[
    {
        "image_filename": "designv10_8_0002321_jsvi.2000.2950-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002321_jsvi.2000.2950-Figure3-1.png",
        "caption": "Figure 3. Measurement points of vibration.",
        "texts": [
            " Figure 2 shows the drive unit which was developed for sound and vibration measurement of linear motion rolling bearings [11]. The drive unit consists of a motor, a coupling, support bearings, a sliding screw, sliding guides, a pusher, and a concrete bed. The pro\"le rail of a test linear bearing is \"xed on the concrete bed by bolts. The carriage of the test linear bearing is driven through a coupling, support bearings, a sliding screw, sliding guides and a pusher from a motor. Therefore, when the motor rotates at a constant speed, the carriage of the test linear bearing can be driven at a constant linear velocity. Figure 3 shows the measurement points of the vibration. To measure the vibration of the test linear bearing, an accelerometer was attached to the carriage. The measurement points, mounting positions of the accelerometer, were A, B, C and D on the carriage as shown in Figure 3. The vibration of the test linear bearings was detected by the accelerometer when the carriage with a constant linear velocity passed the center in the longitudinal direction of the pro\"le rail. The detected signal of the vibration was ampli\"ed by a charge ampli\"er and a measuring ampli\"er, and it was examined by a digital spectrum analyzer as shown in Figure 4. In the vibration measurement, the linear velocity of the carriage was varied in 7 steps in the range of 0)333}1)167 m/s. The object vibration in this study is the vibration of the test linear bearing itself"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002450_robot.1990.126126-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002450_robot.1990.126126-Figure1-1.png",
        "caption": "Figure 1: PUMA 560",
        "texts": [
            " 25), we obtain : P*XR=PTX+PTV2Xa A base solution XB is obtained with a vector xb, such that : XB1= X I + v 2 1 x b XB2 = x 2 + v22 x b = 0 (27) x b is solution of the linear system : v22 x b = - x2 (28) P must be chosen for V22 to be regular. Starting from the last row of V2 we extract the first regular (c-b)x(c-b) matrix, which gives the subscript of the columns W: j to be deleted and defines the matrix P. From (Eq. 27) and (Eq. 28). the numerical values of the base parameters are given by: 1 XBl X 1 - V11 V22-1 X2 PTXB=[ XB2 ]=[ 0 (29) 5-1 A The PUMA 560 manipulator is chosen as an example of a 6 joints serial link manipulator, Figure 1. The geometric parameters are given in table 1. There are 60 standards inertial parameters. The values of the matrices d(q,i,q),do(q,q), h(q,q) can be calculated directly numerically. We have preferred to make use of the symbolic expressions, automatically computed using the software package SYMORO[18]. There are 11 functions hi which are constant and which correspond to 11 zero columns of d or do. These columns and the corresponding parameters are eliminated because they have no effect on the dynamic model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003898_s11661-008-9660-9-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003898_s11661-008-9660-9-Figure13-1.png",
        "caption": "Fig. 13\u2014Geometry and meshing of thin plate and substrate used for the thermomechanical model.",
        "texts": [
            " A mechanical model based on SYSWELD\u2019s material library was coupled to the thermal formulation in order to calculate deformation and stress during deposition as well as the final residual stress of the built plate. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 39A, DECEMBER 2008\u20143159 The mechanical model uses an additive constitutive relation for strains due to elastic, thermal, and plastic deformation, including transformation-induced plasticity. Details of the development and implementation of the mechanical model are reported elsewhere.[16] The geometry and finite element mesh used for the simulations are shown in Figure 13. The structure was built by overlapping 10 single tracks of material, each with a length of 10.0 mm, a thickness of 0.5 mm, and a width of 1.0 mm. This produced a plate 5-mm tall. The plate was fabricated on the surface of a substrate that was 1-mm thick, 4-mm wide, and 10-mm long. Although smaller than the actual plates, the model configuration serves well the purpose of illustrating the sensitivity of stress to process parameters, and the modeling results will compare with the experimental measurements in a qualitative way, in addition to saving considerable computational time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003827_j.engstruct.2008.05.011-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003827_j.engstruct.2008.05.011-Figure3-1.png",
        "caption": "Fig. 3. Semi-circular arch loaded in plane.",
        "texts": [
