0 \u00delx 1 me\u00f0 \u00dely 1\u00fe e\u00f0 \u00delz \u00bc lxlylz: The assumption of low strain e 1 yields Appendix: Viscoelasticity 55 1 me\u00f0 \u00de2 1\u00fe e\u00f0 \u00de ffi 1 2me\u00f0 \u00de 1\u00fe e\u00f0 \u00de ffi 1\u00fe 1 2m\u00f0 \u00dee \u00bc 1: Poisson\u2019s ratio for incompressible materials is m = 1/2 from the above equation. Note 1.2 When \u22121 < cos 2h < 1 is satisfied, the extreme value is located away from h = 0\u00b0 and h = 90\u00b0. Because ET EL ELET=GLT EL \u00feET \u00fe 2mLET\u00f0 \u00de\\1 is satisfied, GLT > EL/{2(1 + mL)} is obtained considering the relation EL \u2212 ET > 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003697_iecon.1994.397792-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003697_iecon.1994.397792-Figure3-1.png",
        "caption": "Fig. 3 - Flowchart of D X scheme.",
        "texts": [
            " In this paper the attention is mainly focused on the influence of torque and stator flux band amplitudes on drive perfmance, then reference is made to the more usual selection strategy of Tab. I. TAB. 1 - VOLTAGE VBCTQR SELECTION STRATEGY. Assuming the stator flux lying in the k-th sector @=1,2,..6) of the dq plane, V, or Vw2 can be selected in order to increase the torque, while zero voltage vector V, is utilised to denease the toque. DIGITAL IMPLEMESTATION The DTC scheme requires as input variables the desired values of torque and flux and calculates, at each samplq period, the stator voltage required to drive the flux and torque-to the reference values. Fig. 3 illustrates the computational flow of the implemented system. The D S P - M controller reads in the torque and flux references, the DC link voltage and two line currents at the beghmg of each sampling period. Then the controller executes the A/D conversions, pafonns all the neceSSBIy computations and outputs the invexter switching state. The DSP, even if characterised by multiplication capability and h@ speed, needs a certain amount of time to execute the entire control algorithm. This time, together with the time required for overcurrent protection and diagnostic facility, determines the minimum value of the sampling period f"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000349_tec.2020.2995902-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000349_tec.2020.2995902-Figure2-1.png",
        "caption": "Fig. 2. Schematic of building up the different subdomains of concentric models. (a) original eccentric motor. (b) concentric model (part 1). (c) concentric model (part 10).",
        "texts": [
            " For the case of np\u22601, 2 1 0 2 2 2 2 ( 1)*( ) 2( ) ( 1) * 1 1( ) 1 [1 ( ) ] [( ) ( ) ] np npm m n r r np np nps s mr rr r r r m r R R D D M R Rnp A R R Rnp R R R \u2212\u2212 + \u2212 + = + \u2212\u2212 \u2212 \u2212 \u2212      (10) 1 1 1( ) ( ) ( )np np nps s m m R R r B R r R \u2212 + \u2212= + (11) 1 1 1( ) ( ) ( )np np nps s m m R R r C R r R \u2212 + \u2212= \u2212 + (12) 11 1 ( ) n n M D np np M np = \u2212 + (13) 1 2n n nM M npM= + (14) and for the case of np=1, 2 2 2 2 0 2 2 2 *( ) *( ) ( ) ln( ) * 1 1 [1 ( ) ] [( ) ( ) ] m mr r n s s s r mr r r rr r s r s m R RR R D D M R R R R A RR R R R R \u2212 + = + \u2212 \u2212 \u2212 \u2212      (15) 21 ( )sR B r = + (16) 21 ( )sR C r = \u2212 + (17) 1 1 1 | 2 1 | n n p n n p M D M = = = = = \u2212 (18) 1 2n n nM M M= + (19) where \u03bcr is the relative permeability of PM, r is the radius of air-gap in polar coordinates. To consider the non-uniform air-gap caused by eccentricity, the original eccentric machine is divided into several concentric subdomains along the air-gap circumferential direction [7, 12], while the reference center is chosen at the rotor center Or, as shown in Fig. 2(a). The number of concentric subdomain models is chosen as the number of stator slots q. Then, the points which determine the equivalent air-gap length (gei) of each subdomain are chosen at the intersections of each subdomain center line and the stator inner surface, as shown in Fig. 2(a). The different equivalent air-gap lengths can be calculated by cosine law, as shown in the following formula 2 2 02 cos( )ei s s i mg R e R e R= + \u2212  \u2212 \u2212 (20) in which, i=1, 2, \u2026, q, and \u03b1i is the angular position of the ith slot opening center in the stator reference; \u03b80 is the initial angular position of the minimum air-gap length. Based on the different air-gap lengths, a series of concentric subdomains can be established, examples given in Fig. 2(b) and (c), which are corresponding to the 1st and 10th subdomains addressed in Fig. 2(a). It is worth noting that the rotor of different subdomains is the same as the original eccentric motor, and the stator needs to change accordingly. After predicting the air-gap flux density of each concentric subdomains by formula (9), the air-gap flux density of the original eccentric motor can be integrated as follows: , ( , ) , ( , ) ri r si ei i si ei B B B B =  =         (21) where Bri and B\u03b8i are the radial and circumferential air-gap flux densities of the original eccentric motor, respectively; \u03b8si and \u03b8ei determine the start and end angular position of each subdomain, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003486_robot.1996.509284-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003486_robot.1996.509284-Figure11-1.png",
        "caption": "Figure 11: The 2-type 3-1-type 1 mechanism",
        "texts": [
            " Using equation (9) we compute the value of A and substitute the result in equation (11) which become an equation in sine and cosine of 8. Using the classical half-angle transformation we get a 4-order polynomial in T = tan(O/2). A geometrical interpretation can be given if we consider the mechanism A ~ B I B ~ B ~ A ~ : the coupler curve described by this mechanism is of degree 4. The solution of the direct kinematics are obtained by intersecting the coupler curve with the line described by B2 as member of chain 2: consequently there is at most 4 intersection points. 2.3.5 This mechanism is presented in figure 11. If we con- 2-type 3 and 1 type 1 sider the mechanism A I B ~ B ~ B ~ A ~ it can be shown that B3 describes a coupler curve of order 4 with full circularity (i.e. 2). Consequently as the solutions of the direct kinematics problem for B3 are obtained by intersection this curve with the circle centered at A3 the number of real intersection points will be at most 4. Using the notation of figure 6 we write first that A2 belongs to the line coming from the platform: ( rcose + ccos(8 + al) - u)sin(8 + a2) - ( r s in6 + csin(8 + al)) cos(@ + ag) = 0 (12) Then we write that point B3 should be at distance 1-3 from A3: (Tcos8 + acos(8 + a3) - + (T sin 8 + a sin(8 + a3) - = ri (13) We use the linear equation (12) to compute r which is then back substituted in equation (13), now an equation in the sine and cosine of 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.19-1.png",
        "caption": "Fig. 7.19: Cutting the Link i of a Manipulator",
        "texts": [
            "73) where the inertia effects due to the elastic vibrations have been neglected, which makes sense because they are usually very small. The evaluation of equation (7.73) goes straightforward and gives the nominal elastic deviations for a robot along a given path with given forces. It should be noted, that for the curvature control to follow we also need the nominal curvature values, which are calculated by cutting the corresponding link i at the location of the strain gauges and applying the multibody formulas for the evaluation of the cut forces and torques for the nominal magnitudes of the rigid robot (see [223] and Figure 7.19). The internal forces and torques at the cut point R are then determined by applying the projection equations (7.53) for a rigid robot and without any elastic components to that part of the manipulator, which have been cut 7.2 Trajectory Planning 447( \u2202vRi \u2202q\u0307r )T { mi [ (v\u0307Ri + \u02dc\u0307\u03c9RirRSi) + \u03c9\u0303Ri(vRi + \u03c9\u0303RirRSi) ] \u2212 fRi } + + ( \u2202\u03c9Ri \u2202q\u0307r )T {( ISi + mir\u0303RSir\u0303TRSi ) \u03c9\u0307Ri+ + \u03c9\u0303Ri ( ISi + mir\u0303RSir\u0303TRSi ) \u03c9Ri + mir\u0303RSi(v\u0307Ri + \u02dc\u0307\u03c9RirRSi)\u2212mRi } = 0, (7.74) for all links starting with the link i up to the end effector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.111-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.111-1.png",
        "caption": "Fig. 12.111 Flow distribution in soil at a slip ratio of 30% (reproduced from Ref. [153] with the permission of Tire Sci. Technol.)",
        "texts": [
            "110 shows the calculated rut shape of a tire with a slip ratio of nearly 100% and the calculated cone penetration resistance of soft soil. The tire sinkage is nearly 110 mm, and the result is in good qualitative agreement with common measurement simulation 0 20 40 60 80 0 20 40 60 80 Pressure [kPa] S he ar re si st an ce [k P a] Fig. 12.108 Comparison of shear resistance between numerical simulation and experimental data (reproduced from Ref. [153] with the permission of Tire Sci. Technol.) 12.6 Traction on Soil 909 phenomena. Figure 12.111 is a flow diagram of a tire driving at a slip ratio of 30% on hard soil. Most of the soil beneath the tire flows backward, and the motion of the soil is limited to the shallow part of the soil region aligned to the top surface of the tire. The gross traction is dominant, and the motion resistance is low. The gross traction at a slip ratio of 30% is produced by pushing the soil between the lugs backward. The right figure in Fig. 12.112 shows the motion resistance distribution 910 12 Traction Performance of Tires per unit area in this state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003221_s0094-114x(98)00081-0-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003221_s0094-114x(98)00081-0-Figure7-1.png",
        "caption": "Fig. 7. 3-RPS spatial manipulator.",
        "texts": [
            " These equations are developed by considering the moment equilibrium of the upper link about the preceding joint axis, the moment equilibrium of the upper and middle links about the axis of the joint preceding the middle link and the moment equilibrium of the entire leg about the axis of the base joint. Once the reaction forces of all the three legs are determined, the \u00aenal system of equations can be derived as in the case of 3-PRPS manipulator. The kinematics of the 3-RPS parallel manipulator, shown in Fig. 7, is quite similar to the 3- PRPS case with the only exception that the prismatic actuation at the base will be absent and there will be only one prismatic actuation, namely that along the direction of the leg. The leg vector, linear velocity at the prismatic joint and angular velocities of the leg are given by S t q\u00ff b; _L s _S ; W _S \u00ff _Ls L k As this is a 3-DOF mechanism having six output variables, there will be 3 constraint equations from the system kinematics. Due to these positional constraints, constraint forces or ``Lagrange Multipliers'' will come into picture and these forces will be essentially in the direction of the revolute joint axis, along which there is no linear motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003221_s0094-114x(98)00081-0-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003221_s0094-114x(98)00081-0-Figure5-1.png",
        "caption": "Fig. 5. 3-PRPS spatial manipulator.",
        "texts": [
            " Replacement of the universal joints at the base by spherical joints results in a 12-DOF system with six passive degrees of freedom. This situation is handled by incorporating the passive rotations as additional generalized coordinates and the \u00aenal system of equations can be derived in the form of Eq. (7). Details of the dynamic formulation for these two cases of the Stewart platform are not given here and can be found in Dasgupta and Mruthyunjaya [10]. As the next example, let us consider the 6-DOF 3-PRPS hybrid manipulator shown in Fig. 5 which has two prismatic actuations in each leg. Denoting the leg vector, displacement of the prismatic joint at the base, leg-length and unit vector along the leg as S, D, L and s, respectively, the position analysis yields S t q\u00ff b\u00ffDk; D t q\u00ff b k; L kSk; s S=L where q=Rp is the vector from platform origin to platform-connection-point expressed in the base frame. Inverse velocity analysis similarly gives the velocity of the platform point and subsequently the displacement rates of the sliding (actuated) joints and the common angular velocity of middle and upper parts of the leg as _S _t o q; _D k _S ; _L s _S ; W _S \u00ff _Dk\u00ff _Ls L k Next, for the acceleration analysis, we have S t a q o o q 23 Grouping the terms involving t\u00c8 and a together, we have S ap u1 where ap t a q From this, we get the accelerations D\u00c8 at the sliding joints and the angular acceleration of middle and upper parts of the leg as D k ap u2; L s ap u3; A k s L ap u4 k where u2 k u1; u3 s u1 LkWk2; u4 k s L u1 \u00ff 2 kWk _L L Now from these basic equations we can obtain the accelerations of the centres of gravity of the lower, middle and upper parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000877_j.tafmec.2020.102611-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000877_j.tafmec.2020.102611-Figure1-1.png",
        "caption": "Fig. 1. Specimens with continuous radius between ends according to ASTM E466-15: (a) dimensions after milling and (b) orientation in the building platform.",
        "texts": [
            " In this work the fatigue strength of additively manufactured AlSi10Mg samples obtained by using three different combinations of process parameters and two different building directions was assessed. Results obtained were related to the microstructural feature of produced samples in terms of defects and fracture surface morphology. The AlSi10Mg samples were obtained by LPBF process, using an AM 400 Renishaw ensuring 0.5 mm allowance, and then by milling (roughness after machining, 1.9 \u00b1 0.6 \u03bcm). Geometry and dimensions of the samples, according to ASTM E466-15 are shown in Fig. 1a. The AM 400 machine was equipped by a 400 W pulsed laser with a beam diameter equal to 70 \u03bcm. The platform dimensions were 250 mm \u00d7 250 mm \u00d7 300 mm. The building platform temperature was 170 \u00b0C. Argon was used as protective gas against powder oxidation. The chemical composition of the hypoeutectic alloy powder is collected in Table 1. Particle size of the powder was in the range of 15\u201345 \u03bcm. Six different sets of process parameters were identified, according to the results of a previous investigation [33], and summarized in Table 2. X identifies the specimens perpendicular and Y identifies the specimens parallel to the recoater motion, as shown Fig. 1b. In Table 2, the nominal process parameters prescribed by the manufacturer are highlighted. The energy density Ed (J/mm3) is also computed using the following formula [33]: =Ed et\u00b7P s\u00b7h\u00b7d (1) where et is the exposure time in \u03bcs, P is the power in W, s is the point distance in \u03bcm, h is the hatch space in \u03bcm and d is the layer thickness equal to 30 \u03bcm (Fig. 2). 10 samples for each set underwent to fatigue tests (load ratio R = 0) carried out by using an MTS 809 multiaxial test machine with a maximum force of 50kN"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure13-1.png",
        "caption": "Fig. 13 Coordinate systems Sp and So",
        "texts": [
            " 10 is connected to he machine element 10 and represents the machine root angle etting. System Sc Fig. 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter. System Sp is connected to the machine element 9 and represents he work head setting motion Fig. 12 . System So is connected to he machine element 8 and represents the work head offset setting ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 motion Fig. 13 . Sw is connected to the work 8 and represents the work rotation with angular parameter Fig. 14 . System Se is connected to the eccentric setting element and represents the radial setting Fig. 15 . System Sj is connected to the tilt wedge base element which performs rotation relatively to the eccentric element to set the swivel angle j Fig. 16 . System Si is connected to the cutter-head carrier which performs rotation relatively to the tilt wedge base element to set the tool tilt angle i Fig. 17 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000968_j.addma.2021.102203-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000968_j.addma.2021.102203-Figure3-1.png",
        "caption": "Fig. 3. Geometry of the component and substrate. (a) Overhead view. (b) Isometric view.",
        "texts": [
            " The relative positions of the laser output head and the CMT torch are indicated in Fig. 2a. The height of the bottom of the laser output head is 225 mm, and the angle between the laser output head and the substrate is 40\u25e6. As illustrated in Fig. 2b, a fixture is designed for mounting substrates where both ends of the substrate are clamped, and lateral movement on one side is restricted. During fabrication, the welding mode was CMT pulse advanced (CMT-PADV), and the process parameters of the laser-CMT process are shown in Table 2. Fig. 3 presents the geometric size of the thin-wall part and substrate. The two ends of the substrate have a footstep for clamping. In this R. Li et al. Additive Manufacturing 46 (2021) 102203 experiment, three types of path strategies viz. same direction motion (SDM), reciprocating motion (RM), and SRM were applied to build tenlayer thin-wall samples with arc and line features, as illustrated in Fig. 4. For the SDM path strategy, the scanning direction is consistent in the ten layers, and the swelling in the arc striking and inclination in the arc extinguishing are accumulated layer by layer [32], resulting in a significant height difference between the beginning and the end of the trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure14.46-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.46-1.png",
        "caption": "Fig. 14.46 Vehicle model in straight driving. Reproduced from Ref. [26] with the permission of Tire Sci. Technol.",
        "texts": [
            "0 0 1 2 3 h: +10% control Fig. 14.44 Effect of tire design on wear energy (tread thickness h + 10%) [25] W ea r e ne rg y (1 0\u2212 3 J /c m 2 ) Step of irregular wear \u03b4 (mm) Fig. 14.45 Effect of tire design on wear energy (friction coefficient l \u2212 10%) [25] 1068 14 Wear of Tires Suppose that a vehicle moves straight, tires have plysteer and conicity, the side slip angle of the vehicle is denoted b, the steering angle of the front tires is denoted d and the camber and toe are only applied to the front axle as shown in Fig. 14.46. The following nomenclature is used in Fig. 14.46. l, lf, lr length from the front axle to rear axle and lengths from the center of gravity to front and rear axles c, d, b toe angle, steering angle and vehicle side slip angle aL, aR slip angle (front left wheel, front right wheel) CfL, CfR cornering force (front left wheel, front right wheel) MfL, MfR aligning torque (front left wheel, front right wheel) Cr cornering force (rear wheel) Mr aligning torque (rear wheel) CPf, CPr plysteer force (front wheel, rear wheel) MPf, MPr torque due to the plysteer force (front wheel, rear wheel) 14.9 Effect of Vehicle Alignment on Tire Wear 1069 Cof, Cor conicity force (front wheel, rear wheel) Mof, Mor torque due to the conicity force (front wheel, rear wheel) Kf, Kr cornering stiffness (front wheel, rear wheel) Tf, Tr aligning stiffness (front wheel, rear wheel) Ct camber thrust Sign conventions in Fig. 14.46 are that a side force is positive if it acts toward the right side of the direction of motion, a moment is positive if it is counter clockwise and an angle is positive if it is clockwise. The equilibrium equation of side forces in Fig. 14.46 is CfL \u00feCfR \u00fe 2Cr CPf cos aL CPf cos aR 2CPr cos b \u00bc 0; \u00f014:135\u00de where both Cor and Cof are assumed to cancel out for the left and right wheels. Assuming the relation aL, aR, b 1, Eq. (14.135) can be rewritten as CfL \u00feCfR \u00fe 2Cr 2CPf 2CPr \u00bc 0: \u00f014:136\u00de The equilibrium equation of moments in Fig. 14.46 is MfL \u00feMfR \u00fe 2Mr 2MPf 2MPr \u00fe 2CPf lf 2CPrlr CfLlf cos b CfRlf cos b\u00fe 2Crlr cos b \u00bc 0; \u00f014:137\u00de where both Mor and Mof are assumed to cancel out for left and right wheels. Assuming the relation aL, aR, b 1, Eq. (14.137) can be rewritten as MfL \u00feMfR \u00fe 2Mr 2MPf 2MPr \u00fe 2CPf lf 2CPrlr CfLlf CfRlf \u00fe 2Crlr \u00bc 0: \u00f014:138\u00de Assuming the relation aL, aR, b 1, we have CfL \u00bc aLKf ; CfR \u00bc aRKf ; Cr \u00bc bKr; MfL \u00bc aLTf ; MfR \u00bc aRTf ; Mr \u00bc bTr: \u00f014:139\u00de Furthermore, the geometrical relations are aL \u00bc b d\u00fe c aR \u00bc b d c : \u00f014:140\u00de Using Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure3-1.png",
        "caption": "Fig. 3. Generated helic",
        "texts": [
            " For example, Gupta and Walowit [13] simulated he contact behaviour of an elastic layer on an elastic substrate, ssuming smooth and frictionless contact based on Sneddon\u2019s 1 62 (2007) 1281\u20131288 t t t p a a r e l h t b f b d R t [ r e p s t a o a m f f m f b m a m r f s b a w i u m b 2 m a i p d p p t a l d p a t C b o then read into the FEA software through using Python script interfacing with the solver. The full 2D gear geometry is then generated through rotation copying the one single tooth. Fig. 3 282 K. Mao / Wear 2 heory. They derived the mathematical formulation relating to he problems of a layered elastic surface indented by an elasic indenter. More recently, the smooth and frictionless contact roblem of multi-layer systems has been solved by Elsharkawy nd Hamrock [14]. Further development has been made by Cole nd Sayles [15] in considering the frictionless contact of real ough multi-layer systems. Attempts have been made by Mao t al. [16,17] to tackle the even more realistic real rough, multiayer contact problem where frictional forces are involved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure6.38-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure6.38-1.png",
        "caption": "Fig. 6.38 Deformation of a sidewall with a uniformly applied lateral force",
        "texts": [
            " This is because the assumption of the rigid body of the tread area may not be satisfied owing to the low belt tension at the belt end. Furthermore, the locations of the ends of the first and second belts are different for belted radial tires. (1) Lateral spring rate due to carcass tension (tensile spring rate) Suppose that the tire carcass is connected from point D of the belt end to point B of the bead area and that the lateral force q/2 per unit length in the circumferential direction is uniformly applied to half the tire as shown in Fig. 6.38a. Instead of applying the external force to point D in Fig. 6.38a, the constrained displacement is applied to point B in Fig. 6.38b. When the applied constrained displacement is dzB at point B, the reaction at point D is q/2. Considering that there are two sidewalls of a tire, the lateral fundamental spring rate ks of a tire is expressed as ks \u00bc 2 q=2 dzB \u00bc q=dzB: \u00f06:94\u00de In the calculation of ks using Eqs. (6.89) and (6.94), considering that rD is fixed, there are four unknowns, namely dzB and q, and rC and /D, in the terms A and B of Eq. (6.90). The equations used to determine the four unknowns are Eq. (6.89) for 6.4 Fundamental Spring Rates Based on the Equilibrium Shape \u2026 341 the natural equilibrium shape, the inextensibility equation of the cord and the equation for the force equilibrium between q and inflation pressure",
            "95), we obtain d/D drc \u00bc @L @rc = @L @/D U0 k \u00bc dzB \u00bc @zB=@rc \u00feU0 @zB=@/D\u00f0 \u00dedrc ndrc; \u00f06:96\u00de where n \u00bc @zB=@rc \u00feU0 @zB=@/D: \u00f06:97\u00de The equation for the force equilibrium in the z-direction is (Fig. 6.39) pp r2D r2c \u00bc F2prD; \u00f06:98\u00de where F is the force per unit length in the circumferential direction at radius rD in the z-direction, and p is the inflation pressure. Equation (6.98) is rewritten as 342 6 Spring Properties of Tires F \u00bc p r2D r2c =2rD: \u00f06:99\u00de Considering that the force variation dF corresponds to q/2 of Fig. 6.38, Eq. (6.99) is rewritten as dF \u00bc q 2 \u00bc d p 2rD r2D r2c : \u00f06:100\u00de Using the condition drD = 0 in Fig. 6.38b, Eq. (6.100) is rewritten as q \u00bc 2prc=rD drc: \u00f06:101\u00de Using Eqs. (6.96), (6.97), (6.100) and (6.101), the lateral fundamental spring rate ks(c) per unit length at point D is given as ks\u00f0c\u00de \u00bc q k \u00bc 2prc nrD \u00bc 2prc rD @L @/D @zB @/D @L @rc @zB @rc @L @/D n \u00bc @zB @rc @L @/D @zB @/D @L @rc @L @/D : \u00f06:102\u00de Equation (6.102) is linearly proportional to the inflation pressure p but ks(c) will be nonlinear when dzB is large. To consider the nonlinearity, ks(c) must be iteratively solved by updating drC and d/D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure19-1.png",
        "caption": "Fig. 19. Illustrations of: (a) the volume of designed body, (b) auxiliary intermediate surfaces, (c) determination of nodes for the whole volume, and (d) discretization of the volume by finite elements.",
        "texts": [
            " The development of finite element models using CAD computer programs is time expensive, requires skilled users for application of computer programs and has to be done for every case of development of gear geometry and the position of meshing desired for investigation. The developed approach is free of all these disadvantages and is summarized as follows: Step 1: Using the equations of both sides of tooth surfaces and the portions of the corresponding rim, we may represent analytically the volume of the designed body. Fig. 19(a) shows the designed body for onetooth model of the pinion of a face-gear drive. Step 2: Auxiliary intermediate surfaces 1\u20136 as shown in Fig. 19(b) can be determined. Surfaces 1\u20136 enable to divide the tooth in six parts and control the discretization of these tooth subvolumes into finite elements. Step 3: Analytical determination of node coordinates is performed taking into account the number of desired elements in longitudinal and profile directions (Fig. 19(c)). We emphasize that all nodes of the finite element mesh are determined analytically and the points lying on the surfaces the tooth belong to the real gear tooth surfaces. Step 4: Discretization of the model by finite elements (using the nodes determined in previous step) is accomplished as shown in Fig. 19(d). Step 5: Setting of boundary conditions for the gear and the pinion are accomplished automatically under the following conditions: (i) Nodes on the two sides and bottom part of the portion of the gear rim are considered as fixed (Fig. 20(a)). (ii) Nodes on the two sides and the bottom part of the pinion rim form a rigid surface (Fig. 20(a) and (b)). Such rigid surfaces are three-dimensional structures that may perform translation and rotation but cannot be deformed. (iii) The advantage of consideration of pinion rim rigid surfaces mentioned above is as follows: (a) their variables of motion (its translation and rotation) are associated with a single point chosen as the reference point M; (b) point M is located on the pinion axis of rotation (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003922_j.jappmathmech.2007.01.003-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003922_j.jappmathmech.2007.01.003-Figure2-1.png",
        "caption": "Fig. 2.",
        "texts": [
            "6) Here (t) is the Dirac delta function. Of course, the velocity jumps at the beginning and end of a period can be combined into a single jump, but representation (2.6) is convenient because it agrees with conditions (2.3). The times t = 0 and t = T are regarded as equivalent. Integrating relations (2.5) with the initial condition from (2.2), we obtain a piecewise-linear law for the displacement (2.7) To satisfy conditions (2.2), it is necessary to require that (2.8) The two-phase motion is shown in Fig. 2. It can be characterized for given value of L by two independent positive parameters u1 and u2. The remaining parameters are expressed, according to conditions (2.8), in terms of u1 and u2 by the relations (2.9) In the case of two-phase motion, an upper limit can be imposed on the relative velocity of mass m. We then have the constraints (2.10) where U > 0 is a specified constant. For the three-phase motion we use 1, 2 and 3 to denote the lengths of the segments of constant relative acceleration, and we use w1, \u2212w2 and w3 to denote the acceleration values in these segments, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000816_j.mechmachtheory.2020.103870-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000816_j.mechmachtheory.2020.103870-Figure11-1.png",
        "caption": "Fig. 11. Schematic of the tooth modification.",
        "texts": [
            " Although the partial load is caused by the asymmetric rim structure instead of the axis misalignment, similar phenomena can be observed: As the wear cycles increase, the axial wear distribution tends to be uniform (see Fig. 10 c and 10 d). For gear pairs with asymmetric rim structure, uneven axial load distribution will lead to severe wear at one edge. As a consequence, the gear pair is more vulnerable to localized defects (such as spalling, pitting and breakage). Tooth modification is widely applied to optimize load distribution and reduce the vibration. As one of the lead modifications, helix angle modification (also known as slope modification) is adopted to compensate the partial load (see Fig. 11 ). The contact stress under different amounts of helix angle modification is shown in Fig. 12 a. Aiming at minimizing the maximum contact stress, the optimal amount of helix angle modification is acquired ( C \u03b2= 16.4 \u03bcm) (see Fig. 12 b). Apart from the helix angle modification, tip relief modifications are also introduced to reduce the vibration. The sum of the first three Fourier harmonics of the static transmission error is chosen as the object function. The optimization model of the tip relief modification can be written as: min A 1 + A 2 + A 3 s "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000421_j.ymssp.2020.106740-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000421_j.ymssp.2020.106740-Figure6-1.png",
        "caption": "Fig. 6. Experimental test device schematic (blue color represents changed components).",
        "texts": [],
        "surrounding_texts": [
            "In order to validate the effectiveness of the proposed method, this paper designs 20 sets of different degrees of gear pitting conditions. The acceleration sensor collects the raw gear vibration signals into an adaptive 1D separable convolution with the residual connection. The sampling rate was set as 10.24 kHz, the file extension was TXT, and the sampling time was 6 s. The acceleration sensor was mounted on the gearbox housing. The test rig is shown in Figs. 5 and 6. The experimental device consists mainly of two 45 kW Siemens motors and a gearbox and its cooling and lubrication device. The main parameters of the gearbox are shown in Table 2.\nDifferent degrees of gear pitting are shown in Fig. 7 and Table 3. Health state 1 is normal gear. The intermediate teeth of Health state 2 and 3 have about 10% and 30% pitting, respectively. Health state 4 and 5 have 50% pitting for the middle teeth, and adjacent gears also have varying degrees of pitting.\nAll experiments in this paper were carried out with a load of 50 Nm and a rotational speed of 400, 500, 600, and 700 rpm, respectively. The raw vibration signal in the z-axis direction of the gear is shown in Fig. 8. Each row represents a vibration signal of the different gears pitting at the same speed, and each column represents the same gear pitting health state and different rotational speeds. It can be seen from the figure that the raw vibration signal of the gear in Health state 4 has a large amplitude, which may be caused by the mutual vibration between the two gears. The gear signals of the other four cases are not too obvious.\nA major challenge for machine learning is that if poor data is entered into the system, the performance of the system will gradually decline. Before providing data to a machine learning model, first, check for the existence of data outliers. If there is any need to perform a data cleanup operation, remove the outliers in advance. In order to understand the raw vibration signal of the gear, the range and the number of amplitudes are visually displayed through the histogram. Fig. 9 is a histogram of the frequencies of four different loads, each of which takes 5000 points to plot the frequency histogram of the amplitude. It can be seen from the histogram that the four loads all show a normal distribution, and some of them are farther away from the zero point, especially in the case of 700r/min, the normal gear also has some amplitudes between 1 and 2. point. The data collected is not particularly perfect. We use these raw data for fault detection of gear pitting.\nThe data of the training set, the verification set, and the test set are not duplicated. The amount of data in each sample signal is 1536. The number of samples for each speed training set, verification set, and test set is 1600, 300, and 100, respectively. So the sample size input to the network is 6400, 1200, and 400, respectively. The number of channels of the separable convolution network was 32, 64, 128, and 128, respectively. Strides were 1, pooling size was 2, the batch size was 512,",
            "activation was relu, and the padding operation is to keep the size of the data the same as before and after the convolution. The loss used categorical cross entropy, the optimizer used RMSprop, the original learning rate was 2e-5, and the NVIDIA 1080Ti was used for training the model. Table 4 shows the method proposed in this paper, the connection mode of each corresponding layer, the size and the number of corresponding parameters.\nThe method proposed in this paper and other machine learning methods are used to classify the gear pitting faults with mixed operating health state. Selected Health state 1 and Health state 3 to binary classification. The corresponding gears are",
            "Table 3 The approximate percentage of wearing area.\nPitting percentage Upper tooth Middle tooth Lower tooth\nHealth state 1 Normal Normal Normal Health state 2 Normal 10% Normal Health state 3 Normal 30% Normal Health state 4 10% 50% Normal Health state 5 30% 50% 10%\nFig. 8. Raw vibration signals of gears."
        ]
    },
    {
        "image_filename": "designv10_2_0003948_978-3-642-48819-1-Figure4.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003948_978-3-642-48819-1-Figure4.3-1.png",
        "caption": "Fig 4.3.1 General RRRR spherical linkage",
        "texts": [
            " The next example illustrates how to apply this method to spherical linkages. Example 4.3.1 Analysis of the general RRRR s2herical linkase. The MDH can be applied, of course, to general spherical linkages, following the same procedure applied to the universal joint. The fact that the MDH introduces other variables besides the input and the output, however, produces very cumbersome equations, algebraically difficult to handle. The alternate method proves, in this case, to be particulary helpful. Consider the RRRR spherical linkage appearing in Fig 4.3.1 210 Let ~O' ~O' SO' go and ~,p,g,g be the position vectors of points A, B, C and D in a reference configuration and in a time-varying configuration, respectively. Furthermore, let Q and ~ be the rotation matrices carruing links 2 and 4, respectively, from the reference to the current configurations. Thus, (4.3.4) and c=Rc - --0 (4.3.5) Clearly, ~=~O and g=gO\u00b7 The cosine of a 3 in both the reference and the current configurations is (4.3.6a) and ( ) bTc cosa3 cur = (4.3.6b) where Ilbo II and II Co II are assumed unity, without loss of generality. Since link 3 is rigid, u3 remains constant throughout the linkage motion and, since II~II = 11~011 and II~II lie II, one obtains -0 T T ~ ~ = ~o~o (4.3.7) or, substituting the relations (4.3.4) and (4.3.5) in the above equation, (4.3.8) which is the scalar input-output relationship meant to be obtained. The only variables appearing in eq. (4.3.8) are $ , contained in Q, and ~ , contained in R. Define the coordinate axes appearing in Fig 4.3.2, with Xi and Xo directed along the axes of R12 and R41 , respectively. z. ,z 1 9 Fig 4.3.2 Fixed coordinate axes containing the axes of R12 and R41 Matrices Q and ~, referred to i- and 0- axes respectively, are given as 0 0 0 0 1 (Q) . 0 cos1jJ -sin1jJ , (~)o 0 cos~ -sin~J (4.3.9) _ 1 0 sin1jJ cos1jJ 0 sincp coscp 211 212 vectors band c are shown in Figs 4.3.3a and 4.3.3b -0 -0 Hence, cosa2 COSCl4 (!?O) i sina2COSlj!0 (co)o sina4cosCPO (4.3.10) sina2sinwO sina4 sincpO In order to perform the products appearing in eq. (4.3.8) it is necessary to express all vectors and matrices in the same coordinate axes. The transformation matrix carrying the i-axis into the o-axes, referred to the i-axes, is given as X. l - Z. l cosa 1 -sinal 0 sinal cosa 1 o o o _}--BO Wo - - - -- (al (bl Fig 4.3.3 Reference configuration of points Band C. (4.3.11) /,h ..- ...... \"'0 / / ). / / / ,/ The product b T -0 T 9 ~ ~o needed in eq. (4,3.8) is next computed T T (g~o I ~ ~o~ ~~o ;= (4.3.12) which yiedls (4.3.13) When eq. (4.3.13) is substituted into eq. (4.3.8) one obtaines the desired input-output equation (4.3.13a) in which ~ and \u00a2 are measured from the reference values ~o and \u00a2o' respectively, as defined previously. If the said angles are measured from the plane of the axes of R12 and R41 , instead, then the latter equation becomes (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003838_s0301-679x(03)00094-x-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003838_s0301-679x(03)00094-x-Figure3-1.png",
        "caption": "Fig. 3. Rolling and spinning contacts between ball and race.",
        "texts": [
            " For the materials he investigated, different geometry gave different k-values between 2 and 10 kg per oneeighth of an inch depending on the groove forms in the rings. One week later, on 26 January 1901, Stribeck published the second half of the paper \u2018Ball bearings for varying loads\u2019 (Kugellager fu\u0308r beliebige Belastungen), and there the friction in ball bearings was analysed. He elegantly split the power loss in each contact point into one rolling resistance component and one spinning resistance component, see Fig. 3. By summing up the power loss components, it was obvious that the power loss was proportional to the ratio of ring diameter to ball diameters, or for full complement bearings proportional to the number of balls. The bearings should have a small number of large balls to get low power loss. Stribeck needed to know the load distribution between the balls, and assumed then that only the contact points were deformed, and the rings had no bending deformations. For a bearing with zero radial play, the load per ball was proportional to cosg 3/2 where the angle g was measured from the ball with the maximum load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003948_978-3-642-48819-1-Figure6.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003948_978-3-642-48819-1-Figure6.6-1.png",
        "caption": "Fig 6.6.1 RSSR function generating linkage",
        "texts": [
            "83\u00b0 Dimensions of the optimal linkage: a 1 = 1.0000, a 2 = 0.0515, a 3 = 0.9945, a 4 = 0.1154 The minimum value attained by the objective function was z=0.1008. The procedure thus reduced z to a 10.83% of its initial value. The foregoing linkage was analysed for a whole revolution of its input crank. Its transmission angle attained a mean value of 90\u00b0. Its cosine thus attained an r.m.s. value of 12, i.e. 0.3175. Example 6.6.2 Synthesise an RSSR spatial linkage of the type of that appearing in Fig 5.2.1, which is here reproduced in Fig 6.6.1 for quick reference, to generate a given set {$.,\u00a2.} n1 of input-output values. 1 1 Furthermore, its input link should be a crank, whereas its mechanical advantage, as large as possible. 343 344 Solution: The input-output synthesis equation for the given linkage was written down as eq. (5.2.15). The input is now measured from a given reference line making an angle \u00a2o with the Z. (liz )axis, counterclockwise as viewed from ~ 0 axis Xi. The output angle is measured, in turn, from a given reference line making an angle ~O with the Zi axis, counterclockwise as viewed from axis Xo"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure4.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure4.1-1.png",
        "caption": "Fig. 4.1",
        "texts": [
            " By the 1970s, with the impetus from dynamical systems, non-linear analysis, non-linear differential equations, and the aid of highly effective numerical calculation methods, the mathematical theory of bifurcation has begun to take shape and find wide uses in mechanics, physics, chemistry, biology, ecology, cybernetics, numerical calculation, engineering, technology, economics and sociology. At present, the study of bifurcation is advancing in-depth and at high speed both in theory and application. In practice, since many systems contain one or more parameter, we determine whether or not the topological structure of a system changes when continuous slight changes in parameters take place. Let us examine a few examples first. Liapunov-Schmidt Reduction 85 Example 1 Bifurcation of the buckling of a wire arch Imagine an arch made of a metallic wire, Fig. 4.1(a) and (b). The wire arch can be used to demonstrate buckling caused by gravity. The equation of the arch in motion is When the length I of the wire arch is very small, eq. (4.1) has only one stable solution e = 0 (expressing a perpendicular state), Fig. 4.1(b). When I < Ie (the critical value of the loss of stability), the position of leftward or rightward buckling of the arch is stable. When 10 < I < Ie' there may be three stable steady solutions: the upright one (8 = 0) , the leftward buckling or rightward buckling (8 *' 0). When I> Ie' the arch cannot keep upright but inclines leftward or rightward. The relationship between the change in length of the wire and the number of positions can be expressed by a curve. This is the bifurcation diagram of the wire arch, Fig. 4.1(c). The e in the figure is the state variable, and the length I of the wire is the bifurcating parameter. It can be seen from the bifurcation diagram that with variation of the magnitude of the wire, i.e., from large to small or vice versa, the path in the bifurcation diagram varies. Such a phenomenon is called hysteresis. Example 2 Consider a one-dimensional system (4.2) where 11 E ~ is a bifurcating parameter. From eq. (4.2) we know that when 11:-:; 0, eq. (4.2) has an equilibrium branch x = 0, which is asymptotically stable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.37-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.37-1.png",
        "caption": "Fig. 8.37",
        "texts": [
            " In order to explain the motional characteristic, we take the section (x,z) of the integral curve on a plane such as x = 0 where z = y'. The motion portrait consists of many discrete points. The following example belongs to a two-dimensional iteration: 300 Bifurcation and Chaos in Engineering For instance, when E = 1112, the motion of plane ozy must be limited to the . .. 1212 1 3 1 IsopotentIallme V = 1/12: \"2 z +\"2 y -\"3 y = 12 ' namely inside the outermost solid line in Fig. 8.36.(a). A possible periodic solution is the particle vibration between M (0, 0.5) and N (0, - 0.366) on the xy plane, shown as CD in Fig. 8.37. This motion is represented by the outermost solid line in Fig. 8.36(a). Equivalent to this periodic motion is <V in Fig. 8.37. The particle vibrates between ~ and S. The motion corresponds to the period-2 points A and B in Fig. 8.36(a). The trace a>, which corresponds to the period-2 points C and D, is a periodic solution. In addition, there is an unstable periodic solution. Its trace on the xy plane is shown by \u00ae in Fig. 8.37. Its section on the y-axis and its corresponding z (=.Y) give four hyperbolic points, namely the four points F,E,G,H in Fig. 8.36(a). The solutions around the elliptic periodic points A,B or C,D are almost periodic solutions. There are chaos regions around the hyperbolic periodic points E, F, G, H, which are similar in structure to the chaos river networks presented in Fig. 8.31, but the chaos river is very narrow. The initial value (Yo,zo) has little chance of dropping into the chaos river. On the whole, the motion of the system is basically regular, an almost periodic solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003291_robot.1997.619069-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003291_robot.1997.619069-Figure1-1.png",
        "caption": "Fig. 1. S C A M robot : frames and joint variables.",
        "texts": [],
        "surrounding_texts": [
            "In order to eliminate any derivation of velocity in the identification process, a model based on the energy theorem has been proposed [6,11]. This model can be obtained in a differential form calculating the power of the system with the Lagrange equation (Eq. 1) : q T I- = qT (-( li --) aL - E) + q r f (it aq H(q, q) = E(q, @ + U(q) is the total energy of the system. h(q7@ is the (1xNp) row matrix of the energy functions hi(q,q), inclutding friction effect : a(H+ Iq' I'f dt) hi(q, 4) = - axi The power identification model is defined by (Eq.8). Integrating both sides of (Eq.8) between 2 times t, and tb yields the energy identification model : t b t b JqTrdt = H(q,q)(tb)- H(q,q)(ta)+ jqTrfdt =Ah X t a t a (9) Ah is the (IxNp) regressor row matrix defmed from the energy function row matrix h(q, q) : The energy model as the power model is a scalar equation whose symbolic equations are easier to calculate and manipulate than the vector equations of the dynamic model [ 101."
        ]
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure1-1.png",
        "caption": "Fig. 1 Similarity between aerodynamics and tire mechanics [1]",
        "texts": [
            " The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface The article \u201cResearch footprint of professor Akasaka\u201d edited by the alumni of the Akasaka Laboratory stated that the tire mechanics of a vehicle correspond to the aerodynamics of an airplane and fluid mechanics of a vessel. As shown in Fig. 1, the relationship between the cornering force and self-aligning torque with respect to the slip angle corresponds to that between the lift and moment of an airplane with respect to the angle of incidence. The rolling resistance corresponds to the air drag while the standing wave of a tire corresponds to the Mach wave. Furthermore, when the speed exceeds a critical speed, heat is generated such that a thermal barrier is encountered for a tire or airplane. Considering the similarity between aerodynamics and tire mechanics and the importance of aerodynamics to an airplane, it is easily imagined how important tire mechanics are to a vehicle [1]",
            " Changes in social demand related to global and local environmental problems resulted in a paradigm change for the four fundamental functions of a tire. The important functions of a tire have shifted from the four fundamental functions listed above to rolling resistance in addressing global warming, wear in addressing material sustainability and tire/road noise in addressing daily-life environments. The fact that a tire, just one part of a vehicle, realizes many functions simultaneously can be explained by the composite structure of the tire. In the case of a passenger tire as shown in Fig. 1.1, fiber-reinforced rubber (FRR), which is rubber material reinforced by fiber, is used for the tire tread and sidewall. The composite of steel cord and rubber is used for the tire tread, which is in contact with the road, \u00a9 Springer Nature Singapore Pte Ltd. 2019 Y. Nakajima, Advanced Tire Mechanics, https://doi.org/10.1007/978-981-13-5799-2_1 1 while the composite of fabric cord and rubber is used for the sidewall. Furthermore, the rubber itself is a microscopically particle-reinforced composite made of polymer, sulfur and carbon black or silica. FRR has also been used as a material of flexible products, such as belts and hoses. Figure 1.2 shows the properties of FRR and other materials. Young\u2019s modulus of the reinforcement of FRR is more than 100 times that of rubber. Meanwhile, Young\u2019s modulus of the reinforcement of fiber-reinforced plastic (FRP) is about 10 times that of plastic. The difference in Young\u2019s modulus between 2 1 Unidirectional Fiber-Reinforced Rubber the reinforcement and matrix is responsible for the anisotropic property of FRR that does not exist for FRP [1]. A rubber/plastic dispersion material, such as particles of thermoplastic elastomer rubber, is also categorized as FRR",
            " Materials used in industry generally have an axis of elastic symmetry. For example, unidirectionally reinforced laminates possess symmetry with respect to 1.1 Composite Materials Used for Tires 3 the fiber axis, and laminates with a bias angle have 180\u00b0 rotational symmetry with respect to the bisector of the bias angle. We suppose that when properties in x- and y-directions are the same as those in the z-direction, the coordinate system rotated 180\u00b0 around the z-axis is expressed by x\u2032, y\u2032 and z\u2032 (=z) as shown in Fig. 1.3. The stress and strain then change sign according to cyz \u00bc cy0z0 czx \u00bc cz0x0 syz \u00bc sy0z0 szx \u00bc sz0x0 : \u00f01:4\u00de The substitution of Eq. (1.4) into Eq. (1.3) yields rxx ryy rzz syz szx sxy 0 BBBBBB@ 1 CCCCCCA \u00bc E11 E12 E13 0 0 E16 E12 E22 E23 0 0 E26 E13 E23 E33 0 0 E36 0 0 0 E44 E45 0 0 0 0 E45 E55 0 E16 E26 E36 0 0 E66 0 BBBBBB@ 1 CCCCCCA exx eyy ezz cyz czx cxy 0 BBBBBB@ 1 CCCCCCA \u00f01:5\u00de A material expressed by Eq. (1.5) is called a monoclinic material and has 13 elastic constants. Furthermore, when 180\u00b0 rotational symmetry is satisfied with respect to not only the z-axis but also the x- and y-axes, Eq",
            "9) yields rxx ryy sxy 8>< >: 9>= >; \u00bc E 1\u00fe m\u00f0 \u00de 1 2m\u00f0 \u00de 1 m m 0 m 1 m 0 0 0 1 2m 2 2 64 3 75 exx eyy cxy 8>< >: 9>= >;: rzz \u00bc E 1\u00fe m\u00f0 \u00de 1 2m\u00f0 \u00de exx \u00fe eyy \u00f01:13\u00de A unique property of rubber is that the volume of rubber does not change even when an external force is applied to the rubber. This property is referred to as incompressibility and m \u2245 0.5 is satisfied.2 Because the relation m = 0.5 cannot be substituted into Eqs. (1.9) and (1.13), a value near m \u2245 0.5, such as m \u2245 0.49 is used for the analysis of rubber as a linear elastic material. The coordinate system shown in Fig. 1.4 is used for a composite. L and T, respectively, indicate the direction of the fiber and the direction perpendicular to the fiber. When the L-axis rotates through angle h from the x-axis and the direction of rotation is counterclockwise, the sign of h is defined to be positive. When the stress is approximated by a plane stress, the relations of stresses in the two coordinate systems shown in Fig. 1.4 are expressed by 2Note 1.1. 6 1 Unidirectional Fiber-Reinforced Rubber rxx ryy sxy 8>< >: 9>= >; \u00bc cos2 h sin2 h sin 2h sin2 h cos2 h sin 2h sin 2h=2 sin 2h=2 cos 2h 2 64 3 75 rL rT sLT 8>< >: 9>= >; rL rT sLT 8>< >: 9>= >; \u00bc cos2 h sin2 h sin 2h sin2 h cos2 h sin 2h sin 2h=2 sin 2h=2 cos 2h 2 64 3 75 rxx ryy sxy 8>< >: 9>= >;: \u00f01:14\u00de Strain in the x\u2032- and y\u2032-coordinate system is expressed by eL \u00bc @u0 @x0 eT \u00bc @v0 @y0 cLT \u00bc @u0 @y0 \u00fe @v0 @x0 ; \u00f01:16\u00de L\u03c3 T\u03c3 L x y LT\u03c4 0>\u03b8 TL\u03c4 T where x\u2032 and y\u2032, respectively, coincide with the L- and T-axes",
            " The rotational relation between (x, y) and (x\u2032, y\u2032) is given by x0 y0 \u00bc m n n m x y x y \u00bc m n n m x0 y0 ; \u00f01:17\u00de where m \u00bc cos h n \u00bc sin h: \u00f01:18\u00de The strain {eL, eT, cLT} T acting on the composite is transformed to the strain {exx, eyy, cxy} T in the x- and y-coordinate system: exx eyy cxy 8< : 9= ; \u00bc cos2 h sin2 h sin 2h=2 sin2 h cos2 h sin 2h=2 sin 2h sin 2h cos 2h 2 4 3 5 eL eT cLT 8< : 9= ;; \u00f01:19\u00de which can be rewritten with tensor notation as exx eyy cxy=2 8< : 9= ; \u00bc cos2 h sin2 h sin 2h sin2 h cos2 h sin 2h sin 2h=2 sin 2h=2 cos 2h 2 4 3 5 eL eT cLT=2 8< : 9= ;: \u00f01:20\u00de Suppose that the stress and strain vectors in the different coordinate systems are expressed by x y v u u\u2019 v\u2019 \u03b8 O P x\u2019 y\u2019 L T Fig. 1.5 Coordinate transformation for strain 8 1 Unidirectional Fiber-Reinforced Rubber f rxg \u00bc rxx ryy sxy 8>< >: 9>= >; f rLg \u00bc rL rT sLT 8>< >: 9>= >; f exg \u00bc exx eyy cxy 8>< >: 9>= >; f eLg \u00bc eL eT cLT 8>< >: 9>= >; f exg \u00bc exx eyy cxy=2 8>< >: 9>= >; f eLg \u00bc eL eT cLT=2 8>< >: 9>= >;: \u00f01:21\u00de Introducing the transformation matrix [T], the same rule of transformation for the stress and strain can be expressed by f rxg \u00bc \u00bdT 1f rLg f exg \u00bc \u00bdT 1f eLg; \u00f01:22\u00de where the transformation matrix [T] and inverse matrix [T]\u22121 are given by \u00bdT \u00bc cos2 h sin2 h sin 2h sin2 h cos2 h sin 2h sin 2h=2 sin 2h=2 cos 2h 2 64 3 75 \u00bdT 1 \u00bc cos2 h sin2 h sin 2h sin2 h cos2 h sin 2h sin 2h=2 sin 2h=2 cos 2h 2 64 3 75: \u00f01:23\u00de 1",
            " Hence, Ui is considered to denote the elastic constants of the ply. Furthermore, Table 1.1 shows that Exx, Eyy, Exy and Ess contain the invariants U1, U4 and U5, which are independent of the orientation angle h. The invariants satisfy U5 \u00bc U1 U4\u00f0 \u00de=2: \u00f01:51\u00de There are thus two independent invariants. We consider the physical meaning of Exx in Eq. (1.45) as an example. Exx is expressed by Exx \u00bc U1 \u00feU2 cos 2h\u00feU3 cos 4h: \u00f01:52\u00de Equation (1.52) consists of three terms, the contribution of each being shown in Fig. 1.6. Exx is composed of the invariants U1, U2 with a period of p and U3 with a period of p/2. It is clear that U2 = U3 = 0 is satisfied for an isotropic material, such as steel or aluminum. The material behaves in an isotropic manner if U1 is larger than U2 and U3 and in an anisotropic manner if U1 is smaller than U2 and U3. 1.3 Mechanics of a Composite 15 (1) Tensile modulus of a composite When only stress rxx is applied in the x-direction with orientation angle h measured from the principal L-axis of the orthotropic material as shown in Fig. 1.7, the stress vector is expressed by 16 1 Unidirectional Fiber-Reinforced Rubber The substitution of Eq. (1.53) into the first equation of Eq. (1.46) yields exx \u00bc Cxxrxx rxx=Ex eyy \u00bc Cxyrxx mxrxx=Ex cxy \u00bc Cxsrxx; \u00f01:54\u00de where we note that Ex is different from Exx in Eq. (1.45). Ex is determined with the zero transverse and shear stress boundary condition, while Exx is determined with the zero transverse and shear strain boundary condition. Figure 1.7 shows that, when stress is applied in the x-direction, there is not only tensile deformation in the x-direction and compressive deformation in the y-direction but also shear deformation. From Eq. (1.54), we obtain Ex \u00bc rxx=exx \u00bc 1=Cxx mx eyy=exx \u00bc Cxy=Cxx: \u00f01:55\u00de Calculating the inverse matrix [E]\u22121 of Eq. (1.39), Cxx and Cxy can be expressed using Eij. The substitution of Cxx and Cxy into Eq. (1.55) yields The direction in which Ex is maximized or minimized can be obtained by solving the relation dEx/dh = 0 in Eq",
            " 18 1 Unidirectional Fiber-Reinforced Rubber The direction in which Gxy is maximized or minimized can be summarized as7 \u00f0i\u00de Gxy;max \u00bc Gh\u00bc0 \u00bc Gh\u00bc90 \u00bc GLT in the case that \u00f0EL \u00feET \u00fe 2mLET\u00de [ELET=GLT ; \u00f01:62a\u00de \u00f0ii\u00de Gxy;max \u00bc Gh\u00bc45 \u00bc ELET=\u00f0EL \u00feET \u00fe 2mLET\u00de in the case that \u00f0EL \u00feET \u00fe 2mLET\u00de\\ELET=GLT ; \u00f01:62b\u00de \u00f0iii\u00de Gxy;max \u00bc GLT \u00bc ELET=\u00f0EL \u00feET \u00fe 2mLET\u00de in the case that EL \u00feET \u00fe 2mLET \u00bc ELET=GLT : \u00f01:62c\u00de When an orthotropic material is used to control shear deformation, the direction of the fiber must be appropriately determined by considering the above relationship. For example, when the modulus of the fiber is much larger than that of the matrix, the angle between the x-direction and the direction of the fiber should be 45\u00b0 according to Eq. (1.62b). Figure 1.9 shows the case of nylon\u2013rubber composites where Young\u2019s modulus of fiber Ef = 3.45 GPa, Young\u2019s modulus of matrix Em = 5.52 MPa, the volume fraction of the fiber Vf = 0.326, the Poisson\u2019s ratio of fiber mf = 0.45 and the Poisson\u2019s ratio of matrix mm = 0.49 [4, 5]. For any cord\u2013rubber ply, the shear modulus Gxy has a maximum value at h = 45\u00b0. (3) Comparison of the modulus and transformed stiffness of a composite Figure 1.10 compares the modulus Ex and transformed stiffness Exx where the elastic properties are the same as those for Fig. 1.9. The two stiffnesses are defined by L T xE xyG 0 30 60 90 x y Cord angle (deg) \u03b8 El as tic p ro pe rty (M Pa ) 10 102 103 1 104 Fig. 1.9 Young\u2019s modulus Ex and shear modulus Gxy versus the cord angle h for 840/2 nylon\u2013rubber ply. Reproduced from Ref. [5] with the permission of Rubber Chem. Technol. 7See Footnote 5. 1.3 Mechanics of a Composite 19 rxx \u00bc Exexx for ryy \u00bc sxy \u00bc 0 rxx \u00bc Exxexx for eyy \u00bc cxy \u00bc 0; \u00f01:63\u00de where Ex is given by the constrained deformation (strain), while Exx is given by the free-boundary condition of in-plane shear stress and lateral normal stress. There is a large difference between the two stiffnesses",
            " Therefore, the stiffness of a tire belt has a value between Ex and Exx. The micromechanics are considered in deriving the average properties of a composite, where the stress and strain components are averaged over the composite. The discussion is limited to a fiber-reinforced composite in this chapter. Once the properties of the composite are described, the properties of the laminate of the composite can be easily calculated. The composite used in a tire has a low volume fraction of fiber and can be modeled by gathering the fiber and matrix as shown in Fig. 1.11. 20 1 Unidirectional Fiber-Reinforced Rubber (1) Modulus of the composite in the direction of the fiber (parallel model) The direction of the fiber is in the L-direction, while the fiber and matrix are aligned in parallel as shown in Fig. 1.11. When the strain is applied in the L-direction and we can assume that the strains of the fiber and matrix are the same, we have ef \u00bc em \u00bc ec; \u00f01:64\u00de where the subscripts f, m and c, respectively, indicate the fiber, matrix and composite. Assuming that the materials behave elastically, the stress/strain relations are expressed by rf \u00bc Efef \u00bc Efec rm \u00bc Emem \u00bc Emec rc \u00bc Ecec; \u00f01:65\u00de where rf, rm and rc are, respectively, the stresses of the fiber, matrix and composite. The total load Pc applied to a composite is expressed by Pc \u00bc Pf \u00fePm \u00bc rfAf \u00fe rmAm \u00bc \u00f0EfAf \u00feEmAm\u00deec \u00bc ELAcec; \u00f01:66\u00de where Pf and Pm are the loads acting on the fiber and matrix while Af, Am and Ac are, respectively, the sectional areas of the fiber, matrix and composite",
            " Vm=\u00f0Vm \u00feVv\u00de\u00bd Em; \u00f01:70\u00de where Vv is the volume fraction of voids. Because the FRR composite generally satisfies the relation Ef Em, Eq. (1.67) can be simplified as EL EfVf : \u00f01:71\u00de To increase the modulus in the fiber direction, the volume fraction of the fiber or the modulus of the fiber needs to be increased without sacrificing other functions, such as adhesion between the fiber and matrix. Walter [5] compared predictions made using Eq. (1.67) with the measurements of 167/2 Kevlar aramid\u2013rubber plies with different fiber volume fractions as shown in Fig. 1.12. The prediction is in good agreement with the measurement. (2) Modulus of a composite in the direction transverse to the fiber (series model) When a load is applied in the direction transverse to the fiber, we can assume that the fiber and matrix are connected in series as shown in the right figure of Fig. 1.11. The modulus of a composite in the direction transverse to the fiber ET is given by 1 ET \u00bc Vf Ef \u00fe Vm Em ! ET \u00bc EfEm EmVf \u00feEf\u00f01 Vf\u00de : \u00f01:72\u00de Equation (1.72) is called the inverse rule of mixtures. measurement prediction Fiber volume fraction Vf Lo ng itu di na l m od ul us E L (G Pa ) 0 0.1 0.2 0.30 0.4 0.8 1.2 1.6 2.0Fig. 1.12 Comparison of the prediction made using Eq. (1.67) and measurement as a function of fiber volume fraction Vf for 167/2 Kevlar\u2013 rubber ply (Ef = 6.03 GPa, Em = 7.93 MPa). Reproduced from Ref. [5] with the permission of Rubber Chem. Technol. 22 1 Unidirectional Fiber-Reinforced Rubber (3) Poisson\u2019s ratio of a composite in the fiber direction and shear modulus of a composite Referring to Fig. 1.11, the Poisson\u2019s ratio of a composite in the fiber direction mL and the shear modulus of a composite GLT are given by mL \u00bc mfVf \u00fe mm\u00f01 Vf\u00de GLT \u00bc GfGm GmVf \u00feGf\u00f01 Vf\u00de ; \u00f01:73\u00de where Gf and Gm are given by Gf \u00bc Ef 2\u00f01\u00fe mf\u00de Gm \u00bc Em 2\u00f01\u00fe mm\u00de : \u00f01:74\u00de 1.4.2 Modified Micromechanics (1) Transverse Young\u2019s modulus of a composite Simple material models for EL and mL are good enough for design use. However, the corresponding models for ET and GLT are of questionable value. Chamis [6] thus developed an improved micromechanics model for ET and GLT based on a square fiber-packing array and a method of dividing the representative volume element (RVE) into subregions. Figure 1.13 shows the RVE where the round fiber is changed to a square having the same area as the round fiber and divided into subregions [7]. The equivalent square fiber has the dimension sf \u00bc ffiffiffi p 4 r d: \u00f01:75\u00de Referring to Fig. 1.14, the equations of the force equilibrium and compatibility are derived for subregion B: rf \u00bc rm \u00bc rT ; \u00f01:76\u00de em\u00f0s sf\u00de\u00fe efsf \u00bc eLs; \u00f01:77\u00de where rf, rm, ef and em are, respectively, the stress and strain of the fiber and matrix, while eL and rT are, respectively, the strain and external stress in the subregion of the RVE. 1.4 Micromechanics 23 The stress/strain relationships are expressed by ef \u00bc rf=Ef ; em \u00bc rm=Em; eT \u00bc rT=ETB; \u00f01:78\u00de where EfT, Em and ETB are, respectively, the transverse Young modulus of the fiber and the Young moduli of the matrix and subregion B",
            "79) yields 1 ETB \u00bc ffiffiffiffiffi Vf p EfT \u00fe 1 ffiffiffiffiffi Vf p Em : \u00f01:81\u00de Hence, ETB in subregion B is expressed by ETB \u00bc Em 1 ffiffiffiffiffi Vf p 1 Em EfT : \u00f01:82\u00de 24 1 Unidirectional Fiber-Reinforced Rubber The transverse Young\u2019s modulus of RVE, ET, is derived using the parallel model and expressed by ET \u00bc sf s ETB \u00fe s sf s Em: \u00f01:83\u00de The substitution of Eqs. (1.80) and (1.82) into Eq. (1.83) yields ET \u00bc 1 ffiffiffiffiffi Vf p Em \u00fe ffiffiffiffiffi Vf p Em 1 ffiffiffiffiffi Vf p 1 Em EfT : \u00f01:84\u00de (2) Shear modulus of a composite Referring to Fig. 1.15, the equations of the shear force equilibrium and the compatibility relation are similarly derived for subregion B: sf \u00bc sm \u00bc sLT ; \u00f01:85\u00de cm\u00f0s sf\u00de\u00fe cfsf \u00bc cLTs: \u00f01:86\u00de The stress/strain relationships are cf \u00bc sf=GfLT cm \u00bc sm=Gm cT \u00bc sT=GLTB; \u00f01:87\u00de where GfLT, Gm and GLTB are, respectively, the shear modulus of the fiber on the L\u2013 T plane and the shear moduli of the matrix and subregion B. Using Eqs. (1.80) and (1.87), Eq. (1.86) is rewritten as GLTB \u00bc Gm 1 ffiffiffiffiffi Vf p 1 Gm GfLT : \u00f01:88\u00de 1",
            " Jones [10] showed that when the relation n = 0 is satisfied, the Halpin\u2013Tsai equation with respect to ET in Eq. (1.94) reduces to the inverse rule of mixtures given as Eq. (1.72), whereas a value of n = \u221e yields the rule of mixture given as Eq. (1.67). The interpretation of the curve-fitting parameter, n, as a measure of the degree of fiber reinforcement thus has a theoretical basis. The transverse composite modulus ET calculated using the Halpin\u2013Tsai equation is shown as a function of the fiber volume fraction for different constituent modulus ratios as shown in Fig. 1.17. Figure 1.18 shows the transverse modulus of a 28 1 Unidirectional Fiber-Reinforced Rubber composite as a function of the fiber volume fraction Vf calculated using the Halpin\u2013 Tsai equation (Eq. 1.94) and upper and lower bounds (Eq. 1.93). The value calculated using the Halpin\u2013Tsai equation is between the upper and lower bounds. UDCRR is a composite of rubber reinforced by cords placed at even intervals in parallel as shown in Fig. 1.12. UDCRR is the most important part of rubber products and has important anisotropic properties. The following various models for UDCRR have been proposed [11]. (1) Gough\u2013Tangorra equation Gough and Tangorra [12] proposed expressions specifically tailored to the properties of cord-reinforced rubber. The transverse modulus is expressed as ET \u00bc 4Em 1 Vf\u00f0 \u00de EfVf \u00feEm 1 Vf\u00f0 \u00def g 3EfVf \u00fe 4Em 1 Vf\u00f0 \u00de : \u00f01:97\u00de They also used a simple approximation for the shear modulus and assumed a Poisson\u2019s ratio mL = 0.5. (2) Akasaka\u2013Hirano equation The Akasaka\u2013Hirano equations [13] are a simplified version of the rule of mixtures and the Gough\u2013Tangorra equation: Fiber volume fraction: Vf lower bound upper bound M od ul us ra tio : E T/E m Halpin-Tsai equation 0 0.2 0.4 0.6 0.8 1 Ef=50.5 GPa Em=3 MPa 1 10 102 103 104 105 Fig. 1.18 Transverse modulus of the composite as a function of the fiber volume fraction calculated using the Halpin\u2013Tsai equation (Eq. 1.94) and upper and lower bounds (Eq. 1.93) 1.4 Micromechanics 29 EL \u00bc EfVf ET \u00bc 4 3 Em GLT \u00bc Gm \u00bc Em 2\u00f01\u00fe mm\u00de mL \u00bc 0:5 mT \u00bc 0: \u00f01:98\u00de (3) Clark equation Clark [14] used an energy method to formulate expressions for the lamina elastic constants without requiring detailed cord properties, such as the shear modulus and Poisson\u2019s ratio. The theory uses a stiffening parameter / indicating the degree of stiffening imposed by the cord structure: EL \u00bc EfVf \u00fe 12 Gm 1 Vf ET \u00bc Gm 4 4 2\u00fe/ \u00fe 4\u00fe 2/ 2\u00fe/\u00f0 \u00de2 1 Vf / \u00bc EfVf 1 Vf 2Gm GLT \u00bc Gm 1 Vf mL \u00bc 0:5: \u00f01:99\u00de (4) Akasaka\u2013Kabe equation Akasaka and Kabe [15] proposed a model for the transverse modulus of cord-reinforced rubber. Figure 1.19 shows the model, where the cord has a rectangular cross section and is laterally placed at even intervals. rT is uniform tensile stress transverse to the fiber direction and rfL, efL, rmL and emL are, respectively, the 30 1 Unidirectional Fiber-Reinforced Rubber stress and strain of the fiber in the fiber direction and the stress and strain of the matrix in the fiber direction. Using Eq. (1.68), Eqs. (1.67) and (1.73) can be rewritten as EL \u00bc EfVf \u00feEmVm mL \u00bc mfVf \u00fe mmVm 1=GLT \u00bc Vf=Gf \u00feVm=Gm: \u00f01:100\u00de Referring to Eq",
            " 36 1 Unidirectional Fiber-Reinforced Rubber The substitution of Eq. (1.119) and h = h* into Eq. (1.56) yields Ex\u00f0h \u00de \u00bc 3ET=4 \u00bc Em: \u00f01:122\u00de At h = h*, Ex takes the minimum value Em, which is Young\u2019s modulus for rubber. The reinforcing effect of cords is thus completely lost at h = h* for UDCRR and the uniform normal stress vector {rx, 0, 0}. Kabe [15] compared micromechanics and experimental results for UDCRR, where the elastic constants for composite were Ef = 2.85 GPa, Em = 5 MPa, mf = 0.4 and mm = 0.5 (Fig. 1.24). The relation GLT/ET 1/4 in Eq. (1.113) is in good agreement with the experimental results except for Vf = 0 and Vf = 1. The ratio of GLT calculated using Eq. (1.73) to ET calculated using the Akasaka\u2013Kabe equation (given as Eq. 1.108) agrees with the measurement better than that calculated using the simplified Halpin\u2013Tsai equation (given as Eq. 1.116). 1.5 1.0 0.5 0.5 0 30 60 90 C xs \u00d7E T \u03b8 (deg) Fig. 1.23 Relationship between CxsET and cord angle h [15] 1.6 Mechanics of UDCRR Under an FRR Approximation 37 The rolling resistance of a tire is related to the energy loss due to the viscoelastic properties of the compound and FRR. The viscoelastic properties of a UDCRR plate are important to the rolling resistance and other performance factors of a tire. The general idea of viscoelasticity is described in the Appendix. Chandra et al. [16] made a comparative study of mechanical damping models classified as analytical models and finite element models",
            " For the FRR composite, Tabaddor [30] and Fujimoto [31] applied a complex modulus model. Kalishke et al. [32, 33] extended Aboudi\u2019s method of cells to predict six damping coefficients. Koishi et al. [34, 35] predicted the loss tangent using the finite element method and by modeling the composite employing homogenization. Akasaka-Kabe Halpin-Tsai measurement Fiber volume fraction Vf 0 0.2 0.4 0.6 0.8 1.00 0.2 0.4 0.1 0.3 0.5 0.25 0.5 Ef=2.85 GPa, Em=5 MPa \u03bdf=0.4, \u03bdm=0.5 G LT /E T (0.357)(0.334) Fig. 1.24 Comparison of the transverse modulus between models and measurement [15] 38 1 Unidirectional Fiber-Reinforced Rubber (1) On-axis ply damping The damping properties of a laminate can be analyzed employing the approach of the law of mixtures in the micromechanics discussed in Sect. 1.4.2. Saravans and Chamis [17] applied the energy method to the single-fiber RVE of the square packing array shown in Fig. 1.13, as a unified micromechanics approach. The specific damping capacity of material w is defined as the ratio of the dissipated strain energy D to the maximum stored energy U: w \u00bc D=U \u00bc 2pg; \u00f01:123\u00de where \u03b7 is the loss factor or the loss tangent tan d defined by g \u00bc E00=E0: \u00f01:124\u00de Here, E0 and E00 are the real and imaginary parts of the complex Young\u2019s modulus E : E \u00bc E0 \u00fe jE00: \u00f01:125\u00de DL \u00bc 1 2 Z Vf wfLrfLefLdVf \u00fe 1 2 Z Vm wmrmemdVm; \u00f01:126\u00de where wfL, rfL, efL and Vf are, respectively, the specific damping capacity of fiber, stress and strain of the fiber in the longitudinal direction and the volume fraction of the fiber",
            " Applying a similar derivation as used for Eq. (1.81), the transverse loss factor of composite \u03b7T is expressed as11 gT \u00bc gfT ffiffiffiffiffi Vf p ET EfT \u00fe gm 1 ffiffiffiffiffi Vf p ET Em ; \u00f01:130\u00de where \u03b7fT and EfT are the transverse loss factor of the fiber and transverse Young\u2019s modulus of the fiber. ET is the transverse Young\u2019s modulus of a composite defined by Eq. (1.84). The assumption of transverse isotropy gives gT \u00bc gZ ; \u00f01:131\u00de where characteristics are the same for the T-direction and Z-direction in Fig. 1.15. Furthermore, the shear loss factor for the in-plane shear damping of a composite, \u03b7LT, is given by gLT \u00bc gfLT ffiffiffiffiffi Vf p GLT GfLT \u00fe gm 1 ffiffiffiffiffi Vf p GLT Gm ; \u00f01:132\u00de where \u03b7fLT and GfLT are the shear loss factor of the fiber and the shear modulus of the fiber. GLT is the in-plane shear modulus of a composite defined using Eq. (1.89). The out-of-plane shear loss factor of a composite, \u03b7TZ, is given by gTZ \u00bc gfTZ ffiffiffiffiffi Vf p GTZ GfTZ \u00fe gm 1 ffiffiffiffiffi Vf p GTZ Gm ; \u00f01:133\u00de where \u03b7fTZ and GfTZ are the out-of-plane shear loss factor of the fiber and the out-of-plane shear modulus of the fiber",
            " Meanwhile, the hysteretic strain energy loss of a composite is defined by D \u00bc 1 2 Z V rLf gT wL eLf gdV : \u00f01:136\u00de Comparing Eq. (1.135) with Eq. (1.136), we obtain wx \u00bc T\u00bd T wL T\u00bd T: \u00f01:137\u00de where \u00bd wL is expressed by the diagonal matrix wL \u00bc wL 0 0 0 wT 0 0 0 wZ 2 4 3 5; \u00f01:138\u00de with wL, wT and wZ, respectively, being the damping capacities in the L-, T- and Zdirections. (3) Comparison of prediction and experiment results Saravanos and Chamis [17] compared the results obtained using their model with measurement for various fiber volume fractions as shown in Fig. 1.25. The matrices are intermediate-modulus high-strength (IMHS) epoxy and intermediate-modulus low-strength (IMLS) polyester. The fibers are E-glass, high-modulus surface-treated graphite (HM-S) and high-tensile surface-treated graphite (HT-S). They concluded 12The relationship [R]\u22121[T]\u22121[R] = [T]T is satisfied. 1.7 Viscoelastic Properties of a UDCRR Plate 41 that their theory is acceptable for fiber volume ratios within the range of interest for most engineering applications. Chandra et al. [16] compared the various approaches of loss factor formulations",
            " The prediction is in good agreement with the measurement for various mode shapes. The damping value depends on the mode shape and the damping in a composite plate increases with more twisting. 1.7 Viscoelastic Properties of a UDCRR Plate 43 Koishi et al. [34, 35] predicted the loss tangent using the finite element method whereby a composite was modeled employing the homogenization method. They calculated the relationship between the volume fraction of the fiber Vf and the loss tangent of FRR as shown in Fig. 1.28. tan dL and tan dT are, respectively, the loss tangents in the longitudinal and transverse directions. The ratio of the fiber modulus tan\u03b4T(Ef /Em=101) Lo ss ta ng en t ( in de x) 0 0.2 0.4 0.6 0.8 1.0 0.50 1.00 Fiber volume fraction Vf tan\u03b4T(Ef /Em=102) tan\u03b4T(Ef /Em=103) tan\u03b4L(Ef /Em=101) tan\u03b4L(Ef /Em=102) tan\u03b4L(Ef /Em=103) Lo ss ta ng en t ( in de x) Cord angle (degree) 0 30 60 90 0.05 Homogenization method Experiment Law of mixture 0.20 0.10 0.15 Fig. 1.29 Comparison of the equivalent loss tangent calculated employing homogenization and experimental results. Reproduced from Ref. [35] with the permission of Tire Sci. Technol. Ef to the matrix modulus Em was changed parametrically. When the ratio Ef/Em was increased to 103, which is the value for a composite used in tires, it was observed that the equivalent loss tangent in the longitudinal direction can be approximated by the loss tangent of the fiber, while the equivalent loss tangent in the transverse direction can be approximated by the loss tangent of the rubber material. Figure 1.29 shows the computed loss tangent and the measurement for different cord angles. The loss tangent obtained using the homogenization method agrees well with the experimental values. However, the predictions made using the law of mixtures do not agree with the experimental values. Kalishke [33] proposed a formulation of viscoelasticity for fiber-reinforced material at small and finite strains and obtained the hysteresis curve of layers in a laminate. The composite of SFRR is also used for rubber products where fibers (of polyamide, polyester or aramid) are aligned in rubber",
            " The following empirical equation can be used to predict the modulus of a composite containing fibers that are randomly oriented in a plane: Erandom \u00bc 3 8 EL \u00fe 5 8 ET : \u00f01:144\u00de Ashida [43] studied the effect of the fiber orientation on the dynamic storage modulus E\u2019 of SFRR when the fiber was 10 percent vol. nylon or polyester (polyethylene terephthalate, PET) and the matrix was the chloroprene rubber (CR). The dynamic storage modulus E\u2019 of SFRR in the direction h measured from the fiber direction can be also expressed by the first and third equations of Eq. (1.38): 1 Eh \u00bc cos4 h EL \u00fe sin4 h ET \u00fe 1 GLT 2mL EL sin2 h cos2 h 1 Gh \u00bc 1 GLT \u00fe 1\u00fe 2mL EL \u00fe 1 ET 1 GLT sin2 2h: \u00f01:145\u00de l/d E L (p si ) Nylon/rubber composite 0 10 103 Halpin-Tsai Ef /Em =97.3 \u03bdf =0.35 104 105 103 102 measurement Fig. 1.30 Comparison of predictions from the Halpin\u2013 Tsai equation and measurements [7] 46 1 Unidirectional Fiber-Reinforced Rubber The assumption that Gh is constant in any direction is satisfied for SFRR, and the second term of the second equation of Eq. (1.145) must be zero. Equation (1.145) can thus be simplified as 1 Gh \u00bc 1 GLT \u00bc 1\u00fe 2mL EL \u00fe 1 ET : \u00f01:146\u00de The substitution of Eq. (1.146) into Eq. (1.145) gives 1 Eh \u00bc cos2 h EL \u00fe sin2 h ET ; \u00f01:147\u00de where EL and ET are, respectively, the moduli in the direction of the fiber and the direction transverse to the fiber. Figure 1.31 shows that the calculation results obtained using Eq. (1.147) are in good agreement with the measurements. Ashida [44] measured the modulus of SFRR. The ratio of the dynamic storage modulus E0 h in the direction h measured from the fiber direction to the dynamic storage modulus in the fiber direction (h = 0\u00b0) E\u2019 of SFRR is shown in Fig. 1.32. The SFRR consisted of 10 percent vol. polyester fiber (PET) having lengths of 0.5, 1, 2 and >4 mm and CR. The storage modulus decreases remarkably in the range h = 0\u00b0 to 30\u00b0 and is almost constant in the range h = 45\u00b0\u201390\u00b0 for SFRR with any length of fibers. Angle \u03b8 (deg) E\u00b4 (M Pa ) theory PET nylon 0 30 60 90 100 200 300 400 0 experiment \u03b8 Fig. 1.31 Effect of the fiber orientation on the dynamic storage modulus for PET\u2013CR composites filled with fibers. Reproduced from Ref. [43] with the permission of Nippon Gomu Kyokai 1.8 Mechanics of Short-Fiber-Reinforced Rubber (SFRR) 47 Ashida [44] measured the temperature dependence of the loss tangent tan d of SFRR as shown in Fig. 1.33 where fibers were 10 percent vol. polyester fiber (PET) having lengths of 0.5, 1, 2 and >4 mm and the matrix was CR. tan d in the Vf=10 % \uff1a0.5mm \uff1a1mm \uff1a2mm \uff1amore than 4mm Angle \u03b8 (deg) E\u00b4 \u03b8 / E\u00b4 || 0 30 60 90 0.5 0 \u03b8 1.0Fig. 1.32 Effect of the fiber orientation and length on the dynamic storage modulus for PET\u2013CR composites filled with fibers. Reproduced from Ref. [44] with the permission of Nippon Gomu Kyokai 48 1 Unidirectional Fiber-Reinforced Rubber direction of the fiber decreases when fibers are blended and the length of fibers is longer. tan d near room temperature related to the rolling resistance of a tire decreases with an increasing length of fibers. tan d of SFRR with a 6-mm fiber length has two peaks, at 30\u00b0 and 140\u00b0. The former peak is related to CR and the latter peak is related to PET. The peak of CR increases, and the peak of PET decreases a decreasing length of fibers. The effect of fibers on properties of SFRR weakens at a fiber length less than 4 mm even though the volumes of fibers are the same. Ashida [43] also measured the effect of the orientation angle h of fibers on the loss tangent tan d of SFRR when fibers were nylon and the matrix was CR as shown in Fig. 1.34. tan d decreases up to 80 \u00b0C with decreasing orientation angle h. The peaks of tan d at \u221228\u00b0 and 100 \u00b0C are, respectively, related to CR and nylon. The value of the former peak decreases, while the value of the latter peak increases with decreasing orientation angle h. Hence, as h increases, the effect of fibers on tan d strengthens. Problems 1:1 Derive Eq. (1.7). 1:2 Derive Eqs. (1.38) and (1.45). 1:3 Derive Eqs. (1.57) and (1.62). 1:4 A lamina consisting of continuous fibers randomly oriented in the plane of the lamina is said to be planar isotropic, and the elastic properties in the plane are isotropic. Find an expression for lamina stiffnesses of a planar isotropic lamina. Hint: Use Eq. (1.48) and integrate with respect to h. \uff1a\u03b8=0 \uff1a\u03b8=45 \uff1a\u03b8=90 \uff1aCR Vf=10 % Temperature (\u2103) ta n\u03b4 0 120 160 100 \u221280 10\u22121 10\u22122 8040\u221240 Fig. 1.34 Effect of the fiber orientation on tan d for nylon in a CR composite with fibers. Reproduced from Ref. [43] with the permission of Nippon Gomu Kyokai 1.8 Mechanics of Short-Fiber-Reinforced Rubber (SFRR) 49 1:5 Derive Eq. (1.118). 1:6 Derive Eq. (1.130). 1:7 The constituent materials in the carbon/epoxy composite have the properties Ef = 220 GPa, Em = 3.45 GPa and Vf = 0.506. Estimate the transverse moduli of the composite using the rule of mixtures of Eq. (1.72), modified formula of Eq. (1.84) and the Halpin\u2013Tsai equation of Eq",
            " Integrating De in the volume of the structure, the energy loss in a period DE and the initial strain energy E0 are expressed by DE \u00bc p Z V erf gT E00\u00bd erf gdV E0 \u00bc 1 2 Z V erf gT E0\u00bd erf gdV : \u00f01:173\u00de Equations (1.171) and (1.173) give the modal damping ratio fr expressed by 54 1 Unidirectional Fiber-Reinforced Rubber fr \u00bc 1 2 R V erf gT E00\u00bd erf gdVR V erf gT E0\u00bd erf gdV : \u00f01:174\u00de Hence, if the complex elastic matrix \u00bdE is known, fr can be calculated from the strain energy distribution of the mode corresponding to the real eigenvector. Notes Note 1.1 Incompressibility of Rubber Rubber has specific properties that the volume is maintained under external forces. Referring to Fig. 1.35a, the incompressibility is expressed by 1\u00fe ex\u00f0 \u00delx 1\u00fe ey ly 1\u00fe ez\u00f0 \u00delz \u00bc lxlylz: The low-strain assumptions ex, ey, ez 1 yield ex \u00fe ey \u00fe ez \u00bc 0: Figure 1.35b shows the deformation of the element where the external force is applied in the z-direction. When the strain along the z-axis is e, strains along the xand y-axes can be expressed by e and Poisson\u2019s ratio m. Referring to Fig. 1.35b, the incompressibility can be expressed by 1 me\u00f0 \u00delx 1 me\u00f0 \u00dely 1\u00fe e\u00f0 \u00delz \u00bc lxlylz: The assumption of low strain e 1 yields Appendix: Viscoelasticity 55 1 me\u00f0 \u00de2 1\u00fe e\u00f0 \u00de ffi 1 2me\u00f0 \u00de 1\u00fe e\u00f0 \u00de ffi 1\u00fe 1 2m\u00f0 \u00dee \u00bc 1: Poisson\u2019s ratio for incompressible materials is m = 1/2 from the above equation. Note 1.2 When \u22121 < cos 2h < 1 is satisfied, the extreme value is located away from h = 0\u00b0 and h = 90\u00b0. Because ET EL ELET=GLT EL \u00feET \u00fe 2mLET\u00f0 \u00de\\1 is satisfied, GLT > EL/{2(1 + mL)} is obtained considering the relation EL \u2212 ET > 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000630_tro.2021.3060969-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000630_tro.2021.3060969-Figure11-1.png",
        "caption": "Fig. 11. Multiple initial grasping postures of the gripper. (a) All fingers close. (b) two fingers adjust distance. (c) All fingers adjust distance. (d) Two fingers adjust distance and all fingers adjust angles. (e) All fingers spread out. (Upper: CAD models of various postures; lower: prototype images of various postures; scale bar: 4 cm).",
        "texts": [
            " As the tapered angle increases, the fingertip becomes sharper, so we achieve high curvature difference along the finger from the root to tip, but low tip force. Considering these conflicting effect, we chose a medium tapered angle of 6.22\u25e6 for our final design, for which, the curvature ranges from 26 to 8 m\u22121, from root to tip, and the tip force is more than 80% of that for the all-straight fingers (tapered angle of 0\u25e6.) The gripper obtains various initial grasping postures through the distance- and angle-adjusting actuators, as shown in Fig. 11. It is able to close up all finger actuators for pinching small objects [see Fig. 11(a)], and it is able to open the angle of facing fingers and expand distance of same-side fingers for enveloping relatively large objects [see Fig. 11(e)]. Besides, there are many Authorized licensed use limited to: Dalhousie University. Downloaded on May 25,2021 at 12:16:37 UTC from IEEE Xplore. Restrictions apply. states in between for grasping objects with special geometries (e.g., a long and thin rod), by continuously adjusting the inflating pressures of the distance- and angle-adjusting actuators [see Fig. 11(b)\u2013(d)]. Besides the initial posture adjustment capability, the gripper is compact and lightweight. The design parameters of the gripper are summarized in Table I. In its most compact state [see Authorized licensed use limited to: Dalhousie University. Downloaded on May 25,2021 at 12:16:37 UTC from IEEE Xplore. Restrictions apply. Fig. 11(a)], the length, width, and the height of the gripper are 100, 60, and 170 mm, respectively. The maximum change of distance between fingers on same sides is 64.4 mm at 90 kPa (64.4% of the gripper\u2019s initial length), and the maximum opening angle of the gripper is 140\u25e6 at 143 kPa (initial angle as 0\u25e6). Through the aforementioned efforts, the gripper is able to grasp various objects, from short and tiny ones, to long and thick ones. To quantitatively evaluate the gripper\u2019s grasping capability, we set up two apparatuses to measure its gripping force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.41-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.41-1.png",
        "caption": "Fig. 5.41: Sketch of VARIO-ML System (courtesy AGCO/Fendt)",
        "texts": [
            " The German company Agco/Fendt as one of the leading enterprises of modern tractor technologies developed for that purpose a very efficient power transmission including for low speeds a hydrostatic drive and for larger speeds a gear system with the possibility of mixing the power transmission according to external requirements. The hydrostat system possesses the great advantage to develop very large torques especially at low speeds and at standstill. Figure 5.3.1 ilustrates the kernel of the power transmission, and Figure 5.41 presents a sketch of the overall system. Following this sketch we recognize that the torque of the Diesel engine is transmitted via a torsional vibration damper (1) to the planet carrier (5) of the planetary gear set (2). The planet gear distributes the power to the sunwheel (4) and the ring gear (3). This ring gear drives via a cylindrical gear pair the hydraulic pump (6), which itself powers the two hydraulic motors (7), where the oil flow from pump to motor depends on the pump displacement angle \u03b1",
            " The crankshaft of the Diesel engine is described by a rigid body (2) with one DOF, which is loaded by the torque from the combustion pressure. They must be determined from measurements of the combustion process and correctly projected to the crankshaft model. The front PTO (power take off, 20, 21) is connected to the engine by a vibration damper. Also the planetary set (7) and all auxiliary equipment (5) are driven more or less directly by the engine. The model follows the diagrammatic sketch of Figure 5.41 with some extensions. They concern mainly the two power take off systems, front PTO and rear PTO, and also the front and rear axles with the tires. We shall come back to all components. Figure 5.3.2 pictures a very classical mechanic-hydraulic system, where the physical relations are obvious. Therefore it represents a good example how to establish a mechanical (or physical) model, which is equivalent to the real world problem. As already mentioned, engineering mechanics nor engineering physics are not deductive sciences thus requiring as a rule bundles of assumptions and neglections without destroying the principal information base of a system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003287_pres.1996.5.4.393-FigureI-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003287_pres.1996.5.4.393-FigureI-1.png",
        "caption": "Figure I. A simplified model of the human arm.",
        "texts": [],
        "surrounding_texts": [
            "University of Pennsylvania Philadelphia, Pennsylvania 19104\nA simple inverse kinematics procedure is proposed for a seven degree of freedom model of the human arm. Two schemes are used to provide an additional constraint leading to closed-form analytical equations with an upper bound of two or four solutions, Multiple solutions can be evaluated on the basis of their proximity from the rest angles or the previous configuration of the arm. Empirical results demonstrate that the procedure is well suited for real-time applications.\nIntroduction\nPresence, Vol. 5, No. 4, Fall 1996, 393-401 \u00a9 1996 by the Massachusetts Institute of Technolog/\nReal-time inverse kinematics is a key component of a human modeling system. For example, in interactive figure manipulation it is convenient for the user to specify the desired location of the hand instead of explicitly manipulating the arm joints. Another important application of inverse kinematics occurs in the playback of motion capture data where joint angle trajectories must be inferred from the movement of sensors positioned on the body.\nMechanisms with more than six degrees of freedom, such as the human arm, are said to be redundant because they have more flexibility than required to achieve a given end-effector position and orientation. In robotics applications redundancy is often exploited to satisfy additional objectives such as torque optimization, and singularity and obstacle avoidance. It is generally impossible to solve for these additional criteria analytically so a numerical procedure must be used. For example, Klein (1984) used a generalized pseudoinverse technique to avoid joint limits and obstacles. Suh and Hollerbach (1987) also used the pseudoinverse to minimize torque utilization. In the computer graphics community, Maciejewski (1990) used a generalization of the pseudoinverse to generate smooth trajectories for articulated figures. Zhao and Badler (1994) implemented a flexible inverse kinematics technique that allows the user to specify multiple positioning and aiming goals for high degree of freedom figures. In their scheme, the inverse kinematics task is cast into a constrained nonlinear programming problem that is solved using a modified quasi-Newton algorithm. Koga, Kondo, Kuffner, and Latombe (1994) developed a two-phase inverse kinematics procedure for generating \"natural\" looking arm postures. They use a sensorimotor transformation model, proposed by Soechting and Flanders (1989a, b) to obtain an initial guess for an arm posture that matches physiological observations ofhuman subjects. Because the solution is not exact, the joint angles are then refined by an optimization procedure until a precise solution is achieved.\nThe chief advantages of a numerical method are flexibility and generality: a\nTolani and Badler 393",
            "394 PRESENCE: VOLUME 5, NUMBER4\npropose two simple schemes for reducing the degrees of freedom to yield a system ofequations with closed-form solutions. The two methods are combined to construct a\nsimple but effective inverse kinematics procedure for the human arm.\n2 A Simple Model of the Human Arm\nThe human arm, particularly the shoulder-clavicle complex, is a complicated mechanical structure that is challenging to model accurately. Badler, Phillips, and Webber (1993) discuss a sophisticated model for the human arm and the implementation of its inverse kinematics for interactive tasks. However, in our application real-time performance is the chief concern so we are willing to use a simpler model that permits fast closed-form solutions to the inverse kinematics equations. The human arm can be crudely modeled as a seven degree of freedom mechanism consisting of a spherical joint for the shoulder, a revolute joint for the elbow, and a spherical joint for the wrist. This admittedly simple model neglects scapula movement and forearm pronation but is visually adequate for many applications. Placing a fixed coordinate system {0} at the shoulder and moving coordinate systems {i} (i = 1..7) at each joint, define A\u00a1 as the 4x4 homogeneous coordinate transformation from frame [i\n\u2014 1} to frame {i} as a function of joint variable 8,-. In the model shown in Figure 1, the values for A\u00a1 are\nsingle procedure can be used for a variety ofmanipulators, optimization criteria and constraints can be incorporated, and solutions for redundant manipulators can be obtained. However, numerical algorithms are computationally expensive and often fall short of real-time requirements. Moreover, most numerical methods furnish only a single answer even though multiple solutions exist. Finally, stability and convergence problems often occur near a singularity of the Jacobian. For these reasons, an analytical solution is often preferable. Because the human arm is redundant there are an infi-\nnite number of solutions for a given wrist position. We\nAj = R,(e,-) =\nA2 = Rx(62) =\nA3 = R2(63)T(0,0,L1)\nc\\ -si 0 0 il cl 0 0 0 0 10 0 0 0 1\n10 0 0 0 c2 -j2 0 0 s2 0 0\nc3 -s3 s3 c3\nc2 0\n0 0\n0 1\n0 0\n0 0 1 LI 0 1",
            "Tolani and Badler 395\nA4 = Ry(e4)T(0,0,1,2)\nA5 = Ry(85) =\nA* = Rx(86) =\nA7 = R,(67) =\nc4 0 s4 s4L2 0 10 0\n-s4 0 c4 c4L2 0 0 0 1\n\" c5 0 j5 0^ 0 10 0\n-\u00ed5 0 c5 0 0 0 0 1\n10 0 0\" 0 cd -s6 0 0 i6 cd 0 0 0 0 1\nc7 -s7 0 0\" s7 c7 0 0 0 0 10 0 0 0 1\nwhere ci and\u00ab are used to denote cos (8,) and sin (6\u00bf) and LI andL2 are constants representing the lengths of the upper and lower arm.\nGiven Awrist, the desired position and orientation of the wrist frame relative to the shoulder frame, the inverse kinematics problem is to find a set of angles \u2022i,. . . , 87 that satisfies the following equation:\nA1A2A3A4A5A5A.7 \u2014 Avltist If the components ofAwrist are denoted as\n>11 gl2 gl3 gl4 g2l g22 g23 g24 g3l g32 g33 g34\n0 0 0 1\n(1)\nA . =-awrist (2)\nthe vector p = \\gl4,g24,g34]T is the position of the wrist measured in the fixed coordinate system. Given p, the elbow angle 84 is uniquely determined by the distance of the wrist from the shoulder according to the formula\n(3)64 = ir \u00b1 arceos LI2 + L22 -\n2LLL2\nAlthough there are two solutions for 84 only one answer is physically realizable because ofjoint limits. Equation (1) is\nunderconstrained as A^ specifies six, rather than seven, independent quantities so there are an infinite number of values for 0l5 82,83,85,86, and 87 that satisfy (1). To obtain a finite set ofsolutions an additional constraint must be provided. We propose two schemes that lead to simple closedform analytic solutions.\n3 Scheme I : Specifying the Elbow Position\nKorein (1985) first noted that a natural parameterization for the extra degree of freedom of the arm can be based on the observation that if the position of the wrist is fixed the elbow is still free to swivel about an axis from the wrist to the shoulder. Consider the diagram shown in figure two, where s, e, and w define the positions of the shoulder, elbow, and wrist, respectively. As the swivel angle <J) varies, the elbow traces the arc of a circle lying on a plane whose normal is parallel to the wrist-toshoulder axis. To mathematically describe the circle and 4> we first define the normal vector of the plane by the unit vector in the direction of the wrist to the shoulder\nw n =\nw- s (4)\nAdditionally, we need two unit vectors \u00fb and v that form a local coordinate system for the plane containing the circle. Setting \u00fb to be the projection of the\n\u2014 z axis onto the plane gives\nu =\n-z + (z \u2022 n)\u00e2 -z + (z \u00f1)\u00f1||\nand v is obtained by taking the crossproduct v = n x \u00fb. The center of the circle c, and its radius r can be derived by simple trigonometry\nc = s + cos (a)Lln r = LI sin (a)\n(5)\ncos (a) =\nsin (a) =\nL22- LI2 - w\n-2Ll||w L2 sin (i);) \u00bbII (6)\nw - s I ij; = it\n\u2014\n64"
        ]
    },
    {
        "image_filename": "designv10_2_0001015_j.addma.2020.101834-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001015_j.addma.2020.101834-Figure1-1.png",
        "caption": "Fig. 1. Motivation and rational behind the proposed triple-finger micro-gripper design. (a) Excessive force exerted by a 2D parallel jaw gripper deforms or even damages the soft object. (b) Insufficient force or mis-placement of the 2D gripper causes the object to slip or escape. (c) A truly 3D gripper offers a robust solution to capture and manipulate the free-form objects. (d) The monolithic design to miniaturize 3D robotic gripper from meter-scale to millimeter-scale, in which the magnetic actuator and flexure respectively fulfills the functions the hydraulic actuator and hinge used in the meter-scale counterpart.",
        "texts": [
            " Recognizing these difficulties, the silicon micro-machining process, which was originally developed for the Micro-Electro-Mechanical Systems (MEMS), has been widely used for fabricating micro-grippers with actuatable moving parts [6\u201310]. As the silicon micro-machining process is mainly limited to fabricate planar structures, the most common micro-gripper designs used in many applications are still the two dimensional (2D) parallel jaw grippers [11]. This device may suffice for grasping and manipulating rigid objects in a controlled environment; however, these tasks remain sufficiently challenging to be performed on soft, free-form objects. As illustrated in Fig. 1, excessive grasping force can deform or even damage the soft object (Fig. 1(a)). In contrast, insufficient gripping force or inaccurate placement of the gripper may cause the object to slip or escape (Fig. 1 (b)). A truly 3D gripper, like the multi-finger gripper illustrated in Fig. 1 (c), could offer a much more robust solution for manipulating the free-form objects, without the need for precise control of position and grasping force. Fabricating miniaturized multi-finger grippers featuring sophisticated 3D geometry has far exceeded the capability of the mainstream micro-machining process, however. While recent researches have focused on origami structures capable of transforming initially fabricated 2D structures into 3D multi-finger grippers or actuators [12\u201316], the ability to fully unleash the freedom in fabricating complex 3D micro-grippers remains highly desirable",
            " Synergizing 3D printing processes and in-process manipulation of embedded magnetic particles can potentially enable more complex structures and actuations. However, due to the precipitation of magnetic particles, time-consuming particle arranging process and requirements in flexibility of structures, only initially fabricated 2D planar films or 2.5D (repeating cross-section) structures have been demonstrated [37, 38]. Here we report a method to 3D print magnetically-driven triplefinger micro-gripper using a high-resolution micro-continuous liquid interface production (\u03bcCLIP) process [39,40]. As illustrated in Fig. 1(d), this study aims to shrink a meter-sized triple-finger gripper with 1000\u00d7 deduction in its linear dimensions, to a millimeter-scale device. While the macroscopic gripper often constitutes the assembly of various functional components, such as hydraulic actuators, joints, and mechanical structures, it becomes increasingly challenging to assemble the miniaturized components. Thus, we proposed a monolithic design to eliminate the need for assembly process. In achieving this, we optimized composition of the magnetically-active photopolymerizable resin to mitigate the trade-off between mechanical compliance and magnetic actuation forces to maximize the gripping motion",
            " Video S3 (Supplementary Information) shows the repeated close and open action of the double-finger gripper at the driving voltage of 8 V. The 3D printed double-finger gripper with 30 wt% solid loading magnetic resin shows satisfactory magnetic response and the capability to grasp objects in microscale. Supplementary material related to this article can be found online at doi:10.1016/j.addma.2020.101834. We then incorporated the optimized actuation mechanism into the proposed triple-finger magnetic micro-gripper illustrated in Fig. 1(d). As shown in Fig. 4(a), the micro-gripper comprises three embracing actuating fingers arranged in a symmetric configuration. Each of the actuating fingers is actuated by the relative motion of the connected center floating block and the fixed outer shell. For the consideration of the energy efficiency, the micro-gripper is designed to remain closing as its natural state. By supplying voltage to the electromagnet coil, the induced upwards motion of the center blocks will cause three fingers to tilt outwards and thus, open the gripper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003787_1.1644545-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003787_1.1644545-Figure3-1.png",
        "caption": "Fig. 3 The geometry, coordinate and loading of the ball bearing model",
        "texts": [
            " Kb is the 5 by 5 Jacobian stiffness matrix of the bearing given by Kb53 kxx kxy kxz kxux kxuy kyx kyy kyz kyux kyuy kzx kzy kzz kzux kzuy kuxx kuxy kuxz kuxux kuxuy kuyx kuyy kuyz kuyux kuyuy 4 (15) Transactions of the ASME 0/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F Bearing Global Equilibrium Each rolling element has three degrees of freedom. Choosing the inner ring groove center as the origin, the load vector of inner ring to a rolling element j is written as Qj5$QrQzM %T ~Fig. 3!. For ball bearings the moment M is zero. The displacement vector corresponding to Qj can be defined similarly as uj5$uruzu%T. The local displacement uj can be obtained from the global displacement d using the transformation matrix @Rf# from the bearing center to inner groove center, and is written as uj5@Rf# jd (16a) Transforming the ball force vectors Qj into the equivalent force vectors at the bearing center, and summing the forces over all balls, the global force equilibrium can be established as F1( j51 n @Rf# j TQj50 (16b) where n is the number of balls bearings, Qj is the force vector of the j th ball, and the transformation matrix @Rf# is given by @Rf#5F cos f sin f 0 2zp sin f zp cos f 0 0 1 rp sin f 2rp cos f 0 0 0 2sin f cos f G (17) In Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.28-1.png",
        "caption": "Fig. 2.28: Details of an Impact",
        "texts": [],
        "surrounding_texts": [
            "Impulsive motion takes places for a variety of reasons including the classical contact of two or more bodies, a sudden stop of some fluid flows or a velocity jump due to \u201cdynamic locking\u201d [161]. The last phenomenon was and still is a subject of many discussions and many contributions. A practical example represents the chattering chalk on a blackboard. The contacts and the impacts of two or more bodies will be of the main interest here, and therefore we shall focus on some basic aspects of such collisions.\nThe interest for understanding impact phenomena was always very large, because impacts possess the possibility to augment considerably the forces for a lot of practical processes like hammering or forcing piles into the ground (in German the \u201cbear\u201d). Therefore all great scientists and engineers worked in the one or other way on impact phenomena. Aristoteles, Galilei, Newton, Marcus Marci, Huygens, Euler, Poisson, Coulomb and many others paved the way to a modern theory of impulsive motion (see [259]).\nIf two or more bodies collide impulsively and with arbitrary direction, the contact zone will be deformed in normal and in tangential direction thus storing elastic potential energy with respect to these two directions. The deformation in tangential direction depends for a given state before the impact at least to a large extent on the properties of the contacting surfaces, especially on the roughnesses, which are for technical surfaces in the order of magnitude of some micrometers (\u00b5). Under the influence of the relative velocities, friction and the stored energies we get different results.\nFirstly and the energy losses being small the bodies might separate again very quickly, where the directions of the separation depend on the velocity before the impact, the frictional features and the impulse storage. We might also get a reversal of the incoming motion depending mainly on the properties in tangential direction [15]. The point of contact, averaged over the deformed contact zone, will be usually different from that point, where the spring forces due to the elastic deformation of the contact zone apply. This has influence on the whole contact process, which becomes significant for pairings of soft materials [15].\nSome typical properties of a single impact are indicated in Figure (2.28). Two bodies will impact if their relative distance rD becomes zero. This event is then a starting point for a process, which usually is assumed to have an extremely short duration. Nevertheless, deformation of the two bodies occurs, being composed of compression and expansion phases. The forces governing this deformation depend on the initial dynamics and kinematics of the contacting bodies. The impulsive process ends when the normal force of contact vanishes",
            "2.5 On Contacts and Impacts 69\nand changes sign, because a contact cannot realize tension forces. We do not consider adhesion phenomena. The condition of zero relative distance cannot be used as an indicator for the end of an impact, because it does not necessarily indicate also a vanishing contact force. In the general case of impact with\nfriction we must also consider a possible change from sliding to sticking during the impulsive process, or vice versa, which includes frictional aspects as treated later. In the simple case of only normal velocities we sometimes can idealize impacts according to Newton\u2019s impact laws, which relate the relative velocity after an impact with that before an impact. Such an idealization can only be performed if the force budget allows it. In the case of impacts by hard loaded bodies we must analyze the deformation in detail. Gear hammering taking place under heavy loads and gear rattling taking place under no load are typical examples [200].\nAs in all other contact dynamical problems, impacts possess complementarity properties. For ideal classical inelastic impacts either the relative velocity is zero and the accompanying normal constraint impulse is not zero, or vice versa. The scalar product of relative velocity and normal impulse is thus always zero. For the more complicated case of an impact with friction we shall find such a complementarity in each phase of the impact. Friction in one contact only is characterized by a contact condition of vanishing relative distance and by two frictional conditions, either sliding or sticking (see Figure 2.29).",
            "A typical property of contacts, whatsoever, is the fact, that kinematic magnitudes indicating the beginning of a contact event become a constraint at that time instant, where a contact becomes \u201cactive\u201d. For example: a nonzero normal distance between two bodies going to come into contact indicates a \u201cpassive\u201d contact state with zero normal constraint force. In the moment it is zero, then the relative distance represents a constraint accompanied by a constraint force, and the contact is \u201cactive\u201d. In tangential direction it is similar: Non-zero tangential velocity (sliding) means a zero \u201cfriction reserve\u201d \u00b50|FN |\u2212|FTC | = 0 (see Figure 2.30). This tangential relative velocity becomes zero for stiction and represents then a constraint accompanied by a tangential constraint force. The end of a contact event or better of an active contact state will be always indicated by a constraint force or a combination of constraint forces. The normal constraint force becomes zero indicating a separation, and the friction reserve becomes zero indicating a change from sticking to sliding. In more detail this means:\nFrom the contact constraint rD = 0 we get a normal constraint force FN which, according to Coulomb\u2019s laws, is proportional to the friction forces, or better vice versa, the friction forces are proportional to the normal force in the contact. For sliding FTS = \u2212\u00b5FN sgn(vrel), and for stiction FT0 = \u2212\u00b50FN , where \u00b5 and \u00b50 are the coefficients of sliding and static friction, respectively. Stiction is indicated by vrel = 0 in tangential direction and by a surplus of the static friction force over the constraint force, \u00b50|FN | \u2212 |FTC | \u2265 0. If this friction reserve becomes zero the stiction situation will end, and sliding will start again with a nonzero relative acceleration arel in the tangential direction. Again we find here complementary behavior: Either the relative velocity (acceleration) is zero and the friction reserve (saturation) is not zero, or vice versa. The product of relative acceleration and friction surplus is always zero.\nWe may take that in a more classical way. Having stiction we are situated within the friction cone connected with the contact under consideration. The"
        ]
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.73-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.73-1.png",
        "caption": "Fig. 5.73: Rocker Pin Model [249]",
        "texts": [
            "4 on the pages 131, or we might choose a regularized force law approximating Coulomb\u2019s law. In the first case we are able to describe stick-slip effects, in the second case not. For the planar case Srnik [250] developed both models, unilateral and regularized ones and compared the two with much success. The contact situation as a whole is pictured by Figure 5.72. Neglecting its eigendynamics the pair of rocker pins can be modeled as one single massless spring acting only perpendicular to the model plane, which is identical with the pulley-chain plane. Figure 5.73 shows the model and the forces acting in the contact plane. The oblique contact planes are symmetrical with respect to the two pulley sheaves. The pin danamics can be neglected thus allowing a quasi-static investigation. The normal contact force FN acts perpendicular to the contact plane, and the frictional forces FT,r and FT,c are parallel to this plane. The pins change their length due to elastic effects, which have two parts. The pin as an elastic strut will be shortened by the pressure force FP on the one, and it will be compressed in its contact together with the sheave surface by the same force on the other side (Figure 5.73). From this we get \u2206lP = \u2206lstrut + 2\u2206lHertz , with \u2206lstrut = fP cstrut , \u2206lHertz = f 2 3 P cHertz . (5.111) The coefficients cstrut and cHertz may be taken from some standard text books, for example [147] and [118]. To solve the above equation for the force FP is a bit cumbersome. Therefore we use a least square approximation in the from [250] FP = c1\u2206lP + c2\u2206l 3 2 P + c3\u2206l2P . (5.112) With respect to mathematical modeling we refer to the chapters 3.3 on the pages 113 and 3.4 on the pages 131, where the fundamental equations and the necessary algorithms are discussed in some detail"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.40-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.40-1.png",
        "caption": "Fig. 7.40: Force Equilibrium for Mating Tolerance",
        "texts": [
            "141) where nM is the number of driven axes and n is a unit vector denoting the cartesian insertion direction. hi(q0) is the torque necessary at joint i to balance the gravitational forces, it is equal to the i-th component of h(q0). For a maximization of \u03bbmax, its inverse is taken as the second criterion G2 = 1 \u03bbmax . (7.142) Optimization Criterion - Mating Tolerance The deviation \u2206xG from the desired path for a given static force depends on the endpoint stiffness, reduced to the Cartesian gripper coordinates, see Figure 7.40. A quasistatical force equilibrium at the gripper yields \u2206xG = Q\u22121 red\u03bb+\u2206xP , Qred = ([ JTG JRG ] Q\u0303 \u22121 [ JTG JRG ]T)\u22121 . (7.143) \u2206xP is the deviation resulting from the clearance between the two parts and from the stiffness of the parts themselves. Therefore it depends only on the mating process itself and needs not to be considered here. For a maximization of \u2206xG the reduced stiffnesses Qred in the lateral directions must be minimized. Together with a weighting factor gQ, which contains the cartesian directions, in which the tolerances are critical, this forms the criterion for the maximization of the mating tolerance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.3-1.png",
        "caption": "Fig. 5.3 Equilibrium of inflation pressure p and cord tension tc",
        "texts": [
            "1 Studies on Tire Shape 243 radii are orthogonal to each other. b is the orientation angle of a ply measured from the circumferential direction. In Fig. 5.1, Euler\u2019s theorem in differential geometry gives the radius of curvature R: 1=R \u00bc sin2 a=r1 \u00fe cos2 a=r2: \u00f05:3\u00de Referring to Fig. 5.2, the substitution of the relation r2 = r/sin / into Eq. (5.3) yields 1=R \u00bc sin2 a=r1 \u00fe cos2 a sin/=r: \u00f05:4\u00de Substituting Eq. (5.4) into Eq. (5.2), we obtain p tc nr \u00bc sin2 a r1 \u00fe cos2 a r sin/: \u00f05:5\u00de Referring to Fig. 5.3, the force equilibrium in the z-direction between the pressure p on a circular ring from rC to r and the tensile force tcsin a is expressed by z z 244 5 Theory of Tire Shape pp\u00f0r2 r2C\u00de \u00bc tcN sin a sin/; \u00f05:6\u00de where N is the number of cords in a tire and is given by N \u00bc 2prnr sin a: \u00f05:7\u00de Eliminating tc and nr in Eq. (5.5) using Eqs. (5.6) and (5.7), we obtain 2r r2 r2C \u00bc 1 r1 sin/ \u00fe cot2 a r : \u00f05:8\u00de In the first quadrant (r 0, z 0) of the r\u2013z plane in Fig. 5.3, we have r1 \u00bc \u00f01\u00fe z0\u00f0r\u00de2\u00de3=2 z00\u00f0r\u00de sin/ \u00bc dzffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dr2 \u00fe dz2 p \u00bc z0\u00f0r\u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe z0 2\u00f0r\u00dep \u00bc r r2 ; \u00f05:9\u00de where z0\u00f0r\u00de is expressed as z0\u00f0r\u00de \u00bc dz\u00f0r\u00de=dr: \u00f05:10\u00de The substitution of both equations of Eq. (5.9) into Eq. (5.8) yields z00 \u00f01\u00fe z0 2\u00dez0 \u00bc 2r r2 r2C cot2 a r : \u00f05:11\u00de The rearrangement of Eq. (5.11) gives 2rdr r2 r2C \u00bc dz0 \u00f01\u00fe z0 2\u00dez0 \u00fe cot2 a r dr: \u00f05:12\u00de Integrating Eq. (5.12) with respect to r, we obtain1 r2 r2C \u00bc C z0ffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe z0 2 p exp Zr rref cot2 a r dr 0 @ 1 A; \u00f05:13\u00de where rref is an arbitrary point used to define the interval of integration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000774_j.addma.2021.101884-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000774_j.addma.2021.101884-Figure4-1.png",
        "caption": "Fig. 4. (a) Three dimensional FEM model and (b) temperature-dependent thermal properties of the HSLA-100 steel.",
        "texts": [
            " The experimental data were compared with the numerical results to verify the accuracy of the proposed computational model. Finite element analysis (FEA) was performed to study the rapid thermal cycles experienced by the HSLA-100 steel plates prepared by UDED and DED. A numerical simulation of the repair process for realsize damaged samples was performed. The model was made up of eight node hexahedral and prismatic linear elements. A finer mesh was applied in the RZ, and a coarser mesh was employed in the outer substrate zone (Fig. 4(a)). The governing equation for the nonlinear transient heat transfer analysis is expressed by Eq. (1): \u2202 \u2202x [ kx(T) \u2202T \u2202x ] + \u2202 \u2202y [ ky(T) \u2202T \u2202y ] + \u2202 \u2202y [ kz(T) \u2202T \u2202z ] +Q(x, y, z, t) = \u03c1(T)Cp(T) \u2202T \u2202t (1) where \u03c1(T) is the density, Cp(T) is the specific heat capacity and k(T) is the thermal conductivity. Q denotes the applied volumetric heat flux. The temperature-dependent thermal properties of the HSLA-100 steel are shown in Fig. 4(b). The initial temperature of the substrate was set to 20 \u25e6C. Natural convection and thermal radiation losses were applied to the outer surfaces built in the thermal model. The boundary condition can be given by Eq. (2) [28]: kn(T) \u2202T \u2202n + qs + hc(T \u2212 T\u221e)+ \u03b5\u03c3 ( T4 \u2212 T\u221e 4) = 0 (2) where qs is the boundary heat flux (W m\u2212 2), kn is the thermal conductivity normal to the surface, \u03b5 is the emissivity, \u03c3 is the Stefan-Boltzmann constant (5.68 \u00d7 10\u2212 8 W/(m2 \u25e6C4)) and hc is the convective heat transfer coefficient (W/(m2 \u25e6C))"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.25-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.25-1.png",
        "caption": "Fig. 11.25 Relation among the relative average sliding velocity V 0, velocity of the road VR and velocity of the tread base VB",
        "texts": [
            " If the static friction coefficient ls is the same in all directions, the force equilibrium is expressed by qzls\u00f0 \u00de2\u00bc f 2x \u00fe f 2y ; \u00f011:97\u00de where qz is the parabolic function given by Eq. (11.46). If we assume the relations a 1, s 1 and Cx = Cy = C for simplicity, using Eqs. (11.46), (11.89), (11.90) and (11.97), lh is obtained as11 lh \u00bc l 1 CF 3lsFz ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tan2 a\u00fe s2 p CF \u00bc Cbl2=2; \u00f011:98\u00de where Fz is the load given by Eq. (11.47). (3) Side force and self-aligning torque in the sliding region The sliding direction in the sliding region is shown in Fig. 11.25, where V 0 is the relative sliding velocity between the tread base and the road, VR is the road velocity, and VB is the velocity of the tread base. Referring to Fig. 11.25, it follows that12 11Note 11.9. 12Note 11.10. 742 11 Cornering Properties of Tires s tan h \u00bc tan a 0 h p\u00f0 \u00de: \u00f011:99\u00de The side forces of a tire in the sliding region are given by F00 x \u00bc b Z l lh ldqz cos hdx1 F00 y \u00bc b Z l lh ldqz sin hdx1: \u00f011:100\u00de Assuming that the tread approximately moves on line BC of Fig. 11.24 in the sliding region, the moment is integrated around the z-axis. The self-aligning torque of a tire in the sliding region is given by M00 z \u00bc b Z l lh ldp y0 cos h\u00fe x1 l 2 sin h dx1: \u00f011:101\u00de Here, y0 is the lateral distance of line BC measured from the x-axis: y0 \u00bc x1 l\u00f0 \u00delh tan a lh l \u00fe y0; \u00f011:102\u00de where y0 is given by Eq",
            " In the case of braking (s > 0), 796 11 Cornering Properties of Tires 4lspm x l 1 x l \u00bc x ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2 x s 2 \u00feC2 y sin 2 a q x \u00bc l 1 l 4lspm ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2 x s 2 \u00feC2 y sin 2 a q : Assuming Cx = Cy = C and considering pm = 3Fz/(2 lb) and CFa = Cl2b/2, we obtain lh \u00bc l 1 CFa 3lsFz ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe sin2 a p ffi l 1 CFa 3lsFz ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe tan2 a p : In the case of driving (s < 0), x \u00bc l 1 l 4lspm ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2 x s 2 \u00feC2 y \u00f01\u00fe s\u00de2 tan2 a q ; where Cx = Cy = C and, in a manner similar to the case of braking, we obtain lh \u00bc l 1 CFa 3lsFz ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe\u00f01\u00fe s\u00de2 tan2 a q ffi l 1 CFa 3lsFz ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe tan2 a p : Note 11.10 Eq. (11.99) The following relations are obtained referring to Fig. 11.25. In the case of braking, s \u00bc VR cos a VB VR cos a \u00bc a a\u00feVB ; tan h \u00bc d a ; tan a \u00bc d a\u00feVB ) a a\u00feVB d a \u00bc d a\u00feVB ) s tan h \u00bc tan a: In the case of driving, s \u00bc VR cos a VB VB \u00bc a VB ; tan h tan h0 \u00bc d a ; tan a \u00bc d VB ) a VB d a \u00bc d VB ) s tan h \u00bc tan a: Note 11.11 Eq. (11.104) Using Eq. (11.99), we obtain sin h \u00bc tan a= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe tan2 a p \u00bc h tan a cos h \u00bc s= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 \u00fe tan2 a p \u00bc hs: Equation (11",
            " The force equilibrium equation is 1042 14 Wear of Tires f CScombined \u00bc ldqz\u00f0x\u00de: \u00f014:71\u00de Scombined is thus given by Scombined \u00bc f ldqz\u00f0x\u00def g=C; \u00f014:72\u00de where C is the shear spring rate of the tread per unit area in the direction of the resultant force. Referring to Eq. (7.14), C is expressed by the shear spring rates per unit area along the principal axes (i.e., X- and Y-directions), CX and CY: C \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C2 X cos2 /\u00feC2 Y sin 2 / q ; \u00f014:73\u00de where / is the angle of the sliding direction measured from the X-direction. Meanwhile, referring to Fig. 11.25, the sliding direction h measured from the direction of the tread base velocity is obtained as follows. In braking \u00f0s[ 0\u00de; h \u00bc tan 1 fy=fx \u00bc tan 1 Cy sin a Cxs : \u00f014:74\u00de In driving \u00f0s\\0\u00de; h \u00bc tan 1 fy=fx \u00bc p\u00fe tan 1 Cy 1\u00fe s\u00f0 \u00de tan a Cxs : \u00f014:75\u00de Considering that the wear occurs in the sliding region, the wear energy per unit area per rotation of the tire, Ew, is given by Ew \u00bc Z2pre 0 ldqz\u00f0x\u00dedScombined \u00bc Z l lh ldqz\u00f0x\u00dedScombined \u00bc Z l lh ldqz\u00f0x\u00de dScombined dx dx; \u00f014:76\u00de where ld is the kinetic friction coefficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001121_j.matdes.2021.109685-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001121_j.matdes.2021.109685-Figure11-1.png",
        "caption": "Fig. 11. Schematic representation of the graph theory approach for the test case of the arch without support. There are four main steps in the approach.",
        "texts": [
            " The graph theory approach represents the part as discrete nodes, which entirely eliminates the tedious meshing steps of FE analysis. (2) Elimination of matrix inversion steps. While FE analysis rests on matrix inversion at each time-step for solving the heat diffusion equation, the graph theory approach relies on matrix multiplication, shown in Eq. (9), which greatly reduces the computational burden. We now briefly describe the manner in which the graph theory approach is adapted for thermal modeling in LPBF. The graph theory approach is illustrated schematically in Fig. 11 in the context of the arch-shaped parts without supports. Step 1: Represent the part\u2019s geometry in terms of randomly sampled nodes. The key idea of the graph theory approach is to convert the part geometry into a number of discrete nodes [48]. First, the part geometry in the form of the STL file is converted into a set of discrete nodes, and a fixed number of N nodes will be sampled randomly. The position of these N nodes will be recorded in terms of their spatial coordinates (x, y, z). In the ensuing steps, the temperature at each time step will be stored at these nodes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003961_s11044-007-9088-9-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003961_s11044-007-9088-9-Figure4-1.png",
        "caption": "Fig. 4 Nomenclature",
        "texts": [
            " The principle of transference can be stated as follows [2, 54, 61]: 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. 6.1 Applications of the principle of transference In 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, as shown in Fig. 4, s is the displacement of the body along the screw axis. With reference to the geometry of Fig. 6, 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 = t u. 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 generalized 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 \u2022 R\u03021 and R\u03022 are the initial and final positions of a line vector framed to the rigid body, respectively (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure7-1.png",
        "caption": "Fig. 7 Basic geom",
        "texts": [
            "org/about-asme/terms-of-use h e o b c a w a b i r g p w s g F p c s o fi w s 1 Downloaded Fr obbed tooth surfaces are kinematically generated by the cutting dges of the blades, an exact description of the cutting edge gemetry in space is very important. The blade edge geometry can e described in the coordinate system St that is connected to the utter head with rotation parameter . The primary parameters that ffect the cutting edge geometry are: nominal blade pressure angle , blade offset angle , rake angle , and effective hook angle hich defines the inclination of the front face relative to the cutter xis. Figure 7 shows the basic geometry of the inside and outside lade edges which are represented in the coordinate system Sb that s fixed to the front face of the blade. The origin Ob coincides with eference point M with reference height hb. Generally, the blade eometry consists of four sections: a blade tip, b Toprem, c rofile, and d Flankrem. Sections a and d are circular arcs ith radii re and rf, respectively. Sections b and c can be traight lines, circular arcs, or other kinds of curves. Section c enerates the major working part of a tooth surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure2.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure2.30-1.png",
        "caption": "Fig. 2.30: Friction Cone and friction reserve",
        "texts": [
            " A typical property of contacts, whatsoever, is the fact, that kinematic magnitudes indicating the beginning of a contact event become a constraint at that time instant, where a contact becomes \u201cactive\u201d. For example: a nonzero normal distance between two bodies going to come into contact indicates a \u201cpassive\u201d contact state with zero normal constraint force. In the moment it is zero, then the relative distance represents a constraint accompanied by a constraint force, and the contact is \u201cactive\u201d. In tangential direction it is similar: Non-zero tangential velocity (sliding) means a zero \u201cfriction reserve\u201d \u00b50|FN |\u2212|FTC | = 0 (see Figure 2.30). This tangential relative velocity becomes zero for stiction and represents then a constraint accompanied by a tangential constraint force. The end of a contact event or better of an active contact state will be always indicated by a constraint force or a combination of constraint forces. The normal constraint force becomes zero indicating a separation, and the friction reserve becomes zero indicating a change from sticking to sliding. In more detail this means: From the contact constraint rD = 0 we get a normal constraint force FN which, according to Coulomb\u2019s laws, is proportional to the friction forces, or better vice versa, the friction forces are proportional to the normal force in the contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.13-1.png",
        "caption": "Fig. 5.13: Electrostatic micromirror. According to [Jaeck93]",
        "texts": [
            " The optical fibers are coated with a thin metal layer so that they can be actuated electrostatically. If an electric voltage is applied across one of the electrodes, the fiber is attracted by this electrode. Therefore, by con trolling the voltage of both electrodes, the fiber can be exactly aligned. The metal layer of the optical fiber is applied by a sputtering process, and the groove is produced by the bulk micromachining technique on a (001) silicon substrate. The smallest distance between the optical fiber and the electrode is Electrostatic micromirror Figure 5.13 shows a sketch of an electrically driven micromirror proposed in [Jaeck93]. The device consists of a micromirror which can be tilted about a torsion beam with respect to a base made from silicon. Two positioning elec trodes, one for addressing and one for landing, are mounted underneath the mirror. If a voltage of approximately 31 Vis applied to the address electrode, the mirror rotates 7.6\u00b0 and touches the landing electrode which is grounded. In order to bring the mirror back to its original position the voltage is decrea- 128 5 Microactuators: Principles and Examples sed to 16 V"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure10-1.png",
        "caption": "Fig. 10. Primary configuration of the 8R kinematotropic metamorphic mechanism. (a) The primary configuration (b) Its prototype.",
        "texts": [
            " The twist angle \u03b1 of adjacent joints is \u03c0/ 2 , the parameters of the derived origami-inspired 8R mechanism are as follows: a 12 = a 23 = a 34 = a 45 = a 56 = a 67 = a 78 = a 81 = a { \u03b112 = \u03b134 = \u03b156 = \u03b178 = \u03c0/ 2 \u03b123 = \u03b145 = \u03b167 = \u03b181 = \u2212\u03c0/ 2 { d 1 = d 3 = d 5 = d 7 = 0 d 2 = d 4 = d 6 = d 8 = 0 (4) where a i (i +1) denotes length of link i (i + 1) , \u03b1i (i +1) is twist of link i (i + 1) , d i is referred as offset of joint i , \u03b8i is the angle of rotation from x i and x i +1 about axis z i , a > 0 based on the geometric conditions. Fascinatingly, the special derived 8R mechanism has one four-fold rotation axis, and four two-fold rotation axes perpendicular to it, hence the mechanism has D 4 rotational symmetry [56] . The rotational symmetry group D 4 is the union of the rotational symmetry operations with order 4. Fig. 10 gives the primary configuration of the 8R kinematotropic metamorphic mechanism, in which the axes of joints E, F, G, and H intersect at point O , the points O 1 and O 2 are the intersections of joints B 1 , B 2 and B 3 , B 4 , respectively. The mechanism exhibits two-fold plane symmetry with the mutually perpendicular planes OEG and OFH. The origin of a global reference frame O-XYZ is located at point O, the Z-axis is aligned with the intersection of planes OEG and OFH, the X-axis is perpendicular to the plane OEG and Y-axis is set following the right-handed rule"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001277_j.compositesb.2021.108667-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001277_j.compositesb.2021.108667-Figure2-1.png",
        "caption": "Fig. 2. Dimensions of tensile specimen.",
        "texts": [
            " The diffraction patterns and the elemental composition of samples were acquired using a transmission electron microscope (TEM, JEM-2100), and the TEM foils were prepared using electrothinning. Tensile tests were performed to investigate the mechanical propertie of Ti6Al4V and TMC2 and conducted at room temperature at the strain rate of 10\u2212 3s\u2212 1 using CMT6104 universal tensile testing machine. A non-contact extensometer was employed to measure the tensile strain. Dimensions of the tensile specimen is shown in Fig. 2. The single-track experiment was the basis of the entire subject research and the key step in determining the process parameters for LMD. The purpose of this is to observe and select the ideal microstructure and the appropriate melt pool morphology. Table 2 lists in detail the designed process parameters. Fig. 3(a) shows the stereomicroscope cross-sectional images of the single-track TMCs in different parameters. The results show that the structure of the melt pool with different proportions of B4C and molding parameters were consistent: columnar grains growth perpendicular to the substrate with epitaxial growth from the parent grains in the bottom of the molten pool, and fine equiaxed grains appeared in the near surface region with excessive undercooling, which corroborates the literature [16]",
            " 8, when the test parameters of the scanning angle range of 30\u25e6\u201390\u25e6, and the scan rate of 10\u25e6/min were observed. The phase analysis results showed that in-situ TMCs are mainly composed of \u03b1-Ti, \u03b2-Ti, TiC and TiB phases whereas, the Ti6Al4V matrix is primarily composed of \u03b1 and \u03b2 X. Meng et al. Composites Part B 212 (2021) 108667 dual phase structure. Result indicated that the reinforced phases TiC and TiB prepared in-situ with reaction of B4C and Ti6Al4V in the LMD process matched the SEM images. The close-up view (Fig. 2(b)) more clearly showed changes of peaks intensity and position in the diffraction patterns between 50\u25e6 \u2264 2\u03b8 \u2264 80\u25e6. With further addition of B4C, the intensity of TiC and TiB peaks have increased, the position of the matrix diffraction peak also shifted to left, and the diffraction angle decreased nearly 0.4\u25e6, since the lattice constant of Ti6Al4V matrix has increased due to formation of interstitial solid solution with solid solution of B and C atoms. Fig. 9 shows the TEM images of the Ti6Al4V and TMC2, and the diffraction patterns of these phases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003689_ja00182a013-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003689_ja00182a013-Figure13-1.png",
        "caption": "Figure 13. Model for the magnetic interactions within the trinuclear site.",
        "texts": [
            " Two kinds of effects are expected: ( 1 ) exchange coupling of the three coppers will generate excited spin states that may be probed by magnetic susceptibility measurements and by variable-temperature EPR and MCD spectroscopies and (2) the EPR and MCD spectra associated with the ground S = state can exhibit features from all three coppers. These effects will be considered for both the resting trinuclear site and the anion-bound forms. In order to model these various forms, the spin-coupling formalism will be used to consider isotropic exchange interactions among the three coppers in several limiting cases defined in Figure 13. Note that case I corresponds to the limit where the type 3 coupling is much greater than the type 2-type 3 interactions. This situation corresponds to the earlier models of the type 2 and type 3 sites, in which type 2 Cu2+ can be considered a magnetically isolated S = ion and the type 3 site a strongly antiferromagnetically coupled dimer with an S,, = 0 ground state. The other cases involve type 2-type 3 couplings, and more complex magnetic coupling schemes must be considered. First, we consider the effects of type 2-type 3 interactions on the energies of the excited spin multiplets. In a symmetric trinuclear site where the couplings between each of the type 3 coppers and the type 2 copper are equivalent (case 11, Figure 13) the spin Hamiltonian can be written as43 H = -2J(Sz&, + s 2 6 3 8 ) - 2J3a38 s3a.s38 where J is the coupling between the type 2 and each of the type 3 coppers and J3a38 is the coupling between the type 3 coppers. The three S = ions are coupled to give one quartet state and two doublet states labeled a and b. The quartet arises from parallel orientation of all three spins. The doublet states are defined by an intermediate quantum number s* = sj, + s38; for state a , S* = 0, and for state b S* = 1",
            " The C-term intensities in the trinuclear site are weighted by the same ci coefficients that govern the EPR spin Hamiltonian parameters, and the C-term MCD associated with the a ) state is given by Cole et al. where the Co(it in eq 8 refers to the C terms associated with electronic transitions at each of the three coppers in the trinuclear site. These expressions lead to clear predictions regarding the effects of the type 2-type 3 magnetic interactions on the EPR and LMTCD spectra of the laccase trinuclear copper site for the various cases listed in Figure 13. In case I JJ3a3BI >> IJz3,1, lJ2381 and the ground-state coefficients are c2 = I , c3, = cy+= 0, reflecting an S = state localized on the type 2 Cu . Interestingly, in case 11 the doublet wave functions do not mix, and ~ 2 3 , and ~ 2 3 8 will also equal zero regardless of the magnitude of JZ3, = J 2 3 g relative to J3a3 Thus, the paramagnetism will be localized on the type 2 Cut' and the EPR and C-term MCD of the trinuclear site will only reflect the properties of the type 2 Cu2+ if J23a and J23s are small relative to the type 3 coupling or if they are equal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000349_tec.2020.2995902-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000349_tec.2020.2995902-Figure5-1.png",
        "caption": "Fig. 5. Flux density distribution of the SPM motor calculated by FEA.",
        "texts": [
            " The complex relative air-gap permeance waveforms of the SPM motor under eccentric (e=0.3mm) and non-eccentric conditions is shown in Fig. 4. It is shown that the eccentricity has an obvious influence on complex relative air-gap permeance, and the improved complex relative air-gap permeance can effectively consider the effect of slotting when the motor is eccentric. The local saturation exists in the stator due to the nonlinearity of the core material in the SPM motor, which is a non-negligible factor to calculate the air-gap flux density accurately. Fig. 5 shows the no-load flux density distribution of the SPM motor calculated by FEA, which the main parameters of the motor are listed in Table I. It is observed that stator core of the motor is saturated under the circumstances. Authorized licensed use limited to: University College London. Downloaded on May 23,2020 at 09:16:17 UTC from IEEE Xplore. Restrictions apply. 0885-8969 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000159_j.ijfatigue.2020.105946-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000159_j.ijfatigue.2020.105946-Figure6-1.png",
        "caption": "Fig. 6. Example of FE mesh of the unit cell and boundary conditions used to calculate the notch factor. d is a unitary displacement.",
        "texts": [
            " The load was applied at a constant 0.1 N/s rate with a dwell time of 10 s. Six measurements were performed on a parallel and a perpendicular section to the printing direction for a specimen of each batch. A set of numerical simulations were carried out to assess the lattice responses in the linear regime only using Ansys\u00ae Mechanical APDL, Release 18.0 (Canonsburg, Pennsylvania, U.S.A). A reduced model consisting of one unit cell (Fig. 1b and, after meshing with 3D 20 node structural continuum elements, Fig. 6) for both the nominal geometry and the as-built geometry was developed with results later compared with their experimental counterparts. For the base material (bulk Ti6Al-4 V), we use the following properties: elastic modulus of 113 GPa and Poisson\u2019s ratio of 0.34. The FE models were used to calculate the fatigue notch factor K f at the filleted joints defined assuming a worstcase scenario of notch sensitivity =q 1 (full notch sensitivity) [23]: = =K K maximum principal stress at the joint nominal homogeneous stressf t (1) Where the nominal homogeneous stress is the ratio between the load on the unit cell and the nominal area of the unit cell (L \u00d7 L)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003605_j.talanta.2003.11.021-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003605_j.talanta.2003.11.021-Figure4-1.png",
        "caption": "Fig. 4. (A and B) Cyclic voltammograms of a NiHCNF/CCE modified electrode (two-step sol\u2013gel method), (a) in 0.1 M phosphate buffer (pH 7) containing 0.5 M NaCl (b) in the presence of 10 mM hydrazine (c) in the presence of 20 mM hydroxylamine. (C) as (A and B) for modified NiHCNF/CCE prepared by one-step sol\u2013gel method.",
        "texts": [
            " It can be seen that the peak potential moved to more negative values along with a decrease in the K+ concentration, suggesting that an ionization process must be included in the oxidation and deionization must be included in the reduction (reaction 2). At high concentration of K+ cyclic voltamograms split to two pairs. K2[NiIIFeII(CN)6] \u2192 K[NiIIFeIII(CN)6] + K+ + e\u2212 (2) A similar electrochemical behavior was reported for electrode surfaces modified with metal hexacyanoferrates [13,20,49\u201352]. The utility of the modified CCEs prepared with one and two-step sol\u2013gel technique for oxidation hydrazine and hydroxylamine was evaluated by cyclic voltametry. Fig. 4 shows the cyclic voltamograms for two kinds CCEs in the presence and absence of hydrazine and hydroxylamine. As can be seen in Fig. 4A and B for CCE modified by a two-step sol\u2013gel technique, after addition hydrazine or hydroxylamine the anodic peak current increased noticeably with a catalytic peak occurring at 0.55 V(versus Ag/AgCl) while the cathodic peak decreased or disappeared. At the surface of a bare CCE, the hydrazine and hydroxylamine are not oxidized until 0.85 V. Thus, a decrease in over-potential and enhancement of peak current for hydrazine and hydroxylamine oxidation are achieved with the modified electrodes. The catalytic activity of CCE prepared by one-step sol\u2013gel technique for oxidation hydrazine and hydroxylamine is shown in Fig. 4C. As shown in this case, the catalytic current is low and the (Icat/NiHCF) is about 1.3 versus 2.3 and 3 for modified CCE prepared by one-step sol\u2013gel method in the catalytic oxidation of NH2NH2 and NH2OH, respectively. These results indicate that the monolayer adsorbed at one-step modified CCE has high catalytic activity in comparison to multilayers molecules of the modifier entrapped in the carbon composite lattice. Fig. 5 shows the influence of hydrazine concentration on the cyclic voltamograms of the modified electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003943_tmag.2004.825185-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003943_tmag.2004.825185-Figure2-1.png",
        "caption": "Fig. 2. Symbols.",
        "texts": [
            " This work was supported by the Foundation for Polish Science, Warsaw, Poland. The authors are with the Department of Electrical Engineering and Automatic Control, Technical University of Opole, PL 45-036 Opole, Poland (e-mail: luk@po.opole.pl; mjagiela@po.opole.pl; rwrobel@po.opole.pl). Digital Object Identifier 10.1109/TMAG.2004.825185 In this paper, the simplified model for torque calculation, only partially supported by the 3-D one, is developed. To describe this model, we introduce the symbols shown in Fig. 2. The PM is divided into identical slices. Define a vector including angular displacements of consecutive slices: . Due to cross linkage fluxes, the torque density is not constant along the motor axis. It can be assumed that the th PM slice, where generates the cogging torque , which can be approximated as (1) where area under the th segment of the torque density curve along the direction; total area under the torque density curve along the direction; weighting coefficient (see Fig. 3); angular variation of cogging torque determined from 3-D model (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003949_s10846-007-9137-x-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003949_s10846-007-9137-x-Figure5-1.png",
        "caption": "Fig. 5 The C5 Robot (position of the frames and description of a C5 joint)",
        "texts": [
            " 30, we start by calculating the term J viVP, by differentiating Eq. 31 we obtain: v i \u00bc v P \u00fe v P P1Pi \u00fe vP vP P1Pi\u00f0 \u00de \u00f048\u00de Which can be rewritten as: v i \u00bc I3 dP1Pi h i V P \u00fe vP vP P1Pi\u00f0 \u00de \u00f049\u00de Using Eq. 26, we deduce: J viVP \u00bc vP vP P1Pi\u00f0 \u00de \u00f050\u00de Finally, since S = I6, and S = 0, Eq. 30 gives: hrobot \u00bc vP vP MSP\u00f0 \u00de vP IPvP\u00f0 \u00de MPI3dMSP g\u00fe X3 i\u00bc1 I3dP1Pi AXi vP vP P1Pi\u00f0 \u00de J iq i \u00fe hXi \u00f051\u00de 5.1 Description of the C5 Robot [8] The C5 parallel robot consists of a base and a platform linked together by six linear actuators (Fig. 5) [8]. The platform is designed by a cube. Each leg is embedded in the base at point Bi and connected to one face of the mobile platform through a C5 joint at point Pi. The base frame, \u22110, is located such that leg 1 and 2 are parallel to the x-axis, legs 3 and 4 are parallel to the y axis and legs 5 and 6 are parallel to the z-axis. The platform frame, \u2211P, is located at the front right top corner (Fig. 5), the frame axes are defined as in Fig. 5. The C5 joint is a complex joint with three rotational and two translational degrees of freedom, it is constructed by a spherical joint tied to two cross sliding plates (point Pi is located at the centre of the spherical-joint of leg i). 5.2 Calculation of the Jacobian Matrices The Cartesian variable of leg i transmitted to the platform is the displacement along the normal to the planar face of the platform on which the leg is connected, thus the kinematic model of leg i is given by the following scalar equation: vi \u00bc rTi aiq i \u00f052\u00de vi is the terminal velocity of leg i, ai denotes the (3\u00d71) unit vector along the leg i axis, such that: a1 \u00bc a2 \u00bc 1 0 0\u00bd T ; a3 \u00bc a4 \u00bc 0 1 0\u00bd T ; a5 \u00bc a6 \u00bc 0 0 1\u00bd T ri is the (3\u00d71) unit vector normal to the planar face of the platform on which the leg is connected, such that: r1 \u00bc r2 \u00bc s; r3 \u00bc r4 \u00bc n; r5 \u00bc r6 \u00bc a where (s, n, a) represent the columns of the orientation matrix of the platform frame with respect to the base frame: 0RP \u00bc s n a\u00bd \u00bc sx nx ax sy ny ay sz nz az 24 35 \u00f053\u00de Thus, the Jacobian of leg i is given by the scalar: Ji \u00bc rTi ai \u00f054\u00de The velocity of point Pi, denoted vi, as a function of Vp is given as follows: vi \u00bc rTi vp \u00fe vp PPi \u00f055\u00de Thus Jvi is the Jacobian matrix which transforms the platform velocity to point Pi, and projects it on the ri axis, it is obtained as: Jvi \u00bc rTi rTi cPPi h i \u00f056\u00de The inverse kinematic model of the robot gives the active joint velocities as a function of the velocity of the platform, where: q a \u00bc q 1 q 2 q 3 q 4 q 5 q 6 h iT \u00f057\u00de using Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure8.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure8.32-1.png",
        "caption": "Fig. 8.32: Leg configuration",
        "texts": [
            " Microrobot using a piezoelectric actuation principle The next example discusses two microrobots which were reported in [Magn94], [Magn95] and [Fati95]. The first one, a one-armed microrobot is named PROHAM (Piezoelectric Robot for Handling Microobjects); it is eq uipped with a piezoelectrically driven base platform and a manipulator which can hold different tools. The second robot is named MINIMAN (MINiatu rized MANipulation robot); it uses a similar platform as PROHAM, but has a more versatile two-armed manipulator. Both models will be discussed below. The platforms of both robots move with the help of three piezoceramic legs, Fig. 8.32. The 13 mm long legs are made of VIBRIT 420 ceramics; they are sintered in a tubular form and can change their length when a voltage is applied (Section 7.3.2). The outer diameter of the legs is 2.2 mm and the inner one 1 mm. They are readily available on the market and are inexpensive. Each leg is covered with two metal electrodes, an outer and an inner one. They are used to force the ceramic leg to change its length when a voltage is applied to it. The applied electric field either causes the ceramic to grow or shrink, depending on the polarisation of the electric field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.67-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.67-1.png",
        "caption": "Fig. 5.67: Movable Sheave with Backlash [249]",
        "texts": [
            " The whole set is supported by two elastic bearings with the same stiffness and damping in the two bearing directions. The corresponding forces write Fbearing,x = c(xR \u2212 xR,0) + dx\u0307R, Fbearing,y = c(yR \u2212 yR,0) + dy\u0307R. (5.107) 5.5 CVT - Rocker Pin Chains - Plane Model 283 The pulley set and the shaft possess the same rotational speed, if we assume nearly no backlash in circumferential direction between the shaft and the movable sheave. But the backlash between movable sheave and pulley shaft must be considered, because it allows a translational motion and some tilt (Figure 5.67). The corresponding force law is a linear spring with backlash. The oil pressure poil itself has two parts, the pressure p0 coming from the oil supply and the pressure generated by centrifugal forces. We get poil = p0 + 1 2 \u03c1\u03c92 R ( r2 \u2212 r2 0 ) (5.108) with the appropriate values from the design charts. The force due to the oil pressure follows from an integration over the surface A and gives Foil = ra\u222b r0 2\u03c0\u222b 0 prd\u03d5dr = Ap0 + kcentri\u03c9 2 R, (5.109) which means, that the oil pressure force is proportional to the pressure in the oil chamber and to the square of the rotational speed of the shaft-pulleysystem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003348_la000110j-Figure13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003348_la000110j-Figure13-1.png",
        "caption": "Figure 13. Conceptual model of nanoparticle-myoglobin films with three adsorbed protein layers on rough pyrolytic graphite electrodes.",
        "texts": [
            " 1997, 101, 2224-2231. (17) While viscoelastic effects can bias estimates of mass by QCM,9 this is unlikely for these dry films since regular mass growth was observed for MnO2/PDDA and Mb/SiO2 films. (18) Lvov, Y.; Ariga, K.; Kunitake, T. Colloids Surf., A 1999, 146, 337. (19) Kendrew, J.; Phillips, D.; Stone, V. Nature 1960, 185, 422. this ratio an upper limit. Nevertheless, these rough estimates suggest that Mb molecules coat the SiO2 particles rather completely and should be in close contact in the film (Figure 13). Assuming that Mb has restricted mobility within the film, we speculate that a close-packed interstitial protein network may be involved in \u201celectron hopping\u201d20 by selfexchange reactions between MbFeII and MbFeIII to propagate charge through the film during CV. The average electron self-exchange distance would then depend on the relative protein orientations in the film, which are not known, but should be on the order of the molecular diameter of Mb, about 4 nm.2a In the nine-bilayer Mb/ SiO2 film, the estimated fraction of electroactivity suggests that at least half of the Mb molecules in the film can participate in this process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure5.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure5.3-1.png",
        "caption": "Fig. 5.3 Fig. 5.4",
        "texts": [
            " It is easy to see that of '3f/c is not unique, see Fig. 5.2 . In order to ensure that the derivative of the phase portrait at (0,0) is continuous, take the expression for the centre manifold '3f/c as '3f/ C (, I x~O, when y>o ) = ~(XJY) x=Ke'II', when y:So (5.6) C h 0 dx 0 C C c For '3f/ w en y> , x = 0 dy = -; = 0, i.e. '3f/ is a tangent to S ; lor y::;; 0, x = Kelly, when y tends to zero in the negative direction, we obtain dx = 0, so that dy '3f/c is a tangent to SC too. The derivative of '3f/c at (0,0) is unique, see Fig. 5.3. There are different centre manifolds for different K at (0,0), i.e. '3f/c is not unique, but its derivative at (0,0) is unique. In this manner, we are sure that the Taylor series of '3f/c is unique, but may not be convergent. This series is asymptotic if the amplitude is small. Centre Manifold Theorem and Normal Form of Vector Fields 157 5.1.3 Calculation of the Centre Manifold For convenience, suppose that &\" = {O}, nil = 0, n, + nc = n. Consider the system y' = I(y), lEek (U), k ~ I, U E ;t:\" is an open set, 1(0) = 0, A = Dyl(O) Linearizing eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.71-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.71-1.png",
        "caption": "Fig. 10.71 Coordinate system for the acoustic cavity noise and tire cross section. Reproduced from Ref. [75] with the permission of JSAE",
        "texts": [
            "10 Acoustic Cavity Noise of Tires 649 flqp \u00bc c ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pp a b 2 \u00fe 2l a\u00fe b 2 \u00fe qp L 2s b[ 0:5a \u00f010:98\u00de and the mode acoustic shape is given by wlqp\u00f0r; h; x\u00de \u00bc qc2Gpl\u00f0r\u00de cos\u00f0ph\u00de cos\u00f0kxqx\u00de with q; p; l \u00bc 0; 1; 2; . . .; \u00f010:99\u00de where Gpl\u00f0r\u00de \u00bc Y 0 p\u00f0kpl\u00deJp kpl r a J 0p\u00f0kpl\u00deYp kpl r a : \u00f010:100\u00de Jp is the Bessel function of the first kind, and Yp is the Bessel function of the second kind. (3) Energy approach for acoustic cavity noise (3-1) Kinetic energy and potential energy of acoustic cavity noise Yamauchi and Akiyoshi [75] studied acoustic cavity noise employing the energy method. The tire acoustic cavity is expressed by an angular displacement w at h in the cylindrical coordinate system of Fig. 10.71. r is the distance from the center of the wheel to the center of gravity of the cross-sectional tire acoustic cavity. The kinetic energy T and potential energy V of the acoustic cavity are expressed by T \u00bc 1 2 Z2p 0 qAr3 @w\u00f0h; t\u00de @t 2 dh V \u00bc 1 2 Z2p 0 EAr @w\u00f0h; t\u00de @h 2 dh; \u00f010:101\u00de where q, A and E are, respectively, the density, the area of the cross section and the modulus of the volume elasticity of gas inside the tire\u2013wheel assembly. (3-2) Natural frequency In the case of a freely suspended tire, the radius r and the cross-sectional area A do not change in the circumferential direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.86-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.86-1.png",
        "caption": "Fig. 5.86: A hydraulic piston microactuator. Courtesy of the Karlsruhe Re search Center, IMT",
        "texts": [
            " If a voltage is applied to one of the electrodes, the corresponding air channel closes, Fig. 5.85b. All jets can be individually controlled this way. A prototype system was able to accurately move a 1 mm2, 300 ~-tm thick silicon plate; the operating voltage was 90 V and the air pressure 2 kPa. The main body of the device was a silicon wafer into which a 7 x 9 matrix of 63 rectangular air channels (100 ~-tm x 200 ~-tm) were etched anisotropically. The size of the entire microsystem is 2 mm x 3 mm. Hydraulic piston microactuator in Figure 5.86. The actuator chamber with its inlet for its operating fluid, e.g. 5.9 Hydraulic and Pneumatic Microactuators 205 water, was made by the LIGA process. The unit contains a force-transmit ting piston which can be moved along the side walls of the chamber by a fluid. The device is covered by a glass plate (not shown in the figure) . A stop groove is added to absorb excessive adhesive which may ooze out when the glass cover plate is being fixed; this is necessary to prevent the piston from sticking to the walls of the chamber"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.19-1.png",
        "caption": "Fig. 6.19: Capacitive measurement of accelerations",
        "texts": [
            " Acceleration microsensors will help to improve the comfort, safety and driving quality of automobiles. However, in order for them to become a product of general interest, their production costs must be drasti cally lowered. As with pressure (Fig. 6.4 and Fig. 6.5), acceleration is usually detected by piezoresistive or capacitive methods. Mostly an elastic cantilever is used to which a mass is attached. When the sensor is accelerated the mass displaces the cantilever and the displacement is picked up by a sensor. Such a sensor is shown in Figure 6.19. It uses the capacitive measuring method to record deflection. From the deflection the acceleration can be calculated. Piezoresistive principle 231 To effectively measure acceleration with this principle, piezoresistors are pla ced at points of the cantilever where the largest deformation takes place. The stability and accuracy of the sensor improves with increasing number of pie zoelements. If a mass moves due to acceleration, it deforms the piezoresis tors, thereby changing their resistance, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000025_j.jmsy.2020.06.019-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000025_j.jmsy.2020.06.019-Figure6-1.png",
        "caption": "Fig. 6. Cutter location surface and tool envelope surface.",
        "texts": [
            " The tool-axis-orientation of at any time t can be expressed as: \u2211 \u2211= \u2212 = \u23a1 \u23a3 \u23a2 \u2212 \u23a4 \u23a6 \u23a5 = = a r ru R u u R d N u d N u( ) 1 [ ( ) ( )] 1 ( ) ( ) C u C j n j u j k j n j j k 0 , 0 , (6) Step 3: Substitute Eqs. 5 and 6 into the equation = +r a bu v u v u( , ) ( ) ( ) of ruled surface, the cutter location surface r u v( , )a can be obtained as follows: \u2211 \u2211 = \u2212 + = + \u23a1 \u23a3 \u23a2 \u2212 \u23a4 \u23a6 \u23a5 = = r u v v p u vp u p u v R d N u d N u ( , ) (1 ) ( ) ( ) ( ) 1 ( ) ( ) a u C j n j u j k j n j j k 0 , 0 , (7) Step 4: The envelope surface of the tool can be obtained by offsetting the obtained cutter location surface with a tool radius Rc, as shown in Fig. 6, namely the machined blade surface. The five-axis flank milling simulation of the CI_DRSB is performed in NREC MAX-5 platform with the cutting parameters shown in Table 1, which demonstrates that the presented method is feasible and the generated tool path is reasonable. In addition, an end milling simulation of the original CI_FFSB with the same cutting parameters are conducted to compare with the above result, as shown in Figure 7. Although the difference of machining time depends on various machining parameters, such as feed rate speed, cutting depth and allowed error, the machining efficiency has been obviously improved from CI_FFSB to CI_DRSB due to the change of cutting edge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003751_s0924-0136(02)00846-4-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003751_s0924-0136(02)00846-4-Figure2-1.png",
        "caption": "Fig. 2. Geometry and deflection in angular ball bearing. (a) Geometry of the ith ball-race contact, (b) deflection of the ith ball-race contact.",
        "texts": [
            " A five degrees of freedom model for the spindle system, which was developed by Aini et al. [10], and refined by Alfares and Elsharkawy [11], is utilized in this study. In this model, the spindle is assumed to be rigid, the centrifugal effects and torsional vibrations of the spindle are neglected, the balls of the bearings are assumed to be massless, the cage angular velocity is assumed to be constant, and any sources of damping are assumed to be negligible. For completeness of the paper, a brief description for the mathematical model is given in Appendix A. Fig. 2a shows the geometry of the ith ball of an angular contact ball bearing which in contact with the inner and outer races. The local Hertzian contact force Wi and deflection di relationship between ball i and inner and outer races of angular contact ball bearing may be written as follows [13]: Wi \u00bc Kd3=2 i (1) where K is the total stiffness coefficient per ball. The total deflection di of the ith ball-race contact is shown in Fig. 2b. In this figure the center of curvature of the outer race Oo is assumed to be the fixed origin. The initial preload Pr is assumed to act axially (in the z-direction) which will cause an axial displacement from Oi to (Oi)1 for the free center of curvature of the inner race. Furthermore, the external radial loading due to the grinding process (Fx and Fy) will move (Oi)1 to a final position (Oi)2. The preload contact angle ap and the initial contact deflection d0 due to the elasticity of the bearings for a given preload Pr can be determined by solving the following equations simultaneously using the iterative Newton\u2013Raphson scheme: n\u00f0Kd3=2 0 \u00de sin ap \u00bc Pr (2) d0 \u00bc A cos a0 cos ap 1 (3) where A is the initial distance between the centers of curvature of the inner and outer races, a0 the unloaded contact angle due to interference fitting of bearings DCd and is calculated from the following equation [13]: a0 \u00bc cos 1 1 Cd DCd 2A (4) where Cd \u00bc do di 2D (5) Eq. (2) is derived from the force balance in the axial direction and Eq. (3) from the initial contact deflection (see Refs. [13,14]). The applied axial preload will cause initial displacement Z0 in the axial direction (see Fig. 2b). The initial displacement Z0 can be determined from the following equation: Z0 \u00bc d0 sin\u00f0ap a0\u00de cos ap (6) The initial contact load per ball W0 due to initial axial preloading Pr can be obtained from W0 \u00bc Kd3=2 0 (7) This initial contact load will act as the initial loading conditions for the five degrees of freedom model of the grinding machine spindle (see Appendix A). Table 1 shows the data used in the present study which were taken from [10,15]. The experimental measurements by Malkin [12] for the grinding forces (Fx and Fy) as a function of grinding wheel wear rate percentage wr (percentage of wheel surface consisting of wear flats) for five different workpiece materials are displayed in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure4-1.png",
        "caption": "Fig. 4 Geometry of the blade edge",
        "texts": [
            " 3 Geometry of Generating Blade Edges Definition of the blade reference radius Rb is different between face milling and face hobbing. In face milling, the inside and outside blades have deferent reference radii referred at the blade tip. For face hobbing, both sides of blades have the same reference radius, which is defined at mean point with reference height hb from the blade tip. In order to include both cases, a generalized blade geometry consisting of four sections is considered as shown in Fig. 4. A coordinate transformation is applied to switch the face-milling blade geometry to the face-hobbing blade geometry. In some designs, Toprem and Flankrem are used to relieve tooth root and tip surfaces in order to avoid root contact interference and tip edge contact. In the grinding process, Toprem and Table 1 Kinematics of face milling versus face hobbing Pinion Gear Process Generated Generated Formate Face milling Generating roll: w=Ra c Generating roll: w=Ra c c=0 Intermittent indexing Intermittent indexing Intermittent indexing Face hobbing Generating roll: w=Ra c Generating roll: w=Ra c c=0 Continuous indexing: w=Rtw t Continuous indexing: w=Rtw t Continuous indexing: w=Rtw t Transactions of the ASME 6 Terms of Use: http://www",
            " In most ases, blades are not exactly placed with the front faces in the xial cross section of the cutter head. In the case of the faceilling grinding process, the edge geometry in the axial cross ection of a grinding wheel is considered. We consider that the tooth surface of the generating gear is ormed by the trace of a cutting edge of the tool whose geometry an be defined by the position vector and the unit tangent repreented in the cutter head coordinate system St as rt = Mtb , , ,Rb rb u 3 tt = Mtb , , ,Rb tb u 4a ere, vector rb u and tb u are defined in Fig. 4; matrix Mtb epresents the coordinate transformation from blade face coordiate system Sb to St. Determination of transformation matrix Mtb s based on the geometric description of the rake, hook, and blade lot offset angles shown in Fig. 5 and can be defined as a multilication of three homogeneous matrices as ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/201 Mtb = M M M 4b where M , M , and M are represented as M = cos sin 0 0 \u2212 sin cos 0 0 0 0 1 0 0 0 0 1 4c M = 1 0 0 0 0 cos sin 0 0 \u2212 sin cos 0 0 0 0 1 4d M = cos \u2212 sin 0 Rb cos sin cos 0 Rb sin 0 0 1 0 0 0 0 1 4e 4 Generalized Tooth Surface Generation Model Today, free-form CNC hypoid generators are widely employed in manufacturing of spiral bevel and hypoid gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003887_978-94-011-4120-8_41-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003887_978-94-011-4120-8_41-Figure1-1.png",
        "caption": "Figure 1. Closed loop with 2 dof Figure 2. Closed loop with 3 dof",
        "texts": [
            " The dimension of {S(N)} is 3 and the equation of Chebychev can be used with d=3, fi =3 , 'A can be any integer and is equal to 3 if we use three fixed motors. We'll show that a system of three limbs, each limb having five degrees of freedom, can be also a rotational platform about a given fixed point. A tripod with 5-dof general limbs, will produce a 3-dof motion with no special algebraic property (Lee, and Shah, 1987). We are looking for structural and geometrical conditions in each limb in order to generate rotation about a fixed point. Fig. 1 shows, on its right, one limb made of a sequence of five kinematic pairs (lower pairs of degree of freedom 1) and a spherical pair of centre N . The limb and the spherical pair connect in-parallel a frame F and a moving platform M. The whole is a single closed loop mechanism. Employing the Chebychev formula (d=6), we obtain that this mechanism has 2 degrees of freedom. Actually we wish 3 degrees of freedom for the moving body M and therefore we seek an exception to the previous formula of mobility"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.29-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.29-1.png",
        "caption": "Fig. 5.29: Coupling of Ring Gear and Output Drive",
        "texts": [
            " The toothing is modeled according to the equations given in the section \u201dToothing\u201d, where the geometrically caused phase shifts between the curves of the tooth stiffnesses of the single gear trains have to be taken into account. The vector of the generalized coordinates may contains either 4 or 6 degrees of freedom depending on the pitch motion under consideration. Due to the stiffness of the shafts and the small clearance in the bearings the 4 degrees of freedom qT = (x, y, z, \u03b1) were selected in this case. The way of modeling the ring gear R is influenced by the connection between the ring gear and the output shaft O (see figure 5.29), due to various design configurations which lead to different dynamical behavior of the ring gear. If ring gear and output flange are welded together the ring gear can be regarded as stiff having 4 or 6 degrees of freedom. Otherwise if the ring gear like in this case is coupled to the output flange by the carrying toothing pictured in figure 5.29, the small thickness of the ring gear and the clearance between R and O require an elastic model that allows the correct reproduction of the movements within the tooth-work. Lachenmayr presents in [134] an elastic model of a ring gear which provides a function for the planar deformation of the neutral axis in radial and circumferential direction starting from the rigid body position like illustrated in figure 5.27. Complying with the model of the Rayleigh beam the neutral axis is not stretched and the circumferential deformations \u2206\u03c8 cancel out: 2\u03c0\u222b 0 \u2206\u03c8d\u03d5 = 2\u03c0\u222b 0 [\u03c8n(0)\u2212 \u03c8n(\u03d5)]d\u03d5 = 0 (5",
            "28 v = (cos(2\u03d5), \u00b7 \u00b7 \u00b7 , cos(n\u03d5), sin(2\u03d5), \u00b7 \u00b7 \u00b7 , sin(n\u03d5))T = [cos(i\u03d5) sin(i\u03d5)]T (5.64) do not fulfil the closing condition \u03c8(0) = \u03c8(2\u03c0). In practice a small number of shape functions is sufficient because the oscillations with high frequencies are not of interest for the dynamic behaviour of the total system. Based on the deformation coordinates the kinematic correlations and the equations of motions of the elastic ring gear are derived. The alternative to the welding of ring gear and output is the connection by the toothing shown in Figure 5.29 [73] which transmits the torque by the elastic contact of the teeth. The clearance between the teeth in radial and circumferential direction enables an additional relative movement between ring gear and output shaft. Figure 5.29 makes clear, that the induced friction forces possess a remarkable influence on the deformation of the ring gear, contingent on the number of teeth and the size of the clearance. Therefore the couplings between ring gear and output shaft are modelled in detail for every single tooth as force elements with clearance and radial friction forces according to figure 5.30. Again the relative normal and tangential distances and velocities within the contacts of Figure 5.30 can be evaluated by elementary considerations from the kinematics of gear meshing [215],[170]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure22-1.png",
        "caption": "Fig. 22. Five pairs of teeth face-gear drive finite element model.",
        "texts": [
            " However, in the model of the face-gear tooth (Fig. 21(b)), each longitudinal section, due to its particular length, have to be divided into proper finite elements considering together all portions of the face-gear tooth profile. The finite element analysis has been performed for two versions of face-gear drives of common design parameters represented in Table 3. The versions correspond to face-gear drives with conventional and rounded fillet, respectively (Fig. 4). The finite element mesh of five pair of teeth of version 2 is represented in Fig. 22. Elements C3D8I [5] of first order enhanced by incompatible modes to improve their bending behavior have been used to form the finite element mesh. The total number of elements is 67,240 with 84,880 nodes. The material is steel with the properties of Young\u2019s Modulus E \u00bc 2:068 108 mN/mm2 and Poisson\u2019s ratio 0.29. A torque of 1600 Nm has been applied to the pinion for both versions of face-gear drives. Fig. 23 shows the whole finite element model of the gear drive. Figs. 24 and 25 show the maximum contact and bending stresses obtained at the mean contact point for gear drives of two versions of fillet (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.68-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.68-1.png",
        "caption": "Fig. 5.68: Approximation of Sheave Deformation [249]",
        "texts": [
            " Furtheron and by regarding the deformation structure, we find a linear increase of the sheave deformation with the contact radii and in circumferential direction a cosineform. This is plausible for physical reasons, because the heaviest load on the sheave surface comes along the arc of wrap of the chain. Here we get the maximum deformations. Therefore the following assumptions are reasonable. The deformations of the sheave are proportional to the contact radius in radial direction and to a cos-function in circumferential direction. They are linearly dependent on the oil pressure, and they can be expressed by a tilt angle \u2206\u03d1 (Figure 5.68). The maximum depends on the position of the contact forces, and we assume a symmetric stiffness distribution with respect to the two sheaves of the pulley. We then can establish the following formulas \u2206\u03d1 =\u2206\u03d1max(Foil) cos (\u03d5\u2212 \u03d50(Ttilt)) , \u2206\u03d1max(Foil) = cE(r, \u03d5)oilFoil \u03d50 = \u03c0 2 + arccos Ttilt,x\u221a T 2 tilt,x + T 2 tilt,y , Ttilt,x Ttilt,y Trot  = \u2211 i r\u0303SCiFCi \u03d1(\u03d5, Foil, Ttilt) = \u03d10 + \u2206\u03d1(\u03d5, Foil, Ttilt) (5.110) The maximum tilt \u2206\u03d1max depends linearly on the oil pressure force Foil, which is plausible. The vectors rSCi and FCi are radial positions and forces at the contact points of the pins within the arc of wrap, respectively. The rest is clear from Figure 5.68. 5.5 CVT - Rocker Pin Chains - Plane Model 285 Proceeding with the elastic pulleys via Ritz-approach modelling we have to establish suitable nets of the meshes and to evaluate the eigenforms, which we shall use as shape functions. For each pulley set we consider two elastic bodies, the fixed sheave together with the pulley shaft and the movable sheave alone, which has to be coupled with the shaft within the framework of elastic multibody dynamics. Figure 5.69 gives an impression of the undeformed and deformed configuration of the pulley-shaft-system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003870_tia.2006.872930-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003870_tia.2006.872930-Figure8-1.png",
        "caption": "Fig. 8. Open-circuit field distributions with ten-pole rotor at peak coggingtorque position. (a) 1 slot. (b) 12 slots.",
        "texts": [
            " Again, a good agreement is achieved, although the measured result is lower, which may be attributed to the nonideal magnetization and tolerances in the magnet dimensions, as well as end-effects and measurement error. IV. 12-SLOT TEN-POLE MOTOR The synthesis technique has also been applied to a 12-slot ten-pole motor, of which the outer stator diameter and axial length are 100 and 50 mm, respectively, and the airgap length and magnet thickness are 1 and 3 mm, respectively. The width of the stator-slot openings is 2 mm, while the magnets are again parallel magnetized, have a remanence of 1.2 T, a relative recoil permeability of 1.05, and a pole-arc/pole-pitch ratio of 1.0. Fig. 8 shows open-circuit field distributions for the one-slot stator and 12-slot stator motors, while Fig. 9 shows the resulting cogging-torque waveforms and the associated harmonic spectra. Again, there is an excellent agreement between the resultant cogging-torque waveform deduced directly from the finite-element analysis and the synthesized coggingtorque waveforms. Since the least common multiple Nc of the one-slot ten-pole motor is ten, the cogging-torque periodicity is 36\u25e6 mechanical, while for the 12-slot ten-pole motor, Nc = 60, C = 2, and the cogging-torque periodicity is only 6\u25e6 mechanical, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000523_tmech.2019.2943007-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000523_tmech.2019.2943007-Figure1-1.png",
        "caption": "Fig. 1. Structure of an UVMS.",
        "texts": [
            " Then, it has the discrete Hamilton-Jacobi-Bellman inequality: Vf (\u03c7(tk+N+1)\u2212 \u03c7ref (k))\u2212 Vf (\u03c7(tk+N )\u2212 \u03c7ref (k))+ \u2016\u03c7(tk+N )\u2212 \u03c7ref (k)\u20162Q + \u2016K(\u03c7(tk+N )\u2212 \u03c7ref (k))\u20162R \u2264 0 (3) where Vf (\u03c7) = \u03c7T\u03a0\u03c7, \u03c7ref (k) is the tracking reference. In this section, the controlled model of the UVMS is deduced from the kinematics. Its mechanical and physical constraints of the inputs/states are stated. Then, we formulate the problem of tracking moving target as our control objective. Without loss of generality, the UVMS consists of a 6-DoFs vehicle and an n-DoFs manipulator mounted on the vehicle. Two types of reference frames of the UVMS are shown in Fig. 1. Let q, q\u0307, q\u0308 denote the position, velocity and acceleration of the UVMS, where q := [qv, qm] T \u2208 R6+n consists of the 6 DoFs of underwater vehicle qv := [X,Y, Z, \u03c6, \u03b8, \u03c8] T \u2208 R6 (surge, sway, heave, roll, pitch, yaw) and the n joint positions of manipulator qm := [q6+1, q6+2, \u00b7 \u00b7 \u00b7, q6+n] T \u2208 Rn. The state space model of the UVMS is established referring to the kinematic model. Define the velocities of (6 + n) DoFs 1083-4435 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.76-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.76-1.png",
        "caption": "Fig. 5.76: Convex Set for the Pin/Sheave Contact",
        "texts": [
            "118) all contact forces are a function of the minimal coordinates of the bodies under consideration. If the relative velocity g\u0307 vanishes, a transition from sliding to stiction is going to take place. In this case, the friction law (5.119) gives only an upper limit for the magnitude of the stiction force. After it is reached, a transition from stiction to sliding is possible. By eliminating the normal force with the help of equation (5.118), one obtains an elliptical cone in dependency of the pin\u2019s force FP , representing the convex set of the valid stiction area (Figure 5.76): (FRr \u2212 FRr ,M )2 R2 r + F 2 Rt R2 t \u2264 1 (5.120) with Rr = \u00b50 FP cos\u03d1(1\u2212 \u00b52 0 tan2 \u03d1) , radial semi axis, Rt = \u00b50 FP cos\u03d1 \u221a 1\u2212 \u00b52 0 tan2 \u03d1 , azimuthal semi axis, FRr ,M = \u00b52 0 sin\u03d1FP cos2 \u03d1(1\u2212 \u00b52 0 tan2 \u03d1) , radial displacement of the center. (5.121) In the case of a sticking contact, the vector of the frictional force points to an inner point of the stiction cone, whereas in the sliding case its tip is positioned on the surface. The semi axis as well as the radial displacement of the center (equations (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.52-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.52-1.png",
        "caption": "Fig. 5.52: Functioning principle of the micromotor. According to [Wagn92]",
        "texts": [
            " Linear micromotor 171 Numerous research projects are concerned with the development of electro magnetic linear actuators. Since almost all present efforts to design linear ac tuators are based on the silicon technology, the available structures are li mited to a height of about 20 ~-tm, which means that the forces that can be produced are very weak. There are few devices using planar coils; a linear motor with a sliding rare earth magnet is discussed in [Wagn92]. The magnet slides in a channel between two silicon chips which are attached to a glass substrate. The operating principle of this motor is depicted in Fig. 5.52. Planar coils located in the silicon chips are progressively energized to generate the linear motion of the magnet. There are 8 pairs of planar coils, integrated in parallel to the guiding channel of the chip, Fig. 5.53. The coils opposite one another are driven sequentially with a current of the same magnitude so that a travelling perpendicular magnetic field (parallel to the magnetization of the permanent magnet) is produced. Thus, the magnet is pulled along the channel in a synchronous manner by the moving magnetic field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000456_j.addma.2020.101086-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000456_j.addma.2020.101086-Figure1-1.png",
        "caption": "Fig. 1. (a) The adopted heat treatment cycles in this study, including initial annealing, intercritical reheating, followed by different cooling cycles, (b) the WAAM fabricated part indicating the locations of tensile samples.",
        "texts": [
            " To further reduce the heat accumulation during WAAM in the previously deposited layers, 10-min dwell time was implemented between deposition of consecutive layers, ensuring a less than 165 \u00b0C interpass temperature as recommended by AWS A28/A5 standard [29]. Following the fabrication process, two types of heat treatment processes, including air-cooling and water-quenching, were conducted on both rolled and WAAM fabricated components to modify the microstructure and the resultant mechanical properties of the ship plates. Fig. 1a depicts a graphical illustration of different heat treatment cycles used in this study. Prior to performing the heat treatment cycles, all samples were annealed by heating up to 1000 \u00b0C (above Ac3 line) for 30min and then furnace-cooled to ensure providing a homogenous microstructure before applying the main heat treatment cycles. Following this annealing step, the samples were held at the intercritical austenitizing temperature of 800 \u00b0C (between Ac1 and Ac3) for 1 h, and then subjected to different cooling rates, i",
            "2 mm from each side of the part and eliminate the as-printed surface roughness, providing a flat surface suitable for the subsequent cutting process. The tensile test samples were then prepared by water jet cutting machine with a total length of 100mm, a gauge length of 25mm, and a thickness of 5mm as recommended by ASTM E8m-04 [31]. In order to study possible existing anisotropy in mechanical properties, the tensile testing was performed along the deposition and building directions in the WAAM part (see Fig. 1b), and also the rolling and transverse directions in the rolled sample. To avoid considering outliers and achieve meaningful average values, at least five samples were subjected to uniaxial tensile testing for each tested direction. Fig. 2a shows a three-dimensional optical microscopy image of the as-received rolled ship plate (EH36) containing a banded microstructure with an interval of \u223c 40 \u03bcm, which is elongated along the rolling direction. According to the SEM micrographs shown in Fig. 2b and c, the microstructure of the as-received ship plate consists of ferrite grains (F) beside pearlite regions (P) with a fine lamellar morphology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003630_027836499201100504-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003630_027836499201100504-Figure1-1.png",
        "caption": "Fig. 1. Robotics Research model K-1207 arm.",
        "texts": [],
        "surrounding_texts": [
            "469\nThis article presents a kinematic analysis of seven-degree-offreedom serial link spatial manipulators with revolute joints. To uniquely determine the joint angles for a given end-effector position and orientation, the redundancy is parameterized by a scalar variable that defines the angle between the arm plane and a reference plane. The forward kinematic mappings from joint space to end-effector coordinates and arm angle and the augmented Jacobian matrix that gives end-effector and arm angle rates as functions of joint rates are presented. Conditions under which the augmented Jacobian becomes singular are also given and are shown to correspond to the arm being either at a kinematically singular configuration or at a nonsingular configuration for which the arm angle ceases to parameterize the redundancy.\n1. Introduction\nRobot manipulators that have more joint degrees of freedom (DOFs) than the minimum number needed to perform some tasks of interest are referred to as &dquo;redundant&dquo; to indicate the existence of the excess degrees of freedom. Although redundancy is obviously a task-dependent concept, manipulators with greater than six DOFs are usually called redundant, because the classic problem of end-effector position and orientation control for a &dquo;spatial manipulator&dquo; can be handled by a 6-DOF robot arm (Hollerbach 1984; Burdick 1988). Redundancy can be exploited for a variety of applications-singularity avoidance, collision avoidance, enhancement of mechanical advantage, manipulability enhancement, subtask performance, and so on-which greatly increase the flexibility and use of robot arms.\nThe Robotics Research arms form a family of commercially available 7-DOF revolute joint serial link manipulators that offer one extra degree of joint space redundancy over that needed for the basic task of endeffector placement and orientation. These arms can be described as having a spherical-revolute-spherical (i.e., 3R-1R-3R) joint arrangement that can be referred to as anthropomorphic (Hollerbach 1984). In this article, a scalar parameterization, 1j;, is given of the redundancy. For the Robotics Research arm, 7./J is defined as the &dquo;arm\nangle&dquo; (a natural redundancy parameter for anthropomorphic arms [Hollerbach 1984]), which is the angle between the plane passing through the arm and a reference plane. The forward kinematic mappings from joint space to end-effector coordinates and 7jJ are then given. We also present the augmented Jacobian, JA, which gives end-effector rates and ~ as functions of joint rates. Although in this article a particular emphasis is placed on the Robotics Research arms (in particular, the model K1207 arm) and the use of the arm angle for resolving redundancy, many of the results developed here apply equally to any arbitrary 7-DOF manipulator with the use of any appropriate redundancy-resolving scalar parameter, not necessarily the arm angle.\nBecause of the displacement of joint axes (&dquo;nonzero joint offsets&dquo;), the Robotics Research arms have no known analytic closed-form inverse kinematic solutions for specified end-effector coordinates and redundancy parameter ~. Consequently, the importance of differential kinematics (i.e., of the Jacobian) is increased, because at this time most approaches to solving the inverse kinematics and controlling the end-effector motions of nonsolvable arms are based on differential methods. For example, a &dquo;resolved-rate&dquo; (or &dquo;inverse Jacobian&dquo;) kinematic control approach used for nonredundant arms (Whitney 1969) has been extended for general task space control (Baillieul 1985; Seraji and Colbaugh 1990), as well as to find\nat Kungl Tekniska Hogskolan / Royal Institute of Technology on March 7, 2015ijr.sagepub.comDownloaded from",
            "470\njoint angles for a 7-DOF arm given end-effector coordinates and ~o (Seraji et al. 1991; Long 1992). Similarly, an augmented &dquo;Jacobian transpose&dquo; approach has been used for redundant arm control in task space (Seraji 1989). Alternatively, end-effector motions can be controlled using pseudoinverse techniques (Liegeois 1977), which are based on the use of the pseudoinverse of the end-effector Jacobian rather than on using the inverse (or transpose) of the augmented Jacobian.\nIn order to control the 7-DOF arm motion in Carte-\nsian task space while simultaneously controlling ~b, it is generally required that the augmented Jacobian remains nonsingular. The singularities of the augmented Jacobian are of two types: the &dquo;kinematic singularities&dquo; of the end effector itself and additional &dquo;algorithmic singularities&dquo; corresponding to arm configurations for which the augmented Jacobian is singular even if the end effector is in a kinematically nonsingular configuration. Therefore, for the purposes of simultaneously controlling end-effector motions and ~, it is desirable to find both the algorithmic and kinematic singularities for the augmented Jacobian. We give an analytic expression for an algorithmic singularity measure appropriate for the augmented Jacobian derived in this article and discuss conditions for which the Robotics Research K-1207 arm and the related &dquo;zero offset&dquo; arm of Hollerbach (1984) are algorithmically and kinematically singular (i.e., the conditions for which the augmented Jacobian becomes singular). Because of space limitations, most proofs are omitted from this article. A\nmore complete version of the article containing all the proofs and some numerical examples can be found in Kreutz-Delgado et al. (1990).\n2. Forward Kinematics\n2.1. Mapping from Joint Space to End-Effector Coordinates\nThe Robotics Research model K-1207 arm is a 7-DOF\nmanipulator with nonzero offsets (denoted by the nonzero link lengths ai, i = 1, - - -, 6) at each of the joints, as shown in Figures 1 through 3. Denavit-Hartenberg (DH) link frame assignments are given in accordance with the convention described in Craig (1986) and Yoshikawa (1990). This assignment results in the interlink homogeneous transformation matrix\nwhere 0; denotes the ith joint angle (Craig 1986). The D-H parameters for the K-1207 arm are given in Table 1.\nat Kungl Tekniska Hogskolan / Royal Institute of Technology on March 7, 2015ijr.sagepub.comDownloaded from",
            "471\nThe link frame assignments for the K-1207 are given in Figure 2, where the arm is shown in its zero configuration. The link i coordinate frame is denoted by Ft, with coordinate axes (5~i, ~i, Fi) and origin 0~,. The associated interlink homogeneous transformation matrices, z-ITi\u2019 i = 1, ~ ~7, are easily found from the above expression evaluated for the D-H parameter values listed in Table 1. If the link length parameters az, i = 1, - - -, 6 are set to zero, the 7-DOF all-revolute anthropomorphic arm described in Hollerbach (1984) is retrieved; we call this arm the zero-offset arm. The forward kinematic function, iF7, which gives the position and orientation of the end effector as a function of the joint angles 0 = (B1, ~ ~ ~, B~)T, is iT7 = tT) ... 6T7. When these multiplications are performed to obtain a symbolic form for o-l\u2019~, the resulting expression is complex because of the multitude of nonzero joint offsets and the fact that no two consecutive joints axes are parallel. Rather than construct and implement the symbolic expression, it is more efficient to numerically compute the forward kinematic function iT7 via a link-by-link iteration of the form\nexploiting special structural properties of the homogeneous transformation matrices during each link update (Orin and Schrader 1984; Fijany and Bejczy 1988; Long 1992). Furthermore, it is useful to explicitly have the interlink homogeneous transformations, \u2019-\u2019Ti, as important quantities (such as the vectors w, e, and p defined later) can then be computed. In fact, such quantities are often direct by-products of the intermediate steps of the iteration (1). The iteration (1) is by no means the only possibility for iteratively computing the forward kinematics, and ( 1 ) can be modified to yield different intermediate results as needed (for example, the iteration can be done for a reverse iteration with i = 7, ~ ~ ~, 1) (Orin and Schrader 1984; Fijany and Bejczy 1988). However, it is sufficient for the purposes of this article to focus solely on (1).\nWhen the arm is in a kinematically nonsingular configuration, there will generally exist one excess joint degree of freedom for the task of end-effector control, as there are seven joint angles available to position and orient the end effector-a task that requires only six degrees of freedom. As a result, for a fixed end-effector frame, there is generally a one-dimensional subset of joint space (a &dquo;self-motion manifold&dquo;) that maps to this configuration. Actually, there are finitely many, up to 16 in the most general case, such self-motion manifolds or &dquo;poses&dquo; (Burdick 1988; Burdick and Seraji 1989). The extra degree of freedom represented by a self-motion manifold can be used to attain some additional task requirement, provided that this task can be performed independently of end-effector placement (Egeland 1987; Seraji 1989). Furthermore, the imposition of an auxiliary task constraint can provide sufficient additional information to uniquely determine the joint angles (Oh et al. 1984; Seraji 1989; Seraji and Colbaugh 1990) (within the multiplicity of solutions represented by the pose). This scalar additional task variable is denoted by 0 in this article and is assumed to be a parameterization of the self-motion manifolds that map to a given end-effector frame. We say\nat Kungl Tekniska Hogskolan / Royal Institute of Technology on March 7, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_2_0000231_tie.2021.3073313-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000231_tie.2021.3073313-Figure7-1.png",
        "caption": "Fig. 7 The corresponding vibration mode of the first three orders resonance frequency.",
        "texts": [
            " Similarly, friction force of 60 mN was applied on the upper and bottom surfaces of the driving foot in the flexural direction. The simulation results are shown in Fig. 6. The flexural displacement of the driving foot is 6.49 \u03bcm. The maximum stress is 0.006 GPa which is lower than the yield strength of 0.2 GPa. The modal analysis of the actuator was also accomplished aiming for researching the dynamic performance. The first three order resonance frequencies were 1730.2Hz, 2850.76Hz and 9114.6Hz, the corresponding vibration modes were shown in Fig. 7. It can be noted that the vibration modes of the first three order resonance frequencies all happened on the T shape beam structure, including bending and torsional vibrations. After accomplishing the structural design, it is necessary to perform the dynamic simulation to validate the design and predict the system behavior before prototyping. The simplified rigid body model of the needle insertion device is shown in Fig. 8. The translation and rotation of the shaft are separately transferred from the reciprocal longitudinal and flexural movement of the driving foot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000668_j.jmapro.2020.04.014-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000668_j.jmapro.2020.04.014-Figure1-1.png",
        "caption": "Fig. 1. A schematic of selective laser melting.",
        "texts": [
            " However, the use of Ti-6Al-4 V in selective laser melting (SLM) powder bed fabrication, an additive manufacturing (AM) process, offers the benefits of recycling the remaining unprocessed metal powder, geometrical freedom in product design, and time and energy efficiencies [3,4]. In this process, a metal powder is applied layer-by-layer in building up a formed product, each layer anchored to the previous one by the complete fusion of the metal powder by a laser beam. The laser spot moves along a scanning pattern which is generated and controlled by a CAD model of the part to be built. Fig. 1 presents a schematic of a typical powder-bed fusion system. SLM is an attractive manufacturing process for the aerospace, automotive, and other technological industries [5\u20137]. However, many factors affect the final printed products, namely, the laser power, laser scanning speed, the thickness of the metal powder layers, the printer\u2019s accuracy, and other printing conditions. Additionally, the ranges of these factors are quite wide. For example, the maximum laser power can reach more than 180W, the laser scanning speed can reach7 m/s, and the metal powder layer thickness is unlimited"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003925_j.automatica.2006.11.017-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003925_j.automatica.2006.11.017-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed, reference-parallel and body-fixed frame.",
        "texts": [
            " The process plant model, which simulates the real physics of plant dynamics as close as possible including process disturbance, 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 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 dynamic positioning, 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 (SZrensen, 2005a, 2005b). \u2022 The Earth-fixed reference frame is denoted as the XEYEZEframe, in which the vessel\u2019s position and orientation coordinates are measured relative to a defined origin (center of the Earth). Each position reference system (e.g. GPS, hydro acoustics, etc.) has its own local coordinate system, which has to be transformed into the common Earth-fixed reference frame. \u2022 The body frame XYZ is fixed to the vessel and thus moving along with it. For convenience, the body frame is often chosen at the vessel\u2019s center of gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure15.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure15.4-1.png",
        "caption": "Fig. 15.4 Wave patterns generated by a ship within a channel. Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [
            " [2 1] T hr ee -d im en si on al m od el (e xp lic it m et ho d) E I be nd in g st iff ne ss ,E x ex te ns io na ls tif fn es s, T x ci rc um fe re nt ia lt en si on ,T y m er id ia n te ns io n, k r ra di al sp ri ng ra te ,k t ci rc um fe re nt ia ls pr in g ra te ,c r ra di al da m pi ng ,c t ci rc um fe re nt ia ld am pi ng ,c x ci rc um fe re nt ia l da m pi ng 15.1 Studies on Standing Waves in Tires 1133 carcass, kt is the fundamental circumferential spring rate of the carcass, cr is the radial damping of the carcass, ct is the circumferential damping of the carcass, and cx is the damping of the tread band in the circumferential direction. FEA can be classified into explicit FEA and implicit FEA. Suppose that a ship in a channel moves more quickly than the wave propagation as shown in Fig. 15.4. The angle of the bow wave, h, is expressed by sin h \u00bc Vc=V ; \u00f015:3\u00de where V is the ship speed and Vc is the wave propagation speed. Because the rhomboidal bow wave moves as the same speed as the ship, it appears stationary when observed from the ship. When a toroidal tire is expanded to a flat plate as shown in Fig. 15.5, the external force rotates opposite to the rotation direction in the rotating coordinate system fixed to the tire. The external force corresponds to the ship in Fig. 15.4. The standing wave, which occurs when the tire speed is higher than the wave speed in the tire, corresponds to the bow wave or the Mach wave of sound. Similar to the bow wave of a ship in a channel, the standing wave propagates in a tire. Because the wave in the width direction propagates to the bead and is reflected by the bead, 1134 15 Standing Waves in Tires this wave becomes a stationary wave like a string vibration. Hence, the shape of the standing wave of the expanded tire in Fig. 15.5 is different from the rhomboidal shape in Fig. 15.4. Lower figures in Fig. 15.5 show wave patterns of the first and third modes. 15.2 Simple Explanation of a Standing Wave 1135 (1) Fundamental equations of membrane theory Sakai [2] developed one-dimensional model of a standing wave. When the inflation pressure is too high in bias tires, the flexural stiffness of the carcass can be neglected and membrane theory can be applied to the standing wave. Furthermore, the radial spring of the carcass is neglected for simplicity. The force equilibrium between the carcass tension and the inflation pressure p in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003744_ip-d.1982.0002-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003744_ip-d.1982.0002-Figure1-1.png",
        "caption": "Fig. 1 State paths of 2nd-order system",
        "texts": [
            "2 Scalar illustrative example To illustrate some of the basic concepts of VSS design, consider the scalar system x2(t) = -al{t)xx(t)-a2(t)x2{t) (altaitb>0)_ (14) x = (xi, x2) T is the state vector and Cj, a2 and b are constant or time-varying parameters whose precise values may be unknown. Consider the discontinuous control u = x2 > 0 x2 < 0 05) where c > 0 and u* =\u00a3u . The switching function is s = ex i + x2, and the line s = 0 is the surface on which the control has a discontinuity. It can be readily shown that the state x reaches the switching line s = 0 in a finite time T, as depicted in Fig. 1 for suitable choice of u*, u~. The state x crosses the switching line and enters the region s < 0, resulting in the value of u being altered from u+ to u~. Depending on the values of the system parameters, the state trajectory may continue in the region of s < 0, yielding bangbang control. Alternatively, the state trajectory may immediately recross the switching line and enter the region s > 0. This yields sliding (or chatter) motion. Assuming that the switching logic works infinitely fast, the state x is constrained to remain on the switching line s = 0 by the control which oscillates between the values u+ and u~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure13.74-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure13.74-1.png",
        "caption": "Fig. 13.74 Standards of the tire load and inflation pressure of tires with the same rim diameter but different tire widths [5]",
        "texts": [
            "149), the load capacity W is expressed as W \u00bc 2ppdH ffiffiffiffiffi aS p : \u00f013:153\u00de Because the durability of a tire is related to the flexibility factor d (= h/H), d is a constant that defines the load capacity W. For example, when the cross-sectional shapes of tires are similar, the value of H/ S is the same among tires. The load capacity W is then given by W \u00bc ka1=2S3=2: \u00f013:154\u00de If the inflation pressure p is constant in Eq. (13.154), k is also constant. Equation (13.154) shows that the tire width S is more effective in terms of increasing the load capacity than the tire diameter a for tires of similar shape. Suppose that tires A and C have similar shapes for the same inflation pressure as shown in Fig. 13.74. Substituting the similarity equation into Eq. (13.154), the load capacity for tire C (WC) and the load capacity for tire A (WA) have the relationship WC \u00bc S2=S1\u00f0 \u00de2WA; pA \u00bc pC: \u00f013:155\u00de As another example, suppose that tires B and C have the same sectional shape but that the rim radius of tire B is smaller than that of tire C as shown in Fig. 13.74. The load capacity of tire B (WB) is smaller than the load capacity of tire C (WC), owing to the difference in the rim radius between tires B and C. Notes 1011 1012 13 Rolling Resistance of Tires The load factor of Eq. (13.154) decreases with increasing rim radius when the tire radius and width are the same, as shown in the left figure of Fig. 13.75. When only the rim radius increases without a change in the tire radius, the tire width must increase to maintain the load capacity, as shown in the right figure of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000105_j.chemosphere.2021.130141-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000105_j.chemosphere.2021.130141-Figure5-1.png",