            " Principal inertia axis could be different of the section ones, which means product of inertia to be considered (middle part of the system). This expression has permitted to annotate the solution in matrix forms. This above expression has been demonstrated to be a valued didactic tool for explaining Strength of Materials courses in graduate students [38]. 3. Circular arch in global coordinates The parametric equations chosen to represent the circular arch geometry are given by: x = r cos(s/r); y = r sin(s/r); z = 0 considering the radius r , centre in the origin of coordinates and the curve contained in the plane xy as shown in Fig. 3. Known these equations, versors of the curve in the Frenet frame can be projected in the global coordinate system as follows: t = (\u2212 sin(s/r), cos(s/r), 0) ; n = (\u2212 cos(s/r),\u2212 sin(s/r), 0) ; b = j = (0, 0, 1) . Neglecting the shearing deformation and assuming that the section inertia product is null, the resulting differential system (from general equation (7)) for a circular arch loaded inplane is expressed by DVx + qx = 0 DVy + qy = 0 \u2212 cos(s/r) Vx \u2212 sin(s/r) Vy +DMz + mz = 0 \u2212 Mz EIz +D\u03b8z \u2212 \u0398z = 0 \u2212 sin2(s/r) EA Vx + sin(s/r) cos(s/r) EA Vy + cos(s/r) \u03b8z +D\u03b4x \u2212 \u2206x = 0 sin(s/r) cos(s/r) EA Vx \u2212 cos2(s/r) EA Vy + sin(s/r) \u03b8z +D\u03b4y \u2212 \u2206y = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002898_0890-6955(95)00091-7-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002898_0890-6955(95)00091-7-Figure3-1.png",
        "caption": "Fig. 3. Relation between reference coordinate frame and tool frame.",
        "texts": [],
        "surrounding_texts": [
            "The transformation of axes from one link to another can be described completely by four kinematics parameters, called D - H parameters (see Fig. 2). Let us assume that the transformation between frame (n - 1) and frame (n) is given by A,: A,, = R(Z,O,,). T(O,O,d,,). T( ot~,O,O).(X,a,,) (1) a~ = movement along axis x.; an = turn around x.. 226 R. Md. Mahbubur et al. If the joints are prismatic then \u00ae. is constant and d. is variable. In the case of a revolute joint, O. is variable and the others are constants. The total transformation is denoted by the matrix T. If the A,. matrix describes transformation with respect to the base coordinate system, then Tto t -- Am.Ts.A L (3) where AL contains the tool length L. The position of the tool tip is described by 4 \u00d7 4 homogeneous matrix: Trot = ny Gy ay py (4) Gz az Pz 0 0 where [ax, ay, az] T is the tool direction and [Px, Py, Pz] T is the tool tip position in the base coordinate system (see Figs 3-5, Table I), and where cos (iMJT) is the cosine of angle (dot product) between the iM and JT axes. Ttot = Am.Ts.A L -cosCcosB -sinC -cosCsinB -cosC.sinB-L + X | -sinCcosB cosC -sinCsinB sinC.sinBL + Y-am Trot / / sinB 0 - c o s B - c B . L - ~ Z \" ~ - d m [ o 0 0 1 (6) (7) The direction cosine of the tool is given by 228 R. Md. Mahbubur et aL ail \"-cosCsinBav = -sinCsinB a - cosB =I arctan(a ) [ Xp+COsCsin., ] - _ ly, + inCsin L-aq L Zp+cBL+dm ] (8) (9) (I0) 2.2. Zero reference model The machine zero point is the point where the joint displacements are zero. The displacement in the reference coordinate system is given by Tmt= Am'AI~2~3~4~5\" ~ (11) where A i is the transformation matrix in the reference coordinate system and is described by the Rodrigues equation and To is the transformation at the machine zero position. 2.2.1. Rotation around an arbitrary axis. If the rotational axes are not perpendicular to each other (although they should be), then there exists rotation around an arbitrary axis in the space; the dot product of two orthogonal axes is not zero [for example, cos(90) = 0, but cos(89.99) ~ 0]. Though the variation is small, we cannot neglect it because small variations in angular error gives a large tool tip deviation from the desired position depending on the length of tool and the spindle pivot distance. Let us now think about three-dimensional rotations of a point P around a line with a direction cosine of l, m and n. P* is the new position of P after rotation O. The rotation matrix is given by the Rodrigues equation [7, 8]: R = I F v 0 + c 0 lmvO-nsO lnv0+ms0 0 ImvO+nsO m2v0+c0 mnvO- /sO 0 lnv0-ms0 mnvO +/sO n2v0 + cO 0 0 0 0 1 (12) where v\u00ae is 1 - cosO, sO is sin\u00ae and cO is cos\u00ae. p . = [ R 0 0 0 (I-R)P~].p (13) Where P* and P are the final and initial points, respectively, and I is the identity matrix. P~ is the point where the axis of rotation passes. 2.2.1.1. Revolute joint. If the joint is revolute then we need five parameters to describe the rotation completely: two for the direction cosine, two for rotation center offsets, one for the rotation angle (\u00ae). 2.2.1.2. Prismatic joint. For the prismatic joint, we need three independent parameters to describe it completely. Here the displacement is d and the direction cosine is [1, m, n] from which two are required. The transformation is given by Positioning accuracy improvement in five-axis milling by post processing 229 0 0 1 O d . m 0 1 (14) 0 0 Now the final transformation is given by Ttot = Am'A t'A2\"A3\"Aa'As'To (15) To is the transformation at the zero position and Ai is the transformation based on the Rodrigues equation. 