        "caption": "Fig. 5. The contour and 3D response surface plots to show the interaction effects of operational parameters at central points: The interaction of pH and Na2SO4 (Current density \u00bc 10 mA cm 2, Reaction time \u00bc 30 min) (a), The interaction of pH and current density (Na2SO4 concentration \u00bc 0.03 M, Reaction time \u00bc 30 min) (b), The interaction of current density and reaction time (pH \u00bc 7, Na2SO4 concentration \u00bc 0.03 M) (c).",
        "texts": [
            " This indicates that the threedimensional architecture of the CF/b-PbO2 anode can provide a larger specific surface area, which in turn enhances the electrocatalytic activity of the anode in the degradation of organic pollutants (Liu et al., 2017). Fig. 4(b) reveals that the pore size distributions for both electrodes are between 1.2 and 4 nm. In addition, the pore volume (Vp) for CF/b-PbO2 and G/b-PbO2 electrodes was 0.003873 and 0.002174 cm3 g 1, respectively. The main characteristics of graphite substrate and G/b-PbO2 electrode are provided in the supplementary material (Fig. S4; Fig. S5, and Text S1). 3.2. Effect of independent variables on system response (diuron removal efficiency) Fig. 5 shows the effect of independent variables on the system response at central points as contour and 3D response surface plots. The interaction effect of the initial pH of the solution and the concentration of Na2SO4 electrolyte is shown in Fig. 5(a). As can be seen, at a concentration of 0.04 M Na2SO4, the reaction time of 30 min and the current density of 10 mA cm 2, by increasing the initial pH of the solution from 3 to about 5.7, the diuron removal efficiency increased from about 79.9% to 83.2%. However, with a further increase in pH in the range of 5.7e11, the removal efficiency of diuron, with a significant decrease, reached 70.4%. In addition, the lowest diuron removal efficiency of 60% was predicted at a pH of 11 and a concentration of 0",
            " He showed that increasing the pH of the solution in the range of 3e11 significantly reduced the removal efficiency of hexazinone. In his study, the optimum pH was considered to be 5 (Yao et al., 2019). Also, in a study conducted by Xu et al. for the electrocatalytic degradation of methylene blue with the Ti/TNTs/FeeCeePbO2 anode, the highest COD removal efficiency was obtained at pH \u00bc 5. In addition, increasing the pH in the range of 7e11 significantly reduced the efficiency of the electrocatalytic degradation system (Xu et al., 2018). As shown in Fig. 5(a), the removal efficiency of diuron depends on the Na2SO4 concentration. Under the conditions, i.e., the reaction time of 30 min, the current density of 10 mA cm 2, and the solution pH of 5.68, the diuron removal efficiency was increased from 74.8 to 83.2% by increasing the Na2SO4 concentration from 0.01 M to about 0.04 M. However, a further increase in Na2SO4 concentration to 0.05M reduced diuron removal efficiency to about 82%. The presence of an appropriate concentration of Na2SO4 electrolyte in electrochemical degradation systems improves electron transfer in the reaction solution and leads to increased production of HO radicals at the anode surface (Samarghandi et al",
            "5 and the removal efficiency decreased under strong acidic and alkaline conditions. However, in the presence of NaCl electrolyte, the highest removal efficiency was observed under very acidic conditions (pH \u00bc 1.5). Also in the presence of persulfate electrolyte, the highest removal efficiency was obtained under strong acidic (pH \u00bc 1.5) and strong alkaline (pH \u00bc 12) conditions (Li et al., 2020). The effect of current density on diuron removal efficiency as a function of initial solution pH and reaction time was depicted in Fig. 5(b) and (c). As shown in Fig. 5(b), at the initial solution pH of 5.4, the reaction time of 30 min, and the Na2SO4 electrolyte concentration of 0.03 M, increasing the current density from 5 mA cm 2 to 13.4 mA cm 2 suggestively increases the removal efficiency from about 72.7 to 84%. However, further increase in current density to 15 mA cm 2 has a clear inhibitory effect on diuron removal; so that the removal efficiency of diuron is reduced to about 83.7%. Fig. 5(c) also shows the highest removal efficiency at a current density of 13.6 mA cm 2. As shown in Fig. 5(c), under conditions including a current density of 13.6 mA cm 2, a pH of solution 7, and a concentration of 0.03 M Na2SO4, the diuron removal efficiency was improved from 67.9% to about 96.5% by increasing the reaction time from 10 to 50 min. Performing all electrochemical reactions in an EAOP depends on the current applied to the electrolytic cell. Increasing the current density in optimal values leads to more production of HO radicals at the anode surface, which results in increased system efficiency in the degradation of organic pollutants (Xia et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003949_s10846-007-9137-x-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003949_s10846-007-9137-x-Figure4-1.png",
        "caption": "Fig. 4 Link frames of one leg",
        "texts": [
            " We note that the legs of this robot have the same structure as the classical Gough\u2013Stewart parallel robot [34]. Assuming that Bi is the point connecting leg i to the base and Pi is the point connecting leg i to the platform. The frame \u22110 is defined fixed with the base, its origin is B1, and frame \u2211P is fixed with the mobile platform with P1 as origin. We place these frames as shown in Fig. 3: The notations of Khalil and Kleinfinger [20], are used to describe the geometry of the tree structure composed of the base and the legs. The definition of the local link frames of leg i are given in Fig. 4, while the geometric parameters are given in Table 1. The following parameters are used: aj denotes the frame antecedent to frame j, \u03bcj and \u03c3j describe the type of joint: \u2013 \u03bcj=1 if joint j is active and \u03bcj=0 if it is passive, \u2013 \u03c3j=1 if joint j is prismatic and \u03c3j=0 if it is revolute, \u2013 The parameters (\u03b3j, bj, \u03b1j, dj, \u03b8j, rj) are used to determine the location of frame \u2211j with respect to its antecedent frame. 4.2 Calculation of the Jacobian Matrices The following notations are used: P1Pi Position vector between points P1 and Pi, vi Linear velocity of point Pi, it is calculated in terms of the platform velocity as follows: vi \u00bc vp \u00fe wp P1Pi \u00f031\u00de qa Vector of the active joint variables, (first and third variables of each leg) with: qji Denotes the position variable of joint j of leg i, qi Vector of the joint variable of leg i, it does not take into account the variables of the spherical joint between the leg and the platform: qi \u00bc q1i q2i q3i\u00bd T \u00f033\u00de The Jacobian matrices required to calculate the dynamic model are calculated as follows: (1) The inverse kinematic model of a leg, which gives the joint velocities (q : 1i, q : 2i, q : 3i, i=1\u20133) as a function of the linear velocity of point Pi connecting leg i with the platform. It corresponds to the inverse kinematic model of a serial structure with three joints (RRP): q : i \u00bc J 1 i vi \u00f034\u00de J 1 i is the (3\u00d73) inverse Jacobian matrix of leg i. It is calculated by inverting Ji The Jacobian matrix of leg i, is calculated as follows [2, 7, 24]: Ji \u00bc a1i BiPi a2i BiPi a3i\u00bd \u00f035\u00de with: aji the unit vector along the joint axis j of leg i, BiPi position vector from Bi to Pi, BiPi=Li.a3i, where Li the length of leg i, see Fig. 4. In terms of the geometric parameters of the legs given in Table 1 we obtain Ji. Inverting analytically Ji we compute the matrix J 1 i . As an example, the matrix J 1 1 with respect to frame \u22110 is given by: 0J 1 1 \u00bc Sq1i=Li Sq2i 0 Cq1i=LiSq2i Cq1iCq2i=Li Sq2i=Li Cq2iSq1i=Li Cq1iSq2i Cq2i Sq1iSq2i 24 35 \u00f036\u00de C* and S* represent, respectively, cos(*) and sin(*). We note that the 3d row elements of 0J 1 i represent the components of the unit vector along the prismatic joint axis 0a3i. The singular configurations of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000968_j.addma.2021.102203-Figure23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000968_j.addma.2021.102203-Figure23-1.png",
        "caption": "Fig. 23. Von Mises stress distributions part of different path strategies. (a) path strategy 1. (b) path strategy 2. (c) path strategy 3.",
        "texts": [
            " Path strategy 1 is similar to the SDM path strategy; the depositing sequence and direction of odd and even layers are identical. Long and transverse weld beads are deposited from left to right, followed by short stiffeners from left to right. In path strategy 2, the depositing direction of even layers is opposite to that of odd layers, as the RM path strategy does. In path strategy 3, the long and transverse weld bead is divided into two segments. The deposition direction of odd layers is from both sides to the middle. Even layers are from the middle to both sides, and the trend is similar to the SRM path strategy. Fig. 23 presents the von Mises stress distributions of the load-carry frame part in different path strategies. The maximum residual stress is found at the junction of the ends of the bead and the substrate. In path strategy 1, the von Mises on the substrate presents an asymmetric distribution; in path strategy 2, it is symmetrically distributed. In path strategy 3, stress concentration occurs at the midpoint of the weld bead because of the arc striking and extinguishing at this position. Fig. 24 illustrates the nephogram of distortion along the height direction of the part in different path strategies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure2.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure2.11-1.png",
        "caption": "Fig. 2.11 Tension\u2013twisting coupling deformation",
        "texts": [
            " Similarly, because the relations r\u00f01\u00dex \u00bc r\u00f02\u00dex and r\u00f01\u00dey \u00bc r\u00f02\u00dey are satisfied, the stresses rx and ry in a bias laminate become zero. When only shear stress is applied to a bias laminate, the normal stresses of each layer r\u00f01\u00dey and r\u00f02\u00dey are generated. Because the signs of the normal stresses are opposite and the absolute values are the same, a bending moment is generated at the side of a bias laminate. This bending moment is expressed by Mx \u00bc t2r\u00f01\u00dex My \u00bc t2r\u00f01\u00dey : \u00f02:61\u00de This bending moment causes bending deformation. As shown in Fig. 2.11, there is twisting deformation when in-plane stress is applied to a bias laminate. This is called tension\u2013twisting coupling, which does not occur for the uniform orthotropic plate. 2.3 Properties of a Bias Laminate 75 (1) Elastic properties of a bias laminate under the FRR approximation When uniform stress {rx, 0, 0} is applied to a bias laminate, Eq. (2.50) can be rewritten as rx \u00bc Exxex \u00feExyey 0 \u00bc Exyex \u00feEyyey: \u00f02:62\u00de The modulus of a bias laminate Ex in the x-direction is therefore Ex \u00bc rx=ex \u00bc Exx E 2 xy=Eyy: \u00f02:63\u00de Similarly, the modulus of a bias laminate Ey in the y-direction, shear modulus Gxy, and Poisson\u2019s ratios mx and my are given by Ey \u00bc Eyy E 2 xy=Exx my \u00bc Exy=Exx mx \u00bc Exy=Eyy Gxy \u00bc Ess; \u00f02:64\u00de where Exx, Eyy and Exy are defined by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000628_j.mechmachtheory.2021.104262-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000628_j.mechmachtheory.2021.104262-Figure15-1.png",
        "caption": "Fig. 15. Schematic of the mesh stiffness measurement.",
        "texts": [
            " The difference between the elastic strain energies calculated by Eq. (34) and Eq. (35) is less than 6% [20] . Hence, we can determine the elastic strain energies by Eq. (38) [20] . \u03c3a v = \u03c3max 2 K a v (38) U = \u222b v ol \u03c3 2 max 4 K 2 E dV (39) a v Using Hooke\u2019s law \u03c3 = E\u03b5 and substituting into Eq. (38) , the elastic strain energy can be written as U = \u222b v ol \u03b5 2 max E 4 K 2 a v dV (40) Then, the bending stiffness of the gear tooth can be expressed as [10 , 20] . K b p\u00b7g = F 2 2 U (41) A schematic diagram of the measurement of the mesh stiffness is shown in Fig. 15 . Strain gauges are pasted on the tooth root of the ring gear. A tachometer is installed on the sun gear shaft to measure the rotation speed, and a torque meter is installed on the shaft of the carrier to measure the loading torque. The rotational speed of the sun gear is controlled at a very low speed, which can be considered a quasi-static duration. As shown in Fig. 16 , the experimental setup contains a drive motor, a load motor, two belt drives and a planetary gearbox. The physical parameters of the planetary gears are the same as presented in Table 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure6.21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure6.21-1.png",
        "caption": "Fig. 6.21",
        "texts": [
            "20, and on ~ po the closed orbits tend to packing. -=;...-.-------------------- ~ll Fig. 6.20 HopfBifurcation 223 Given a non-linear system y' = !(Y,Il), which has a trivial solution, that is !(0,1l) = o. Suppose that the linear operator A(Il) = Dy!(O,Il) has n eigenvalues {AI (IlP\"2 (Il), .. . ,AI/(Il)}\u00b7 Bifurcation will occur if the real part of some eigenvalue Re(Ai(ll)) = O. Now we shall consider the case Il E i/?2, and let III = Il, 112 = , namely Il E (1l,0'). If Ai (1l,0') = 0 or Re(Ai(Il,O')) = 0, bifurcations will occur as shown in Fig.6.21. Generally, these curves intersect at isolated simple points, and when the parameter Il varies and intersects with Ai = 0 or Re(A;) = 0, the sign of Ai will change, so there may be simple or Hopf bifurcation. We can see that the trivial solution Y = 0 is stable for all the parameters (1l,0') below the curve or equivalently 'A.; < 0 and Re(A;) < O. Definition 6.1 The curve Ai = 0 or Re(A,) = 0 is said to be neutrally stable if the boundary ABeD of the shadowed region enclosed by the curves Ai = 0, Re(A;) = 0 is stable. For a fixed ,let Il increase through Aj = 0 or Re(A) = 0 (j = 1,2,3) and simple or Hopf bifurcations will occur as shown in Fig. 6.21. But if 0' = O'ij (as 0'12 or 0'23 in Fig. 6.21), the theory described above will not hold. There will be two zero eigenvalues for 0'12' and for 0'23 there will be a pair of conjugate complexes with real zero part and a zero eigenvalue. Fixing 0' = 0' j' let us consider the initial value problem: y'=!(Y,Il), YEi/?\", IlEi/?, with !(O,Il)=O,A(Il)=D/O,Il),A(O) having a two-dimensional null space. Suppose that the system has been reduced to 224 Bifurcation and Chaos in Engineering the following two-dimensional system by using LS reduction or the centre manifold theorem: x' = g(x,fl), g:it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure13.76-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure13.76-1.png",
        "caption": "Fig. 13.76 Koutny\u2019s tire model. Reproduced from Ref. [88] with the permission of Tire Sci. Technol.",
        "texts": [
            " Notes 1011 1012 13 Rolling Resistance of Tires The load factor of Eq. (13.154) decreases with increasing rim radius when the tire radius and width are the same, as shown in the left figure of Fig. 13.75. When only the rim radius increases without a change in the tire radius, the tire width must increase to maintain the load capacity, as shown in the right figure of Fig. 13.75. Note 13.4 Koutny\u2019s Tire Model [88] Koutny\u2019s tire model is an empirical tire model where the equator of a loaded tire is assumed to be expressed by three curvatures as shown in Fig. 13.76. The polar angle / is measured from the line SD. The curvature is zero in the contact area (0 / w1), 1/rc in the free region (w / p) and 1/kcrc in the transition region (w1 / w), where 0 kc 1 is an empirical factor. We assume that the center S of the underformed circle with radius r0c is also the center of the equatorial arc for w / p. An equation for the displacement x is then obtained: 1 kc\u00f0 \u00derc cosw\u00fe rckc \u00bc r0c x ) rc \u00bc r0c x 1 kc\u00f0 \u00de cosw\u00fe kc : \u00f013:156\u00de Let 2U(x) be the length of the equator in the circumferential direction under deformation x",
            " Obviously, U 0\u00f0 \u00de \u00bc pr0c and U\u00f0x\u00de \u00bc 1 kc\u00f0 \u00derc sinw\u00fe kcrcw\u00fe rc p w\u00f0 \u00de: \u00f013:157\u00de Representing the shrinkage length of the equator as K(x), we obtain U\u00f0x\u00de\u00feK\u00f0x\u00de U\u00f00\u00de \u00bc 0: \u00f013:158\u00de The substitution of Eqs. (13.156) and (13.157) into Eq. (13.158) yields an expression for the angle w: r0c x p\u00fe 1 kc\u00f0 \u00de sinw w\u00f0 \u00def g 1 kc\u00f0 \u00de cosw\u00fe kc \u00feK\u00f0x\u00de pr0c \u00bc 0: \u00f013:158\u00de Here, kc and K(x) are expressed by equations that are determined by curve fitting the experimental data: kc\u00f0x\u00de \u00bc 6\u00fe 5 W L0 30 ffiffiffi 4 p 1 1 x r0c 2 ; K\u00f0x\u00de \u00bc kG x r0c 3 : \u00f013:159\u00de where 2 W is the section width of a tire in Fig. 13.76. The coefficient kG is chosen as kG \u00bc 3500e 6C k0Ge 4C 0:4 ; C \u00bc W L0 ffiffiffiffiffiffiffiffiffiffi z1r0c 50L0 s : \u00f013:160\u00de Notes 1013 k0G increases with the rigidity of the belt and k0G \u00bc 1:1 for a truck/bus tire sized 11.00R20. Equation (13.158) for deformation x is only solvable numerically, and it is possible to represent the dependence of the radius rc on the polar angle /: rc\u00f0/\u00de \u00bc r0c x cos/ 0 /\\w1 \u00bc rc 1 kc\u00f0 \u00de cos w /\u00f0 \u00de \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k2c 1 kc\u00f0 \u00de2sin2 w /\u00f0 \u00de q( ) w1 /\\w \u00bc rc w / p; \u00f013:161\u00de where w1 \u00bc tan 1 1 kc\u00f0 \u00derc sinw r0c x : \u00f013:162\u00de 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.6-1.png",
        "caption": "Fig. 8.6: Friction in a Harmonic Drive Stage [137]",
        "texts": [
            " The model in [226] distinguishes in a first step the speed directions and introduces a degree q1 of freedom for the driving and a DOF q2 for the driven direction: J1q\u03081 = Tan \u2212 1 i \u03bbG \u2212 ( 1 i sign(q\u03071)\u00b5G1\u03bbG + 1 i2 d1q\u03071 + 1 i4 b1q\u03071 3), J2q\u03082 = \u2212Tab + \u03bbG \u2212 (sign(q\u03072)\u00b5G2\u03bbG + d2q\u03072 + b2q\u03072 3). (8.23) The magnitude \u03bbG is the transmitted torque, the moments of inertia of the input and output sides are denoted by J1, J2, and the friction data of the equations 8.21 and 8.22 are split up for the two directions b = b1 + b2, d = d1 + d2, \u00b5 = \u00b5G1 + \u00b5G2. (8.24) In a further step we consider the Harmonic Drive gear as a unilateral system and apply the reduced mechanical model of Figure 8.6. The pinion with the degree of freedom q1 is driven by the torque Tan and meshes with the gear wheel with a degree of freedom q2 and with an output torque Tab. The configuration is here represented by one tooth pairing only though the contact ratio of the Harmonic Drives is very large. We have normal forces Fn and friction forces Fr, the last ones arising by the relative motion in the tooth contact. Applying this model to Harmonic Drives requires some approximations: \u2022 Due to the large contact ratios we do not consider every individual tooth pairing, but we consider an average of them",
            " Modeling Harmonic Drive Gears always includes many questions of modeling bilateral constraints with friction, which represents a difficult problem. In the following we shall consider two approaches, a more or less complete one and a simplified one. The calculation of such gears require large computing times, hence an adequate simplification makes sense. We start with the complete model and take note of the fact, that the gear equations of motion have to be integrated into the system equations. According to Figure 8.6 each of the Harmonic Drive Gears possesses at least two degrees of freedom , an input DOF q1 and an output DOF q2, which corresponds to the joint degree of freedom. Thus we have to add for every gear an additional degree of freedom. Having that in mind and considering the gear equations of motion (8.25) these equations may be written for the sliding case as The Jacobian matrix WGN projects the averaged normal forces \u03bbG onto the degrees of freedom of the gear q = (q1 q2)T . The matrix HG includes the friction coefficients for the determination of the friction forces and torques from the averaged normal forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.62-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.62-1.png",
        "caption": "Fig. 12.62 Predicted deformation of snow and the shear stress distribution in the contact patch [84]",
        "texts": [
            " Sipes and the friction coefficient between the tire and snow surfaces are ignored because this simulation is focused on predicting the shear force of snow in a void. The appearance of the predicted snow surface and a comparison 12.3 Traction on Snow 859 with the snow-covered road surface are shown in Fig. 12.61. The track of the tread pattern is observed on the predicted snow surface, which is in good qualitative agreement with a photograph. One advantage of numerical simulation is that we can make visible what we cannot observe in an experiment. For example, the predicted shear stress distribution of a tire on snow can be predicted as shown in Fig. 12.62. The shear stress is mainly generated at the lateral grooves of the tread pattern. A comparison of the 860 12 Traction Performance of Tires shear stress distributions of tires with various pattern designs shows that the new tread pattern can be effectively designed by simulation. (3) Validation of predictability The predictability of simulation was validated by comparing experimental results with the prediction for several basic tread patterns. The tire size was 195/65R15, the inflation pressure was 200 kPa, the load was 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.8-1.png",
        "caption": "Fig. 8.8: Foot Model and Kinematics [137]",
        "texts": [
            " With respect to the foot contacts we have two possibilities, namely modeling the ground forces in a unilateral way, which means rigid body contacts and set-valued forces, or modeling the ground forces by smooth contact laws in the form of spring-damper characteristics. We shall consider both possibilities. Unilateral model For this case we take the general contact kinematics from section 2.2.6 on page 31, applied to the specific case of the JOHNNIE-feet [137]. The geometry of the foot plates is depicted in Figure 8.8. The foot possesses four cylindrical contact elements in the four corners of the foot plate, which is subdivided into two parts connected by a joint to assure static definiteness. The vector from the inertial coordinate system I to the potential contact point K1 is composed by the three vectors 8.2 Walking Dynamics 521 rOK1 = rO + rOM + rMK1, (8.27) which can be expressed in any coordinate frame. The direction of rMK1, though, has to be oriented in such a way as to fulfill the contact conditions 2.102 and 2.103 on page 39. This results in rMK1 = r\u2217MK1 |r\u2217MK1| R with r\u2217MK1 = (nb \u00d7 nk)\u00d7 nk (8.28) The radius R is explained by Figure 8.8, and the potential contact point results from a projection of the point K1 onto the ground plane with the direction nb. For simulation purposes the ground plane is oriented parallel to the x-y-plane of the inertial coordinate system resulting in a simple form of the contact equations. The normal distance between the points K1 and K2 writes gN = |rD| = nTb (rK1 \u2212 rK2). (8.29) Together with the vector rOK1 from equation (8.27) we then get for the time derivatives r\u0307K1 = r\u0307O + \u03c9\u03031rO,K1 = JO,1q\u0307 + (J\u0303R,1rO,K1)q\u0307 =WK1q\u0307 (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-25-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-25-1.png",
        "caption": "Figure 2-25. Evolution of a linear induction motor from a rotating induction motor.",
        "texts": [
            " By adjusting the field current to produce a leading power factor, the supply inverter can be line commutated removing the need for forced commutation of the switching devices except at low values of speed. Wound field synchronous motors are useful in traction applications where a wide speed range at constant power is required. The adjustment of the field current in this range is similar to that of a commutator motor. 2.11. LINEAR MOTORS The major properties of a linear induction motor can be appreciated by considering the evolution of the induction motor of Figure 2-25a. In this motor, the rotor consists of an iron core surrounded by a conducting ring of aluminum or copper. Suppose a cut is made along the dotted line and the machine is unrolled. The result is shown in Figure 2-25b, which has a two-pole stator or primary and the rotor or secondary has been extended indefinitely. The synchronous speed of this linear induction motor is given by \u03bd^\u03c8- m/s (2.20) where z is the wavelength of a two-pole section of the primary and us is the angular frequency of the supply. A linear induction motor typically has four to eight poles, but the number need not be an even number or even an integer. The velocity-torque relation for a linear induction motor is roughly similar to that of the rotating induction motor but differs due to a number of factors",
            " Thus, the power factor of a linear motor tends to be low. Large linear induction motors have been used in public transit vehicles, highspeed trains, materials handling, extrusion processes, and the pumping of liquid metals. Small linear motors are used in a variety of applications such as curtain pullers and sliding door closers. Linear synchronous motors have been proposed and tested for a number of lowspeed transit and high-speed train applications [48, 49]. These motors have a primary similar to the three-phase stator shown in Figure 2-25b. The secondary may be a set of either permanent magnets or superconducting magnets. The magnets may be installed on the underside of the vehicle interacting with energized sections of primary on the track. The performance principles are similar to those of rotating synchronous motors. 2.12. CONCLUSION A wide variety of choices of electrical motors is now available for use with variable speed, variable frequency drives. No single type is ideal for all applications. The optimum choice for a particular drive depends on a detailed assessment of the system design criteria that are considered to be important, criteria such as initial cost, lifecycle cost, dynamic performance, ease of maintenance, robustness, weight and envir- 76 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.17-1.png",
        "caption": "Fig. 3.17: Forces in a Multibody Contact (i)",
        "texts": [],
        "surrounding_texts": [
            "as discussed in chapter (3.1.2), thus leading to a set of differential algebraic equations (DAE\u2019s) with additional inequalities resulting from the transition laws with respect to the unilateral contacts. We arrange the constraint vectors for normal and the constraint matrices for tangential constraints from the equations (2.132) in the following form WN =[\u00b7 \u00b7 \u00b7wNi \u00b7 \u00b7 \u00b7 ] \u2208 IRf,nN , i \u2208 IN , WT =[\u00b7 \u00b7 \u00b7WTi \u00b7 \u00b7 \u00b7 ] \u2208 IRf,2nT , i \u2208 IT . (3.135) The constraint matrices are projection matrices, called Jacobians, which project magnitudes of the constraint space into the space of the generalized coordinates. Vice versa, to go from the space of the generalized coordinates into the constraint space, we need the transpose of the constraint matrices. According to Figure (3.17) we have for an active contact the following forces in normal and tangential direction Fni = \u03bbnini, Fti1 = \u03bbti1ti1, Fti2 = \u03bbti2ti2. (3.136) These forces act in Figure (3.17) on the body (j) in a positive sense, according to the chosen coordinate frame, and this means with +Fni, +Fti1 and with +Fti2, and they act on body (j+1) in a negative sense, according to the usual cutting principle, and this means with \u2212Fni, \u2212Fti1 and with \u2212Fti2. The vectors ni, ti1 and ti2 are unit vectors, and therefore the absolute values of the constraint forces are given by the three magnitudes \u03bbni, \u03bbti1 and \u03bbti2, one in normal and two in tangential directions. For all active contacts we may collect these \u03bb-values in the following vectors \u03bbN (t) =  ... \u03bbni(t) ...  \u2208 IRnN , i \u2208 IN , \u03bbT (t) =  ... \u03bbti(t) ...  \u2208 IR2nT , i \u2208 IT , \u03bbti(t) =[\u03bbti1(t), \u03bbti2(t)]T \u2208 IR2. (3.137) 3.4 Multibody Systems with Unilateral Constraints 137"
        ]
    },
    {
        "image_filename": "designv10_2_0003221_s0094-114x(98)00081-0-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003221_s0094-114x(98)00081-0-Figure3-1.png",
        "caption": "Fig. 3. Three-DOF planar parallel manipulators.",
        "texts": [
            "Vd \u00ff Idu l sin f\u00ff y ddTV0 \u00ff Iul u sin f\u00ff y ccTV0 U Gg\u00ff V lu sin f\u00ff y Proceeding in a manner similar to the previous mechanism, we get the \u00aenal equations of motion by considering the force balance of the output point and the closed-form equations are derived in the form M t Z Ht RExt 22 where M X2 i 1 Qi; Z X2 i 1 Ui; H d1 l1 sin f1 \u00ff y1 d2 l2 sin f2 \u00ff y2 and t t1 t2 T Three-degree-of-freedom planar parallel manipulators have been studied extensively in literature. Dynamic formulation of the eight-bar 3-DOF parallel manipulator (shown in Fig. 3a) and that of a similar manipulator with revolute actuations have been reported by Revathi et al. [12] and by Ma and Angeles [13], respectively. The present method can be applied to both the cases as well as to a manipulator with di erent types of legs. Adding a fourth leg in parallel results in a statically redundant manipulator (Fig. 3b). For all these manipulators, the previously described procedures have to be applied to evaluate the reaction forces at the platform point. After evaluating the reaction forces at the platform connection points, the force and moment equilibrium of the platform is considered to arrive at the \u00aenal dynamic equations. Due to space limitations, the detailed analysis of these manipulators are not presented here and the same can be found in Choudhury [14]. A single-loop six-bar mechanism (with the link farthest from the base as output) is an example of a planar hybrid manipulator with two legs, one having two actuations and the other having one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure10.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure10.8-1.png",
        "caption": "Fig. 10.8 -11-- 3.316 x 10-4 sec",
        "texts": [],
        "surrounding_texts": [
            "10.9 shows the displacement response predicted in this study using the time-centred Euler scheme. In Fig. 10.9, the deflection I)is defined as, 370 Bifurcation and Chaos in Engineering The dynamic buckling of the arch occurs at the load level at which a sudden increase in the deflection ratio is measured. Fig. 10.9 shows that at Po = 0.202, it oscillates about a position of approximately 0 = -0.5, and that at Po = 0.203 it snaps through at t = 60.0, and oscillates about a position of approximately 0 = -4.0. Therefore, for T from 0 to 90.0, the buckling load predicted here lies between Po = 0.202 and"
        ]
    },
    {
        "image_filename": "designv10_2_0000025_j.jmsy.2020.06.019-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000025_j.jmsy.2020.06.019-Figure4-1.png",
        "caption": "Fig. 4. Three-points offset method.",
        "texts": [
            " In theory, an approximately developable ruled surface can not be absolutely enveloped by the tool whose radius of curvature is bigger than zero due to distortion characteristics. In order to depress the interference caused by the inconsistency between tool curvature and surface curvature, a three-point off set method [42] based on local neighborhood optimization is adopted. Three points refer to three intersections between ideal tool axis orientation and offset curves, which are used to calculate the initial cylindrical-cutter-position surface. As shown in Fig. 4, given that the machined ruled surface is = +r a bu v u v u( , ) ( ) ( ), the offset surface r u v( , )o can be expressed as: = + \u2202 \u2202 \u00d7 \u2202 \u2202 \u2202 \u2202 \u00d7 \u2202 \u2202 r r r r r ru v u v R u v u u v v u v u u v v ( , ) ( , ) ( , ) ( , ) / ( , ) ( , )o c (1) where Rc denotes the radius of the tool nose. r r ru u u( ), ( ), ( )o o o 0 0.5 1 are the iso-parametric curves where =v 0, =v 0.5 and =v 1 of r u v( , )o respectively. The tool axis orientation Tb and r u v( , )o intersect at two endpoints, r u( , 0)o s0 and r u( , 1)o s1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure21-1.png",
        "caption": "Fig. 21 Coordinate systems applied for TCA",
        "texts": [
            " ooth contact under load has been investigated and the Loaded ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 TCA has been developed 19\u201322 . Meanwhile, TCA has been not only used as a tool of analysis, but also integrated as a part of synthesis procedures 6\u20138,11 . TCA is a process of simulation of meshing and contact of a pair of gears under light load. Therefore, simulation of changes of the assembly errors and misalignments are taken into account. For this purpose, the adjusting parameters E, G, P, and are incorporated into the TCA model Fig. 21 . The output of a TCA program are the scaled graphs of transmission errors and tooth bearing contact patterns that predict the results from a bevel gear testing machine. By replacing the subscript \u201cw\u201d in the previous equations with subscript \u201c1\u201d and subscript \u201c2,\u201d respectively, a pair of mating tooth surfaces of the pinion and the gear can be represented in the coordinate systems S1 and S2 that are connected to the pinion and the gear respectively, as follows, for the pinion r1 = r1 u1, 1, 1 n1 = n1 u1, 1, 1 t1 = t1 u1, 1, 1 f1 u1, 1, 1 = 0 32 NOVEMBER 2006, Vol",
            "org/about-asme/terms-of-use 1 Downloaded Fr for generated gear r2 = r2 u2, 2, 2 n2 = n2 u2, 2, 2 t2 = t2 u2, 2, 2 f2 u2, 2, 2 = 0 33 for non-generated gear r2 = r2 u2, 2 n2 = n2 u2, 2 t2 = t2 u2, 2 34 322 / Vol. 128, NOVEMBER 2006 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 Further, the mating tooth surfaces are transformed into a common coordinate system Sf that is connected to the frame of the gear drive and with origin Of located at the theoretical crossing point of the gear axis. The relationship of coordinate systems in Fig. 21 simulates the running meshing of the gear pair shown in Fig. 20 and incorporates the adjusting parameters E, G, P, and . In case of spiral bevel gear drives, E0=0 is assumed. The axes Z1 and Z2 coincide with the rotation axes of the pinion and the gear, respectively. The origins O1 and O2 of systems S1 and S2 would be at the theoretical crossing point if the adjusting param- hing of design A Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use e r t b o M b f t o es J Downloaded Fr ters G=0 and P=0 are assumed. Denoting 1 and 2 as the otational motion parameters of the pinion and the gear respecively shown in Fig. 21, we can obtain for the pinion r f 1 = r f 1 u1, 1, 1, 1 n f 1 = n f 1 u1, 1, 1, 1 t f 1 = t f 1 u1, 1, 1, 1 f1 u1, 1, 1 = 0 35 for generated gear r f 2 = r f 2 u2, 2, 2, 2 n f 2 = n f 2 u2, 2, 2, 2 t f 2 = t f 2 u2, 2, 2, 2 f2 u2, 2, 2 = 0 36 for non-generated gear r f 2 = r f 2 u2, 2, 2 n f 2 = n f 2 u2, 2, 2 t f 2 = t f 2 u2, 2, 2 37 The basic condition of two tooth surfaces 1 and 2 Fig. 22 eing in contact at a common point P is that the position vectors f the pinion and the gear coincide and their normals are collinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003239_s0032-5910(01)00283-2-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003239_s0032-5910(01)00283-2-Figure2-1.png",
        "caption": "Fig. 2. The impact of a sphere on a flat plane.",
        "texts": [
            " It has also allowed a large number of results to be produced from precisely the same impact angle, so that averaging can improve further the reliability of the measurements. This attention to all aspects of the system has allowed measurements to be obtained of particle rotation, normal restitution coefficient to within 28 of glancing incidence, and tangential restitution coefficient to within 28 of normal impact, with much higher accuracy and reproducibility than have been achieved by previous authors. In this section, a number of results from rigid body theory and from elastic analysis will be summarised. Fig. 2 shows the situation of a non-rotating sphere approaching a flat, semi-infinite solid at a speed V and angle u , so thati i tan u sV rV . The sphere rebounds at an angle u , withi ti ni r a reduced speed V and a forward rotation of v . Becauser r it is more convenient for this particular case, the scalar w xnotation of Ning 17 is used here rather than the more w xgeneral vector form used by Walton 15 and others. The rotation and directions of the normal and tangential velocity components are defined in Fig. 2. Subscripts n and t refer to normal and tangential directions, respectively, and i and r correspond to initial values and those after rebound, respectively. Upper case velocities refer to the centre of mass, and lower case refer to the contact patch on the sphere. A simple view of the oblique collision of a sphere with a flat surface can be taken by using classical rigid-body theory, in which deformations of either surface are negligible. As will be shown later, many aspects of this model are also valid for practical impacts when small elastic deformations are involved",
            " The ratio of the rebound and impact speeds is the overall coefficient of restitution e, defined here as es VrV . Two other useful parameters which describe ther i behaviour of the centre of mass after rebound are the normal and tangential restitution coefficients e and e ,n t where e sV rVn nr ni e sV rVt tr ti \u017d . w xFrom Eq. 1 , Ning 17 noted that the value of e can bet linked to v byr 5 V sinui i v s 1ye 2\u017d . \u017d .r t2 R The relative movement of the contact patch on the sphere after impact is also a useful parameter for indicating the nature of the contact. For the present case of zero initial spin, Fig. 2 illustrates that the relationships between \u017d .the centre of mass motion V and the velocity compo\u017d .nents of the contact patch \u00d5 are: \u00d5 sVni ni \u00d5 sVti ti \u00d5 sVnr nr \u00d5 sV yRv 3\u017d .tr tr r Some previous authors have used the parameter b , the tangential restitution coefficient of the contact patch, to represent tangential motion. Using the kinetics of the rigid sphere, b can be related to the centre of mass coefficient e by:t \u00d5 5 7tr b'y s y e 4\u017d .t \u00d5 2 2ti Also, an expression linking the rebound angle of the w xcontact patch, u , with the other measured parameters 17cr is 2 tanu 5cr e s e q 5\u017d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000556_j.mechmachtheory.2021.104265-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000556_j.mechmachtheory.2021.104265-Figure2-1.png",
        "caption": "Fig. 2. Intersecting axes.",
        "texts": [
            " This paper\u2019s method is mainly aimed at the general six-DOF manipulators with simple geometry: they have at least one pair of adjacent axes intersecting; except for that, the other adjacent joints\u2019 axis are only perpendicular or parallel to each other. Literature [50] concluded that \"the robotic kinematic chain is cut into two branches at the origin of the joint coordinate or at the intersection point of the axes of the targeted coordinates.\" From our perspective, it is best to choose the intersection point as the first cut point in intersecting axes. Given the i th joint axis of a six-DOF manipulator intersects the ( i + 1)th joint axis, i = 1,2,\u20265, shown in Fig. 2 , P is the intersection point, scalar \u03b2 is the angle between the adjacent axes. Take point P as the cut point to get two sub-chains and set it as the endpoint of the two sub-chains. For the sake of description, the one containing i th joint is denoted as the subchain L, and the other one having ( i + 1)th joint is marked as the sub-chain R. As can be seen from the figure, the position of the endpoint P is not affected by the rotation of the two joints. The axial direction of the two joints is not affected by the rotation of the corresponding joint too"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003734_s0022112007007835-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003734_s0022112007007835-Figure2-1.png",
        "caption": "Figure 2. A sketch of the arrangement of a bottom heavy squirmer. Gravity acts in the g-direction, while the squirmer has orientation vector e, radius a and its centre of mass distance h from its geometrical centre.",
        "texts": [
            " 2006) and, more recently, for negative values of \u03b2 (unpublished) from which an arbitrary interaction can be interpolated. We will exploit the database in constructing Fsq , which represents the pairwise superposition of the interaction of two squirmers. If the squirmer is bottom-heavy, there is an external torque acting on the squirmer and this must be equal to the hydrodynamic torque, so that the net torque on the squirmer is zero. If the distance of the centre of gravity is h from the centre of the squirmer, in the opposite direction to its swimming direction in undisturbed fluid (see figure 2), then there is an additional torque of Ftor = 4 3 \u03c0a3\u03c1he \u2227 g, (2.5) where \u03c1 is the density, g is the gravitational acceleration vector, and the gravitational direction is g/g. Although the governing equation of squirmer motions (2.1) does not in principle allow the spheres to overlap, there are cases of very small separation in which numerical errors associated with the integration of U\u2217 in time can lead to an apparent overlap. In order to avoid the prohibitively small time step needed to overcome this problem, we introduce a repulsive force, as used by Brady & Bossis (1985, 1988): Frep = \u03b11 \u03b12 exp(\u2212\u03b12\u03b5) 1 \u2212 exp(\u2212\u03b12\u03b5) r r , (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001039_j.addma.2021.102002-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001039_j.addma.2021.102002-Figure1-1.png",
        "caption": "Fig. 1. Achieving application specific manufacture with L-PBF. An alloy that exhibits wide processing window with L-PBF and allows formation of heterogeneous and hierarchical features, can be used to manufacture different components with varying microstructural requirements. Illustration shows how the microstructural requirements for different components within a product may vary: engine components require thermally stable, coarsegrained microstructure, attainable at small laser power and slow scanning speed, whereas the vehicle frame requires fine-grained microstructure, for enhanced room-temperature strength, attainable at high laser power and fast scanning speed.",
        "texts": [
            " In either case, strength-ductility trade-off impales the material; such behavior is common in Al-Si [19\u201321] and Al-Ce [29] alloys. It is therefore evident that the current strategies for designing Al alloys for L-PBF lead to a trade-off between alloy printability and performance [2]. This work proposes a strategy that integrates grain refinement and eutectic solidification for design of Al alloys for L-PBF. The resulting alloy may consequently exhibit a wide processing window and thus, excellent printability, alongside an HGS and hierarchical as-built microstructure. Fig. 1 summarizes how L-PBF can be used for application specific manufacture of such Al alloys. Addition of elements that: a) can aid in heterogeneous nucleation of fine-equiaxed \u03b1-Al grains, and b) can form a terminal eutectic with Al, may assist in developing an Al alloy with synergistic printability and performance [2]. Grain refinement would occur within the melt pool only at those sites where primary grain refining phases are present and/or where favorable G to R ratios for CET exist. Note that the primary grain refining phases may \u201cdecorate\u201d only specific sites in the as-built microstructure due to formation of the remelting zones [17,18,30]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.6-1.png",
        "caption": "Fig. 4.6 Definition of b0",
        "texts": [
            "1 DLT of a Two-Ply Bias Belt with Out-of-Plane \u2026 193 u00 \u00bc e0x v00 \u00bc h/\u00f0y\u00de ; \u00f04:9\u00de where /(y) is a function related to compression in the width direction owing to the tensile strain e0 in the x-direction. The displacements in the middle plane u0 and v0 are expressed by u0 \u00bc u00 \u00fe Du\u00feDu 2 \u00bc e0x e0 X1 n\u00bc1 Cn sin 2pnn a \u00fe sin 2pnn a 2 \u00bc e0x e0 X1 n\u00bc1 Cn sin 2pnx a sin 2pny b0 v0 \u00bc v00 \u00fe Dv\u00feDv 2 \u00bc h/\u00f0y\u00de f0\u00f0s\u00de X1 n\u00bc1 Cn sin 2pnn a sin 2pnn a 2 \u00bc h/\u00f0y\u00de f0\u00f0s\u00de X1 n\u00bc1 Cn cos 2pnx a sin 2pny b0 : \u00f04:10\u00de Referring to Fig. 4.6, b0 is expressed as b0 \u00bc a tan a: \u00f04:11\u00de Note that the periodic displacement is generated even in the middle plane as shown in Eq. (4.10). (2) Displacements of the cord and rubber of lamination Referring to the deformation of the cord and rubber of a laminate in Fig. 4.7, the nonperiodic interlaminar shear strains wx0 and wy0 are expressed by 194 4 Discrete Lamination Theory Note that Eq. (4.12) is similar to Eqs. (3.75) and (3.77) in MLT. Rearranging Eq. (4.12), the displacements u and v are given by u \u00bc u0 \u00fe hwx0 Hw;x v \u00bc v0 \u00fe hwy0 Hw;y ; \u00f04:13\u00de where H \u00bc h\u00fe h0=2: \u00f04:14\u00de The nonperiodic displacements in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure9.23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure9.23-1.png",
        "caption": "Fig. 9.23 Free-body diagram of the tread ring",
        "texts": [
            "58) 569 bij \u00bc A0 j sin j /r cj sin i/r\u00f0 \u00de sin i/f\u00f0 \u00de i \u00fe cos i j\u00f0 \u00de/r \u00fe jcjf g cos i j\u00f0 \u00de/f \u00fe jcjf g 2 i j\u00f0 \u00de cos i\u00fe j\u00f0 \u00de/r jcjf g cos i\u00fe j\u00f0 \u00de/f jcjf g 2 i\u00fe j\u00f0 \u00de 2 66664 3 77775 for i 6\u00bc j bij \u00bc A0 j sin j /r cj sin i/r\u00f0 \u00de sin i/f\u00f0 \u00de i sin jcj /r /f 2 cos i\u00fe j\u00f0 \u00de/r jcjf g cos i\u00fe j\u00f0 \u00de/r jcjf g 2 i\u00fe j\u00f0 \u00de 2 6664 3 7775 for i \u00bc j cij \u00bc A0 j cos j /r cj cos i/r\u00f0 \u00de cos i/f\u00f0 \u00de i cos i j\u00f0 \u00de/r \u00fe jcjf g cos i j\u00f0 \u00de/f \u00fe jcjf g 2 i j\u00f0 \u00de cos i\u00fe j\u00f0 \u00de/r jcjf g cos i\u00fe j\u00f0 \u00de/f jcjf g 2 i\u00fe j\u00f0 \u00de 2 66664 3 77775 for i 6\u00bc j cij \u00bc A0 j cos j /r cj cos i/r\u00f0 \u00de cos i/f\u00f0 \u00de i \u00fe sin jcj /r /f 2 cos i\u00fe j\u00f0 \u00de/r jcjf g cos i\u00fe j\u00f0 \u00de/f jcjf g 2 i\u00fe j\u00f0 \u00de 2 6664 3 7775 for i \u00bc j dij \u00bc A0 j sin j\u00f0/r cj\u00de cos\u00f0i/r\u00de cos\u00f0i/f \u00de i \u00fe sin \u00f0i j\u00de/r \u00fe jcjf g sin \u00f0i j\u00de/f \u00fe jcjf g 2\u00f0i j\u00de sin \u00f0i\u00fe j\u00de/r jcjf g sin \u00f0i\u00fe j\u00de/f jcjf g 2\u00f0i\u00fe j\u00de 2 66664 3 77775 fori 6\u00bc j dij \u00bc A0 j sin j\u00f0/r cj\u00de cos\u00f0i/r\u00de cos\u00f0i/f \u00de i \u00fe cos\u00f0jcj\u00de /r /f 2 sin \u00f0i\u00fe j\u00de/r jcjf g sin \u00f0i\u00fe j\u00de/f jcjf g 2\u00f0i\u00fe j\u00de 2 6664 3 7775 1 kT fori \u00bc j ei \u00bc a cos/r sin i/r\u00f0 \u00de sin i/f\u00f0 \u00de i \u00fe sin i 1\u00f0 \u00de/rf g sin i 1\u00f0 \u00de/ff g 2 i 1\u00f0 \u00de \u00fe sin i\u00fe 1\u00f0 \u00de/rf g sin i\u00fe 1\u00f0 \u00de/ff g 2 i\u00fe 1\u00f0 \u00de 2 6664 3 7775 for i 6\u00bc 1 ei \u00bc a cos/r sin i/r\u00f0 \u00de sin i/f\u00f0 \u00de i \u00fe /r /f 2 \u00fe sin i\u00fe 1\u00f0 \u00de/rf g sin i\u00fe 1\u00f0 \u00de/ff g 2 i\u00fe 1\u00f0 \u00de 2 664 3 775 for i \u00bc 1 570 9 Contact Properties of Tires fi \u00bc a cos/r cos i/r\u00f0 \u00de cos i/f\u00f0 \u00de i \u00fe cos i 1\u00f0 \u00de/rf g cos i 1\u00f0 \u00de/ff g 2 i 1\u00f0 \u00de \u00fe cos i\u00fe 1\u00f0 \u00de/rf g cos i\u00fe 1\u00f0 \u00de/ff g 2 i\u00fe 1\u00f0 \u00de for i 6\u00bc 1 fi \u00bc a cos/r cos i/r\u00f0 \u00de cos i/f\u00f0 \u00de i \u00fe cos i\u00fe 1\u00f0 \u00de/rf g cos i\u00fe 1\u00f0 \u00de/ff g 2 i\u00fe 1\u00f0 \u00de for i \u00bc 1: Notes Note 9.1 Eq. (9.1) The free-body diagram for the tread ring is shown in Fig. 9.23, where a is the radius of the undeformed tread ring. Force equilibriums in the tangential and normal directions are expressed by T \u00fe dT ds ds cos d/ 2 T cos d/ 2 V sin d/ 2 V sin d/ 2 V \u00fe dV ds ds sin d/ 2 \u00bc 0 frds\u00fe T \u00fe dT ds ds sin d/ 2 \u00fe T sin d/ 2 V cos d/ 2 \u00fe V \u00fe dV ds ds cos d/ 2 \u00bc 0: Appendix Explicit Expression of Eq. (9.58) 571 Neglecting the higher-order terms, we obtain dT=ds V=q \u00bc 0 T=q\u00fe dV=ds fr \u00bc 0 ; where s is the length along the tread ring. Note 9.2 Eq. (9.18) When the wheel is fixed and the system is stationary, Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003794_robot.1991.131747-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003794_robot.1991.131747-Figure1-1.png",
        "caption": "Figure 1: Position of the robot in the plane",
        "texts": [
            " The motion of the robot is achieved by actuators which provide torques acting: 011 tlie rotation and/or tlie orieiitatioii of the axis of some of the wheels. We now introduce the definition of the generalized c e ordinates and some additional notations which will allow us to describe tlie configuration and tlie dynamics of the robot. I130 CH2969-4/91/0000/1130$01.00 0 1991 IEEE 2.1 Robot position Colisider an inertial reference frame { O , I I , I 2 } in the plai i r of iiiotioii. Define a. reference point Q on tlie h ~ l l e y , and a basis ( 2 1 , 2 2 ) a,ttached to the trolley (sec, Fig.1). The position of the trolley in the plane is completely specified by the following 3 variables : 0 2 ~ y : the coordinates of the reference point Q in the inertial frame, 0 tr : the orientation of the basis {zl , 22) with respect to the inertial basis. We define the vector as : E = (.c y try ( 5) 2.2 Characterization of a wheel W e iiow characterize the position of a particular wheel (see Fig. 2). Consider the mobile frame {Q, 2 1 , 2 2 ) a.t(,aclied to the trolley. T h e center B of the wheel is cuiiiic~ctecl to the trolley by a rigid rod -4B (of constaiit Ic i igh d ) , which can rotale a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure32-1.png",
        "caption": "Fig. 32. Contact and bending stresses in the middle point of the path of contact on pinion tooth surface for modified involute helical gear drive wherein the generation is performed by plunging of the grinding worm.",
        "texts": [
            " The finite element analysis has been performed using the design parameters shown in Table 1. A finite element model of three pairs of contacting teeth has been applied for each chosen point of the path of contact. Elements C3D8I [3] of first order (enhanced by incompatible modes to improve their bending behavior) have been used to form the finite element mesh. The total number of elements is 45,600 with 55,818 nodes. The material is steel with the properties of Young s modulus E \u00bc 2:068 105 MPa and Poisson s ratio 0.29. A torque of 500 Nm has been applied to the pinion. Fig. 32 shows the contact and bending stresses obtained at the mean contact point for the pinion. The variation of contact and bending stresses along the path of contact has been also studied. Figs. 33 and 34 illustrate the variation of contact and bending stresses for the pinion and the gear, respectively. The stress analysis has been performed as well for the example of a conventional helical involute drive with an error of the shaft angle of Dc \u00bc 30 (Fig. 35). We remind that the tooth surfaces of an aligned conventional helical gear drive are in line contact, but they are in point contact with error Dc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000658_rpj-07-2019-0182-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000658_rpj-07-2019-0182-Figure5-1.png",
        "caption": "Figure 5 Schematic of EB gun used by Arcam (a) (Additive Manufacturing, 2019), plasma EB gun used in xBeam equipment (b) (Kovalchuk et al., 2018) and image of the internal gun used by Sciaky (c) (Worldwide Leaders in Industrial Metal 3D Printing Technology and EB Welding Solutions, 2019)",
        "texts": [
            " Apart from this, as the loose powder is spread on the table, the x-y motion of the table is avoided. So, the EB has to reach the whole table, which is done by deflection coils. However, when throw location of the EB changes, the circularity of the EB diameter deviates. Stigmator coils are used to maintain the circularity of the EB. All these above points have been taken care of in the EB gun for the process EBM by Arcam (Additive Manufacturing, 2019). Their EB gun is thermionic emission-based (Additive Manufacturing, 2019). The schematic of the EB gun has been shown in Figure 5. For the wire deposition-based process EBAM by Sciaky, EB gun is also the thermionic-based (Worldwide Leaders in Industrial Metal 3D Printing Technology and EB Welding Solutions, 2019). In the case of the wire deposition process, the wire comes laterally with respect to the central energy source, as shown in Figure 5(c). In a non-linear trajectory, feeding of the wire keeps on changing from front feeding to side feeding to back feeding. This variation in the feeding mechanism can result in geometrical errors and variation in mechanical properties (Kapil et al., 2019). To avoid this, the process should be omnidirectional. To attend omnidirectionally, the EB gun has to configure such that wire and EB interaction remains consistent during the process. Sciaky uses a rotary table to achieve this omnidirectionally, as shown in Figure 2(b). Recently, xBeam has developed a plasma-based gun which is a coaxial wire with a hollow conical EB (Kovalchuk et al., 2018). This gun has been given central guide-ways of the copper for the wire to come coaxially. xBeam has come up with a very compact and economical solution for the omnidirectional deposition (Kovalchuk and Ivasishin, 2019). A schematic of the EB gun used by xBeam has been shown in Figure 5(b). In Table IV, EB guns used by all the commercial systems have been given. The vacuum is paramount for EB technology, as, in atmospheric pressure, electrons collide with air molecules and release the energy. Development of vacuum technology has a direct impact on EB technology. In the case of a thermionicbased EB gun, severe vacuum is required to avoid oxidation of the cathode material, defocusing of the EB due to the collision between molecules and electron and arc production between electrodes (Schultz, 1993)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.22-1.png",
        "caption": "Fig. 8.22 Enveloping model of a tire on a cleat. Reproduced from Ref. [11] with the permission of Guranpuri-Shuppan",
        "texts": [
            "170) is expressed by w\u00f0h\u00de \u00bc C1e k1h \u00feC0 1e k1h \u00feC2e k2h \u00feC0 2e k2h \u00feC3e k3h \u00feC0 3e k3h: \u00f08:176\u00de When D \u00bc q22 \u00fe q31\\0 is satisfied, solutions to the cubic equation in terms of k2 are given by k21 \u00bc 2 ffiffiffiffiffiffiffiffi q1 p cos /=3\u00f0 \u00de A1=3 k22 \u00bc 2 ffiffiffiffiffiffiffiffi q1 p cos /=3\u00fe 2p=3\u00f0 \u00de A1=3 k23 \u00bc 2 ffiffiffiffiffiffiffiffi q1 p cos /=3\u00fe 4p=3\u00f0 \u00de A1=3 cos/ \u00bc q2=\u00f0q1 ffiffiffiffiffiffiffiffi q1 p \u00de; 0\\/\\p: \u00f08:177\u00de When a cleat is pressed at the center of the contact patch of a tire, the deformation of the tire has left\u2013right symmetry at h = 0 as shown in Fig. 8.22. Equation (8.176) can thus be rewritten as w\u00f0h\u00de \u00bc C1 e k1h \u00fe e k1 2p h\u00f0 \u00de \u00feC2 e k2h \u00fe e k2 2p h\u00f0 \u00de \u00feC3 e k3h \u00fe e k3 2p h\u00f0 \u00de ; \u00f08:178\u00de where the relation 0 < k1 < k2 < k3 is satisfied and Ci denotes the parameters determined by the boundary conditions. When the displacement at the center of a cleat is d, the boundary condition is expressed as 504 8 Tire Vibration w\u00f00\u00de \u00bc d: \u00f08:179\u00de The left\u2013right symmetry at point a\u2032 in Fig. 8.22 requires w0\u00f00\u00de \u00bc 0: \u00f08:180\u00de The condition of the inextensibility of the tread ring in the circumferential direction is expressed as Zp 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a\u00few\u00f0 \u00de2 \u00few02 q dh \u00bc pa: \u00f08:181\u00de Using Eqs. (8.179) and (8.180), the relations of Ci are obtained as C1 \u00bc k2 d\u00feC3 1\u00fe e 2pk3 1 e 2pk2 C3k3 1 e 2pk3 1\u00fe e 2pk2 =DA C2 \u00bc C3k3 1\u00fe e 2pk1 1 e 2pk3 k1 d\u00feC3 1\u00fe e 2pk3 1 e 2pk1 =DA DA \u00bc k2 1\u00fe e 2pk1 1 e 2pk2 k1 1 e 2pk1 1\u00fe e 2pk2 ; \u00f08:182\u00de where C3 is the unknown parameter determined by Eq",
            "183) can be rewritten as Q \u00bc XN n\u00bc0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a\u00few nDh\u00f0 \u00def g2Dh2 \u00fe w nDh\u00feDh\u00f0 \u00de w nDh\u00f0 \u00def g2 q pa; \u00f08:184\u00de where Dh (= p/N) is a small angle in the circumferential direction. When point b on the tread ring moves to point b\u2032, the length ab is equal to the length a\u2032b\u2032 owing to the inextensibility of the tread ring in Fig. 8.22. When points b and b\u2032 are, respectively, located at angles h1 and h2 measured from point a, we have ah1 \u00bc Zh2 0 ds \u00bc Zh2 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a\u00few\u00f0h\u00def g2 \u00few0\u00f0h\u00de2 q dh: \u00f08:185\u00de The force in the radial direction fr and the force in the circumferential direction ft at point b\u2032 on the tread ring are expressed by 8.4 Tire Models Rolling Over Cleats (Ride Harshness) 505 fr \u00bc w\u00f0h1\u00dek\u0302r ft \u00bc a\u00few\u00f0h1\u00def g h2 h1\u00f0 \u00dekt; \u00f08:186\u00de where k\u0302r is the revised radial fundamental spring rate of the sidewall [11]",
            "189) are explicitly ah1 \u00bc Pm 1 n\u00bc0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a\u00few\u00f0nDh\u00def g2Dh2 \u00fe w\u00f0nDh\u00feDh\u00de w\u00f0nDh\u00def g2 q h2 \u00bc mDh Fz \u00bc 2 PN 1 n\u00bc0 fz\u00f0nDh\u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a\u00few\u00f0nDh\u00def g2Dh2 \u00fe w\u00f0nDh\u00feDh\u00de w\u00f0nDh\u00def g2 q : \u00f08:190\u00de Using the first equation of Eq. (8.190), C3 in Eq. (8.182) is determined iteratively. The deformation of the enveloping tire is obtained using Eq. (8.178). The depression due to the cleat (envelope height) em in Fig. 8.22 means that a tire can completely envelope the cleat up to the height em, when a tire is deformed by (d \u2212 em) and rolls on a flat surface. Hence, the relation between the envelope height em and the load Fz is the countermeasure of the envelope property of a tire. (2-2) Analysis of the envelope properties of tires The deformation of a tire (175/70R13) loaded on a cleat is calculated using Eq. (8.190). The measured circumferential tension r0hA is given by 33.3p0 kN as discussed in Sect. 8.2.2, and the radial and circumferential fundamental spring constants (kr and kt) are calculated using Eq",
            "23b shows the load\u2013deflection curve for inflation pressures of 200 and 250 kPa. Figure 8.24 shows the relation between the envelope height em and displacement of a tire on a cleat for inflation pressures of 200 and 250 kPa. The envelope height em is almost one-third of the displacement of a tire on a cleat and is insensitive to the inflation pressure. Sakai [11] reported that the calculation is in good agreement with measurements. Figure 8.25 shows the displacement at the top of the tire du in Fig. 8.22 increases with increasing inflation pressure, while the displacement at the vertical position of a tire df does not change much with increasing inflation pressure. 8.4 Tire Models Rolling Over Cleats (Ride Harshness) 507 (1) Elastic ring model Zegelaar [21] investigated the enveloping response of a tire with respect to the trapezoid cleat using the elastic ring model with tread springs of Fig. 8.9. Figure 8.26a shows the shape of the trapezoid cleat used as road unevenness. To solve the contact problem between a cleat and a tire, the boundary conditions of the contact problem are expressed as qx;i \u00bc kpx xr;i xi if zr;i zi [ 0 qz;i \u00bc kpz zr;i zi if zr;i zi [ 0 qx;i \u00bc 0 if zr;i zi 0 qz;i \u00bc 0 if zr;i zi 0; \u00f08:191\u00de where the x-axis is the horizontal axis and the z-axis is the vertical axis normal to a flat contact surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.36-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.36-1.png",
        "caption": "Fig. 6.36: Contact Kinematics for Link and Sprocket",
        "texts": [
            " Keeping in mind that a link is modeled as a rigid body, we have no elasticity between the two contact points of a bushing link. To the next link with contact there are two spring elements of the two joints. In reality however the elasticity of the chain plate acts between each contact. To consider these effects, we suppose that each link has one contact to the sprocket. Because of the fact, that we do not deal with chain rollers, we define a contour circle with the diameter of a chain roller seated in the reference point HL of a link (Figure 6.36). Contact between a Link and a Guide Modeling the contact between a link and a guide the link plate is the contact partner (Figure 6.37). Some varieties of the contact configuration may appear, for example contact in the front or rear side of the link, or along the link plate, which must be considered separately, see [69]. Corresponding to the contact model above, a contour circle with the diameter of the plate width is used. The high rotation speed of combustion engines induces high relative velocities at the contact points between the links and the guides"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003544_jra.1987.1087145-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003544_jra.1987.1087145-Figure6-1.png",
        "caption": "Fig. 6. TH8 robot.",
        "texts": [
            " By \u201cgeneral robot\u201d we mean that all the geometric and inertial parameters are supposed general except q l , dl, c q , and qn which are considered equal to zero (recall that this definition of frame 0 and frame n can be done for any robot). Note that if we had used the same symbolic procedure with the classical Denavit and Hartenberg notation, the number of WPli.XXi+DV23i.PISli+U21i.XZi- U3li.XYi+(DV33i-DV22i).YZi WP2i.YYi+DV13i.PIS2i+ U32i.XYi- Ul2i.YZi+(DVlli-DV33i).XZi WP3i.ZZi+DV12i.PIS3i+ U13i.YZi- U23i.XZi+(DV22i-DVlli).XYi KHALIL AND KLEINFINGER: DYNAMIC MODELS OF TREE STRUCTURE ROBOTS 523 TABLE I11 Robot General Robot Stanford TH8 (Fig. 6) SCEMI (Fig. 7) Method Operation n d.0.f n = 6 General Simplified\" General Simplified\" General Simplified\" Luh [8] Kane [ I l l b Renaud [ 121 Horak [23] Vukobratovic [ 131 The without given regrouping methodd with *** regrouping multiplication addition multiplication addition multiplication addition multiplication addition multiplication addition multiplication addition, multiplication addition 137n - 22 lOln - 11 not given not given not given not given lOln - 129 90n - 118 lOln - 129 90n - 118 800 800 8 0 595 ' 595 595 646 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001033_j.jmapro.2021.01.012-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001033_j.jmapro.2021.01.012-Figure9-1.png",
        "caption": "Fig. 9. Redesign of Aeronautical Hardware for WAAM.",
        "texts": [
            " The manufacture of an aeronautical fitting was performed, in order to analyze the feasibility of WAAM as a manufacturing technology in this case study. In Fig. 8, the steps for its manufacture from the CAD part to the final part are defined. The fitting was firstly redesigned, to address the key dimensional features. The parts were then manufactured with different materials using previously tested parameters for WAAM additive technology. Finally, the additive manufacturing part was milled to the key dimensions of the final fitting geometry. The redesign of the part is shown below, in Fig. 9, with the original design on the left. The key feature dimension is the area (blue colored on the right CAD part) where the holes are placed and the substrate has been integrated as part of the final fitting. Extra-material necessary for the finishing of the WAAM manufactured part is also represented in the CAD part to the far right. The total cubic volume of the deposition to form the part was 440 cm3. Once the CAD design of the raw part is ready for WAAM, the machine or CAM programming is performed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.2-1.png",
        "caption": "Fig. 7.2 Shear spring rate of a tire block pattern (where the lower surface is constrained in the thickness direction)",
        "texts": [
            " The fundamental properties of the block pattern are the contact pressure distribution in the contact area, the change in contact area due to the lateral and longitudinal forces and the block rigidity defined by the ratio of the reaction to the displacement of a block surface. The fundamental properties are evaluated by experiment or using an analytical tool or numerical tool, such as the finite element method, in the process of tread pattern design. The shear deformation of a tread block with height h and length a due to a lateral shear force is shown in Fig. 7.2. The total shear displacement d is expressed by the addition of the displacement due to pure shear deformation d1 and the displacement due to bending deformation d2. When the upper surface is fixed to the rigid surface 376 7 Mechanics of the Tread Pattern and the lower surface sticks to a road, the bending displacement d2 can be expressed by the addition of bending displacements of two cantilever beams with length h/2 as shown in Fig. 7.2. The total shear displacement d is expressed by [2] d \u00bc d1 \u00fe d2 \u00bc f h AG \u00fe 2 f \u00f0h=2\u00de3 3EI ; \u00f07:1\u00de where E is Young\u2019s modulus of rubber, G is the shear modulus of rubber, and f is the shear force applied to the lower surface. I and A are, respectively, the moments of inertia of the cross section of the block and contact area: I \u00bc a3b=12 A \u00bc ab ; \u00f07:2\u00de where b is the block width in the direction perpendicular to the page. Equations (7.1) and (7.2) and the relation G = E/3 for rubber yield the block rigidity (i.e., shear spring rate of the block) K1: K \u00bc f d \u00bc abE 3t 1\u00fe 1 3 h a 2h i : \u00f07:3\u00de Meanwhile, when the lower surface does not stick to the road, the deformation of the block is shown in Fig. 7.3 and different from the deformation in Fig. 7.2. The block rigidity is expressed by [3]2 Total shear displacement Shear Bending 1Note 7.1. 2See Footnote 1. 7.1 Shear Spring Rate of the Tire Block Pattern 377 K \u00bc f d \u00bc abE 3t 1\u00fe 4 3 h a 2h i : \u00f07:4\u00de The value of 1/3 in the denominator of Eq. (7.3) and the value of 4/3 in the denominator of Eq. (7.4) are related with the ratio of bending displacement to shear displacement. These values depend on the boundary condition of the lower surface. When the ratio of bending displacement to shear displacement is denoted a, Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001175_j.matchar.2021.110969-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001175_j.matchar.2021.110969-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic representation of tensile sample orientations on the build plate. (b) 3D design of cantilever. Specimen geometry of (c) tensile samples and (d) cantilever samples with dimensions in mm. Also, a typical printed tensile sample and cantilever sample are shown in (e) and (f), respectively.",
        "texts": [
            " Recrystallized grains are enriched by coherent twin-boundaries without any preferred alignment, when the as-built grains show low angle grain boundaries aligned with the building direction. Static recrystallization leads to isotropic yield strength and elongation behavior of parts after 8.5 h of high-temperature heat-treatment. However, the small difference in ultimate tensile strength between heattreated vertical and horizontal samples is attributed to the remaining asbuilt columnar grains. In the present study, an EOS M290 was utilized to produce tensile samples in vertical and horizontal directions with 3 repetitions (Fig. 1). The Hastelloy X powder supplied by EOS was used with a D50 < 30 \u03bcm [7] and the nominal chemical composition shown in Table 1. All samples were printed with laser power of 195 W, hatch distance of 0.09 mm, layer thickness of 0.04 mm, laser scanning speeds of 850 mm/s and 1300 mm/s, and a 67\u25e6rotation in laser scanning direction between successive layers [16]. During the printing process, the build plate temperature was kept at 80 \u25e6C. In addition, for deflection measurements, cantilevers were also printed on LPBF substrates with the geometry and dimensions shown in Fig. 1(d). High-temperature heat-treatments were performed on the tensile and cantilever samples. The LPBF Hastelloy X samples were placed in an alumina crucible and then heated up to 1177 \u25e6C (the solutionizing temperature for Hastelloy X [18]) in a horizontal quartz tube furnace under an ultra-high purity argon atmosphere. A ramp-up of 5 K/min and different holding times of 3, 6, and 8.5 h were used followed by water quenching. A Keyence VK-X250 confocal laser microscope was utilized for microstructure observation after etching the polished cross-sections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.17-1.png",
        "caption": "Fig. 6.17: Mechanical Model of the R5 Timing Gear Train",
        "texts": [
            " The helical gears with an helix angle of 15\u00b0 are pivoted on case-fixed pins, with the exception of wheel 31. Wheel 31 is shrinked on the water pump shaft, and this shaft is pivoted on a roller bearing in the water pump housing. Therefore all wheels, with the exception of wheel 31, are taper bore mounted, which has to be examined for possible vibration enlargement of the overall system. We place the inertial coordinate system in the origin of the crankshaft wheel, wheel 1, with the z-axis in direction of the crankshaft axis (see the Figures 6.16 and 6.17). Figure 6.17 depicts only the main features of the mechanical model, which comprises 56 bodies with altogether 97 degrees of freedom being interconnected by 137 force law elements. With respect to the model details we refer to the methods presented in chapter (6.1) on page 329, which we also shall apply in the following without presenting the formal details. We shall give only a description. The gear wheels are modeled with three degrees of freedom, a rotational one for the wheel rotation around the z-axis and two translational ones for translational motion in the bearings",
            " Nevertheless it should be noted that the calculation process discussed above still includes some neglections and approximations, but the results are realistic. Table 6.2 illustrates the bearing geometries. It should be noted that wheel 5 does not have an own bearing, it is fixed to the camshaft. The camshaft itself is carried on the cylinder head structure by six bearings. The motion of the crankshaft wheel (wheel 1) is prescribed kinematically. Wheel 1 itself is part of the crankshaft and has no own bearing. The camshaft is modeled by a sequence of single masses connected by rotatory springs, as indicated in Figure 6.17. Each of the mass elements posses one rotational degree of freedom. The fuel is injected into the motor cylinders by a especially developed fuel injection pump system generating very large pressures. Each cylinder has its own pump system driven by the camshaft, which transmits its motion by the injection cams and the roller rocker arms to the piston of the injection pumps. The piston moves downwards and compresses the fuel, which flows via a system of channels, the annular gap around the needle of the nozzle and the nozzle itself to the cylinder (see Figure 6",
            " The injection takes place within a few degrees of the crankshaft angle. The maximum of the injection pressure increases up to a speed of 4250 rpm, which represents the value of the limiter speed. The ignition point sequence is (1-2-4-5-3). Figure 6.20 depicts also the measured injection pressure versus the crankshaft angle. Every cylinder has an intake and an exhaust valve, which are driven by valve trains. The corresponding mechanical model includes the cam, the solid valve lifter, the valve head and the valve shaft according to Figure 6.17. Going back to the first Figure 6.16 we noticed one main drive train with the wheels (1, 2, 3a3b, 30, 3, 4, 5) and two side branches, one with the wheel (10) only and one with the wheels (20, 21, 22, 23). Wheel (10) drives the oil pump, wheel (22) the generator and wheel (23) the power steering pump and the air 6.2 Timing Gear of a 5-Cylinder Diesel Engine 353 conditioning compressor. We shall give some indications on modeling and on simulations with respect to loads and noise. Figure 6.21 illustrates the scheme of these side branches and the corresponding mechanical model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.69-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.69-1.png",
        "caption": "Fig. 5.69: FEM Model of the Pulley with Shaft [249]",
        "texts": [
            " The vectors rSCi and FCi are radial positions and forces at the contact points of the pins within the arc of wrap, respectively. The rest is clear from Figure 5.68. 5.5 CVT - Rocker Pin Chains - Plane Model 285 Proceeding with the elastic pulleys via Ritz-approach modelling we have to establish suitable nets of the meshes and to evaluate the eigenforms, which we shall use as shape functions. For each pulley set we consider two elastic bodies, the fixed sheave together with the pulley shaft and the movable sheave alone, which has to be coupled with the shaft within the framework of elastic multibody dynamics. Figure 5.69 gives an impression of the undeformed and deformed configuration of the pulley-shaft-system. The Ritz-shape-functions for both bodies are the eigenvectors of the FEMbased modal analysis. From this we have no continuous functions describing the bodies\u2019 deformations, but only nodal informations. The masses of the bodies are concentrated in the nodes and, hence, integrals over the body\u2019s volume have to be transformed to summations over the nodes. The nodal structure makes also a certain interpolation scheme for the contact points mandatory, because we cannot expect the contact points to be positioned at the nodes",
            "115) The point Di belongs to the link i under consideration and the point Bi+1 to it\u2019s successor i + 1. Building all individual equations for each link and combining them in an appropriate way we get finally for the rigid body Bi: Miq\u0308 = hi(q, q\u0307, t) (5.116) These equations of motion for each body are decoupled kinematically as long as no stiction forces occur. Therefore, the mass matrix of the entire system has a block-diagonal structure enabling a symbolic inversion. For elastic bodies like the pulley-shaft system of Figure 5.69 we go back to the equations of motion formulated in chapter 3.3.4 on page 124 mainly represented by the relations (3.120), (3.121) and (3.127) on the pages starting with page 125. The shape functions u\u0304i are determined from a modal FEManalysis. Performing the evaluations given by the relations (3.127) on page 127 comes out with the same formal set of equations as given with (5.116), but with an extended meaning (see [250]). According to equation (3.120) the elastic deformations enter the equations of motion(3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.3-1.png",
        "caption": "Fig. 12.3 Contributions of shear stress in the adhesion region and the sliding force in the sliding region to the total braking force (reproduced from Ref. [2] with the permission of JSAE)",
        "texts": [
            " We here define the critical clip ratio scritical as that when the whole contact area becomes the sliding region. Substituting lh = 0 into Eq. (12.8), scritical is obtained as scritical \u00bc 3lsFz=CFs: \u00f012:17\u00de speak decreases with increasing X = ls/ld. In the particular case that ls/ld = 1, speak = scritical is satisfied. When the whole contact area becomes the sliding region (lh = 0), the term of the adhesion region in Eq. (12.13) is zero. The braking force Fx is then given by Fx \u00bc ldFz: \u00f012:18\u00de The right figure of Fig. 12.3 shows the contribution of forces in the adhesion and sliding regions to the total braking force calculated using Eq. (12.16). The vertical axis of the figure is normalized by the load. There are both adhesion and sliding regions in the contact patch in the case that 0 s < scritical while there is only the sliding region in the contact patch in the case that scritical s 1. The force in the adhesion region is dominant at a small slip ratio while the force in the sliding region is dominant at a large slip ratio. Note that Fig. 12.3 is similar to Fig. 11.7. 2Note 12.2. 3See Footnote 2. 12.1 Traction Performances on Dry and Wet Surfaces 811 (3) Comparison between experiment and calculation Yamazaki et al. [3] compared the calculation made using Eq. (12.15) with experimental results. The tire size was 185/70R13, the inflation pressure was 190 kPa, and the drum tester was covered with a safety walk (#600). Parameters used in the calculations were Cx = 0.133 MPa/mm, b = 101 mm, l = 129 mm, l0d = 1.3, 812 12 Traction Performance of Tires ld = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure15.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure15.6-1.png",
        "caption": "Fig. 15.6 Cross-sectional tire shape",
        "texts": [
            "5 show wave patterns of the first and third modes. 15.2 Simple Explanation of a Standing Wave 1135 (1) Fundamental equations of membrane theory Sakai [2] developed one-dimensional model of a standing wave. When the inflation pressure is too high in bias tires, the flexural stiffness of the carcass can be neglected and membrane theory can be applied to the standing wave. Furthermore, the radial spring of the carcass is neglected for simplicity. The force equilibrium between the carcass tension and the inflation pressure p in Fig. 15.6 is expressed by p \u00bc T/ r \u00fe Th a ; \u00f015:4\u00de where T/ and Th are the carcass tensions in the width and circumferential directions in Fig. 15.7, and r and a are, respectively, the radius of the tire cross section and the principal radius of curvature corresponding to the tire radius. When the cord angle is a, Th and T/ can be expressed by the cord tension per unit length in the width direction Tc: Th \u00bc Tc cos2 a: \u00f015:5\u00de 1136 15 Standing Waves in Tires The relation between Th and T/ is T/ \u00bc Th tan2 a: \u00f015:6\u00de From Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000419_j.ymssp.2019.106583-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000419_j.ymssp.2019.106583-Figure4-1.png",
        "caption": "Fig. 4. Loading conditions with (a) N = 1 (b) N = 2 (c) N = 3.",
        "texts": [
            " As the ceramic rings and balls of the bearing are of high stiffness, the inner ring has very small deformations at the contact areas with the loaded balls, and the deformations at each contact area between the inner ring and loaded ball can be regarded as independent. The oil film on the surfaces of the balls and rings are extremely thin in starved lubrication conditions, and the thickness of the oil film are neglected when considering the loading conditions of the balls. Then according to the geometric conformity principles, N can only be 1, 2 and 3, and the loading conditions with N = 1, 2 and 3 are shown respectively in Fig. 4. In this paper, the type of the full ceramic ball bearing is 7009C, and the geometric parameters are shown in Table 1. The rotation speed is set as 9000 r/min, and the axial preload is 500 N. The oil film has little impact on the motion of balls in starved lubrication condition, and the hydrodynamic forces and viscous forces from the lubrication oil are neglected. The cases of uneven loading conditions are calculated to make a comparison with the case of even loaded. Assuming that the uneven loading condition only affects the number of loaded balls, and has no impact on the orbital motion of the balls"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001114_j.jallcom.2021.158868-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001114_j.jallcom.2021.158868-Figure1-1.png",
        "caption": "Fig. 1. Dimensions of printed specimens, along with the reference coordinate system.",
        "texts": [
            " Process parameters used for printing such as laser power, exposure time and point distance, lied within the machine\u2019s capabilities, resulting in an equivalent volumetric energy density of 165 J/mm3. Parts were built on a 250 mm \u00d7 250 mm polycrystalline steel substrate plate, which are commercially available and the most commonly used to print on the AM400 LPBF system. Two specimen geometries were fabricated for this study: cubes with a dimension of 10 mm \u00d7 10 mm \u00d7 10 mm, and blocks with a dimension of 50 mm \u00d7 10 mm \u00d7 50 mm. Their geometries are illustrated in Fig. 1, along with the corresponding reference coordinate system, where the build direction (BD) is aligned with the z-axis. Cubes were used for density and microstructural analysis, while blocks were prepared for tensile testing, which will be described later in this section. No heat treatment was performed after fabrication and all the analysis on this work was done on the parts in the as-built state. The cubes were sectioned in half parallel to the YZ plane, mounted, and ground up to 800 grit SiC abrasive paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000210_j.jmapro.2019.12.048-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000210_j.jmapro.2019.12.048-Figure15-1.png",
        "caption": "Fig. 15. Schematic illustration of notch at the (a) top and (b) side surface on SLM specimen.",
        "texts": [
            " In all the cases SLM specimens have lower impact toughness to that of the wrought 15-5 PH stainless steel which may be due to the presence of micron size pores and defects present in SLM specimens [19]. 3.5.2.3. Anisotropy and heat treatment. Effect of notch orientations (Fig. 2b) on impact toughness with and without solution annealing is presented in Fig. 14. Impact toughness of as-built side notch specimens is found to be higher than that of as-built top notch specimens. This indicates that asbuilt SLM specimens show anisotropic behaviour in impact toughness. As depicted in Fig. 15 impact loading is perpendicular to the build layers for specimens having notch at the top surface, whereas it is parallel to the build layers for specimens having notch at the side surface. In case of side notch, when impact load is applied all the build layers collectively resist against force applied, as a result it takes more time for crack to initiate and propagate, and thus in this process absorbs more energy before it finally breaks. However, such phenomenon does not happen when the load is perpendicular to the build layers in case of notch at the top surface and it takes less time for crack to initiate, propagate, and as a result absorbs less energy before it finally breaks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.26-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.26-1.png",
        "caption": "Fig. 7.26: Structure of Snap Fastener",
        "texts": [
            " The force\u2013 distance graphs are shown in Figure 7.25. The left diagram contains the measurement, the right the calculations. The correspondence between both curves is very good. The maximum of the mating force arises, when the ring is entering the hole. Inside the cylinder the load is constant. Snap Fastener Snap fasteners are widespread fixtures in automated assembly. They consist of three different characteristic parts: the snap hook, the elastic support for the hook and the counterpart or chamfer (see Figure 7.26). The support consists of a beam like in the figure, a plate or an even more complicated structure. We make the assumption that the snap hook and the chamfer are rigid and only the compliant support is flexible. We have to introduce a local L\u2013frame, fixed to the snap hook, to describe the elasticity in the system. The deformations should be linear elastic, so that the vector ArAL = (wx, wy, wz)T contains the displacement and the vector A\u03d5AL = (\u03d5x, \u03d5y, \u03d5z)T represents the orientation between the A\u2013 and L\u2013 system, expressed in the A\u2013frame (indicated by the left lower index). With this description the compliance in the support can be reduced to a stiffness matrix K between the A\u2013 and the L\u2013frame. This is symbolized by the spring in Figure 7.26. Generally, the stiffness matrix K has the dimension K \u2208 IR6,6. The relationship between the linear deformations and the linear elastic reaction forces has then the following form:( Af Am ) = K ( ArAL A\u03d5AL ) \u2208 IR6, (7.98) where Af is the vector of the forces and Am is the vector of the torques acting at the origin of the L frame when the deformations ArAL and A\u03d5AL are imposed. The description of the geometry is easy for the snap fasteners under consideration. The counterpart is a simple cuboid and the hook a polygonal part with six corners"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.42-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.42-1.png",
        "caption": "Fig. 5.42: Rotary reluctance motor",
        "texts": [
            " If the coils are excited with a phase-shifted current, a displacement of the rotor can be obtained due to the energy change in the magnetic field between the rotor and stator. These mo tors can be used for positioning or manipulation of various technical devices. Rotary reluctance motors are also of interest to many applications, e.g . for medical purposes such as minimal invasive surgery and diagnosis; they can also be used in entertainment electronics such as miniaturized drives for portable devices. Figure 5.42 shows a scheme of a three phase rotary reluc tance motor. It has a permanent magnet rotor with externally extended poles and a stator with internally extended poles; around the latter the electrical coils are wound. A magnetic field is created with these coils. For the reali zation of a rotary reluctance motor it is important to have a different number of teeth on the stator from that on the rotor, because otherwise all the mag netic loops have the same phase. This would make it impossible to generate a rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure14-1.png",
        "caption": "Fig. 14. Shaper profiles and normals to shaper profiles.",
        "texts": [
            " The meshing of the worm and the shaper is schematically illustrated in Fig. 12. 3.3. Analytical consideration of simultaneous meshing of surfaces Rs, Rw, and R2 Designations Rs, Rw, and R2 indicate surfaces of the shaper, worm, and face gear, respectively. Simultaneous meshing of Rs, Rw, and R2 is illustrated in Fig. 13. Shaper surface Rs is considered as a given generating one. Surfaces Rw and R2 are generated as the envelopes to the family of a shaper surface Rs. Step 1: Shaper surface Rs is represented as an involute surface of a spur gear (Fig. 14) determined by the equations xs \u00bc rbs\u00bdcos\u00f0hs \u00fe gs\u00de \u00fe hs sin\u00f0hs \u00fe gs\u00de ; ys \u00bc rbs\u00bd sin\u00f0hs \u00fe gs\u00de hs cos\u00f0hs \u00fe gs\u00de ; zs \u00bc us: \u00f05\u00de Here us and hs are surface parameters; parameter gs determines half of the width of the space on the base cylinder; rbs is the radius of the base cylinder. Parameters hs and gs are shown in Fig. 14; parameter us is directed along the zs axis. The upper and lower signs in equation of ys\u00f0hs\u00de correspond to profiles I and II, respectively. Step 2: The worm surface Rw is determined in coordinate system Sw (Fig. 10) by the following equations [8]: rw\u00f0us; hs;ws\u00de \u00bcMws\u00f0ws\u00ders\u00f0us; hs\u00de; \u00f06\u00de orw ous orw ohs orw ows \u00bc fws\u00f0us; hs;ws\u00de \u00bc 0: \u00f07\u00de Here vector function rw\u00f0us; hs;ws\u00de is the family of shaper surfaces Rs represented in Sw; matrix Mws\u00f0ws\u00de describes coordinate transformation from Ss to Sw; Eq. (7) is the equation of meshing between Rs and Rw",
            " Such a point is located at the bottom of the thread of the worm as shown in Fig. 18(b). This is the maximum value for ws that allows us to generate a worm with regular points only. The installment of the shaper will affect the maximum rotation ws that can be performed during the process of generation. Due to the internal tangency between surfaces Rs and Rw (Fig. 12), we must consider the rotation applied to the shaper tooth to calculate the maximum number of turns of the thread. In the definition of the shaper (Fig. 14) the blank has been considered. Therefore, to calculate the maximum number of turns of the thread we have to remove from the value of ws the angle wN . For a symmetric gear drive such a value is equal to half of the angular step: wN \u00bc 360 Ns 1 2 \u00bc 6 \u00f031\u00de where Ns is the number of teeth of the shaper. The corresponding worm rotation angle is ww \u00bc \u00f0ws wN \u00de msw \u00bc \u00f018:3 6 \u00de 30 \u00bc 369 that corresponds to 369=360 \u00bc 1:025 turns of the thread of the worm. Considering the two limitations for both sides, we obtain 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003557_s0039-9140(02)00362-4-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003557_s0039-9140(02)00362-4-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of FIA setup. (A) Carrier solution (2 /10 1 M NaOH); (B) oxidant solution (SDCC or TCCA); P, peristaltic pump; S, sample solution; H, sealed housing; M, mirror; F, glass spiral flow cell; D, detector; I, computing integrator; C, computer; W, waste.",
        "texts": [
            "200 g of DCF (Fluka) in 0.10 M sodium hydroxide and diluting to 250 ml with the same alkaline solution. Stock solution of citrate (2 /10 1 M) was prepared by dissolving 14.705 g of sodium citrate (Merck) in water, and diluting to 250 ml with water. The minimum number of dilution steps possible was used for preparation of more dilute solutions. All other common laboratory chemicals were of the best grade available. A schematic diagram of the flow injection chemiluminescence analyzer is shown in Fig. 1. The 12-channel peristaltic pump (Desaga PLG) was equipped with silicon rubber tubes (1 mm i.d.). The sample was injected with a Rheodyne sample injector, model 7125. The carrier stream merged with oxidant solution stream (SDCC or TCCA) in a spiral flow cell in front of a photomultiplier tube (PMT). The flow cell was a glass spiral (2 mm i.d, 600 ml internal volume) positioned in front of a mirror in a sealed housing. The signals from the PMT (RCA 931 VA) were sent to a computing integrator (Philips PU 4815) and then to an IBM-compatible computer (model 486 DX4) using an RS232 port. The FIA configuration used is outlined in Fig. 1. In order to achieve good mechanical and thermal stability, the instrumental system was allowed to run for 10 min before the first measurement was made. A solution of 1 /10 3 M oxidizing agent of SDCC and/or TCCA and a solution of 2 /10 1 M NaOH (carrier stream) was each pumped at 3.8 ml min 1. The carrier stream merged with the oxidant solution stream in the spiral flow cell in front of the PMT. The light emitted is detected by PMT with no wavelength discrimination. The blank solution which only contained 5 /10 6 M DCF was injected into the carrier stream with the aid of an injection valve (600 ml loop) and a stable blank signal was recorded, then the sample or standard hydrazine solutions which contained not only 5 /10 6 M DCF but also an appropriate concentration of hydrazine was injected into the carrier stream and the CL signal was recorded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000301_s13369-020-04742-w-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000301_s13369-020-04742-w-Figure4-1.png",
        "caption": "Fig. 4 Membership function a fuzzy input, b fuzzy output, where P is positive, Z is zero, and N is negative",
        "texts": [
            " (36)upid = k\u0302pe + k\u0302i \u222b edt + k\u0302de\u0307 (37) x\u0308 = fn + gnu \u2212 k1e\u0307 \u2212 k2e x\u0308 + k1e\u0307 + k2e \u2212 fn \u2212 gnu = 0 \u2212fn \u2212 gnu + Ad = 0 (38)s\u0307 = e\u0308 + k1e\u0307 + k2e = \u2212fn \u2212 gnu + Ad (39)ss\u0307 = \u2212s [ gnupid + fn \u2212 Ad ] (40) \u0307\u0302 kp = s\ud835\udefdpsgn(g)e \u0307\u0302 ki = s\ud835\udefdisgn(g) \u222b edt \u0307\u0302 kd = s\ud835\udefddsgn(g)e\u0307 1 3 For the compensator, three fuzzy rules are set out as outlined in (41) [46, 47] where P is positive, Z is zero and N is negative. where triangular and singleton characteristics are used to define the input and the output membership functions as shown in Fig.\u00a04a, b, respectively. Through the centre-ofgravity method, the defuzzification is accomplished as follows: where wi(i = 1, 2, 3) is the firing strength and bounded as ( 0 \u2264 wi \u2264 1 ) and the total of wi is not greater than one and unique for the case of the triangle membership function. To decrease the loading of calculations, let r1 = r\u0302, r2 = 0, and r3 = \u2212r\u0302. Therefore, as mention by [46], only one of four circumstances will happen for any value of input s as follows: Case 1 Only rule 1 is triggered (s > sa,w1 = 1,w2 = w3 = 0) Case 2 Rule 1 and 2 are triggered simultaneously ( 0 < s \u2264 sa, 0 < w1,w2 \u2264 1,w3 = 0) Case 3 Rule 2 and 3 are triggered simultaneously ( sb < s \u2264 0,w1 = 0, 0 < w2,w3 \u2264 1) Case 4 Only rule 3 is triggered ( s \u2264 s b ,w1 = w2 = 0,w3 = 1) (41) Rule 1 \u2236 If s isP, the ufc is P Rule 2 \u2236 If s is Z, the ufc isZ Rule 3 \u2236 If s isN, the ufc isN (42)ufc = \u22113 i=i riwi\u22113 i=1 wi = r1w1 + r2w2 + r3w3 (43)ufc = r1 = r\u0302 (44)ufc = r1w1 = r\u0302w1 (45)ufc = r3w3 = \u2212r\u0302w3 Then, the (43\u201346) can be reproduced as: Furthermore, it can be seen from [46, 47] By substituting (36) into (21), it is revealed that The error equation governing the system can also be obtained after a straightforward manipulation of (22), (26) and (49) as follows: If an approximation error occurs, the idea controller can be reformulated as: where refers to an approximation error and is supposed to be limited by 0 \u2264 | | \u2264 E , where E is a positive constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure8-1.png",
        "caption": "Fig. 8 Coordinate systems S1, S2, and Sf",
        "texts": [
            " Equations 20 and 21 provide stable convergence of the iteration because solving the vector equation n1f =n2f has been avoided. Derivation of Eqs. 20 and 21 is based on the condition that the unit normals of the mating tooth surfaces are collinear at the contact point and described in the following steps: Step 1. The mating gear and pinion are assembled in the initial running position defined by dimensions E, G, P, and 0 together with their corresponding assembly adjustments E, G, P, and . This is represented as the coordinate transformations from systems S1 and S2 to Sf and illustrated in Fig. 8. The corresponding coordinate transformation matrices M f1 and M f2 can be easily obtained by observation from Fig. 8. As a result, the unit normals may be represented as n10f = n10f u1, 1, 1 = M f1n1 u1, 1, 1 n20f = n20f u2, 2, 2 = M f2n2 u2, 2, 2 24 Step 2. The mating pinion and gear are rotated with angular displacements 1 and 2 with respect to their axes of rotation so that the initial normals n10f and n20f are aligned parallel. Math- ematically, following vector equation should be satisfied JANUARY 2007, Vol. 129 / 35 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use H t d e b t w g v w a m E a w F c d 3 Downloaded Fr n1f = n2f 25 ere, n1f and n2f are the new normals obtained through the rotaion and are represented in the same coordinate system Sf",
            " For this purpose, we recall that a genralized vector n0 is rotated an angle about an axis represented y a unit vector e and the resulting vector n can be represented in he same coordinate system as n = e \u00b7 n0 e \u2212 cos n0 e e \u2212 sin n0 e 26 hich is known as the Euler-Rodrigues\u2019 formula 3,23 . Analoously, using this formula, we can represent the rotated normal ectors n1f and n2f as n1f = e1 \u00b7 n10f e1 \u2212 cos 1 n10f e1 e1 \u2212 sin 1 n10f e1 27 n2f = e2 \u00b7 n20f e2 \u2212 cos 2 n20f e2 e2 \u2212 sin 2 n20f e2 28 here e1 and e2 are the constant unit vectors collinear with the xes of the pinion and the gear, respectively, and can be deterined directly from Fig. 8. Substituting Eqs. 27 and 28 into q. 25 , we are able to explicitly solve the vector equation 25 nd obtain 1 = sin\u22121 cos 1 e2 \u00b7 e1 e1 \u00b7 n10f \u2212 e2 \u00b7 n20f e1 n10f e2 \u2212 1 29 2 = sin\u22121 cos 2 e1 \u00b7 e2 e2 \u00b7 n20f \u2212 e1 \u00b7 n10f e2 n20f e1 \u2212 2 30 here 1 = tan\u22121 n10f e1 e1 \u00b7 e2 n10f e1 \u00b7 e2 31 2 = tan\u22121 n20f e2 e2 \u00b7 e1 n20f e2 \u00b7 e1 32 or application of Eq. 22 or 23 , an input parameter must be hosen, say 1. The rest of the tooth surface parameters can be etermined. 6 / Vol. 129, JANUARY 2007 om: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure2.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure2.7-1.png",
        "caption": "Fig. 2.7: Principle of neural prosthetics. According to [CISC91]",
        "texts": [
            " The chip should have no physical connection to the outer world, neither for control nor for energy sup ply. It contains a capacitive pressure sensor and an interface for telemetric information and energy transfer. A schematic diagram is shown in Figure 2.6. A future application of MST is neurotechnology, where researchers inves tigate the implantation of microstructured neuronal connections between re generating peripheral nerves and external electronics for the restoration of certain neural functions, Fig. 2.7. A sieve-shaped microstructure serves as a neuronal interface. The holes in the silicon interface chip are surrounded by recording/stimulating electrodes which allow recording and stimulation of in dividual axons. Thereby researchers can gain important information about the complex organization of the peripheral nervous system. The depicted elec trode arrangement was succesfully implanted between the cut ends of peri pheral taste fibers of rats and nerve fibers functionally regenerated through the microholes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure11-1.png",
        "caption": "Fig. 11. Illustration of formation of helicoid surface by screw motion of a cross-profile of the helicoid.",
        "texts": [
            " (2) The helicoid tooth surfaces are in point contact and this is achieved by the modification of the cross- profile of the pinion tooth surface. This statement is illustrated for the example in Fig. 10 wherein an involute helicoid of the gear and pinion modified helicoid are shown. Profile crowning of the pinion is provided because the cross-profile is deviated from the involute profile. The gear and the pinion tooth surfaces are in point contact provided by mismatched crossed profiles. (3) The formation of each of the mating helicoids may be represented as the result of screw motion of the cross-profile. Fig. 11 shows the formation of a helicoid by a family of planar curves that perform a screw motion about the axis of the helicoid. (4) The screw parameters p1 and p2 of the profile-crowned helicoids have to be related as p1 p2 \u00bc x\u00f02\u00de x\u00f01\u00de ; \u00f022\u00de where x\u00f0i\u00de (i \u00bc 1; 2) is the angular velocity of the helicoid. (5) The common normal to the cross-profiles at point M of tangency of profiles passes through point I of tangency of the centrodes (Fig. 10). (6) It is easy to verify that during the process of meshing, point M of tangency of cross-profiles performs in the fixed coordinate system a translational motion along a straight line that passes through M and is parallel to the axes of aligned gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.66-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.66-1.png",