2.2.2. Error model offive-axis machine tools. Joint axes orientations are varied with the degree of misalignment. If we find the value of l and n in the reference coordinate system then m is given by m = l ~ 1 2 - n 2 (16) The location of the actual joint varies with the location of the plane. In the modeling of the zero position, the machine zero position and the coordinate system are defined before defining the unit vector of each axis. The unit vector from Fig. 4. is defined as follows (Table 2): [l,m,n] are the direction cosines of individual axis in the reference coordinate system. The rows 0-4 are for the five axes of the machine. The above model is for the ideal case. According to Table 2, the X-axis should pass through the point Po [Po~, Poy, Poz] with a direction cosine [1,0,0]. If Pot is the real point [Po#:Por] through which the X-axis passes then aPo = Oi + (Pyor-eyo) j + (Pzor-Pzo)k (17) where APoy=(Py:Poy) and APo~--(Po=--Poz) are small deviations in the position of the origin in the base Y- and Z-directions, respectively. The actual direction cosine of joint one is given by Uo = [ ~l =m~-n~,mo, no I (18) Extending the idea to all joints results in Table 3 where the unknown direction and position values can be found by the calibration process. 230 R. Md. Mahbubur et al. Table 3 describes the real machine geometry with either arbitrary rotation or a displacement axis. [P,, p , Pz] r is the transformation at the zero position. [P~, Pyr, Pzr] 7 is the actual location (offsets) of the axis. If we know the direction cosine of the actual axis and the offsets we can find the tool tip and the orientation of the tool axis vector for a given displacement of joints using Equation (13) and Equation (14). We shall try to find the direction cosine of Table 3 by measuring the real machine and find the tool tip in the base coordinate system. [ l O O P x 0 1 0 P y A,,= 0 0 1 P ~ 0 0 0 1 - 1 0 0 0 ] =/o ,oo / /o o_1 L O 0 0 1 J Tto~ = Am'AI'A2\"A3\"A4\"As'To Trot = (19) (20) - c o s C c o s B -s inC -cosCsinB -cosCsinB-L + X + P, -sinCcosB cosC -sinCsinB -sinCsinBLz + Y + Py sinB 0 -cosB -cosBL z + Z + Pz 0 0 0 1 (21) (22) where A~, A2, A3, A4, A5 all are based on Rodrigues equation, To is transformation with respect to reference coordinate system when all joints displacements are zero."
        ]
    },
    {
        "image_filename": "designv10_8_0003827_j.engstruct.2008.05.011-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003827_j.engstruct.2008.05.011-Figure8-1.png",
        "caption": "Fig. 8. Uniformly loaded helical beam with varying cross-section.",
        "texts": [
            " Circular helical beam in global coordinates In this example, the parametric equations that represent the helix geometry are: x = a cos(s/c), y = a sin(s/c) and z = bs/c being c = \u221a a2 + b2. The basis change matrix from Frenet frame to global reference system is given by:[ t n b ] = [ \u03c5tx \u03c5ty \u03c5tz \u03c5nx \u03c5ny \u03c5nz \u03c5bx \u03c5by \u03c5bz ][ i j k ] = 1 c [ \u2212a sin(s/c) a cos(s/c) b \u2212c cos(s/c) \u2212c sin(s/c) 0 b sin(s/c) \u2212b cos(s/c) a ][ i j k ] . Neglecting the shearing deformation and assuming that the section inertia product is null, the resulting differential system is given in Box V. The example considers a helical beam with variable crosssection as shown in Fig. 8. The data for the example are: Parameters a = 1.2 m and b = 3/(2\u03c0)m. Variable diameter d(s) = (d(sI)(sII \u2212 s)+ d(sII)(s\u2212 sI))/(sII \u2212 sI). With d(sI) = 0.15 m and d(sII) = 0.075 m. Area and inertias A(s) = \u03c0d2; It(s) = \u03c0d4/32; In(s) = Ib(s) = \u03c0d4/64. Length of the beam varies from initial I (sI = 0) to final II (sII = 2\u03c0c) points. Elastic moduli E = 210 kN/mm2 and G = 80 kN/mm2. Uniform distributed applied load force qz = \u22122 kN/m. The graphs of internal forces and deflections components for the circular helical beam with variable cross-section for the fixedfree supports, are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.31-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.31-1.png",
        "caption": "Figure 7.31 The top and side views of the specimen.",
        "texts": [
            " For example, for the aluminum bar, 11 = lo + .:ll, or 11 = lo(1 + E1)' Therefore: 11 = lo (1 + E1) = 30(1 + 0.00143) = 30.0429 cm 12 = lo (1 + E2) = 30(1 + 0.00320) = 30.0960 cm In other words, the increase in length of the aluminum bar and the steel rod is less than 1 mm. Stress and Strain 141 142 Fundamentals of Biomechanics R=7l ~ Example 7.3 An experiment was designed to determine the elastic modulus of the human bone (cortical) tissue. Three al most identical bone specimens were prepared. The specimen size and shape used is shown in Figure 7.31, which has a square (2 x 2 mm) cross-section. Two sections, A and B, are marked on each specimen at a fixed distance apart. Each specimen was then subjected to tensile loading of varying magnitudes, and the lengths between the marked sections were again measured electronically. The following data were obtained: Applied Force, F (N) Measured Gage Length, i (mm) 5.000 o 240 480 720 5.017 5.033 5.050 Determine the tensile stresses and strains developed in each specimen, plot a stress-strain diagram for the bone, and deter mine the elastic modulus (E) for the bone"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002657_70.345948-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002657_70.345948-Figure6-1.png",
        "caption": "Fig. 6. Nine DOF Cartesian goal planning.",
        "texts": [