        "caption": "Fig. 5.66: Rigid Body Model of the Pulley [249]",
        "texts": [
            " As the elastic deformations are very small, nevertheless influencing heavily the contact processes, we shall consider a RITZ-approach following the theory discussed in chapter 3.3.4 on pages 124. The shape functions we evaluate from a FEM-calculation for the pulleys. It turnes out however, that the dynamic influence of the deformations themselves are very small. This allows us to replace the Ritz-approach by Maxwell\u2019s method of influence numbers representing practically the sheave elasticity by an areal spring, the areal stiffness distribution of which is calculated by a static FEM-analysis. We start with the rigid pulley set (Figure 5.66). The whole set is supported by two elastic bearings with the same stiffness and damping in the two bearing directions. The corresponding forces write Fbearing,x = c(xR \u2212 xR,0) + dx\u0307R, Fbearing,y = c(yR \u2212 yR,0) + dy\u0307R. (5.107) 5.5 CVT - Rocker Pin Chains - Plane Model 283 The pulley set and the shaft possess the same rotational speed, if we assume nearly no backlash in circumferential direction between the shaft and the movable sheave. But the backlash between movable sheave and pulley shaft must be considered, because it allows a translational motion and some tilt (Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure18-1.png",
        "caption": "Fig. 18. Illustration of worm singularities: (a) regular points A of shaper that generate worm singularities; (b) singularities B on worm thread surface.",
        "texts": [
            " The computational procedure for the determination and avoidance of worm singularities is as follows: Step 1: Using equation of meshing (7), we are able to determine the lines of contact of the shaper and the worm in the plane of shaper parameters \u00f0us; hs;ws\u00de as functions of the generalized parameter ws. Fig. 17 illustrates such lines for both sides of shaper space. Step 2: Using Eq. (24), we may determine the image of worm singular points in plane \u00f0us; hs;ws\u00de (Fig. 17). Step 3: Using Eqs. (7) and (24) and equations of the shaper tooth surface, we may determine the lines of shaper regular points that generate the worm singularities. Step 4: Using coordinate transformation from the shaper surface to the worm thread surface, we may determine: (i) regular points A on the shaper surface (Fig. 18(a)), and (ii) singularity points B on worm surface (Fig. 18(b)) that are generated by points A. Only one line of worm singularity points is represented in Fig. 18(b) due to limitations of rotation angle of the worm. Singularities of the worm may be avoided by limitation of turns of the worm thread as shown in Fig. 18(b). The worm dressing is based on generation of its surface Rw point by point by a plane or by a conical disk that has the same profile that the rack cutter that generated the shaper. The execution of motions of the disk or the plane with respect to the worm is accomplished by application of a CNC machine. The determination of instantaneous installments of the grinding disk with respect to the worm requires application of a computer program. The algorithm of the program is based on the following considerations: (1) The worm thread surface Rw is determined as the envelope to the family of shaper surfaces as follows: rw \u00bc rw\u00f0us; hs;ws\u00de; fws\u00f0us; hs;ws\u00de \u00bc 0: \u00f025\u00de Eq",
            " Here ws is the angle of rotation of the shaper; Nwx, Nwy , and Nwz are the components of the normal to the worm surface in the worm coordinate system Sw at point M\u00f0i\u00de. The minimum and the maximum values of hs correspond respectively to the bottom and top of the shaper, calculated with the following equations: hi \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ri rbs 2 1 s i \u00bc \u00f0max;min\u00de: \u00f030\u00de For the considered numerical example the first singularity point (Fig. 17) occurs when ws reaches the value ws \u00bc 18:3 . Such a point is located at the bottom of the thread of the worm as shown in Fig. 18(b). This is the maximum value for ws that allows us to generate a worm with regular points only. The installment of the shaper will affect the maximum rotation ws that can be performed during the process of generation. Due to the internal tangency between surfaces Rs and Rw (Fig. 12), we must consider the rotation applied to the shaper tooth to calculate the maximum number of turns of the thread. In the definition of the shaper (Fig. 14) the blank has been considered. Therefore, to calculate the maximum number of turns of the thread we have to remove from the value of ws the angle wN "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003486_robot.1996.509284-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003486_robot.1996.509284-Figure8-1.png",
        "caption": "Figure 8: The 2-type 1-1-type 3 mechanism",
        "texts": [
            " Therefore we have effectively computed a minimal order polynomial. 2.3.3 This mechanism is presented in figure 9. Here we as%type 21 and 1 type 1 Equations (6)-(5) and (7) are linear in z ,y . Their values are computed and substituted in equation ( 5 ) , leading to an equation in cos 4, sin 4. A.fter substitution of the sine and cosine by their values as function of T = tan(4/2) we get a 6-order polynomial in T , which enables to compute the solution of the direct kinematics. 2.3.2 This mechanism is presented in figure 8. In that c,ase 2-type 1 and 1 type 3 equations (5),(6) are still valid but the third equation is obtained by writing that for given x,y,+ the line going through Bs, whose axis is the prismatic joint axis, meet As: (x + acos(q5 + a ) - U I ) sin(4 + a + a3) - (y + asin($ + a ) - VI) cos(4 + a + ~ 3 ) = O(8) where a3 is the angle between B1 Bs and the prismatic joint axis. Equations (6)-(5) and (8) are still linear in 2, y. Using the same process as in the previous section we get a 6-order polynomial in T , which enables to compute the solution of the direct kinematics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000772_j.precisioneng.2021.01.007-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000772_j.precisioneng.2021.01.007-Figure2-1.png",
        "caption": "Fig. 2. The kinematic scheme of the five-axis parallel machining robot.",
        "texts": [
            " Section 3 presents the weighted regularization identification method and the error compensation method. Section 4 shows the experimental study of error compensation on the five-axis parallel machining robot. After compensation, an M1_160 test piece and an Sshaped test piece are machined and measured to verify the effectiveness of the proposed methods. The conclusion is presented in the last section. The five-axis parallel machining robot has been designed and developed based on the type synthesis and the kinematic optimization [33]. The robot and its kinematic scheme are shown in Fig. 1 and Fig. 2, respectively. The mechanism of this robot can be represented by 4UCU-RCU, where U represents the universal joint, C represents the active cylinder joint and R represents the revolute joint. The active cylinder joint is realized by a ball screw, a nut and a motor. The motor connects and actuates the nut. The ball screw matches the nut and passes through the motor. Thus the ball screw has active linear motion and passive self-rotation with respect to the motor. This design makes the robot\u2019s structure concise with less passive joints, but at the expense of increased difficulties of kinematic error modeling",
            " In these chains, the ball screw is connected to the spindle with a universal joint, and the motor is connected to the base with a universal joint. A1 is the intersection point of the revolute joint\u2019s axis and the ball screw\u2019s axis in the 1st chain. Ai (i = 2,3,4,5) is the center of the universal joint on the spindle in the i-th chain. Bi (i = 1, \u2026,5) is the center of the universal joint on the base in the i-th chain. The spindle of the five-axis parallel machining robot can realize three translational motion and two rotational motion. As shown in Fig. 2, the reference frame O-xyz is fixed on the base, which is the base reference frame. O is the center of the circle on which B1, B2 and B3 locate. The reference frame O\u2032-x\u2032y\u2032z\u2032 is fixed on the spindle, which is the moving reference frame. Under the reference frame O-xyz, the coordinate of O\u2032 represents the position of the spindle. The rotation matrix from O-xyz to O\u2032-x\u2032y\u2032z\u2032 represents the posture of the spindle. The posture is described by the tilt-and-torsion angles [34] and expressed as R=R1\u22c5R2/R1\u22c5R3 (1) where R1 = \u23a1 \u23a3 cos \u03d5 \u2212 sin \u03d5 0 sin \u03d5 cos \u03d5 0 0 0 1 \u23a4 \u23a6, R2 = \u23a1 \u23a3 cos \u03b8 0 sin \u03b8 0 1 0 \u2212 sin \u03b8 0 cos \u03b8 \u23a4 \u23a6, R3 = \u23a1 \u23a3 cos \u03c8 \u2212 sin \u03c8 0 sin \u03c8 cos \u03c8 0 0 0 1 \u23a4 \u23a6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.56-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.56-1.png",
        "caption": "Fig. 11.56 Simulated deformation of a tire during severe cornering. Reproduced from Ref. [50] with the permission of SAE",
        "texts": [
            " 780 11 Cornering Properties of Tires The vehicle/tire interaction needs to be investigated in designing a suitable tire for a vehicle, because the tires are the only points of contact between the vehicle and the road. However, FEA has not been conducted for the tire/vehicle behavior under extreme operating conditions because it is difficult to analyze the large deformation of rotating tires. Fukushima et al. [50] simulated the tire/vehicle behavior of the J-turn using LS-DYNA and compared the prediction with measurements. Figure 11.56 shows the finite element model of a vehicle and tires and the deformation of the right-front tire near the contact patch in a cornering event. Although the transient behavior cannot be observed in an experiment, a simulation can 11.8 Finite Element Model \u2026 781 provide a transient contact pressure distribution of a tire in cornering. We thus gain insights from the prediction that we cannot get experimentally. The side force and self-aligning torque of a tire are nonlinear with respect to the slip angle and slip ratio"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure3.51-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure3.51-1.png",
        "caption": "Fig. 3.51 Displacements of a plate in bending deformation",
        "texts": [
            " Using the Kirchhoff\u2013Love hypothesis and referring to Fig. 3.50, the in-plane displacements u and v at the position z in the z-direction from the middle plane are expressed as Notes 179 u \u00bc z@w=@x v \u00bc z@w=@y: The in-plane strains at the position z from the middle plane are expressed as ex \u00bc @u @x \u00bc z @ 2w @x2 ey \u00bc @v @y \u00bc z @ 2w @y2 cxy \u00bc @u @y \u00fe @v @x \u00bc 2z @2w @x@y : @2w=@x2; @2w=@y2 and @2w=@x@y are, respectively, the curvatures in the x- and y-directions and the twist. Note 3.4 Eq. (3.111) Referring to Fig. 3.51, the in-plane displacements of a plate in bending deformation are given by u \u00bc R y\u00f0 \u00de sin/ x ffi y/; v \u00bc R y\u00f0 \u00de 1 cos/\u00f0 \u00de ffi R/2 2 ; where R is the radius of curvature of the bending plate, / is an angle at point P, and y is the position in the thickness direction. When / is small, x = R/ is satisfied. Using the curvature j (=1/R), in-plane displacements are expressed by u \u00bc jxy; v \u00bc jx2=2: Note 3.5 Using the relations R = T/X, w = Xxy and X = w/(bL) = //L, we obtain R = TL//. For small /, the relation R = LdT/d/ is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.8-1.png",
        "caption": "Fig. 5.8: Model of the Output Train including the Car Mass [91]",
        "texts": [
            " The tire will be modeled by a linear force element with spring and damper (spring stiffness cR, damping coefficient dR). The tire torque writes correspondingly MR = (\u03d5R \u2212 xcar rR )cR + (\u03d5\u0307R \u2212 x\u0307car rR )dR . (5.12) Braking is governed by the maximal possible brake torque MBmax and a brake pedal coefficient kB, which represents a suitable measure for the brake pedal actuation and has to be measured. The brake torque then writes 5.1 Automatic Transmissions 223 MB = kB MBmax sign(x\u0307car) . (5.13) Combining these equations results in the equations of motion for the output train model according to Figure 5.8 [ JR 0 0 mcar ] \ufe38 \ufe37\ufe37 \ufe38 MAb ( \u03d5\u0308R x\u0308car ) \ufe38 \ufe37\ufe37 \ufe38 q\u0308Ab = ( \u2212MR \u2212MB \u03b7Ab MR rR \u2212 FRoll \u2212 FSt \u2212 FL ) \ufe38 \ufe37\ufe37 \ufe38 hAb + ( MAbS 0 ) \ufe38 \ufe37\ufe37 \ufe38 hAbS . (5.14) The efficiency \u03b7Ab takes into account all losses of the output train. Shafts are very fundamental elements of all machinery. They are something like a blood circulation system distributing and passing on torques within a mechanical system. According to the various design possibilities shafts possess also various influence on the dynamics of the overall system, especially with respect to the eigenbehaviour expressed by eigenfrequencies and eigenfunctions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000810_j.addma.2021.102263-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000810_j.addma.2021.102263-Figure1-1.png",
        "caption": "Fig. 1. Print orientation demonstrating the recoater direction relative to the gas flow; samples for this study were extracted from the columns, which had systematic variations in the printing speed.",
        "texts": [
            " Insights into the corrosion performance are discussed specifically in the context of the underlying defect microstructure and chemical distribution as quantified from our characterization campaign. We show that the microstructure and chemical heterogeneities unique to L-PBF samples impact the uniform and localized corrosion behavior with an explicit dependence on the printing speed. Additively manufactured stainless steel samples were printed from 316L powder (< 0.03% C by mass from Renishaw) via L-PBF processing using a Renishaw AM 250 system following the print configuration shown in Fig. 1. The laser power was held constant at 200 W A using a layer thickness of 50 \u00b5m, point distance along the scan of 50 \u00b5m with 90 \u00b5s exposure time for the laser pulse, and a hatch spacing of 100 \u00b5m. The primary control variable explored in this study was scan speed and included 550, 650, and 700 mm/s, which corresponded to energy densities of 80, 62, and 57 J/mm3, respectively. Over this energy density range, the porosity was maintained below 0.5% as determined from xray computed microtomography, which falls within a range where the corrosion behavior has been shown to be independent of the pore fraction [44]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure14.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.11-1.png",
        "caption": "Fig. 14.11 Deflection in the contact area of an incompletely elastic tread stiffness with hysteresis",
        "texts": [
            " The material obeys Hook\u2019s law for both increasing and decreasing stress but the modulus is different in the two cases. Figure 14.10 is characterized by a shear spring rate of the tread rubber for an increasing side force, Cy \u00bc Cup y , and a shear spring rate of the tread rubber for a decreasing side force, Cy \u00bc Cdown y . The ratio of the two spring rates is q \u00bc Cdown y =Cup y ; \u00f014:32\u00de which is the fraction of the maximum stored energy recoverable during a stress cycle and is referred to as the resilience of the tread rubber. The deflection of the tire tread is shown in Fig. 14.11. Once an element reaches its maximum stress, the corresponding deflection Sy_max remains constant until the local pressure drops to lqz\u00f0x\u00de \u00bc Cdown y Sy max. The deflection then follows the curve lqz\u00f0x\u00de \u00bc Cdown y Sy max. In the case that lh > l/2, as shown in Fig. 14.11a, the wear energy calculated using Eq. (14.12) is given by Sh ea r f or ce Displacement up yC down yC Sy_max 1030 14 Wear of Tires where xh is shown in Fig. 14.11. Using Eq. (14.32), Eq. (14.33) can be rewritten as5 Ew y \u00bc l tan a Z l lh qz\u00f0x\u00dedx\u00fe 1 2 l2 Cup y q2z \u00f0lh\u00de 8< : 9= ; 1 2 l2 Cup y q2z \u00f0lh\u00de\u00f01 q\u00de : \u00f014:34\u00de In the case that lh l/2, as shown in Fig. 14.11b, the wear energy is expressed by Ew y \u00bc l tan a Z l lh qz\u00f0x\u00dedx\u00fe 1 2 l2 Cup y q2z \u00f0lh\u00de 8< : 9= ; 1 2 l2 Cup y q2z \u00f0l=2\u00de\u00f01 q\u00de : \u00f014:35\u00de The first term of Eqs. (14.34) and (14.35)6 corresponds to Eq. (14.12). Referring to Eq. (14.8), at a small slip angle, Eq. (14.34) can be rewritten as Ew y \u00bc q 4lpm\u00f0 \u00de2 2Cup y f2y \u00bc q Cup y l2 2 a2: \u00f014:36\u00de Using Eqs. (14.19) and (14.20), Eq. (14.36) can be rewritten as Ew y \u00bc q F2 y=\u00f0bCup Fa\u00de; \u00f014:37\u00de 5Note 14.1. 6See Footnote 5. 14.2 Wear at a Small Slip Angle and Slip Ratio 1031 where Cup Fa \u00bc Cup y bl2=2: \u00f014:38\u00de The wear energy of rubber with hysteresis loss is expressed by E w \u00bc Ew x \u00feEw y 2pre \u00bc q 2preb F2 x Cup Fs \u00fe F2 y Cup Fa ",
            "30) shows that the wear energy is reduced by the hysteresis loss of rubber, because q is less than a unity. Figure 14.12 shows that the effect of hysteresis on the wear of a tire in cornering is calculated using Eqs. (14.34) and (14.35). The hysteresis parameter q is changed from 0.25 to 1.0 in intervals of 0.25. The calculation uses the same parameters as the calculation in Fig. 14.9: l = 1.0, l = 160 mm, Cup Fs \u00bc 27 MPa=mm and pm = 400 kPa. The critical slip angle defined by the relation lh = l/2 in Fig. 14.11 is about a = 1.06\u00b0 in this case. The wear energy decreases with increasing hysteresis. At a large slip angle, the first term in Eq. (14.33) is dominant, such that the wear energy is independent of the shear spring rate of the tread rubber. Meanwhile, at a small slip angle, the second term in Eq. (14.33) is dominant, such that the wear energy is proportional to the resilience and increases as the square of the slip angle as shown in Eq. (14.36). Schallamach and Turner [11] experimentally evaluated the effect of hysteresis on the wear of a tire as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.39-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.39-1.png",
        "caption": "Fig. 16.39 Coordinate system used to define the forces and moments of tires [35]",
        "texts": [
            " The road crown also causes vehicle pull owing to the component of the gravitational force. Furthermore, the speed, acceleration, load, inflation pressure, wear and steering friction affect vehicle pull. Overall, the construction and pattern of a tire are the most influential parameters for vehicle pull. (1) Force and moment of tires Vehicle pull can be theorized by the tire properties at a small slip angle, because a vehicle is driven straight ahead. The force and moment are usually defined within a right-hand coordinate system as shown in Fig. 16.39. The moving direction is along the x-axis and the direction perpendicularly to the right of the moving direction is deviation displacement right pull (+)left pull (\u30fc) ve hi cl e pa th fre e w he el (1 00 m ) fix ed w he el v=100km/h Fig. 16.37 Test procedure of vehicle pull 1182 16 Tire Properties for Wandering and Vehicle Pull that of the y-axis, while the z-axis points to the road. Note that the slip angle is defined differently in the SAE coordinate system and the adapted SAE coordinate system. This chapter uses the adapted SAE coordinate system as shown in Fig. 16.39. The coordinate system of the drum tester is fixed to the drum as shown in Fig. 16.40a. Because the drum tester is used to measure the uniformity of tires in a tire factory, the plysteer (PS) is calculated by measuring lateral forces in both clockwise (CW) rotation and counterclockwise (CCW) rotation. Meanwhile, the coordinate system for the vehicle dynamics is fixed on the vehicle as shown in 16.3 Vehicle Pull 1183 Fig. 16.40b. The upper figure of Fig. 16.40b represents the right tire of the vehicle, while the lower figure of Fig. 16.40b represents the left tire of the vehicle. Note that the coordinate system of Fig. 16.39 is the same as that of Fig. 16.40b. Suppose that a tire is tested on the drum tester in both clockwise and counterclockwise rotation. The lateral force, the direction of which does not change in clockwise and counterclockwise rotation, is called the conicity. The conicity is related to part of the cone shape of the belt, which is formed by the difference in the circumferential length of the belt in the two shoulders of a tire as shown in Fig. 16.41. Because the conicity has the same property as the camber thrust, it is also called pseudo-camber"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.30-1.png",
        "caption": "Fig. 5.30: Force Directions of the Contact",
        "texts": [
            " The clearance between the teeth in radial and circumferential direction enables an additional relative movement between ring gear and output shaft. Figure 5.29 makes clear, that the induced friction forces possess a remarkable influence on the deformation of the ring gear, contingent on the number of teeth and the size of the clearance. Therefore the couplings between ring gear and output shaft are modelled in detail for every single tooth as force elements with clearance and radial friction forces according to figure 5.30. Again the relative normal and tangential distances and velocities within the contacts of Figure 5.30 can be evaluated by elementary considerations from the kinematics of gear meshing [215],[170]. We get 248 5 Power Transmission gN =w\u0304T N (q, t)q, g\u0307N = wT N (q, t)q\u0307 + w\u0302N gT =w\u0304T T (q, t)q, g\u0307T = wT T (q, t)q\u0307 + w\u0302T (5.65) Accordingly the resulting forces acting on output flange and ring gear can also be calculated from normal and tangential fractions in the form FA,O = \u2212n\u03bbN \u2212 t\u03bbT , FA,R = n\u03bbN + t\u03bbT . (5.66) where \u03bbN is divided into the fraction \u03bbNc caused by the contact stiffness and the fraction \u03bbNd caused by the damping properties, equivalent to the 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.12-1.png",
        "caption": "Fig. 8.12: ZMP Forces and Torques",
        "texts": [
            " Both models are very well known since long time, and they are applied in nearly all modern walking machines considering the arguments just given above. The ZMP model is nothing else but the application of the equivalence principle of classical statics generating from force-couples a force alone. The inverted pendulum model is a very popular example for advanced course exercises together with laboratory models. The relation with respect to walking is nicely presented by some Japanese papers, for example [156], [78], [121]. For the zero moment point we get the simple relation (see Figure 8.12) FZMP = F F , TZMP = T F + F F \u00d7 rF,ZMP = 0. (8.62) The index F denotes the point F, where we know the forces and torques at the feet. The last equation can be solved for the unknown vector rF,ZMP to the zero moment point. The condition, that this point has to be positioned within the foot supporting area, provides us only with a static stability information, which is sometimes helpful. In the following we shall discuss that a bit. Human walking is characterized by two phases, not considering here the phase without ground contact taking place only for running"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001173_acsami.0c18449-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001173_acsami.0c18449-Figure7-1.png",
        "caption": "Figure 7. Schematic of the swing behavior of the bilayer film under continuous UV light illumination.",
        "texts": [
            " Thus, it is not the orientation change of AZs that is responsible for the swing behavior upon light illumination. Unlike the oscillators constructed by energy input periodically (Figure S17a)49 or by a self-shadowing effect29,30,50\u221252 having a high frequency (Figure S17b), the present bilayer strip receives energy continuously during the chaotic swing process. Although the theory of this chaotic behavior is still underway, a possible mechanism is proposed according to the obtained results. As shown in Figure 7, the strip starts to bend due to the photoinduced expansion effect, when it receives actinic light. Under the continuous photoirradiation conditions, the strip keeps moving forward since the driving force (D) is larger than the resistance force (R). Then, it passes through the equilibrium position (D = R) due to the inertia gained during https://doi.org/10.1021/acsami.0c18449 ACS Appl. Mater. Interfaces 2021, 13, 6585\u22126596 6590 actuation. When the strip reaches its maximum deflection angle, the resistance force becomes larger than the driving force (D < R)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure3.44-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure3.44-1.png",
        "caption": "Fig. 3.44 Model for the buckling phenomenon of a two-ply bias belt due to a compressive force",
        "texts": [
            "200) indicates that kcr is proportional to dfilament cosa which is related to the diameter of a wire and the bias angle, the biquadratic root of Young\u2019s modulus of wires Ef and the biquadratic root of the tread thickness H. Sakai [13] also used a model of a beam on an elastic foundation to analyze the tire belt under the buckling phenomenon resulting from an in-plane bending moment, as shown in the Appendix. Asano [9] developed MLT for the two-ply bias belt under buckling due to a compressive force. He used the model shown in Fig. 3.44, which is the same as that in Fig. 3.39. The axis in the thickness direction z(i) is defined from the middle plane of the tire belt, N(i) is the membrane force in the x-direction with a tensile force 16Note 3.7. 3.8 MLT of the Buckling of a Two-Ply Bias \u2026 167 having a positive value, M(i) is the bending moment with the clockwise direction on the left side being positive, Q(i) is the shear force with the z-direction on the left side being positive, and the subscript (i) indicates the upper belt (i = 2) or lower belt (i = 1)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003838_s0301-679x(03)00094-x-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003838_s0301-679x(03)00094-x-Figure1-1.png",
        "caption": "Fig. 1. Test set-up for ball deformation measurements.",
        "texts": [
            " Stribeck applied sound physical principles to his experimental investigations, and used the theoretical background information available at that time. In his very well known study on the load-carrying capacity of ball bearings Stribeck [2] gave scientific basis for the development of a large industry. He used the Hertzian contact theory, which by then had been known for 20 years, to connect the loads on the different balls to the external load. He then compared the loads on single ball contacts of different geometry, which were needed to give visible plastic deformations. He used three balls in contact, see Fig. 1, a steel plate sandwiched between two balls, and more conforming contacts of the type found in deep-groove ball bearings. Stribeck\u2019s studies, which were commissioned by the Deutsche Waffenund Munionsfabriken, Berlin, were epoch-making in their effect on the ball-bearing industry. Its major impact arose from the analysis of the carefully conducted experiments, see Fig. 2, and the sound appreciation of Hertzian contact theory, together with the presentation of practical formulae in a form suitable for the bearing designer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.15-1.png",
        "caption": "Fig. 7.15: Elastic Link - Coordinates and Deformation Details [196]",
        "texts": [
            "3 on the pages 113 and the following ones we model an elastic manipulator as a multibody system including rigid and elastic components. Furtheron we assume that all elastic deformations are small. Therefore motion can be characterized by a nonlinear gross movement by the rigid robot with elastic joints superimposed by small elastic deformations due to the elasticity of the links. The complete motion of the elastic manipulator, namely gross motion and elastic motion, might be described for each body using three coordinate systems, an inertial one like (I) in Figure 7.15, a conveniently chosen body-fixed frame (R) and an element-fixed coordinate system (E), to give an example. Note that (R) is already rotated and shifted by the joint angles and by all elastic deformation of the predecessor bodies with (j < i). A mass element of the link i is elastically shifted by a vector rei(x, t) and rotated by a vector \u03d5ei(x, t). It has already been pointed out, that the choice of the various and neccessary coordinate systems is to a certain extent arbitrary, but nevertheless it should follow some practical rules of econmy and convenience with respect to all evaluations following from that choice. We shall proceed here a bit different from the presentation at the beginning (section 7.2.1), where we built up a relative kinematics by considering a body i and its predecessor (i-1). Nevertheless the results are of course comparable. An arbitrary point of an elastic link (Figure 7.15), defined originally in the element-fixed coordinates (E) by Er can be written in the body-fixed system (R) by the relation Rrtotal = R(r0 + x + re) + ARE \u00b7 Er (7.47) with the transformation matrix ARE from (E) to (R). Considering only small elastic deformations the transformation ARE can be approximated by (see section 2.2.8 on page 47) ARE \u2248(E + \u03d5\u0303e) + O(2) \u2208 IR3,3, ARE \u2248  1 \u2212\u03b4 \u03b2 \u03b4 1 \u2212\u03b1 \u2212\u03b2 \u03b1 1  \u2248  1 \u2212v\u2032 \u2212w\u2032 v\u2032 1 \u2212\u03b1 w\u2032 \u03b1 1 + O(2) (7.48) with the following magnitudes: E the identity matrix and (\u00b7)\u2032 derivation with respect to x, for example v\u2032 = dv dx ",
            " Considering in a first step manipulators with tree-like structure and altogether j joints (Figure 7.16), the position vector rp from the inertial frame to the contact point can be written in the form (see equations (7.4)) rp = j\u2211 i=1 { i\u220f k=1 [E + \u03d5\u0303e]k\u22121 \u00b7AEk\u22121Rk } Lk\u22121 \u00b7 (xi + rei)Li , (7.49) 7.2 Trajectory Planning 439 where Li refers to the total lenght ofthe link i and AEk\u22121Rk is the transformation from Rk to Ek\u22121, which for revolute joints is the usual elementary rotation matrix. With the help of the vectors defined in Figure 7.15 the absolute translational and rotational velocities of a mass element come out with vEi =v0i + r\u0307ei + \u03c9\u03030i(xi + rei), \u03c9Ei =\u03c90i + \u03d5\u0307ei, } Ri - frame (7.50) vi =(E + \u03d5\u0303ei)T \u00b7 vEi, \u03c9i =(E + \u03d5\u0303ei)T \u00b7 \u03c9Ei. } Ei - frame (7.51) All the magnitudes of these equations depend on the rigid, qr \u2208 IRfr , and elastic generalized coordinates, qe \u2208 IRfe , where fr and fe denote the number of rigid and elastic degrees of freedom. The elastic coordinates enter the equations of motion via a Ritz-approach (equation (3.121) on page 125), which for rEi can be written rEi(xi, t) =  ui(xi, t) vi(xi, t) wi(xi, t)  =  u\u0304i(xi)Tqe,ui(t) v\u0304i(xi)Tqe,vi(t) w\u0304i(xi)Tqe,wi(t)  , (7.52) Where u\u0304i, v\u0304i, w\u0304i denote the vector of the shape functions for link i. Applying this approach, collecting all elastic coordinates in a vector qe, taking into account the dependencies vi(qr,qe, q\u0307r, q\u0307e) and \u03c9i(qr,qe, q\u0307r, q\u0307e), applying the momentum equation to the mass element of Figure 7.15, arranging the forces with respect to active and passive properties, applying Jourdain\u2019s principle and regarding the equations (7.50) to (7.52) we arrive at the equations of motion of a linearly elastic robot (see also the relations (3.127) on page 127): \u2022 rigid body coordinates: n\u2211 i=1 \u222b Bi {[( \u2202v0i \u2202q\u0307r ) + (x\u0303i + r\u0303ei)T ( \u2202\u03c90i \u2202q\u0307r )]T \u00b7 [(v\u0307Ei + \u03c9\u03030ivEi)dmi \u2212 dFai]+ + ( \u2202\u03c90i \u2202q\u0307r )T (E + \u03d5\u0303ei)[dIi\u03c9\u0307i + \u03c9\u0303idIi\u03c9i \u2212 dTai] } = 0 (7.53) \u2022 deformation coordinates: n\u2211 i=1 \u222b Bi {[( \u2202v0i \u2202q\u0307e ) + (x\u0303i + r\u0303ei)T ( \u2202\u03c90i \u2202q\u0307e ) + ( \u2202r\u0307ei \u2202q\u0307e )]T \u00b7 \u00b7 [(v\u0307Ei + \u03c9\u03030ivEi)dmi \u2212 dFai]+ + [( \u2202\u03c90i \u2202q\u0307e ) + ( \u2202\u03d5\u0307ei \u2202q\u0307e )]T (E + \u03d5\u0303ei)[dIi\u03c9\u0307i + \u03c9\u0303idIi\u03c9i \u2212 dTai] } = 0 (7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000921_j.matdes.2020.109040-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000921_j.matdes.2020.109040-Figure3-1.png",
        "caption": "Fig. 3. Scheme of samples and sections position in: (a) \u2013walls, (b) \u2013 bricks; sections are indicate figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " Bricks were manufactured using a continuous raster strategy at a ts of 100 cm/min, and the raster pitch was either 2.50 mm or 2.75 mm. The parameters for brick manufacturing were also set so that the best geometry was formed \u2013 a narrower pitch led to a lack of penetration, while a wider pitch led to a lack of fusion between the neighboring beads of a layer. Tensile tests were carried out on a H25KT machine (Tinius Olsen), tensile samples were cut from walls in the OX and OZ directions and from bricks in the OX, OY, and OZ directions (Fig. 3). The preparation of cylindrical samples with a diameter of 3 mm and a length of 15 mm was carried out in accordance with GOST 6996\u201366. Longitudinal (ZOX) and transverse (ZOY) sections of walls and bricks (Fig. 3) were prepared using the Buehler grinding system. Macro- and microstructure images were obtained using a DMI 5000 M metallographic microscope (Leica). Scanning electron microscopy (SEM) was performed with a MIRAD 3 N (Tescan), and the chemical composition of the deposited metal was determined using the Energy Dispersive X-Ray Spectroscopy (EDS)module of theMIRAD 3N. The porosity of the samples was evaluated by processing the binarized macrostructure images in MATLAB. The image of the fractured surface of a sample after a tensile test was obtained using an Octonus digital microscope with multi-light photometric stereo technology"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000265_j.jfranklin.2020.12.026-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000265_j.jfranklin.2020.12.026-Figure1-1.png",
        "caption": "Fig. 1. Earth-fixed frame and body-fixed reference frame.",
        "texts": [
            " Compared with the constant threshold event-triggering mechanism, the adaptive vent-triggering mechanism we proposed can effectively reduce the number of triggering and lleviate the burden of communication network. . Problem formulation .1. Dynamic modeling for networked UMV system In this section, a three-degree-of-freedom anchored marine vehicle equipped with thrusters s selected as the target plant model, by the fact that the nominal high-order state-space model s similar to the Nomote model [29] . In Fig. 1 , the earth-fixed frame and body-fixed frame are hown, where x 0 , y 0 , and z 0 are the longitudinal axis, the transverse axis, and the normal axis, espectively, x, y, and z are earth-fixed reference frame. Then, the body-fixed mathematical quations of marine vehicle are described as follows:  \u0307 v(t ) + N v(t ) + G\u03b7(t ) = u(t ) (1) here v(t ) = [ v 1 (t ) . . . v 3 (t ) ]T denote the velocity vector, and v 1 (t ) , v 2 (t ) , v 3 (t ) are elocity vectors in surge, sway, and yaw, respectively. \u03b7(t ) = [ x p (t ) y p (t ) \u03d5(t ) ]T , where p (t ) and y p (t ) are positions and \u03d5(t ) is the marine vehicle yaw angle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000061_s00339-017-1143-7-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000061_s00339-017-1143-7-Figure8-1.png",
        "caption": "Fig. 8 Morphology of scan track in the cross-sectional view at Y = 0.1 mm (P = 180 W and v = 1600 mm/s)",
        "texts": [
            " Figure 7b shows that the Peclet number increases with increasing the scanning speed, and its value for the dense phase was considerably larger than that for the powder phase. This indicates that the heat transport between liquid and powder was more rapidly than 540 Page 6 of 15 W. Pei et al. it between liquid and solidified track, resulting in an elongated molten pool. At extremely high scanning speed, the instable liquid track breaks up into balling to attain the equilibrium state based on the Plateau\u2013Rayleigh instability law [11]. As Fig. 8 shows that at a relatively high scanning speed of 1600 mm/s, the track shows a discontinuous morphology consisting of a number of disconnected balls. The LED decreases with decreasing the laser power at a fixed scanning speed. Figure 9 shows the influence of laser power (P = 150 W and P = 180 W) on the morphology of melting track at a constant scanning speed of 1000 mm/ s. As a sufficiently high laser power P = 180 W applied during SLM, a scan track with relatively smooth surface and a sound metallurgical bonding between the track and the substrate was achieved, as shown Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003887_978-94-011-4120-8_41-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003887_978-94-011-4120-8_41-Figure5-1.png",
        "caption": "Figure 5. Detail of a U-joint in Fig. 4",
        "texts": [
            " Each limb is made of a prismatic joint between two elements, which are endowed with two universal joints at their two extremities. A universal joint is a sequence of two revolute pairs, the axes of which ar~e intersecting and perpendicular. The axes of two revolute pairs of two universal joints, that are attached to the upper and lower members of each limb are parallel to each other and are perpendicular to the axis of the prismatic joint. For each limb, the axes of two revolute pairs, of two universal joints, that are connected to the base and the moving plate are converging at a given fixed point N (see Fig. 4, Fig. 5). The limbs may have the same size and may be separated by 120 degrees at the points of connection with the moving and base platforms. Different types of jacks can be implemented to vary the lengths of the 400 prismatic joints and therefore, to control the orientation of the moving platform. This 3-dof rotational platform is very close to the first translational platform of Tsai (1996). The new architecture of Di Gregorio and Parenti-Castelli (1998) , which is a generalisation of the previous Tsai platform can be considered also for the rotational platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001767_t-aiee.1918.4765578-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001767_t-aiee.1918.4765578-Figure5-1.png",
        "caption": "FIG. 5 FIG. 6",
        "texts": [
            " dB is there-dH fore a ratio of magnetomotive forces and can also be replaced by the ratio of the corresponding ampere turns; ampere turns required to drive through the air gap x an infinitesimal increased B in flux density, divided by the ampere turns per pole required to drive through the magnetic circuit of the machine with the correct air gap the same increase in flux density. Looking closer into the approximations which we introduced ROSENBERG: MAGNETIC PULL 1433 in formula (3), we find: If x is large and if the magnetization characteristic were a straight line (Fig. 5), the sum B2 + B1 would actually be greater than 2B. In Fig. 5 the value 2+ is shown dotted in. If, however, the characteristic is strongly curved (Fig. 6), B2 + B1 will be slightly smaller than 2 B. For hard pulling over, when x reaches the greatest possible value, the saturation will in any case be high enough that the curvature of the characteristic is marked. We are therefore certain that, on this score, formula (3) does not give too low values for the extreme case. A very important question is, now: How does the expression of formula (3) change with growing excitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.15-1.png",
        "caption": "Fig. 7.15",
        "texts": [
            " So, the fixed point on the rotating plane equals the subharmonic solution, and the disturbing force turns one circle when the plane rotates three turns. Assuming 1 . 1 x = c; cos-rot + 11 sm -rot 3 3 (7.81) x' 1 . 1 Y = -- = -c;cos-rot + 11 sm-rot ro/3 3 3 (7.82) the amplitude can be solved by the equation \u00b7 M th d in Bifurcation Theory Application of the A veragmg e 0 253 254 Bifurcation and Chaos in Engineering (7.83) so, the solution is (7.84) The subharmonic solution can be obtained only when the value of damping is small; ro is a little bit larger than 3roo' when E > O. As shown in Fig. 7.15, there are possibly three solutions when ro = ro'. CD x = A~I) coJ!.ro '( +pC.,I\u00bb) + AI(l) cos(ro '( +p~I\u00bb+ ... i \\3 i The first harmonic solution has already been obtained. The second solution is unstable. The third subharmonic solution is what we want to determine. We can see, therefore, that the component of the harmonic wave is somewhat weaker, i.e. A?) < A?), when harmonic solution exists. When ro = ro', the occurrence of subharmonic solutions is determined by the initial conditions. The phase diagram of the averaging equation on the rotating plane is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.22-1.png",
        "caption": "Fig. 5.22: Mechanical Model of a Toothing",
        "texts": [
            " Basically there can be differentiated between the three versions: \u2022 Rigid transmission \u2022 Force element with clearance \u2022 Engagement with impacts The last one will be used for gear trains with backlashes, which can generate rattling or hammering phenomena [200]. The examination of the effects of parameter excitations induced by the meshing gear wheels requires a meticulous consideration of the elasticity of the toothing. Furthermore some swaying of the rotational speed of the shafts may cause a change in the direction of force transmission. For that reason the force element with clearance has to be chosen for the toothing inside the planetary gear. Figure 5.22 schematically illustrates the design of this widely used force element [126], [217]. Parallel to the stiffness, which is effective only for contacting teeth, a damper generates a force along the direction n of the line of action. If the load is changing, and the back flanks of the tooth profiles are coming into contact, the force changes its direction to n\u2032. The forces acting on the points T1 and T2 can be computed by F T1 = \u2212n\u03bbN , F T2 = n\u03bbN , \u03bbN = \u03bbN (gN , g\u0307N) = \u03bbNc + \u03bbNd (5.57) 5.2 Ravigneaux Gear System 243 where \u03bbN is the scalar force depending on the relative distance gN between the tooth profiles and the approaching velocity g\u0307N "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.16-1.png",
        "caption": "Fig. 6.16: Structure of the Timing Gear R5 (courtesy VW)",
        "texts": [
            " Controling ignition is the main task of timing systems, but they also drive and control various ancillary systems like a generator, an oil pump, a power steering pump, a water pump and an airconditioning compressor. With increasing requirements with respect to comfort these ancillary systems grow in number and performance, and as a matter of fact they influence the dynamics of the timing system considerably. The general structure of the timing gear set of the Volkswagen R5 Diesel engine is illustrated by Figure 6.16. The whole set is located at the engine rear between engine and clutch. It includes 12 helical gears forming one direct branch to the camshaft and altogether three smaller branches to ancillary components. 6.2 Timing Gear of a 5-Cylinder Diesel Engine 347 The camshaft is driven by the main branch with wheel 1 of the crankshaft, with the three indermediate wheels 2, 3a3b, 4 and with the wheel 5 of the camshaft. The transmission ratio camshaft/crankshaft = 1/2 is realized by the double wheel 3a3b. The valves and the pump-nozzle-elements for the five cylinders are operated by the cams on the camshaft. Figure 6.15 gives an impression of the real world timing gear, and Figure 6.16 depicts the corresponding details, the camshaft, the rocker arms,the pn-elements (pn=pumpnozzle) and the valves. The oil pump is driven by wheel 10, which is the only wheel of the side branch 1. The power steering pump and the airconditioning compressor are driven by wheel 23 and the generator by wheel 22, which together form the side branch 2. Finally the side branch 3 consists only of wheel 30 for the water pump. The crankshaft and all ancillary equipment are not shown in Figure 6.16. The helical gears with an helix angle of 15\u00b0 are pivoted on case-fixed pins, with the exception of wheel 31. Wheel 31 is shrinked on the water pump shaft, and this shaft is pivoted on a roller bearing in the water pump housing. Therefore all wheels, with the exception of wheel 31, are taper bore mounted, which has to be examined for possible vibration enlargement of the overall system. We place the inertial coordinate system in the origin of the crankshaft wheel, wheel 1, with the z-axis in direction of the crankshaft axis (see the Figures 6",
            " The maximum of the injection pressure increases up to a speed of 4250 rpm, which represents the value of the limiter speed. The ignition point sequence is (1-2-4-5-3). Figure 6.20 depicts also the measured injection pressure versus the crankshaft angle. Every cylinder has an intake and an exhaust valve, which are driven by valve trains. The corresponding mechanical model includes the cam, the solid valve lifter, the valve head and the valve shaft according to Figure 6.17. Going back to the first Figure 6.16 we noticed one main drive train with the wheels (1, 2, 3a3b, 30, 3, 4, 5) and two side branches, one with the wheel (10) only and one with the wheels (20, 21, 22, 23). Wheel (10) drives the oil pump, wheel (22) the generator and wheel (23) the power steering pump and the air 6.2 Timing Gear of a 5-Cylinder Diesel Engine 353 conditioning compressor. We shall give some indications on modeling and on simulations with respect to loads and noise. Figure 6.21 illustrates the scheme of these side branches and the corresponding mechanical model. It differs slightly with respect to Figure 6.16, where the two split wheels are missing and replaced by just one wheel. The introduction of the two-wheeled gear rig was an experiment to reduce noise. One parameter influencing noise considerably is backlash, and one possible measure to overcome backlash is such a set of two split wheels. Therefore we find between (w20) and (w22, w23) the two gear wheels (w21a, w21b), Figure 6.21. Following the Figure 6.21 we have to model three ancillary branches of the timing gear wheel set. The simplest one is the oil pump drive includ- ing only wheel (10)",
            " Selecting two examples from a large amount of such measurements we show the torques of the camshaft for the driving and braking cases. Figure 6.22 confirms the models with about an accuracy of 10%, which is excellent before the background of a rather complicated system dynamics with clearly recognizable hammering effects. In addition we have to consider the elasticity of the bearings, which influence the results in a clear way. So the irregularities of the rotational camshaft speed becomes twice as large for elastic bearings in comparison to rigid bearings. Therefore the final design of the timing gear train as shown in Figure 6.16 includes in addition a plate arranged before the housing wall with the goal to support the gear wheels not only one-sided at the housing but two-sided in the housing and the plate. 356 6 Timing Equipment to rq u e s [N m ] After these verifications the model is used to perform many parameter variations for design improvement. In a first run the torques at the camshaft and the forces of the gear meshes and the bearings turned out to be very large. For example, the maximum torques of the camshaft were about 240 Nm for the driving and -130 Nm for the braking case",
            " We investigate stationary dynamics for speeds of 750 rpm to 4250 rpm in relatively small steps, and we consider as reference stiffness especially for the clutches a the values at a temperature of 20\u25e6C. By practical experience from the VW test bed it was known, that the case without climate compressor load and with nearly no generator load was the worst case with some damage of the Gates- clutch. It turned out furtheron, that the spanning of the gears (w21a,b) has no influence on this situation, which is determined mainly by the dynamics of the whole ancillary branch system and not so much by the backlashes. Even with only one gear wheel (21) according to Figure 6.16 we got similar results. Figure 6.23 illustrates a typical simulation result in form of a time series of the gear meshes. Not all gears of Figure 6.21 are shown. The results illustrate the characteristic 6.2 Timing Gear of a 5-Cylinder Diesel Engine 357 hammering of such timing gears under load, for our case with a the 2.5 th engine order (f=50 Hz, 2.5f= 125 Hz, T=0.008 s). to rq u e [N m ] For evaluating the parameter influences with respect to the clutch load a large amount of simulations have been performed, which came out with the following results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001183_j.oceaneng.2021.109416-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001183_j.oceaneng.2021.109416-Figure1-1.png",
        "caption": "Fig. 1. Coordinates definition of USV motioning in the horizontal plane.",
        "texts": [
            " In addition, comparing with the switching structured FTSMC (Zhang and Guo, 2020), the developed one is continuous and enjoys a simpler structure for application. The rest of this paper is organized as follows. In Section 2, the USV model and preliminaries are introduced. The main results of this paper involving dynamic transformation and controller designing are presented in Section 3. Numerical verification and comparison results are given in Section 4. The conclusion is drawn in Section 5. In this brief, we consider that motions of the USV are defined in the horizontal plane. Two coordinates are defined in Fig. 1 to describe USV\u2019s B. Zhou et al. Ocean Engineering 236 (2021) 109416 motion, i.e., the earth-fixed coordinate OEXEYE and the body-fixed coordinate OBXBYB. Under these two coordinates, the kinematic model of the USV is given as (Dai et al., 2017): \u23a7 \u23a8 \u23a9 x\u0307 = ucos(\u03d5) \u2212 vsin(\u03d5) y\u0307 = usin(\u03d5) + vcos(\u03d5) \u03d5\u0307 = r (1) Here, states x, y and \u03d5 are defined with respect to OEXEYE, where x, y stand for USVs\u2019 position and \u03d5 denotes the yaw angle. u, v and r respectively stand for the surge velocity, sway velocity and yaw velocity related to OBXBYB"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000245_j.conengprac.2018.03.015-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000245_j.conengprac.2018.03.015-Figure1-1.png",
        "caption": "Fig. 1. North-east-down frame and ship-fixed frame (Fossen, 2011).",
        "texts": [
            " The main contributions in this paper are as follows: (1) The adaptive laws together with the observer provide online estimates of unknown time-varying disturbances, especially in the absence of a priori knowledge of the ship dynamic model parameters. (2) In the simultaneous presence of ship unknown model parameters and unknown time-varying disturbances, it is the first time that the global asymptotic regulation of the positioning errors is achieved. (3) The proposed DP control law has both the adaptability to the ship dynamic model parameter perturbations and the robustness against unknown time-varying disturbances. The ship\u2019s motions are described in two right-hand coordinate frames as shown in Fig. 1. The earth-fixed frame indicated by \ud835\udc42\ud835\udc4b0\ud835\udc4c0\ud835\udc4d0 is an inertial frame and the ship-fixed frame indicated by \ud835\udc34\ud835\udc4b\ud835\udc4c\ud835\udc4d is a noninertial frame. The origin \ud835\udc42 of the earth-fixed frame can be chosen as any point on the earth\u2019s surface. The axis \ud835\udc42\ud835\udc4b0 is directed to the north, the axis \ud835\udc42\ud835\udc4c0 is directed to the east, and the axis \ud835\udc42\ud835\udc4d0 points towards the center of the earth. When the ship is port-starboard symmetric, the origin \ud835\udc34 of the ship-fixed frame is located at the gravity center of the ship. The axis \ud835\udc34\ud835\udc4b is directed from aft to fore, the axis \ud835\udc34\ud835\udc4c is directed to starboard, and the axis \ud835\udc34\ud835\udc4d is directed from top to bottom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.105-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.105-1.png",
        "caption": "Fig. 5.105: Model of an Element",
        "texts": [
            " Accordingly, this pulley has one degree of freedom qp = (\u03b1sec) T , which is an angle of rotation. The pulley equations of motion write Mpu\u0307p = hp +W p \u03bb (5.148) with the positive definite, constant and diagonal mass matrixMp. The vector hp is only depending on the time t: hp = hp(t). Thus the matrices \u2202 hp \u2202 qp and \u2202 hp \u2202 up used for the numerical integration are zero matrices [81]. 5.7 CVT - Push Belt Configuration 321 The elements are modeled by rigid bodies, describing each element m by three degrees of freedom qm = (ym, zm, \u03b1m)T . The model of one single element is depicted in Fig. 5.105, where the center S of gravity is determined by the translational positions y and z. The modeling of the whole CVT is performed in the plane containing the axes AA of all elements. The M elements are described by the generalized coordinates qe = ( qT1 , . . . , q T M )T , resulting in the equations of motion Meu\u0307e = he +W e \u03bb (5.149) with the positive definite, constant and diagonal mass matrixM e. The vector he is constant and summarizes forces due to gravity. Thus the matrices \u2202 he \u2202 qe and \u2202 he \u2202 ue are zero matrices"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003876_s10957-007-9305-y-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003876_s10957-007-9305-y-Figure2-1.png",
        "caption": "Fig. 2 Construction of (\u03c3j+1, s\u0302j+1) from (\u03c3j , sj ) in Step 3 of Algorithm 3.1",
        "texts": [
            " In Step 1 it has \u03c3j := {\u03c3j (1), . . . , \u03c3j (N(j))}, and it solves the problem P\u03c3j to the extent of computing a Kuhn-Tucker point sj := (\u03c4j,1, . . . , \u03c4j,N(j)) T . At Step 2, suppose that D(\u03bej ) < 0, so that the algorithm computes g \u2208 and t \u2208 [0, T ] such that Dg,t (\u03bej ) = D(\u03bej ). Assume that t \u2208 (\u03c4j,i\u22121, \u03c4j,i) for some i = 1, . . . ,N(j) + 1; the analysis for the case where t = \u03c4j,i is similar (as will be evident later) and hence it is omitted. Let us use the notation g = f\u03c3( ). Next, consider Step 3, where Fig. 2 can be used as a visual aid. Here, we have that \u03c3j+1 = {\u03c3j (1), . . . , \u03c3j (i), \u03c3 ( ), \u03c3j (i), . . . , \u03c3j (N(j) + 1)}, (17) and s\u0302j+1 = (\u03c4j,1, . . . , \u03c4j,i\u22121, t, t, \u03c4j,i , . . . , \u03c4j,N(j)) T \u2208 RN(j+1), (18) where N(j + 1) = N(j) + 2. Note that t is the time of two switching points and the modal function g is inserted between them for an interval of length 0. Moreover, if we use the notation s\u0302j+1 := (\u03c4j+1,1, . . . , \u03c4j+1,N(j+1)) T , then \u03c4j+1,k = \u03c4j,k for all k = 1, . . . , i \u2212 1; \u03c4j+1,i = \u03c4j+1,i+1 = t ; and \u03c4j+1,k = \u03c4j,k\u22122 for all k = i + 2, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.30-1.png",
        "caption": "Fig. 5.30: Design of a piezoelectric chopstick hand. According to [Arai93]",
        "texts": [
            "tm thick actuator membrane with a diameter of Chopstick gripper A very important application area for piezoelectric actuators is the fine manipulation/adjustment of microobjects. Piezoactuators can precisely posi tion these objects with an accuracy of about 10 nm. The development of a piezoelectric microhand for manipulating tiny objects has been pursued for the past several years [Arai92], [Arai93]. Two piezo-driven chopstick-like fingers, each having 6 degrees of freedom, are designed to manipulate micro objects like a human hand, Fig. 5.30. The two-finger design was specially conceived to work in the microworld, where gravity and moments of inertia play only a very minor role. Therefore, two fingers are sufficient for manipu lating microobjects. 5.3 Piezoelectric Microactuators 147 148 5 Microactuators: Principles and Examples Two prototypes of the chopstick microfingers were developed and are shown in Figure 5.31. A parallel link mechanism was used to construct both proto types. It is made up of 6 prismatic piezo connecting elements which are connected to the base plate and end effector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure4.10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure4.10-1.png",
        "caption": "Fig. 4.10 Shear stress sxy and interfacial shear stress sC",
        "texts": [
            "23), the interlaminar shear stress szx and szy can be obtained as szx \u00bc Gmwx szy \u00bc Gmwy : \u00f04:96\u00de The shear stress sxy is given by sxy \u00bc Gmcxy \u00bc Gm u;y \u00fe v;x : \u00f04:97\u00de 4.1 DLT of a Two-Ply Bias Belt with Out-of-Plane \u2026 213 Suppose that exC, eyC and cxyC are strains at the interface between the cord and rubber in the (x, y) coordinate system. The interfacial shear stress sC can be calculated as sC \u00bc GmcC \u00bc Gm eyC exC sin 2a\u00fe cxyC cos 2a : \u00f04:98\u00de When the sign of sC is negative (i.e., sC < 0), sC is applied to the cord in the direction shown by the dotted line in Fig. 4.10. Akasaka and Shouyama [1] analyzed a two-ply bias laminate employing DLT. The parameters used in the analysis were Ef = 104 N/cord, Df = 10\u22124 Nm2, Cf = 10\u22124 Nm2, Em = 5 MPa, a = 4 mm, b = 20 mm, h0 = tf = 1 mm, h = 0.5 mm, d = 2 mm, a = 30 deg, b0 = 2.3 mm, af = 1 mm, am = 1 mm. Figure 4.11 shows the distribution of the tensile stress ratio rx/e0 of a two-ply laminate with bias angle a = 30\u00b0 at the cross section x = 0. The distribution of the tensile stress ratio is like the teeth of a comb owing to the difference in stiffness between the cord and rubber"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000092_tcyb.2019.2921254-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000092_tcyb.2019.2921254-Figure2-1.png",
        "caption": "Fig. 2. Two-link planar manipulator.",
        "texts": [
            " Similar to (33), taking the time derivative of V5 yields V\u03075 \u2264 \u2212c3V5 + c5 (51) where c3 is the same as before and c5 is a positive constant given as c5 = 2\u2211 i=1 2\u2211 j=1 \u03b3i 2 Kij\u03c1iKij + n\u2211 i=1 1 2 W\u2217T Di \u03c3DiW \u2217 Di + n\u2211 i=1 1 2 W\u2217T i \u03c3iW \u2217 i + 1 2 d\u0304T(I + \u03b2kd)d\u0304 + 1 2 \u03b5\u0304T D(ZD) ( 2\u03b2kd + k2 a ) \u03b5\u0304D(ZD) + 1 2 \u03b5\u0304T(Z)\u03b5\u0304(Z) + 1 2 nD \u2225\u2225kaW\u2217 d \u2225\u22252 . (52) Theorem 2: Similar to case 1, for the robotic system considering the TLOE of actuators (41), with bounded initial conditions, SGUB stability is obtained with the DO constructed as (49) and \u03b1 designed as (31). The prescribed performance of the tracking error is guaranteed, namely, \u2200t > 0, ki(t) < ei(t) < ki(t). Consider a rigid robot with a uniform mass distribution shown in Fig. 2. Assumed to move on the Cartesian space, the joint variables vector q of the robot is given as q = [ \u03b81 \u03b82 ] = [ q1 q2 ] . (53) Then, M(q), C(q, q\u0307), and G(q) in the dynamics model can be similarly obtained as in [79]. Parameters of the robot are given as m1 = 1 kg, m2 = 0.85 kg, l1 = 0.3 m, l2 = 0.4 m. (54) The desired trajectory is set as \u03b81 = sin(t) and \u03b82 = cos(2t), the states are initialized at \u03b81(0) = 1, \u03b82(0) = 0, and \u03b8\u03071(0) = \u03b8\u03072(0) = 0, and the initial configuration of the neural network weight is 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.4-1.png",
        "caption": "Fig. 5.4 Cord length",
        "texts": [
            "18) yields z\u00f0r\u00de \u00bc ZrA r Affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p dr: \u00f05:19\u00de Because the radius of curvature r1 in Eq. (5.9) is given by r1 = B/(dA/dr), r1 in the tire cross section is expressed by2 r1 \u00bc B dA=dr \u00bc r\u00f0r2A r2C\u00de 2r2 \u00fe\u00f0r2 r2C\u00de cot2 a exp ZrA r cot2 a r dr 0 @ 1 A: \u00f05:20\u00de 2Note 5.2. 246 5 Theory of Tire Shape The substitution of Eq. (5.18) into Eq. (5.21) yields ds \u00bc Bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p dr: \u00f05:22\u00de The length of a line element along the cord direction, dL, is defined by dL = ds/sin a as shown in Fig. 5.4. Using Eq. (5.22), the ply length L is obtained as L \u00bc 2 ZrA rB dL \u00bc 2 ZrA rB dL ds ds dr dr \u00bc 2 ZrA rB B= sin affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p dr: \u00f05:23\u00de The term R rA r cot2 a r dr in the expression for A in Eq. (5.17) can be determined if the cord path or the function of a(r) is defined. The cord path of a bias tire cannot be clearly defined using a simple equation because it depends on the material, manufacturing process and other factors. Tire shapes with typical cord paths are reviewed in the following sections"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure8.42-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure8.42-1.png",
        "caption": "Fig. 8.42 Cleat impact simulation and vertical axle force [35]",
        "texts": [
            " For example, the magnitude of the longitudinal force at the peak is different from the measurement, if the Coriolis force and centrifugal force are not considered. 8.4 Tire Models Rolling Over Cleats (Ride Harshness) 521 Kamoulakos et al. [34] first analyzed a tire rolling over a cleat employing explicit FEA and showed that the axle force variation in the time domain qualitatively agreed with measurements. In recent years, explicit FEA has also been applied to a tire rolling over a cleat as shown in Fig. 8.42 [35, 38]. The vertical axle force is illustrated in Fig. 8.42. Appendix 1: Representations of Tire Mode Shapes R and T in Fig. 8.43, respectively, denote the radial and transversal modes. The natural modes of the tire, whether radial or transversal, are said to be integer modes if the distortion has an even number of nodes and semi-integer modes if the distortion has an odd number of nodes. Note that, by convention, the contact patch is 522 8 Tire Vibration not counted as a node for radial modes, whereas it is for transversal modes, and the representation in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003467_tvcg.2005.13-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003467_tvcg.2005.13-Figure2-1.png",
        "caption": "Fig. 2. Local coordinate frames attached to the nodes.",
        "texts": [
            " To accommodate large deformations, the stiffness matrix K in (4) should be replaced by K\u00f0u\u00de. Therefore, we must deal with a governing equation of the form: M\u20acu\u00feC _u\u00feK\u00f0u\u00deu \u00bc F: \u00f09\u00de Let u\u00f0t\u00de \u00bc \u00bdui\u00f0t\u00de \u00bc \u00bduT 1 \u00f0t\u00de uT n \u00f0t\u00de T. Then, the ith threedimensional vector ui\u00f0t\u00de represents the displacement of the ith node from its original position, measured in the global coordinate frame. In order to measure the local rotations with respect to the global coordinate frame, we embed a local coordinate frame fig at each node i, as shown in Fig. 2, such that, at the initial state, it is aligned with the global coordinate frame. We use the notation fig\u00f0t\u00de to refer to the local coordinate frame at time t. Let Ri\u00f0t\u00de be the rotation matrix representing the orientation of fig\u00f0t\u00de and _uL i \u00f0t\u00dedt be the differential displacement of the ith node at time t dt measured from fig\u00f0t dt\u00de. Then, the finite displacement ui\u00f0t\u00de measured from the global coordinate frame is given by ui\u00f0t\u00de \u00bc Z t 0 Ri\u00f0 \u00de _uL i \u00f0 \u00ded : \u00f010\u00de The above procedure must be carried out for every node"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000009_j.apsusc.2019.02.142-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000009_j.apsusc.2019.02.142-Figure2-1.png",
        "caption": "Fig. 2. Scanning strategy of selective laser melting.",
        "texts": [
            " TC4 alloy (15mm\u00d715mm\u00d75mm) as substrate were prepared by selective laser melting (SLM) used a commercial fine spherical TC4 (wt %) alloy powder (Al: 6.1, V: 4.1, Fe: 0.12, C: 0.01, O: 0.13, N: 0.01, H: 0.001, and Ti: balance) by prep. The morphology of the powders under a scanning electron microscope (SEM, \u03a3IGMA) is shown in Fig. 1. To obtain an even denser sample, the optimum SLM process parameters were laser power of 500W, with a laser beam diameter of 120 \u03bcm, layer thickness of 100 \u03bcm and laser scanning speed of 200mm/ s was carried out to build the sample. Meanwhile, as shown in Fig. 2, divide the part area in small rectangular sectors with width of 2mm and laser scanning direction between layers is rotated by 90\u00b0 (so-called cross-hatching technique) [23,24]. After fabrication, the SLM samples were cleaned by ultrasonic treatment, and then ready for MAO treatment. Fig. 3 presents the optical microstructure of SLM-produced TC4 alloy in this study. Some columnar \u03b2 grains oriented along the building direction are presented in Fig. 3(a). In addition, a large amount of acicular \u03b1\u2032 martensite is also existed in the microstructure of SLMproduced TC4alloy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003446_s00332-002-0493-1-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003446_s00332-002-0493-1-Figure9-1.png",
        "caption": "Fig. 9. Asymptotic helices. (a) The curvature, and (b) the torsion of the asymptotic helices in a perversion, as functions of the applied tension.",
        "texts": [
            " (52) Equation (52) is a fourth-degree polynomial equation for \u03ba for which there is exactly one real solution in 0 < \u03ba < K , the physically relevant case, for 0 < T < K 2/ . The asymptotic curvature \u03ba varies monotonically from K to 0 as the tension T varies from 0 to K 2/ . The tension T = K 2/ is the critical tension above which the solution representing a perversion does not exist. At T = 0, the filament is a ring with radius K \u22121, and for T \u2265 K 2/ the filament is straight. The curvature as a function of the tension is obtained by solving (52) and is seen in Figure 9a. Furthermore, the first integrals are I1 = 2 K 2 + ( 3 \u2212 4 ) K\u03ba + 2 (1 \u2212 )\u03ba2, (53) I2 = T 2, (54) I3 = 0, (55) where \u03ba is given by the solution of (52). We can now deduce the boundary conditions necessary to produce a perversion solution as we have defined it. We have defined a perversion in an idealized form as a heteroclinic orbit. In this setting, for a rod with intrinsic curvature K in the direction d1, and a tension T applied at the ends at \u00b1\u221e, the boundary conditions are given by the asymptotic condition (46)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000360_j.jmapro.2021.03.040-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000360_j.jmapro.2021.03.040-Figure14-1.png",
        "caption": "Fig. 14. Residual Stress profile after the melting of layer (a) 1, (b) 2, (c) 3, and (d) 4 for laser power at the value of 200 W, hatch spacing at the value of 50 \u03bcm and scanning speed at the value of 600 mm/s.",
        "texts": [
            " As the depth of melt pool is greater than powder layer, when point n of layer 2 melts, point n in layer 1 also undergoes re melting and re solidification cycle. This causes stress relaxation and rebuilding of stresses. As can be seen from Fig. 13(c)\u2013(e), during the melting of layer 2, 3 and 4 previous layers also undergoes re melting cycles and hence experience stress relaxation and stress buildup cycles. These complex combinations of stress relaxation and stress buildup phenomena lead to the final stress profile inside SLM fabricated component. Fig. 14(a) represent the stress distribution after the printing of layer 1, whereas (b), (c) and (d) shows the stress distribution after printing of layer 2, 3, and 4 respectively for hatch spacing at the value of 50 \u03bcm, scanning speed at the value of 600 mm/s and laser power at the value of 200 W. Equivalent stress values at the surface of each layer were observed to be lower than the maximum equivalent stress in the component. Moreover, the maximum stress lies at the interface of melted powder layer and baseplate, and inside the baseplate close to the melted region, as shown in Fig. 14(a). Similar profile can also be seen for next layers in Fig. 14(b)\u2013(d). The possible reason for maximum stress values around the interface region of powder bed and the substrate is the constrained nature of this location. As the temperature tends to decrease the material tends to contract, however as it is surrounded by multiple sides, this restricts its contraction and hence result in higher stress values at this location [35]. Also, the baseplate is significantly larger in size as compared with the fabricated component. Therefore, the capacity for head conduction is also significantly high. This results in large temperature gradients as well as large cooling rates at these locations. This is also a possible reason for high residual stresses at these locations. The maximum stress after printing of layer 1 was 288.5 MPa, whereas, maximum stress value observed on the surface of layer 1 was lower i.e., 268 MPa approximately. Furthermore, it can also be observed from Fig. 14, that the equivalent stress values at the surface keep on decreasing as the number of layers increases. Similar behavior can also be observed from Fig. 13(a). The possible reason for this decrease in residual stress can be the decreasing thermal gradient between melted layer and the surroundings resulting in a slow cooling rate. These slow cooling rates results in lower stress values as layer number increases. These findings are in accordance with previous investigations that the locations of maximum stresses are inside the already deposited layers and equivalent stress values keep decreasing as we move away from the baseplate [15,26]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.8-1.png",
        "caption": "Fig. 16.8 Control of camber thrust through the crown radius and belt construction. Reproduced from Ref. [9] with the permission of JSAE",
        "texts": [
            " The tread stiffness can be controlled by the stiffness of the belt and Young\u2019s modulus of the tread rubber, the crown profile and the sidewall profile. The side stiffness is typically controlled by the sidewall tension through the sidewall profile and the stiffness of the carcass, chafer and bead filler. Note that these factors are also related to other performances, such as the maneuverability, rolling resistance and tread wear. Okano et al. [9] studied the effects of the crown profile and belt construction of a tire on the camber thrust as shown in Fig. 16.8. Rut wandering can be improved by reducing the number of belts to reduce the tread stiffness and by rounding the crown profile to strengthen the lateral shear force in a freely rolling tire. The yaw fluctuates with time in wandering, and the peak to peak of the yaw rate is thus selected as a metric of wandering. Figure 16.9 shows that the subjective evaluation of the wandering phenomenon correlates well with the peak to peak of 1164 16 Tire Properties for Wandering and Vehicle Pull the measured yaw rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure9.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure9.2-1.png",
        "caption": "Fig. 9.2 Tread contact geometry. Reproduced from Ref. [2] with the permission of J. Appl. Mech.",
        "texts": [
            " Referring to the left figure of Fig. 9.3 and neglecting the structural spring in Sect. 6.1.2, kr is simply expressed by the radial fundamental spring rate of a tire due to the tensile stiffness [44]3: rk \u03c4 aa p a a p \u03c4 p rk rk Tk Tk Tk bFig. 9.1 Side view and meridional section of an elastic ring model for tires. Reproduced from Ref. [2] with the permission of J. Appl. Mech. 2Same as Eq. (8.49). 3Same as Eq. (6.13). 542 9 Contact Properties of Tires kr \u00bc 2 dQ0 dw w\u00bc0 \u00bc p cos/s \u00fe/s sin/s sin/s /s cos/s : \u00f09:9\u00de Referring to Fig. 9.2, the tread ring compression k is geometrically expressed by k \u00bc w\u00fe d0 a 1 cos h\u00f0 \u00de; \u00f09:10\u00de where d0 is the displacement at the center of the contact patch and a is the radius of the tread ring. The circumferential tension T is decomposed into two parts: T \u00bc T0 \u00feDT ; \u00f09:11\u00de where T0 is the tension of the tread ring due to the inflation pressure p, while DT is the additional tension due to the deformation. Referring to the right figure of Fig. 9.3, the force equilibrium equation is 9.2 Contact Analysis of Tires Using an Elastic Ring Model 543 T0 \u00bc abp 2aQ0: \u00f09:12\u00de Suppose that h in Fig. 9.2 is the contact angle connecting the contact region and the free region. The continuity condition is applied to h as boundary condition. Using Eq. (9.10), the displacement d0 is determined by the condition that k is zero at h . d0 is expressed by d0 \u00bc w h \u00f0 \u00de\u00fe a 1 cos h \u00f0 \u00de; \u00f09:13\u00de where a \u00bc a\u00fe s and s is the thickness of the tread rubber. The contact pressure q is given by q \u00bc kTk \u00bc kT w\u00fe d0 a 1 cos h\u00f0 \u00def g: \u00f09:14\u00de The total load Fz is obtained by integrating the contact pressure over the contact region: Fz \u00bc 2b Zh 0 akT w\u00fe d0 a 1 cos h\u00f0 \u00def gdh: \u00f09:15\u00de Substituting Eqs",
            "25) are given by rf \u00bc 0; c3; c4; \u00f09:27\u00de where c3 and c4 are expressed by c3 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe a2T0 2EI 1\u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 l2 p r c4 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe a2T0 2EI 1 ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 l2 p : r \u00f09:28\u00de In each region, there are the five integration constants for the homogeneous differential equation. Considering the left\u2013right symmetry in Fig. 9.2, the circumferential displacement v, the tangent of radial displacement w0 and the transverse shear force V must all be zero at h = 0, p. These boundary conditions are expressed by5 vc \u00bc 0 w\u00f01\u00de c \u00bc 0 w\u00f03\u00de c \u00few\u00f01\u00de c \u00bc 0 at h \u00bc 0; \u00f09:29\u00de 5Note 9.3. 546 9 Contact Properties of Tires vf \u00bc 0 w\u00f01\u00de f \u00bc 0 w\u00f03\u00de f \u00few\u00f01\u00de f \u00bc 0 at h \u00bc p; \u00f09:30\u00de where, using Eq. (9.6), the circumferential displacement v in each region can be obtained by integrating w with respect to h. Because the displacement, tangent, moment, shear and tension must be continuous at the contact angle h \u00bc h , the boundary conditions can be expressed by vc \u00bc vf wc \u00bc wf w\u00f01\u00de c \u00bc w\u00f01\u00de f w\u00f02\u00de c \u00fewc \u00bc w\u00f02\u00de f \u00fewf w\u00f03\u00de c \u00few\u00f01\u00de c \u00bc w\u00f03\u00de f \u00few\u00f01\u00de f : \u00f09:31\u00de Using the second equation of Eq",
            " 9.7, kT denotes the tread spring rates, while kr and kt, respectively, denote fundamental spring rates in the radial and circumferential directions. a is the radius of the tread ring, and a is the radius of the tread surface. In the right figure of Fig. 9.7, /f and /r are, respectively, the contact angles at the leading edge (front) and trailing edge (rear), w is the radial displacement of the tread ring, and d0 is the overall tire displacement at the center of the contact patch. Referring to Fig. 9.2, the displacement k of the tread rubber is approximated using Eq. (9.10), in which the displacement v in the circumferential direction is neglected because v is much smaller than w. The contact pressure q(/) is expressed by Eq. (9.14). (1) Tire response to a concentrated force The fundamental equation of the inextensible elastic ring model for a tire is given as Eq. (8.109) when the tire axis is fixed. The wheel is only allowed to rotate at a p=1.28 MPa 0.1 0.2 0.3 Contact angle (degree) 0 C on ta ct p re ss ur e (M Pa ) p=2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000691_j.rinp.2019.01.002-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000691_j.rinp.2019.01.002-Figure10-1.png",
        "caption": "Fig. 10. Principal stress profile at different scan speed (a) 100mm/S (b) 200mm/S (c) 300mm/S and (d) 400mm/S.",
        "texts": [
            " This quantitative value gives a clear indication that minute deformation takes place in the build part due to the thermal strain. Effect of scan speed on thermal residual stress Laser scan speed is also an important processing parameter which directly affects the sintering mechanism as well as the thermal residual stress in the build part in direct metal laser sintering. The finite element simulations are carried out by changing the scan speed from 100mm/S to 400mm/S, keeping the laser power 100W constant for all the cases. Fig. 10 shows the principal stress distribution of the multi-component powder layer in direct metal laser sintering process. From the simulation profile, it is observed that with the increase in scan speed, the average stress in the build part decreases. This is because of the gradual decrease in laser energy density, as the interaction time between the laser beam and powder bed reduces. As a result, it will decrease the temperature gradient and cooling rate in the powder bed. Increasing the scan speed from 100mm/S to 400mm/S caused the stress decreased from 170"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure8-1.png",
        "caption": "Fig. 8. Coordinate systems applied for simulation of meshing, II.",
        "texts": [
            " PII: S0094-114X(02)00050-2 The contents of the paper cover: (1) A brief summary of the existing geometry and the output of tooth contact analysis (TCA) computer program developed for simulation of meshing and contact. (2) Modified geometry of face-gear drives based on application of a shaper that is conjugated to a parabolic rack-cutter. (3) Concept of generation of face-gears by grinding or cutting worms, analytical derivation of worm thread surface, and its dressing. Nomenclature ai\u00f0i \u00bc d; c\u00de pressure angles for asymmetric face-gear drive for driving (i \u00bc d) and coast (i \u00bc c) sides (Fig. 9) Dc change of shaft angle (Fig. 8) DE change of shortest distance between the pinion and the face-gear axes (Fig. 7) Dq axial displacement of face-gear (Fig. 8) kw crossing angle between axes of shaper and worm (Fig. 21) cm shaft angle (Figs. 4, 8, 12) Ri \u00f0i \u00bc s; 1; 2;w\u00de tooth surface of the shaper (i \u00bc s),the pinion (i \u00bc 1), the face-gear (i \u00bc 2) and the generating worm (i \u00bc w) wj \u00f0j \u00bc r; e\u00de angle of rotation of the shaper (j \u00bc r) and the pinion (j \u00bc e) considered during the process of generation (Fig. 11) wi \u00f0i \u00bc s;w\u00de angle of rotation of the shaper considered during the process of generation of the face-gear (i \u00bc s) and the worm (i \u00bc w) (Figs. 12, 21) wi \u00f0i \u00bc 2;w\u00de angle of rotation of the face gear (i \u00bc 2) and the worm (i \u00bc w) considered during the process of generation (Figs",
            " However, the path of contact of the involute face-gear drive is oriented along the surface cross-section, and errors of alignment cause the shift of the bearing contact as shown in Fig. 6. The gear drive is sensitive to error Dc of the crossing angle formed between the axes of the face-gear and the pinion, but the shift of the bearing contact caused by the error Dc may be reduced by the axial displacement Dq of the face-gear [13]. The following coordinate systems are applied for TCA: (a) coordinate system Sf , rigidly connected to the frame of the face-gear drive (Fig. 7(a)); (b) coordinate systems S1 (Fig. 7(a)) and S2 (Fig. 8(b)), rigidly connected to the pinion and the face-gear respectively; and (c) auxiliary coordinate systems Sd, Se and Sq, applied for simulation of errors of alignment of face-gear drive (Fig. 8(a) and (b)). All misalignments are referred to the gear. Parameters DE, B, and B cot c determine the location of origin Oq with respect to Of (Fig. 7(b)). The location and orientation of coordinate systems Sd and Se with respect to Sq are shown in Fig. 8(a). The misaligned face-gear performs rotation about the ze axis (Fig. 8(b)). TCA results shown in Fig. 6 have been obtained for numerical example of design parameters shown in Table 1. The proposed geometry is based on the following ideas: i(i) Two imaginary rigidly connected rack-cutters designated as A1 and As are applied for the generation of the pinion and the shaper, respectively. Designation A0 indicates a reference rackcutter with straight line profiles (Fig. 9). (ii) Rack-cutters A1 and As are provided by mismatched parabolic profiles that deviate from the straight line profiles of reference rack-cutter A0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000331_j.msea.2019.04.003-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000331_j.msea.2019.04.003-Figure2-1.png",
        "caption": "Fig. 2. Dimensions of fatigue specimens.",
        "texts": [
            " Specimens were cut from the base plate using wire-cut electro-discharge machining (WEDM) process (Make: Electra Mexicut, India). Since precipitation hardening does not occur directly during part fabrication of SLM specimens [10] few specimens from above two groups were heat treated in a muffle furnace (Make: UR Biococtin, India) under argon gas environment following the heat treatment schedules mentioned in Table 2. After heat treatment, both heat treated and non-heat treated cylindrical specimens were machined using computer numerically controlled lathe as per Fig. 2 and their gauge lengths were polished using different grades of SiC papers to reduce any effect of surface machining. Surface roughness was measured using a non-contact laser baser surface profilometer (Model: optoNCDT, Make: Micro-epsilon, USA) and it came out to be \u223c0.9 \u03bcm. Specimens were tested under rotating bending fatigue testing condition using a rotating bending fatigue testing machine (Model: HSM20, Hi-Tech limited, UK) operating at 25 Hz frequency. S-N curves (Fig. 6 and Fig. 7) were plotted keeping stress amplitude along Y-axis and number of cycles to failure along X-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000488_tmech.2019.2945525-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000488_tmech.2019.2945525-Figure6-1.png",
        "caption": "Fig. 6 Experimental setup of the VS test",
        "texts": [
            " The transformation matrixes \ud835\udc47i from \ud835\udc43\ud835\udc56 \u2212 \ud835\udc65\ud835\udc43\ud835\udc56 \ud835\udc66\ud835\udc43\ud835\udc56 \ud835\udc67\ud835\udc43\ud835\udc56 to \ud835\udc5c\ud835\udc43 \u2212 \ud835\udc65\ud835\udc43\ud835\udc66\ud835\udc43\ud835\udc67\ud835\udc43 and \ud835\udc47\u03c4 from \ud835\udc43\ud835\udf0f \u2212 \ud835\udc65\ud835\udc43\ud835\udf0f \ud835\udc66\ud835\udc43\ud835\udf0f \ud835\udc67\ud835\udc43\ud835\udf0f to \ud835\udc5c\ud835\udc43 \u2212 \ud835\udc65\ud835\udc43\ud835\udc66\ud835\udc43\ud835\udc67\ud835\udc43 can be described by \ud835\udc47\ud835\udc56 = [ 1 0 0 \ud835\udc5f\ud835\udc43 \ud835\udc50\ud835\udf03\ud835\udc56\ud835\udc43 0 1 0 \ud835\udc5f\ud835\udc43\ud835\udc60\ud835\udf03\ud835\udc56\ud835\udc43 0 0 1 0 0 0 0 1 ] (11) and \ud835\udc47\ud835\udf0f = [ 1 0 0 \ud835\udc43\ud835\udf0f\ud835\udc65 0 1 0 \ud835\udc43\ud835\udf0f\ud835\udc66 0 0 1 \ud835\udc43\ud835\udf0f\ud835\udc67 0 0 0 1 ] (12) \ud835\udc43\ud835\udc56 \ud835\udc43 defined as \ud835\udc43\ud835\udc56 in \ud835\udc5c\ud835\udc43 \u2212 \ud835\udc65\ud835\udc43\ud835\udc66\ud835\udc43\ud835\udc67\ud835\udc43 can be described by \ud835\udc43\ud835\udc56 \ud835\udc43 = \ud835\udc47\ud835\udc56\ud835\udc47\ud835\udf0f \u22121 \ud835\udc43\ud835\udf0f \ud835\udc43 (13) where \ud835\udc43\ud835\udf0f \ud835\udc43 is \ud835\udc43\ud835\udf0f in \ud835\udc5c\ud835\udc43 \u2212 \ud835\udc65\ud835\udc43\ud835\udc66\ud835\udc43\ud835\udc67\ud835\udc43 According to the transformations between \ud835\udc5c\ud835\udc43 \u2212 \ud835\udc65\ud835\udc43\ud835\udc66\ud835\udc43\ud835\udc67\ud835\udc43 and \ud835\udc5c\ud835\udc35 \u2212 \ud835\udc65\ud835\udc35\ud835\udc66\ud835\udc35\ud835\udc67\ud835\udc35, \ud835\udc43\ud835\udc56 can be described by \ud835\udc43\ud835\udc56 = \ud835\udc470\ud835\udc47\ud835\udc56\ud835\udc47\ud835\udf0f \u22121\ud835\udc470 \u22121\ud835\udc43\ud835\udf0f (14) We define [ \ud835\udc45\ud835\udc56 \ud835\udc5d\ud835\udc56 0 1 ] = \ud835\udc470\ud835\udc47\ud835\udc56\ud835\udc47\ud835\udf0f \u22121\ud835\udc470 \u22121 (15) According to the equivalent transformation of differential motion and (8), \ud835\udf06\ud835\udc62,\ud835\udc56 can be described by \ud835\udf06\ud835\udc62,\ud835\udc56 = [ \ud835\udc45\ud835\udc56 \ud835\udc47 \u2212\ud835\udc45\ud835\udc56 \ud835\udc47\ud835\udc46(\ud835\udc5d\ud835\udc56) 0 \ud835\udc45\ud835\udc56 \ud835\udc47 ] (16) where \ud835\udc46(\ud835\udc5d\ud835\udc56) is the antisymmetric matrix of \ud835\udc5d\ud835\udc56\uff0c \ud835\udc46(\ud835\udc5d\ud835\udc56) = [ 0 \u2212\ud835\udc5d\ud835\udc56\ud835\udc67 \ud835\udc5d\ud835\udc56\ud835\udc66 \ud835\udc5d\ud835\udc56\ud835\udc67 0 \u2212\ud835\udc5d\ud835\udc56\ud835\udc65 \u2212\ud835\udc5d\ud835\udc56\ud835\udc66 \ud835\udc5d\ud835\udc56\ud835\udc65 0 ] (17) Substituting (3), (8) and (9) into (7), the equation can be obtained by \ud835\udf0f = \ud835\udc3e \ud835\udc62 (18) where \ud835\udc3e = \u2211 \ud835\udf06\ud835\udc62,\ud835\udc56 \u22121\ud835\udc58\u2032\ud835\udc58\ud835\udc56\ud835\udf06\ud835\udc62,\ud835\udc56 3 \ud835\udc56=1 is the stiffness matrix of the parallel mechanism. 1083-4435 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. A. VS Test The VS mechanism is tested to verify the stiffness model by deflecting the end-effector while measuring the reaction force under different effective length of Ni-Ti rods. As shown in Fig. 6, the manipulator and the motion stage are fixed on a platform. A force sensor (Resolution: 2.5 mN , OMD-10-SE-10N, Optoforce Ltd.) is attached on the motion stage. The surgical tool of the manipulator keeps in touch with the top of the sensor. The manipulator is set as two types of stiffness states with \ud835\udc59\ud835\udc56 = 15 \ud835\udc5a\ud835\udc5a and 30 mm. In each state, the micro head was rotated to drive the end-effector of the manipulator (\ud835\udc48 ) at a step of 0.5 mm with a displacement along the direction perpendicular to the central axis of the manipulator for 5 times, together with respective reaction forces (\ud835\udf0f) recorded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000826_j.apm.2020.11.027-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000826_j.apm.2020.11.027-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the molten pool front model. (a) The simplified model of the molten pool in SLM. (b) Quarter ellipsoid shell model of molten pool front. (c) A segment of the interface between the rear and front part",
        "texts": [
            " Analytically calculated results are identical to the experimental and CFD (computational fluid dynamics) simulation ones. Through the predictive analysis using the proposed model, correlations between molten pool geometry and processing parameters are revealed. Further investigations demonstrate the potential of the model for providing an optimized process window of SLM. It is observed in experiments [15] and simulations [11] that there is a depression region at the laser spot, caused by recoil pressure. In the depression bottom, the molten pool can be divided into the front and the rear parts (Fig. 1a). The molten pool front is exposed to the laser beam while the rear part remains outside of the laser beam [16]. As a result, the molten pool front can be regarded as a control volume to study the heat balance without considering the complicated elongated shape of the molten pool rear. An analytical model is derived from the energy balance within the molten pool front, which is assumed In the quasi-stationary models [13, 17], the consideration of heat balance in the molten pool involves the following terms: the absorbed laser energy EL, the conducted energy to the surrounding solid EC, and the fusion latent heat of the newly melted metal EF",
            " 3 Total absorptivity of the molten pool front with varying molten pool geometries The flow of melted metal plays an important role in the formation of molten pool. The material is melted at the front, then flows to the rear part of molten pool, bringing the thermal energy and mass backward. In the analytical model, the molten pool front is considered as a control volume. The volume flow rate of liquid-state metal from the front to the rear of molten pool is ?\u0307? = \ud835\udf0b\ud835\udc4f\ud835\udc50 2 \ud835\udc63#(4) where v is the scanning speed of the laser beam. As shown in the interface between the front and the rear of the molten pool (Fig. 1 c), the temperature at the liquid-solid surface \u03a3in is the melting temperature Tm. At the outer surface of the molten pool wall, namely the gas-liquid surface \u03a3out, the liquid temperature is set to be approximately the boiling temperature Tb. The temperature of the outflow to the rear wall is assumed to be the average temperature of the two surfaces, namely (Tb + Tm) / 2. Thus, the difference between the inflow and outflow energy is \ud835\udc38out \u2212 \ud835\udc38in = ?\u0307?\ud835\udc50\ud835\udc5d\ud835\udf0c \ud835\udc47b + \ud835\udc47m 2 \u2212 ?\u0307?\ud835\udc50\ud835\udc5d\ud835\udf0c\ud835\udc47m = \ud835\udf0b\ud835\udc4f\ud835\udc50 2 \ud835\udc63\ud835\udc50\ud835\udc5d\ud835\udf0c \ud835\udc47b \u2212 \ud835\udc47m 2 #(5) where  is the density, and cp is the specific heat of the material",
            " Following the Fourier\u2019s law, the total amount of heat conduction EC is determined by calculating the temperature gradient at the interface between the solid zone and the molten pool front \u03a3in \ud835\udc38C = \u222b \ud835\udf15\ud835\udc47 \ud835\udf15\ud835\udc5b \u22c5 \ud835\udf05\ud835\udc51\ud835\udc46 \ud835\udef4in #(7) where  is the coefficient of heat conduction at Tm. The temperature gradient along the interface is assumed uniform and the thickness of the molten pool front is also considered constant. Under these assumptions, the conducted heat is mainly influenced by the heat conductivity, the surface area of the molten pool front wall, and the temperature gradient perpendicular to the interface. Therefore, the result of the 1-D heat conduction equation is applied to calculate the temperature gradient approximately. As shown in Fig. 1c, the z-axis along the molten pool thickness is introduced. Then the inner and outer surfaces are expressed as z = 0 and z = z0, respectively. The temperature is a function of z. For the 1-D thermal problem, the temperature distribution is [23]. \ud835\udc47(\ud835\udc67) = (\ud835\udc47b \u2212 \ud835\udc470)erfc ( \ud835\udc67 2\u221a\ud835\udc37\ud835\udc610 ) + \ud835\udc470#(8) where Tb and Tm are the temperatures of the inner and outer surfaces of the molten pool front wall respectively, and T0 is the temperature at z = \u221e, namely the ambient temperature. The function erfc represents the complementary error function",
            " Considering the physical features in the MED zone, the present model works well to give a prediction of molten pool dimensions. Since the keyhole induced pores and lack of fusion are the defects to avoid in the SLM process [4], the inaccuracy of the model in the LED and HED zones is outweighed by the high efficiency and extensive applicability of the present model. It is proved to be a powerful and practical tool to predict the molten pool dimensions and evaluate the process quality. The shape of the molten track cross-section, namely the b-c plane (Fig. 1), plays a critical role in the layer-layer and track-track overlapping between molten pool boundaries [33]. Three typical parameter combinations from LED, MED, and HED zones respectively are chosen to investigate the molten pool shape features under different energy density levels, corresponding to Tracks 15, 5, and 24. The molten pool dimensions of the three tracks are listed in Table 3. In Fig. 14, the cross-section molten pool boundaries are outlined based on the single-track SLM experiments and analytical model, respectively",
            "4 m/s 88.4 107.3 105.5 17.8 41.2 35.9 250 W, 1 m/s 161.8 146.2 151.9 130.9 144.6 137.0 200 W, 0.32 m/s 241.5 188.2 198.7 319.9 306.9 224.8 Table 3. Molten pool dimensions from experiments, numerical simulations and analytical predictions. Fig. 14 Experimental (solid lines) and predicted (hidden lines) molten pool outlines, and SLM processing conditions are (a) 50 W, 0.4 m/s (LED). (b) 250 W, 1 m/s (MED). (c) 200 W, 0.32 m/s (HED) The longitudinal-section shape of the molten pool, namely the a-c plane (Fig. 1), plays a less important role in the determination of the final quality of SLM processed products. However, the longitudinal-section shape contributes to the understanding of the physical mechanisms in SLM and justify the assumptions in the present analytical model. The information in longitudinal-section is covered in single-track SLM experiments and it is difficult to physically capture the local geometry experimentally due to the small temporal and spatial scale. As a consequence, the numerical simulation results are used to study the longitudinal-section behavior of the molten pool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003565_tie.2003.817488-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003565_tie.2003.817488-Figure5-1.png",
        "caption": "Fig. 5. Color bars and parameters.",
        "texts": [
            " These targets are found by DINDs, but since it is difficult to match the blobs found correctly, further clues are required to identify each target. For this, color bars, located under the targets, are utilized. The color bars consist of several colored fields. Each of the fields can have one TABLE I CAMERA A, ROBOT DIRECTION = 0 TABLE II CAMERA B, ROBOT DIRECTION = 0 of eight predefined colors. With this technique, we are able to distinguish the mobile robots and localize the robot by considering the relationship shown in Fig. 5. There are some other methods for localizing the mobile robots with camera sensors. The best way is to localize the mobile robots without adding any artificial equipment to the robots. However, to achieve a highly robust system, we decided to adopt color bars. A tradeoff relationship exists between using additive equipment and the ro- bustness of the system. However, in this case, we have many advantages, such as the identification of mobile robots, highprecision positioning, etc., using energy-free passive equipment only",
            " From this process, the DIND is also able to recognize which robot it is. The geometrical relationships, stored in the database, are compared between the color codes, and the pose of the robot is generated. The pose of the robot is calculated from the pairs of color codes with the same time stamp. The pose of a robot is estimated from the geometrical relationship, if at least one pair is recognized. Below are the equations used to estimate the position and orientation of a robot. The parameters are described in Fig. 5 (2) (3) (4) (5) (6) (7) where ( , , ) is the pose of the robot and ( , ) is the position of the color bar ( ). Actually, there exist six possible pairs in four color bars. However, only four pairs are utilized in the system, due to the empirical decision-making process. 2) Mobile Robot Control With DIND: The mobile robot control module produces control input for the mobile robots. A DIND senses mobile robots, and a vision server module estimates its pose. According to the desired path and the estimated pose, the control inputs for the mobile robots are generated and transferred to the mobile robots through wireless LAN (IEEE 802"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003486_robot.1996.509284-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003486_robot.1996.509284-Figure9-1.png",
        "caption": "Figure 9: The 2-type 2-1-type 1 mechanism",
        "texts": [
            " Using the notation of the figure we may write two equations stating that points B1, Bz are at distance T I , rz from A I , Az: 2-type 1 and 1 type 2 z2 + y 2 = r: (5) (z + ccos4 - u ) ~ + (y + csin4)' = ri (6) Then we write that point Bg should be on the line going through As(u1, w1) with unit vector v('uz, wy): (z + a cos(4 + a ) - ul)wY - (y + a sin(++ a ) - q ) w Z = O (7) crank A I B ~ B ~ B z I A ~ . The coupler curve described by B2 is a sextic with full circularity [3] meaning that the number of real intersection points of the coupler curve with the circle described by B:! when it rotates around A2 is at most 6. Every intersection point defines a solution for the (direct kinematics of the mechanism. Therefore we have effectively computed a minimal order polynomial. 2.3.3 This mechanism is presented in figure 9. Here we as%type 21 and 1 type 1 Equations (6)-(5) and (7) are linear in z ,y . Their values are computed and substituted in equation ( 5 ) , leading to an equation in cos 4, sin 4. A.fter substitution of the sine and cosine by their values as function of T = tan(4/2) we get a 6-order polynomial in T , which enables to compute the solution of the direct kinematics. 2.3.2 This mechanism is presented in figure 8. In that c,ase 2-type 1 and 1 type 3 equations (5),(6) are still valid but the third equation is obtained by writing that for given x,y,+ the line going through Bs, whose axis is the prismatic joint axis, meet As: (x + acos(q5 + a ) - U I ) sin(4 + a + a3) - (y + asin($ + a ) - VI) cos(4 + a + ~ 3 ) = O(8) where a3 is the angle between B1 Bs and the prismatic joint axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001207_tec.2021.3056557-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001207_tec.2021.3056557-Figure12-1.png",
        "caption": "Fig. 12. Experimental setup of subject PMSM drive system at UBC lab.",
        "texts": [
            "org/publications_standards/publications/rights/index.html for more information. The performance of the proposed HCC is depicted in Fig. 11, wherein it can be seen that the harmonic current magnitudes track the references very well in steady state and during transient. V. EXPERIMENTAL RESULTS In this section, the proposed method is validated experimentally on a PMSM with large cogging torque and nonsinusoidal back EMF. The parameters of the machine and all controllers are summarized in the Appendix B and C. The experimental setup is shown in Fig. 12, which includes a twolevel VSI, a torque transducer, and a dynamometer. The DSP TMS320F28377D has been used in all experiments to carry out all computations related to the proposed control methodology and SV-PWM operation, where the sampling frequency and the inverter switching frequency were set to 10 kHz. The considered sampling frequency also limits the highest current harmonic that can be considered by the proposed HCC filter (i.e. up to half of the sampling frequency. The performance of the proposed method is evaluated in steady state and during transients"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.28-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.28-1.png",
        "caption": "Fig. 7.28: Snap Fastener with a Beam as Elastic Support",
        "texts": [
            " The system of nonlinear equations has then the dimension IR6+3n, where n is the number of contacts n = 1, 2 or 3. The transformation into the gripper system is rather simple:( Gf Gm ) = AGL ( LfN +L fR LrGP \u00d7 (LfN +L fR) ) . (7.102) The determination of the stiffness matrix K is still missing. It represents the compliances of the parts. The elastic support might consist of a beam (Figures 7.26 and 7.28) or a plate (Figure 7.30). We apply beam and plate theory, respectively. In a first step we regard the snap fastener from Figure 7.28. According to the picture the displacement in the xA (wx) and yA (wy) direction and the twist around the xA (\u03d5x) and zA (\u03d5z) axes are constrained. The stiffness in these directions would be very high compared to the other elements of K, therefore generating approximately zeros in the first, second, fourth and sixth rows and columns. From beam theory (BERNOULLI\u2013beam) the deflection curve is derived from the following differential equation: EIy(x)w\u2032\u2032\u2032 z (x) = \u2212Fz , Iy(x) = 1 12 (a + x l (b\u2212 a))3c. (7.103) The parameters a, b, c and l can be seen from Figure 7.28, and E is the modulus of elasticity. Integrating equation (7.103) three times and using the boundary conditions wz(0) = 0, w\u2032 z(0) = 0 and EIy(l)w\u2032\u2032 z (l) = \u2212My, yields a relationship between the displacement wz and the twisting angle \u03d5y (\u03d5y = \u2212w\u2032 z(l)) of the beam and the force Fz and the moment My. With a = 5mm, b = 2.7mm, c = 20mm, l = 40mm and E = 2700N/mm2 we obtain the following stiffness relationship Fx Fy Fz Mx My Mz  =  0 0 0 0 0 0 0 0 0 0 0 0 0 0 45.5 0 638.8 0 0 0 0 0 0 0 0 0 638.8 0 14285.4 0 0 0 0 0 0 0   wx wy wz \u03d5x \u03d5y \u03d5z  . (7.104) Our model is verified by a comparison of measurements and calculations. Measurements were made using again the single axis force measurement machine. Figure 7.29 shows the force vs. distance for the insertion of the upper half of the snap fastener from Figure 7.28. Fx is the force in the direction of insertion, and Fz acts perpendicularly. When mating the complete fitting with both parts, Fx becomes twice as large, and Fz disappears because of symmetry. 7.3 Dynamics and Control of Assembly Processes with Robots 463 Our second example is a snap fastener with a plate as elastic support from Figure 7.30. Here the displacement in the xA (wx) and yA (wy) direction and the twist around the zA (\u03d5z) axes are constrained. ThereforeK contains zeros in the first, second and sixth rows and columns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000486_j.ymssp.2019.04.056-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000486_j.ymssp.2019.04.056-Figure1-1.png",
        "caption": "Fig. 1. Diagram of the proposed dynamic model: (a) 4-DOF dynamic model of the deep groove ball bearing in Cartesian coordinate system; (b) relative motion between the inner and outer rings in radial plane and the contact deformation between the rolling elements and the raceways.",
        "texts": [
            " Cui and Zhang [42] used the depth and width of the defect area on the bearing cross-section to calculate the deformation of rolling element, and found that the double impact phenomenon is related to the size of the defect. The above studies calculated the change in contact force based on the different positions of the rolling element in the defect area. Although some of the authors considered the three-dimensional geometric relationship between the rolling elements and the defect area, the curvatures of the defect edges were ignored. Fig. 1(a) shows the 4-DOF dynamic model of the deep groove ball bearing in Cartesian coordinate system. The model is based on the model developed by Petersen and Howard [21]. The inner and outer rings are assumed to be firmly fitted to the shaft and the bearing pedestal, respectively. The total mass of the outer ring and the bearing pedestal is mo, the total mass of the inner ring, shaft and rotor is mi. The mass and the inertia of the rolling element are ignored. The displacements of the outer and inner ring in the horizontal and vertical directions are (xo(t), yo(t)) and (xi(t), yi(t))",
            " ; N \u00f01\u00de where ub(t) is the cage angular position; N is the number of the rolling elements; xb is the nominal rotational speed of the cage and given by xb \u00bc xi 2 1 dbcosa dm ; dm \u00bc 1 2 \u00f0di \u00fe do\u00de \u00f02\u00de where xi is the rotational speed of the shaft; db is the diameter of the rolling element; a is the contact angle; dm is the pitch diameter of the bearing; di and do are the inner and outer diameters of the bearing, respectively. A static radial load W is applied to the shaft in negative direction of the y-axis. Fig. 1(b) shows the relative motion between the inner and outer rings in radial plane and the contact deformation between the rolling elements and the raceways. According to the Hertzian contact theory, the total load-deflection constant between the rolling elements and the raceways can be calculated by [43] K \u00bc 1 \u00bd\u00f01=ki\u00de1=n \u00fe \u00f01=ko\u00de1=n n \u00f03\u00de where ki and ko are the contact stiffness between the rolling element and the inner/outer raceway, respectively; n is the loaddeflection exponent, n = 3/2 for ball bearings and n = 10/9 for roller bearings",
            " Fig. 15(a)\u2013(e) presents the dynamic contact forces between the rolling elements and the raceways at a lower rotational speed. In order to facilitate the analysis, the rotational speed of the cage is set to xb = 30 rpm (fi = 0.5 Hz), because the lower rotational speed can make the dynamic contact force change slowly, and reduce the vibration response of the bearing system. Fig. 15(a) shows the dynamic contact forces between the adjacent three rolling elements (No. 4, 5 and 6 rolling element in Fig. 1(b)) and the raceways of a healthy bearing. The contact force in the unload zone is zero and the maximum contact force occurs at the center of the load zone. When the contact force of No. 5 rolling element reaches the maximum, the contact force of the No. 4 rolling element is equal to No. 6. During the rotation of the shaft, the contact force of the rolling element changes periodically, and resulting in the varying compliance vibration of the bearing. Fig. 15(b)\u2013(e) shows the dynamic contact forces between the adjacent three rolling elements and the raceways with different sizes of localized defect (on outer raceway)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000794_tsmc.2020.3004659-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000794_tsmc.2020.3004659-Figure2-1.png",
        "caption": "Fig. 2. Mobile manipulator used as the test bed.",
        "texts": [
            " Step 3: Design the actual NN-based adaptive control input (24) and the adaptation laws \u02d9\u0302\u03c1h(t) in the form of (25) and \u02d9\u0302 \u03b8 in the form of (27). a) Choose suitable Qi, i \u2208 S according to Theorem 1. b) Select suitable parameters k > 0 and \u03b7 > 0 and choose \u03bd and \u03b4(t) to obtain the control input (24). c) Choose suitable scalars \u03b3q\u03b8 , \u03c3q\u03b8 > 0, \u03b3h\u03c1 > 0, and \u03c3h\u03c1 > 0, (h = 1, . . . ,m) to determine the adaptation laws (25) and \u02d9\u0302 \u03b8 (27). IV. SIMULATION RESULT In this section, the results of the simulations studies carried out on a mobile manipulator (see Fig. 2) with hybrid joints are presented to illustrate the effectiveness of the proposed approach. The dynamics of the mobile manipulator is described as follows: M(q)q\u0308 + V(q, q\u0307)q\u0307 + G(q)+ d(t) = B(q)\u03c4. (57) It is to be noted that the hybrid joints can be switched to either active (actuated) or passive (underactuated) mode as needed. The system therefore switches stochastically between active and passive systems. An increased effort thus needs to be made in the design of this manipulator to guarantee stability and robustness under joint switching"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure10.74-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure10.74-1.png",
        "caption": "Fig. 10.74 Wheels with attached parts having a closed edge and open edge. Reproduced from Ref. [75] with the permission of JSAE",
        "texts": [
            "10 Acoustic Cavity Noise of Tires 653 The direction and frequency of excitation change for a rolling tire as shown in Fig. 10.73. The natural mode is thus dispersed across a wide range of frequencies, and the effect of the new wheel is equivalent to a large damping effect. (1-2) Validation Equation (10.110) shows that the dispersion of frequency increases by increasing the coefficients related to sin 2h or cos 2h, r c2, r s2, A c2 and A s2. The parts of the new wheel are located symmetrically on the opposite side of the rim as shown in Fig. 10.74. Figure 10.74a, b, respectively, corresponds to the wheel with attached parts having a closed edge and the wheel with attached parts having an open edge. There are variations in r and A in the circumferential direction of the wheel with the closed edge but not for the wheel with an open edge. Figure 10.75 shows the vehicle interior noise measured at 50 km/h in a drum test. The wheel with the closed edge is effective in terms of reducing the cavity resonance noise, whereas the wheel with the open edge is not effective"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000520_j.addma.2019.100808-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000520_j.addma.2019.100808-Figure1-1.png",
        "caption": "Fig. 1. Dimensions of the deposit and substrate. The clamps position and the four lines along which calculated data are extracted are shown. Line 1 and 2 are on the top surface of the deposit. Line 3 and 4 are at the substrate-deposit interface where the data for warping and delamination are examined. The measuring points of von Mises stress (P1 and P2) using the hole drilling method are also shown.",
        "texts": [
            " Deposition patterns for the rectangular components with (a) long deposition pattern, (b) short deposition pattern and (c) spiral deposition pattern, and the corresponding morphology of the Ti-6Al-4V components deposited by (d) long deposition pattern, (e) short deposition pattern and (f) spiral deposition pattern. consists of a computer numerical control (CNC) table with three degrees of freedom (x, y and z), a chamber filled with argon, a gas tungsten arc welding (GTAW) equipment and a wire feeder [13]. Since the deposits are rectangular in shape, rectangular substrates are used for convenience. The detailed dimensions of the deposit and substrate are shown in Fig. 1. The hot rolled substrate of same material as the feeding wire was mechanically polished before use. The substrate was restricted with four clamps at the four corners during the deposition process, as indicated in Fig. 1. The deposition parameters are listed in Table 1. Three rectangular deposits of the same size were fabricated using three different deposition patterns, long, short and spiral patterns. The schematic for the three deposition patterns are shown in Fig. 2 (a\u2013c). For long deposition pattern, the scanning direction was along the longer side of the rectangular deposit as shown in Fig. 2(a). However, the scanning direction was reversed between two successive hatches. For short deposition pattern, the scanning direction was along the shorter side of the rectangular deposit as shown in Fig",
            " The figures show that these deposits were successfully fabricated with no discontinuity, humps or splash around the corners. The contour of the component fabricated using long deposition pattern has undulations along the shorter sides of the deposit (Fig. 2d). In contrast, undulations are found along the longer sides in the component printed using short raster pattern (Fig. 2e). The component deposited using spiral pattern (Fig. 2f) has a relatively smoother contour than the other two patterns. The residual stresses were measured using hole drilling method [14] at two locations (P1 and P2 in Fig. 1) on the top surface of the deposits at the end of the deposition process after the removal of clamps. Two holes with a diameter and depth of 1.5 mm and 2mm respectively were drilled at the two specified locations. Three-element gauges were positioned around the hole to measure the strains based on which residual stresses were calculated. Although the experiments provided local values of strains and residual stresses, these measurements do not provide the 3D distribution of residual stresses in the components",
            " The flow stress and plastic strain with temperature-dependent plasticity were calculated using the von Mises yield criterion [27]. The thermal strain was computed with the temperature-dependent coefficient of thermal expansion [26]. \u0394\u03b5Tr was neglected in this model for simplicity. Calculations of residual stresses and distortion were also performed using the finite element based software Abaqus [22]. The substrate was restricted with four clamps at the four corners of the substrate as shown in Fig. 1. Therefore, the boundary conditions for the mechanical model was applied by constraining the movements of the nodes under the four clamps. When the printing was done and the substrate cooled down to the room temperature, clamp removal was simulated by deactivating the constraints from these nodes. To investigate the effects of transient temperature fields on the evolution of stresses during the deposition and cooling process, the Ti6Al-4V component fabricated using long deposition pattern is selected as an example",
            " 4 and 5 it is evident that the residual stresses and distortion evolve depending on the transient temperature field and are largely controlled by the deposition pattern. Therefore, the stresses of Ti-6Al-4V components printed using three different deposition patterns are compared below. To compare the x-component of residual stresses for three deposition patterns, variations in temperature and resulting stress evolutions have been investigated during the cooling process. Fig. 6 (a\u2013f) show the variations in temperature and x-component of stresses along line 1 (Fig. 1) at different time during cooling of Ti-6Al-4V components fabricated using three deposition patterns. For the deposit fabricated using short deposition pattern, change in temperature along line 1 (Fig. 6 b) during cooling is very less which results in low residual stresses in the component (Fig. 6 e). However, for the component made using long deposition pattern, largest change in temperature (\u0394T) is observed near the long edge of the deposit where the last hatch is deposited as shown in Fig. 6 (a)",
            " This large variation in temperature during cooling results in sharp change [28] in residual stresses (\u0394 \u03c3) at the same location as shown in Fig. 6 (d). For the spiral deposition pattern, the region near the center of the deposit cools down to the room temperature at the end. Therefore, the largest change in temperature (\u0394T) is observed at the mid-length of line 1 as shown in Fig. 6 (c). This large variation in temperature results in sharp change in residual stresses (\u0394 \u03c3) at the same location as shown in Fig. 6 (f). Fig. 7 shows the variations in temperature and y-component of stresses along line 2 (Fig. 1) at different time during cooling for the components fabricated using three deposition patterns. For the deposit fabricated using the long deposition pattern, change in temperature along line 2 (Fig. 7 a) during cooling is very less. Therefore, there is no significant change in the stress field during the cooling as shown in Fig. 7 (d). However, sudden change of stresses from tensile to compressive occurs due to the removal of the clamps as explained before. For the component made using short deposition pattern, largest change in temperature (\u0394T) is observed near the short edge of the deposit where the last hatch is deposited as shown in Fig",
            " For the spiral deposition pattern, the region near the center of the deposit cools down to the room temperature at the end. Therefore, the largest change in temperature is observed near the mid-length of line 2 as shown in Fig. 7 (c). This large variation in temperature results in sharp change in residual stresses at the same location as shown in Fig. 7 (f). The aforementioned calculated stress results show fair agreement with the experimental measurements. For example, Fig. 8 shows that the calculated Mises residual stresses along line 2 (Fig. 1) agree with the corresponding experimental results for Ti-6Al-4V deposits printed using the three deposition patterns. The slight mismatch between the computed and experimental results is primarily caused by the measurement error of hole drilling method and the assumptions made in the thermomechanical model. It is evident from the figure that along the same line the residual stresses can be significantly different depending on the deposition pattern used. These differences can be more pronounced for various alloy systems with different thermo-physical and mechanical properties",
            " In addition, for both alloys, the deposits with spiral pattern (Fig. 10 c and f) have the highest stresses values compared to the other depositions. Delamination of the component mainly depends on the stresses (\u03c3) at the substrate-deposit interface and the yield stress (Y) of the alloy at room temperature. A delamination index, d*, is proposed here to evaluate the susceptibility to delamination of WAAM components and is expressed as: d* = \u03c3/Y (2) For both the alloys, two lines (line 3 and 4 as indicated in Fig. 1) are selected at the substrate-deposit interface to study the influence of different deposition patterns on delamination of the components. Stress components along x and y directions are considered to calculate the delamination index along line 3 and 4, respectively. Fig. 11 (a\u2013f) show that for a particular pattern, the stress distributions for both alloys are similar. However, the magnitudes of stresses are different because of the dissimilar mechanical properties of the two alloys. Fig. 11 (g\u2013l) shows the corresponding delamination index for both the alloys along line 3 and 4 respectively",
            " However, the room-temperature yield strength of Ti-6Al-4V is around 3 times higher than that of IN 718. Therefore, Ti-6Al-4V is less susceptible to delamination than IN 718 for a given set of processing conditions. Warping of the components primarily depends on the vertical deformation (uz) of the component and the substrate thickness (d). A warping index, w*, is proposed here to evaluate the susceptibility to warping for AM components and is expressed as: w* = uz / d (3) Fig. 12 shows the warping index along line 4 (Fig. 1) for the components fabricated with three deposition patterns under the same processing conditions for both alloys. It can be found that in the substratedeposit interface, the warping is similar for both alloys with a certain deposition pattern, which can be attributed to the similar molten pool size of the two alloys (Fig. 3). For both alloys, the warping of the deposits with long and spiral deposition patterns is higher than that with short deposition pattern. Since shorter tracks shrink less during cooling, the component fabricated with short deposition pattern exhibits the least deformation and warping among the three deposition patterns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure10-1.png",
        "caption": "Fig. 10. Illustration of cross-profiles of profile-crowned helicoids.",
        "texts": [
            " The pinion profile-crowned tooth surface in this case may be represented as Rr\u00f0hc;wr\u00de \u00bc rr\u00f0uc\u00f0hc;wr\u00de; hc;wr\u00de: \u00f021\u00de Two profile-crowned helicoids are considered. The concept of the meshing is based on the following considerations discussed in [5\u20137,13]: (1) The helicoids transform rotation between parallel axes. (2) The helicoid tooth surfaces are in point contact and this is achieved by the modification of the cross- profile of the pinion tooth surface. This statement is illustrated for the example in Fig. 10 wherein an involute helicoid of the gear and pinion modified helicoid are shown. Profile crowning of the pinion is provided because the cross-profile is deviated from the involute profile. The gear and the pinion tooth surfaces are in point contact provided by mismatched crossed profiles. (3) The formation of each of the mating helicoids may be represented as the result of screw motion of the cross-profile. Fig. 11 shows the formation of a helicoid by a family of planar curves that perform a screw motion about the axis of the helicoid. (4) The screw parameters p1 and p2 of the profile-crowned helicoids have to be related as p1 p2 \u00bc x\u00f02\u00de x\u00f01\u00de ; \u00f022\u00de where x\u00f0i\u00de (i \u00bc 1; 2) is the angular velocity of the helicoid. (5) The common normal to the cross-profiles at point M of tangency of profiles passes through point I of tangency of the centrodes (Fig. 10). (6) It is easy to verify that during the process of meshing, point M of tangency of cross-profiles performs in the fixed coordinate system a translational motion along a straight line that passes through M and is parallel to the axes of aligned gears. The motion of a contact point along line M\u2013M may be represented by two components: (i) transfer motion with gear i (i \u00bc 1; 2) that is performed as rotation about the gear axis. (ii) relative motion with respect to the helicoid surface that is a screw motion with parameter pi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001002_s00170-021-06785-1-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001002_s00170-021-06785-1-Figure1-1.png",
        "caption": "Fig. 1 Solid model coordinate system with filament pathing output from Markforged Eiger software. Through the z-direction, the sample will be built up in layers with xy layers constructed of \u201cshell\u201d pathing surrounding the + or \u2212 45\u00b0 infill pathing",
        "texts": [
            " Sections of material were also taken from each face of a printed part to quantify build variability by measuring porosity, grain size, and nanoindentation hardness and stiffness. The influence of nano-scale variation on bulk properties will be discussed. Samples in this study were produced on a Markforged Metal X printer using their Atomic Diffusion Additive Manufacturing (ADAM) process [19]. The process uses a proprietary polymer/wax/metal filament pathed in a series of concentric shells with an infill alternating at positive and negative 45\u00b0 angles to the x or y axis to make up the remainder of the volume (Fig. 1). Accordingly, if the sample dimension in the xy plane is smaller than the shell thickness, then the sample will be built of all shells (without infill). An illustration of the print build coordinate system and pathing output is shown in Fig. 1. The Metal X system will build samples with this pathing arrangement by default expanding the desired sample geometry by 20% to accommodate sample shrinkage after sintering. Samples are optionally printed atop a flat build of material called a \u201craft\u201d so that in the sintering process any frictional or thermal cooling forces are equal in both in-plane directions. If a raft is used, a layer of 0 and then 90\u00b0 infill is used by default before pathing alternating positive and negative 45\u00b0 infill for the remainder of the volume. The raft is separated from the intended part with a thin layer of sacrificial ceramic. The angle of the infill path is measured with respect to the build plate for which parts were aligned along the longest axis of the build, for example in Fig. 1 the angle would be measured with respect to the x axis. After the sample has been printed, it is designated \u201cgreen\u201d and is placed in a bath of Opteon for a minimum of 6 h to remove wax; after the removal, the part is designated \u201cbrown.\u201d Brown samples were found to lose 4.15% (Cv = 0.25%) of their mass in this study after washing. To complete the manufacturing process, brown samples were sintered in a tube furnace for 26 h according to a sintering profile designated by Markforged simply noted as typical for 17-4 SS",
            " In general, the microstructure is comparable with what one would expect for commercially available 17-4PH stainless steel that has undergone heat treatment [23]. \u00d72.5 magnification images of the inspected faces showed little \u201cvisible to the eye\u201d porosity on the xy (Fig. 11) and xz faces (which were very similar) while the yz face showed a regular and repeating pattern. The pattern on the yz face is a result of the 45\u00b0 to orthogonal orientation of the printing filament to that plane which can be visualized in Fig. 1 or 9. This filament-packing phenomenon is similar to FDM methods and is part of what leads to lower strength and stiffness when loaded in the y or z direction (T5) compared with x (T4). If the material were cut along the extrusion direction intersecting the repeating pattern, the observer might expect to see channels that extend the length of the part along the filament extrusion path. \u00d720magnification images were processed by conversion to grayscale (0\u2013255 black to white intensity) with porosity defined at a threshold of <145\u2013155 intensity (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure4.5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure4.5-1.png",
        "caption": "Fig. 4.5: Pressure drop in an orifice",
        "texts": [
            " In this case it is necessary to verify the validity of the assumption p\u0304 > 0 because the bilateral constraint alone does not prevent negative values of p\u0304. 4.2 Modeling Hydraulic Components 193 In the following we shall give some examples of modelling elementary valves and more complex valves as a network of basic components. Physically, any valve is a kind of controllable constraint, wether the working element be a flapper, ball, needle or the like. Orifices with variable areas are used to control the flow in hydraulic systems by changing the orifice area. As illustrated in Figure 4.5 the pressure drop in an orifice shows a nonlinear behavior. The classical model to calculate the pressure drop \u2206p in dependency of the area AV and the flow rate Q is the Bernoulli equation. \u2206p = \u03c1 2 ( 1 \u03b1AV )2 Q |Q| (4.12) The factor \u03b1 is an empirical magnitude with regard to geometry- and Reynoldsnumber-depending pressure losses. It must be determined experimentally. As long as the valve is open the pressure drop can be calculated as a function of the flow rate and the valve area, eq. 4.12. As shown in Figure 4.5 the characteristic becomes infinitely steep when the valve closes. In most commercial simulation programmes this leads to numerical ill-posedness and stiff differential equations for very small areas. In order to avoid such numerical problems the characteristic for the pressure drop of closed valves can be replaced by a simple constraint equation: Q = Av = 0, or Av\u0307 = 0. (4.13) This constraint has to be added to the system equations when the valve closes. In the case of valve opening it has to be removed again"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003544_jra.1987.1087145-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003544_jra.1987.1087145-Figure7-1.png",
        "caption": "Fig. 7. Scemi robot.",
        "texts": [
            " By \u201cgeneral robot\u201d we mean that all the geometric and inertial parameters are supposed general except q l , dl, c q , and qn which are considered equal to zero (recall that this definition of frame 0 and frame n can be done for any robot). Note that if we had used the same symbolic procedure with the classical Denavit and Hartenberg notation, the number of WPli.XXi+DV23i.PISli+U21i.XZi- U3li.XYi+(DV33i-DV22i).YZi WP2i.YYi+DV13i.PIS2i+ U32i.XYi- Ul2i.YZi+(DVlli-DV33i).XZi WP3i.ZZi+DV12i.PIS3i+ U13i.YZi- U23i.XZi+(DV22i-DVlli).XYi KHALIL AND KLEINFINGER: DYNAMIC MODELS OF TREE STRUCTURE ROBOTS 523 TABLE I11 Robot General Robot Stanford TH8 (Fig. 6) SCEMI (Fig. 7) Method Operation n d.0.f n = 6 General Simplified\" General Simplified\" General Simplified\" Luh [8] Kane [ I l l b Renaud [ 121 Horak [23] Vukobratovic [ 131 The without given regrouping methodd with *** regrouping multiplication addition multiplication addition multiplication addition multiplication addition multiplication addition multiplication addition, multiplication addition 137n - 22 lOln - 11 not given not given not given not given lOln - 129 90n - 118 lOln - 129 90n - 118 800 800 8 0 595 ' 595 595 646 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003486_robot.1996.509284-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003486_robot.1996.509284-Figure3-1.png",
        "caption": "Figure 3: The equivalent chain for a. BPR chain",
        "texts": [
            " Hence the remaining link (attached at M and a t the revolute joint of the moving platform) can only turn around the revolute joint at M . Therefore this chain can be substituted by the chain of type 1. Clearly every chain whose free joints (the joints which are not actuated) are of the revolute type can be substit,uted by a type 1 chain. Consider now the chain BPR: when the first :revolute joint is locked point B can only trainslate alon,g the line D parallel to the prismatic actuator axis while the moving platform can rotate around the joint at B (figure 3). Consequently this chain can be substituted by a type 2 kinematic chain. Clearly every chain whose free joints are prismatic and revolute (in this order, starting from the ground) can be substituted by a type 2 chain. Finally consider the chain REP: .when the prismatic joint is locked point B can rotate around A and translate along the prismatic joint axis, but the angle between this axis and the platform should remain constant (figure 4). Hence this chain can be substituted by a type 3 chain. Clearly every chain whose free joints are revolute and prismatic (in this order, starting from the ground) can be substituted by a type 3 chain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000048_j.rser.2016.09.042-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000048_j.rser.2016.09.042-Figure5-1.png",
        "caption": "Fig. 5. (a) The working principle of fuel cell components in alcohol tester; (b) BACtrack (a kind of alcohol tester) connected to a phone [73].",
        "texts": [
            "75 mmol/L and varies in a linear fashion between the response current. The enzyme electrode does not interfere with ascorbic and uric acids present in the system or matter with other electrically active material exhibiting a stable behavior. The proposed cell is simple and easy to operate while also not time consuming, overall a reliable detection method for blood glucose to meet clinical needs. In addition, fuel cell has been applied for the purpose of breath alcohol tester [71]. The core elements of the fuel cell sensor [72] (as illustrated in Fig. 5a), consist of two platinum electrodes and porous acid electrolyte interlayers. The alcohol in exhaled air gets oxidized to acetic acid and water through the fuel cell, generating a voltage proportional to the concentration of alcohol. A commercial alcohol tester named BACtrack (blood alcohol content (BAC)) is due to hit the market, with technologically compatible features since it can be combined with smart phones via Bluetooth [73] (as shown in Fig. 5b). This product can not only test the user whether it is safe to drive a car but also indicates how long would brain with platinum as catalyst; (b)The integrated multi-scale biofuel cells [63]. it take to clear from alcohol. Therefore, it is anticipated to have broad market prospects. At present, fuel cells can be also used to measure the oxygen concentration of mixed gas from respirator in clinic. Thus, they were called as medical oxygen battery or oxygen sensors [74]. Such fuel cells will be installed between the suction sides of the patient containing an empty oxygen mixer with oxygen as the oxidant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure14-1.png",
        "caption": "Fig. 14. The configuration with three independent open-chains.",
        "texts": [
            " The two sub-chains constraint-screw systems can be derived as follows: S r l1 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 11 = ( 0 , 0 , 0 , 0 , 1 , 0 ) T S r 12 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 13 = ( 0 , 0 , 1 , c, 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 21 = ( 0 , 0 , 0 , 0 , 1 , 0 ) T S r 22 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 23 = ( 0 , 0 , 1 , \u2212c, 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad (15) where c is the length of OO 1 in the Y-axis. According to Eqs. (9) and (10) , card \u3008 S r \u3009 = 6 , dim S r = 4 . Thus, the rank is changed, and the configuration with parametric constraints \u03b1 = \u2212\u03c0/ 2 , \u03b2 = \u2212\u03c0/ 2 is singular. Hence, the mobility is m = 8 \u2212 6 \u00d7 1 + 6 \u2212 4 = 4 , the mechanism has four DOFs in this singular configuration. As illustrated in Fig. 14 , axes of joints E, F, G, and H are collinear, while axes of joints B 1 , B 2, and B 3 , B 4 are collinear, respectively. The configuration can also be described as a mechanism with three independent open-chains. A global coordinate frame O-XYZ is set up as shown in Fig. 14 . Based on the above assumption, the number of independent loops l is 1. The corresponding constraint-screw multiset can be derived as follows: S r l1 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 11 = ( 0 , 0 , 0 , 0 , 1 , 0 ) T S r 12 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 13 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 14 = ( 0 , 0 , 1 , d, 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 21 = ( 0 , 0 , 0 , 0 , 1 , 0 ) T S r 22 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 23 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 24 = ( 0 , 0 , 1 , \u2212d, 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad (16) where d is the length of O O in the Y-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000486_j.ymssp.2019.04.056-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000486_j.ymssp.2019.04.056-Figure7-1.png",
        "caption": "Fig. 7. (a) con",
        "texts": [
            " The relative displacement under the condition of type 2 can be described by lze2\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bduj\u00f0t\u00de ud1 q ro \u00fe rocos\u00bduj\u00f0t\u00de ud1 \u00f0ud1 6 uj\u00f0t\u00de < uj1\u00de lze2\u00f0t\u00de \u00bc lrs max \u00f0uj1 6 uj\u00f0t\u00de 6 uj2\u00de lze2\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bdud2 uj\u00f0t\u00de q ro \u00fe rocos\u00bdud2 uj\u00f0t\u00de \u00f0uj2 < uj\u00f0t\u00de 6 ud2\u00de 8>>< >>: \u00f016\u00de Diagram of the relative displacement of rolling element moving towards the bottom of defect area in normal direction under the condition of type 1: r defect area; (b) leave defect area. where uj1 and uj2 are the angular positions of the contact position j1 and separate position j2, respectively, and are given by uj1 \u00bc ud1 \u00fe arccos 2\u00f0ro\u00felsr max\u00de\u00f0rb ro\u00de l2sr max 2ro\u00f0rb ro lsr max\u00de uj2 \u00bc ud2 arccos 2\u00f0ro\u00felsr max\u00de\u00f0rb ro\u00de l2sr max 2ro\u00f0rb ro lsr max\u00de 8< : \u00f017\u00de Fig. 7 shows the displacement of the rolling element moving towards the bottom of defect area in normal direction under the condition of type 3. The rolling element and the bottom surface of defect area are in contact at position j3 and separated at position j4. Before the rolling element contacts with the bottom surface as well as after it separates from the bottom surface, the relative displacement is equal to lze(t) in type 1. The motion path of the rolling element during contacts with the bottom surface is equivalent to moving along the straight line (bb00 in Fig. 7) between the contact position j3 and the separate position j4. The relative displacement under the condition of type 3 can be described by lze3\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bduj\u00f0t\u00de ud1 q ro \u00fe rocos\u00bduj\u00f0t\u00de ud1 \u00f0ud1 6 uj\u00f0t\u00de < uj3\u00de lze3\u00f0t\u00de \u00bc ro\u00fehmin rb cos\u00bduc uj\u00f0t\u00de \u00ferb ro \u00f0uj3 6 uj\u00f0t\u00de 6 uc\u00de lze3\u00f0t\u00de \u00bc ro\u00fehmin rb cos\u00bduj\u00f0t\u00de uc \u00ferb ro \u00f0uc 6 uj\u00f0t\u00de 6 uj4\u00de lze3\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bdud2 uj\u00f0t\u00de q ro \u00fe rocos\u00bdud2 uj\u00f0t\u00de \u00f0uj4 < uj\u00f0t\u00de 6 ud2\u00de 8>>>>>< >>>>: \u00f018\u00de where uj3 and uj4 are the angular positions of the contact position j3 and separate position j4, respectively, and are given by uj3 \u00bc uc arctan rosin\u00f0uc ud1\u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2rbhmax1 hmax1 2 p rocos\u00f0uc ud1\u00de\u00fehmax1 rb uj4 \u00bc uc \u00fe arctan rosin\u00f0ud2 uc\u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2rbhmax1 hmax1 2 p rocos\u00f0ud2 uc\u00de\u00fehmax1 rb 8>< >: \u00f019\u00de Replace dd(t) in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000286_j.optlaseng.2019.05.020-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000286_j.optlaseng.2019.05.020-Figure9-1.png",
        "caption": "Fig. 9. Schematic of (a) vision system and (b) camera kits; (c) cropped image and (d) extraction of the melt pool (rectangle beam spot) [73] .",
        "texts": [
            " Morphology (digital cameras) Besides in-situ temperature monitoring, sensing and control of the elt pool morphology has a significant influence on the geometrical ccuracy and microstructural features of the finished part as well as the dhesion between layers. In general, the monitoring systems, mainly omprise (high-speed) CCD or CMOS cameras with optical filters, are sed for a top-down view coaxial with the heating laser, and/or for side view to acquire height profile information and particle fields fter exiting nozzles [74\u201378] . Fig. 9 (a) and (b) schematically show a ision system with camera kits for top-down viewing developed by Lei t al. [73] . This system is screwed to the laser head so that the melt pool s always in the field of view during process, and the recording frame ate is 31 frames/s. Considering the extreme high-temperature condiion, a 808 nm narrow band filter is used, which only permits the light p a r B i t l d e c a [ o p s a w d p i c e e b 3 o s d p e p ass at specific wavelengths. A neutral attenuator and an adjustable perture also allow weakening the intense light. Moreover, the lens equires to be shielded by a quartz glass from the attack of particles. y extracting the geometrical characteristics of the melt pool using mage processing technology ( Fig. 9 (c) and (d)), their correlation with he process parameters is modeled. For a simpler DLD process (i.e., the aser head stay in a fixed position with the substrate on a rotary table uring the cladding of one track), thanks to the optics (dichroic mirror, tc.) integrated into the laser head, the light emitted by melt pool an be observed using a high-speed camera (up to 67,000 frames/s) way from the laser head [27] . It is worth mentioning that Haley et al. 79] have recently and impressively presented a work on the direct bservation of interactions between the powder particles and the melt ool using four high-speed cameras (up to 200,000 frames/s), four lens ystems, and three illumination systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000301_s13369-020-04742-w-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000301_s13369-020-04742-w-Figure2-1.png",
        "caption": "Fig. 2 Inertial coordinate systems and body-fixed frame for X configuration quadrotor [52]",
        "texts": [
            " The body frame of the fuselage is assumed to be sym- metrical for the XY axis. 3. The centre of mass coincides with the origin of the body-fixed frame. 4. The propellers are regarded as rigid and there is no blade flapping. 5. At any time, the four propellers operate under the same conditions, which means that all propellers have the same thrust coefficient and response torque coefficient. Let the earth-fixed frame and the body-fixed frame be considered as E = { XE, YE, ZE } and Q = { XQ, YQ, ZQ } , respectively, as seen in Fig.\u00a02. Generalized quadrotor coordinates 1 3 consist of six degrees of freedom in which (x, y, z) describe the absolute positions and ( , , ) are roll, pitch and yaw angle, respectively, used to describe the orientation. Consequently, the model can be divided into two coordinate subsystems: translational and rotational and defined as follows: where, vector , (3) indicates the position of the quadrotor relative to the inertial frame, vector , (4) indicates the attitude of the quadrotor. The relationship between the bodyfixed reference frame, {Q} and the earth-fixed original reference frame, {E} is satisfied as {Q}T = RT \u00d7 {E}T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.23-1.png",
        "caption": "Fig. 7.23: O\u2013Ring in a Groove on a Piston",
        "texts": [
            " The first one is an O\u2013ring mounted on a piston to be inserted into a corresponding cylinder hole. The second one is a snap fastener, which plays an important role in automated assembly. The task is to find the correct relationship between the displacement and orientation rIG and AIG of the gripper with respect to the environment and the forces and moments f and m acting due to the deformation of the parts. For this purpose we have to introduce an additional local frame L, necessary to describe the deformation of the workpiece. O-Ring Figure 7.23 depicts an elastic ring mounted in a groove of a piston. It is inserted into a hole with a rounded chamfer at the beginning and possibly also at the end. This is a typical application of O\u2013rings in hydraulic cylinders or pneumatic valves. In the hole there might be notches serving as entrance or outlet. An analytical solution for the stresses and strains in the elastic ring with approaches from continuum mechanics is not possible because the displacements and also frequently the material laws are nonlinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003838_s0301-679x(03)00094-x-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003838_s0301-679x(03)00094-x-Figure7-1.png",
        "caption": "Fig. 7. Sellers-bearing with ring-lubrication.",
        "texts": [
            "28 Ns/m2, at 40 \u00b0C, it was 0.075 Ns/m2, and at 100 \u00b0C, the viscosity was 0.012 Ns/m2. The flame point was 180 \u00b0C. By comparing the viscosity variation for different temperatures, Stribeck found that the thin Velocite Spindle Oil changed its viscosity in the same way between 20 and 50 \u00b0C as a heavy mineral oil between 80 and 110 \u00b0C, see Fig. 6. Stribeck\u2019s test bearings were different from most modern journal bearings, in that the bearing width (230 mm) was much larger than the diameter (70 mm), see Fig. 7. This made the bearing sensitive for shaft bending and misalignment. To avoid temperature transients, causing temperatures at different points in the bearing to differ by a few degrees, measurements were made slowly. Steady state temperatures were reached after 2\u2013 3 h of running. That also showed Stribeck that most machines in transient use never would reach the steady state temperature. Stribeck\u2019s experiments clearly indicated that the higher the speed is, the higher is also the bearing load when the minimum coefficient of friction is experienced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure3.39-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure3.39-1.png",
        "caption": "Fig. 3.39 Tire model of a two-ply bias belt on an elastic foundation [9]",
        "texts": [
            "200) indicates that kcr is proportional to dfilament cosa which is related to the diameter of a wire and the bias angle, the biquadratic root of Young\u2019s modulus of wires Ef and the biquadratic root of the tread thickness H. Sakai [13] also used a model of a beam on an elastic foundation to analyze the tire belt under the buckling phenomenon resulting from an in-plane bending moment, as shown in the Appendix. Asano [9] developed MLT for the two-ply bias belt under buckling due to a compressive force. He used the model shown in Fig. 3.44, which is the same as that in Fig. 3.39. The axis in the thickness direction z(i) is defined from the middle plane of the tire belt, N(i) is the membrane force in the x-direction with a tensile force 16Note 3.7. 3.8 MLT of the Buckling of a Two-Ply Bias \u2026 167 having a positive value, M(i) is the bending moment with the clockwise direction on the left side being positive, Q(i) is the shear force with the z-direction on the left side being positive, and the subscript (i) indicates the upper belt (i = 2) or lower belt (i = 1). Using Eq. (2",
            " 3:5 Comparing Puppo and Evensen\u2019s solution to Eq. (3.30) with McGinty et al.\u2019s solution to Eq. (3.60), prove that the difference in solutions is the terms including h/h0. Sakai [13] used a beam on an elastic foundation to analyze the tire belt under the buckling phenomenon caused by the in-plane bending moment as shown in Fig. 3.46. The belt of a radial tire is supported by the carcass spring and when the lateral force is applied to a tire, the tire belt bends laterally. This model is similar to that in Fig. 3.39. However, we note that ky in Fig. 3.46 is the carcass spring while kT in Fig. 3.39 is the tread spring. The equation for the belt bending with tension T0, which will be discussed in Note 11.6 of Chap. 11, is EIz d4y dx4 T0 d2y dx2 \u00fe kyy \u00bc 0; \u00f03:218\u00de where E, Iz and ky are, respectively, Young\u2019s modulus of the belt in the circumferential direction (N/m2), the moment of inertia of area (m4) and the spring rate of the carcass per unit length in the x-direction (N/m2). The tension T0 (N) is uniformly distributed in the width direction. 172 3 Modified Lamination Theory Assume that the solution to Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000458_j.addma.2020.101147-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000458_j.addma.2020.101147-Figure8-1.png",
        "caption": "Fig. 8. Schematic representation of a microcrack generation mechanism, (a) Adhesion of a power particle without proper melting (side view), (b) Crack initiation at the interface of adhered particles and molten material (side view), (c) Front view of the same.",
        "texts": [
            " High laser power induced high energy at the action zone that produced a cyclone in the Argon atmosphere. The powder particles were, thus, pulled and assisted to move towards the surface of the melt pool, and adhered to it [36,37]. Hence, sample-II-5 got the lowest adhered powder particles, which was manufactured by the lowest laser power, i.e., 55W. However, scanning speed played an important role in solidification timing and shrinking of the melt pool [13]. The microcrack generation mechanism has been explained with the help of the schematic diagram in Fig. 8. High laser power, along with high scanning speed, induced much higher energy on the focal circle compared to the surrounding heat affected zone. This caused lower viscosity in the center and higher viscosity at the periphery side. Thus, a steep thermal gradient had been generated between the center and periphery of the melt pool, that introduced a high Marangoni effect. This effect evolved a tendency in the molten material to flow radially inward of the melt pool [28]. This phenomenon assisted a few adhered and partially melted powder particles to get inside of the melt pool which remained there as partially melted particles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000159_j.ijfatigue.2020.105946-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000159_j.ijfatigue.2020.105946-Figure8-1.png",
        "caption": "Fig. 8. As-built strut cross-section parameters with standard deviation classified according to the inclination of the struts to the printing plane. The dashed bars indicate the as-designed value of the strut diameter (670 \u00b5m for batches A to D and 500 \u00b5m for batch E). In the Appendix (Table A1), the numerical values are listed.",
        "texts": [
            "090 mm) \u2022 unit cell with average as-built geometrical parameters measured in batch E (L = 3 mm, tz ab= 0.527 mm, R = 0.442 mm) The as-built geometrical parameters are listed in the Appendix and discussed in Paragraph 3.3.1. In the models representing the as-built unit cell, the fillet radius is equal to the smallest value among the average values of the three categories in which the measured radii are classified (R+, R- and Rlat, as defined in Fig. 9). The diameter of the struts is the average diameter of the struts aligned with the loading direction (in all cases tz ab, as in Fig. 8). Solving the FE model for the nominal geometry of batch B is not needed because it is the same of batch A. On the other hand, since failure occurs in the struts and not at the junction, modelling the as-built geometry of batch B requires a more accurate approach which is left for future work. A convergence study was performed for each FE model by refining the mesh and calculating the error on the maximum principal stress for each level of mesh refinement with respect to the finest one. The results were deemed to have converged satisfactorily when the error was equal or below 1%",
            " To distinguish the struts failed by fatigue from those failed by static tension, the fracture surfaces were investigated under a JEOL JSMIT300LV scanning electron microscope (SEM). Fig. 7 shows optical micrographs representative of the morphology of each batch. The nominal lattice is overlaid to compare the as-built and the as-designed architecture. Although the compensation leads to a satisfactory correspondence between the as-built and the as-designed lattice, the horizontal struts (parallel to the printing plane) are more irregular than the vertical struts in all the batches (as also indicated by the wider error bars on txy z ab , and txy xy ab , in Fig. 8). In Fig. 7A, for instance, the horizontal strut on the bottom is considerably thinner in the middle than towards the junction. This is a well-known phenomenon in overhanging PBF parts which are supported prevalently by the powder and not solid material. Where planned, the filleted junctions were reproduced satisfactorily, although the fillets on the underside of the horizontal struts seem more irregular than those above the struts. On the other hand, it is quite striking the sharpness of the junctions in batch D, compared to the other specimens",
            " The fatigue tests were stopped after a 1 Hz decrease in frequency (4\u20135 broken struts) and then the two parts of the specimen where separated via a monotonic tensile load. It is thus possible to identify the nucleation site of the fatigue crack, given that the fatigue fracture surfaces are smooth, while the fracture surface of the struts failed by monotonic load show the typical dimples. The magnified fracture surfaces of the struts failed by fatigue are enclosed in red dashed rectangles and the white arrows indicate the fatigue crack propagation direction. Table A1 Nominal and as-built cross-section parameters (see parameters definition in Fig. 8). Batch CAD As-built strut cross-section parameters t0(\u00b5m) tz ab txy z ab , txy xy ab , \u00b5(\u00b5m) \u03c3(\u00b5m) Dev. from CAD(%) \u00b5(\u00b5m) \u03c3(\u00b5m) Dev. from CAD(%) \u00b5(\u00b5m) \u03c3(\u00b5m) Dev. from CAD(%) A 670 693 27 3.4 769 97 14.8 587 45 \u221212.4 B 670 705 27 5.2 759 115 13.3 590 58 \u221211.9 D 670 698 28 4.2 811 118 21.0 575 48 \u221214.2 E 500 527 28 5.4 524 88 4.8 450 53 \u221210.0 Table A2 Nominal and as-built strut junction parameters (see parameters definition in Fig. 9). Batch CAD As-built struts junction parameters R(\u00b5m) R+ R- Rlat \u00b5(\u00b5m) \u03c3(\u00b5m) Dev"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003949_s10846-007-9137-x-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003949_s10846-007-9137-x-Figure3-1.png",
        "caption": "Fig. 3 Base frame \u22110 and Platform frame \u2211P",
        "texts": [
            " universal joint (U) at the base (the first one is actuated) and a 3 d.o.f. spherical joint (S) at the platform. The lengths of the legs are actuated using prismatic joints (P). We note that the legs of this robot have the same structure as the classical Gough\u2013Stewart parallel robot [34]. Assuming that Bi is the point connecting leg i to the base and Pi is the point connecting leg i to the platform. The frame \u22110 is defined fixed with the base, its origin is B1, and frame \u2211P is fixed with the mobile platform with P1 as origin. We place these frames as shown in Fig. 3: The notations of Khalil and Kleinfinger [20], are used to describe the geometry of the tree structure composed of the base and the legs. The definition of the local link frames of leg i are given in Fig. 4, while the geometric parameters are given in Table 1. The following parameters are used: aj denotes the frame antecedent to frame j, \u03bcj and \u03c3j describe the type of joint: \u2013 \u03bcj=1 if joint j is active and \u03bcj=0 if it is passive, \u2013 \u03c3j=1 if joint j is prismatic and \u03c3j=0 if it is revolute, \u2013 The parameters (\u03b3j, bj, \u03b1j, dj, \u03b8j, rj) are used to determine the location of frame \u2211j with respect to its antecedent frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-15-1.png",
        "caption": "Figure 2-15. Phasor diagrams for PM motor (a) for maximum torque per ampere, (b) for unity power factor, (c) for leading power factor.",
        "texts": [
            " Electrical Machines for Drives Operating region Figure 2-14. Torque-angle relation for PM motor. increasing the current lead angle \u00df as shown in the phasor diagram of Figure 2- 15b. As shown in the operating region of Figure 2-14, this causes only a small reduction in torque. For regeneration, the rotor angle \u00df is made similarly negative. For a voltage-driven PM drive, the magnitude of the supply voltage and its frequency are made proportional to the motor speed. Operating conditions equivalent to those of Figure 2-15a and b can be employed by appropriate adjustment of the angle \u03b4 by which the stator voltage phasor leads the field axis. However, the motor can also be operated with a leading or capacitive stator current by increase of the angle \u03b4 as shown in Figure 2-15c. This condition is particularly desirable for some large drives since it allows use of a load-commutated inverter, that is, one where the switches are turned off by their currents going to zero rather than requiring auxiliary turn off means [2]. Demagnetization of a part of the magnet can occur if the flux density in that part is reduced to less than the knee point flux density BD shown for various magnet (c) 2.5. Synchronous Permanent Magnet Motors 59 materials in Figure 2-12. This can result in permanent reduction in torque capability since it is usually not feasible to remagnetize the magnets without disassembly of the motor. As seen in the phasor diagrams of Figure 2-15, the stator current in the driving mode is normally controlled to lead the effective magnet current by 90\u00b0 or more. The effect of this stator magnetic field is to increase the air gap flux density near the leading edge of each magnet and decrease it near the lagging edge. With normal values of stator current, the effect of the air gap flux in producing torque is relatively unchanged. The limiting value of permissible stator current is that which brings the flux density down to the value BD at the lagging edge",
            " Increase in the number of poles increases the switching frequency and the losses in the iron. It decreases the ratio of aligned to unaligned inductance somewhat. If the motor is operated in the linear mode with no significant saturation in the iron, the torque can be expressed as TJI% N-m (2-15) where i is the phase current, L is the phase inductance (where L is the inductance of the energized phase), and \u03b2 is the rotor angle. To the extent that the inductance is proportional to the overlap angle, the torque can be essentially constant. The expression of Figure 2-15 is useful only for values of the current / for which the inductance is independent of current. To achieve high torque and power from a given frame size, most switched reluctance motors are operated so that the poles are significantly saturated when aligned and energized. The average torque that these motors can produce may be assessed from the magnetizing characteristics relating the phase flux linkage \u03bb to the coil current ; when in the aligned and unaligned positions [1]. A typical set of relations for the 6/4 motor is shown in Figure 2-24"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure15.19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure15.19-1.png",
        "caption": "Fig. 15.19 Tire deformation on a drum",
        "texts": [
            "8) uses the fixed coordinate system, while Eq. (15.10) uses the rotating coordinate system. The relations @ @trotation \u00bc @ @tfixed \u00fe @ @n @n @t fixed \u00bc @ @tfixed \u00feV @ @n @2 @t2rotation \u00bc @2 @t2fixed \u00fe 2V @2 @n@tfixed \u00feV2 @2 @n2 \u00f015:73\u00de are thus satisfied for the time derivatives in each coordinate system. The second terms in the above equations are related to the Coriolis force, and the contributions of the second terms are smaller than those of the first and third terms. Note 15.2 Eqs. (15.29) and (15.30) Figure 15.19 gives \u03c8 d w0 a RD \u03be0 \u03be \u03b8 0\u03b8 0\u03c8 Notes 1155 When the shape of the drum is expressed in the coordinate system of the tire, the distance between the tire surface and the drum surface, w0, which corresponds to the displacement from the tire surface to the drum surface, is given by w0 \u00bc a2h2 2 1 a \u00fe 1 RD d: \u00f015:75\u00de Using the relations n0 = ah0 and n = ah, w0 is rewritten as w0 \u00bc n2 n20 2 1 a \u00fe 1 RD : \u00f015:76\u00de 1. E.R. Gardner, T. Worswick, Behaviour of tyres at high speed. Trans. I.R.I. 27, 127\u2013146 (1951) 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure15-1.png",
        "caption": "Fig. 15. Illustration of line Q of singularities.",
        "texts": [
            " Singularities of R2 may be avoided by observations of inequality oR2 owr oR2 ohr 6\u00bc 0 \u00f020\u00de A more simple approach is based on the theorem [8] that states that at the point of surface singularity we have v\u00f0s\u00de \u00fe v\u00f0s2\u00de \u00bc 0 \u00f021\u00de existing and proposed design, in Fig. 14(a) and (b), respectively. Line Q is the image of points of singularities. Lines L2s are the lines of tangency between the shaper and the face-gear. Point K\u00f0h r ; ur max\u00de determines the verge of the area where singularities of R2 do not exist. Investigation shows that lines of contact are tangents to line Q of singularities (Fig. 15) that is a common line for two branches of the fillet surface. Fig. 16 shows the influence of the parabola coefficient ar of the parabolic profile of the rackcutter and the gear ratio on the possible tooth length of the face-gear. Results of investigation of undercutting and pointing are shown in Fig. 16, that represents the influence of gear ratio m2s and parabola coefficient ar on the coefficient c represented in Eq. (1). The type of a surface may be defined by the Gaussian curvature that represents the product of surface principal curvature at the chosen surface point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure16.44-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure16.44-1.png",
        "caption": "Fig. 16.44 LF and AT at a small slip angle",
        "texts": [
            "40b as FCT y \u00bc LF0 cw LF0 ccw =2 FPS y \u00bc LF0 cw \u00fe LF0 ccw =2 MCT z \u00bc AT0 cw AT0 ccw =2 MPS z \u00bc AT0 cw \u00feAT0 ccw =2 \u00f016:17\u00de where FCT y , FPS y , MCT z and MPS z are, respectively, the conicity, plysteer, conicity moment and plysteer moment. The lateral force (LF) and self-aligning torque (AT) are measured at a small slip angle, (e.g., 0\u00b0 and \u00b11\u00b0) in the evaluation of vehicle pull. If the force and moment are measured on a drum, they are underestimated owing to the short contact length on the drum. The force and moment for vehicle pull therefore must be measured using a flat-belt machine to exclude the effect of drum curvature. AT does not become zero at the slip angle a2 at which LF becomes zero as shown in Fig. 16.44, because the lines for LT and AT do not intersect on the x-axis. The value of AT at the slip angle a2 at which LF is zero is called the residual aligning torque (RAT), while the value of LT at the slip angle a1 at which AT is zero is called the residual cornering force (RCF). (a1 \u2212 a2) is called the aligning torque static phase (ATSP). RAT, RCF and ATSP are metrics for vehicle pull, and one metric can be expressed in terms of the other metrics. 16.3 Vehicle Pull 1185 LF at a = 0, LF0, in Fig. 16.44 is the summation of the conicity FCT y and plysteer FPS y . AT at a = 0, AT0, in Fig. 16.44 is the summation of the conicity moment MCT z and plysteer moment MPS z . AT and LF in Fig. 16.44 are given by LF \u00bc CFaa\u00feFPS y \u00feFCT y ; \u00f016:18\u00de AT \u00bc CMaa\u00feMPS z \u00feMCT z ; \u00f016:19\u00de where CFa (=\u2202LF/\u2202a) and CMa (=\u2202AT/\u2202a) are the cornering stiffness and the aligning torque stiffness. Eliminating a using Eqs. (16.18) and (16.19), we obtain 1186 16 Tire Properties for Wandering and Vehicle Pull AT \u00bc CMa=CFa LF\u00feCMa=CFa FPS y \u00feFCT y \u00feMPS z \u00feMCT z : \u00f016:20\u00de Substituting LF = 0 into Eq. (16.20), RAT is given as RAT \u00bc CMa=CFa FPS y \u00feFCT y \u00feMPS z \u00feMCT z : \u00f016:21\u00de Substituting AT = 0 into Eq. (16.20), RCF is given as RCF \u00bc CFa=CMa MPS z \u00feMCT z \u00feFPS y \u00feFCT y : \u00f016:22\u00de Using Eqs. (16.21) and (16.22), the relation of RAT and RCF is given as (Fig. 16.45) RAT \u00bc CMa=CFa RCF: \u00f016:23\u00de Referring to Fig. 16.44, RCF and RAT are expressed as RCF \u00bc CFa a1 a2\u00f0 \u00de RAT \u00bc CMa a1 a2\u00f0 \u00de: \u00f016:24\u00de The relations among RCF, RAT and (a1 \u2212 a2) (denoted ATSP) are a1 a2 \u00bc RAT=CMa \u00bc RCF=CFa: \u00f016:25\u00de RCF, RAT and ATSP are thus interchangeable with each other. Similar to Eq. (16.17), RAT and RCF are decomposed into plysteer and conicity components in the vehicle coordinate system: PRCF \u00bc RCFCW \u00feRCFCCW\u00f0 \u00de=2 CRCF \u00bc RCFCW RCFCCW\u00f0 \u00de=2 PRAT \u00bc RATCW \u00feRATCCW\u00f0 \u00de=2 CRAT \u00bc RAFCW RATCCW\u00f0 \u00de=2; \u00f016:26\u00de where CW and CCW, respectively, denote clockwise and counterclockwise rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000231_tie.2021.3073313-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000231_tie.2021.3073313-Figure3-1.png",
        "caption": "Fig. 3. The exploded view of inertial piezoelectric actuator mounted in the body of the needle insertion device.",
        "texts": [
            " The connecting frame is designed to guarantee the relative position of the shaft and the actuator. A ball plunger is used as the contact force adjustment mechanism with its roller against the bottom surface of the driving foot. A pair of screw thread interface is also designed for integration application with other surgery platform. The longitudinal-flexural composite piezoelectric actuator is mainly composed of a flexure beam, a piezoelectric stack and two pieces of piezoelectric ceramic slates, as shown in Fig. 3. The upper surface of the driving foot, which is at the end of the T shape cantilever of the flexure beam, directly contacts with the shaft. The flexure beam is the critical elastic deformable part of the piezoelectric actuator. The base concentric circular plate, with variable thickness, generates longitudinal displacement under the force of piezoelectric stack. The sandwiches structure of T shape cantilever and piezoelectric ceramic slate works as a bimorph bender to produce flexural deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure6.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure6.7-1.png",
        "caption": "Fig. 6.7 Fig. 6.8",
        "texts": [
            " a;(O) = b;(O) = 0, from the non-semi simple case condition we know that: tr A(/l) = 0 and detA(O) = O. When /(O,/l) = 0, but /l\u00ab 1, then tr A(/l) \"* 0 and det A(/l) \"* 0, and both are small quantities. We can take Qi and bi as the functions of det A(/l) and tr A(/l). If J = la(detA(/l), tr A(/l))1 \"* 0 a(/lp /l2) ~I =~l =0 (6.144) is satisfied, we can calculate two parameters /ll and /l2 as functions of detA and tr A. Transversality (crossing) condition. If J\"* 0 is satisfied, then curve det A(/l) = 0 crosses tr A(/l) = 0, but is not tangential, as shown in Fig. 6.7. Suppose x = \u00b1~-UI and u 2 = tr A(/l) (6.145) 210 Bifurcation and Chaos in Engineering then if 8(a\"a2) *\" 0 this is the same as making a one to one change of variables, and 8(1l,,1l2) transforming parameters III and 112 into a l and a 2 (see Fig. 6.8). So the universal unfolding of eq. (6.142) can be taken as , [;] = [:1 ~J[;] +[x2 +:;t+ hot] (6.146) where b20 (0) = I, bll (0) = I, A(Il) = [al ~Il) a 2 ~IlJ (6.147) By eq. (6.145) we know that a l = -det[ 0 I ], and a 2 = tr[ 0 I ], a l a 2 a l a 2 when 1l=0, detA(O)=O=trA(O), so a l =0,a2 =0, and by eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure4.11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure4.11-1.png",
        "caption": "Fig. 4.11: Network model of a 4-way valve",
        "texts": [
            " Multistage valves can be modelled in a similar way as a network consisting of servovalves and pistons, which themselves are working elements of a higher stage valve. Figure 4.10 shows the working principle of a 4-way valve. Moving the control piston to the right connects the pressure inlet P with the output B and simultaneously the return T with the output A. If one connects the outputs A and B with a hydraulic cylinder, high forces can be produced with small forces acting on the control piston. The valve works like a hydraulic amplifier. Figure 4.11 shows a network model of the 4-way valve. The areas of the orifices AV 1 . . . AV 4 are controlled by the position x of the piston. The orifice areas are assumed to be known functions of the position x. The parameter \u03b4 4.2 Modeling Hydraulic Components 197 covers a potential deadband. To derive the equations of motion the lines in the network are assumed to be flow channels with cross sectional areas A1 . . . A4. The fluid is incompressible since the volumes are usually very small, and the bulk modulus of the oil is very high"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000231_tie.2021.3073313-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000231_tie.2021.3073313-Figure5-1.png",
        "caption": "Fig. 5 Simulation results in the longitudinal direction. (a) Displacement. (b) Stress. (The voltage of 120 V was applied on the piezoelectric stack and the friction force of 60 mN was exerted on the upper and bottom surface in the opposite direction of UX.)",
        "texts": [
            " In order to validate the static model and optimize the structural dimensions, a finite element analysis model was established. The maximum deflection, von Mises stress and resonance frequency were simulated. The geometry dimensions of the actuator were adjusted according to the simulation results to meet the displacement demand, yield criterion as well as structural stiffness requirements. The optimized dimensions were shown in the TABLE I, All the material parameters used in the simulation were provided by the suppliers. The corresponding ANSYS simulation results of this group of dimensions were shown in the Fig. 5 and Fig. 6. TABLE. I Dimensions of Flexure Beam Symbol Description Value (mm) L Length of the cantilever. 26 w Width of the cantilever. 6.8 tm Thickness of the cantilever. 2.5 tp Thickness of piezoelectric ceramic slate. 0.5 lf Width of driving foot. 4 lh Height of driving foot. 16.8 a Outer radius of the thin-walled concentric circular plate 6 r0 Inner radius of the thin-walled concentric circular plate. 3.6 h Thickness of the thin-walled concentric circular plate 0.9 Authorized licensed use limited to: Carleton University",
            " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 4 When the longitudinal displacement was analyzed, voltage of 120 V was applied on the piezoelectric stack which was inside the cylinder case. The friction force of 60 mN was exerted on the upper and lower surface in opposite movement directions to simulate the contact with the shaft and the plunger. A mechanical fixed constraint was exerted on the bottom of the stainless-steel stack case. As shown in Fig. 5, the maximum longitudinal displacement is 8.27 \u03bcm, the maximum stress is 0.154 GPa, occurring at the thickness transition area of the flexure beam\u2019s base circular plate, which is lower than the yield strength. For the simulation of flexural defection, voltage of 120 V was exerted on both piezoelectric ceramic slates which were glued on the sides of the T shape beam. Similarly, friction force of 60 mN was applied on the upper and bottom surfaces of the driving foot in the flexural direction. The simulation results are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure21-1.png",
        "caption": "Fig. 21. Finite element models of (a) one-tooth of the pinion and (b) one-tooth of the face gear.",
        "texts": [
            " The development of the finite element model of the face gear is complicated due to the specific structure of the face-gear tooth. Fig. 3(a) shows that the tooth surface of the face gear is formed as a combination of: (i) an envelope to the family of shaper generating surfaces, and (ii) the surface of the fillet generated by the edged top of the shaper (or by the rounded top of the shaper, Fig. 4). The authors could overcome this obstacle by the development of an algorithm that determines the finite elements considering simultaneously the root, fillet, and the active part (the envelope) of the face-gear tooth. Fig. 21(a) and (b) show the finite element models of one-tooth of the pinion and the face gear, respectively. In the case of the pinion tooth model, five finite elements have been considered on the root and fillet portions (Fig. 21(a)). However, in the model of the face-gear tooth (Fig. 21(b)), each longitudinal section, due to its particular length, have to be divided into proper finite elements considering together all portions of the face-gear tooth profile. The finite element analysis has been performed for two versions of face-gear drives of common design parameters represented in Table 3. The versions correspond to face-gear drives with conventional and rounded fillet, respectively (Fig. 4). The finite element mesh of five pair of teeth of version 2 is represented in Fig. 22"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000349_tec.2020.2995902-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000349_tec.2020.2995902-Figure8-1.png",
        "caption": "Fig. 8. Slot model. (a) original slot model. (b) simplified slot model.",
        "texts": [
            " The flux flowing in the stator is calculated from the air-gap field distribution and expressed as 0 0 /2 ' (2 ) slot _ /2 k s k s b R s k s eq r b R R l B d k q + \u2212 = =     (37) 0 0 /2 ' (2 1) slot _ /2 k t s k s b R s k s eq r b R R l B d k q + \u2212 \u2212 + = =     (38) where leq is the stack length, \u03c4t is the stator tooth pitch, \u03b8k is the angular position of kth slot center. To facilitate the division of flux tubes, the bottom of stator slot is simplified according to the area equivalence principle, as shown in Fig. 8, in which the r\u2019 can be approximately equivalent to ' 4 r r   (39) It is worth noting that the B\u2019 slot_r in (37) is different from the Bslot_r in (34). Considering the effect of saturation, the radial and circumferential components of air-gap flux density can be expressed as ' slot_ ( ) ( )r r sr a s bB B B B B= +  + +   (40) ' slot_ ( ) ( )s a r sr bB B B B B= +  \u2212 +    (41) where Bsr and Bs\u03b8 are radial and circumferential components of air-gap flux density produced by the equivalent current and can be described as [25] 0 sov 1 ( )sin( ( )) q k sr v k k i B K F r v =  = \u2212       (42) 0 sov 1 ( )cos( ( )) q k s v k k i B K G r v =  = \u2212       (43) where Fv, Gv and Ksov can be calculated as 2 2 1 ( ) ( ) ( ) 1 ( ) vr v v vrs s R v r rF r Rr R R + = \u2212 (44) 2 2 1 ( ) ( ) ( ) 1 ( ) vr v v vrs s R v r rG r Rr R R \u2212 = \u2212 (45) 0 sov 0 sin( ) 2 2 s s b v R K b v R = (46) where ik is the equivalent current at the ith slot opening, b0 is the stator slot opening width; v is the order of the Fourier series terms of equivalent current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000431_j.cirpj.2020.12.004-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000431_j.cirpj.2020.12.004-Figure5-1.png",
        "caption": "Fig. 5. Schematic arrangement of AFSD [175].",
        "texts": [
            " By rotating the hollow non-consumable tool and romoting rapid heat generation through the contact friction etween shoulder and material and between material and ubstrate, the feedstock material can be plasticized and softened o bind the substrate by the activation of plastic deformation at he interface. Transverse motion of the shoulder results in the eposition of a single track of material, typically several hundreds f microns thick [174]. The first layer is formed by the tool travel cross the surface of the substrate. After the deposition of the initial layer, tool height is adjusted and subsequent layers are added upon the initial one to make the 3D parts. The schematic diagram of the AFSD process is shown in Fig. 5. Three models of AFSD machine developed by Meld company are now commercially available but still developments are going on to further enhance the effectiveness of the process. Since AFSD is a solidstate metal additive process, the inherent defects associated with fusion-based MAM processes like porosity, hot cracking, and solidification related defects are nearly absent. Though AFSD results in fine-grained microstructure with enhanced mechanical properties, the effectiveness of the process in achieving the desired performance depend on the processing parameters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003314_tia.2003.821816-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003314_tia.2003.821816-Figure1-1.png",
        "caption": "Fig. 1. A-phase winding configuration and principle of radial force production.",
        "texts": [
            " Hence, the finite-element analysis cannot be used in a real-time controller of rotor radial positions, because a short sampling period is required from the controller in order to realize stable suspension. This paper proposes a method for fast calculation of the radial force and the torque of a bearingless switched reluctance motor operating in a region of magnetic saturation. It is shown experimentally that the proposed method is effective in calculating the radial force and the torque under conditions of magnetic saturation. Fig. 1 shows an -phase stator winding configuration and the principle of radial force production. The motor main winding consists of four coils connected in series. On the other hand, the radial force windings and consist of two coils each. These coils are separately wound around confronting stator teeth. The - and -phase windings are situated on the one-third and two-thirds rotational positions of the phase, respectively. As the number of stator poles is 12, these three phases are excited for every 15 , and the rotor rotates in the clockwise direction. The rotor angular position is defined as at the aligned position of the phase. The rotor angular position of Fig. 1 is ( 10 ). Dimensions of a test motor are shown in Table I. 0093-9994/04$20.00 \u00a9 2004 IEEE The thick solid lines show the symmetrical four-pole fluxes produced by the four-pole motor main winding current . The broken lines show the symmetrical two-pole fluxes produced by the two-pole radial force winding current . It is evident that the flux density in the air gap is increased, because the direction of the two-pole fluxes is the same as that of the four-pole fluxes. On the other hand, the flux density in the air gap is decreased, as the direction of the two-pole fluxes is opposite to that of the four-pole fluxes",
            " Radial force can continuously be generated by these three phases for every 15 , i.e., from the start of overlap and up to the aligned positions. An atmosphere has a magnetically linear nature with no saturation. Accordingly, gap permeance composed of an atmosphere is invariably constant, even if magnetic saturation arises in rotor and stator poles by means of a high magnetomotive force. Namely, the flux of an air gap invariably keeps linearity to gap permeance. Therefore, the flux of the air gap shown in Fig. 1 can be written as (1) where is the gap permeance of the air gap, and is the magnetic potential difference of the air gap. Thus, the magnetic energy stored in the air gap can be derived from (1) as (2) Equation (2) is always valid in any operating region ranging from linear region to saturated region. The magnetic attraction force of the air gap can be derived from the derivative of the magnetic energy with respect to the rotor displacement . The magnetic attraction force can be written as (3) The proportional coefficient of the magnetic attraction force is a function of the rotor angular position and the dimensions of the test motor",
            " The radial force and the torque under conditions of magnetic saturation can be calculated in real time by means of (5)\u2013(7). However, it is necessary to make the following matters clear in order to make use of (5)\u2013(7). First is the theoretical formulae of the proportional coefficient and , i.e., the gap permeance . Second is the relationship between the magnetic potential difference of an air gap and the stator winding currents, i.e., the magnetic potential difference and the magnetomotive forces. The gap permeance of the air gap shown in Fig. 1 can be divided into three parts of permeances as shown in Fig. 2. consists of straight magnetic paths. and consist of fringing magnetic paths. In general, the magnetic paths of the permeances and are approximated with the straight lines and the circle lines of the infinitesimal width as shown in Fig. 2. However, this common permeance method using the straight lines and the circular lines results in the following problem. It follows from (4) and (7) that the torque is proportional to the derivative of the gap permeance with respect to the rotor angular position "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.20-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.20-1.png",
        "caption": "Fig. 3.20: Linearization of the Friction reserve [279]",
        "texts": [
            "4 Multibody Systems with Unilateral Constraints 143 \u03bbN =[\u00b7 \u00b7 \u00b7\u03bbNi \u00b7 \u00b7 \u00b7 ]T \u2208 IRnN , i \u2208 IN , \u03bbT =[\u00b7 \u00b7 \u00b7\u03bbTTi \u00b7 \u00b7 \u00b7 ]T \u2208 IR2nT , i \u2208 IT , G\u0304N ={G\u0304N\u03b1\u03b2} \u2208 IRnN ,lnT , \u03b1 = (1, 2, \u00b7 \u00b7 \u00b7nN), \u03b2 = (1, 2, \u00b7 \u00b7 \u00b7nT ), {G\u0304N\u03b1\u03b2} = { G\u0304Ni \u2208 IR1,l for i \u2208 IN \u2229 IT 0 \u2208 IR1,l for i \u2208 IN \\ IT G\u0304T =diag[\u00b7 \u00b7 \u00b7 G\u0304Ti \u00b7 \u00b7 \u00b7 ] \u2208 IR2nT ,lnT , i \u2208 IT . (3.157) We have defined above the relative tangential accelerations \u00a8\u0304g as the accelerations within the friction polytopes and with the direction to the polytope boundary (see Figure 3.20). These accelerations are given by g\u0308 = \u2212G\u0304T \u00a8\u0304g \u2208 IR2nT , with g\u0308 = [\u00b7 \u00b7 \u00b7 g\u0308Ti \u00b7 \u00b7 \u00b7 ]T \u2208 IR2nT , i \u2208 IT (3.158) The friction laws as given with the relations (3.154) to (3.25) provide us with a sufficient number of equations for the case with independent contact constraints, they cannot be applied for the cases with dependent constraints. As a next step we shall carry together all relations for evaluating the complete equations of motion for the independent constraint case. Replacing in the equations (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000420_j.triboint.2020.106200-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000420_j.triboint.2020.106200-Figure4-1.png",
        "caption": "Fig. 4. Machining strategy for the full-immersion slotting to assess the tool wear.",
        "texts": [
            " The milling process parameters are reported in Table 1: the cutting speed vc and the feed per tooth fz were chosen from the tool supplier datasheet. For each specimen, a new tool was used in order to avoid any influence of the tool wear on the experimental results. Prior to use, each mill cutter was imaged using a FEI\u2122 Quanta 400 Scanning Electron Microscope (SEM) to inspect the cutting edge radii and verify the absence of any possible production defects, such as damages or microcracks. Fig. 3 shows an example of SEM images of a virgin tool. Fig. 4 shows the chosen machining strategy for the full-immersion slotting to assess the tool wear. The full acceleration at the tool engagement was guaranteed by making the machining operation start sufficiently far from the workpiece. To progressively analyze the tool wear, both the tools and the machined surfaces were examined every 10 slots (i.e. every 200 mm of cutting length) up to their failure. SEM inspection was carried out using both the Everhart - Thornley Detector (ETD) and the Backscattered Electron Detector (BSED) to check the worn tools in the same orientations and magnifications used for the virgin ones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003895_002-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003895_002-Figure2-1.png",
        "caption": "Figure 2. Immunosensor performance is based on the principles of solid-phase immunoassays. In order to improve sensitivity, immunosensors frequently work under competitive configurations. (a) The analyte competes with a labelled analyte-derivative for the binding sites of the antibody immobilized at the transducer surface. The nature of the label is dependent of the transducer system. (b) The analyte competes with an immobilized analyte derivative for the binding sites of the (labelled or unlabelled) antibody in solution. Binding of the antibody to the sensing surface produces greater physicochemical variations improving the sensitivity of the immunosensor.",
        "texts": [
            " Environmental contaminants are often small size molecules which makes the detection of the binding event even more difficult. This is the reason why most devices reported to date perform indirect measurements by using competitive immunoassay configurations and/or labels such as enzymes, fluorescent chemicals or electrochemically active substances. Amplification of the signal thus takes place by detecting the physical properties (electroactivity, fluorescence, etc) of a label or a product of an enzymatic reaction (see figure 2(a)) or the binding of the antibody to the sensing surface instead of that of the analyte (see figure 2(b)). In order to detect trace level contaminants, indirect measurements are especially necessary if using amperometric and potentiometric electrochemical transducers. As we will see below, there have been some approaches towards direct detection of the analyte using piezoelectric or optical devices [25\u201327], however the detection limits reached so far are still not sufficient for direct and reliable quantification of trace pollutants in the environment. Another limitation of immunosensors is the fact that the antibody\u2013antigen interaction is not readily reversible, in contrast to most enzyme based biosensors where there is a catalytic event"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure19-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure19-1.png",
        "caption": "Fig. 19. Generation of double-crowned pinion surface R1 by a plunging disk: (a) initial positions of pinion and disk; (b) schematic of generation; (c) applied coordinate systems.",
        "texts": [
            " 7) amr parabola coefficient of the parabolic function for the modified roll of feed motion apl parabola coefficient of plunging by grinding disk or by grinding worm b parameter of relative tooth thickness of pinion and gear rack-cutters EDp shortest center distance between the disk and the pinion (Figs. 18 and 19) Ewp shortest center distance between the worm and the pinion (Fig. 24) ld, lc parameters of location of point of tangency Q and Q , respectively (Fig. 6) lp translational motion of the pinion during the generation by grinding disk (Fig. 19) m module m12, mwp gear ratios between pinion and gear and between worm and pinion, respectively Mij matrix of coordinate transformation from system Sj to system Si n \u00f0j\u00de i , N \u00f0j\u00de i unit normal and normal to surface Rj in coordinate system Si Ni number of teeth of pinion (i \u00bc 1; p), gear (i \u00bc 2) or worm (i \u00bc w) p1, p2 screw parameters of the pinion and the gear, respectively ri radius of pinion (i \u00bc p1; p), gear (i \u00bc p2) or worm (i \u00bc w) pitch cylinder rd1 dedendum radius of the pinion r i radius of pinion (i \u00bc p1) or gear (i \u00bc p2) operating circle (Fig",
            " 18(c) shows line LrD obtained on surface RD. Rotation of LrD about the axis of RD enables representation of surface RD as the family of lines LrD. Step 2. It is obvious that screw motion of disk RD about the axis of pinion tooth surface Rr provides surface Rs that coincides with Rr (Fig. 18(d)). (iv) The goal to obtain a double-crowned surface R1 of the pinion is accomplished by providing of a com- bination of screw and plunging motions of the disk and the pinion. The generation of double-crowned pinion tooth surface is illustrated in Fig. 19 and is accomplished as follows: (1) Fig. 19(a) and (b) shows two positions of the generated double-crowned pinion with respect to the disk. One of the two positions with center distance E\u00f00\u00de Dp is the initial one, the other with EDp\u00f0w1\u00de is the current position. The shortest distance E\u00f00\u00de Dp is defined by Eq. (29). (2) Coordinate system SD is rigidly connected to the generating disk (Fig. 19(c)) and is considered as fixed. (3) Coordinate system S1 of the pinion performs a screw motion and is plunged with respect to the disk. Auxiliary systems Sh and Sq are used for a better illustration of these motions in Fig. 19(c). Such motions are described as follows: Screw motion is accomplished by two components: (a) translational displacement lp that is collinear to the axis of the pinion, and (b) rotational motion w1 about the axis of the pinion (Fig. 19(b) and (c)). The magnitudes lp and w1 are related through the screw parameter p of the pinion as lp \u00bc pw1: \u00f030\u00de Plunging motion is accomplished by a translational displacement apll2p along the shortest distance direction (Fig. 19(c)). Such motion allows to define the shortest distance EDp\u00f0w1\u00de (Fig. 19(b) and (c)) as a parabolic function EDp\u00f0w1\u00de \u00bc E\u00f00\u00de Dp apll2p: \u00f031\u00de The translational motions lp and apll2p are represented as displacement of system Sq with respect to system Sh. The same translational motions are performed by system S1 that performs rotational motion of angle w1 with respect to system Sq. (4) The pinion tooth surface R1 is determined as the envelope to the family of disk surfaces RD gen- erated in the relative motion between the disk and the pinion. The installment of the grinding worm with respect to the pinion may be represented on the basis of meshing of two helicoids"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.43-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.43-1.png",
        "caption": "Fig. 5.43: Kinematic Connection, for example Gear Mesh",
        "texts": [
            "84) where c and d are spring and damper coefficients, respectively, J are mass moments of inertia, D is the Lehr attenuation constant (practically D \u2248 0.02-0.05 for our case), G the modulus of shear and \u03c1 the material density. The torqes M1,k,M2,k come again from couplings to the neighboring bodies or environment. All interconnections with elasticity must be examined with respect to the magnitude of these elasticities. In our case the stiffness of all tooth meshings is so large, that the coressponding frequencies exceed the frequency range of interest by far. Therefore we are able to model such gear meshes as a purely kinematical connection. Figure 5.43 illustrates such a connection. The two parts are under the load of the contraint force F12 and the torques M1,k,M2,k. If we have a kinematical connection with a ratio (i1,2 = \u03d51 \u03d52 = r2 r1 ), for example, we are able to define a Jacobian by q\u0307 = ( \u03d5\u03071 \u03d5\u03072 ) = ( 1 1 i1,2 ) \u03d5\u03071 = Q \u03d5\u03071 (5.85) The equations of motion of the configuration of Figure 5.43 write J1\u03d5\u03081 = M1,k + F12r1 J2\u03d5\u03082 = M2,k \u2212 F12r2 } =\u0302Mq\u0308 = h, (5.86) which can be transformed with the help of the Jacobian (eq. (5.85) and with the reduced mass moment of inertia J = J1 + J2 i21,2 to yield QTMQ q\u0308 = QTh =\u21d2 J\u03d5\u03081 = M1,k + M2,k i1,2 , (5.87) The constraint force F12 eliminates by the multiplication with the Jacobian Q. The tractor power transmission system includes several Cardan shafts, especially for all PTO systems. Cardan shafts are sources of parameter excited vibrations with their sub- and super-harmonic resonances, which can become dangerous"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003943_tmag.2004.825185-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003943_tmag.2004.825185-Figure3-1.png",
        "caption": "Fig. 3. Two-phase brushless dc (BLDC) motor. (a) Cross section. (b) Physical model.",
        "texts": [
            " To describe this model, we introduce the symbols shown in Fig. 2. The PM is divided into identical slices. Define a vector including angular displacements of consecutive slices: . Due to cross linkage fluxes, the torque density is not constant along the motor axis. It can be assumed that the th PM slice, where generates the cogging torque , which can be approximated as (1) where area under the th segment of the torque density curve along the direction; total area under the torque density curve along the direction; weighting coefficient (see Fig. 3); angular variation of cogging torque determined from 3-D model (see Fig. 4). The quantities and are determined from the standard 3-D finite-element field model by integration of an appropriate component of the Maxwell stress tensor over the surface of each 0018-9464/04$20.00 \u00a9 2004 IEEE pole slice for the basic configuration of PM poles (all slices in aligned position) [2]. In addition, the cogging torque variation is determined by integration of Maxwell stresses over the rotor surface for the same case. In this paper, a new two-phase outer-rotor brushless dc motor with the geometry shown in Fig. 3 is considered, whereas Fig. 4 presents the finite-element mesh of the machine used in calculations. The generalized scalar potential (GSP) formulation was used for determining of magnetic field distribution. Variation of the quantity versus motor length is dependent on machine geometry. In general, it can be approximated with a stairs-like function. For the considered motor, the weighting coefficient as well as the angular variation of cogging torque are plotted in Figs. 5 and 6, respectively. According to the earlier assumptions, for any configuration of PM poles, the overall cogging torque is composed of elementary torques produced by each pole slice shifted by the angle (2) Although the cogging torque values obtained from this model are not very accurate, they are useful to indicate a direction of change in the cogging torque while rearranging pole shape in the optimization process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.34-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.34-1.png",
        "caption": "Fig. 6.34: Resonating quartz sensor as a chemical sensor",
        "texts": [
            " A change of mass of the sensor, which is caused by a chemical reaction between the substance to be analyzed and the sensitive layer, is indirectly measured and the concentration is determined from this. The work ing principle of a resonating sensor is based on measuring the behavior of a standing acoustic wave in a mechanical structure which can resonate like a membrane or cantilever. The mass may also be a solid. A typical resonating sensor contains a piezoelectric quartz which has two metal electrodes at tached to it and which is covered by a chemically sensitive material, Fig 6.34. 6.5 Chemical Sensors 245 If an alternating current is applied to the electrodes at the resonance frequen cy, a longitudinal wave is produced in the quartz. A chemical in contact with the sensitive layer causes a change of the resonator mass, thereby the reso nant frequency changes. This change indicates a certain concentration. Waveguide sensor principle The behavior of surface acoustic waves, like Raleigh or Lamb waves, can be used in so-called waveguide sensors to detect chemical substances. The Lamb wave detectors are the most interesting ones for MST since they have a very high sensitivity and a wide spectrum of possible applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure6.23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure6.23-1.png",
        "caption": "Fig. 6.23",
        "texts": [
            "186) and gk = 0, k = 1,2 Rescaling variables and taking fl = E \u00ab 1, x = EX, y = EY, we have gk (EX,Ey,E) = E2 gk (X,y,E) + 0(E3) = E2{(UkX+~ky)+akx2 +2bkxY+ Cky2} +0(E3) (6.187) (6.188) and we can obtain the solution g = \u00b0 when E = \u00b0 by using the implicit function theorem, namely gk(X,y,O) = 0, k = 1,2 (6.189) Equation (6.189) is an equation of two variables (x,y). They are second curves passing through the trivial solution (0,0). In general, they are ellipses, parabolas or two straight lines. Using higher algebra we can solve the intersecting points. Example 1. Figure 6.22 shows the cases of ellipses and a group of hyperbolas. Example 2. Figure 6.23 shows the cases of two groups of hyperbolas. Generally, we can see from Fig. 6.22 and Fig. 6.23 that the two quadric curves of (x,y)gm = \u00b0 and g, = \u00b0 intersect at zero, two or four points. In the case we are discussing, as the zero solution exists forever, the nontrivial solution is one or three. Figure 6.24(a), (b) shows the degenerate cases which two groups of curves are tangential. In this case, there will be one or three solutions, namely, there will be zero or two non-trivial solutions. Since the degenerate case is structurally unstable, these cases are very easy to be disturbed. From these considerations we see that the quadric eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.38-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.38-1.png",
        "caption": "Fig. 11.38 Generalized skewed-parabola Dgsp(x1/l; n, f) describing the contact pressure profile in the circumferential direction. Reproduced from Ref. [10] with the permission of Tire Sci. Technol.",
        "texts": [
            "5 Neo-Fiala Model 759 is inclined forward. The pressure distribution given by Eq. (11.72) therefore becomes a generalized skewed-parabola function that expresses the forward inclination of qz(x1): qz\u00f0x1\u00de \u00bc n\u00fe 1 n Fz wl Dgsp x1 l ; n; f Dgsp x1 l ; n; f \u00bc 1 2 x1 l 1 n 1 f 2 x1 l 1 n o : \u00f011:145\u00de The generalized skewed-parabola function Dgsp(x1/l; n, f) can easily express the forward inclination of qz(x1) using the parameter n to control the shape of the pressure distribution and f to control the inclination as shown in Fig. 11.38. The fundamental equations and the procedure used to calculate the cornering properties of a tire in a combined slip (in braking) are as follows. (i) A generalized skewed-parabola function is used for the pressure distribution Dgsp(x1/l; n, f) according to Eq. (11.145). (ii) The pressure distribution in the circumferential direction receives feedback in the form of the inclination parameter f while the circumferential movement of the contact patch xc is calculated using either f \u00bc CMfMz xc=l \u00bc 1=2 CMcMz=l 2 \u00f011:146a\u00de or f \u00bc CfFx xc=l \u00bc 1=2\u00feCxcFx: \u00f011:146b\u00de 760 11 Cornering Properties of Tires (iii) Mz is fed back to the slip angle of the wheel a0 to calculate the effective slip angle a21: a \u00bc a0 Mz=Rmz: \u00f011:147\u00de (iv) The sliding point rh is determined (where rh = 0 is used in the case that rh < 0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000212_j.addma.2020.101037-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000212_j.addma.2020.101037-Figure2-1.png",
        "caption": "Fig. 2. The setup of numerical simulation: (a) mesh block of the model, (b) dimensions of the initial fluid cross-section, and (c) laser power density followed the Gaussian distribution.",
        "texts": [
            " Finally, the crystallographic features were revealed by EBSD analysis performed on a Helios NanoLab 660 SEM equipped with an Oxford EBSD detector. DED process was simulated by commercial computational fluid mechanics (CFD) software with customized heat and focal subroutines. Two distinct interfaces, i.e. IN625 deposition on SS316L and SS316L deposition on IN625, were modeled separately. For simplification, a partial cylinder was added on the bottom metal to represent the deposited particles during the deposition process, as depicted in Fig. 2(a). A total number of 416,000 cells with 0.1 mm cell size were employed in the simulation. The dimensions of the initial fluid cross-sections are indicated in Fig. 2(b). The power density of the laser spot was assumed to follow the Gaussian distribution (Fig. 2c), where the peak power density in the central region was approximately 283 W/mm2. Free surfaces of both materials were tracked by volume-of-fluid, which can be represented by Equation 1, where F is fluid volume fraction; u, v and w represent velocity components in x, y and z directions, respectively. The mixture of the two different materials was completely driven by the flow field, i.e. no inter-diffusion was considered in the model. The material properties after the mixture were averaged over the volume fraction of the material as indicated in Equation 2, where   is the averaged material property after mixture, 1f , 1 and 2f , 2 are volume fractions and material properties of SS316L and IN625, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure3-1.png",
        "caption": "Fig. 3 shows the finite element model of five pairs of contacting teeth. The use of several teeth in the models has the following advantages:",
        "texts": [],
        "surrounding_texts": [
            "This section covers stress analysis and investigation of formation of bearing contact of contacting surfaces. The performed stress analysis is based on the finite element method [17] and application of a general computer program [3]."