            " In the planar examples shown, the apparent collisions of the links with the obstacle boundaries arise out of the fact that checking is performed for the tips of each link only. A more complete collision detection procedure is being developed for spatial arm planning. The remaining examples illustrate applications to a spatial redundant 9 DOF arm. This consists of a PUMA 600 manipulator mounted on a platform providing additional linear, rotate and tilt joints. (See [ 3 3 ] for details of the CIRSSE dual-arm robotic testbed.) Fig. 6 shows the output sequence for joint path end-point planning to a specified task space positiodorientation in the presence of an obstacle. Fig. 7 shows the path sequence generated for a path following task incorporating a straight line translation coupled with a rotation of 180\u201d about the tip I- axis. Because of the manipulator joint limits, this can only be accomplished by switching the PUMA\u2019S pose from elbow-up to elbow-down at some intermediate point. As in the planar examples, the present algorithm accomplishes a smooth transition between these arm configurations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003118_ip-a-1:19880074-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003118_ip-a-1:19880074-Figure1-1.png",
        "caption": "Fig. 1 Filamentary turns on an infinite ferromagnetic core",
        "texts": [
            " It is felt that these formulas could, for example, find immediate application in the detailed analysis of the behaviour of transformer windings under surge conditions. Since the formulas are based on the rigorous solution of Maxwell's equations, they necessarily take full account of eddy currents induced into the core. In particular, frequency dependence owing to skin effect is properly represented. Also, use of the formulas in circuit analysis will cause damping effects consistent with actual eddy-current losses. The physical arrangement under consideration is shown in Fig. 1. The ferromagnetic core, taken to be infinitely long, is treated as a homogeneous medium of conductivity <J2 a n d permeability \\ilr in the radial direction and /i22 in the axial direction, thus allowing for the possibility of grain orientation. The core radius is b. A filamentary turn of radius a encircles the core at z = 0, and carries a sinusoidal current i^. This is represented in the ensuing frequency domain analysis by /^, i.e. i^t) = 1$ e\"0' where co is the angular frequency. The mutual impedance between the energising turn and a second (open) filamentary turn of radius r located at an axial separation z follows directly from the solution for the electric field intensity E^ = E^r, z)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002691_1.1357163-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002691_1.1357163-Figure5-1.png",
        "caption": "Fig. 5 Radial loaded ball bearing interference",
        "texts": [
            " Here, the contact angles of the ball at the inner race and the outer race are assumed to be the same because the centrifugal force acting on the ball is ignored. Similarly, the coordinates of any point on the outer surface as shown in Fig. 2, are given as: ~xo ,yo ,zo!5~jo ,ho50,zo!1gW o1hW o (9) where gW o5go~cos ciW1sin c jW! (10.a) go5do/22ro (10.b) and hW o5ho@~cos u cos c!iW1~cos u sin c! jW1~sin u!kW # (11.a) ho5ro (11.b) We assume that the bearing elastic deformation in the x-direction due to the externally-applied load in the same direction is dr ~In Fig. 5, the direction in parallel to the gravity force is defined as the x-direction!. And the total elastic deformation in the z-direction ~parallel to shaft axis! due to the externally-applied load in the axial direction is da . Then the coordinates, jo and zo in Eq. ~9! can be given as: jo52dr (12.a) zo5~ro2D/2!sin a01do (12.b) 306 \u00d5 Vol. 123, JUNE 2001 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/07/20 here, the two elastic deformations, dr and da , can be readily obtained from the experimental measures of the displacement gauge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure6.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure6.3-1.png",
        "caption": "Figure 6.3 Internal forces and moments.",
        "texts": [
            " These are called the internal force and internal moment vectors. Of course, the same argument is true for the other part of the object. Furthermore, for the overall equilibrium of the object, the force vectors and moment vectors on either surface of the cut section must have equal magnitudes and opposite directions (Figure 6.2). For a three-dimensional object, the internal forces and moments can be resolved into their components along three mutually per pendicular directions, as illustrated in Figure 6.3. The force and moment vector components measured at the cut sections take special names reflecting their orientation and effects on the cut sections. Assuming that x is the direction normal (perpendicu lar) to the cut section, the force component Px in Figure 6.3 is called the axial or normal force, and it is a measure of the pulling or pushing action of the externally applied forces in a direction perpendicular to the cut section. It is called a tensile force if it has a pulling action trying to elongate the part, or a compressive force if it has a pushing action tending to shorten the part. The force components Pyand Pz are called shear forces, and they are mea sures of resistance to the sliding action of one cut section over the other. Their subscripts indicate their lines of action"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.29-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.29-1.png",