        ]
    },
    {
        "image_filename": "designv10_2_0003227_s100510170283-Figure21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003227_s100510170283-Figure21-1.png",
        "caption": "Fig. 21. Schematic of the stray field lines from an infinite transversally magnetized cylinder (M \u2016 y\u0302). These are circles tangential to the magnetization vector and having radii inversely proportional to n, n being integer. Also shown are the realistic and unrealistic tip trajectories considered in Figure 20 (thick solid lines).",
        "texts": [
            " One trivial though valid argument to explain the substantial differences in the MFM contrasts calculated for the two kinds of tip trajectories (realistic and unrealistic) consists in saying that the stray field from the magnetized body is not probed at the same locations in the two cases. Furthermore, these differences may be accounted for qualitatively by examining how the trajectories cross the stray field lines associated with the magnetized cylinder. For an infinite transversally magnetized cylindrical wire, the stray field lines are circles tangential to the magnetization vector [38], as sketched in Figure 21. As the tip is moved along a realistic trajectory and travels up or down the cylinder flanks, it is subjected to rapid changes in stray field, hence in magnetic force, as revealed by the large density of field lines that are crossed in the vicinity of the cylinder sides. Thus, strong MFM contrasts may be recorded, which are either absent or proportionally much less pronounced when the tip is flown along a rectilinear trajectory, not probing the stray field in a so tight manner around the cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000360_j.jmapro.2021.03.040-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000360_j.jmapro.2021.03.040-Figure8-1.png",
        "caption": "Fig. 8. Temperature distribution for laser power at the value of 200 W, scanning speed at the value of 600 mm/s and hatch spacing at the value of 50 \u03bcm when melting of layer (a) 1 (b) 2 (c) 3 and (d) 4 completes.",
        "texts": [
            " The complex thermal gradient involved in the SLM process is the most prominent factor that leads to the generation of large residual stresses in components. Therefore, an accurate evaluation and prediction of the influence of several parameters on thermal behavior is of paramount importance. The thermal distribution during SLM after melting completion of each layer with hatch spacing at the value of 50 \u03bcm, scanning speed at the value of 600 mm/s and laser power at the value of 200 W can be seen in Fig. 8. An exceptionally high temperature i.e., up to 2800 \u25e6C approx., was observed during SLM, as shown in Fig. 8. Moreover, it can also be observed that the overall temperature of melted region and substrate region also increases with the increase in number of layers. Fig. 9 shows the thermal histories at center point of different layers for hatch spacing at the value of 50 \u03bcm, scanning speed at the value of 600 mm/s and laser power at the value of 200 W. As the laser coincides with the center point of layer 1, its temperature changes to approx.2700 \u25e6C, as shown in Fig. 9 (b). As soon as the laser moves away from this point the temperature falls rapidly to a much smaller value of approximately 500 \u25e6C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.46-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.46-1.png",
        "caption": "Fig. 5.46: Components of the micromotor. Courtesy of the Institut fiir Mikro technik GmbH, Mainz",
        "texts": [
            "6 A, the motor could reach its maximum rotational speed of 30000 rpm. A minimum current of 150 rnA is necessary for a stable function of the motor. After about 50 million revolutions, no changes in the original operating behavior was noticed. Hybrid rotational micromotor A 3 mm long reluctance motor the components of which are partially made by the LIGA process was developed and reported in [Ehrf93]. Figure 5.45 illustrates the dimensions of this micromotor. The motor's components are shown in Figure 5.46. The stator having microrods as its main machine ele ments, the rotor and the spacer ring were made by the LIGA technique in order to ensure tolerances below 5 J!ffi. The other motor parts were made by conventional precision machining techniques and are commercially available. The motor drive uses the reluctance principle. The micromotor generates a rotating magnetic field with the help of electric current in the stator coils; this brings the low-retentive rotor into motion. The rotor is placed on a shaft; the latter has a diameter of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure11-1.png",
        "caption": "Fig. 11. The primary configuration of the equivalent representation.",
        "texts": [
            " Further, the mobility can be calculated from the modified Kutzbach-Gr\u00fcbler mobility criterion [57\u201359] as: m = g \u2211 i =1 f i \u2212 6 l + card \u3008 S r \u3009 \u2212 dim S r = 8 \u2212 6 \u00d7 1 + 4 \u2212 4 = 2 (10) where m is the number of mobility, g is the number of joints, f i is the degree of freedom of the i th joint, l is the number of independent loops, card \u3008 S r \u3009 is the cardinal number of the constraint-screw multiset and dim S r is the dimension of the constraint-screw system. Hence, g = 8 , f i = 1 , l = 1 , card \u3008 S r \u3009 = 4 , dim S r = 4 . The mobility m = 8 \u2212 6 \u00d7 1 + 4 \u2212 4 = 2 . The 8R kinematotropic metamorphic mechanism with primary configuration has two degrees of freedom (DOFs) and satisfies the conventional mobility formula. Besides, we could also establish the global reference frame and screws as illustrated in Fig. 11 , the single-loop mechanism can be supposed to be a parallel mechanism with two limbs S l1 and S l2 composed of joints B 1 , F, B 2 , G and B 3 , H, B 4 , E, respectively. S r l1 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 11 = ( \u2212 q 1 c \u03b11 2 p 1 c \u03b21 2 s \u03b11 2 , 1 , 0 , \u2212 l 1 q 1 c \u03b21 s \u03b11 , \u2212 l 1 q 1 c \u03b11 s \u03b21 c \u03b21 2 s \u03b11 2 , l 1 q 1 c \u03b11 c \u03b21 s \u03b11 2 )T S r 12 = ( n 1 c \u03b11 2 p 1 c \u03b21 2 s \u03b11 2 , 0 , 1 , l 1 n 1 c \u03b21 s \u03b11 , l 1 n 1 c \u03b11 s \u03b21 c \u03b21 2 s \u03b11 2 , \u2212 l 1 n 1 c \u03b11 c \u03b21 s \u03b11 2 )T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 21 = ( \u2212 q 1 c \u03b11 2 p 1 c \u03b21 2 s \u03b11 2 , 1 , 0 , \u2212 l 1 q 1 c \u03b21 s \u03b11 , \u2212 l 1 q 1 c \u03b11 s \u03b21 c \u03b21 2 s \u03b11 2 , \u2212 l 1 q 1 c \u03b11 c \u03b21 s \u03b11 2 )T S r 22 = ( \u2212 n 1 c \u03b11 2 p 1 c \u03b21 2 s \u03b11 2 , 0 , 1 , \u2212 l 1 n 1 c \u03b21 s \u03b11 , \u2212 l 1 n 1 c \u03b11 s \u03b21 c \u03b21 2 s \u03b11 2 , \u2212 l 1 n 1 c \u03b11 c \u03b21 s \u03b11 2 )T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad (11) where \u03b11 denotes the angle between the X-axis and axis of joint B 1 , \u03b21 is the angle between the Y-axis and axis of joint B 2 , a 1 is the distance from the origin O to the axis of joint F, l 1 = a 1 \u221a (s \u03b11 + s \u03b21 ) 2 + c \u03b11 2 + c \u03b21 2 , p 1 = c \u03b11 (1 + s \u03b11 s \u03b21 ) , q 1 = c \u03b21 ( 1 + s \u03b11 s \u03b21 ) , n 1 = s \u03b11 c \u03b21 2 \u2212 c \u03b11 2 s \u03b21 . It is obvious that Eq. (8) and Eq. (11) are the same, therefore the screws S 1 , S 3 , S 5 , S 7 and S 2 , S 4 , S 6 , S 8 are interchangeable, respectively. When the angles of joints E, F, G, and H rotate \u03c0/ 2 , they are in the original position with joints B 1 , B 2 , B 3 , B 4 . This is the kaleidocycle property, which is illustrated in the following Section 6 . The expressions in Eq. (8) show that the constraint screw has no meaning when the 8R kinematotropic metamorphic mechanism in Fig. 11 reaches the following four particular conditions: (1) pc \u03b22 s \u03b12 = 0 (2) c \u03b2s \u03b1= 0 (3) c \u03b22 s \u03b12 = 0 (4) c \u03b2s \u03b12 = 0 i.e., \u03b1= k 1 \u03c0 2 or \u03b2= 2 k 2 + 1 2 \u03c0, \u03b1, \u03b2 \u2208 [ \u2212\u03c0, \u03c0 ] . (12) Similarly, the particular conditions make the constraint screw meaningless can be derived from expression in Eq. (11) : \u03b11 = k 1 \u03c0 2 or \u03b21 = 2 k 2 + 1 2 \u03c0, \u03b11 , \u03b21 \u2208 [ \u2212\u03c0, \u03c0 ] . (13) Eqs. (12) and (13) give the parametric constraints for the angles between the axis of the joint and the coordinate system. When \u03b1= 0 , the axis of joints E is aligned with the X-axis and further the axis of joint E and G are collinear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003772_s002211200200126x-Figure31-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003772_s002211200200126x-Figure31-1.png",
        "caption": "Figure 31. Hele-Shaw cell geometry. (a) Experimental set-up and double ring (upper and side views). (b) Spontaneous opening and burst of a double ring of ethylene glycol and silicone oil. The bar is 2 cm long.",
        "texts": [
            " We develop two other cases, in this section, namely, double rings in a Hele-Shaw cell, and trains in an irregular tube. 6.3.1. Spontaneous burst of a double ring We first describe an experiment achieved in a Hele-Shaw cell. The experimental set-up is composed of two horizontal square glass planes (10\u00d7 10 cm2), separated by microscope slides (thickness 1 mm). A hole (3 mm diameter) has been drilled at the centre of the upper plane. There, two concentric drops of ethylene glycol and silicone oil are introduced with a syringe (figure 31a). When some air is blown through the hole (bubble of radius r2), the double ring formed spontaneously closes back if r2 is small, but grows up and finally bursts if r2 is large enough (figure 31b). The description of the dynamics of the double ring is rather technical and just relies on an adaptation to a cylindrical geometry of the relations derived in \u00a7 3 (Bico 2000). The expression of the driving pressure is nevertheless interesting since the critical hole size observed may remind us of the study by Taylor & Michael (1973) on the stability of a hole in a liquid sheet. Two types of curvature are present in this problem: the successive rings radii r1, r12 and r2 and the gap \u03b4 between the two plates. The Lapalace pressure difference between the inner and the outer radii is: \u2206P = 2\u2206\u03b3 \u03b4 \u2212 \u03b31 r1 \u2212 \u03b312 r12 \u2212 \u03b32 r2 with \u2206\u03b3 = \u03b31 \u2212 \u03b312 \u2212 \u03b32. (43) The effect of the curvatures of the rings is to close back the system. Since their amplitudes are reduced when the hole becomes larger, the driving pressure \u2206\u03b3/\u03b4 finally dominates, which leads to the extension of the double ring. The condition for opening is thus: r2 > \u03b32 2\u2206\u03b3/\u03b4 \u2212 \u03b31/r1 \u2212 \u03b312/r12 . (44) In the example of figure 31, r1 and r2 are initially 17 mm and 8 mm, which gives the minimum air disk radius r2 = 1.3 mm. A larger disk such as that visible in figure 31(b), opens. Note, finally, the double ring growth does not lead to viscous fingering, as could happen in such a geometry (Saffman & Taylor 1958). 6.3.2. Necks in tubes Porous materials are present in our daily life (paper, concrete materials, granular media), and the application of the bislug system to this complex geometry would be very interesting. We may, for example, imagine coating the surface in pores concrete (without clogging them) with a hydrophobic substance in order to achieve a waterrepellent breathing material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-16-1.png",
        "caption": "Figure 2-16. Cross section of a switched PM motor.",
        "texts": [
            " These values of acceleration are significantly higher than can be achieved with either induction or commutator motors of similar maximum torque rating. PM motors have the additional advantage that their overall mass and volume can be made considerably less than that of other motor types. 2.6. SWITCHED OR TRAPEZOIDAL PM MOTORS The other major class of PM motor drives is alternatively known as trapezoidally excited PM motors, or brushless DC motors, or simply as switched PM motors [31]. Normally, these have stator windings that are supplied in sequence with nearrectangular pulses of current. A cross section of one type of motor is shown in Figure 2-16. In most respects, this switched motor is identical in form with the synchronous PM motor of Figure 2-11. For this two-pole motor, the rotor magnets extend around approximately 180\u00b0 peripherally. The stator windings of this motor are connected in a star as shown in Figure 2-Ha. These windings are generally similar to those of an induction or synchronous motor except that the conductors of each phase winding are full pitched; that is, they are distributed uniformly in slots over two stator arcs each of 60\u00b0. The electrical supply system is designed to provide a current that can be switched sequentially to pairs of the three stator terminals. In the condition shown in Figure 2-16 and Figure 2-17a, current / has just been switched to enter into phase a and exit out of phase c. For the next 60\u00b0 of counterclockwise rotation, two 120\u00b0 stator arcs of relatively uniform current distribution are so placed with respect to the magnets as to produce counterclockwise or driving torque of relatively constant magnitude. As the leading edge of the upper magnet crosses the line between sectors b and a', the current i continues through phase c but is switched to enter through phase b rather than a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000299_tcst.2020.2998798-Figure18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000299_tcst.2020.2998798-Figure18-1.png",
        "caption": "Fig. 18. Implementation of the proposed control algorithm.",
        "texts": [
            " Section V-B2 discusses about the ASV configuration and experimental verification of the proposed algorithm. 2) Experiment: The ASV in Fig. 12 is equipped with sensors, computational, actuation, power supply, and communication units to achieve the autonomous capability. The computational unit is an industrial-grade core 2 duo processor of 1.8 GHz, 4-Gb RAM with Ubuntu 16.04 operating system. Robot Operating System (ROS) Kinetic [38] package is used to integrate various sensors and actuators with its computational unit. Referring to Fig. 18, a block diagram representation of the control implementation is presented. For the experimental evaluation, the desired waypoints considered for simulation were chosen for experimental as well. Referring to Fig. 19, the ASV successfully tracks the assigned waypoints and simultaneously counteracts the unknown wind disturbance. Referring to the results of the path following in Fig. 19 and cross-track error in Fig. 20, it is evident that the proposed guidance law allows the ASV to follow the desired Authorized licensed use limited to: University of Edinburgh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003267_tcst.2003.815608-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003267_tcst.2003.815608-Figure5-1.png",
        "caption": "Fig. 5. Shape of (35).",
        "texts": [
            " From (33), it is clear that the proposed controller guarantees robustness to the variation of moments of inertia in an analytic manner. The discontinuous function like (31) may cause a chattering phenomenon, which is usually undesirable in practice since it involves high-frequency control logic switches and limit cycles. The system could even become unstable as a result of the chattering phenomenon when an unmodeled structure dynamics is excited [18]. To avoid the chattering phenomenon, (31) is replaced by (34) where is a positive constant and the function is defined as follows: (35) The shape of is shown in Fig. 5. Instead (35), a smooth function that does not include nondifferentiable points like or in (35) may be used, but the expected improvement is not much. The selection of is a tradeoff problem. As becomes smaller, the left side of (33) becomes more negative. In this case, the chattering is more likely to happen. In contrast, the reverse is true when is large. By trial and error, it is recommended that has a value between 0.1 and 0.3. For the proposed controller, is chosen. From the definition of , the following inequality is obtained (36) Substituting (34) into the second term of the right-hand side of (28) and using (36) yields (37) Similarly, the control gains and can be designed as (38) (39) where and are the known maximum uncertainties of and , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure11-1.png",
        "caption": "Fig. 11. For derivation of tangency of surfaces Rs and R2 and generation of the face gear by the worm.",
        "texts": [
            " For the purpose of simplification of derivations, we consider the tangency of those surfaces that are equidistant to Rs, R2, and Rw and pass through point P determined in Sa as (Figs. 10 and 11) r\u00f0P\u00dea \u00bc rps 0 0 T \u00f02\u00de where rps is the radius of the pitch circle of the shaper. The derivation of crossing angle kw is based on the following procedure: Step 1: We consider initially the tangency at P of surfaces that are equidistant to Rs and R2. Axes zs and z2 of rotation of the shaper and the face gear are intersected (Fig. 11), and therefore there is an instantaneous axis of rotation OsI that passes through intersection point Om [8]. Point P is chosen on OmI . Tangency of surfaces Rs and R2 is provided because the normals to Rs pass through point P (Figs. 11 and 14). Step 2: Tangency of surfaces Rs and Rw at point P is observed, if the following equation of meshing between Rs and Rw is satisfied at P [8]: N\u00f0s\u00de v\u00f0sw\u00de \u00bc 0: \u00f03\u00de Here N\u00f0s\u00de is the normal to Rs; vector v \u00f0sw\u00de is determined as v\u00f0sw\u00de \u00bc v\u00f0s\u00de v\u00f0w\u00de, where v\u00f0s\u00de and v\u00f0w\u00de are the velocities of point P of the shaper and the worm",
            " Assume that equation of meshing fws \u00bc 0 is satisfied at a point M\u00f0u\u00f00\u00des ; h\u00f00\u00de s ;w\u00f00\u00de s \u00de and at this point we have that ofws=ohs 6\u00bc 0. Then equation fws\u00f0us; hs;ws\u00de \u00bc 0 may be solved in the neighborhood of M by a function of class C1 as hs \u00bc hs\u00f0us;ws\u00de \u00f010\u00de and the worm thread surface Rw may be determined locally as rw\u00f0us; hs\u00f0us;ws\u00de;ws\u00de \u00bc Rw\u00f0us;ws\u00de: \u00f011\u00de Step 1: The derivation of the face-gear surface R2 is based on the following considerations: (i) The shaper and the face gear perform rotations about intersected axes zs and z2 that form angle cm in a non-orthogonal face-gear drive (Fig. 11). Rotations of the shaper and face gear are performed in a fixed coordinate system Sm; zm is the designation of the axis of rotation of the face gear (Fig. 11). (ii) Face-gear tooth surface R2 is determined in coordinate system S2 by the following equations: r2\u00f0us; hs;ws\u00de \u00bcM2s\u00f0ws\u00ders\u00f0us; hs\u00de; \u00f012\u00de or2 ous or2 ohs or2 ows \u00bc f2s\u00f0us; hs;ws\u00de \u00bc 0: \u00f013\u00de Here, parameters of vector function r2\u00f0us; hs;ws\u00de designate surface parameters \u00f0us; hs\u00de of the shaper and generalized parameter of motion ws. The angles of rotation of the shaper, ws, and the face gear, w2, are related as: ws w2 \u00bc N2 Ns \u00f014\u00de where Ns and N2 are the teeth numbers of the shaper and the face gear, respectively",
            " Parameters ww and w2 are the angles of rotation of the worm and the face gear related by the equation ww w2 \u00bc N2 Nw \u00f015\u00de where N2 and Nw are the number of teeth of the face gear and the number of threads of the worm. Usually one thread of worm is applied and Nw \u00bc 1. Parameter lw of translational motion is provided as collinear to the axis of the shaper (see below). The following coordinate systems are applied for derivation of the face gear surface: (i) Fixed coordinate system Sb and Sc where we consider the rotation of the worm (Figs. 10 and 11). (ii) Fixed coordinate system Sm where we consider the rotation of the face gear (Fig. 11). (iii) Movable coordinate system Sw rigidly connected to the worm (Fig. 10) and coordinate system S2 rigidly connected to the face gear. Surface R2 of the face gear generated by the worm is determined by the following equations [7,8,21]: r2\u00f0us; hs;ww; lw\u00de \u00bcM2w\u00f0ww; lw\u00derw\u00f0us; hs\u00f0us;ws\u00de;ws\u00de; \u00f016\u00de or2 ous \u00fe or2 ohs ohs ous or2 ows \u00fe or2 ohs ohs ows or2 oww \u00bc 0; \u00f017\u00de or2 ous \u00fe or2 ohs ohs ous or2 ows \u00fe or2 ohs ohs ows or2 olw \u00bc 0: \u00f018\u00de Here, vector function rw\u00f0us; hs\u00f0us;ws\u00de;ws\u00de \u00bc Rw\u00f0us;ws\u00de \u00f019\u00de represents the worm surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000231_tie.2021.3073313-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000231_tie.2021.3073313-Figure1-1.png",
        "caption": "Fig. 1. The illustration of working principle of 2-DOF actuation. The linear and rotary actuation strategies are shown in (a) and (b), respectively. (c) operating principle. (d) exciting signal in one period.",
        "texts": [
            " A handheld controller was also designed and prototyped to facilitate the open-loop instrument control. The rest of this work is presented in three parts. Device design process was described in chapter II, including the structural design of the needle insertion device and the handheld controller design. Chapter III mainly described the prototype process and experiment to characterize the device performance. Conclusion was given in Chapter IV II. DEVICE DESIGN The operating principle of 2-DOF actuation is shown in Fig. 1. A driving foot, which is at the end of a flexible structure, keeps direct contact with a cylindrical shaft. The flexible structure is capable of elongating or bending under different exciting signals, causing the driving foot to move along or perpendicular to the axial direction of the shaft. The functional principle of inertial actuation is based on stick-slip effect. Taking the linear actuation process as an example, as shown in Fig.1 (c) and (d), the reciprocal movement of the driving foot consists of slow-forward and fast-backward motions. From ta to tb, the driving foot moves forward slowly in the slow-forward motion phase, the shaft will stick with it and move forward together. From tb to tc, the relative sliding happens in the fast-backward motion phase, the shaft will move backward with a smaller step distance due to its inertia. The alternation of stick and slip gives rise to the step motion output of the shaft, on the end of which an arched needle is installed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000045_rnc.3607-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000045_rnc.3607-Figure1-1.png",
        "caption": "Figure 1. Quadrotor model sketch.",
        "texts": [
            " In terms of (2), the relation between the rotation matrix R and the unit quaternionQ satisfies R.Q/ D 2 qTq I3 C 2qq T 2 q : (3) The multiplication operation \u02dd between two unit quaternions Q1 D \u0152 1; q T 1 T and Q2 D \u0152 2; q T 2 T is defined as Q1 \u02ddQ2 D h 1 2 q T 1 q2; 1q2 C 2q1 C q 1 q2 T iT ; (4) and the inverse ofQ1 is defined asQ1 1 D 1; q T 1 T and satisfiesQ1 1\u02ddQ1 D Q1\u02ddQ1 1 D \u01521; 0; 0; 0 T, where \u01521; 0; 0; 0 T is the unit quaternion identity. The configuration of a quadrotor is sketched in Figure 1. With the unit quaternion representing the attitude kinematics, according to [27], the translational and rotational motion equations of the quadrotor are derived as Pp D v; (5) m Pv D mge3 C TRe3; (6) PQ D 1 2 qT I3 C q !; (7) J P! D ! J!C ; (8) Copyright \u00a9 2016 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control (2016) DOI: 10.1002/rnc where p D \u0152px; py ; p\u00b4 T and v D \u0152vx; vy ; v\u00b4 T denote the position and velocity of the quadrotor c.g. in the frame I,m denotes the total mass, g denotes the gravitational acceleration, e3 D \u01520; 0; 1 T is a unit vector, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure12-1.png",
        "caption": "Fig. 12. Lead correction effect.",
        "texts": [],
        "surrounding_texts": [
            "1286 K. Mao / Wear 262 (2007) 1281\u20131288\ni a s h 7 s a fi\ni t l d\n( i s a c i 0 8\no t T s\n5\nl S t s m [ m a\na c t s S b u F\nF t f c i\nFig. 9. Transmission gears.\nIt may be noted that crowning value 18 m from the above s the sum of the two gears, i.e. crowning 10 m for the pinion nd 8 m for the wheel. The gears are currently made from teel carburised with a case depth of about 0.95 mm. The gears ad been hardened and tempered to give a surface hardness of 20 Hv and core hardness of 410 Hv. The gear surfaces have been hot peened to provide improved fatigue resistance. To reduce sperity local concentrated contact, the gears have been super nished with average roughness of 0.056 m (Ra).\nThe failure mechanism is rolling contact fatigue wear resultng in severe surface pitting as shown in Fig. 10. On several teeth here are a few cracks at the surface that run into the carburised ayer and rapidly diminish to thin cracks extending only a short epth into the gear tooth.\nIt has been found that tungsten carbon carbide coating WC/C) can provide significant increase in carburised gear scuffng resistance and wear resistance [33,34]. To improve the gear urface local pitting problem, the gears have been coated with low temperature WC/C (tungsten carbide-carbon) and DLC oatings respectively. The other efforts have been also made, .e. manufacture a deep case nitrided gear with case depth about .5 mm with core hardness 490 Hv and surface hardness about Hv, manufacture duplex treated gears from high standard steel.\nHowever, all the above efforts have made a little improvement f the gear pitting. The current gear pitting has been delayed a litle and no significant reduction of the pitting has been achieved. his is because the gear pitting failure was mainly caused by haft misalignment and assembly deformations.\np d c\n. Gear micro-geometry design against pitting failure\nThe current approach to the gear surface fatigue wear probem is gear surface micro-geometry optimisation as described in ection 2. The optimisation will be under real operating condiions, i.e. gear contact deformation, shaft deflection, interference hrink fit effect and dynamic loadings. All the micro-geometry odifications have been achieved through Python and Abaqus 28] interface. Python script software has been developed for odifying the gear micro-geometry and its running time is only bout 10 min CPU time. The first analysis has been carried out for the original design s shown in Fig. 11 and it clearly shows the high concentrated ontact in the one side near the edge. This high stress concenration is corresponding well with the local contact fatigue wear howing in Fig. 10. The gear specifications can be found in ection 2, the shaft misalignment and assembly deflection have een measured in the experimental tests and its maximum vales are summarized in Table 1 (coordination system as shown in ig. 9).\nThe first micro-geometry modification is lead correction. ig. 12 shows a significant contact improvement compared to\nhat shown in Fig. 11. The concentrated contact area is moved rom one side toward the centre of the facewidth and the highest ontact pressure is reduced as well. The modified lead correction s 37 m instead of the original designed 8 m.\nThe second micro-geometry modification is the gear tooth rofile tip relief. Fig. 13 shows the result from the original esign, 61 m and it shows the second gear tooth started in ontact. This tip relief is over relieved resulting in tip contact\npitting failure.",
            "K. Mao / Wear 262 (20\nc s t t o w t\np t o\na r u r\n6\nc m m s o o p b s\nm T a\nontribution too late, contact ratio low and concentrated contact tress at the lowest point of single tooth contact. Fig. 14 shows he modified design with 36 m tip relief and it can be seen from he figure that the tip contact contribution started earlier than the\nriginal design in Fig. 13. More contact ratio and load sharing ill be achieved from the modified design without causing high\nip local contact.\nR\n[\n[\n[ [\n[\n07) 1281\u20131288 1287\nCrowning of 10 m on pinion and 8 m on wheel gear is roducing even contact stress between the centre of the gear and he edges at the required torque and it can be concluded that the riginal design of crowning is adequate.\nThe recommendations for the gear micro-geometry design re then made based on the modeling results as above. The ecommendations have been used for the gear redesign and manfacturing, the gear contact fatigue wear has been significantly educed and final designed life has been achieved successfully.\n. Conclusions\nAn advanced non-linear finite element method has been sucessfully used to accurately simulate gear contact behaviour. The odels have used true three dimensional gear tooth profiles with icro-geometry modifications under real load conditions. The haft misalignment, deflection and assembly deflection effects n gear surface contact behaviour have been investigated. The ptimised micro-geometry based on the analysis has been proosed to reduce surface contact fatigue failure. The model has een very successfully applied in automotive transmission gear urface fatigue wear reduction.\nThe highly accurate gear micro-geometry modification ethod has improved the gear surface fatigue wear significantly. his method can also be applied to transmission system noise nalysis in term of transmission error reduction.\neferences\n[1] R.J. Drago, Fundamentals of Gear Design, Butterworths, 1988. [2] D.W. Dudley, Handbook of Practical Gear Design, McGraw-Hill Book Co.,\nNew York, 1994. [3] F.L. Litvin, Gear Geometry and Applied Theory, PTR Prentice Hall, 1994. [4] BS 436: British Standard\u2014spur and helical gears, Part 3. Method for cal-\nculation of contact and root bending stress limitations for metallic involute gears, British Standards Institution, 1986. [5] T. Bell, Surface engineering\u2014past, present and future, Surf. Eng. 6 (1) (1990) 31\u201340. [6] Y. Sun, T. Bell, Plasma surface engineering of low-alloy steel, Mater. Sci. Eng. A: Struct. Mater. Properties Microstruct. Process. 140 (1991) 419\u2013434. [7] N. Dingremont, E. Bergmann, P. Collignon, H. Michel, Optimization of duplex coatings built from nitriding and ion plating with continuous and discontinuous operation for construction and hot working steels, Surf. Coat. Technol. 72 (1995) 163\u2013168. [8] M. Vanstappen, B. Malliet, L. Stals, L. Deschepper, J.R. Roos, J.P. Celis, Characterization of TiN coatings deposited on plasma nitrided tool steel surfaces, Mater. Sci. Eng. A140 (1991) 554. [9] U. Huchel, S. Bramers, J. Crummenauer, S. Dressler, S. Kinkel, Single cycle, combination layers with plasma assistance, Surf. Coat. Technol. 76/77 (1995) 211\u2013217. 10] K.J. Ma, A. Bloyce, T. Bell, Examination of mechanical properties and failure mechanisms of TiN and Ti\u2013TiN multiplayer coatings, Surf. Coat. Technol. 76/77 (1995) 297\u2013302. 11] F. Joachim, N. Kurz, B. Glatthaar, Influence of coatings and surface improvements on the lifetime of gears, Gear Technol. (2004) 50\u201356. 12] I.N. Sneddon, Fourier Transform, McGraw-Hill, 1951, pp. 395\u2013410. 13] P.K. Gupta, J.A. Walowit, Contact stress between an elastic cylinder and a\nlayered elastic solid, ASME J. Lubr. Technol. 96 (1974) 250\u2013257. 14] A.A. Elsharkawy, B.J. Hamrock, A numerical solution for dry sliding\nline contact of multi-layered elastic bodies, J. Tribol. ASME 115 (1993) 237\u2013245.",
            "1 62 (20\n[\n[\n[\n[\n[\n[\n[\n[\n[\n[\n[\n[\n[\n[ [\n[ [\n288 K. Mao / Wear 2\n15] S.J. Cole, R.S. Sayles, A numerical model for the contact of layered elastic bodies with real surfaces, ASME J. Tribol. 114 (1992) 334\u2013 340. 16] K. Mao, Y. Sun, T. Bell, A numerical model for dry sliding contact of layered elastic bodies with rough surfaces, Tribol. Trans. STLE 39 (2) (1996) 416\u2013424. 17] K. Mao, T. Bell, Y. Sun, Effect of sliding friction on contact stresses for multi-layered elastic bodies with rough surfaces, J. Tribol. ASME 119 (3) (1997) 476\u2013480. 18] H.E. Hintermann, Adhesion, friction and wear of thin hard coatings, Wear 100 (1984) 381\u2013397. 19] K. Komvopoulos, Elastic\u2013plastic finite element analysis of indented layered media, J. Tribol. ASME 111 (1989) 430\u2013439. 20] A.K. Bhattacharya, W.D. Nix, Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates, Int. J. Solid Struct. 24 (1988) 1287\u20131298. 21] Y. Sun, A. Bloyce, T. Bell, Finite element analysis of plastic deformation\nof various TiN coating/substrate systems under normal contact with a rigid sphere, Thin Solid Films 271 (1995) 122. 22] R.I. Amaro, R.C. Martins, J.O. Seabra, N.M. Renevier, D.G. Teer, Molybdenum disulphide/titanium low friction coating for gear application, Tribol. Int. 38 (2005) 423\u2013434.\n[ [\n[\n07) 1281\u20131288\n23] K. Aslanta, S. Tasgetiren, A study of spur gear pitting formation and life prediction, Wear 257 (2004) 1167\u20131175. 24] M.E. Norman, A new design tool for optimising gear geometry for low noise, C492/034, IMechE (1995) 231\u2013237. 25] Z. Fong, C. Tsay, A mathematical model for the tooth geometry of circularcut spiral bevel gears, J. Mech. Des. 113 (1991) 174\u2013181. 26] C.B. Tsay, J.W. Jeng, H.S. Feng, A mathematical model for ZK-type worm gear set, Mech. Mach. Theor. 30 (1995) 777\u2013789. 27] B. Bair, C. Tsay, ZK-type dual-lead worm and worm gear drives: contact teeth, contact ratios and kinematic errors, J. Mech. Des. 120 (1998) 422\u2013428. 28] Abaqus Version 6.5 Manuals, Abaqus Inc., 2005. 29] D.W. Dudley, Handbook of Practical Gear Design, McGraw-Hill Book Co.,\nNew York, 1994. 30] F.L. Litvin, Gear Geometry and Applied Theory, PTR Prentice Hall, 1994. 31] J.D. Smith, Gears Noise and Their Vibration, 2nd ed., revised and expanded,\nMarcel Dekker Inc., 2003.\n32] H.M. Merritt, Gear Engineering, Pitman Publishing, 1971. 33] A. Bloyce, PVD Coatings wear it well, Mater. World 8 (3) (2000)\n13\u201315. 34] A. Bloyce, T. Michler, PVD coating for gears, Heat Treat. Met. 29 (2)\n(2002) 33\u201338."
        ]
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.39-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.39-1.png",
        "caption": "Fig. 7.39: Impact Sensitivity in the Cartesian Directions [271]",
        "texts": [
            " Scalar optimization criteria are derived from them, the minimization of which yields an improvement of the system\u2019s performance with regard to the respective effect. Optimization Criterion - Impact Sensitivity When the mating parts are getting in contact with each other, impacts are unavoidable. However, their intensity is proportional to the effective mass mred = [ wTM\u22121w ]\u22121 , reduced to the end effector, where w is the projection of the impact direction into the generalized coordinates and depends on the robot\u2019s position as well as on the Cartesian impact direction (see also the relations (3.160) and (3.161) on the pages 144). Figure 7.39 shows an ellipsoid 7.3 Dynamics and Control of Assembly Processes with Robots 481 at the robot\u2019s gripper, from which the reduced end-point inertia for each Cartesian direction can be seen. In order to reduce the impact sensitivity, the volume of that ellipsoid must be minimized. Thus, we define the reduced endpoint inertia matrix Mred as Mred = ([ JTG JRG ] M\u22121 [ JTG JRG ]T)\u22121 \u2208 IR6\u00d76 . (7.139) Depending on the specific needs of the mating process, a 6\u00d7 6 diagonal positive semidefinite matrix gM of weighting factors is introduced for the trade-off between the cartesian directions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003685_022-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003685_022-Figure5-1.png",
        "caption": "Figure 5. Cross section of the clad and substrate.",
        "texts": [
            " By considering equation (21) as the melt pool boundary at plane y = 0, the coordinate of the deepest point (xm, zm) can be obtained as \u2202\u03c6Tm1 \u2202xm = 0, (22) which yields the following equation: \u03c6Tm2 = \u222b\u222b { V 2\u03b1 + 1 R ( V 2\u03b1 + 1 R2 ) (xm \u2212 \u03be) } exp ( \u2212\u03be 2 + \u03b72 \u03c3 2 ) \u00d7 exp ( \u2212 V 2\u03b1 (R + (xm \u2212 \u03be)) ) d\u03be d\u03b7 = 0. (23) By the simultaneous solving of equations (21) and (23), the deepest point of the melt pool (xm, zm) is determined. Dilution is a very important factor in LPD. This parameter shows the amount of powder material dilution as a result of mixing with the substrate material. In this paper with an assumption of ideal mixing inside the melt pool, dilution is defined as (see figure 5) Dilution = Asub Aclad + Asub , (24) where Asub and Aclad are the cross section areas of the substrate and the clad as shown in figure 5, respectively. The experimental validation of the model was performed using a 1000 W LASAG FLS 1042N Nd: YAG pulsed laser, a 9MP-CL Sulzer Metco powder feeder unit and a 4-axis CNC table. The transverse mode of the laser beam was TEM00 and the beam spot diameter on the workpiece was set to 1.4 mm where the laser intensity was Gaussian. Powder was delivered to the processing point through a lateral nozzle, mounted at an angle of 29\u25e6 relative to the laser beam axis. Argon gas was used for carrying the powder and also as a shield gas to shroud the process zone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.35-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.35-1.png",
        "caption": "Fig. 7.35: Rectangular Peg in Hole Configuration",
        "texts": [
            " But they do not rise to such a high level as the contact forces themselves, because the latter act in different directions. This part of the insertion is mainly governed by friction between the parts. Rectangular Peg in Hole Finally we consider a rectangular peg with a chamfer inserted into a rectangular hole, where the geometry is shown in Fig.20 on the left. If we introduce four modeling planes, we can investigate this spatial example in a planar manner. In every side of the peg one such plane is introduced, which is displayed in Figure 7.35 on the right. Two sides are situated within the xy\u2013plane, and two in the xz\u2013plane. There are two different types of contact points: point\u2013 plane and edge\u2013edge. Let the letters a, b, c, d in Figure 7.35 denote points and the numbers 1\u2032, 2\u2032, 3\u2032, 4\u2032, 5\u2032 denote planes. Then there are four possible contact points of the type point\u2013plane: a\u2212 2\u2032, b\u2212 1\u2032, c\u2212 5\u2032, d\u2212 4\u2032. For the other type edge\u2013edge the numbers 1, 2, 3, 4, 5 denote edges on the peg and the letters a\u2032, b\u2032 denote edges of the hole. There exist six potential contacts of this type: 1\u2212 a\u2032, 2\u2212 a\u2032, 3\u2212 a\u2032, 3\u2212 b\u2032, 4\u2212 b\u2032, 5\u2212 b\u2032. Thus we have altogether 40 potential constraints between the peg and the hole with the sketched geometry in the spatial case. Measurements were again conducted with the PUMA 560 manipulator inserting the rectangular peg with the chamfer into the rectangular hole. The starting position of the manipulator was \u03b30 = (4.6\u25e6, \u2212157.2\u25e6, 27.5\u25e6, 0.0\u25e6, \u221250.3\u25e6, 4.6\u25e6)T . The equations of motion of the robot were linearized around this working point. The mating parts can be seen in Figure 7.35, where the peg had the measures a = 45.2mm, b = 45.4mm with a chamfer 45\u25e6 \u00d7 4mm and the hole had the dimensions a\u2032 = 46.0mm, b\u2032 = 45.8mm. The robot\u2019s path during the mating task was 80mm in positive xA direction. We show 7.3 Dynamics and Control of Assembly Processes with Robots 473 here the results of four experiments compared to numerical simulations. The initial lateral displacement between the peg and the hole was set to \u00b14mm in the two cartesian directions yA and zA. Let us first regard the experiments, where the displacement was \u2206yA = \u00b14mm. In Figure 7.36 the gripper forces during insertion Fx and Fy are shown. The upper plots are measurements, the lower plots are the calculated results for the same starting configuration. In both cases there is a peak of Fx versus the manipulator motion, when the chamfer of the peg comes in contact with the upper edge of the hole (see Figure 7.35 on the right, contact points of type 4 \u2212 b\u2032 in case of positive or 2\u2212 a\u2032 in case of negative displacement). After having passed the edge, it is sliding downwards, having contact with one side of the hole (see Figure 7.35, contact points of type 5 \u2212 b\u2032 in case of positive or 1\u2212 a\u2032 in case of negative displacement). The force Fy due to this contact acts towards the center of the hole. More interesting are the experiments, where the displacement was varied in the zA direction: a) \u2206zA = +4mm, b) \u2206zA = \u22124mm. Here the behavior of the manipulator is different for both cases, see Figure 7.37 (top: measurement, bottom: calculation). If there is a displacement \u2206zA = +4mm, there is again a force peak in Fx at the first contact (contact points of type 4 \u2212 b\u2032), when the chamfer slides at the upper edge of the hole"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003231_s0957-4158(99)00057-4-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003231_s0957-4158(99)00057-4-Figure5-1.png",
        "caption": "Fig. 5. The e ect of G-adaptation.",
        "texts": [
            " , m 33 The partial derivatives are calculated as @J @Sj Sj, @J @Ucj Ucj , and @Ucj @Kj, i h Si 34 The sliding function in (5) can be rewritten using (17) and the integral of (4) as S G Xd \u00ff X GXd \u00ff G F X B Ueq Kh S dx 35 Taking the partial derivative of (35) and assigning the constants to g ' which are obtained by multiplication of elements of G and B: @Sj @Kj, i \u00ffg 0 h Si x dx 36 The last form of K-adaptation is obtained as DKj, i g1Sj h Si x dx\u00ff g2Ucj h Si 37 The minimization of the corrective controller (Uc) prevents chattering when the system is on the sliding surface or inside the boundary layer. Minimization outside the boundary layer e ects the overall performance negatively; the reaching time and the error will increase. Consequently, the adaptation of K as in (37) can be modi\u00aeed in a boundary layer (Sb): DKj, i 8>>><>>>: g1Sj h Si x dx\u00ff g2Ucj h Si if \u00ff Sb < Sj < Sb g1Sj h Si x dx otherwise 38 Weight adaptation for the hidden layer also means the adaptation of G. The e ect of G-adaptation is presented in Fig. 5. Similar to the derivation of (33), the gradient descent for G can be derived as DGj, i \u00ffg @J @Sj @Sj @Gj, i \u00ff g Xm k 1 @J @Uck @Uck @Gj, i 39 where j = 1, . . . , m and i = 1, . . . , n. The partial derivatives are calculated as @Sj @Gj, i Ei and @Uck @Gj, i @Uck @h Sj @h Sj @Sj @Sj @Gj, i Kk, j 1 2 1\u00ff h2 Sj Ei 40 The last form of G-adaptation is obtained as DGj, i \u00ffg3SjEi \u00ff g4 1\u00ff h2 Sj Ei Xm k 1 UckKk, j ! 41 M. Ertugrul, O. Kaynak /Mechatronics 10 (2000) 239\u00b1263 251 If, because of the reasons described above, the minimization of Uc is excluded outside the boundary layer, the \u00aenal form of G-adaptation is obtained as DGj, i 8>><>>: \u00ffg3SjEi \u00ff g4 1\u00ff h2 Sj Ei Xm k 1 UckKk, j "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure3.17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure3.17-1.png",
        "caption": "Fig. 3.17 Resultant stress and torsional moment applied to the cut section of a bias belt",
        "texts": [
            "78), the interlaminar shear stresses, szx and szy, are given by szx \u00bc 2GC4 h sinh by \u00bc 2G b h u0 a AxyAys AxsAyy AyyAss A2 ys \u00feXH sinh by cosh bb szy \u00bc 0: \u00f03:98\u00de Finally, the twist angle X of Eq. (3.97) can be determined from the boundary condition for which there is no torsional moment in a bias belt. We recall the relations N\u00f02\u00de xy \u00bc N\u00f01\u00de xy Q\u00f02\u00de x \u00bc Q\u00f01\u00de x M\u00f02\u00de xy \u00bc M\u00f01\u00de xy : \u00f03:99\u00de Using Eqs. (3.71), (3.73), (3.79), (3.80), (3.94) and the last equation of Eq. (3.85), we have N\u00f01\u00de xy \u00bc AxsC3 \u00fe Ass A2 ys Ayy C4b cosh by\u00feAysC6 \u00feAssXH Q\u00f01\u00de x \u00bc h0 h GC4 sinh by Qx \u00bc 2GC4 sinh by M\u00f01\u00de xy \u00bc 2DssX : \u00f03:100\u00de Referring to Fig. 3.17, the condition without a torsional moment in a bias belt can be expressed as Zb b 2M\u00f01\u00de xy \u00feHN\u00f01\u00de xy Fxy dy \u00bc 0; \u00f03:101\u00de where Fx Qx \u00fe 2Q\u00f01\u00de x \u00bc 2 h0 \u00fe h\u00f0 \u00de h GC4 sinh by \u00bc 2H h GC4 sinh by: \u00f03:102\u00de 130 3 Modified Lamination Theory Substituting Eqs. (3.100) and (3.102) into Eq. (3.101), we can determine the twist angle X: X \u00bc u0 a H\u00f0AxyAys AxsAyy\u00de 1 tanh bb\u00f0 \u00de=bbf g 2DssAyy \u00feH2 AyyAss A2 ys 1 tanh bb\u00f0 \u00de=bbf g : \u00f03:103\u00de Substituting Eq. (3.103) into Eq. (3.98), we obtain the interlaminar shear stress szx: szx \u00bc u0 a 2G b h AxsAyy AxyAys AyyAss A2 ys 2DssAyy 2DssAyy \u00feH2 AyyAss A2 ys 1 tanh bb\u00f0 \u00de=bbf g sinh by\u00f0 \u00de cosh bb\u00f0 \u00de : \u00f03:104\u00de The membrane forces of the composite layers N i\u00f0 \u00de jk are given as N\u00f01\u00de x \u00bc N\u00f02\u00de x \u00bc u0 a Axx A2 xy Ayy AxsAyy AxyAys 2 Ayy H2 1 tanh bb\u00f0 \u00de=bbf g 2DssAyy \u00feH2 AyyAss A2 ys 1 tanh bb\u00f0 \u00de=bbf g AxsAyy AxyAys 2 Ayy AyyAss A2 ys 2DssAyy 2DssAyy \u00feH2 AyyAss A2 ys 1 tanh bb\u00f0 \u00de=bbf g cosh by\u00f0 \u00de cosh bb\u00f0 \u00de 2 6666664 3 7777775 N\u00f01\u00de xy \u00bc N\u00f02\u00de xy \u00bc u0 a AxsAyy AxyAys Ayy 1 H2 AyyAss A2 ys\u00f0 \u00de 1 tanh bb\u00f0 \u00de=bbf g 2DssAyy \u00feH2 AyyAss A2 ys\u00f0 \u00de 1 tanh bb\u00f0 \u00de=bbf g 1 cosh by\u00f0 \u00de cosh bb\u00f0 \u00de n o : N\u00f01\u00de y \u00bc N\u00f02\u00de y \u00bc 0 \u00f03:105\u00de Note that the membrane force is not uniformly distributed in the y-direction",
            "533 bias belt folded belt Fig. 3.31 Variation of in-plane flexural rigidity with the belt angle for a bias belt and folded belt. Reproduced from Ref. [10] with the permission of Nippon Gomu Kyokai 3.6 MLT of Three-Ply with Coupling Deformation 151 Akasaka et al. [11] studied torsional rigidity including twist\u2013extension coupling deformation of a two-ply steel belt and interlaminar shear deformation. Figure 3.32 shows the bias belt under torsional loading. The belt structure is the same as the belt structure of Fig. 3.17. The fundamental equations are Eqs. (3.81) and (3.83). The displacement functions for the twist\u2013extension coupling deformation are defined by Eq. (3.85) because the stiffness matrix A i\u00f0 \u00de ab has anti-symmetric properties for a bias belt as expressed by Eq. (3.86). The governing differential equations and displacements are, respectively, given as Eqs. (3.87) and (3.94). The integral constants can be determined using the following boundary conditions as shown in Fig. 3.33. (i) No axial force: Zb b N 1\u00f0 \u00de x \u00feN 2\u00f0 \u00de x dy \u00bc 0 \u00f03:156\u00de (ii) No stress at belt ends: N 1\u00f0 \u00de x \u00bc N 2\u00f0 \u00de y \u00bc N 1\u00f0 \u00de xy \u00bc N 2\u00f0 \u00de xy \u00bc 0 at y \u00bc b \u00f03:157\u00de 152 3 Modified Lamination Theory (iii) Torque equilibrium in an arbitrary cross section: Zb b M\u00f01\u00de xy \u00feM\u00f02\u00de xy \u00feHN\u00f01\u00de xy Qx \u00feQ\u00f01\u00de x \u00feQ\u00f02\u00de x y n o dy \u00bc T \u00f03:158\u00de Here, N i\u00f0 \u00de x , M i\u00f0 \u00de xy and Q i\u00f0 \u00de x are, respectively, the membrane force, the moment and the transverse shear force of the i-th layer while Q is the transverse shear force of the middle layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.44-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.44-1.png",
        "caption": "Fig. 5.44: Model of a Cardan Shaft",
        "texts": [
            "85) and with the reduced mass moment of inertia J = J1 + J2 i21,2 to yield QTMQ q\u0308 = QTh =\u21d2 J\u03d5\u03081 = M1,k + M2,k i1,2 , (5.87) The constraint force F12 eliminates by the multiplication with the Jacobian Q. The tractor power transmission system includes several Cardan shafts, especially for all PTO systems. Cardan shafts are sources of parameter excited vibrations with their sub- and super-harmonic resonances, which can become dangerous. Therefore good models are obligatory. An excellent survey is given in [240]. We choose a model with four bodies interconnected by springs and dampers (see Figure 5.44). The four equations of motion write J1\u03d5\u03081 = +MG12,1 + M1 J2\u03d5\u03082 = \u2212MG12,2 + c(\u03d53 \u2212 \u03d52) J3\u03d5\u03083 = +MG34,3 + c(\u03d52 \u2212 \u03d53) J4\u03d5\u03084 = \u2212MG34,4 + M4  =\u0302Mq\u0308 = h with MG12,2 = MG12,1 sin2 \u03d51+cos2 \u03d51 cos2 \u03b112 cos\u03b112 and MG34,3 = MG34,4 sin2 \u03d54+cos2 \u03d54 cos2 \u03b134 cos\u03b134 (5.88) To not loose a good overview we have left out the damping terms. The complete force element of the shaft between \u201d1\u201d and \u201d2\u201d comprises a linear damper 5.3 Tractor Drive Train System 263 d and linear spring c. Between the shaft parts (1 - 2) and (3 - 4) we have a kinematical relation of the well-known form ([240], [49]) \u03d5i+1 = \u03d5i+1(\u03d5i) = arctan( tan\u03d5i cos\u03b1 ), (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000200_admt.201900293-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000200_admt.201900293-Figure3-1.png",
        "caption": "Figure 3. The printing parameters that affect the shape memory performance.",
        "texts": [
            " During the printing process, the filament undergoes temperatures above its Tm while being extruded, which results in the stretching and alignment of polymer chains along the direction of deposition. The shape memory properties of PLA can be affected by the molecule alignment rising from stretching,[35] which offers us the possibility of controlling the effects of shape memory by adjusting the printing parameters. Therefore, the coordination of shape and color response speed can be achieved by regulating the Rr and Vr. Figure 3 shows the printing parameters that can be controlled and that affect shape memory performance during the printing process, including the nozzle temperature (Tp), nozzle height (Lp), geometric thickness (Hp), fill rate, and fill angle (\u03b8f). First, to study the influence of the printing temperature Tp on the shape memory characteristics, we ensure that the other printing parameters are consistent: Lp = 200 \u00b5m, Hp = 1 mm, printing speed (Vp) = 25 mm s\u22121, \u03b8f = 0\u00b0. The shape memory performance of the 4D samples with four different nozzle temperatures was characterized by being thrown in 80 \u00b0C water"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.54-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.54-1.png",
        "caption": "Fig. 6.54: Gaps due to Eccentricity",
        "texts": [
            " Gaps generated by eccentricity are gaps, which we do not want to have, but which we nevertheless must consider, at least if experiments indicate an influence of such phenomena. As tensioners are usually cheap components with sometimes spacious manufacturing tolerances, and as additionally the piston of a tensioner is only supported by the cylinder, we get linear and angular displacements influencing the tensioner characteristic. The asymmetric position and orientation of the piston in the cylinder is mainly caused by the motion of the guide, where the piston is fixed by a rotary joint thus following this motion [111].This induces eccentricities (see the examples of Figure 6.54). In gaps of tensioners the volume flow by pressure difference dominates the motion. Experience shows that for these cases the influence of gap eccentricity can be approximated by simply modifying the geometrical coefficient \u03b1\u2206p according to [61] in the following form \u03b1\u2206p = \u2212A h2 12\u03b7l ( 1 + 1, 5\u03b53 ) with \u03b5 = e h . (6.132) \u03b5 is the relative eccentricity with 0 \u2264 \u03b5 \u2264 1. As the influence of the gap height h is with h3 very large, we get for a displaced piston with contact on one side an increase of the volume flow in the gap by a factor of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003734_s0022112007007835-Figure17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003734_s0022112007007835-Figure17-1.png",
        "caption": "Figure 17. Squirmer-averaged velocity vectors relative to the background flow field under various sq conditions (g/g = \u2212x, c = 0.1 and \u03b2 =5). The vectors are divided by sq in order to show all the vectors in the same figure. (a) Gbh = 10, (b) Gbh =100.",
        "texts": [
            " This tendency is similar to that expected for solitary squirmers swimming in the x-direction. The normal stress differences are strongly dependent on the squirmers\u2019 orientation, and their sign changes at \u03b8x = \u03c0/4. Next the effect of Sq is investigated under the conditions of c =0.1, Gbh = 10 and 100, and \u03b2 = 5. The squirmer-averaged velocity vectors for Gbh =10 and 100 are shown in figures 17(a) and 17(b), respectively. The dimensionless swimming velocity of a solitary squirmer is equal to Sq so the vectors in figure 17 are divided by Sq in order to show all the vectors in the same figure. We see that the squirmers tend to swim more in the x-direction as either Gbh or Sq is increased. The effect of Gbh is straightforward, and the effect of Sq may be explained as follows. Strong squirming motion induces strong interaction between squirmers, so the effect of the background vorticity of the shear flow decreases as Sq is increased. The effect of Sq on the particle stress component Hxy is shown in figure 18 (c = 0.1, Gbh = 10 and 100, and \u03b2 = 5)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000231_tie.2021.3073313-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000231_tie.2021.3073313-Figure14-1.png",
        "caption": "Fig. 14 The handheld controller for the needle insertion device. (a) The exploded view. (b) The appearance of the handheld controller prototype.",
        "texts": [
            " 6 The front panel layout and the user interface are designed as follows: A SWITCH button is designed to achieve the switch between the single step mode and continuous mode. The amplitude and frequency of the signal can be configured after pressing the designed CONFIG button. Four direction buttons are designed to control the direction of the needle movement. Right and left buttons control the forward and backward translation of the arched needle. Up and down buttons are used to control the clockwise and counterclockwise rotations. The exploded view of handheld controller is shown in Fig. 14 a). The microcontroller and key components are all integrated on the motherboard. A USB port is designed as the power port and data interface for programming or communication. An aviation plug connector is installed to transfer signal reliably. The appearance of the handheld controller prototype is shown in Fig. 14 b). III. EXPERIMENT In order to investigate the characteristics of the needle insertion device system, the experimental set-up is developed and a series of experiments are carried out. A prototype of the needle insertion device was developed for evaluating the feasibility and performance of the design. As shown in the Fig. 15, the flexure beam made of 2A12 aluminum alloy and the stainless-steel case were fabricated using CNC lathe machine (Sogaa Technology Co., Ltd, Shenzhen, China). The piezoelectric stack and piezoelectric ceramic slates were purchased from suppliers (PTH2502515301, Pant, China)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000349_tec.2020.2995902-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000349_tec.2020.2995902-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram for SPM motor with faults.",
        "texts": [
            " The effect of slotting is considered in the third step by conformal mapping, which is a method calculated from the conformal transformation of the slot geometry. The effect of stator saturation is considered in the fourth step by MEC method, and the expression of cogging torque is derived in the last step. Subsequently, the results calculated by the proposed method are then compared with FEA results and discussed in section V. The conclusions are drawn at the end of the paper. The schematic diagram of SPM motor with rotor eccentricity and PM defects is shown in Fig. 1. Three kinds of PM defects are considered in this paper, which are magnet misplacement, remanence variation, and pole-arc deviation, respectively. As shown in Fig. 1, there are two coordinate systems, XsOs-Ys, and Xr-Or-Yr, which are fixed to the stator center and rotor center, respectively. The counterclockwise direction is recognized as the positive direction of the motor rotation. The main geometric parameters are as follows: Rm, the radius of magnet surface; Rs, the inner radius of stator core; Rr, the outer radius of rotor core; e, the radial distance between stator and rotor center; \u03b1p, the pole-arc to pole-pitch ratio; \u0394\u03b1p, the polearc to pole-pitch ratio; \u0394\u03b1p, the deviation of pole-arc to pole- pitch ratio; \u0394Br, the deviation of magnet remanence from its desired value; \u0394\u03c4, the angle of the PM misplaced from its desired location; gei, the equivalent air-gap length of each concentric subdomain, which will be explained later"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000002_j.engfailanal.2018.04.050-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000002_j.engfailanal.2018.04.050-Figure3-1.png",
        "caption": "Fig. 3. The forces and moment applied on the jth ball.",
        "texts": [
            " = + + \u2212 \u2212A BD \u03b1 \u03b4 R \u03b8 \u03c8 R \u03b8 \u03c8 d \u03c8 \u03b1sin cos sin ( ) sin ,j z x j y j j1 o i i o (6) = + + \u2212 \u2212A BD \u03b1 \u03b4 \u03c8 \u03b4 \u03c8 r d \u03c8 \u03b1cos sin cos ( ) cos ,j x j y j L j2 o o (7) where BD denotes the unloaded relative distance between inner and outer raceway groove curvature centers O and B. D=[\u03b4x, \u03b4y, \u03b4z, \u03b8x, \u03b8y]T denotes the displacement vector, which consists of five degrees of freedom in ACBB. rL denotes the radial clearance, Ri denotes the orbit radius of the inner race groove curvature center, which is represented as follows = + \u2212R d f D \u03b10.5 ( 0.5) cos .i m i o (8) The jth ball is in the force equilibrium state as the bearing operates. The relations of forces and moment applied on jth ball are shown in Fig. 3, the jth ball is subject to the centrifugal force Fcj, gyroscopic moment Mgj and contact forces Qij, Qoj between jth ball and inner/outer raceways [30,33]. The formulae of above variables are represented as follows =F md \u03c91 2 ,jc m m 2 (9) =M J\u03c9 \u03c9 \u03b2sin ,jg R m (10) =Q K \u03b4 ,j ji i i 1.5 (11) =Q K \u03b4 ,j jo o o 1.5 (12) where m is the mass of ball, \u03c9m is the angular speed of ball rotating around the axis of bearing, J is the moment of inertia of ball rotating around the axis of itself, \u03c9R is the angular speed of ball rotating around the axis of itself, \u03b2 is the angle between axis of bearing and axis of ball itself, Ki and Ko are the contact stiffness between ball and inner/outer raceways [32]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure1.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure1.9-1.png",
        "caption": "Fig. 1.9",
        "texts": [
            " This is written as: m(x) = {p E Z' I there exists a sequence t1 < t2 < ... < t\" -c> +00 such that <p'\" x -c> p}. In the same way we can define a -limit point set as follows: a(x) = {p E Z' I there exists a sequence t1 > t2 > ... > t\" -c> -00 such that <p'\" x -c> p}. 18 Bifurcation and Chaos in Engineering Example 1 Consider the linear system: y'= -y, yeO) = 0 The solution ofthe system is yet) = Ce- I for the equilibrium point y = O. The orbit passing through the equilibrium point is reO) = O. The phase space is V = ;Ii? (see Fig. 1.9(a\u00bb and the phase time course is (t,q/y) = (t,Ce- l ) (see Fig. 1.9(b\u00bb. co(y): y = 0, co(y) = 0, y>O, Y < 0, co(y) = 0, a(y): y = 0, a(y) = 0, y > 0, a(y) = $, y < 0, a(y) = $. where $ is null set. Example 2. Consider the logistic equation: y'= y(l- y), Y E it:. The equilibrium point of the system is where y = 0 and y = 1, and the solution is y: .(1): ( I) . Th, ph\"\" diagnun \"\"d th' phM' tim\"o\",,,, \"\" ,hown 1- 1-~ e- I Yo in Fig. 1.1 O. ! The limit sets are ~ \u2022 1 co (y) = 0 for y > 0 I ~ co(y) = $ for y < 0 . 0 and coCO) = 0 = a(O) a(y) = 0 for y < 1 a(y) = $ for y > 1 a(l) = 1 = co(l) l (a) Example 3 Consider the two-dimensional system: x'= -y+x(l-x2 - /) y'= x+ y(1-x2 _ y2) By introducing a transformation x = rcose"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001213_j.mechmachtheory.2021.104245-Figure17-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001213_j.mechmachtheory.2021.104245-Figure17-1.png",
        "caption": "Fig. 17. Bifurcation configuration of evolved 4R linkage. (a) Bifurcation configuration of 4R mechanism (b) Its prototype.",
        "texts": [
            " Thus, the constraint-screw multiset can be derived as follows: S r l1 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 11 = ( 1 , 0 , 0 , 0 , 0 , f c \u03b8 ) T S r 12 = ( 0 , 1 , 0 , 0 , 0 , f s \u03b8 ) T S r 13 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S r 21 = ( 1 , 0 , 0 , 0 , 0 , \u2212 f c \u03b8 ) T S r 22 = ( 0 , 1 , 0 , 0 , 0 , \u2212 f s \u03b8 ) T S r 23 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad (20) where \u03b8 denotes the angle between the Y-axis and line OG, f is the length of OG. According to Eqs. (9) and (10) , card \u3008 S r \u3009 = 6 , dim S r = 4 . Hence, the mobility is m = 6 \u2212 6(1) + 6 \u2212 4 = 2 . Further, the motion of the other two joints E and G are restricted when the adjacent links EB 1 , EB 4, and GB 2 , GB 3 are also partially overlapped, respectively. Consequently, the overconstrained 4R linkage in Fig. 17 can be evolved from the 8R mechanism with renumbered new links B 2 B 3 and B 4 B 1 . The axes of joints B 1 , B 3, and B 2 , B 4 are collinear, respectively. The screws and the corresponding constraint-screw multiset of the mechanism can be written as follows: S r l1 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 11 = ( 0 , 0 , 0 , 0 , 0 , 1 ) T S r 12 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 13 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r 14 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad S r l2 = \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S r 21 = ( 0 , 0 , 0 , 0 , 0 , 1 ) T S r 22 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r 23 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S r = ( 0 , 0 , 1 , 0 , 0 , 0 ) T \u23ab \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23ad (21) 24 Apparently, the number of independent loops l is 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000700_j.matdes.2019.107881-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000700_j.matdes.2019.107881-Figure6-1.png",
        "caption": "Fig. 6. (a) Schematic of how the simulationmodel is related to the experimental setup. (b) Simulated temperature profile, revealing the isotherms derived from the HAZwhen the laser is in themiddle of the 3rd scanning line. (c) Simulated temperature history at 3 chosen points revealing the heating effects of the 2nd and 4th scanning lines on the 3rd scanning. Curves are as color-coded with respect to the isotherms in (b).",
        "texts": [
            " From the above analyses, it is suggested that the high dislocation density, high-density of grain boundaries in the as-built material as well as the heterogeneous nature of the microstructure contribute to the superior mechanical properties of our SLM printed 4130. To understand the thermal history and effects underlying themicrostructural heterogeneity, the associated heat transfer in the SLMprocess was investigated using a laser absorption and heat transfermodel as developed in our previous work [25]. Simulation model here consists of 5 successive scanning lines, of which the effects by the adjacent scanning lines on the temperature profiles of the 3rd scanning line and the 2 layers beneath it were investigated (Fig. 6a,b). Based on calculations from this model, cooling rates were calculated to be on the order of 106 K/s, several orders of magnitude far above the quenching rate required for martensite formation in 4130 [35]. It can be seen from the temperature profile in Fig. 6b that there is a significant part of the second layer below the melting temperature but above the Ae3 temperature which may be calculated by Andrews equation [36] for 4130 to be 786 \u00b0C. The Ae3 temperature is the temperature at which austenite becomes the only thermodynamically favored phase at equilibrium. Research has shown that displacive austenite reversion can occur in lowalloy steels [37] at sufficiently high heating rates and the austenitefinish temperature is above but still closer to Ae3 than would be expected for diffusive austenite reversion. As such, re-austenization is expected to take place at some temperature above Ae3 despite the short time frame of the heating and cooling. As can be seen from the heating and cooling profiles in Fig. 6c, the isotherm corresponding to Ae1, which is the temperature at which austenite begins to become thermodynamically favored, is very close to the Ae3 isotherm due to the steep thermal gradient. Fig. 6c shows that as the subsequent adjacent track is scanned, the temperature along the center of the previously scanned track experiences a limited rise not beyond Ae3. To explain the associated microstructural evolution, a model based on simulation studies is proposed in Fig. 7; describing the initial printed microstructure from each individual scanning pass of the laser to the final bulk microstructure. Upon laser scan, apart from the melt-track in the powder layer, the area bounded by the melting temperature isotherm is also remelt"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001175_j.matchar.2021.110969-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001175_j.matchar.2021.110969-Figure12-1.png",
        "caption": "Fig. 12. 3D optical scanned images of as-built and annealed samples. [Note: the deflection of the cantilever\u2019s tip is alleviated after 8.5 h of heat-treatment].",
        "texts": [
            " On the other hand, after the annealing process, the strain hardening rate was observed to be higher in the horizontal direction compared to the vertical one. This can be attributed to the remaining as-built columnar grains in the microstructure after 8.5 h of annealing (Fig. 5 (h,p)). To investigate the effectiveness of the heat-treatment process in terms of relieving the internal stresses, cantilevers were produced on LPBF substrates and support structures. In the as-built sample, after cutting cantilevers from the support structure, the deflection of the cantilever\u2019s tip was around 2.1 \u00b1 0.1 mm (Fig. 12(a,b)). However, annealing of the sample for 8.5 h before support removal results in no significant deflection of the cantilever after the cutting process (Fig. 12 (c,d)). Interaction between the elastic stress fields around dislocations may generate internal stresses in the material [20]. For example, the repulsive force between two positive and parallel screw dislocations is F = Gb2 2\u03c0x, where G, b, and x are the shear modulus of the material, Burgers vector, and distance between the dislocations, respectively [20,41]. As dislocation density increases in the material, the average distance between dislocations decreases, which in turn, increases the internal stresses"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000301_s13369-020-04742-w-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000301_s13369-020-04742-w-Figure1-1.png",
        "caption": "Fig. 1 \u00d7-mode configuration of quadrotor UAV",
        "texts": [
            " Compared to APID without Fuzzy [37, 41, 40], the proposed method use fuzzy to compensate chattering phenomenon by SMC. The rest of the paper is organized as follows. Section II describes the dynamic model of the quadrotor in ( \u00d7 ) mode configuration. Section III shows the design of the APIDC for both attitude and position control of the quadrotor. Section IV presents the simulation results of the APIDC system without and with the presence of external disturbance and comparison with PID and SMC, and finally, Section V contains the conclusion of the paper. The \u2018X\u2019 configuration quadrotor, as illustrated in Fig.\u00a01, comprises four symmetrical arranged rotors. To eliminate the anti-torque effects, the motors (1 and 2) are running in the counter-clockwise direction whereas the other motors (3 and 4) are driven in the clockwise direction [6, 48, 49]. Several assumptions are made in order to simplify the quadrotor\u2019s mathematical model. The assumptions are as follows [50]: 1. The fuselage is assumed to be rigid. 2. The body frame of the fuselage is assumed to be sym- metrical for the XY axis. 3. The centre of mass coincides with the origin of the body-fixed frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003620_s0045-7825(02)00215-3-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003620_s0045-7825(02)00215-3-Figure5-1.png",
        "caption": "Fig. 5. Shape of the modified fillet of the face gear.",
        "texts": [
            " Investigation shows that the surface points of the face gear are hyperbolic ones. This means that the product of principal curvatures at the surface point is negative. The fillet of the face-gear tooth surface of a conventional design (Fig. 3) is generated by the edge of the shaper. The authors have proposed to generate the fillet by a rounded edge of the shaper as shown in Fig. 4 that allows the bending stresses to be reduced approximately in 10%. The shape of the modified fillet of the face gear is shown in Fig. 5. The length of the face-gear teeth has to be limited by dimensions L1 and L2 (Fig. 6) to avoid [8]: (i) undercutting in plane A, and (ii) tooth pointing in plane B. The permissible length of the face-gear tooth is determined by the unitless coefficient c represented as c \u00bc \u00f0L2 L1\u00dePd \u00bc L2 L1 m \u00f01\u00de where Pd and m are the diametral pitch and the module, respectively. The magnitude of coefficient c depends mainly on the gear ratio m12 \u00bc N2=N1 and is usually in the range 8 < c < 15. TCA is designated for simulation of meshing and contact of surfaces R1 and R2 and enables us to investigate the influence of errors of alignment on transmission errors and shift of bearing contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000522_j.ijsolstr.2019.09.007-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000522_j.ijsolstr.2019.09.007-Figure5-1.png",
        "caption": "Fig. 5. Overview of origami specimen microstructure. Locations and orientations of extracted facets are shown in (a), with etched micrographs (20x) of each in (b)\u2013(f). Further magnification (50x) of (b) and (c) is shown in Fig. 6 .",
        "texts": [
            " Subsequently, we will take the nominal relative density values o be those obtained from the CAD model, and the experimental alues to be those from the mass measurements. .2. Specimen microstructure Several facets from a small thick-walled specimen were exracted, mounted, and polished. They were then etched with Glycregia for one minute in order to assess the microstructure resultng from the SLM process, and its sensitivity to facet orientation. he locations and orientations of these facets, as well as optical icrographs of each, are shown in Fig. 5 . The various facets are d origami cellular materials: Additive manufacturing, properties, i.org/10.1016/j.ijsolstr.2019.09.007 6 J.A. Harris and G.J. McShane / International Journal of Solids and Structures xxx (xxxx) xxx Please cite this article as: J.A. Harris and G.J. McShane, Metallic stacked origami cellular materials: Additive manufacturing, properties, and modelling, International Journal of Solids and Structures, https://doi.org/10.1016/j.ijsolstr.2019.09.007 J.A. Harris and G.J. McShane / International Journal of Solids and Structures xxx (xxxx) xxx 7 Please cite this article as: J",
            " McShane / International Journal of Solids and Structures xxx (xxxx) xxx Table 1 Nominal and experimental relative densities for the three origami specimens. Small thick-walled Small thin-walled Large thick-walled Nom. Analytical 26.4% 13.2% 26.4% CAD 22.2% 11.5% 22.2% Exp. From CT 2D 31.0% 20.4% 24.6% From CT 3D 29.3% 23.8% 18.7% From mass 30.5% 18.9% 19.1% Fig. 7. Overview of tensile coupon microstructures and locations of following micrographs. 4 s p c a p s r b d s m Y 2 s t S l c p t similar to one another in terms of microstructural feature sizes, and are relatively free from porosity. Some irregularly shaped voids apparent in Fig. 5 are artefacts of the polishing and etching process (a consequence of thin facets with large thickness variations, resulting in occasional through-etching). Further magnification of Fig. 5 (b) and (c) are shown in Fig. 6 . The microstructure is representative of SLM processed 316L stainless steel ( Harris et al., 2017; Casati et al., 2016; Wang et al., 2017 ): curved melt pool boundaries are apparent, in a consistent orientation with respect to the build direction. There are several grains within the melt pools, with some fine sub-grain structure apparent. Fine sub-grain structures have been attributed to the rapid solidification conditions ( Winter et al., 2014; Casati et al., 2016; Harris et al",
            " 3 3 Two build operations were required due to the quantity of specimens. The first build contained 8 small thin-walled origami specimens, 8 small thick-walled o t c Please cite this article as: J.A. Harris and G.J. McShane, Metallic stacke and modelling, International Journal of Solids and Structures, https://do .1. Microstructure of dogbone specimens The microstructures revealed by etching and polishing the grip ections of dogbone test specimens are shown in Fig. 7 , for comarison with the origami specimens shown in Fig. 5 . The mirostructural features and feature sizes in the dogbone specimens re similar to those in the cellular specimens. However, more orosity is apparent in the dogbone specimens. Close inspection hows the pores to be approximately spherical, with diameters anging from approximately 10\u201330 \u03bcm, occurring primarily at the ases of the melt pools. This is indicative of a gas-bubble-related efect, either by contaminants introduced during the gas atomiation of the powder, or by excessive laser power density causing aterial vaporisation ( Tang et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000420_j.triboint.2020.106200-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000420_j.triboint.2020.106200-Figure1-1.png",
        "caption": "Fig. 1. LPBF Ti6Al4V samples configuration and build-up orientation. The colored face indicates the one that will be machined afterwards.",
        "texts": [
            " The machined surface quality was evaluated using 3D profilometry, whereas the effect of the tool wear evolution on the chip morphology, machined surface defects, and burrs extent was further assessed through SEM observations. Moreover, a novel insight into the correlation between the cutting tool life and the AM-induced anisotropy of the workpiece was given. LPBF Ti6Al4V (grade 5) rectangular prisms (15 \ufffd 30 \ufffd 10 mm3) were manufactured at four orientations ranging from 0\ufffd to 90\ufffd with respect to the horizontal plane of the powder bed (Fig. 1). The four prisms will be hereafter named 0deg, 36deg, 72deg, and 90deg to differentiate the manufacturing inclination. The reference system XYZ to refer to throughout the paper is the one shown in Fig. 1. The MYSINT100 SISMA\u2122 machine was used for the parts manufacturing, which is characterized by a cylindrical building volume with a base of 100 mm in diameter and a height of 100 mm. The chamber works under inert atmosphere of argon. The laser unit has a maximum power of 200 W and a spot diameter of 30 \u03bcm. The plasma-atomized Ti6Al4V powder was supplied by LPW Technology\u2122 in the size range between 15 and 45 \u03bcm. The prims were manufactured using the island scanning strategy with laser power of 105 W, scanning speed of 950 mm/s, hatch spacing and layer thickness of 80 \u03bcm and 20 \u03bcm, respectively",
            " The measurement of the columnar prior \u03b2 grains width and of the \u03b1 lamellae thickness was carried out using Matlab\u2122 on six different micrographs at 50\ufffd and 1000\ufffd of magnification, respectively. The Leitz\u2122 Durimet microhardness tester was used to perform Vickers microhardness measurements with a load of 100 g for 30 s following the ASTM E92-17 standard [17]. Three series, each with ten indentations, were performed on the XZ lateral surface of every sample, perpendicular to the upper face (the colored one in Fig. 1). The three series were randomly distributed far enough from each other, spacing the indentations of 60 \u03bcm. The microhardness values were recorded for each indentation and the average value calculated. To evaluate the effect of the build-up direction on the LPBF Ti6Al4V machinability, full slots were machined on the upper surface of each specimen (the colored one in Fig. 1). The tests were carried out using the ultra-precision micro-milling machine Kugler\u2122, Micromaster 5X under Minimum Quantity Lubrication (MQL) conditions using a vegetablebased oil, the Accu-Lube\u2122 LB 5000, which is known to be effective for difficult to cut materials, beside the other MQL benefits [18,19]. The oil mist was supplied to the cutting zone at 50 mm of distance with an angle of about 30\ufffd by a flexible nozzle of 0.5 mm of diameter, with a flow rate and air pressure of 150 ml/h and 0.70 MPa, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.87-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.87-1.png",
        "caption": "Fig. 5.87: Chain Link Model",
        "texts": [
            " All degrees of freedom can be collocated in qP = (x, y, zM , \u03d5,\u2206\u03d1F , \u03b30,F , \u2206\u03d1M , \u03b30,M )T . The relative distances and the complementary behavior, as indicated in Figure 5.86, can then be formulated as follows: gi = grig,i + gel,i = g+ i \u2212 g\u2212i , g\u2212i = c\u22121 rp Frp,i, gel,i = \u2211 j wijFrp,j g+ i = \u2211 j wijFrp,j + c\u22121 rp Frp,i + grig,i g+ = WFrp + grig, with Frp \u2265 0, g+ \u2265 0, FTrpg + = 0 (5.125) Each link represents an elastic body with three translational rigid body degrees of freedom and in addition the elastic degrees of freedom. The angles \u03b2L and \u03b3L, shown in Figure 5.87, kinematically depend on the translational position of the successor link. In order to describe the orientation and elastic deformation of a pin some more degrees of freedom qel = (qTel,x qTel,y) T have to be introduced. We distinguish between the radial (y) and azimuthal (x) directions. Thus the set of generalized coordinates can be written as qL = (xL yL zL qTel) T . The links are kinematically interconnected by pairs of rocker pins. The elasticity and the translational damping of the joint is taken into account by the link force element whereas the rotational damping and the axial friction between the pair of pins is considered by the joint force element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure12-1.png",
        "caption": "Fig. 12. Operating circles in an aligned gear drive: (a) change of center distance DE \u00bc 0 when no errors are applied; (b) DE 6\u00bc 0.",
        "texts": [
            " 19) m module m12, mwp gear ratios between pinion and gear and between worm and pinion, respectively Mij matrix of coordinate transformation from system Sj to system Si n \u00f0j\u00de i , N \u00f0j\u00de i unit normal and normal to surface Rj in coordinate system Si Ni number of teeth of pinion (i \u00bc 1; p), gear (i \u00bc 2) or worm (i \u00bc w) p1, p2 screw parameters of the pinion and the gear, respectively ri radius of pinion (i \u00bc p1; p), gear (i \u00bc p2) or worm (i \u00bc w) pitch cylinder rd1 dedendum radius of the pinion r i radius of pinion (i \u00bc p1) or gear (i \u00bc p2) operating circle (Fig. 12) ri position vector of a point in coordinate system Si sa parameter of pinion topland (Fig. 28) si displacement of pinion (i \u00bc c) or gear (i \u00bc t) rack-cutter during the generation of profile- crowned pinion or gear, respectively (Fig. 9) s1, s2 dimensions of pinion and gear rack-cutter teeth, respectively (Fig. 6) Si\u00f0Oi; xi; yi; zi\u00de coordinate systems (i \u00bc a; b; c; e; k; t;m; r; s; 1; 2; f ; q; h;D) \u00f0ui; hi\u00de parameters of surface Ri The existing design and manufacture of involute helical gears provide instantaneous contact of tooth surfaces along a line",
            " The resulting motion of the contact point in the fixed coordinate system is a translational motion with the velocity piX \u00f0i\u00de along line M\u2013M since rotations in transfer and relative motions are performed with X\u00f0i\u00de \u00bc x\u00f0i\u00de. (7) It is easy to verify that the contact point moves over the helicoid surface along a helix that is generated by point M while it performs a screw motion over the surface of the helicoid. The path of contact on the surface of the helicoid is a helix which radius qi and the lead angle ki are related by pi \u00bc qi tan ki (i \u00bc 1; 2). (8) The meshing of the mating helicoids is not sensitive to the change of the center distance. Considering the drawings of Fig. 12, it is easy to verify that the change of the center distance does not cause trans- mission errors. We may assume that the crossing profiles form a center distance E 6\u00bc E. This may affect that the point of tangency will be M instead of M and the pressure angle will be a instead of a. The new radii of centrodes will be r pi (i \u00bc 1; 2). However, the line of action in the fixed coordinate system is again a straight line that is parallel to the gear axes, but passes now through point M instead of M ",
            " Results of computation are as follows: (1) Drawings of Fig. 15 illustrate the shift of bearing contact caused by error DE. (2) The path of contact is orientated indeed longitudinally (Figs. 15, 16(b) and (c)). (3) Error DE of shortest center distance does not cause transmission errors. The gear ratio m12 remains constant and of the same magnitude m12 \u00bc x\u00f01\u00de x\u00f02\u00de \u00bc N2 N1 : \u00f028\u00de However, change of DE is accompanied with the change of radii of operating pitch cylinders and the operating pressure angle of cross-profiles (Fig. 12). (4) The main disadvantage of meshing of profile-crowned tooth surfaces is that Dc and Dk cause a dis- continuous linear function of transmission errors as shown in Fig. 16(a). Such functions cause vibra- tion and noise and this is the reason why a double-crowned pinion instead of a profile-crowned one is applied. Errors Dc and Dk cause as well the shift of the bearing contact on the pinion and gear tooth surfaces. Our investigation shows that the main defects of the gear drive for the case wherein L 6\u00bc 0 and Dc 6\u00bc 0 are the unfavorable functions of transmission errors, similar to the one shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000587_jestpe.2021.3057665-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000587_jestpe.2021.3057665-Figure1-1.png",
        "caption": "Fig. 1. Structure of MG-IPMBM.",
        "texts": [
            " Its purpose is to replace the existing drive device with high efficiency, low speed and high torque drive. In Section II, the structure and field circuit coupling simulation model of the MG-IPMBM will be introduced. Section III describes the transient electromechanical characteristics of the MG-IPMBM. In Section IV, a prototype and experimental platform are built, and the test results are given. Finally, several conclusions are drawn in Section V. The MG-IPMBM is composed of two parts, the internal PM motor, and the external MG, its structure is shown in Fig. 1. The high-speed inner rotor (HIR) of MG-IPMBM is composed of PM motor\u2019s rotor and MG high-speed rotor (MGHR) through a stainless steel ring, the low-speed outer rotor (LOR) of MG-IPMBM is the low-speed rotor of MG. The two rotor PMs are arranged in Halbach array, and the arrow indicates the magnetizing direction. Because of the Halbach array, the magnetic field in the yoke of the rotor core is relatively weak, so the thickness of the yoke can be appropriately reduced, which not only saves the silicon steel material but also reduces the total volume of the MG-IPMBM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure9.7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure9.7-1.png",
        "caption": "Fig. 9.7 Elastic ring model for contact analysis [7]",
        "texts": [
            "0 Contact angle (degree) 0 5 10 15 middle ribcenter rib outer rib middle center outer 20 Fig. 9.5 Comparison of the contact pressure distribution in the circumferential direction between calculation and measurement (TBR 10.00R20). Reproduced from Ref. [2] with the permission of J. Appl. Mech. 9.2 Contact Analysis of Tires Using an Elastic Ring Model 549 Gong [7] used the same model as Huang et al. [5, 6] to solve the contact problem of the elastic ring model for a tire by applying Fourier series expansion in the circumferential direction. As shown in Fig. 9.7, kT denotes the tread spring rates, while kr and kt, respectively, denote fundamental spring rates in the radial and circumferential directions. a is the radius of the tread ring, and a is the radius of the tread surface. In the right figure of Fig. 9.7, /f and /r are, respectively, the contact angles at the leading edge (front) and trailing edge (rear), w is the radial displacement of the tread ring, and d0 is the overall tire displacement at the center of the contact patch. Referring to Fig. 9.2, the displacement k of the tread rubber is approximated using Eq. (9.10), in which the displacement v in the circumferential direction is neglected because v is much smaller than w. The contact pressure q(/) is expressed by Eq. (9.14). (1) Tire response to a concentrated force The fundamental equation of the inextensible elastic ring model for a tire is given as Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure7.8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure7.8-1.png",
        "caption": "Fig 7.8",
        "texts": [
            "1<; + 0.975'11) sinl.6tcosl.6t (7.63) 246 Bifurcation and Chaos in Engineering The solution corresponding to C;(O) = 0,11(0) = 0 is shown in Fig. 7.7. Its fixed points are C; = C;A = -0.634, 11 =l1A = 0.06. This satisfies eq. (7.63). When t ~ 00, every solution (as the curve in the figure) tends to this fixed point. Now, we average eq. (7.63), and obtain C;' = -0.065C; - 0.487511 11' = 0.4875C; + 0.0511 + 0.3125 (7.64) The solution with the initial condition C;(O) = 0 and 11(0) = 0 is shown in Fig7.8. Comparing it with Fig. 7.7, we can see the averaging results. The fixed points are the same in both figures. Application of the Averaging Method in Bifurcation Theory 247 The general form of the averaging equation of the non-linear forced vibrating system is x\" +ro~x = E/(X,X') + EFcosrot Using the coordinate transformation x = ~cosrot + T\\sinrot x' . - = y = ~smrot + T\\cosrot ro This means adding a condition ~' cos rot + T\\' sinrot = 0 Substituting (7.66) into (7.65), we have (ro~ - ro 2 }~cosrot + (ro~ - ro 2 )T\\sinrot - ro~'sinrot + roT\\' cosrot = E/( ~cosrot + T\\sinrot",
            " For the original vibration system, the motion finally tends to S or S' , depending upon the initial conditions. These two regions are twinned to each other. The proper change of the initial condition will cause great variation in the final stationary states. 252 Bifurcation and Chaos in Engineering The twinning of the two-attractor regions, however, is not the whole of the problem. Fig. 7.13 is the phase diagram of the averaging equation on the rotating plane. Let us discuss again the phase diagram of the averaging equation and the real equation as shown in Fig. 7.8 and Fig. 7.7. Can we guess the type of Fig. 7.7 from Fig. 7.8 ? It is possible in linear systems, because there is only one equilibrium point A. However, it is rather complicated if we guess the real c; plane curves from Fig. 7.13. Roughly speaking, the periodic wave added to the track line in Fig. 7.13 will not be large if the amplitude is not large. So even if the shape of the dividing line is not as smooth as that in Fig. 7.14, we can still divide the plane into two parallel bands, that is to say, there exist two attractor regions. But, if the amplitude of the disturbing force is large enough, then the amplitude of the wave to be added is large"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure7-24-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure7-24-1.png",
        "caption": "Figure 7-24. Low-inductance design of large VSIs.",
        "texts": [
            "on, \u03a1,-0\u03ba within the semiconductors are small compared to the snubber losses PLC. Since PLC, the largest loss component, as well as P\u00a1.on and -P,-0fr increase proportionally to the switching frequency F, it becomes plainly recognizable why high-power GTO inverters can be operated only with a maximum switching frequency of F \u00ab 300 Hz per GTO or rather less ( < 200 Hz) in practical applications [38]. With conventional RLCD snubber circuits (Figure 7-20), these disadvantages become clearly obvious. Even if improved snubber circuits (Figure 7-24) [39, 40] with reduced losses (about 60%) are used, the problems still cannot be solved properly. The use of energy recovering snubber circuits leads to further improvements, but also to voluminous and expensive solutions and\u2014if common to all three phases\u2014to restrictions in the PWM pulse patterns. Therefore, one main objective for large drives configurations must be, to reach a given maximum speed with the lowest possible switching frequency and the lowest possible current and torque harmonics (see Section 7",
            " The control method should be changed at fx \u00bb 65 Hz from PWM switching with F= 300 Hz to switching with fundamental frequency F=f\\ = 65- 130 Hz. Voltage source inverters need a careful mechanical design. Due to the physical size of the circuit components, to the space needed for electrical insulation and to the increased distances to the hot snubber resistors, all current loops must be regarded as parasitic inductances. Currents, switched off within these loops by semiconductors cause high dv/dt and voltage stresses which reduce the attainable rated power. Lowinductance design therefore is a must! Figure 7-24 left shows the four loops a, blt b2, and c in a two-level GTO inverter circuit with RLCD snubbers [39] in which currents are switched with high di/dt. These loops have to be kept as small as possible. Figure 7-24 right shows how this has to be done basically: \u2022 Low-inductance capacitors CDC with sandwiched connections to the semiconductors (loop a) \u2022 Snubber capacitors C and diodes located as close as possible to the GTOs (loops b\\, b2) \u2022 Snubber resistors R with low-inductance design and sandwiched connections to the other snubber elements (loop c). 384 7. High-Power Industrial Drives Snubber inductors L in toroidal form keep the magnetic field inside the choke, thus avoiding inductive heating of neighboring metallic components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003221_s0094-114x(98)00081-0-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003221_s0094-114x(98)00081-0-Figure6-1.png",
        "caption": "Fig. 6. 3-RRRS spatial manipulator.",
        "texts": [
            " After substituting the expressions obtained from kinematic relationship, and simplifying, we get F \u00ffQap U kfk sfs 31 The expressions for Q and U are given by Q mussT mu L s k ru snT nsT mu mm md kkT a1 L2 nnT U mu s g \u00ffmus W W ru \u00ffmuu3 \u00ff mu L s k ru u4 s h mu mm md k g \u00ff muW W ru mmW W rm mdW W rd k\u00ff 2mu _Lk W s \u00ff mu mm u1 \u00ffmu k s u3 i k 1 L muk ru g mmk rm g \u00ff k W Iu Im W \u00ffmuk ru s u3 \u00ff a1u4 n where a1 mm k rm 2 mu k ru 2 k Iu Im k Finally, we consider the force and moment equilibrium of the platform to obtain \u00ffMp t a R o o R Mpg X3 i 1 Fi 0 32 and \u00ffMpR t a R o o R MpR g\u00ff Ipa \u00ff o Ipo X3 i 1 qi Fi 0 33 Combining the above two equations and including external forces, M t a Z HF RExt MExt 34 where M 2666664 MpE3 X3 i 1 Qi \u00ff Mp ~R X3 i 1 Qi ~q i Mp ~R X3 i 1 ~q iQi Ip Mp R2E3 \u00ff RRT X3 i 1 ~q iQi ~q i 3777775 Z 2666664 Mp o o R \u00ff g \u00ffX3 i 1 Ui o Ipo MpR o R o \u00ff g \u00ffX3 i 1 qi Ui 3777775 H k1 k2 k3 s1 s2 s3 q1 k1 q2 k2 q3 k3 q1 s1 q2 s2 q3 s3 F fk1 fk2 fk3 fs1 fs2 fs3 T The dynamic formulation of the 3-RRRS hybrid manipulator (see Fig. 6) is conceptually similar to the 3-PRPS case described above. Here, each of the three legs of the manipulator is a 3-R serial chain, two of the revolute joints being actuated. Thus, the entire con\u00aeguration of a leg can be described in terms of the three joint angles. For the task-space modeling, after determining the platform point from the task-space coordinates, the inverse kinematics of this 3-R chain has to be carried out for position, velocity and acceleration. For solving the reaction force at the spherical joint, we need three scalar equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000055_j.msea.2017.02.004-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000055_j.msea.2017.02.004-Figure6-1.png",
        "caption": "Fig. 6. The scheme of sample preparation for impact loading of XY (a) and Z (b) type samples.",
        "texts": [
            " This, however, is not the case with cast material (Fig. 5b). Here, the fracture is also ductile but the sizes of the dimples vary from a few to tens of microns and fracture-associated damage is strongly developed in the direction normal to the fracture surface. The latter trait seems to be related to the distribution of preferred void nucleation sites in the inherently non-homogeneous material. Samples for planar impact tests (20 mm diameter disks of nominal thickness 0.3, 1, 2 3 and 4 mm) were cut from the parts with Z orientation, as shown in Fig. 6. Moreover, samples of the same geometry were cut from the ingot of the cast alloy. This was done so as to study the decay of an elastic precursor wave in both the SLM and cast alloys. From XY oriented parts only disks of 2-mm thickness were prepared. All of the disks were grinded to approximately 1 mrad parallelism, and prior to the planar impact tests the 2 mm-thick disks were used for determination of the longitudinal cl and shear cs speeds of sound (pulse-echo technique, 5 MHz transducers). The bulk speed of sound was calculated as c c c= \u2212 4/3b l s 2 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003777_s0045-7825(03)00367-0-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003777_s0045-7825(03)00367-0-Figure1-1.png",
        "caption": "Fig. 1. Contact lines on an involute helical tooth surface.",
        "texts": [
            " 28) si displacement of pinion (i \u00bc c) or gear (i \u00bc t) rack-cutter during the generation of profile- crowned pinion or gear, respectively (Fig. 9) s1, s2 dimensions of pinion and gear rack-cutter teeth, respectively (Fig. 6) Si\u00f0Oi; xi; yi; zi\u00de coordinate systems (i \u00bc a; b; c; e; k; t;m; r; s; 1; 2; f ; q; h;D) \u00f0ui; hi\u00de parameters of surface Ri The existing design and manufacture of involute helical gears provide instantaneous contact of tooth surfaces along a line. The instantaneous line of contact of conjugated tooth surfaces is a straight line L0 that is the tangent to the helix on the base cylinder (Fig. 1). The normals to the tooth surface at any point of line L0 are collinear and they intersect in the process of meshing the instantaneous axis of relative motion that is the tangent to the pitch cylinders. The concept of pitch cylinders is discussed in Section 2. The involute gearing is sensitive to the following errors of assembly and manufacture: (i) the change Dc of the shaft angle, and (ii) the variation of the screw parameter (of one of the mating gears). Angle Dc is formed by the axes of the gears when they are crossed, but not parallel, due to misalignment (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure11-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure11-1.png",