        "caption": "Figure 4.29 Example 4.5.",
        "texts": [
            " Since the beam is in equilibrium, we can utilize the conditions of equi librium to determine the reactions. For example, consider the translational equilibrium of the beam in the y direction: Now, consider the rotational equilibrium of the beam about A (a) (b) (c) w w w and assume that counterclockwise moments are positive: M-lP=O M=l P Note that the reactive moment with magnitude M is a \"free vector\" that acts everywhere along the beam. Example 4.5 Consider the uniform, horizontal beam shown in Figure 4.29. The beam is fixed at A and a force that makes an angle fJ = 30\u00b0 with the horizontal is applied at B. The magnitude of the applied force is P = 100 N. C is the center of gravity of the beam. The beam weighs W = 50 N and has a length l = 2 m. Determine the reactions generated at the fixed end of the beam. Solution: The free-body diagram of the beam is shown in Figure 4.30. The horizontal and vertical directions are indicated by the x and y axes, respectively. Px and Py are the scalar components of the applied force P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002320_s0956-5663(97)00072-9-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002320_s0956-5663(97)00072-9-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of immobilization methods studied. (1) Adsorption. (2) Covalent immobilization on photoactivated nylon. (3) Adsorption of conjugated peroxidase. (4) Immobilization through antibodies specific for HRP 5 Immobilization through avidin-biotin linkage.",
        "texts": [
            " When the enzyme is immobilized on the surface of different types of membrane the nature of the polymer comprising the membrane can significantly affect the accumulation rate of radicals as intermediates and, consequently, the light emission. The aim of this work was to compare different immobilization techniques for HRP and antibodies, and to optimize the conditions for enhanced chemiluminescence detection on the membrane surface for use in chemiluminescent bio- and immunosensors. The immobilization methods studied in our work are schematically depicted in Fig. 1. The attachment of the enzyme was achieved in accordance with three principles. The first means the nonspecific adsorption and covalent fixation of native peroxidase directly on the surface of the membrane. By means of physical adsorption the protein is attached to the polymeric support by weak interactions such as hydrogen bonds, and ionic, polar and hydrophobic interactions. The advantage of this procedure is that it does not require any additional chemicals and, consequently, there is no danger of contaminating the solution to be analysed by excess reagents or reaction products",
            " RESULTS AND DISCUSSION HRP immobilization In order to find the most useful immobilization method it is very important to choose the appropriate parameter for the estimation of enzyme concentration, as well as its catalytic activity on a membrane. We found that direct estimation of HRP concentration on the membrane surface by standard biochemical methods is limited by the non-sufficient sensitivity of the methods. In order to compare the efficiency of immobilization procedures, we estimated the apparent specific activity of immobilized HRP using 2,2'-azinobis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS). The values of surface specific activity of HRP immobilized on porous supports by different methods (Fig. 1) are presented in Table 1. In the comparison of various immobilization procedures, the HRP surface specific activity was maximal for the enzyme attached through a streptavidinbiotin linkage for all studied membranes. Methods involving biospecific immobilization of HRP through a streptavidin-biotin linkage or antibodies offered products with a higher catalytic activity of approximately 15-20-fold for nylon and fourfold for nitrocellulose, compared with the immobilization of native enzyme directly on support"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002466_s004220050558-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002466_s004220050558-Figure3-1.png",
        "caption": "Fig. 3. a The hip joint has a variable sti ness CHIP and damping jHIP. b The resulting torqueangle T - a relationship is realized by two muscle pairs",
        "texts": [
            " Increasing the sti ness of both the muscles by an equal amount results in an increase in joint sti ness, similar to co-contraction in biological organisms (Winters et al. 1988). The stance leg elongation is modeled by a linear spring-damper combination with sti ness CLEG and damping jLEG (Fig. 2a), here realized by two muscles (Fig. 2b). This simpli\u00aecation is often made in biomechanical models of running (Alexander 1984; McMahon 1984). The hip joint is modeled by a rotational springdamper combination with sti ness CHIP and damping jHIP (Fig. 3a), here realized by two \u00afexor-extensor muscle pairs (Fig. 3b). With the sti ness and damping terms added to (1), the complete equations of motion can be written in the following general form: M x x N x; _x _x G x C x D _x 2 where C x 3 1 sti ness matrix, D _x 3 1 dissipation matrix. The matrices M;N;G;C, and D are derived and given as a function of system parameters in Appendix A. Without an energy supply, a (non-conservative) oscillation of a mass-spring-damper system will decay. So muscles need to do work within a cycle if the energy losses are to be compensated for",