        "caption": "Fig. 11. For generation of shaper and pinion by rack-cutters: (a) generation of the shaper, (b) installment of pinion rack-cutter, and (c) generation of the pinion.",
        "texts": [
            " 9) Dc change of shaft angle (Fig. 8) DE change of shortest distance between the pinion and the face-gear axes (Fig. 7) Dq axial displacement of face-gear (Fig. 8) kw crossing angle between axes of shaper and worm (Fig. 21) cm shaft angle (Figs. 4, 8, 12) Ri \u00f0i \u00bc s; 1; 2;w\u00de tooth surface of the shaper (i \u00bc s),the pinion (i \u00bc 1), the face-gear (i \u00bc 2) and the generating worm (i \u00bc w) wj \u00f0j \u00bc r; e\u00de angle of rotation of the shaper (j \u00bc r) and the pinion (j \u00bc e) considered during the process of generation (Fig. 11) wi \u00f0i \u00bc s;w\u00de angle of rotation of the shaper considered during the process of generation of the face-gear (i \u00bc s) and the worm (i \u00bc w) (Figs. 12, 21) wi \u00f0i \u00bc 2;w\u00de angle of rotation of the face gear (i \u00bc 2) and the worm (i \u00bc w) considered during the process of generation (Figs. 12, 21) h\u00f0i\u00de j ; u\u00f0i\u00dej \u00f0j \u00bc s; 1\u00de surface parameters of the rack-cutter for the shaper (j \u00bc s) and the pinion (j \u00bc 1), for driving side (i \u00bc d) and coast side (i \u00bc c) (Fig. 9) Ews shortest distance between the axes of the worm and the shaper (Fig",
            " Normal Nr to the shaper rack-cutter is represented as Nr\u00f0ur\u00de \u00bc cos ad \u00fe 2arur sin ad sin ad \u00fe 2arur cos ad 0 2 4 3 5 \u00f05\u00de Similarly we may represent vector function re\u00f0ue; he\u00de of pinion rack-cutter A1 and normal Ne\u00f0ue\u00de. The designed parabolic profiles of rack-cutters As and A1 are represented in Fig. 9. We apply for derivation of shaper tooth surface Rs: (i) movable coordinate systems Sr and Ss that are rigidly connected to the shaper rack-cutter and the shaper, and (ii) fixed coordinate system Sn (Fig. 11(a)). Rack-cutter As and the shaper perform related motions of translation and rotation determined by (rpswr) and wr (Fig. 11(a)). The shaper tooth surface Rs is determined as the envelope to the family of rack-cutter surfaces As whereas considering the equations rs\u00f0ur; hr;wr\u00de \u00bc Msr\u00f0wr\u00derr\u00f0ur; hr\u00de \u00f06\u00de Nr\u00f0ur\u00de v\u00f0sb\u00der \u00bc fsr\u00f0ur;wr\u00de \u00bc 0 \u00f07\u00de Here vector function rs\u00f0ur; hr;wr\u00de represents in Ss the family of rack-cutter As tooth surfaces; matrix Msr\u00f0wr\u00de describes coordinate transformation from Sr to Ss; vector function Nr\u00f0ur\u00de represents the normal to the rack-cutter As (see Eq. (5)); vr is the relative (sliding) velocity. Eq. (7) (the equation of meshing) yields fsr\u00f0ur;wr\u00de \u00bc xrNys yrNxb rpsNyb wr \u00bc 0 \u00f08\u00de Finally, we represent surface of the shaper by vector function rs\u00f0ur\u00f0wr\u00de;wr; hr\u00de \u00bc Rs\u00f0wr; hr\u00de \u00f09\u00de The normal to the shaper is represented in coordinate system Ss as Ns \u00bc oRs owr oRs ohr \u00f010\u00de Movable coordinate systems Se and S1 are rigidly connected to the pinion rack-cutter and pinion, respectively (Fig. 11(b) and (c)); S n is the fixed coordinate system. The installment angle Db (Fig. 11(b)) is provided for the improvement of the bearing contact between the pinion and the face-gear (see Section 6). Derivations similar to those applied in Section 4.1 are based on the following procedure: Step 1: We obtain the family of pinion rack-cutters represented in coordinate system S1 as r1\u00f0ue; he;we\u00de \u00bc M1e\u00f0we\u00dere\u00f0ue; he\u00de \u00f011\u00de where matrix M1e describes coordinate transformation from Se via S n to S1 (Fig. 11(b) and (c)). Step 2: Using the equation of meshing between the rack-cutter and the pinion, we obtain ue\u00f0we\u00de \u00bc xeNye yeNxe rp1Nye we \u00f012\u00de Generation of R2 by a shaper is represented schematically in Fig. 4. We apply for the derivation of R2 (see Fig. 12): (i) movable coordinate systems Ss and S2, rigidly connected to the shaper and the face-gear, respectively, and (ii) fixed coordinate system Sm and Sp, rigidly connected to the housing of the generating equipment. Surface R2 of the face-gear is determined as the envelope to the family of shaper surfaces Rs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000488_tmech.2019.2945525-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000488_tmech.2019.2945525-Figure5-1.png",
        "caption": "Fig. 5 Schematic diagram of the parallel mechanism",
        "texts": [
            " Various types of handles can be attached to the terminal mechanical interface of the master device including 1) the handle with an electrosurgical pencil for the monopolar electrotome; 2) the handle with a switch for the electrocoagulator; and 3) the handle with a cylinder block which can be rotated and triggered for the needle holder, forceps, and scissor (Fig. 2 (f)). The purpose of the stiffness modeling in this section is to evaluate the stiffness of the manipulator quantitatively, providing a reference for the application of the VS mechanism. Table II summarizes the notation used in this paper. 1083-4435 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. As shown in Fig. 5, \ud835\udc5c\ud835\udc35 \u2212 \ud835\udc65\ud835\udc35\ud835\udc66\ud835\udc35\ud835\udc67\ud835\udc35 at the base platform is defined as the base coordinate frame. \ud835\udc35\ud835\udc56 are the intersections of chains and the base platform. \ud835\udc56 ( \ud835\udc56 = 1,2,3) is the number of chains. \ud835\udc59\ud835\udc56 is the length of chains. \ud835\udc5c\ud835\udc43 \u2212 \ud835\udc65\ud835\udc43\ud835\udc66\ud835\udc43\ud835\udc67\ud835\udc43 attached to the moving platform formed by universal joints \ud835\udc43\ud835\udc56 is the moving coordinate frame. \ud835\udc43\ud835\udc56 \u2212 \ud835\udc65\ud835\udc43\ud835\udc56 \ud835\udc66\ud835\udc43\ud835\udc56 \ud835\udc67\ud835\udc43\ud835\udc56 is the coordinate system attached to \ud835\udc43\ud835\udc56 , where \ud835\udc65\ud835\udc43\ud835\udc56 \ud835\udc66\ud835\udc43\ud835\udc56 plane coincides with \ud835\udc65\ud835\udc43\ud835\udc66\ud835\udc43 plane. \ud835\udc5f\ud835\udc35 and \ud835\udc5f\ud835\udc43 are the radiuses of the circles which are formed by \ud835\udc35\ud835\udc56 and \ud835\udc43\ud835\udc56 , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.44-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.44-1.png",
        "caption": "Fig. 5.44 Comparison of displacements in the bead area under loading (reproduced from Ref. [21] with the permission of Tire Sci. Technol.)",
        "texts": [
            " The TCOT shape has a larger radius of curvature in the bead area than the natural equilibrium shape. The carcass ply tension in the bead area is therefore higher for the TCOT tire than for the tire with a natural equilibrium shape. Owing to this tensile effect, the flexural rigidity of the TCOT tire is higher than that of the tire with a natural equilibrium shape in the bead area. The bead area deformation is smaller for the TCOT tire than for the tire with a natural equilibrium shape during loading, as shown in Fig. 5.44. The strains at the ply end are lower for the TCOT tire than for the tire with a natural equilibrium shape under loading. Both the compressive strain during inflation and the small strain during loading improve the bead durability of TCOT tires. Compared with the tire having a natural equilibrium shape, the TCOT tire was found to have 40% greater durability in a drum test according to the distance traveled until bead failure. The TCOT shape has improved not only belt and bead durability but also the rolling resistance through the control of the tension distribution in the belt and carcass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.5-1.png",
        "caption": "Fig. 5.5 Cord path for a cured tire, plies on a building drum and diamond elements of the carcass (reproduced from Ref. [10] with the permission of Tire Sci. Technol.)",
        "texts": [
            "22), the ply length L is obtained as L \u00bc 2 ZrA rB dL \u00bc 2 ZrA rB dL ds ds dr dr \u00bc 2 ZrA rB B= sin affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 A2 p dr: \u00f05:23\u00de The term R rA r cot2 a r dr in the expression for A in Eq. (5.17) can be determined if the cord path or the function of a(r) is defined. The cord path of a bias tire cannot be clearly defined using a simple equation because it depends on the material, manufacturing process and other factors. Tire shapes with typical cord paths are reviewed in the following sections. Figure 5.5 shows the cord path for a cured tire, plies on a building drum and diamond elements of the carcass. When a green tire on a building drum is inflated such that it becomes a cured tire, the orientation angle of plies changes owing to the 5.2 Theory of the Natural Equilibrium Shape Based on Netting Theory 247 increase in radius from rdrum to rcure. The pantograph deformation is derived under two assumptions: a cord is inextensible and there is no slip at the cross-point of two plies. The cord path of pantograph deformation can be applied to various rubber products for which the cord modulus is much greater than the rubber modulus and agrees reasonably well with measurements. For example, it can be applied to the bias plies of a bias tire and the belt of a radial tire. Referring to Fig. 5.5, the length of the diamond shape in the circumferential direction is proportional to the radius of the position. This relation gives rcure= cos acure \u00bc rdrum= cos adrum \u00bc const.; \u00f05:24\u00de where adrum is the orientation angle at radius rdrum on a building drum (Fig. 5.5b) and acure is the orientation angle at radius rcure on a cured tire (Fig. 5.5a). If the cord is extended by stretch Ct, which is the ratio of the current length to reference length, Eq. (5.24) is rewritten as3 rcure=\u00f0Ct cos acure\u00de \u00bc rdrum= cos adrum: \u00f05:25\u00de Suppose that the orientation angle at radius rA is aA in Fig. 5.5. Using Eqs. (5.24) and (5.25), the orientation angle a at radius r is obtained as rA= cos aA \u00bc r= cos a; \u00f05:26\u00de rA=\u00f0Ct cos aA\u00de \u00bc r= cos a: \u00f05:27\u00de 3Problem 5.1. 248 5 Theory of Tire Shape We derive the tire shape under the assumption of cord inextensibility. Eliminating a in the first equation of Eq. (5.17) using Eq. (5.26), we obtain A \u00bc \u00f0r2 r2C\u00de exp ZrA r r cos2 aA r2A r2 cos2 aA dr 0 @ 1 A \u00bc \u00f0r2 r2C\u00de exp 1 2 log\u00f0r2A r2 cos2 aA\u00de rA r \u00bc \u00f0r2 r2C\u00de r2A r2 cos2 aA 1=2 rA sin aA : \u00f05:28\u00de The substitution of Eq",
            "112) that ET \u00bc Em Vm 1 m2m \u00bc 2G\u00f01\u00fe mm\u00de Vm 1 m2m \u00bc 2G Vm 1 mm\u00f0 \u00de : From the above equation, q1 is given by q1 \u00bc 2G hh0 sin2 a ET cos2 a\u00fe 1 4 sin 2 a \u00bc Vm 1 mm\u00f0 \u00de hh0 sin2 a cos2 a\u00fe 1 4 sin 2 a : 1218 Solutions Substituting mm = 1/2 into the above equation, we obtain q1 \u00bc Vm 2hh0 sin2 a cos2 a\u00fe 1 4 sin 2 a \u00bc Vm hh0 sin2 a 2 3 2 sin 2 a : Meanwhile, Eq. (3.60) can be rewritten as s2 \u00bc Vm hh0 sin2 a 2 3 2 sin 2 a\u00fe h h0 Vm cos2 a : Comparing the expression for q1 with the expression for s2, we see that the difference between the two expressions is the term including h/h0. 4.1 Answer omitted 4.2 Answer omitted 5.1 All nodes of adjoining diamonds of Fig. 5.5 are on the same radius or same meridian because of symmetry. The radius rcure can be obtained by summing the distances between vertexes of all diamonds whose nodes lie on the circumferential line. Denoting the length of a side of a diamond by lcure, we have 2prcure \u00bc 2Nlcure cos acure; \u00f0A5:1\u00de where N is the total number of diamonds or the total number of plies. Consider the same diamonds, no longer on a drum but on a vulcanized tire. They now lie on a radius rdrum, with the total number N remaining the same"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003910_j.wear.2006.06.019-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003910_j.wear.2006.06.019-Figure5-1.png",
        "caption": "Fig. 5. Gear profile generation.",
        "texts": [
            " For the mating pair of teeth under load, it is not possible o have the next tip enter contact in the pure involute position ecause there would be sudden interference corresponding to he elastic deflection and the corner of the tooth tip would gouge nto the mating surface [31]. Manufacturing errors can add to his effect that is the reason to relieve the tooth tip to ensure that he corner does not dig in. The gear profile functions with tip relief can be obtained rom the following approach. For a given rack O1a (with tandard pressure angle of \u03b11) and ab (with pressure angle f \u03b12 for tip relief) as shown in Fig. 5, the correspondng involute profiles can be obtained from the gear meshing rinciple. y n p t b x Assuming: global co-ordinate: OXY; rack local co-coordinate: O1X1Y1 (originally located at OXY); gear local co-coordinate: O2X2Y2. The equation for O1a line is: 1 = x1 tan(\u03b11) (1) If a point M1 in O1a line will contact with the gear, the rack eeds to be moved a distance b1 (O1O) to achieve the normal of oint M1 cross with point O according to the gear conjugating heory: y1 1 = tan(\u03b11) + x1 (2) For co-ordinate transformation from O1X1Y1 to OXY: = x1 \u2212 b1, y = y1 1 62 (2007) 1281\u20131288 O x y w a \u03d5 s y w n M b x O x y w a \u03d5 s i o m f i i o o i a a m l a g c i f R w w w m t f l F 3 s c m c p l 284 K"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure8.18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure8.18-1.png",
        "caption": "Fig. 8.18",
        "texts": [
            "33) 284 Bifurcation and Chaos in Engineering So, H(XPX2) = constant is the orbit of the solutions, that is 1 3 1 2 1 2 H(X I ,X2 ) = -Xl +-X2 --Xl = const 3 2 2 (8.34) We know from eq. (8.31), when Il = 0, (0,0) is a hyperbolic saddle point, and (x? ,0) is a centre point. Suppose that there is a homoclinic orbit at point o. It is the unstable manifold of this saddle, and also the stable manifold of this point, that is to say, the starting phase point from any point of this orbit, when t ~ \u00b1oo, tends to the same point 0 (0, 0). See Fig. 8.18(a) , where (x?,D) is centre. When Il < 0, the Hamiltonian system is transformed into a positive dissipative system, and the center changes to a sink. See Fig. 8.18(b). When Il> 0, the Hamiltonian system is transformed into a negative dissipative system, and the centre changes to a source. See Fig. 8.18(c). We know from Fig. 8.18, when Il = 0, the phase structure of this orbit has undergone a change in nature, and hence a bifurcation occurs. We shall study an example of a heteroclinic orbit once again. Suppose (8.35) When Il = 0, let xi = xi = 0, so we can obtain two saddles. For the heteroclinic orbit, see Fig. 8.19. Brief Introduction to Chaos 285 The heteroclinic portrait is a stable manifold of a saddle point, but an unstable manifold of another saddle point. Here, what we called the manifold, generally speaking, means the curve or curved surface in Euclid space",
            " there exists H(x) so that fl = 8H '/2 = - 8H , and suppose there exists a critical point in the 8X2 8xI closed curve po = {q0(t)lt E ;e}U{po}of H. Thus, there is a continuous family qf1. (t),a E (-1,0) of periodic orbits which fill the whole po when a ~ 0, q\" (t) tends to pO, that is limsupd(q\"(t),po) = 0 where d(x,po) = Int Ix - ql a ..... O tE~ qePCI As we know, there is no chaos in a two-dimensional space, such as an insect flying on an aircraft, and it is required that the flying orbit does not repeat. Thus, the orbit must either flyaway or reduce to a point. See Fig. 8.18(c), (b). Now, let us make a small perturbation with a period T to system (8.36). Suppose g E e'(;ex ;e,;e2): g(x,t + T) = g(x,t), v (x,f) E ;e2 x;e. Then eq. (8.36) is transformed into a non-autonomous system after the small disturbance x' = I(x) + Eg(X,t) (8.37) Now, let us consider the change in the structure of the orbit of eq. (8.37) near the orbit pO, especially the change of the unstable manifold 1fI: and the stable manifold 7et: at pO. To do this, we must transform the non-autonomous system (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003630_027836499201100504-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003630_027836499201100504-Figure3-1.png",
        "caption": "Fig. 3. Definition of the arm plane SEW.",
        "texts": [
            " PROPOSITION 4.3. Let ~b denote the arm angle defined in Section 2. Then, J\u2019 = con7 + CT Jee where Proof. Note that Wn = 0, because a pure self-motion results in a zero wrist motion. Equations (21) and (27) taken together then yield (30). 0 There are two possible ways that co as given by (30) can vanish. First, it may be that En = 0, so that a selfmotion causes no motion of the elbow point at all. Secondly, it may be that Eh 54 0, but the resulting elbow motion is entirely in the plane SEW (see Fig. 3), so that (ill x p)TEf\u00ed = 0. In either case, it is apparent that selfmotion has nothing to do with a change of the arm angle 1/J. Assuming that the arm is not at a kinematic singularity (i.e., m ~ 0), the algorithmic singularities are precisely those configurations for which a self-motion causes no change in the arm angle 1.j;. 4.3. Singular Configurations of the 7-DOF Manipulator In this section, we give conditions that correspond to the zero-offset 7-DOF arm and the Robotics Research K-1207 arm in a kinematic or algorithmic singular configuration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.43-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.43-1.png",
        "caption": "Fig. 5.43: Electromagnetic micromotor. Courtesy of the University of Wisconsin-Madison (Department of Electrical and Computer Engineering)",
        "texts": [
            " In general, electromagnetic microactuators are useful when efficiency is less important than reliability and safety. Rotational electromagnetic micromotor with gears For several years, the SLIGA technique (Section 4.2.5) has been investigated for the manufacture of electromagnetic micromotors [Guck92], [Chri92], (Guck93]. The process allows the making of metallic structures from nickel of only 300 Jtm height. The precision which can be obtained makes it possible to produce various planar micromechanisms, such as electromagnetic reluc tance motors with gears, Fig. 5.43 and Fig. 4.33. The structure produced from galvanically plated nickel is 100 Jtm high and consists of several gears and a reluctance motor. A rotational speed of 10000 rpm is possible. The gap bet ween the motor shaft and the rotor is only 500 nm. This nickel-nickel system has very low friction, which gives the motor excellent dynamic properties. The coil windings of the stator pole are made of an aluminum alloy wire using wire bonding; direct etching of U-like bridges has proven to be problematic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003942_1.1334379-Figure12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003942_1.1334379-Figure12-1.png",
        "caption": "Fig. 12 View of the Harmonic Drive Test Apparatus",
        "texts": [
            " In order to justify this argument, we develop a mathematical dynamic model of the harmonic drive system that takes into consideration the pure kinematic error as well as the flexibility of the drive. The experimentally measured kinematic error was compared to the profile generated by simulation and good agreement was observed, indicating that our hypothesis of the decomposition of the kinematic error is very reasonable. In order to develop a mathematical dynamic model of the Harmonic Drive Test Apparatus of Fig. 12 in Appendix A, its schematic ~shown horizontally for convenience! is given in Fig. 5. The figure illustrates the parameters of the system, whose values are displayed in Table 1. The parameters were computed from the geometry of the system and by performing experiments at differ- Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http ent speeds to obtain estimates on viscous damping factors and constant frictional torque. To account for the effects of flexibility, we assume that a torsional spring exists between input and output side of the drive characterized by a constant stiffness coefficient",
            " It also implies that the flexibility-induced component in the kinematic error is mostly the source of the high-frequency components of kinematic error reported in the literature. The previous decomposition of the kinematic error into a pure component u\u0303p and a flexibility-induced component u\u0303s will be further analyzed in this section by outlining our findings on some of the important factors that influence one or both of these components. The observations reported in these sections are from tests we conducted on the Harmonic Drive Test Apparatus of Fig. 12 in Appendix A. When appropriate, we made comparison with simulation results using our dynamic model derived in the previous section. 3.1 Load-Dependence. We present results of experiments carried out to test the load-dependence of the pure component of the kinematic error u\u0303p . The procedure for the experiments is similar to that designed for obtaining the basic form, except that now the output shaft of the harmonic drive is loaded with a torsional load applied by means of a weight and pulley arrangement, as shown in Fig. 8 ~note that the inertia disc in this figure corresponds to the inertial load pointed out in Fig. 12 and Fig. 5!. It was observed that as the load increases, the kinematic error ~peakto-peak! amplitude decreases. Similarly, the profile of the kinematic error also shows a corresponding change but is not reported in this study. Figure 9 shows a plot ~fitted experimental data points! of kinematic error peak-to-peak amplitude as the load is varied. As the figure shows, the amplitude is very sensitive to load Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F variations at smaller loads",
            " The dedicated apparatus for experimental examination of the kinematic error in harmonic drive gears is reported in Hejny and Ghorbel @19# and is briefly described here. The system is composed of a servo motor, a harmonic drive unit ~HDC-40 with reduction ratio 50!, and an inertial load. Different sensors are used to measure various system states. The motor position is monitored by a rotary encoder (resolution50.045\u00b0), the load position is measured by a laser rotary encoder (resolution50.0018\u00b0), and the load torque is measured with a DC operated non-contact rotating torque sensor. Figure 12 shows the photograph of the system. As can be seen, the system operates in the vertical plane. Hence, there are no errors in the assembly of the drive because of possible deflection due to gravity. The system is designed with Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F high stiffness so as to avoid assembly deformations when the torque load is applied on the drive. An additional attachment ~see Fig. 8! is developed to load the drive with constant torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000962_s11071-021-06238-0-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000962_s11071-021-06238-0-Figure2-1.png",
        "caption": "Fig. 2 Diagram of the relative position between a rolling element and the races",
        "texts": [
            " 3) degrees of freedom considered in this model, whereNb represents the number of rolling elements. The contact stiffness between the jth rolling element and the raceways is denoted by kin and kout for inner race and outer race, respectively. The damping between the jth rolling element and the raceways is represented by c. The friction coefficient between each rolling element and each raceway is represented by l. 2.1 Contact forces between a rolling element and the races The relative position relationship between the jth rolling element and the races is shown in Fig. 2. A Cartesian coordinate for the inner race (xi, yi) and a polar coordinates for the rolling elements (dr,j, wm,j; j = 1, 2, 3, \u2026, Nb) are established to describe the motions of inner race and rolling elements. The original positions of the inner race and the jth rolling element are shown by the dashed line. It is assumed that the inner race center (oi) coincides with the outer race center (oo) in the initial state. The contact deformations between the jth rolling element and the races in the dynamic process are determined by the geometric relationship of their positions. As shown in Fig. 2, the relative position between the inner race and the outer race is X ! r \u00bc xi yi \" # \u00f01\u00de The relative position between the jth rolling element and the inner race can be written as X ! rr;j \u00bc d ! r;j X ! r;j \u00bc dr;j sinuj xi dr;j cosuj yi \u00f02\u00de where uj is the angular position of the jth rolling element, which can be expressed by uj \u00bc \u00f0j 1\u00de 2p Nb \u00fe wm;j \u00f03\u00de When the rolling element contacts with the raceway, the contact force arises and the contact deformation will be positive. Whenever the contact deformation is zero or negative, indicating that the rolling element loses contact with the raceway, the contact deformation is set to zero, and is signified by the subscript \u2018\u2018"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure14.94-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.94-1.png",
        "caption": "Fig. 14.94 Local slip model and shear deformation of tread (reproduced from Ref. [21] with the permission of JSAE)",
        "texts": [
            "89) can be rewritten as gV sin a\u00fe ktreadVtc sin a \u00bc l AVtc \u00feB\u00f0 \u00de: The above equation can be rewritten as lA ktread sin a \u00bc gV sin a lB\u00f0 \u00de=\u00f0Vtc\u00de: The substitution of the above equation into equation for n yields n \u00bc l ktread g ktread AV \u00feB \u00fe 1 ktread lB\u00fe gV sin a\u00f0 \u00de e ktread g tc \u00bc gV ktread lA ktread sin a e ktread g tc : The substitution of n and t = T + tc into equation for y yields y \u00bc l ktread AV T \u00fe tc g ktread \u00feB \u00fe gV ktread l ktread A sin a e ktread g T : Note 14.9 Shear Spring Rate Between Adjacent Blocks Fujikawa et al. [23] estimated the intra-shear stiffness of a block. As shown Fig. 14.94, the shear strain c at longitudinal position x and vertical position z is expressed by c\u00f0x; z\u00de \u00bc z h dy\u00f0x\u00fe lE\u00de dy\u00f0x\u00de lE ; where lE is the distance between adjacent elements. The shear force f(x) acting between the tread elements is therefore expressed by 1122 14 Wear of Tires f \u00f0x\u00de \u00bc bG Zh 0 c\u00f0x; z\u00dedz \u00bc bhG 2 dy\u00f0x\u00fe lE\u00de dy\u00f0x\u00de lE \u00bc bhG 2lE Ddy: From the above equation, the intra-shear stiffness k2 is obtained as k2 = bhG/ (2lE), where b is the width of the block. Meanwhile, the shear stiffness of a block element t0tread is expressed as t0tread \u00bc blEG=h"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000455_j.msea.2020.139001-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000455_j.msea.2020.139001-Figure6-1.png",
        "caption": "Fig. 6. SLM-1 and 2 samples after fracture.",
        "texts": [
            " [35] and Wan et al. [36]. Fig. 5d\u2013f shows the bright field TEM image and corresponding SAED patterns of the SLM-2 alloy, in which the \u03b1 and \u03b10 phases are also observed. The \u03b10 phase is mainly composed of the {1011}\u03b1\u2019 twinning substructure in a zigzag plate-like morphology. The similar results were found by Cao et al. [37] and Liu et al. [38]. Different from the SLM-1 alloy, no \u03b1\u2019\u2019 phase is observed in the SLM-2 sample. This may be resulted from the slower cooling rate in the SLM-2 alloy than in the SLM-1 alloy. Fig. 6 presents the fractured SLM-1 and SLM-2 samples after tensile failure, from which the strength of both samples are obtained and included in Table 3. The tensile strength is 1236 MPa and 1065 MPa for the SLM-1 and SLM-2 alloys, respectively. By measuring the length change of individual sample after tensile fracture, the elongation values are 8.5% and 13.6% for the SLM-1 and SLM-2 alloys, respectively. The elongation of SLM-2 alloy is 5.1% higher than that of SLM-1 alloy, but the tensile strength is 171 MPa lower. The enhanced elongation of SLM2 sample can be further proved by the obvious necking after tensile test, which was not observed in the SLM-1 sample, as shown in Fig. 6. The results in present study indicate that building orientation of the SLM process affects the microstructure and phase compositions of Ti\u20136Al\u20134V alloy and thus plays an important role in the mechanical Table 2 Phase contents in SLM-1 and SLM-2 alloys. Ti\u20136Al\u20134V Volume Fraction (%) \u03b1/\u03b10 ratio \u03b2 phase \u03b1 phase \u03b10 phase SLM-1 9.69 35.16 55.15 0.60 SLM-2 14.23 53.74 32.03 1.68 Fig. 2. XRD patterns of SLM-1 and SLM-2 samples. Z. Xie et al. Materials Science & Engineering A 776 (2020) 139001 performances of the final bulk material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.23-1.png",
        "caption": "Fig. 3.23: Woodpecker Model",
        "texts": [
            " We start with jamming in a downward position, moving back again due to the deformation of the spring, and including a transition from one to three degrees of freedom between phases 1 and 2. Step 3 is jamming in an upward position (1 DOF) followed by a beak impact which supports a quick reversal of the \u03d5-motion. Steps 5 to 7 are then equivalent to steps 3 to 1. The system possesses three degrees of freedom q = (y, \u03d5M , \u03d5S)T , where \u03d5S and \u03d5M are the absolute angles of rotation of the woodpecker and the sleeve, respectively, and y describes the vertical displacement of the sleeve (Figure 3.23): Horizontal deviations are negligible. The diameter of the hole in the sleeve is slightly larger than the diameter of the pole. Due to the resulting clearance, the lower or upper edge of the sleeve may come into contact with the pole. This is modeled by constraints 2 and 3. Further contact may occur when the beak of the woodpecker hits the pole, which is expressed by constraint 1. The special geometrical design of the toy enables us to assume only small deviations of the displacements. Thus a linearized evaluation of the system\u2019s kinematics is sufficient and leads to the dynamical terms and constraint magnitudes listed below. For the dynamics of the woodpecker we apply the theory section 3.5 on page 158 for impacts with friction, but we assume that no tangential impulses are stored during the impulsive processes. The mass matrix M , the force vector h and the constraint vectors w follow from Figure 3.23 in a straightforward manner. They are M =  (mS + mM ) mSlM mSlG mSlM (JM + mSl 2 M ) mSlM lG mSlG mSlM lG (JS + mSl 2 G)  3.4 Multibody Systems with Unilateral Constraints 153 h =  \u2212(mS + mM )g \u2212c\u03d5(\u03d5M \u2212 \u03d5S)\u2212mSglM \u2212c\u03d5(\u03d5S \u2212 \u03d5M )\u2212mSglG  ; q =  y \u03d5M \u03d5S  wN1 =  0 0 \u2212hS  ; wN2 =  0 hM 0  ; wN3 =  0 \u2212hM 0  wT1 =  1 lM lG \u2212 lS  ; wT2 =  1 rM 0  ; wT3 =  1 rM 0  . (3.177) For a simulation we consider theoretically and experimentally a woodpecker toy with the following data set: Dynamics: mM = 0.0003; JM = 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure14.74-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.74-1.png",
        "caption": "Fig. 14.74 Comparison of wear energy distributions [51]",
        "texts": [
            " (4) New technology resulting from numerical wear simulation Kaji [49] studied the effect of the three-dimensional shape of the block pattern on wear by conducting the global\u2013local analysis in implicit FEA, because a wear energy machine cannot measure wear energy at the block edges owing to the size of the triaxial force sensor. The tire size was LVR 195/70R15, and the case study was a comparison of the wear energy distribution for a conventional block shape and a block with mild curves at its edges, referred to as an adaptive contact (AC) block. The AC block is designed to maintain uniformity of the contact pressure by applying the optimization procedure discussed in Sect. 7.5.2. The predicted wear energy at the edge of the conventional block is greater than that at the edge of the AC block as shown in Fig. 14.74. The AC block has less circumferential shear stress and slip as shown in Fig. 14.75. This is because the edge of the AC block gradually makes contact with the ground in contrast with the edge of the conventional block as shown in Fig. 14.75. The effectiveness of the AC block was validated in an indoor wear drum test. Figure 14.76 shows the worn profile and the tread loss calculated from the difference in the block profile between the new and worn tires. The AC block wore uniformly compared with the conventional block"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure11.12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.12-1.png",
        "caption": "Fig. 11.12 Top view of the string and equilibrium of forces in the contact region [29]",
        "texts": [
            "1 Tire Models for Cornering Properties 719 where v is the displacement of the string in the y-direction and ks, S1, D and fy are, respectively, the lateral carcass spring rate per unit length in the circumferential direction, the tension of the string in the circumferential direction, the shear force and the side force on the contact patch. The shear force D is proportional to the shear angle \u2202v/\u2202x: D \u00bc S2 @v=@x; \u00f011:24\u00de where S2 is the tension related to the shear deformation. We here introduce the equivalent total tension S (=S1 + S2). Using Eqs. (11.24) and (11.23) can be simplified as S @2v=@x2 ksv \u00bc qy: \u00f011:25\u00de Because fy is zero outside the contact patch, Eq. (11.25) can be rewritten as S @2v=@x2 ksv \u00bc 0 for xj j[ a; \u00f011:26\u00de where a is half the contact length. Figure 11.12 shows the deformation of the string model near the contact patch. We also introduce the relaxation length r expressed by r \u00bc ffiffiffiffiffiffiffiffiffi S=ks p : \u00f011:27\u00de Using Eqs. (11.27) and (11.26) is rewritten as r2 @2v=@x2 v \u00bc 0 for xj j[ a: \u00f011:28\u00de If the relaxation length is shorter than the tire circumference, the displacement at the trailing edge v2 is not affected by the displacement at the leading edge v1. Displacements of the string outside the contact patch can be independently solved at the leading and trailing edges: 720 11 Cornering Properties of Tires v \u00bc C1e x=r for x[ a v \u00bc C2ex=r for x\\ a: \u00f011:29\u00de Considering the boundary conditions v = v1 at x = a and v = v2 at x = \u2212 a, we obtain @v=@x \u00bc v1=r for x # a @v=@x \u00bc v2=r for x \" a; \u00f011:30\u00de where x#a denotes that x gradually decreases toward a while x\" \u2212 a denotes that x gradually increases toward \u2212a. Considering that the slope of the string is continuous between the inside and outside of the contact patch at the leading edge, we obtain @v=@x \u00bc v1=r for x \" a; x \u00bc a; x # a: \u00f011:31\u00de (2) Force and moment of the string model The force and moment of the string can be calculated from the displacement in the contact patch v, the lateral carcass spring rate per unit length ks in the circumferential direction and the tension of the string S as shown in Fig. 11.12. The side force Fy is given by Fy \u00bc ks Za a vdx\u00fe S v1 \u00fe v2\u00f0 \u00de=r: \u00f011:32\u00de The self-aligning torque around point O is obtained through the addition of the lateral and circumferential components. The self-aligning torque due to the lateral displacement of the string v is given by M0 z \u00bc ks Za a vxdx\u00fe S a\u00fe r\u00f0 \u00de v1 v2\u00f0 \u00de=r: \u00f011:33\u00de The self-aligning torque due to the circumferential displacement u is given by M z \u00bc Cx Za a Zb 2 b 2 uydxdy; \u00f011:34\u00de where Cx is the shear spring rate of the tread per unit area in the circumferential direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.9-1.png",
        "caption": "Fig. 5.9: Rigid Shaft Model",
        "texts": [
            " According to the various design possibilities shafts possess also various influence on the dynamics of the overall system, especially with respect to the eigenbehaviour expressed by eigenfrequencies and eigenfunctions. The longitudinal dynamics of a car is mainly concerned by shifting gears on the one and influenced by the rotational behaviour of the shafts on the other side. Therefore we shall focus on that rotational behaviour, where we have to distinguish rigid and elastic shafts. Rigid shafts are the simplest possible elements of a machine including an input, an out put torque and a rotational inertia (Figure 5.9). Therefore the equation of motion is simply J\ufe38\ufe37\ufe37\ufe38 MSW \u03d5\u0308\ufe38\ufe37\ufe37\ufe38 q\u0308SW = ManS \u2212MabS\ufe38 \ufe37\ufe37 \ufe38 hSWS . (5.15) Elastic shafts represent the simplest possible case of an elastic multibody element, as far as rotational linear elasticity is concerned. Assuming only linear elastic deformations gives us two modeling alternatives, namely applying some Ritz approach according to chapter 3.3.4 on page 124 or just discretizing the shaft into a limited number of shaft elements. Anyway, the number of shape functions of a Ritz approach as well as the number of the shaft elements depend on the frequency range of the system under consideration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001096_j.msea.2021.141299-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001096_j.msea.2021.141299-Figure14-1.png",
        "caption": "Fig. 14. Calculated longitudinal(a) and transverse(b) residual stress results when including transformation strain and neglecting transformation strain at mid yz cross-section for the Ti6Al4V samples.",
        "texts": [
            " By comparing the simulation results for the model when neglecting transformation strain (No \u03b5Trp) and experimental measurements, it can be clearly found that the longitudinal stress predicted by the model is much larger than the experimental, the maximum error is about 80.7%, and the error between the predicted transverse stress and the experimental value has reached 53.9%. It illustrates that the solid-state phase transformation has a stress relaxation effect during the SLM Ti6Al4V process. A similar research result can be found in the literature [8,41]. Fig. 14 shows the calculated residual stress results when including transformation strain and neglecting transformation strain at mid yz cross-section for the Ti6Al4V samples. As analyzed in section 2.3, the effect of solid-state phase transformation on residual stress mainly results from the difference in yield strength and volume change between the primitive phase and the transformed phase. Therefore, two models that only considering the solid-state phase transformation strain induced from the difference in yield strength or volume change between the primitive phase and the transformed phase are arranged, the calculation results are also given in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003302_s0967-0661(01)00105-8-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003302_s0967-0661(01)00105-8-Figure3-1.png",
        "caption": "Fig. 3. Pictures of the SCARA.",
        "texts": [],
        "surrounding_texts": [
            "The experimental comparison is carried out on a twojoints planar direct drive prototype robot manufactured in the laboratory (IRCCyN) (Figs. 1\u20133), without gravity effect. The description of the geometry of the robot uses the modified Denavit and Hartenberg notation (Khalil & Dombre, 1999). The robot is directly driven by two DC permanent magnet motors supplied by PWM choppers. The dynamic model depends on eight minimal dynamic parameters, including four friction parameters: v \u00bc ZZR1 Fv1 Fs1 ZZ2 LMX2 LMY2 Fv2 Fs2 T ; ZZR1 \u00bc ZZ1 \u00feM2L 2; where L is the length of the first link, M2 the mass of link 2, ZZ1 and ZZ2 the drive side moment of inertia of links 1 and 2, respectively, LMX2 and LMY2 the first moments of link 2 multiplied by the length L of link 1, Fv1;Fs1;Fv2;Fs2 are the viscous and coulomb friction parameters of links 1 and 2, respectively. The inverse dynamic model used to compute WLS is written as Eq. (3): where C2 \u00bc cos\u00f0q2\u00de and S2 \u00bc sin\u00f0q2\u00de: The direct dynamic model necessary to compute the extended Kalman filtering algorithm is written as Eq. (11) with q \u00bc q1 q2 T and s \u00bc t1 t2 T : M \u00bc M11 M12 M12 ZZ2 \" # ; M11 \u00bcZZR1 \u00fe ZZ2 \u00fe 2LMX2C2 2LMY2S2; M12 \u00bcZZ2 \u00fe LMX2C2 LMY2S2: The joint position q and the current reference VT (the control input) are collected at a 100Hz sample rate while the robot is tracking a fifth order polynomial trajectory. This trajectory has been calculated in order to obtain a good condition number Cond\u00f0Ww\u00de \u00bc 290 and Cond\u00f0U\u00de \u00bc 100: This means that it is an exciting trajectory taking the whole trajectory all over at the time of the test. Both methods are performed in a closed loop identification scheme (simply joint PD control), using the same data q and s; where each torque sj is calculated as sj \u00bc GTjVTj ; where GTj is the drive chain gain which is considered as a constant in the frequency range of the robot dynamics. Fig. 4 presents the torque of motors 1 and 2."
        ]
    },
    {
        "image_filename": "designv10_2_0000735_j.chemosphere.2020.128104-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000735_j.chemosphere.2020.128104-Figure7-1.png",
        "caption": "Fig. 7. (a) Unprocessed graphene-film of a single layer in a glass substrate, (b) glass substrate with a graphene IPS in its final symmetric pattern, (c) chemical etching patterns of graphene interdigitated electrode at the edge of an IPS pixel, (d) illustration of graphical attempts involved to fabricate conducting ITO channels with a pattern of graphene IPS and a sketch of cross-sectional layer IPS substrate [Copyright @ 2017, Springer Nature] (Varanytsia and Chien, 2017). (e) The schematic representation of electro-optical stimulation surface stabilized in-plane switchable device with GOLC-assembly nanomaterials in confined geometry in ITO-LC cell.",
        "texts": [
            " High quality graphene-enabled polymeric nanomaterials dispersed liquid crystal-graphene oxide/ polymer dispersed liquid crystal (GO-LC/PDMS) composite matrix (Cheng et al., 2015) by geometric confinement are schematically displayed in Fig. 6. In the following, we elaborately analyzed hybrid nanocomposites that could be implemented in switchable device modification and industrial scale utilizations. A typical in-plane switching (IPS) can be efficiently performed via a chemical etching process gradually as shown in Fig. 7, maintaining several steps. The designing process of chemical etching via acid spray for indium-titanium coated (ITO) film patterning and dehydrated etching via plasma techniques for ultra-thin GO-LC film patterning are involved in photolithography. An IPS pixel area with an electrode area of 4 4mm2 dimensions were decorated, and the deposited layers aligned with the inner confining exterior of the substrates. Aligned layers uniformly, and unidirectionally glazed are anti-parallelly joined to the planar alignment of rubbing directions",
            " This method is very much adequate for the calibration of the \u2018Nematic\u2019 (N) phase and \u2018Smectic C\u2019 (Sm C) phases consisting of rod-like molecules as well as for some conjugated polymers. The typical cost-effectivemechanism is very promising, as well as applicable from the laboratory of industrial-scale fabrication for LC cells to commercially produced liquid crystal smart display. Another drawback is that the alignment layers are usually electrically insulated and inhibit charge carrier injection from an electrode to an active layer. Fig. 7(aee) are illustrated graphene-LC device fabrication steps. A single graphene layer film is first deposited over glass substrates in the center. The active area of in-plane switching (IPS) pixel formed by the integration of graphene electrodes and the supplementary ITO contact bus lines were supplied to drive a voltage to graphene layers. The two-electrode system of the electro-optic (EO) in-plane switching prototype substrate was manufactured as shown in Fig. 7(b). Graphene has a negligible light absorbance, which exploited to optimize lighting conditions of backward reflected light, see in Fig. 7(c). Depositing substratewith an additional conductive ITO coating with left and right graphene film edges enables a superior electrical application to the graphene layer. Shadowmasks were used in the center to protect the substrate and the graphene film, which splits the two ITO glass plates to the left and right sectional area. Those conduction sections of the host substrate generate an electric field at the center of the GO-LC hybrid layer. Then the \u2019photo-lithography\u2019 technique was employed in both graphene films and ITO substrate with a photomask and positive photoresist to synthesize single IPS pixels of the hybrid matrix on ITO conducting channels (Varanytsia and Chien, 2017), which is depicted in Fig. 7(d). The durability of ITO defines the directional surface layer alignment of LC through the mechanical rubbing method. However, mechanical rubbing mediated direct impact of graphene and its high sensitivity leads to a reliable, standard industry polyimide (PI) alignment layer material with the high molecular planar quality alignment of LC in a graphene composite electrode cell. Capillary flow is used to distribute the NDLC/ GO-LC samples inside heated cells. The fabricated suspensions generated through this method transfer into an LC cell with photorefractive. The photo-refractive ITO test cell was 0.1 mm thickness that allows surface specimen stabilization as enough ultra-thin. The surface stabilized electro-optically stimulated switchable device is schematically shown in Fig. 7(e). For a representative case, the hydrogen-bonded liquid crystalline compound was investigated by the triangular wave field of oscilloscope studies of novel switching operations. As well as electro-optical studies were attributed to 10 mm indium tin oxide (ITO) coated photo-refractive LC cells with additional surface treatment by polyimide (PI) alignment layer. By capillary action, the isotropic samplewas filled into the host cell. There is no response of current could be identified for the nematic (N) phase regardless of the temperature under an applied voltage up to 38 Vpp mm 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.41-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.41-1.png",
        "caption": "Fig. 6.41: Contact between a Link and a Guide",
        "texts": [
            ", namely checking the contacts to be active or passive, where at the beginning of a contact event we always have kinematical and at the end kinetic indicators. The example we present here was still treated by Lemke\u2019s algorithm. Contact of a Link with a Guide For the contact of a link with a guide we start with the description of the guide contour by equation (6.42) in the form rK(s) = (xK(s) yK(s))T , from which we can derive a contact coordinate system (t,n, b) from the following relationships, using \u03ba as the curvature of the contour (see Figure 6.41 and section 2.2.6 on the pages 31 ff.): t = \u2202rK \u2202s , n = 1 \u03ba \u22022rK \u2202s2 , b = t\u00d7 n, t =t(qG, s), n = n(qG, s), b = const. (6.89) 6.4 Bush and Roller Chains 385 In a guide fixed system the vectors t and n depend only on the parameter s. Applying the formulas of Frenet \u2202t \u2202s = \u03ban, \u2202n \u2202s = \u2212\u03bat, (6.90) and the notation \u2126\u0303Gn = \u2212tbT\u2126G, \u2126\u0303Gt = nbT\u2126G (6.91) we obtain the time derivatives of t and n: t\u0307 =\u2126\u0303Gt+ \u2202t \u2202s s\u0307 = nbT\u2126G + \u03bas\u0307n, n\u0307 =\u2126\u0303Gn+ \u2202n \u2202s s\u0307 = \u2212tbT\u2126G \u2212 \u03bas\u0307t. (6.92) In the following we look at the vector rD from the reference point HL to the body fixed contact point K: rD =rG + rK \u2212 rL, r\u0307D =r\u0307G + \u2126\u0303G rK \u2212 r\u0307L, r\u0308D =r\u0308G + \u2126\u0303G \u2126\u0303GrK + \u02d9\u0303\u2126GrK \u2212 r\u0308L",
            "98) For determining the indicator with respect to contact/detachment we have to subtract the radius of the link contour. The derivative with respect to time leads to the normal velocity of the contour points. Applying equation (6.93) and the condition (6.94) we get 6.4 Bush and Roller Chains 387 g\u0307n =nT (r\u0307D + \u2202rD \u2202s s\u0307) + rTD n\u0307, =nT r\u0307D \u2212 rTDtbT\u2126G + s\u0307(nT t\u2212 \u03barTDt), =nT r\u0307D, (6.99) and from there by an additional time derivation the normal acceleration g\u0308n =nT (r\u0308D + \u2202r\u0307D \u2202s s\u0307) + r\u0307TDn\u0307 =nT r\u0308D + nT (\u2126\u0303G \u2202rK \u2202s )s\u0307\u2212 r\u0307TDtbT\u2126G \u2212 \u03bas\u0307r\u0307TDt =nT r\u0308D \u2212 tT r\u0307DbT\u2126G + s\u0307(bT\u2126G \u2212 \u03batT r\u0307D). (6.100) According to Figure 6.41 the contact forces N and T , acting on the guide and with negative sign on the link, can be written as N = n\u03bb, T = \u2212 vrel |vrel| \u00b5t\u03bb (6.101) With the known directions n and t we use the vector w = JTn to describe the influence of these forces on the motion of the guide and the link. J\u2217 G = ( E3\u00d73,\u2212r\u0303K ) , J\u2217 L = ( E3\u00d73,\u2212Rrollerplaten\u0303 ) wG\u03bb = QT GJ \u2217T G ( n\u2212 vrel |vrel| \u00b5t ) \u03bb, wL\u03bb =\u2212QT LJ \u2217T L ( n\u2212 vrel |vrel| \u00b5t ) \u03bb. (6.102) Contact between a Sprocket and a Link Regarding the contact between a sprocket and a link we achieve very simplified relations for the normal velocity and acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000861_acsami.0c17429-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000861_acsami.0c17429-Figure1-1.png",
        "caption": "Figure 1. Schematic diagram of the SLS fabrication and magnetization process of the magnetism-responsive gripper. The latter allowing the gripper to deform when being exposed to the external magnetic field produced by a magnet nearby.",
        "texts": [
            " The reliability of the numerical model proposed was justified by the excellent consistency in the results obtained using the two approaches. This research proves the feasibility of magnetism-driven 4D printing using the SLS and provides theoretical and methodo- logical guidance for studies on the deformation behavior of magnetic components in a magnetic field. \u25a0 RESULTS AND DISCUSSION The structure of the magnetism-responsive material was designed to be a gripper, which is widely applied in soft robotics. The SLS fabrication and magnetization processes are illustrated in Figure 1. The gripper is composed of two parts: a 30 mm \u00d7 4 mm (diameter \u00d7 height) cylindrical base and five equidistant claws along the base circumference. The front, left, and bottom views with dimensions are shown in Figure S1. The polymer composite powder used for the SLS process comprised thermoplastic polyurethane (TPU) and Nd2Fe14B. The latter acquired permanent magnetism after magnetization, with the maximum magnetic energy product BHmax being 97.02 kJ/m3. During magnetization processes, magnetic particles are synchronously aligned along the direction of the external magnetic field"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure2-23-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure2-23-1.png",
        "caption": "Figure 2-23. Cross section of switched reluctance motor.",
        "texts": [
            " The direct axis inductance of this motor is low because its flux path is largely through the low permeability magnets, while the quadrature axis inductance is large because its flux can circulate in and out of each pole face. Many structural variants of buried-magnet machines have been proposed [37, 38, 39]. Some of these are well suited for high-speed applications. Both the structure and the control of PM reluctance motors are discussed further in Chapter 6. 2.9. SWITCHED RELUCTANCE MOTORS The switched reluctance (SR) motor has a doubly salient structure [40]. The machine shown in cross section in Figure 2-23 has six stator poles and four rotor poles and is denoted as a 6/4 motor. Each stator pole is surrounded by a coil, and the coils of two opposite stator poles are connected in series to form each of the three phase windings. The three phase windings are connected in sequence to a power converter that is normally triggered by a set of shaft position sensors. Consider the rotor position shown in Figure 2-23. If supply current is switched through the coils of phase a, there will be a counterclockwise torque acting to align the adjacent pair of rotor poles with the phase a stator poles. When aligned, if the current is now switched to phase b, the counterclockwise torque will continue. For the machine shown in Figure 2-23, the rotor moves \u03c0/6 radians for each step, and thus 12 switching operations are required per revolution. The direction of the coil current is not significant. The direction of rotation can be changed to clockwise by reversing the sequence of the currents to a, c, b. Many other pole choices are useful, particularly 8/6 (four phase) and 10/8 (five phase) [41]. Increase in the number of poles increases the switching frequency and the losses in the iron. It decreases the ratio of aligned to unaligned inductance somewhat",
            " The average torque that these motors can produce may be assessed from the magnetizing characteristics relating the phase flux linkage \u03bb to the coil current ; when in the aligned and unaligned positions [1]. A typical set of relations for the 6/4 motor is shown in Figure 2-24. 72 2. Electrical Machines for Drives It can be shown that the average torque over one step is equal to the heavily shaded area between the unaligned and fully aligned curves measured in joules (or Wb.A), divided by the rotational angle between steps (i.e., \u03c0/6 rad in Figure 2-23). To optimize this average torque, the slope of the linear part of the aligned characteristic (\u03b2 = 0) can be increased by reduction of the air gap between the aligned poles while the slope in the unaligned position can be adjusted by changing the relative widths of the stator and rotor poles [42]. An approximate expression for the torque can be obtained by noting that the work W done in rotating from unaligned to aligned positions can be expressed as W=kr\\i J (2.16) where the factor kr is in the range from 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure13.13-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure13.13-1.png",
        "caption": "Fig. 13.13 Imposed stress/strain in a two-dimensional tire model. Reproduced from Ref. [23] with the permission of Tire Sci. Technol.",
        "texts": [
            " [22] studied experimentally and computationally the effect of the tread depth on the RR of radial mid-sized truck tires, but they concluded that there was no simple relationship. (2) Simple model of the energy loss of tread rubber (2-1) Simple model of the energy loss of tread rubber Rhyne and Cron [23] considered the two dominant deformations of tread rubber (i.e., compression and longitudinal shear) in analyzing the effects of the inflation pressure, load and modulus of the tread rubber on the RR. Figure 13.13a illustrates the compressive stress imposed on the tread by the inflation pressure and the resulting ground reaction. The magnitude of the compressive stress is assumed to equal the inflation pressure p: rz \u00bc p: \u00f013:42\u00de This stress increases inversely to the volume fraction of rubber in the tread because of the tread pattern, but such an increase is neglected here. Figure 13.13b illustrates the longitudinal shear strain between the relatively inextensible belts and 946 13 Rolling Resistance of Tires the tread surface in contact with a dry surface. This shear strain is approximately given by cxz x=Rb; \u00f013:43\u00de where x is the distance from the center of the contact area and Rb is the belt radius. The maximum shear strain is given by cxz l=\u00f02Rb\u00de; \u00f013:44\u00de where l is the length of the contact patch. Because the shear deformation is reduced due to the bending deformation near the leading and trailing edges, the actual shear strain will be lower than this maximum shear strain",
            "3) that CFa \u00bc @Fy @a0 a0\u00bc0 \u00bc 1 CFa 0 \u00fe 1 3 el 1 1\u00fe CMa 0 Rmz : \u00f0A11:4\u00de Comparing Eq. (13.1) with Eq. (13.6), we have rns \u00bc r0; ens \u00bc e0; rnc \u00bc 00; enc \u00bc 0: Suppose that the area A and radius r are both unity for simplicity in Eq. (13.8). Substituting the relations above into Eq. (13.8), we obtain W \u00bc p X n n rnsens \u00fe rncenc\u00f0 \u00de sin d\u00fe n rncens rnsenc\u00f0 \u00de cos d\u00bd \u00bc pr0e0 sin d: Transforming the above equation using Eq. (13.3), we obtain W \u00bc pr0e0 sin d \u00bc pe20E sin d ffi pe20E 00: The distributions of rxz and exz in Figure 13.13 are shown in the upper figure below, while Eloss is derived assuming that the stress and strain can be expressed by a trigonometric function. The distributions of rxz and exz are thus approximated by the distribution shown in the lower figure. rzz changes from zero to \u2212P, ezz changes from zero to \u2212P/E, rxz changes from \u2212EL/(6Rb) to EL/(6Rb), and exz changes from \u2212L/(4Rb) to L/(4Rb). We thus obtain rzz0 = \u2212p/2, ezz0 = \u2212p/(2E), rxz0 = \u2212E/(6Rb) and exz0 = \u2212l/(4Rb). The substitution of these relations into Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.91-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.91-1.png",
        "caption": "Fig. 5.91: Contact Pin/Sheave for the Movable Side",
        "texts": [
            " These evaluations are very lengthy and tedious, and they have to be performed for every component of the spatial CVT system as presented before (see [239]). Fortunately, the results can be partly simplified and to a certain extend also decoupled by the fact, that the out-of-plane motion is very small compared to the nominal motion. Nevertheless it should be noted, that this refers to kinematics not to forces. Very small geometric changes produce very large changes in the forces, especially contact forces. The determination of the contact forces between pulley and rocker pins we need some definitions according to Figure 5.91. We shall use (L) for the movable, F) for the fixed pulley side and (B) for the pin. Furtheron the indices (I, C, K) stand for inertial, contact point and middle point of the rocker pins. The angles between the corresponding coordinates are also given in Figure 5.91. We additionally consider in the following only one contact point per rocker pin end surface [239] and not two contact points as presented in [167]. 5.6 CVT - Rocker Pin Chains - Spatial Model 309 With these definitions the contact forces between the sheaves and the front faces of the rocker pins are determined by the geometrical gap function g(q) being defined in the axial direction of the undeformed rocker pin. A system of coordinates C is introduced on the cone surface in the middle of the rocker pin end, defined by the triple of circumferential, radial and normal direction (t, r, n) and their forces (Ft, Fr, Fn)",
            " Therefore, the relation \u00b5i(g\u0307i) = \u00b50 [ 1\u2212 exp ( \u2212| g\u0307i vc | )] (5.142) will be sufficient for modeling friction between pins and sheaves. For further evaluations we need the contact forces in an inertial system, which we get from IF c,L/F,i =  sin(\u03d5c) cos(\u03d5c) 0 \u2212 cos(\u03d5c) sin(\u03d5c) 0 0 0 1  i  1 0 \u03c8G 0 1 \u2212\u03b1G \u2212\u03c8G \u03b1G 1  i A\u22121 KiCL/F,i FR,a FR,r szFN  i . (5.143) The normal and tangential contact forces are represented in the C-coordinate frame, the Cz-axis of which is perpendicular to the contact surface. The pin force possesses the direction of the Kz-axis, see Figure 5.91. Considering the motion of the contact points, we introduce contact torques in an exponential approximation as a function \u201dcon\u201d of the normal force Fc, the distance le of the edge of a contact body to the reference point, the radius rc of the contact surface, the rotational contact stiffness cc and the relative rotational displacement \u03d5c. con(Fc, le, cc, \u03d5c) =Fclesign [ 1\u2212 exp ( \u2212|\u03d5c|cc Fcle )] , cc = { cc,max \u2200 Fc : cc,max < Fcrc Fcrc \u2200 Fc : cc,max \u2265 Fcrc (5.144) 5.6 CVT - Rocker Pin Chains - Spatial Model 311 By increasing the contact forces Fc over the limit cc,max/rc the contact area reaches the cross section area, see Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000486_j.ymssp.2019.04.056-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000486_j.ymssp.2019.04.056-Figure4-1.png",
        "caption": "Fig. 4. on the",
        "texts": [
            " 3 shows the simplified three-dimensional geometry of the localized defect on the outer raceway, where ro1 and ro2 are the outer raceway radius and outer raceway groove radius; aa00b00b and cc00d00d are the cross-sections of the defect area on the radial center plane (xooyo plane) and the axial center plane (zooyo plane) of the bearing, respectively. Since the surface of the raceway is a curved surface, the top edges of defect area are composed of two radial arcs with radius of curvature ro1 (green arcs) and two axial arcs with radius of curvature ro2 (blue arcs). Fig. 4(a) and (b) shows the cross-sections of the defect area and raceways on the radial and axial center planes (not to scale), and the rolling element is located at the center position of the defect area. The geometric relationship between the defect area and the rolling element is defined as lo0a \u00bc lo0e \u00bc rb; loa \u00bc loc \u00bc ro1; lab \u00bc la00b00 \u00bc lmn \u00bc hmax1; lzn \u00bc hmin1 lo0c \u00bc lo0s \u00bc rb; lo00c \u00bc lo00s \u00bc ro2; lcd \u00bc lc00d00 \u00bc luv \u00bc hmax2; lrv \u00bc hmin2 hmin1 \u00bc hmin2 \u00bc hmin 8>< >: \u00f012\u00de where rb is the radius of the rolling element; hmax1 and hmin1 are the maximum and minimum depth of the defect area on the radial cross-section, respectively; hmax2 and hmin2 are the maximum and minimum depth of the defect area on the axial cross-section, respectively; hmin1 is equal to hmin2, making them equal to hmin in Fig. 3, and is given by In the radial and axial cross-sections, the maximum displacements of the rolling element moving towards the bottom of defect area in normal direction are lze and lrs in Fig. 4(a) and (b), respectively, which can be described by lze max \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro12sin 2\u00f0uc ud1\u00de q ro1 \u00fe ro1cos\u00f0uc ud1\u00de lrs max \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro22sin 2\u00f0u0 c u0 d1\u00de q ro2 \u00fe ro2cos\u00f0u0 c u0 d1\u00de 8>< >: \u00f014\u00de where uc and u0 c are the center angular positions of the defect area on the radial and axial cross-sections, respectively; ud1 and u0 d1 are the angular positions of the highest points (point a and point c) of the edge of defect area on the radial and axial cross-sections, respectively; ud and u0 d are the circumferential angular extents of defect area on the radial and axial crosssections, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure14-1.png",
        "caption": "Fig. 14 Coordinate systems So and Sw",
        "texts": [
            " 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter. System Sp is connected to the machine element 9 and represents he work head setting motion Fig. 12 . System So is connected to he machine element 8 and represents the work head offset setting ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 motion Fig. 13 . Sw is connected to the work 8 and represents the work rotation with angular parameter Fig. 14 . System Se is connected to the eccentric setting element and represents the radial setting Fig. 15 . System Sj is connected to the tilt wedge base element which performs rotation relatively to the eccentric element to set the swivel angle j Fig. 16 . System Si is connected to the cutter-head carrier which performs rotation relatively to the tilt wedge base element to set the tool tilt angle i Fig. 17 . Through the coordinate transformation from Si to Sw, the position vector and the unit tangent at the current cutting blade point P can be represented in the coordinate system Sw, namely rw = Mwiri u, 20 tw = Mwiti u, 21 where Mwi is a resultant coordinate transformation matrix and is formulated by the multiplication of the following matrices representing the sequential coordinate transformations from Si to Sw, Mwi = MwoMopMprMrsMsmMmcMceMejM ji 22 where matrices Mwo , Mop Em , Mpr Xp , Mrs m , Msm Xb , Mmc , Mce s , Mej j and M ji i can be obtained directly from Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000816_j.mechmachtheory.2020.103870-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000816_j.mechmachtheory.2020.103870-Figure1-1.png",
        "caption": "Fig. 1. Finite element model established in MATLAB: (a) overall view; (b) close-up view for gear tooth.",
        "texts": [
            " The geared rotor dynamic model is used to obtain the dynamic load. Based on the dynamic meshing force, Archard\u2019s wear model is utilized for wear prediction. The LTCA method is utilized to acquire the load distribution on the gear surface. The global deformation is calculated by finite element method and the local deformation is acquired using analytical Hertzian formula. For the convenience of the calculation, a finite element model of the thin-rimmed gear pair is established in MATLAB software (see Fig. 1 ). The total number of the potential contact points is n = n 1 + n 2 + \u2026+ n s . n i ( i = 1,2, \u2026,s ) is the number of the potential contact point of the i th tooth pair. s is the maximum number of the tooth pairs in contact during the meshing process. Generally, the geometrical contact ratio of spur gear pairs is less than two. However, in order to account for the \u2018extended tooth contact\u2019 [24] , s is assumed as three. The expression of the global compliance matrix is: \u03bbb = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 \u03bbp 11 + \u03bbg 11 \u03bbp 12 + \u03bbg 12 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000188_icra.2018.8460632-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000188_icra.2018.8460632-Figure3-1.png",
        "caption": "Fig. 3. The developed robotic boat. (a) Model design; (b) robot prototype.",
        "texts": [
            " 1(b)) whose force efficiency index is 1.0 to achieve efficient propulsion. One additional requirement for this \u201c+\u201d shaped configuration is that the thrusters need to generate both forward and backward forces. Second, a cube-like shape is designed to facilitate aligning multiple boats. One conceptual floating structure created by the cube-like roboat is rendered in Fig. 2. The preconceived full size of roboat is 4 m \u00d7 2 m. For the first iteration, an approximatively 1:4 scale prototype (0.9 m \u00d7 0.45 m) is realized in Fig. 3(a). Third, we use 3D-printing to construct the robotic boat since 3D-printing has proved to be a fast, efficient and low-cost manufacturing process. In particular, we used an Anycubic Kossel 3D printer (\u223c$300) to machine the hull and sealed it by adhering several layers of fiberglass inside. The manufacturing process is illustrated in Fig. 4. Note that because of the volume limitation of the printer, the boat hull is divided into 16 pieces and then spliced into one using selftapping screws. It only takes 60 hours to print the whole hull of the boat",
            " An indoor \u201cGPS\u201d system (Marvelmind robotics) is employed to provide 2 cm position precision of the robot. An IMU (LORD Microstain, 3DM-GX5-25) is positioned parallel to the robot body\u2019s principal axes to monitor the yaw, pitch, roll, linear acceleration and angular velocities of the robot. A 3D LiDAR (Velodyne, Puck VLP-16) is installed on the top center of the robot for future obstacle avoidance and SLAM. LiDAR is not used in this paper. One snapshot of the developed robotic boat is exhibited in Fig. 3(b). The robot runs on the Robotic Operating System (ROS), and its detailed specifications are listed in Table I. Following the notation developed by Fossen [23], the dynamics of a USV can be generically described by the nonlinear differential equation Mv\u0307+C(v)v+D(v)v = \u03c4 (1) where v = [u v r]T denotes the vehicle velocity, which contains the vehicle surge velocity (u), sway velocity (v), and yaw rate (r) in the body fixed frame, M \u2208 R 3\u00d73 is the positive-definite symmetric added mass and inertia matrix, C(v) \u2208 R 3\u00d73 is the skew-symmetric vehicle matrix of Coriolis and centripetal terms, D(v) is the positive-semidefinite drag matrix-valued function, \u03c4 \u2208 R 3\u00d71 the vector of body-frame forces and moments applied to the vehicle in all three DOFs and \u03c4= [\u03c41 \u03c42 \u03c43] T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure18-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure18-1.png",
        "caption": "Fig. 18 Pinion tooth surface model",
        "texts": [],
        "surrounding_texts": [
            "R (\ns\n1\nDownloaded Fr\nepresentation of Tooth Surface of a Non-Generated Formate\u00ae) Member\nAs discussed above, the non-generated Formate\u00ae gear tooth urface is the complementary copy of the generating gear tooth\n320 / Vol. 128, NOVEMBER 2006\nom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201\nsurface which is kinematically formed by sweeping the cutting blade edge along an extended epicycloid lengthwise curve. During the gear cutting process, the cradle is held stationary. Therefore, parameter is assumed zero and Eqs. 23 \u2013 25 can be written as\nrw = rw u, 27\ntw = tw u, 28\nTransactions of the ASME\n6 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "E u\nR b\ne t g m\nw\nE n v i\nt i u f e\nT\na o G s n m i c s T\nJ\nDownloaded Fr\nnw = nw u, 29 quations 27 \u2013 29 provide the position vector, unit tangent, and nit normal of a non-generated gear tooth surface.\nepresentation of Tooth Surface of a Generated Memer In addition to the indexing motion, for a generated member,\nither gear or pinion, the generating roll motion is provided and he generated tooth surface is the envelope of the family of the enerating surface. The position vector, unit tangent, and unit noral of a generated tooth surface can be represented as,\nrw = rw u, , tw = tw u, , nw = nw u, , fw u, , = nw \u00b7 vw = 0\n30\nhere the relative generating velocity vw is determined by\nvw = rw c 31\nquation fw u , , =nw \u00b7vw=0 is called the equation of meshing 11,12 . The vectors are considered and represented in the coordiate system Sw that is connected to the work. A unit cradle angular elocity, i.e., c=1 might be considered. The equation of meshing s applied for determination of generated tooth surfaces.\nThe tooth surface generation model described above is applied o the left-hand work members. For the right-hand members, the nitial cradle angle q0 in Fig. 15 should be replaced by \u2212q0. Figres 18 and 19 show a pair of mating pinion and gear tooth suraces of a face hobbed hypoid gear drive Fig. 20 , which is genrated by using the developed equations.\nooth Contact Analysis (TCA) Tooth Contact Analysis TCA is a computational approach for nalyzing the nature and quality of the meshing contact in a pair f gears. The concept of TCA was originally introduced by The leason Works in the early 1960s as a research tool and applied to piral bevel and hypoid gears 16\u201318 . Application of TCA techology has resulted in significant improvement in the developent of bevel gear pairs under given contact conditions. TCA nvolves iteration processes and must be implemented on a digital omputer. With the development and application of modern highpeed computers, TCA theory has been substantially enhanced.\nooth contact under load has been investigated and the Loaded\nournal of Mechanical Design\nom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201\nTCA has been developed 19\u201322 . Meanwhile, TCA has been not only used as a tool of analysis, but also integrated as a part of synthesis procedures 6\u20138,11 .\nTCA is a process of simulation of meshing and contact of a pair of gears under light load. Therefore, simulation of changes of the assembly errors and misalignments are taken into account. For this purpose, the adjusting parameters E, G, P, and are incorporated into the TCA model Fig. 21 . The output of a TCA program are the scaled graphs of transmission errors and tooth bearing contact patterns that predict the results from a bevel gear testing machine.\nBy replacing the subscript \u201cw\u201d in the previous equations with subscript \u201c1\u201d and subscript \u201c2,\u201d respectively, a pair of mating tooth surfaces of the pinion and the gear can be represented in the coordinate systems S1 and S2 that are connected to the pinion and the gear respectively, as follows,\nfor the pinion r1 = r1 u1, 1, 1 n1 = n1 u1, 1, 1 t1 = t1 u1, 1, 1 f1 u1, 1, 1 = 0\n32\nNOVEMBER 2006, Vol. 128 / 1321\n6 Terms of Use: http://www.asme.org/about-asme/terms-of-use",
            "1 Downloaded Fr\nfor generated gear r2 = r2 u2, 2, 2 n2 = n2 u2, 2, 2 t2 = t2 u2, 2, 2 f2 u2, 2, 2 = 0\n33\nfor non-generated gear r2 = r2 u2, 2 n2 = n2 u2, 2 t2 = t2 u2, 2\n34\n322 / Vol. 128, NOVEMBER 2006\nom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201\nFurther, the mating tooth surfaces are transformed into a common coordinate system Sf that is connected to the frame of the gear drive and with origin Of located at the theoretical crossing point of the gear axis. The relationship of coordinate systems in Fig. 21 simulates the running meshing of the gear pair shown in Fig. 20 and incorporates the adjusting parameters E, G, P, and . In case of spiral bevel gear drives, E0=0 is assumed. The axes Z1 and Z2 coincide with the rotation axes of the pinion and the gear, respectively. The origins O1 and O2 of systems S1 and S2 would be at the theoretical crossing point if the adjusting param-\nhing of design A\nTransactions of the ASME\n6 Terms of Use: http://www.asme.org/about-asme/terms-of-use"
        ]
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.21-1.png",
        "caption": "Fig. 7.21: Comparison of Simulation and Measurements",
        "texts": [
            "77), \u2013 on-line controller with a controller design following criteria of control- lability and stability, \u2022 DIKI: \u2013 direct kinematics from joint space to work space, transformations, Jacobians. To get some confidence in the theory various experiments with a laboratory robot were carried through ([223], [196]). They all confirm modelling and the control concept. Elastic manipulators might be used for polishing tasks, for detecting forms by scanning the shape with the help of sensitive contact forces or for measuring contact forces directly with a robot. From these examples we consider the polishing problem, where the manipulator had to perform a typical polishing motion. Figure 7.21 illustrates a typical example [196]. A three DOF robot with elastic links performs a polishing motion with a prescribed path and with a prescribed normal force (upper left of Figure 7.21). The upper right graph shows a comparison of the precalculated nominal curvature for bending of the lower link with coressponding measurements by strain gauges. The agreement is nearly perfect. The lower part of Figure 7.21 depicts the contact forces in normal and tangential directions, where the normal force is prescibed. Again the agreement is very good, where ths slight differences for the tangential force come from some errors in the sliding friction force at the gripper, which is not perfectly adapted via the corresponding friction coefficient. 7.3 Dynamics and Control of Assembly Processes with Robots 451 Dealing with assembly processes means combining the dynamics and control of one or more manipulators with the dynamics and control of the assembly process under consideration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000017_s11071-019-05348-0-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000017_s11071-019-05348-0-Figure5-1.png",
        "caption": "Fig. 5 Schematic of dynamic model of a spur gear system",
        "texts": [
            " Therefore, it ismore realistic to use the force-dependentmesh stiffness for modeling the dynamic behavior of gear transmission system. In Sect. 2, the calculation process of the mesh stiffness with respect to the load has been illustrated in detail. In the following contents, the dynamic simulation of the gear transmission system is going to be performed by adopting the mesh stiffness calculated under the dynamic condition. The dynamic model of the spur gear transmission system consisting of a pinion and a gear is shown in Fig. 5. The pinion and the gear are assumed to be rigid, and each of them has one torsional degree of freedom (DOF) \u03b8i ( j = p, g for the pinion and the gear, respectively). It is assumed that flexible deformations of pinion and gear are lumped to the nonlinear spring element K and linear damping element cm . The mass moments of inertia are denoted by Jp and Jg, respectively. The symbols rbp, rbg are the radius of the base circle of the pinion and the gear, respectively. The input torque Tp is exerted on the pinion, and the output torque Tg is loaded to the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.94-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.94-1.png",
        "caption": "Fig. 5.94: Joint Kinematics",
        "texts": [
            " To take into account the friction forces between the pair of rocker pins i we calculate the torque T rp,i = \u2212\u00b5lw +1\u222b \u22121 w \u2032 x(\u03be)fi(\u03be)sign(w \u2032T x q\u0307el,x,i)d\u03be with fi(\u03be) = cL lrp (ael,i(\u03be)\u2212 ai) (5.146) as the line load of the pin. The parameter ai is the kinematically unstressed and ael,i is the kinematically stressed length of a link. The forces and torques are visualized in Figure 5.93. In order to take into account the position of the contact line between a pin pair, we have to add an in-plane bending torque T\u03b3 . Regarding the clasp plate stiffness cclasp, we have to project the shear torque Tclasp into the configuration space of a link containing a clasp plate. Figure 5.94 shows the joint kinematics and their parameters. Distinguishing between the reference point and the contact point the link length and contact torque are determined. The rocker pin radius rrp can change according to the following equation with regard to the angle \u2206\u03b3. T\u03b3 = cL(ael \u2212 a)\u2206y = FChain\u2206y, Tclasp,\u03b2 = \u2212Tclasp,\u03c8 = cclasp(\u03c8L \u2212 \u03b2L), rrp = rrp,0 + \u2202rrp \u2202\u2206\u03b3 \u2206\u03b3 (5.147) In close cooperation with a few colleagues and supported significantly by the German Research Foundation (DFG) a large variety of practical cases have 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003942_1.1334379-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003942_1.1334379-Figure1-1.png",
        "caption": "Fig. 1 \u201ea\u2026 Exploded and \u201eb\u2026 assembled view of harmonic drive gear transmission \u201eHarmonic Drive Technologies \u20201\u2021\u2026",
        "texts": [
            " Hence they are popular in applications requiring precision positioning such as robots that manufacture precision components ~e.g. printed circuit boards!, and precise measuring devices. They are widely used in the semiconductor industry for laser mirror positioning. Possible military applications include use in missile fin actuation systems and in fine positioning mechanisms for laser redirection. Harmonic drives are making headway in commercial, industrial, and military applications. A harmonic drive is composed of the components identified in Fig. 1~a!. The wave-generator is an elliptically shaped steel core surrounded by a flexible race bearing. The circular spline is a rigid steel ring with teeth machined into the inner circumference. The flexible spline ~or flexspline! is a thin-walled flexible cup having two fewer teeth on its outer rim than on the inner rim of the circular spline. Upon assembly, the wave-generator is inserted into the flexspline cup which assumes an elliptical shape at that 1Correspondences should be addressed to: Fathi H",
            " 348-3738 Contributed by the Mechanisms Committee for publication in the Journal of Mechanical Design. Manuscript received October 1998. Associate Editor: C. M. Gosselin. 90 \u00d5 Vol. 123, MARCH 2001 Copyright \u00a9 2 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 end. The other end, however, is circular in shape and is attached to the output shaft. The circular spline teeth then mesh with the flexspline teeth at the major axis of the ellipse defined by the wave-generator. A fully assembled harmonic drive is shown in Fig. 1~b!. The most common configuration for the harmonic drive is the speed reduction/torque magnification arrangement. This mode of operation usually consists of the wave-generator as the input port, the flexspline as the output port, and the circular spline fixed to ground and held immobile. In this configuration, the wave-generator rotation corresponds to the motor angle input while the rotation of the flexspline in the opposite direction corresponds to the load angle output. The theory underlying the operation of harmonic drive gears was developed during the mid-1950s @2,3#"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000692_rnc.4465-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000692_rnc.4465-Figure2-1.png",
        "caption": "FIGURE 2 Coordinate of a two-link robotic manipulator",
        "texts": [
            " (43) From (40) and (43), we have 0 \u2264 ||\ud835\udf061|| \u2264 \u221a\u221a\u221a\u221aC2 \u0394 \ud835\udefc\ud835\udf06 + 2 [ V\ud835\udf06(0) \u2212 C2 \u0394 2\ud835\udefc\ud835\udf06 ] e\u2212\ud835\udefc\ud835\udf06t. (44) Then, we obtain lim t\u2192\u221e ||\ud835\udf061|| = C\u0394\u221a \ud835\udefc\ud835\udf06 . (45) Synthesizing (39) and (45), we get lim t\u2192\u221e ||q \u2212 qd|| = C\u0394\u221a \ud835\udefc\ud835\udf06 . (46) It is concluded from (46) and the expression of \ud835\udefc\ud835\udf06 that ||q \u2212 qd|| can be made small by appropriately adjusting design matrices K1 and K2 satisfying (42). Theorem 2 is thus proved. To verify the effectiveness of the proposed robust adaptive tracking control scheme, the simulations are given on a two-link robotic manipulator (Figure 2 ) with time-varying disturbances under actuator saturation. The motion mathematical model of the two-link robotic manipulator is M(q)q\u0308 + C(q, q\u0307)q\u0307 + g(q) = \ud835\udf0f + d, (47) where q = [q1, q2]T is the link position vector, \ud835\udf0f = [\ud835\udf0f1, \ud835\udf0f2]T is the control input vector, and d = [d1, d2]T is the external disturbance vector. The inertia matrix M(q), the centripetal-Coriolis matrix C(q, q\u0307), and the gravity vector g(q) are expressed in detail as follows: M(q) = [ r1 + r2 + 2r3 cos(q2) r2 + r3 cos(q2) r2 + r3 cos(q2) r2 ] (48) C(q, q\u0307) = [ \u2212r3q\u03072 sin(q2) \u2212r3(q\u03071 + q\u03072) sin(q2) r3q\u03071 sin(q2) 0 ] (49) g(q) = [ r4g cos(q1) + r5g cos(q1 + q2) r5g cos(q1 + q2) ] , (50) where r1 = m1l2 1 + m2l2 1 + I1, r2 = m2l2 2 + I2, r3 = m2l1l2, r4 = m1l2 + m2l1, and r5 = m2l2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000486_j.ymssp.2019.04.056-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000486_j.ymssp.2019.04.056-Figure6-1.png",
        "caption": "Fig. 6. Diagram of the relative displacement of rolling element moving towards the bottom of defect area in normal direction under the condition of type 2: (a) contact at position j1; (b) separate at position j2.",
        "texts": [
            " This relative displacement is the normal distance between the blue solid line and the red dotted line, which can be described by lze1\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bduj\u00f0t\u00de ud1 q ro \u00fe rocos\u00bduj\u00f0t\u00de ud1 \u00f0ud1 6 uj\u00f0t\u00de < uc\u00de lze1\u00f0t\u00de \u00bc lze max \u00f0uj\u00f0t\u00de \u00bc uc\u00de lze1\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bdud2 uj\u00f0t\u00de q ro \u00fe rocos\u00bdud2 uj\u00f0t\u00de \u00f0uc < uj\u00f0t\u00de 6 ud2\u00de 8>>< >>: \u00f015\u00de where ud1 and ud2 are the angular positions of the highest point (point a and point a00) of the edge of defect area on the radial cross-section, respectively. Fig. 6(a) and (b) shows the relative displacement of the rolling element moving towards the bottom of defect area in normal direction under the condition of type 2. The rolling element and the top edges (green radial arcs in Fig. 3) of defect area are in contact at position j1 and separated at position j2. Before the rolling element contacts with the top edges as well as after it separates from the top edges, the relative displacement is equal to lze(t) in type 1. The motion path of the rolling element during contact with the top edges is equivalent to moving along the arc line (xx00 in Fig. 6) between the contact position j1 and the separate position j2, and the relative displacement is equal to lsr_max in Eq. (14) constantly. The relative displacement under the condition of type 2 can be described by lze2\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bduj\u00f0t\u00de ud1 q ro \u00fe rocos\u00bduj\u00f0t\u00de ud1 \u00f0ud1 6 uj\u00f0t\u00de < uj1\u00de lze2\u00f0t\u00de \u00bc lrs max \u00f0uj1 6 uj\u00f0t\u00de 6 uj2\u00de lze2\u00f0t\u00de \u00bc rb ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rb2 ro2sin 2\u00bdud2 uj\u00f0t\u00de q ro \u00fe rocos\u00bdud2 uj\u00f0t\u00de \u00f0uj2 < uj\u00f0t\u00de 6 ud2\u00de 8>>< >>: \u00f016\u00de Diagram of the relative displacement of rolling element moving towards the bottom of defect area in normal direction under the condition of type 1: r defect area; (b) leave defect area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure4.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure4.9-1.png",
        "caption": "Fig. 4.9: Basic structures that can be produced in silicon a) (110) silicon; b) (100) silicon",
        "texts": [
            " The walls of the structure are very smooth since the etch rate along the ( 111) crystal face is more than a hundred times higher than the one perpendicular to it, Fig. 4.8. The designa tions (100), (110) and (111) indicate along which crystal face the substrate wafer is cut, i.e. which crystal face is parallel to the substrate's surface. The most often used anisotropic etching solutions are alkaline like potassium hydroxide, sodium hydroxide or EDP (ethylene diamine pyrocatechol). Silicon dioxide or silicon nitride are the main resist materials. Typical structures that can be produced by several crystal orientations are shown in Figure 4.9. The attainable dimensions are limited by the used photolithographic method. They are usually small enough to allow the making of compact cavity patterns in 4.1 Silicon-based Micromechanics 77 the substrate. Therefore, the wet chemical anisotropic etching process has become a key technology of micromechanics. Many different micromecha nical silicon components have been realized with this method. Dry etching involves the exposure of the substrate to an ionized gas. Etching occurs through chemical or physical interaction between the ions in the gas and the atoms of the substrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.1-1.png",
        "caption": "Fig. 5.1 Cord angle and other parameters of a bias tire",
        "texts": [
            " Using their theory, the optimized tire shape can be obtained once the target tire performance is determined. Furthermore, their theory can be applicable to any type of tire having any type of tire performance if the objective function and constraints are properly defined. As previously mentioned, three important theories have been developed in the study of tire shape; natural equilibrium theory for a bias tire [2], natural equilibrium theory for a radial tire [15, 17] and ultimate optimized tire shape theory [22]. The cross-sectional shape of a bias tire is defined using parameters in Fig. 5.1. The carcass tension T is expressed by T \u00bc pR; \u00f05:1\u00de where p is the inflation pressure and R is the radius of curvature along the cord direction. Because the tension is supported using only cords in netting theory, the tension of one cord tc is given by tc \u00bc T=nr \u00bc pR=nr; \u00f05:2\u00de where nr is the multiplicative product of the number of cords in one ply per unit width and the number of plies. Figure 5.2 shows the small element of a tire that is expressed by two radii of curvature, the smallest radius r1 and largest radius r2 called the principal radius. r1 and r2, respectively, are the radii in the meridian (cross-sectional) and circumferential directions. The vectors tangent to the principal 5.1 Studies on Tire Shape 243 radii are orthogonal to each other. b is the orientation angle of a ply measured from the circumferential direction. In Fig. 5.1, Euler\u2019s theorem in differential geometry gives the radius of curvature R: 1=R \u00bc sin2 a=r1 \u00fe cos2 a=r2: \u00f05:3\u00de Referring to Fig. 5.2, the substitution of the relation r2 = r/sin / into Eq. (5.3) yields 1=R \u00bc sin2 a=r1 \u00fe cos2 a sin/=r: \u00f05:4\u00de Substituting Eq. (5.4) into Eq. (5.2), we obtain p tc nr \u00bc sin2 a r1 \u00fe cos2 a r sin/: \u00f05:5\u00de Referring to Fig. 5.3, the force equilibrium in the z-direction between the pressure p on a circular ring from rC to r and the tensile force tcsin a is expressed by z z 244 5 Theory of Tire Shape pp\u00f0r2 r2C\u00de \u00bc tcN sin a sin/; \u00f05:6\u00de where N is the number of cords in a tire and is given by N \u00bc 2prnr sin a: \u00f05:7\u00de Eliminating tc and nr in Eq",
            " The mechanism used to control the belt and carcass tensions can be explained by the force equilibrium. Axisymmetric membrane shell theory for structures implies that an equilibrium normal to a surface gives N/ r1 \u00fe Nh r2 \u00bc p; \u00f05:125\u00de 284 5 Theory of Tire Shape where N/ is the meridian membrane force (i.e., sidewall tension) per unit width of the sidewall, Nh is the circumferential membrane force, r1 is the meridian radius of curvature (of the sidewall), r2 is the circumferential radius of curvature as shown in Fig. 5.1, and p is the inflation pressure. 5.6 Nonequilibrium Tire Shape 285 For radial tires, we can assume that in the sidewall area we have Nh \u00bc 0: \u00f05:126\u00de The sidewall membrane force (tension) N/ is therefore expressed by N/ \u00bc r1p: \u00f05:127\u00de Referring to Fig. 5.37, the total belt tension T0 is given as T0 \u00bc ap 2 b 2r1 sin h\u00f0 \u00de; \u00f05:128\u00de where a is the belt diameter, b is the belt width, and h is the angle between the tangent to the carcass line and the belt. Equation (5.128) shows that the carcass ply tension is proportional to the radius of curvature of the sidewall"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure4.21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure4.21-1.png",
        "caption": "Fig. 4.21",
        "texts": [
            " The bifurcation diagrams are not structurally stable on L(Z2)' Referring to [4], we have L(Z2) = BI (Z2)UBo(Z2)UHI (Z2)UHo(Z2)UD(Z2) The transition sets of eq. (4.169) are (4.170) Liapunov-Schmidt Reduction Ho(Z2): a= 16(1+y)2 HI (Z2) = D(Z2) = <I> where <I> represents an empty set. (u> 0) 3. Bifurcation Diagrams and Their Properties 141 (4.171) We can draw the hypersurface eq. (4.1 71) in three-dimensional space (a, P, y) . We take y as the auxiliary parameter and draw these figures in the plane (a,p). In Fig. 4.21, (a) is the transition variety for q> = and (b) for q> = -1. Fig. 4.22 is the corresponding bifurcation diagrams where K = -I. 142 Bifurcation and Chaos in Engineering The analysis of the mechanical behaviours of the bifurcation shows that: 1) Compared with the previous subsection and [3], this subsection has an extended result, that is, the subharmonic resonance bifurcation has fourteen persistent types. The persistent bifurcation diagrams given in [3] and the previous subsection are part of this subsection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure15-1.png",
        "caption": "Fig. 15 Coordinate systems Sm and Se",
        "texts": [
            " 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter. System Sp is connected to the machine element 9 and represents he work head setting motion Fig. 12 . System So is connected to he machine element 8 and represents the work head offset setting ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 motion Fig. 13 . Sw is connected to the work 8 and represents the work rotation with angular parameter Fig. 14 . System Se is connected to the eccentric setting element and represents the radial setting Fig. 15 . System Sj is connected to the tilt wedge base element which performs rotation relatively to the eccentric element to set the swivel angle j Fig. 16 . System Si is connected to the cutter-head carrier which performs rotation relatively to the tilt wedge base element to set the tool tilt angle i Fig. 17 . Through the coordinate transformation from Si to Sw, the position vector and the unit tangent at the current cutting blade point P can be represented in the coordinate system Sw, namely rw = Mwiri u, 20 tw = Mwiti u, 21 where Mwi is a resultant coordinate transformation matrix and is formulated by the multiplication of the following matrices representing the sequential coordinate transformations from Si to Sw, Mwi = MwoMopMprMrsMsmMmcMceMejM ji 22 where matrices Mwo , Mop Em , Mpr Xp , Mrs m , Msm Xb , Mmc , Mce s , Mej j and M ji i can be obtained directly from Figs",
            " The position vector, unit tangent, and unit noral of a generated tooth surface can be represented as, rw = rw u, , tw = tw u, , nw = nw u, , fw u, , = nw \u00b7 vw = 0 30 here the relative generating velocity vw is determined by vw = rw c 31 quation fw u , , =nw \u00b7vw=0 is called the equation of meshing 11,12 . The vectors are considered and represented in the coordiate system Sw that is connected to the work. A unit cradle angular elocity, i.e., c=1 might be considered. The equation of meshing s applied for determination of generated tooth surfaces. The tooth surface generation model described above is applied o the left-hand work members. For the right-hand members, the nitial cradle angle q0 in Fig. 15 should be replaced by \u2212q0. Figres 18 and 19 show a pair of mating pinion and gear tooth suraces of a face hobbed hypoid gear drive Fig. 20 , which is genrated by using the developed equations. ooth Contact Analysis (TCA) Tooth Contact Analysis TCA is a computational approach for nalyzing the nature and quality of the meshing contact in a pair f gears. The concept of TCA was originally introduced by The leason Works in the early 1960s as a research tool and applied to piral bevel and hypoid gears 16\u201318 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.12-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.12-1.png",
        "caption": "Fig. 5.12: Electrostatic micropositioner. According to [Kiku93]",
        "texts": [
            " Electrostatic rnicropositioner Optical communication networks and optical computers need flexible optical coupling and interfacing techniques. Here, very high precision is required, to align connecting optical fibers; even the smallest deviation can lead to exces sive light attenuation. Also the expensive optical fiber mountings make an economical solution to this problem very difficult. An electrostatic microposi tioner was presented in [Kiku93] for alignment of the optical fibers in the coupling, Fig. 5.12. The whole device consists of two parts: the micropositio ner and a stationary part with integrated optical channels (the latter part is not shown in the picture). It is the task of the micropositioner to align the fibers with their corresponding channels. The micropositioner has a base containing several V-shaped grooves into which the optical fibers to be aligned are placed. The groove itself has a wide part and a narrow part. In the wide part there are alignment electrodes on either side. The optical fibers are coated with a thin metal layer so that they can be actuated electrostatically"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003961_s11044-007-9088-9-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003961_s11044-007-9088-9-Figure6-1.png",