            " In orbit the trailing leg angle at the beginning of the step n Un TL equals the trailing leg angle at the beginning of the step n 1 Un 1 TL . Therefore, uPO cannot be chosen larger than UTL. During the push-o phase the stance leg plantar \u00afexor sti ness (Fig. 2b) will be increased by dCLEG. The push-o phase ends when the swing leg hits the ground. The hip activation is triggered at the beginning of the swing phase. During the activation period the swing leg hip extensor, and the stance leg hip extensor (Fig. 3b) are increased in sti ness by dCHIP. In the model, the inertia of the hip mass is assumed to be zero, so if the orientation of the body is to remain near vertical, a swing leg extensor and contralateral extensor are equally activated. The hip activation phase ends after a time DtHIP has elapsed. The transition takes place when the swing leg hits the ground. On level ground this occurs when: LSL \u00ffR cosuSL \u00ff L0 \u00ffR cosuTL 0 3 It is assumed that as soon as the swing foot hits the \u00afoor, the trailing foot will retract"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.28-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.28-1.png",
        "caption": "Figure 13.28 Pendulum.",
        "texts": [
            " The following example will illustrate the procedure of analyzing the motion of a double pendulum. How ever, the procedure to be introduced can be generalized to ana lyze any multilink system. An important concept associated with linkage systems is the number of independent coordinates necessary to describe the motion characteristics of the parts constituting the system. The number of independent parameters required defines the degrees of freedom of the system. For example, the two-dimensional motion characteristics of the simple pendulum shown in Figure 13.28 can be fully described by 0 that defines the loca tion of the pendulum uniquely. Therefore, a simple pendulum has one degree of freedom. On the other hand, parameters 01 and O2 are necessary to analyze the coplanar motion of bar BC of the double pendulum shown in Figure 13.27, and therefore, a double pendulum has two degrees of freedom. Example 13.4 Double pendulum. Assume that arms AB and BC of the double pendulum shown in Figure 13.29 are undergoing coplanar motion. Let il = 0.3 m and \u00a32 = 0.3 m be the lengths of arms AB and Be, and (h and 02 be the angles arms AB and BC make with the vertical"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.1-1.png",
        "caption": "Figure 14.1 Rotational motion.",
        "texts": [
            "8 Angular Work and Power / 311 14.1 Kinetics of Angular Motion The kinetic characteristics of objects undergoing translational motion were discussed in Chapter 12. Kinetic analyses utilize Newton's second law of motion that can be formulated in terms of the equations of motion and work and energy methods. Sim ilar methods can be employed to analyze the kinetic character istics of objects undergoing rotational motion. Consider an object undergoing a rotational motion in the xy plane about a fixed point 0 (Figure 14.1). Let P be a point on the object located at a distance r from O. As the object rotates, point P moves in a circular path of radius r and center located at O. To be able to analyze the kinetic characteristics of point P using the equations of motion, forces acting on the object and the acceler ation of point P can be expressed in terms of their components normal and tangential to the circular path of motion. If nand t designate the normal (radial) and tangential directions at point P, then the equations of motion can be expressed as: L Fn = man (14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.15-1.png",
        "caption": "Figure 5.15 Forces on the skull form a concurrent system.",
        "texts": [
            " The rotational movement of the trunk is controlled by the simultaneous action of anterior and posterior muscles. The spinal column is vulnerable to various injuries. The most severe injury involves the spinal cord, which is immersed in fluid and protected by the bony structure. Other critical injuries include fractured vertebrae and herniated intervertebral disks. Lower back pain may also result from strains in the lower regions of the spine. Example 5.3 Consider the position of the head and the neck shown in Figure 5.15. Also shown are the forces acting on the Applications of Statics to Biomechanics 97 head. The head weighs W = 50 N and its center of gravity is located at C. F M is the magnitude of the resultant force exerted by the neck extensor muscles, which is applied on the skull at A. The atlantooccipital joint center is located at B. For this flexed position of the head, it is estimated that the line of action of the neck muscle force makes an angle e = 30\u00b0 and the line of action of the joint reaction force makes an angle f3 = 60\u00b0 with the horizontal",
            " Solution: We have a three-force system with two unknowns: magnitudes FM and FJ of the muscle and joint reaction forces. Since the problem has a relatively complicated geometry, it is convenient to utilize the condition that for a body to be in equi librium the force system acting on it must be either concurrent or parallel. In this case, it is clear that the forces involved do not form a parallel force system. Therefore, the system of forces under consideration must be concurrent. Recall that a system of forces is concurrent if the lines of action of all forces have a common point of intersection. In Figure 5.15, the lines of action of all three forces acting on the head are extended to meet at point O. In Figure 5.16, the forces W, F M' and F J acting on the skull are translated to 0, which is also chosen to be the origin of the xy coordinate frame. The rectangular components of the muscle and joint reaction forces in the x and y directions are: FMx = FM cose FMy = FM sine F J y = F J sin f3 (i) (ii) (i i i) (i v) The translational equilibrium conditions in the x and y directions will yield: LFx=O: FJx=FMx L F y = 0 : F J y = W + F My Substitute Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003434_j.automatica.2007.07.013-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003434_j.automatica.2007.07.013-Figure6-1.png",
        "caption": "Fig. 6. History of control input v2 versus time.",
        "texts": [],
        "surrounding_texts": [
            "The main contribution in this paper is that we have discussed the practical stabilizing problems of the class of NWMR with bounded practical inputs, i.e., type(1,2) robot. The original system inputs (in the sense of kinematics) can be guaranteed to stay within the desired upper bounds. It is of note that we have only given the designs of the controllers of kinematic NWMR here. By using the same idea, however, we are optimistic that the stabilizing controller presented here can be extended to nonholonomic dynamic systems. In addition, the stabilizing controller designs of the other type NWMR, i.e., type(2,0) robot, type(2,1) robot and type(1,2) robot can be easily discussed via similar way."
        ]
    },
    {
        "image_filename": "designv10_8_0003271_978-3-642-83957-3_3-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003271_978-3-642-83957-3_3-Figure4-1.png",
        "caption": "Figure 4: Self-Motions of a 3R Planar Manipulator",
        "texts": [
            " n,m is the number of self-motions in the preimage (bounds on the value of n,m will be considered in Section 4). Each Mi can be parametrized by a set of r independent parameters, If = {th,\u00b7\u00b7\u00b7,.pr}, which can be thought of as a natural coordinate system for the self-motions. For given x, the parametrization is typically unique (up to isomorphism), but the parametrization can vary as x varies in the workspace. The self-motion manifolds are best illustrated using two examples: a planar 3R manipulator (Figure 4) which is redundant with respect to the position of its end-effector, and a 4R regional manipulator which is similar to an \"elbow\" manipulator (Figure 5). The self-motion manifolds of the planar manipulator can be computed as follows. Let .p, which is the orientation of the third link relative to a fixed reference system, be the parameter describing the internal motion of the manipulator. There are two possible sets of joint angles, B. = {OI.,02.,03.} and Bb = {Olb,02b,03b}, which place the end-effector at (x\",Y ",
            " For redundant manipulators, these definitions are extended so that a regular value has all regular points in its preimage, a critical value has all critical points in its preimage, and a coregular value is an x which has both regular and critical points in its preimage. where 11,12,13 are the lengths of links 1, 2, and 3. As,p is swept through its feasible range of [-11',11'], equations (8) will generate two I-dimensional manifolds in C. These manifolds may remain separate for all values of,p, in which case there are two disjoint self-motion manifolds, or the two manifolds may meet at two points (corresponding to the singularities of the non-redundant 2R planar manipulator subchain formed by links 1 and 2), to form one self-motion manifold. Figure 4 shows the self-motion manifolds of this planar manipulator (embedded in the configuration space 3-torus) for two different locations of the end-effector. The inverse image of point 1 contains two distinct self-motion manifolds (which appear as non-closed curves because of the cubic 3-torus representation), while the inverse image of point 2 contains only one self-motion. The two distinct self-motion manifolds in the preimage of point 1 physically corresponds to \"up elbow\" and \"down elbow\" self-motions which are an analogous generalization of the \"up elbow\" and \"down elbow\" configurations of a non-redundant two-link manipulator",