        "caption": "Fig. 6 Spherical motion (left) and screw motion about axis h (right)",
        "texts": [
            " The principle of transference can be stated as follows [2, 54, 61]: 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. 6.1 Applications of the principle of transference In 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, as shown in Fig. 4, s is the displacement of the body along the screw axis. With reference to the geometry of Fig. 6, 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 = t u. 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 generalized 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 \u2022 R\u03021 and R\u03022 are the initial and final positions of a line vector framed to the rigid body, respectively (see Fig. 6) \u2022 \u03b8\u0302 = \u03b8 + \u03b5h is the dual angle whose primary part is the angle of rotation and h the displacement along h. Given 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. Let us introduce the vector \u03c4i = tan \u03b8i 2 ui (i = 1,2). (31) It can be demonstrated [48, 72] that the resultant spherical motion is defined by the following vector \u03c43 = \u03c41 + \u03c42 \u2212 \u03c41 \u00d7 \u03c42 1 \u2212 \u03c41 \u00b7 \u03c42 . (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_2_0000639_978-981-13-5799-2-Figure11.3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure11.3-1.png",
        "caption": "Fig. 11.3 Coordinate system and nomenclature. Reproduced from Ref. [2] with the permission of Guranpuri-Shuppan",
        "texts": [
            " This book only discusses theoretical models. Table 11.1 summarizes theoretical models in terms of the shape of the contact pressure distribution, conditions of slip, bending deformation of the tread ring (belt), torsional deformation of the tire, translational lateral deformation of the tread ring, fore\u2013aft deformation of the whole contact patch, slip velocity/temperature dependency of the friction coefficient and transient temperature. The force and moment of a tire with slip angle a are expressed using the coordinate systems shown in Fig. 11.3. One coordinate system is fixed to the wheel while the other is fixed to the vehicle. It is necessary to understand which coordinate system is used in the definition of the force and moment of a tire. We denote the moving direction of the vehicle as the X\u2032-axis and the axis normal to X\u2032-axis as the Y\u2032-axis, while the direction of the wheel is the X-axis and the axis normal to the 710 11 Cornering Properties of Tires T ab le 11 .1 C ha ra ct er is tic s of m od el s di sc us se d in th is ch ap te r M od el pa ra m et er s So lid -t ir e m od el 11 ",
            "77): Fy \u00bc Cyl2hb 1 2 tan a d Cy \u00fe l2 3r2Ky Fy l 1 2 lh 3l \u00fe n\u00fe 1 n 2nFzld ln\u00fe 1 l 2 n l lh\u00f0 \u00de 1 n\u00fe 1 l 2 n\u00fe 1 lh l 2 n\u00fe 1 ( )\" # : \u00f011:79\u00de 736 11 Cornering Properties of Tires The total self-aligning torque Mz is obtained by adding the expressions in Eqs. (11.76) and (11.78): Mz \u00bc Cyl 2 hb lh 3 l 4 tan a\u00fe d\u00fe l2Cy 3r2Ky Fybl2h 4l2 lh l\u00f0 \u00de2 \u00fe n\u00fe 1 n 2nFzld ln\u00fe 1 1 2 l 2 n l 2 2 lh l 2 2 ( )\" 1 n\u00fe 2 l 2 n\u00fe 2 lh l 2 n\u00fe 2 ( )# : \u00f011:80\u00de Neglecting the rolling resistance, the cornering force FCF y in Fig. 11.3 is given by FCF y \u00bc Fy cos a: \u00f011:81\u00de The rolling resistance including the effect of the side force or the drag resistance Fdrag x is given by Fdrag x \u00bc Fy sin a\u00fe gFz cos a; \u00f011:82\u00de where \u03b7 is the rolling resistance coefficient. An iterative calculation is required to solve Eq. (11.79) because Eq. (11.79) contains Fy on both sides. The computational procedure is as follows. 11.2 Cornering Properties with a Large Slip Angle 737 kinetic friction coefficient decreases with the sliding speed, which increases with the tire speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure11.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure11.14-1.png",
        "caption": "Fig. 11.14",
        "texts": [
            " The galloping of electrical conductors is usually produced by a steady wind flowing across a transmission line having an asymmetrical cross-section. This asymmetry may arise from ice or rime deposits during winter or, more rarely, from the stranding of the cable itself. The galloping phenomenon is highly complex because of the non-linear, geometry-dependent, time-varying aerodynamic loads and the resulting large amplitudes of vibration, which may cause interactions between adjacent spans and their support hardware. Now we discuss the two-degree-of-freedom autonomous model of Yu [173, 180], which is illustrated in Fig. 11.14. Its equations of motion are described by my + cyY - sx8+ kyY = Fy 18+ce8-sxY+ ke8= FM (11.42) where Y is the vertical or plunge displacement, 8 is the angle of twist, and a dot superscript denotes differentiation with respect to time. The ky and ko represent the stiffness in plunge and torsion, respectively, and the Cy and Co are the corresponding viscous dampers (which are not shown in Fig. 11.14). Furthermore, m and I are the mass and the moment of inertia of the iced conductor's cross-section, A, about its centre of rotation, O. They are defined by 422 Bifurcation and Chaos in Engineering (11.43) The Sx in eq. (11.42) indicates the eccentricity of the system. It is given by (11.44) where ~ is the generalized mass density over A and sx/m is the lateral position of the centre of gravity measured from O. stream velocity U, the angle of attack, a, is approximately RI \u2022 1 a\",,8--8--y U U (11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003458_j.ymssp.2005.02.009-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003458_j.ymssp.2005.02.009-Figure2-1.png",
        "caption": "Fig. 2. Coupling between the torsional and transverse motions of the gears and shafts: rp\u2014base circle radius of input pinion, rg\u2014base circle radius of output gear, kmb\u2014linear translation tooth stiffness along line of contact and c\u2013c\u2014line of contact.",
        "texts": [
            " The major assumptions, which the dynamic model is based upon, are, (i) resonances of the gearbox casing are neglected, (ii) shaft mass and inertia are lumped at the bearings or the gears, (iii) shaft transverse resonances are neglected, (iv) input and output shaft torsional stiffness is ignored (flexible coupling torsional stiffness is very low), (v) gear teeth profiles are without runout errors, (vi) the teeth are straight along the axial face width without crowning. The coupling between the torsional and transverse motions of the gears and shafts has been developed as shown in Fig. 2, where the linear translation tooth stiffness along the line of contact, kmb; can be calculated from the torsional tooth stiffness via [5], Kmb \u00bc Km r2p , (1) where km represents the torsional mesh stiffness and rp denotes the radius of pinion base circle. This allows the torsional mesh stiffness results calculated by finite element analysis (FEA) to be used in the dynamic modelling. The tooth profile geometrical errors were simulated here as a forcing function input into the model and are represented by a sum of three harmonic terms as shown in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure5.51-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure5.51-1.png",
        "caption": "Fig. 5.51 Design variables used to search for the optimized tire size in terms of minimizing rolling resistance",
        "texts": [
            " Such a difference was difficult to achieve even by changing the tread compound. A test driver noted that a tire designed by the optimized shape was stable from entering to exiting corners. This comment was interestingly similar to that related with a tire 205/60R15 discussed in Sect. 5.7.2-(1). (4) Optimized shape to decrease rolling resistance of tires The GUTT was applied to determine the best tire size for the rolling resistance of a tire. The design variables were the tire sidewall shape and tread width, ri, hi, TW, SW and RW (Fig. 5.51). The rim diameter and overall diameter were fixed. The section width and rim width were determined by the tread width to maintain the ratio of the section width to rim width and the ratio of the tread width to rim width (i.e., SW/RW = const. and TW/RW = const.). The initial tire size was 165R13, and the optimized size became 205/60R13 as shown in Fig. 5.52; the prediction of the rolling resistance showed a 25% reduction. Not only the optimized tire shape but also the optimized tire size was obtained by including the tread width as a design variable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure8-1.png",
        "caption": "Fig. 8 Hook, rake and offset angles",
        "texts": [
            " For a current cutting point P n the blade, the position vector and the unit tangent can be dened in the coordinate system Sb, rb = rb u 14 tb = tb u 15 here u is the parameter. Equations 14 and 15 can be repreented in the cutter head coordinate system St as rt = Mtb , , ,Rb rb u 16 318 / Vol. 128, NOVEMBER 2006 om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/201 tt = Mtb , , ,Rb tb u 17 where matrix Mtb denotes the coordinate transformation from system Sb to St. Determination of transformation matrix Mtb is based on the geometric description of the rake, hook, and blade slot offset angles shown in Fig. 8 and can be defined as a multiplication of three homogeneous matrices as Mtb = M M M 17a where M , M , and M are represented as, M = cos sin 0 0 \u2212 sin cos 0 0 0 0 1 0 0 0 0 1 17b M = 1 0 0 0 0 cos sin 0 0 \u2212 sin cos 0 0 0 0 1 17c M = cos \u2212 sin 0 Rbcos sin cos 0 Rbsin 0 0 1 0 0 0 0 1 17d Coordinate system Si is used to represent the rotation of the cutter head with an angular displacement . From Fig. 6, one can obtain the transformation matrix Mit and ri = Mit rt u = ri u, 18 ti = Mit tt u = ti u, 19 Applied Coordinate Systems Up till now, no paper has been found regarding exact modeling of face hobbing process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure8.5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure8.5-1.png",
        "caption": "Fig. 8.5: Ankle Joint Kinematics",
        "texts": [
            " The ankle joint needs special modeling due to the fact that actuation is realized by a ball screw spindle, see Figure 8.4. Due to this mechanism we get a kinematical closed loop not consistent with the tree-like structure of the machine kinematics. Therefore we choose for the generalized coordinates OAOI = ( cos\u03c8 cos\u03d5\u2212 sin\u03c8 cos\u03d1 sin\u03d5 sin\u03c8 cos\u03d5 + cos\u03c8 cos\u03d1 cos\u03d5 sin\u03d1 sin\u03d5 \u2212 cos\u03c8 sin\u03d5\u2212 sin\u03c8 cos\u03d1 cos\u03d5 \u2212 sin\u03c8 sin\u03d5 + cos\u03c8 cos\u03d1 cos\u03d5 sin\u03d1 cos\u03d5 sin\u03c8 sin\u03d1 \u2212 cos\u03c8 sin\u03d1 cos\u03d1 ) (8.5) the two angles of the universal joint, from which we are able to calculate the position of the ball screw spindles. Figure 8.5 depicts the principle of the ankle joint kinematics. The feet are symmetrical, therefore we can apply the same form of calculations for both feet. Hence, the generalized feet coordinates qB04, qB05 and qB14, qB15 can be replaced by q4, q5. The ball screw spindles are connected to the reference points P0, P1, they are parallel to the y-axis of the lower leg. The rotation of the spindles shift therefore the points S relative to the points P (Figure 8.5) by the amount UrP0S0 = (0 s0 0)T , UrP1S1 = (0 s1 0)T . (8.8) From this we define the degrees of freedom of the spindles by s = (s0, s1)T . Two rigid rods connect the spindle end points S0, S1 with the points A0, A1 at the foot. From this the degrees of freedom of the ankle joint qK = (q4, q5)T are given unambiguously by the coordinates s of the spindles. For the corresponding vector chain we come out with (Figure 8.5) UrS0A0 =UrUK +AUK KrKF +AUKAKF FrFA0 \u2212 UrUP0 \u2212 UrP0S0, UrS1A1 =UrUK +AUK KrKF +AUKAKF FrFA1 \u2212 UrUP1 \u2212 UrP1S1, (8.9) with the transformation matrices AUK =  0 0 1 cos q4 \u2212 sin q4 0 sin q4 cos q4 0  , AKF =  sin q5 cos q5 0 0 0 1 cos q5 \u2212 sin q5 0  . (8.10) With the given lenghts of the connecting rods lV 0, lV 1 we can establish two constraining equations \u03a6 for the evaluation of the ankle joint angles in the form \u03c6 = ( Ur T V 0 UrV 0 \u2212 l2V 0 Ur T V 1 UrV 1 \u2212 l2V 0 ) = 0. (8.11) 8.2 Walking Dynamics 515 Given the spindle positions UrP0S0,U rP1S1, we have now to evaluate the generalized angles qK = (q4 q5)T of the ankle joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure5.25-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure5.25-1.png",
        "caption": "Fig. 5.25: Multi-layered piezoceramic structure. According to [Gibb94]",
        "texts": [
            " Electrodes are printed onto the raw ceramic similar to textile printing, and then the layers are stacked together and burned into a multi-layered structure. The actuators are about 10-200 11m thick, are ope rated by a voltage in a range of 50 and 300 V and can be mass-produced. The goal of current research is to reduce the operating voltage to a range of 5 to 15 V. However, the lifetime of these actuators may be limited by internal mechanical stresses caused by non-homogenities resulting from the elec trodes, Fig. 5.25. Another actuation principle is the cantilever. Piezoelectric cantilever structu res which can be shaped like a tube or a plate make use of this principle. We will discuss the possibilities of tube-shaped piezoelectric microactuators in detail in Chapter 8 in which we describe a microrobot developed at the Uni versity of Karlsruhe [Magn94], [Magn95] and [Fati95] . Most often a plate shaped cantilever type piezoactuator is a bimorphic element consisting of two piezoelectric ceramic plates, Fig. 5",
            " The reflected light is detected and the single points are assembled to form a com plete in-focus picture. The operation of the microscope can be controlled by an external computer, which is advantageous in industrial production. There are also various scanning probe microscopy (Section 2.5) and X-ray diffracto metry methods available which can do testing of micromechanical structures. These methods can also be used in combination with numerical FEM simu lation. For example, the characteristic internal stresses of a multi-layered piezoceramic wafer (Figure 5.25) which are obtained by means of X-ray dif fractometry, are important input values for a numerical simulation of the me chanical-thermal behavior of a structure [Faust93]. Tests can be simplified by using defect simulations obtained in the design phase. A thorough system description (e.g. electric SPICE network model) is necessary to simulate a faulty behavior of a system. Thereby, test signals can be deduced which will detect errors or defects in the real devices. The testability of a microsystem during its operation is also significant in MST, since ageing is much more serious here than in macrodevices"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003787_1.1644545-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003787_1.1644545-Figure4-1.png",
        "caption": "Fig. 4 Contact angle and load of a ball",
        "texts": [
            " The local displacement uj can be obtained from the global displacement d using the transformation matrix @Rf# from the bearing center to inner groove center, and is written as uj5@Rf# jd (16a) Transforming the ball force vectors Qj into the equivalent force vectors at the bearing center, and summing the forces over all balls, the global force equilibrium can be established as F1( j51 n @Rf# j TQj50 (16b) where n is the number of balls bearings, Qj is the force vector of the j th ball, and the transformation matrix @Rf# is given by @Rf#5F cos f sin f 0 2zp sin f zp cos f 0 0 1 rp sin f 2rp cos f 0 0 0 2sin f cos f G (17) In Eq. ~16b!, the global force equilibrium can be solved through the equilibrium of each ball. Figure 4 shows the ball equilibrium, where a i and ae are contact angles, Qi and Qe are contact loads at the inner and outer ring respectively, and Fc is the centrifugal force. Using the notation in Fig. 4, the local force vector can be obtained from the contact load and contact angle at inner ring of the bearing, and written as follows, for ball bearings, Qr52Qi cos a i , Qz52Qi sin a i , M50 (18) Ball Equilibrium From Fig. 4 the load equilibrium at the ball is determined by H Fr Fz J 5 H Qi cos a i2Qe cos ae1Fc Qi sin a i2Qe sin ae J 50 (19) Contact loads in Eq. ~19! are calculated by Hertzian theory for spherical contact, Qi5Kid i 3/2 , Qe5Kede 3/2 . (20) where Ki and Ke are the load-deflection parameters @21#, and d is the ball-raceway contact deformation calculated by the change of center length, rom: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/2 d i5l i2loi , de5le2loe (21) In the above equations, loi and loe are the initial center lengths, while l i and le are center lengths during operation for inner and outer ring respectively as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003426_s0094-114x(97)00094-3-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003426_s0094-114x(97)00094-3-Figure6-1.png",
        "caption": "Fig. 6. The Stewart platform.",
        "texts": [
            " 5 show rare singularities (shown by crosses in this \u00aegure) at isolated points corresponding to some of the orientations. Even if a \u00aener scanning succeeds in \u00aending singular points at other orientations also, it is guaranteed that the continuous singularity barriers of Fig. 4 are removed and the complete workspace can be used e ectively, albeit at the cost of a slight reduction of workspace due to the fourth leg length constraints. The six-degree-of-freedom parallel manipulator known as the generalized Stewart platform shown in Fig. 6 and its redundant version with one additional leg are next compared for their workspaces and singularities. The analysis is similar to the previous example except that here the vectors are three-dimensional and the rotation matrix is given in terms of the role\u00b1pitch\u00b1 yaw angles as R RPY yz; yy; yx Rot z; yz Rot y; yy Rot x; yx where the position and orientation are de\u00aened by t x y z T and yx yy yz T The wrench at the platform is T RT MT T Rx Ry Rz Mx My Mz T which is related to the actuator forces F F1 F2 F3 F4 F5 F6 T for the non-redundant case and F F1 F2 F3 F4 F5 F6 F7 T for the redundant case through the Equation (3)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0001216_tie.2021.3070504-Figure16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0001216_tie.2021.3070504-Figure16-1.png",
        "caption": "Fig. 16. Back-EMF generation principle of FSPM machines.",
        "texts": [
            " Some conclusions can be drawn as, 1) The smaller the order of flux density harmonics in FSPM machines, the greater the contribution to phase back-EMF; 2) The positive or negative contributions of the modulation harmonics are independent of their rotating directions. 3) The back-EMF generation of FSPM machines can be regarded as a combination of several traditional machines with different PPN and the same electrical speed. D. Summary of back-EMF generation The back-EMF generation principle of FSPM machines is summarized in Fig. 16. Firstly, the primitive PM-MMF is merely composed of the original harmonics with PPN of mPpm. Then, by dynamic modulation of rotating rotor to the primitive PM-MMF, the modulation harmonics with PPN of |mPPM\u00b1vPr| and electrical speed of vPr\ua7b7r emerge in air-gap flux density. Finally, The winding works as a filter to select the working harmonics, namely, |mPPM \u00b1 vPr|=jPw, to produce phase back-EMF. Here, the phase back-EMF generation principle of Authorized licensed use limited to: Central Michigan University"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure4.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure4.6-1.png",
        "caption": "Fig. 4.6: Check valve",
        "texts": [
            " In order to solve the system equations one has to distinguish between active constraints (closed valves) and passive constraints (opened valves). The last ones can be removed. The constraint equations avoid stiff differential equations. On the other hand they require to define active and passive sets. Check valves are directional valves that allow flow in one direction only. It makes no sense trying to describe all existing types, so only the basic principle and the mathematical formulation is presented. Figure 4.6 shows the principle of a check valve with a ball as working element. Assuming lossless flow in one direction and no flow in the other direction results in two possible states: \u2022 Valve open: pressure drop \u2206p = 0 for all flow rates Q \u2265 0 \u2022 Valve closed: flow rate Q = 0 for all pressure drops \u2206p \u2265 0 The two states define also a complementarity in the form Prestressed check valves with springs show a modified unilateral behavior, see Figure 4.7. The pressure drop curve of a prestressed check valve can be split into an ideal unilateral part \u2206p1 and a smooth curve \u2206p2 considering the spring tension and pressure losses, see Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000920_j.jmrt.2020.06.090-Figure14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000920_j.jmrt.2020.06.090-Figure14-1.png",
        "caption": "Fig. 14 \u2013 Influence of layer rotation angle on principal",
        "texts": [
            " 4 has been used to estimate the residual stresses in selective laser melting process [41]: e = \u221a 1 2 [( x \u2212 y) 2 + ( y \u2212 z) 2 + ( z \u2212 x) 2 + 6( 2 xy + 2 yz + 2 zx)] (4 where, e is described as equivalent stress, x, y and z are stresses produced in X, Y and Z plane of 3D printing components as per the Cartesian coordinates. xy, yz and zx are the shear stresses at XY, YZ and ZX plane, respectively. In this work, the two types of stresses are produced, hence, the Z component of stresses is equal to zero. Hence, the Eq. (4) is roughness values of 3D printed Al-Si-10Mg alloy. reduced to Eq. (5) that can be used to evaluate the stresses in parts manufactured by selective laser melting processes. e = \u221a x2 + y2 \u2212 x y (5) The results of the surface residual stresses are shown in Fig. 14. The sketch presented in Fig. 14 clearly demonstrated the point of measurement. It is evident from the Fig. 14 that residual stresses were tensile or compressive in nature. Compressive stresses are desirable and augment the resistance of material to crack initiation and propagation leading to enhancement of strength [40,42]. At the same time, tensile residual stresses are highly undesirable and may become the potential reason for early crack initiation. The outer surface of fabricated parts through SLM cools quickly leading to contraction which in turn induces plastic yielding inside the core resulting in the generation of tensile residual stresses. The tensile stresses produced in the components are highly attributed to the geometrical changes as well as mechanical properties. Moreover, if the compressive stresses are included in the component, then the possibility of deformation, fracture, and failure is reduced as compared to the tensile stresses. From Fig. 14, it is clear that at zero-degree layer rotation, the residual stresses generated were tensile in nature while at 45\u25e6 and 90\u25e6 it was compressive in nature. This transformation of tensile to compressive residual stresses may have happened largely due to the change in the thermal gradient that was developed as a result of layer rotation. Layer rotation induced rotation in the heat flux direction resulting in optimal crystal orientation that produced relatively stronger texture as compared to 0\u25e6 degree layer rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure4.15-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure4.15-1.png",
        "caption": "Fig. 4.15 Fig. 4.16",
        "texts": [
            " (4.16), which denotes r2 = s in eq. (4.146), we can calculate the derivatives with respect to sand u: RI~=2(1l+~s)=0, R],=2(fl+~S~ +~=O, R]s., =2. Therefore we obtain the transition sets: Bo: a = 0 {R] = R]~ = O. at (O.fl.a.~)} B]: ~ = 0 (degenerate) {R] = RI~ = RL, = O. at (O.fl,a,~)} Ho: a = _~' {R] = R], = 0, at (O'fl,a,~)} (4.149) H] = D = <f> Drawing the curve for eq. (4.149) in the a - ~ plane and combining the a and ~ axes, we see that the a - ~ plane is divided into six open regions in Fig. 4.15. Each of the six open regions has its own special bifurcation diagram and its form is preserved at all points in the same region. The bifurcation response diagrams have the same topological structures in any region [4]. Below we study the forms of the topological structures in each region when = -1. In region (1) a> 0, ~ > 0, as in eq. (4.148), which has no real solution, but a trivial solution r = O. In region (3) a < 0, ~ > 0, assuming lal>I~. For example, take a=-2,~=I,then r=O,Il=\u00b11.414, fl=0,r 2=(-I\u00b1.J!+8)/2=1,-2, hence r = \u00b1 1, a + ~r2 = 0 and fl = 2, so we have r = \u00b1 1.414 , therefore the topological structure of the response diagram in region (3) is shown in Fig. 4.16. In the same way, we obtain the response diagrams in other regions, see Fig. 4.17. Liapunov-Schmidt Reduction 135 Next we analyse the bifurcation diagrams on transition sets. The intersections of the six regions in Fig. 4.15 are called transition sets. When the parameters vary, through them the structures of the bifurcation diagrams will change. On transition curves BI, HI , H2 ,lh and ~ = \u00b0 of the sets, a and ~ are related by a formula so that the bifurcation equation contains only one unfolding parameter apart from Il. For example, : = \u00b0 is satisfied on the transition curve Ho' so the response diagrams are vertical to the Il-axis near r = 0, and we have Il = \u00b1~ / 2, r = 0. In this case the response diagrams should satisfy the equation IlI"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-55-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-55-1.png",
        "caption": "Figure 4-55. Pulse width modulation with field orientation; current trajectory and rectangular error boundary.",
        "texts": [
            " The corresponding signals are shown in Figure 4-54 [51]. The performance of a predictive current control scheme which maximizes the on-durations of the next two switching-state vectors is illustrated in Figure 4-5lb. Pulse Width Control with Field Orientation. A further reduction of the switching frequency, which may be needed in very-high-power applications, can be achieved by defining a current error boundary of rectangular shape, having the rectangle aligned with the rotor flux vector of the machine, Figure 4-55. This transfers a major portion of the unavoidable current harmonics to the rotor field axis where they have no direct influence on the machine torque; the large rotor time constant eliminates their indirect influence on torque through the rotor flux. The selection of the switching-state vectors is based on prediction, satisfying the objectives that the switching frequency is minimized and that switching at \u00bf-current boundaries is avoided to the extent possible. This can be seen in the oscillogram of Figure 4-55. Using a rectangular boundary area in field coordinates leads to a reduction of switching frequency over what can be achieved with a circular boundary area (Figure 4-5lc) [52]. The torque harmonics are reduced at the expense of increased current harmonics, since the \u00bf-axis current increases. Pulse width modulation methods with on-line optimization target at the minimization of an objective function within a restricted time interval. They rely only on the next, at maximum on the next two switching instants as the basis of optimization"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003221_s0094-114x(98)00081-0-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003221_s0094-114x(98)00081-0-Figure4-1.png",
        "caption": "Fig. 4. Six UPS Stewart platform.",
        "texts": [
            " The analysis is similar to the above manipulators and the derivation of the dynamic equations for this is also reported by Choudhury [14]. The application of the method to a few spatial manipulators is shown in the following. First, a brief outline is given for the 6-DOF fully parallel manipulator called the Stewart platform followed by examples of two hybrid manipulators, namely 3-PRPS and 3-RRRS manipulators. The 3-DOF 3-RPS manipulator also has been included as an example of a ``non-standard'' case. The Stewart platform (see Fig. 4), with its multi-DOF joints and very simple inverse kinematics, is one of the ideal manipulators for the present strategy of dynamic formulation. Consideration of force balance of the upper part of a leg in the direction of the leg yields the component of the leg reaction force (at the platform-connection-point) along that direction in terms of the actuator force. Next, the moment balance of the entire leg is considered and the components perpendicular to the leg are separated out (through cross product with the unit vector along the leg) giving the rest of the reaction components at the platform-connectionpoint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.38-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.38-1.png",
        "caption": "Fig. 7.38: Model of the Manipulator",
        "texts": [
            " When modeling such processes, we can distinguish between the dynamic model of the robot and that of the process dynamics, but we have to consider it in a realistic combination. Industrial robots suitable for complex assembly tasks have to provide at least six degrees of freedom and, to ensure flexible operation, a large workspace. We will therefore focus on manipulators with 6 rigid links and 6 revolute joints, which are very popular in industry. Such a robot can be modelled as a tree-structured multibody system (Figure 7.38). The joints of the first three axes are considered elastic in order to take the finite gear stiffnesses and damping into account, which play an important role in precision assembly. For this purpose a linear force law consisting of a springdamper combination cj , dj , combined with the gear ratio iG,j, j = 1, . . . , 3, is assumed. The gears of the hand axes are considered stiff and the motion of one arm and its corresponding motor is kinematically coupled. Nevertheless we should keep in mind, that in reality the gears of the hand axes are elastic as well",
            " Backlash does not play an important role in modern robots [107], therefore we shall neglect such effects. The robot possesses therefore 9 degrees of freedom, 6 arm angles and 3 free motor angles. The vector q of generalized coordinates writes accordingly 7.3 Dynamics and Control of Assembly Processes with Robots 477 q = ( qM qA ) \u2208 IR9, qM = [ \u03b3M,1 \u03b3M,2 \u03b3M,3 ]T \u2208 IR3, qA = [ \u03b3A,1 . . . \u03b3A,6 ]T \u2208 IR6, (7.130) where \u03b3M,j, \u03b3A,j denote the angle of the j-th motor and arm, respectively, relative to the previous body, see Figure 7.38. Translational and rotational velocities r\u0307j and \u03c9j of the center of gravitiy of each link can thus be calculated recursively starting at the robot\u2019s base (see also equation (7.3)), \u03c9j =\u03c9(j\u22121) +\u2206\u03c9(j\u22121),j , \u2206\u03c9(j\u22121),j = \u03b3\u0307A,j r\u0307j =r\u0307(j\u22121) + ( \u03c9(j\u22121) \u00d7 rCJ,(j\u22121) ) + (\u03c9j \u00d7 rJC,j) , (7.131) where rCJ,(j\u22121) and rJC,j denote the distance vectors between center of gravity (C) and joint position (J), as depicted in Figure 7.38. Particularly, translational and angular velocity of the gripper end point are \u03c9G = 6\u2211 j=1 \u03c9j , r\u0307G = 6\u2211 j=1 [(\u03c9j\u22121 \u00d7 rGJ,j\u22121) + (\u03c9j \u00d7 rJG,j)] + (\u03c96 \u00d7 rGJ,6) . (7.132) The gripper Jacobians, which relate the Cartesian motion of the gripper to the generalized coordinates, write JTG = \u2202 (A60r\u0307G) \u2202q\u0307 \u2208 IR3\u00d79, JRG = \u2202 (A60\u03c9G) \u2202q\u0307 \u2208 IR3\u00d79. (7.133) In this operation, \u02d9rG and \u03c9G are transformed by A60 into a gripper-fixed coordinate frame, so that JTG and JRG are related to the gripper system G (Figure 7.38), which is convenient in manipulation tasks. In the three basic axes the arm angles and the motor angles are connected by a linear force law representing the finite gear stiffnesses: \u03c4A,j = cj ( \u03b3M,j iG,j \u2212 \u03b3A,j ) + dj ( \u03b3\u0307M,j iG,j \u2212 \u03b3\u0307A,j ) , (j = 1, 2, 3) (7.134) cj and dj are stiffness and damping factors of the j-th gear and iG,j is the gear ratio. The equations of motion of the robot with forces acting on the gripper can be written as g := M(q)q\u0308 + f (q, q\u0307)\u2212B\u03c4C \u2212W (q)\u03bb = 0, (7.135) withM \u2208 IR9\u00d79 being the inertia matrix,B \u2208 IR9\u00d76 andW = [ JTTG J T RG ] \u2208 IR9\u00d76 are the input matrices for the 6 motor torques (\u03c4C \u2208 IR6) and gripper forces (\u03bb \u2208 IR6), respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure6.16-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure6.16-1.png",
        "caption": "Fig. 6.16: Ultrasound distance microsensor",
        "texts": [
            " Since the transducer needs some time for recovery after transmission, a \"blind spot\" appears when the detector is too close to an object, which means that an object might not be detected. The results obtained with a new concept of an ultrasound microtransformer were reported in (M2S293]. In this device, two identical independent ultrasound membranes were integrated next to each other on a silicon substrate; one served as a transmitter and the other one as a receiver. The schematic design of a single sensor membrane and the measurement principle are shown in Figure 6.16. a) design of the sensor; b) measurement principle of the sensor. According to [M2S293] The transmitter membrane is brought to resonance electrothermally with integrated heating resistors. The acoustic pressure response is then detected by piezoresistors, integrated in the form of a Wheatstone bridge in the re ceiver membrane. The sensitivity of this prototype was about 3 f.!V/mPa at a bridge voltage of 5V. Capacitive rotational speed sensor In many technical systems like navigation and landing gear controllers, com pact and inexpensive angular speed sensors are required"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003519_robot.1995.525473-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003519_robot.1995.525473-Figure2-1.png",
        "caption": "Figure 2: Top view of the bicycle model rolled away from upright by angle a . Bold arrows indicate wheel directions at the ground plane.",
        "texts": [
            " The yaw-angle B is zero when the contact-line is in the 2 direction. The angle that the bicycle\u2019s plane of symmetry makes with the ground i s the roll-angle, cy E (-./a, ~ / 2 ) . Front and rear-wheel contacts are constrained to have velocities parallel to the lines of intersection of their respective wheel planes and the ground-plane, but free to turn about an axis through the wheel/ground contact and parallel to the z-axis. Let 4 E (-./a, ./a) be the steering-angle between the front-wheel-plane/ground-plane intersection and the contact-line as shown in Figure 2. With 4 we associate a moment of inertia J . For simplicity we will parameterize the steering angle by n := tan($/b). The component of the velocity of the rearwheel/ground contact along the contact line is v,. The velocity of the rear contact perpendicular to this line and in the ground plane is V I . The angle of the contact-line with respect to the x-axis of the groundfixed inertial frame is B. Note that the generalized coordinate corresponding to w, is the the integral in time of the rear-wheel velocity along the path traveled, and the generalized coordinate corresponding to w l is the integral in time of the rear-wheel velocity along a direction perpendicular to the rear-wheel which, by virtue of the constraints, is always zero",
            " A torque generator is associated with the steering variable cl the generalized torque being U,. We consider a vehicle with a rigid or non-existent passenger under automatic control. 3 Equations of Motion We choose a body-frame for the bicycle centered at the rear-wheel ground contact, with one axis pointing forward along the line of intersection of the rear wheel plane with the ground, another axis orthogonal to the first and in the ground plane, and an axis normal to the ground, pointing in the direction opposite to gravity (see Figure 2). The body frame is a natural frame in which to write the Lagrangian of the bicycle for a number of reasons. In particular the rolling constraints take on a very simple form. The generalized velocities of the bicycle are contained in the partitioned coordinates 7: = [&, w,., &IT and s = [B, w 1 l T . In these velocity coordinates the nonholonomic constraints associated with the front and rear wheels, assumed to roll without slipping, are expressed very simply by 3 + A(r, s)7: = 0 or The mapping represented by matrix A(r , s ) is an Ehresmann connection [3], connecting the base velocities r to the fibervelocities S "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000199_j.conbuildmat.2019.06.132-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000199_j.conbuildmat.2019.06.132-Figure1-1.png",
        "caption": "Fig. 1. (a) The size distribution of the gas-atomised powder and the morphology of the powder particles and (b) an image of a SLM-produced samples, including the scanning direction and the chemical compositions.",
        "texts": [
            " The mechanical properties were investigated using tensile experiments and the anticorrosive performance was evaluated via potentiodynamic and potentiostatic polarisations, electrochemical impedance spectroscopy (EIS) and ferric chloride immersion experiment. The anisotropy in the SLMed Hastelloy X parts was also delineated and the tests for each sample were performed at least three times for data reproducibility. The size distribution of the gas-atomised powder and the morphology of the powder particles are shown in Fig. 1(a) and the average diameters are approximately 33 lm for hastelloy X powders. The chemical compositions of the powders used for SLMed hastelloy X were similar to that for the traditional wrought counterpart, as shown in Fig. 1(b). Samples were manufactured using an EOS M290 system (Germany), which was equipped with a 400WYb: YAG fibre laser (1070 nm wavelength), operated at a scan speed of 1000 mm/s and the spot size of 80 lm. The SLMed samples were produced in continuous laser mode with 280 W laser power. Both the hatch spacing and the layer thickness were 25 lm and the layers were scanned in a zigzag pattern, rotated by 67 between each successive layer to reduce the stress concentration. The XOY and XOZ planes were chosen to be the working areas for studying the anisotropy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure14.30-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.30-1.png",
        "caption": "Fig. 14.30 Irregular wear of a ball bearing due to differential sliding. Reproduced from Ref. [24] with the permission of Fujikoshi",
        "texts": [
            "105) yields F1 \u00bc F2 \u00bc D1D2 r1 r2\u00f0 \u00de= D1r1 \u00feD2r2\u00f0 \u00de: \u00f014:107\u00de Wear energies Ew\u00f01\u00de x and Ew\u00f02\u00de x per unit length of tires 1 and 2 are proportional to the square of the difference between the radii: Ew\u00f01\u00de x \u00bc F1s1 \u00bc D1D2 2 r1 r2\u00f0 \u00de2= D1r1 \u00feD2r2\u00f0 \u00de2 Ew\u00f02\u00de x \u00bc F2s2 \u00bc D2 1D2 r1 r2\u00f0 \u00de2= D1r1 \u00feD2r2\u00f0 \u00de2: \u00f014:108\u00de When tire 2 is much narrower than tire 1; the relation D1 D2 is satisfied. The wear energy Ew\u00f02\u00de x of tire 2 can thus be simplified as Ew\u00f02\u00de x \u00bc F2s2 \u00bc D2 r1 r2\u00f0 \u00de2=r21 \u00bc D2 Dr=r1\u00f0 \u00de2: \u00f014:109\u00de Ew\u00f02\u00de x is also proportional to the square of Dr (i.e., the difference between radii). These phenomena are also observed in the wear of ball bearings. When a ball bearing with radius R rolls on a groove with radius R\u2032, which is a little larger than R as shown in Fig. 14.30, the contact shape of the ball bearing is an ellipse and the center of the ball moves more quickly than the edges of the ball. The edges of the ball are thus in a braking condition such that there is sliding at the edges of the ball, which is referred to as differential sliding. Differential sliding always occurs if there is a difference in the contact length between the center and edges. To improve the wear due to differential sliding, a particular cross-sectional shape is used for grooves in a process referred to as crowning",
            " Furthermore, tires should be designed to have metrics near region 3 for a market associated with stronger side forces, like Japan and Europe, while tires should be designed to have metrics near region 1 for markets associated mainly with driving straight, like the USA. Note that the wear and irregular wear are improved by optimizing the crown shape to make the contact pressure distribution uniform as we discussed in Sect. 9.4.3. The metrics of these tires are located in region 2. Note that the idea of changing the shape has also been applied to the grooves of a ball bearing in what is called crowning, where the radius at the edge of the groove is smaller than that at the center of the groove as shown in Fig. 14.30. Figure 14.85 shows common irregular wearing of truck/bus tires resulting from self-accelerated wear due to a braking force as discussed in Sect. 14.8.3. Such irregular wear can be reduced by reducing the braking force in ribs with irregular wear. Kukimoto and Ogawa of Bridgestone developed the technology of a braking control rib (BCR) in Fig. 14.86a, which is a narrow rib dented in relation to adjacent main ribs. Figure 14.87 shows the change in average circumferential shear forces resulting from adding the BCRs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure3.2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure3.2-1.png",
        "caption": "Fig. 3.2 Stress/strain for two laminae and an adhesive layer between them",
        "texts": [
            " The shear deformation in the thickness direction is only considered at the adhesive layer, which means that the in-plane stiffness of the adhesive layer is neglected. The two laminae are identified by the subscripts 1 and 2 numbered from the symmetric plane. The L-axis is the direction of the cords while the T-axis is the direction transverse to the cords. The orientation angles a1 and a2 are measured from the x-axis. The sign of an orientation angle is positive when the L-axis is aligned in the counterclockwise direction from the x-axis. Referring to Fig. 3.2 where h1 and h2 are thicknesses of 1st and 2nd lamina, and h is the thickness of the adhesive layer, the in-plane stresses r i\u00f0 \u00de x ; r i\u00f0 \u00de y ; s i\u00f0 \u00de xy (i = 1, 2) satisfy the equilibrium equations1,2 @r\u00f01\u00dex @x \u00fe @s\u00f01\u00dexy @y \u00fe szx h1 \u00bc 0 @s\u00f01\u00dexy @x \u00fe @r\u00f01\u00dey @y \u00fe szy h1 \u00bc 0; \u00f03:1\u00de 1Problem 3.1. 2See Footnote 1. 3.2 MLT of a Two-Ply Laminate Without Out-of-Plane \u2026 101 @r\u00f02\u00dex @x \u00fe @s\u00f02\u00dexy @y szx h2 \u00bc 0 @s\u00f02\u00dexy @x \u00fe @r\u00f02\u00dey @y szy h2 \u00bc 0: \u00f03:2\u00de ui and vi (i = 1, 2) are, respectively, displacements of each lamina in the x- and ydirections",
            " However, because there are no external forces at the free edges of a laminate with an adhesive layer, each lamina deforms in a manner opposite to the shear stresses at the free edges as shown in the middle and right figures of Fig. 3.6. Hence, interlaminar shear stress is generated at an adhesive layer between two laminae under an extensional load, and this is usually the main cause of tire failures at belt ends. The stress distribution of a symmetric FRR composite is calculated. The properties of each lamina and the adhesive rubber layer of Fig. 3.2 are EL = 2 GPa, ET = 40 MPa, mL = 0.5, mT = 0.01, GLT = 10 MPa, G = 5 MPa, b = 50 mm, h1 = h2 h0 = 5 mm, h = 1, 2, 4 mm. 110 3 Modified Lamination Theory 3.2 MLT of a Two-Ply Laminate Without Out-of-Plane \u2026 111 (szx)max for various orientation angles. szx has a maximum value at about a = 15 deg for any thickness of the adhesive rubber layer, but the maximum value (szx)max decreases with increasing thickness of the adhesive rubber layer. Because the orientation angle of a passenger-car tire\u2019s belt ranges from 20\u00b0 to 30\u00b0, the interlaminar shear stress is near its maximum",
            " In this chapter, after deriving fundamental equations based on the study of Akasaka and Hirano, we discuss MLT for the bias belt under uniaxial deformation. MLT under in-plane bending and out-of-plane torsion will be discussed in Sects. 3.5 and 3.7. 3.3 MLT of a Two-Ply Laminate Including Transverse Stress \u2026 121 The assumptions are that the shear deformation in the thickness direction only occurs in an adhesive rubber layer and the Kirchhoff\u2013Love hypothesis can be adopted for both laminae. Figure 3.14 presents free-body diagrams for the fundamental equations where the subscripts 1 and 2 indicate each lamina. Comparing Fig. 3.14 with Fig. 3.2, the bending moment and shear force are included in Fig. 3.14. Referring to Fig. 3.14, the equilibrium equations are @N\u00f01\u00de x @x \u00fe @N\u00f01\u00de xy @y \u00bc szx @N\u00f01\u00de xy @x \u00fe @N\u00f01\u00de y @y \u00bc szy; \u00f03:65\u00de @N\u00f02\u00de x @x \u00fe @N\u00f02\u00de xy @y \u00bc szx @N\u00f02\u00de xy @x \u00fe @N\u00f02\u00de y @y \u00bc szy; \u00f03:66\u00de @ @x Q\u00f01\u00de x \u00feQ\u00f02\u00de x \u00feQx \u00fe @ @y Q\u00f01\u00de y \u00feQ\u00f02\u00de y \u00feQy \u00bc q\u00f0x; y\u00de; \u00f03:67\u00de 122 3 Modified Lamination Theory @M\u00f01\u00de x @x \u00fe @M\u00f01\u00de xy @y \u00bc Q\u00f01\u00de x \u00fe szx h1 2 @M\u00f01\u00de xy @x \u00fe @M\u00f01\u00de y @y \u00bc Q\u00f01\u00de y \u00fe szy h1 2 ; \u00f03:68\u00de Qx h \u00bc szx Qy h \u00bc szy; \u00f03:69\u00de @M\u00f02\u00de x @x \u00fe @M\u00f02\u00de xy @y \u00bc Q\u00f02\u00de x \u00fe szx h2 2 @M\u00f02\u00de xy @x \u00fe @M\u00f02\u00de y @y \u00bc Q\u00f02\u00de y \u00fe szy h2 2 ; \u00f03:70\u00de where Eqs",
            "9) that the strain in the bottom layer (z = \u2212 t/2) can be expressed as ex ey cxy 8< : 9= ; \u00bc 0:635 2 2:348 0:643 0 8< : 9= ; \u00bc 0:745 0:204 0 8< : 9= ;; Solutions 1215 where the strains at the mid-plane are zero because there are no in-plane forces. It follows from Eq. (2.1) that rx ry sxy 8< : 9= ; \u00bc 20:8874 3:260 0 3:260 11:898 0 0 0 3:789 2 4 3 5 0:745 0:204 0 8< : 9= ; \u00bc 14:886 0 0 8< : 9= ;: 2.9 The extension\u2013shear coupling occurs in the one-layer belt but in bias belt. Both equivalent Young\u2019s moduli are the same at the belt angle 0\u00b0, 54.7\u00b0 (particular angle) and 90\u00b0. 3.1 Referring to Figure 3.2, the force equilibrium in the x-direction is given as r\u00f01\u00dex h1dy\u00fe r\u00f01\u00dex \u00fe @r\u00f01\u00dex @x dx ! h1dy s\u00f01\u00dexy h1dx\u00fe s\u00f01\u00dexy \u00fe @s\u00f01\u00dexy @y dy ! h1dx\u00fe szxdxdy \u00bc 0: We derive equations for displacements as u1 \u00bc A01e ffiffiffi q1 p y \u00fe A01e ffiffiffi q1 p y \u00feA02e ffiffiffi q2 p y \u00fe A02e ffiffiffi q2 p y \u00feA03y\u00feA04 v1 \u00bc A01 Eys Eyy e ffiffiffi q1 p y \u00fe A01 Eys Eyy e ffiffiffi q1 p y \u00feA02 Ess Eys e ffiffiffi q2 p y \u00fe A02 Ess Eys e ffiffiffi q2 p y \u00feC03y\u00feC04 u2 \u00bc A01e ffiffiffi q1 p y A01e ffiffiffi q1 p y \u00feA02e ffiffiffi q2 p y \u00fe A02e ffiffiffi q2 p y \u00feB03y\u00feB04 v2 \u00bc A01 Eys Eyy e ffiffiffi q1 p y \u00fe A01 Eys Eyy e ffiffiffi q1 p y A02 Ess Eys e ffiffiffi q2 p y A02 Ess Eys e ffiffiffi q2 p y \u00feD03y\u00feD04; 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure6.38-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure6.38-1.png",
        "caption": "Fig. 6.38: Joint Kinematics between two Links",
        "texts": [
            " The share of the link dynamics with respect to the overall dynamics can now already be summarized. We get for the mass matrix MG = m ( JTTJT \u2212 1 2 JTT a\u0303JR + 1 2 JTRa\u0303JT ) + JTRIHJR, (6.51) and the centrifugal forces follow from hG = \u22121 2 mJTT \u03c9\u0303G\u03c9\u0303Ga. (6.52) Furtheron we have gravitational forces G = mg and joint forces acting on the link. Including the gravitational force into the equations of motion referenced to the mass center requires a transformation hG = . . . + JTTSG with JTS = \u2202vS \u2202q\u0307G = JT \u2212 1 2 a\u0303JR. (6.53) The joints are approximately modeled like a journal bearing (Figure 6.38). For applying the force law given by Figure 6.33 we need the relative displacements and displacement velocities for a link i and a link j. From joint kinematics we get in a first step \u03b5 = rG,j \u2212 rG,i \u2212 ai, \u03b5\u0307 = vG,j \u2212 vG,i + a\u0303i\u03c9G,i (6.54) The joint displacement and displacement velocity follows then in the form \u03b3 =nT\u03b5, \u03b3\u0307 = nT \u03b5\u0307 n = \u03b5 |\u03b5| for |\u03b5| = 0, n = \u03b5\u0307 |\u03b5\u0307| for |\u03b5| = 0, |\u03b5\u0307| = 0. (6.55) According to the force law of Figure 6.33 the following formulas are applied \u03bbN =d(\u03b3)\u03b3\u0307, within backlash, \u03bbN =c(\u03b3 \u2212 \u03b30) + d\u03b3\u0307 with contact, N =n\u03bbN "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure8.6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure8.6-1.png",
        "caption": "Fig. 8.6: Micro-crawling machine using magnets a) schematic design; b) a prototype of the device. Courtesy of the Eidgenos sische Technische Hochschule, Zurich",
        "texts": [
            " This operating principle can be used in mass production. Micro-crawling machine A few years ago, a research program was started in Switzerland for develo ping new devices and aids for microassembly. Within the framework of this program, a so-called micro-crawling machine was developed, which can ma ke precise inchworm-like movements, and can be used as a driver for a po sitioning table in a microassembly station or as a small mobile robot platform [Codo95]. The device is about 60 mm x 60 mm and consists of two triangular legs, Fig. 8.6. The inner leg is connected to the outer one via three piezo electric stack elements. There are electromagnets embedded in all three cor ners of the outer triangle of the device and one in the center of the inner leg. The device can crawl along by holding on to a ferromagnetic base with one leg and moving the other one. The motion sequence is as follows: in the initial state, the outer leg is fixed to the base by the three magnets (current on) and the inner leg is free (the current is turned off from the inner magnet coil)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003834_1.2359475-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003834_1.2359475-Figure6-1.png",
        "caption": "Fig. 6 A kinematical model of hypoid generators",
        "texts": [
            "org/about-asme/terms-of-use T i s T p fi c m c t E f t n n u i w P t 3 Downloaded Fr Ra = Ra0 + Ra1 + Ra2 2 + \u00af + Ra6 6 Xb = Xb0 + Xb1 + Xb2 2 + \u00af + Xb6 6 s = s0 + sc1 + sc2 2 + \u00af + sc6 6 Em = Em0 + Em1 + Em2 2 + \u00af + Em6 6 Xp = Xp0 + Xp1 + Xp2 2 + \u00af + Xp6 6 m = m0 + m1 + m2 2 + \u00af + m6 6 j = j0 + j1 + j2 2 + \u00af + j6 6 i = i0 + i1 + i2 2 + \u00af + i6 6 5 he generalized machine settings are: i ratio of roll Ra, ii slidng base Xb, iii radial setting s, iv offset Em, v work head etting Xp, vi root angle m, vii swivel j, and viii tool tilt i. he UMC can be applied to both face-milling and face-hobbing rocesses in designing optimized tooth surfaces. Traditional modied roll, helical motion, and vertical motion are actually specific ases of UMC. To develop a generic tooth surface generation odel, the cradle-style generator consisting of 11 motion units is onsidered Fig. 6 . The generating motion of the machine is inegrated by the elemental motion units representing basic settings. ach relative elemental motion is represented by a matrix transormation. The resulting generating motion is obtained through he sequential matrix transformations from the cutter head coordiate system St to the coordinate system Sw that is rigidly conected to the work 13\u201315 . The position vector, unit tangent, and nit normal of the work tooth surface can be generally represented n the coordinate system Sw as rw = rw u, , 6 tw = tw u, , 7 nw = nw u, , 8 here the unit normal vector nw = rw rw tw 9 arameters and are, respectively, the angular increments of he cutter and the cradle rotations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure12.100-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure12.100-1.png",
        "caption": "Fig. 12.100 Simplified wheel\u2013soil interaction model [132]",
        "texts": [
            " Although GTSL and GTFR are different forces in essence, they are included as a shear force due to slip displacement of the soil in a semi-empirical method. The semi-empirical theory involves GTFR and Rc while the computational model includes four forces. (1) Quasi-static motion resistance (1-1) Rigid (wheel) mode The motion resistance Rc in the rigid mode is obtained by integrating the horizontal component of stress normal to the tire surface from the maximum sinkage point to the sinkage starting point as shown in Fig. 12.100. Using Eq. (12.191), Rc is obtained as Rc \u00bc b Zz0 0 qzdx \u00bc b Zz0 0 kc b \u00fe k/ zndz \u00bcb kc b \u00fe k/ zn\u00fe 1 0 n\u00fe 1 ; \u00f012:196\u00de where b is the wheel width. Rc is equal to the work done when a plate with width b per unit length is normally pressed from zero to z0. Hence, the motion resistance is also called the compressive resistance. The maximum sinkage z0 in Eq. (12.196) is given by the equation for the equilibrium between the load Fz and normal stress (average contact pressure) qz: 900 12 Traction Performance of Tires Fz \u00bc b Zl1 0 qzdx \u00bc b Zl1 0 kc b \u00fe k/ zndx: \u00f012:197\u00de Referring to Fig. 12.100, the geometrical relation gives x2 \u00bc 2r z0 z\u00f0 \u00def g z0 z\u00f0 \u00de; \u00f012:198\u00de where r is the tire diameter. When sinkage z0 is small, x is given by x2 \u00bc 2r z0 z\u00f0 \u00de: \u00f012:199\u00de Using Eq. (12.199) and introducing the parameter t defined by z0 \u2212 z = t2, Eq. (12.197) is rewritten as Fz \u00bc b kc b \u00fe k/ Zz0 0 zn ffiffi r pffiffiffi 2 p ffiffiffiffiffiffiffiffiffiffiffiffi z0 z p dz \u00bc b kc b \u00fe k/ ffiffiffiffiffi 2r p Z ffiffiffiz0p 0 z0 t2 n dt: \u00f012:200\u00de Applying Taylor series expansion to (z0 \u2212 t2)n in the above equation, zn0 nzn 1 0 t2 \u00fe is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000084_j.addma.2019.100844-Figure6-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000084_j.addma.2019.100844-Figure6-1.png",
        "caption": "Fig. 6. Test part design. The part has four connected overhanging wedges with width 5mm, height 10mm and angles of 45, 60, 75, and 90 degrees respectively. Dimensions are in millimeters.",
        "texts": [
            " This is limited by either the acquisition rate of the camera hardware (< 10 000 frames/s in this paper), or the digital command rate (100 kHz). Additionally, the physical position of each camera frame trigger can be mapped back to the physical location within the part. The camera trigger scheme and image processing for this experiment are described in Section 3.1. Overhanging structure is identified to study the effectiveness of the GCF based power control. A part is designed with a series of downward facing wedges of angles 45, 60, 75 and 90 degrees (Fig. 6). Nickel alloy 625 (IN625) powder is used, with particle size distribution of D10= 16.4 \u03bcm, D50= 30.6 \u03bcm, and D90= 47.5 \u03bcm. The build plates are 12.5 mm thick IN625, and the AMMT chamber is purged and backfilled with Argon to obtain an oxygen level less than 705mg/m3. The laminar flow unit is used, with flow rate of 300 L/min, although the flow velocity above the build is unknown at this time. Nominal scan parameters for IN625 are based on a commercial LPBF system. Scan speed is 800mm/s, laser power 195W, interlayer rotation 67\u00b0, hatch spacing 100 \u03bcm, and layer thickness 20 \u03bcm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000490_j.ijheatmasstransfer.2019.118990-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000490_j.ijheatmasstransfer.2019.118990-Figure1-1.png",
        "caption": "Fig. 1. Laser cladding process.",
        "texts": [
            " The microstructure evolves from planar to cellular, and to equiaxed dendrites from the substrate\u2013clad interface to the top surface. The transition zone comprised of planar and cellular grains. The solidification characteristics calculated from the numerical model were associated to the grain morphology. 2019 Elsevier Ltd. All rights reserved. Laser cladding is a fundamental type of coating technology that utilizes a concentrated high-power laser beam to melt the surface of base material and in-situ-delivered cladding material. After solidification, the new layer with the desired properties is fabricated [1,2]. Fig. 1 shows the laser cladding process schematically. High-speed steels with high wear resistance, corrosion resistance, and high hardness, are utilized in the laser cladding industry to fabricate protective coatings for metallic surfaces [3,4]. Fig. 2 shows the energy distribution in the laser cladding process. A certain amount of laser energy will first be reflected and absorbed by the powder jet. Greater than half of the attenuated laser energy will then be reflected by the molten pool. A miniscule percentage of the energy absorbed by the molten pool will be lost through radiation and convection, the bulk of which will conduct to the substrate to heat the base material [5,6]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003270_9780470547113-Figure4-8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003270_9780470547113-Figure4-8-1.png",
        "caption": "Figure 4-8. Definition of a current space vector: (a) cross section of an induction motor; (b) stator windings and stator current space vector in the complex plane.",
        "texts": [
            " The space vector approach complies exactly with this requirement. Since the predominant application of three-phase PWM is in controlled AC drive systems, the stator winding of an AC machine will be subsequently considered as a representative AC load. 4.3. An Introduction to Space Vectors 145 \"n U\u00a12 Ul3 \"np Ub 1 2\"d 0 1 , , 2ud 0 0 ?Ud 2 | / 3ud iud 1 0 0 2 3 4 5 6 2 2 \u03c0 \u03c0 (a) (b) (at- 2\u03c0 Consider a symmetrical three-phase winding located in the stator of an electric machine, located for instance in the stator, Figure 4-8a. The three phase axes are defined by the respective unity vector 1, a, and a2, where a = \u03b2\u03c7\u03c1(/2\u03c0/3). Figure 4- 8b is a symbolic representation of the winding. Neglecting space harmonics, the phase currents isa, isb, and isc generate a sinusoidal current density wave (MMF wave) around the air gap as symbolized in Figure 4-8a. The MMF wave rotates at the angular frequency of the phase currents. Like any sinusoidal distribution in time or space, it can be represented by a complex MMF phasor As as shown in Fig 8a. It is preferred, however, to describe the MMF wave by the equivalent current phasor i\u201e because this quantity is directly linked to the three stator currents \u03af'\u03ca\u03b1, ish, isc that can be measured at the machine terminals: h = I (ha + a hb + \u00bfhe) (4-5) The subscript 5 refers to the stator of the machine. The complex phasor in equation 4",
            "5, more frequently referred to in the literature as a current space vector [1] has the same direction in space as the magnetic flux density wave produced by the MMF distribution As. In a similar way, a sinusoidal flux density wave can be described by a space vector. It is preferred, however, to choose the corresponding distribution of the flux linkage with a particular three-phase winding as the characterizing quantity. For example, we write the flux linkage space vector of the stator winding in Figure 4-8 as fs = l,i, (4-6) In the general case, when the machine develops nonzero torque, the two space vectors is of the stator current and ir of the rotor current are nonzero, yielding the stator flux linkage vector as Ts = lsis + lhir (4.7) where ls = lf,+ lsa is the three-phase stator winding inductance, lh is the three-phase mutual inductance between the stator and rotor windings, and lsa is the leakage inductance of the stator. The expression three-phase inductance relates to an inductance value that results from the flux linkage generated by all three-phase currents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure6.4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure6.4-1.png",
        "caption": "Fig. 6.4",
        "texts": [
            "76) 1 where fl2 = - Re[C1 (0)] / a'(O), '2 = --(0l~fl2 + ImCtCO)). Formulae (6.76) are Olo sometimes called HKW (B.D. Hassard, N.D. Kazarinoff and Y-H. Wan) Hopf bifurcation formulae. fl2 determines the direction of bifurcation \"2 determines the change in period. 194 Bifurcation and Chaos in Engineering When 112 \"\" 0 \"\" 't 2' it is the general or non-degenerative case. If 112 = 0 is degenerate, 1l4' ... can be computed, and the numbers 1l2' 114 are called focal numbers. The Hopf bifurcation figure for the non-degenerate case is shown in Fig. 6.4. In the degenerate case, we may study the property of bifurcation according to universal unfolding theory. Refer to [4]. So far, we have studied the existence and the computing method for the bifurcation solution in non-linear ordinary differential systems under the condition of the Hopf bifurcation theorem. Now when we study the stability of the bifurcation solution, we need to use Floquet theory which has been introduced in chapter 1. In this section we shall discuss another example of the application of this theory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003526_1.2337316-Figure9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003526_1.2337316-Figure9-1.png",
        "caption": "Fig. 9 Coordinate systems Sm and Ss",
        "texts": [
            "org/about-asme/terms-of-use c a l s w m v b s C t r p r t s s w p t t J Downloaded Fr onstants; c the applied coordinate systems are directly associted with the physical machine motion elements and visually ilustrated; d the machine is virtually \u201cdisassembled\u201d to clearly how each machine setting and the associated motion elements as ell as the applied coordinate systems; and e a generating curve the edge of a tool blade , instead of a conical surface for face illing , is considered as the generating element. Following proides the detailed description. In order to mathematically describe the generation process, we reak down the relative motion elements of the kinematical model hown in Fig. 5 and attach a coordinate system to each of them. oordinate system Sm Fig. 9 , called the machine coordinate sysem, is connected to the machine frame and considered as the eference of the relative motions. System Sm defines the machine lane and the machine center. System Ss is connected to the sliding base element 11 and repesents its translating motion. System Sr Fig. 10 is connected to he machine element 10 and represents the machine root angle etting. System Sc Fig. 11 is connected to the cradle and repreents the cradle rotation with angular displacement q=q0+ , here q0 is the initial cradle angle and is the cradle increment arameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003818_1.2805242-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003818_1.2805242-Figure1-1.png",
        "caption": "Fig. 1. Forces on a spinning baseball in flight. The drag force FD acts in the \u2212v direction, the Magnus force FM acts in the \u0302 v\u0302 direction, and the force of gravity FG acts downward.",
        "texts": [
            " The goals of the present paper are to report new experimental data for the Magnus force and to use these data to update and extend the earlier investigations of the effect of spin on the flight of pitched or batted baseballs. The present experiment, including the data reduction and analysis, is described in Sec. III. The results are compared to previous determinations of the Magnus force in Sec. IV and the implications for the flight of a baseball are discussed. A summary of our conclusions is given in Sec. V. When a spinning baseball travels through the atmosphere, it experiences the force of gravity in addition to the drag and Magnus forces, FD and FM, as shown in Fig. 1. Conventionally the magnitudes of these forces are parametrized as FD = 1 CD Av2, 1 2 119\u00a9 2008 American Association of Physics Teachers ense or copyright; see http://ajp.aapt.org/authors/copyright_permission FM = 1 2 CL Av2, 2 where A is the cross sectional area of the ball, v is its speed, is the air density 1.23 kg /m3 , and CD and CL are the drag and lift coefficients, respectively.15 We will focus only on CL. Data on other spherical sports balls suggest that CL is mainly a function of the spin factor S=R /v, although it may also be a function of the Reynolds number Re=2 Rv / "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003903_j.1469-7998.1980.tb04222.x-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003903_j.1469-7998.1980.tb04222.x-Figure3-1.png",
        "caption": "FIG. 3 . This diagram is explained in the text.",
        "texts": [
            " A muscle does negative work when it dissipates mechanical energy by extending while exerting tension). It was argued OPTIMUM WALKING TECHNIQUElS 99 that muscles must do positive work whenever the total (kinetic plus potential) mechanical energy of the body increased, and negative work whenever the total decreased. Further, it was argued that when two feet are on the ground simultaneously, one exerting a forward and the other a backward force, the legs must do work against each other as the body advances: one leg must do positive work which is counteracted by negative work done by the other. Figure 3 shows a situation in which this is untrue. Leg A is rigid so that the hip is moving in a circular arc centred on the foot. The force on its foot is aligned with the leg so as to exert no moment about the hip. The model of Alexander & Jayes (1978b) would show leg B doing positive work and leg A negative work at this stage of the stride. However leg A is doing no work, positive or negative, since its length is (for the time being) constant and no moment is acting about any moving joint in it. Such errors are avoided in this paper by calculating separately the work done by each leg",
            " 6 in Alexander & Jayes (1978h) and give E/(mgA2/32k) where E i s the positive work done in a half stride or yU/2f. The numbers labelling the contours in Fig. 7 must thus be multiplied by 16 gk/\u2019A2= 16gk/u2 to obtain values comparable to those in Fig. 6 of the previous paper. A direct comparison can be made b-t ween graphs (b) in the two figures, since both refer to u2/gk=0.2. The graphs are very similar and indicate similar values of U , but they are not identical. The main causes of differences between them are the errors which arose in the previous model as explained in the discussion o f Fig. 3. Figure 7(a), (b), (c) shows that for each value of uz/gk less than I , there is a unique combination of values of /l and q which minimizes U. This is the optimum (/l,q) for economical walking. As uP/gk increases from 0.05 to 0.8, this optimum moves from (approximately) (0.75, 0) to (0.55, 0.8). The previous model (Alexander & Jayes, 19786) showed similarly that as uz/gk increased the optimum moved towards higher values of q but failed to show that it moved towards lower values of p. It seemed to show that p20.6 was optimal at all speeds, probably because the errors indicated by Fig. 3 tended to exaggerate power requirements at higher values of p. The previous model also showed that as u2/gk increases past 1 the optimum moves suddenly to B=O. The new model shows the same (Fig. 7(d)). OPTIMUM WALKING TECHNIQUES 111 These results can be explained qualitatively. The instantaneous power output is the sum of two terms, F,dx/dt and Fydy/dt (equation (2)). The metabolic power requirement is minimized by keeping the sum of these terms as near to zero as possible, throughout the step. Since dxldt and F, are always positive, this requires that Fx and dyldt be kept opposite in sign",
            " It is shown that this mechanism is potentially very effective for running with q = 0, but not for fast walking with high values of y. This may be why men change from walking to running at lower speeds than the inelastic theory suggests. Dr R. F. Ker found and helped to correct a flaw in a draft of this paper. Mews A. S. Jayes and J. van Leeuwen helped in the bifilar pendulum experiment. I have had useful discussions with all these people. Professor G. A. Cavagna supplied the argument illustrated by Fig. 3. This work is part of a programme of research supported by a grant from the Science Research Council. R E F E R E N C E S Alexander, R. McN. (1977). Terrestrial locomotion. In Mechanics and energetics of anima/ locomotion: 168-203. Alexander, R. McN. & Bennet-Clark, H. C. (1977). Storage of elastic strain energy in muscle and other tissues. Alexander, R. McN. & Jayes, A. S. (1978~). Vertical movements in walking and running. J . Zool., Lond. 185: 27-40. Alexander, R. McN. & Jayes, A. S. (19786)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000965_j.ast.2021.106616-Figure1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000965_j.ast.2021.106616-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a quadrotor with four rotors [1].",
        "texts": [
            " The structure of the ANTSMC and the ASTSMC and their combination for attitude and altitude control of UAV infinite time are presented in Sections 4 and 5, respectively. Section 6 has been dedicated to the proposed controllers\u2019 simulation results and their comparisons to the other methods. The paper concludes in Section 7. In the current research, a quadrotor system supported by four rotors is considered to provide turning and moving in diverse directions via increasing and decreasing the total thrust. As can be seen in Fig. 1, the quadrotor has a body-fixed frame B = {O b, Xb, Yb, Zb} and an inertial reference frame E = {O e, Xe, Ye, Ze}. The Euler angles related to an inertial frame are defined as \u03b7(t) = [\u03c6(t), \u03b8(t), \u03c8(t)]T and the angle velocities relevant to the body-fixed frame are introduced as \u03a9 = [\u03a91, \u03a92, \u03a93]T = [p, q, r]T . While the \u03be = [x, y, z]T indicates the quadrotor position, V = [u, v, w]T illustrates the linear velocity in the earth-frame. Some assumptions are considered to derive the dynamical model of the system [1]: \u2022 The quadrotor construction is rigid and symmetrical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000104_s00170-021-06640-3-Figure8-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000104_s00170-021-06640-3-Figure8-1.png",
        "caption": "Fig. 8 Laser radiation pressure calculation. When a laser angle is \u03b8 , a radiation pressure is generated on the layer surface. To investigate pressure influence on keyhole phenomenon, absolute pressure is decomposed into horizontal pressure and vertical pressure",
        "texts": [
            " Based on the layer center p0 ij , position of a random point pk ij is calculated by referring the position of layer center p0 ij . Projection area s1 = s0/cos\u03b8 (1) Power intensity e1 = w0 s1 = w0cos\u03b8/s0 = e0cos\u03b8 (2) Energy density epk ij = e0cos\u03b8pk ij = w0cos\u03b8pk ij /s0 (3) A laser beam exerts radiation force on the powder bed surface. To simplify our model, we assume all the energy and the momentum of the laser beam are fully transferred to the melt pool. That means, all the momentum of the laser beam is fully transferred to the radiation force, shown in Fig. 8. In a practical situation, the absorbed energy is a fixed proportion of a laser beam, and all the data are normalized for training our model. Therefore, this simplification does not significantly influence physical-effect\u2013based porosity prediction. As (4\u201311) expressed, each photon has energy E0 (4) with momentum p0 (5) [15, 16], and where c is the speed of light in a vacuum, h is Planck constant, and \u03bb is the laser light\u2019s wavelength. For each second, the total numberN of photons projected by a laser beam is calculated by laser power w0 (160 J/s) divided by a photon\u2019 power E0, shown in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure3.9-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure3.9-1.png",
        "caption": "Fig. 3.9: Example of a modern multibody system (courtesy Daimler-Chrysler)",
        "texts": [
            " The advantage of gear trains with gear wheels consists in a better component efficiency due to power transmission by form closure, the disadvantage in an only stepwise approximation of the drag-velocity hyperbola. This disadvantage is significantly reduced step by step by introducing automatic gear boxes with up to eight gear stages. The advantage of a CVT configuration consists in a perfect adaptation to the drag-velocity hyperbola, the disadvantage in a lower efficiency due to power transmission by friction and in a somehow limited torque transmission. An additional advantage of the CVT\u2019s is the possibility of very smoothly changing the transmission ratio without any danger of generating jerk. Figure 3.9 on page 113 depicts an example from industry. The following pictures give an impression of the systems and the components. They are of general importance though the configurations shown correspond to the LUK/PIV chain system. The operation of a chain- or beltdriven CVT is for the various configurations always the same. Figure 5.61 depicts the main features. The chain or the belt moves between two pulleys with conically shaped sheaves. One side of these pulleys possesses a movable sheave controlled by a hydraulic system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure4.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure4.14-1.png",
        "caption": "Fig. 4.14: Various bulk micromachining structures. According to [Howe90)",
        "texts": [
            " The crystal orientation of the wafer plays a decisive role (Sec tion 4.1.2.3.1). The silicon wafer is preprocessed with optical lithography and the exposed resist material is removed. By using anisotropic etching solutions selectively on the resist, deep grooves can be made on a substrate. The re maining resist acts as a mask. The resulting form depends only on the crystal orientation of the substrate, i.e. along which crystal face the wafer was cut, Fig. 4.7. Different constructions, such as bridges, beams, membranes etc., can be made by this technique, Fig. 4.14. Many wafers produced this way can be connected by using bonding or other interconnection technologies to form complex three-dimensional structures. The possibilities are still limited, however, since the lattice structure of the silicon crystal is not variable. Simple circular, cylindrical cavities or columns cannot be realized with this method. In order to be able to structure the substrate exactly, additional techniques are necessary to interrupt the etching process at the right time. Otherwise the substrate will simply be etched through"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000931_j.matdes.2021.109605-Figure5-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000931_j.matdes.2021.109605-Figure5-1.png",
        "caption": "Fig. 5. 4D printed complex origami structure with multiple hybrid hinges. (a) Schematic illus structure before and after 4D printing. Scale bar is 15 mm. (d) Miura-ori structure deformed temperature of the SMP. On removing the external force, the deformed miura-ori returned to",
        "texts": [
            " Thus, the proposed hybrid hinge has proven durability and elasticity against folding deformation. Many origami structures are not simply made up of a single hinge, but have multiple hinges, varying in the orientation of the hinge folds, and often have a combination of mountain and valley foldings. Experiments were conducted to confirm the feasibility of fabricating a complex origami structure with multiple hybrid hinges. In this study, a miura-ori structure was chosen as the complex origami structure. Fig. 5(a) shows the 3D print model with 24 hybrid hinges. All hybrid hinge lengths lh were set at 9 mm, and the shrinkable SMP layer was programmed to shrink perpendicular to the axis of rotation of each 4D printing hinge, as shown in the enlarged view in Fig. 5(a). Detailed dimensions, 3D print models, and printing patterns are shown in Fig. S5. Figs. 5(b) and (c) show photographs of the fabricated miura-ori structure before and after 4D printing. Video S1 shows the video of 4D printing process. Fig. 5(c) shows that it is possible to fabricate a complex origami structure with multiple hybrid hinges by immersing into hot water. Additionally, an external force was applied to the miura-ori structure with hybrid hinges below the glass transition temperature of the SMP after 4D printing to fold and unfold it. Video S2 shows the folding deformation achieved by applying an external force. As shown in Fig. 5(d), it is possible to change the shape of the 4D printed miura-ori structure into a small folded shape by applying an external force. We also confirmed that the shape changed from the small folded shape to the original 4D printed shape when the external force was removed. Furthermore, the sample could be unfolded by applying an external force, and we confirmed that the sample recovered to its original 4D printed shape after unloading. Thus, unlike the miura-ori fabricated by conventional 4D printing method [3], the present 4D printing method with a hybrid hinge structure can be used to fabricate complex origami structures that can be largely deformed by applying an external force in an environment below the glass transition temperature of the SMP after 4D printing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003949_s10846-007-9137-x-Figure2-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003949_s10846-007-9137-x-Figure2-1.png",
        "caption": "Fig. 2 Space robot",
        "texts": [
            " Axi is the inertia matrix of leg i referred to the Cartesian space of the terminal point (or frame) of leg i, it is equal to AXi \u00bc J T i AiJ 1 i and hxi is the Coriolis, centrifuge and gravity forces referred to the terminal Cartesian space of leg i, it is given as hXi \u00bc J T i hi Many methods can be used to calculate these terms: hi can be computed using the Newton\u2013Euler inverse dynamic model of leg i by setting q :: \u00bc 0, hi=Hi (qi, q : i, q :: i \u00bc 0) [22, 42], for Ai one can use the method with which he is familiar. To reduce the computational cost the recursive Newton\u2013Euler algorithm using base inertial parameters and customized symbolic methods can be used to obtain hi and Ai [21]. 4.1 Description of the Robot The 6 d.o.f. Space robot [5] is composed of a moving platform connected to a fixed base by three (U-P-S) extendable legs (Fig. 2). The extremities of each leg are fitted with a 2 d.o.f. universal joint (U) at the base (the first one is actuated) and a 3 d.o.f. spherical joint (S) at the platform. The lengths of the legs are actuated using prismatic joints (P). We note that the legs of this robot have the same structure as the classical Gough\u2013Stewart parallel robot [34]. Assuming that Bi is the point connecting leg i to the base and Pi is the point connecting leg i to the platform. The frame \u22110 is defined fixed with the base, its origin is B1, and frame \u2211P is fixed with the mobile platform with P1 as origin"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000559_s40964-021-00180-8-Figure4-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000559_s40964-021-00180-8-Figure4-1.png",
        "caption": "Fig. 4 Graphical representation of main orientations for tensile and fatigue test specimens",
        "texts": [
            " One parameter that is completely controlled by the user of the metal 3D printer and affects the properties of the final component is the object\u2019s orientation inside the building chamber. In 2013, according to ASTM and International Organization for Standardization (ISO), a standardization was enacted regarding both the terminology and the printing orientations of all AM technologies [23]. A coordinate system is defined with the X-axis parallel to the front side of the machine, Z-axis in the vertical direction and the Y-axis is perpendicular to the other two, and the positive direction is determined by the rule of the right hand. Figure\u00a04 shows the graphical representation of tensile and fatigue test specimens accompanied by three capital letters (X, Y, Z), which code the print orientation [24]. In particular, the first letter represents the axis that is parallel to the specimen\u2019s biggest dimension. In the same manner, the second letter is defined based on the next biggest dimension of the part [25]. The build orientation influences the overall quality of the object, i.e. surface quality, dimensional accuracy and mechanical behavior, as it will be discussed in the next section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003389_978-1-4471-1575-5-Figure10.14-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003389_978-1-4471-1575-5-Figure10.14-1.png",
        "caption": "Fig. 10.14",
        "texts": [
            " 14(a), Green's theorem provides the fundamental relationship between the closed line integrals C in the Poincare section L: 2 and the double integrals in the area Q in the left-hand side of eq. (10.125), if Q is integrable. fh/ml f2\"/\"', ( ar ar ) .lJ .lJ (rh/ro j )-+(rb/ro 2)-\u00b7 d8 j d8 2 OOj 00 2 = 1{-rrh)\u00b7d(ro j 8 j )+(rrh)\u00b7d(ro 28 2 ) c (10.126) = 1-r(8,0)rh \u00b7d8+ 1r(2n,8)r12 .d8-1r(8,2n)rh \u00b7d8+ 1r(0,8)r12 \u00b7d8 C1 C2 ('1 c~ = !\"rh[r(2n,8)-r(0,8)].d8+ !\"r12[r(8,2n)-r(8,0)].d8 Furthermore, we have two independent linear variational equations corresponding to the Poincare section of 8 j and8 2 as shown in Fig. 10.14(b). (10.127) Finally, it is easy to find that the asymptotically orbital stability on the Poincare sections can be ensured if i = 1,2 (10.128) are satisfied (Hirsch and Smale [40]). where f,(ul'u2) = l-u,2 -aui -bu~u;, Suppose that ro, > 0 and ro 2 > 0 (10.129) f2(ui'u2)=1-au~-ui and 8>0. are linearly independent such that 382 Bifurcation and Chaos in Engineering ro j \"* 0 (modro k ), j\"* k, and kro 2 + jro,\"* 0 for all integers k,j. In this problem p = q = 2 . Transform eq. (10.129) into a polar co-ordinate (10"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003768_978-3-662-03450-7-Figure4.21-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003768_978-3-662-03450-7-Figure4.21-1.png",
        "caption": "Fig. 4.21: Cross-section of an electrostatic micromotor made by the surface micromachining technique. According to [MIT92]",
        "texts": [
            " Several prototypes will be introduced here; in the following chapters, many additional silicon sensors and actuators will be pre sented. Figure 4.20 shows a microgripper made of polysilicon by the surface micromachining method. The gripper is moved by electrostatic forces which are generated when opposing voltages are applied to two opposite comb-like elements. Such effectors can be used for microsurgical operations and for various microassembly tasks. Another example is an electrostatic micromotor, Fig. 4.21. The motor diame ter is about 100 ~-tm and the distance between the rotor and the stator is about applications. An optical microshutter, which also makes use of the comb actuator principle, is shown in Figure 4.22. This microstructure was made from a 2 f..tm thick po lysilicon layer with the surface micromachining technique. The shutter has a dimension of 100 t.tm x 30 t.tm and can move along the wafer up to 8.3 f..tm under a voltage of 53 V. In Figure 4.23 the cross-section of a high precision optical fiber connection device is shown"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0000639_978-981-13-5799-2-Figure7.1-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure7.1-1.png",
        "caption": "Fig. 7.1 Tread patterns for truck/bus tires. Reproduced from Ref. [1] with the permission of Tokyo Denki University Press)",
        "texts": [
            " Considering that the friction coefficient on a dry surface decreases with increasing contact pressure, it is mathematically proved that a uniform pressure distribution for a block maximizes the friction coefficient. The shape of the block surface that makes the pressure distribution uniform is obtained employing the finite element method combined with an optimization technique, and the tire with the optimized block surface is validated in terms of improving wear, braking performance and maneuverability. Tires are used on various road surfaces, such as dry, wet, snowy and icy road surfaces. Figure 7.1 shows that various tread patterns of truck/bus tires are designed for different requirements. Figure 7.1a shows the lug pattern used for a rough road, Fig. 7.1b shows the rib\u2013lug pattern used for short-range trips and better wear, Fig. 7.1c shows the rib pattern used for long-range trips and high-speed driving, Fig. 7.1d shows the mix-block pattern of tires used for the driving axle and various road surfaces, Fig. 7.1e shows the snow pattern used in winter, and Fig. 7.1f shows \u00a9 Springer Nature Singapore Pte Ltd. 2019 Y. Nakajima, Advanced Tire Mechanics, https://doi.org/10.1007/978-981-13-5799-2_7 375 the studless pattern used for better braking/driving performance on ice in winter. The other pattern for tires is the slick pattern without grooves used for construction vehicles or formula racing cars. The role of voids carved on the tread surface is to drain water out of the contact area on a wet road and to generate a tractive or braking force on a snow-, ice- or mud-covered road. Slanted grooves and longitudinal grooves are required to realize such performance. Hence, some of tread patterns for truck/bus tires consist of block patterns as shown in Fig. 7.1, and tread patterns for passenger tires are mainly block patterns. The fundamental properties of the block pattern are the contact pressure distribution in the contact area, the change in contact area due to the lateral and longitudinal forces and the block rigidity defined by the ratio of the reaction to the displacement of a block surface. The fundamental properties are evaluated by experiment or using an analytical tool or numerical tool, such as the finite element method, in the process of tread pattern design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure7.22-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure7.22-1.png",
        "caption": "Fig. 7.22: The Industrial Robot PUMA 560 and its Joint Model",
        "texts": [
            "3 Dynamics and Control of Assembly Processes with Robots 453 We start with the specific model for the PUMA 560 robot. It possesses six axes and is modeled as a tree-like multibody system with rigid bodies and ideal links. As generalized coordinates we take the relative angles between the bodies: \u03b3A = (\u03b3A1, \u03b3A2, \u03b3A3, \u03b3A4, \u03b3A5, \u03b3A6) T \u2208 IR6, (7.79) as shown in Fig.1a. Since the natural frequency of oscillations due to the stiffness in the first three joints are in the range of interest, an elastic joint model is introduced. A link\u2013joint unit consists of two bodies, the drive and the arm segment (Figure 7.22). They are coupled by a gear model which is composed of the physical elements stiffness c and damping d (see equation (7.12) on page 417). Thus three additional degrees of freedom are introduced between motor shafts and arm segments: \u03b3M = (\u03b3M1, \u03b3M2, \u03b3M3) T . \u2208 IR3. (7.80) In the remaining links no joint model is necessary, because their stiffnesses are high compared to the acting forces, and the elasticity of these joints have no effect on the system dynamics under consideration. Thus we come to altogether nine degrees of freedom \u03b3: \u03b3 = (\u03b3M ,\u03b3A)T \u2208 IR9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003822_s0094-114x(02)00050-2-Figure7-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003822_s0094-114x(02)00050-2-Figure7-1.png",
        "caption": "Fig. 7. Coordinate systems applied for simulation of meshing, I.",
        "texts": [
            " PII: S0094-114X(02)00050-2 The contents of the paper cover: (1) A brief summary of the existing geometry and the output of tooth contact analysis (TCA) computer program developed for simulation of meshing and contact. (2) Modified geometry of face-gear drives based on application of a shaper that is conjugated to a parabolic rack-cutter. (3) Concept of generation of face-gears by grinding or cutting worms, analytical derivation of worm thread surface, and its dressing. Nomenclature ai\u00f0i \u00bc d; c\u00de pressure angles for asymmetric face-gear drive for driving (i \u00bc d) and coast (i \u00bc c) sides (Fig. 9) Dc change of shaft angle (Fig. 8) DE change of shortest distance between the pinion and the face-gear axes (Fig. 7) Dq axial displacement of face-gear (Fig. 8) kw crossing angle between axes of shaper and worm (Fig. 21) cm shaft angle (Figs. 4, 8, 12) Ri \u00f0i \u00bc s; 1; 2;w\u00de tooth surface of the shaper (i \u00bc s),the pinion (i \u00bc 1), the face-gear (i \u00bc 2) and the generating worm (i \u00bc w) wj \u00f0j \u00bc r; e\u00de angle of rotation of the shaper (j \u00bc r) and the pinion (j \u00bc e) considered during the process of generation (Fig. 11) wi \u00f0i \u00bc s;w\u00de angle of rotation of the shaper considered during the process of generation of the face-gear (i \u00bc s) and the worm (i \u00bc w) (Figs",
            " However, the path of contact of the involute face-gear drive is oriented along the surface cross-section, and errors of alignment cause the shift of the bearing contact as shown in Fig. 6. The gear drive is sensitive to error Dc of the crossing angle formed between the axes of the face-gear and the pinion, but the shift of the bearing contact caused by the error Dc may be reduced by the axial displacement Dq of the face-gear [13]. The following coordinate systems are applied for TCA: (a) coordinate system Sf , rigidly connected to the frame of the face-gear drive (Fig. 7(a)); (b) coordinate systems S1 (Fig. 7(a)) and S2 (Fig. 8(b)), rigidly connected to the pinion and the face-gear respectively; and (c) auxiliary coordinate systems Sd, Se and Sq, applied for simulation of errors of alignment of face-gear drive (Fig. 8(a) and (b)). All misalignments are referred to the gear. Parameters DE, B, and B cot c determine the location of origin Oq with respect to Of (Fig. 7(b)). The location and orientation of coordinate systems Sd and Se with respect to Sq are shown in Fig. 8(a). The misaligned face-gear performs rotation about the ze axis (Fig. 8(b)). TCA results shown in Fig. 6 have been obtained for numerical example of design parameters shown in Table 1. The proposed geometry is based on the following ideas: i(i) Two imaginary rigidly connected rack-cutters designated as A1 and As are applied for the generation of the pinion and the shaper, respectively. Designation A0 indicates a reference rackcutter with straight line profiles (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003486_robot.1996.509284-Figure10-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003486_robot.1996.509284-Figure10-1.png",
        "caption": "Figure 10: The 2-type 2-1-type 3 mechanism",
        "texts": [
            " Using the notation of figure 5 we will write first that B2 should belong to the line going through A2 with unit vector v(vC, vy): (9) (A i- rcos(8) -- z,)vY - (rsin(8) - ya)vz = 0 Then we write thizt point B3 should be at distance 7-3 from As: (A + s +a) -- z b ) 2 + (s sin(8 +a) - = T$ (10) Using equation (!J) we compute the value of X and sulbstitute this value in equation (10) which become an equation in sine and cosine of 8. Using the classical half-angle transformation we get a 4-order polynomial in T = tan(8/2). 2.3.4 This mechanism is presented in figure 10. Equation (9) is still valid. A second equation is obtained by writing that the line going through A3 with direction defined by the axis of the prismatic joint of chain 3 has to meet As: 2-type 2 and 1 type 3 (A + s cos(8 + a ) - zb) sin(8 + a + ag) - (s sin(0 + a ) - yb) cos(r9 + a + a s ) = 0 (11) where a3 is the angle between BIB3 and the prismatic joint axis. Using equation (9) we compute the value of A and substitute the result in equation (11) which become an equation in sine and cosine of 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003798_978-3-540-79436-3-Figure5.27-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003798_978-3-540-79436-3-Figure5.27-1.png",
        "caption": "Fig. 5.27: Deformation of the Neutral Axis",
        "texts": [
            " Otherwise if the ring gear like in this case is coupled to the output flange by the carrying toothing pictured in figure 5.29, the small thickness of the ring gear and the clearance between R and O require an elastic model that allows the correct reproduction of the movements within the tooth-work. Lachenmayr presents in [134] an elastic model of a ring gear which provides a function for the planar deformation of the neutral axis in radial and circumferential direction starting from the rigid body position like illustrated in figure 5.27. Complying with the model of the Rayleigh beam the neutral axis is not stretched and the circumferential deformations \u2206\u03c8 cancel out: 2\u03c0\u222b 0 \u2206\u03c8d\u03d5 = 2\u03c0\u222b 0 [\u03c8n(0)\u2212 \u03c8n(\u03d5)]d\u03d5 = 0 (5.62) 5.2 Ravigneaux Gear System 247 Therefore the scalar radial deformation is uniquely described by the coordinate v. Using a modified Ritz approximation with an additional quadratic term, v can be separated into the vector v of the shape functions depending on space only and the vector qel of the time depending elastic degrees of freedom, see also section 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_2_0003961_s11044-007-9088-9-Figure3-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0003961_s11044-007-9088-9-Figure3-1.png",
        "caption": "Fig. 3 Sum of dual vectors",
        "texts": [
            " Compute the dual vectors E\u0302i = A\u0302i \u2016A\u0302i\u2016 (i = 1,2). (8) 2. Compute their cross product E\u03023 = E\u03021 \u00d7 E\u03022 \u2016E\u03021 \u00d7 E\u03022\u2016 . (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. 5.3 Sum of two dual vectors With reference to the geometry of Fig. 3, we wish 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 \u2016A\u03021\u2016 , E\u03022 = A\u03022 \u2016A\u03022\u2016 , 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_2_0000639_978-981-13-5799-2-Figure14.32-1.png",
        "original_path": "designv10-2/openalex_figure/designv10_2_0000639_978-981-13-5799-2-Figure14.32-1.png",
        "caption": "Fig. 14.32 Changes in the contact length and contact pressure due to wear step d [25]",
        "texts": [
            " Meanwhile, when irregular wear is due to intra-rib interaction, Dr is defined as in Fig. 14.31b. 1056 14 Wear of Tires Suppose that the contact shape is rectangular, the contact lengths in the region of normal wear and irregular wear are, respectively, l0 and l, and the step of irregular wear is d. Because the contact length l and maximum contact pressure pm of a tire with irregular wear cannot be analytically solved, they are calculated through FEA. In FEA, part of a rib is dented by d, and l and pm are obtained at the center of the dented area as shown in Fig. 14.32. d and l change with the step of irregular wear as functions of l \u00bc l0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 d=dm4 p pm \u00bc pm0 1 d=dm\u00f0 \u00de; \u00f014:110\u00de where pm0 is the maximum contact pressure in the region of normal wear while dm is the critical step of the irregular wear where the region of step-down wear does not make contact with the road. Hence, if d is larger than dm, there is no wear. 14.8 Progression of Irregular Wear 1057 When the apparent Young modulus of tread, which was discussed in Sect"
        ],
        "surrounding_texts": []
    }
]