            " (12) (13) The inverse solution is real for all values of 1/J in the range [-\"., \".]. The four distinct self-motions of this manipulator can be generated by continuously sweeping 1/J through its 2\". range for fixed (x \u2022 ., y \u2022\u2022 , z \u2022\u2022 ). Figure 6 shows the cubic representation of the projection of these four self-motions onto the 111-112-113 and /12-113-114 3-tori (for the case in which I = 1.0, (x \u2022\u2022 , y \u2022\u2022 , z \u2022\u2022 ) = (0.0,1.0,0.9)). What physical conditions determine whether there are one or two self-motion manifolds in Figure 4, and what is an upper bound on the number of self-motions? The inverse kinematic solution in (8) was found by a reassembly approach. That is, the end-effector is fixed to (x \u2022\u2022 , y.,) by a virtual revolute joint and the structure is broken into two subcomponents (at joint 3), a non-redundant 2R manipulator and a 1R link. Let C3 denote the circle of joint 3 locations formed by rotating link 3 about (x,., y \u2022\u2022 ). In C, the self-motion manifolci of this manipulator will be the product of 2R subchain inverse kinematic pre image of C 3 and the motion of joint 3",
            " If f is restricted to the self-motion manifold, then: (16) However, when f is restricted to a self-motion manifold, dx(tijo) must be zero, and therefore (dB(tijo)/dtij)dtij, which is the tangent space of M;(tij), must be in the null space of the Jacobian. Remark: The null space of the Jacobian matrix, evaluated at a particular joint configuration, Bo , is the tangent to the self-motion manifold at Bo. The collective null spaces of one self-motion is the tangent bundle3 of the self-motion manifold. The set of all Jacobian null spaces over a fixed end-effector location will be the union of all self-motion tangent bundles. For example, the null space of the manipulator in Figure 4 at Bo is a line, R1, tangent to the self-motion manifold at Bo. The collection of all null spaces for one self-motion of this manipulator is diffeomorphic to S1 x R1, a cylinder. Figure 8 shows the tangent spaces of the self-motion manifold over point 2 in Figure 4. 3 For an n-dimensional manifold X, the tangent bundle of X, denoted T(X), is the subset of X x Rn defined by T(X) = {(x,v) f X x Rn:v f Tx(x)}. In other words, the tangent bundle of X is an 2n dimensional manifold formed by \"tacking on\" to every XfX a copy of the tangent space at x. homotopic.4 The self-motions of point 1, which wrap around a generator of C, can not be continuously deformed on the surface of the configuration space torus to the self-motions of point 2. Self-motions which are homotopic to each other form a homotopy class",
            " Only the waist of the figure 8 is a critical point, whereas the other points in the figure 8 are coregular. The preimage of an entire critical value manifold (which is formed by computing f-I(x) as x is swept along the critical value manifold) is a continuous surface, termed a coregu/ar surface. Coregular surfaces are not manifolds, but by virtue of their dimension, they can separate the configuration into disjoint regions. Figure 9 illustrates all of the coregular surfaces for the 3R manipulator of Figure 4. In [2] it Critical Value Manifolds Figure 9: Coregular Surfaces, C-bundles, and W-sheets of a 3R Manipulator is shown that the coregular surfaces divide the configuration space into disjoint regions which are fiber 4 Two maps, fo: X ...... Y and It : X ...... Yare homotopic if there exists a smooth map, F: X x I ...... Y such that F(z,O) = fo(z) and F(z, 1) = It(z). In other words, fo can be deformed to It through a smoothly evolving family of maps. loops in C form a path component in the loop space, which is an equivalence class of loops under homotopy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.6-1.png",
        "caption": "Figure 3.6 Wrench and bolt.",
        "texts": [
            "5, when the fingers of the right hand curl in the direction that the applied force tends to rotate the body about point 0, the right hand thumb points in the direction of the moment vector. More specifically, extend the right hand with the thumb at a right angle to the rest of the fingers, position the finger tips in the direction of the applied force, and position the hand so that the point about which the moment is to be determined faces toward the palm. The tip of the thumb points in the direction of the moment vector. The line of action and direction of the moment vector can also be explained using a wrench and a right-treaded bolt (Figure 3.6). When a force is applied on the handle of the wrench, a torque is generated that rotates the wrench. The line of action of this torque coincides with the centerline of the bolt. Owing to the torque, the bolt will either advance into or retract from the board depending on how the force is applied. As in Figure 3.6, if the force causes a clockwise rotation, then the direction of torque is \"into\" the board and the bolt will advance into the board. If the force causes a counterclockwise rotation, then the direction of torque is \"out of\" the board and the bolt will retract from the board. In Figure 3.7, if point \u00b0 and force F lie on the surface of the page, then the line of action of moment M is perpendicular to the page. If you pin the otherwise unencumbered page at point 0, F will rotate the page in the counterclockwise direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.6-1.png",
        "caption": "Figure 8.6 Triaxial normal stresses.",
        "texts": [
            " The same effect can be repre sented mathematically by adding the individual effects of CTx and CTy. The resultant strains in the x and y directions can be determined as: CTx CTy Ex = Exl + Ex2 = E - v E CTy CTx Ey = Eyl + Ey2 = E - v E (8.6) If required, these equations can be solved simultaneously to ex press stresses in terms of strains: CTx = (Ex + V Ey) E 1 - v2 (Ey + v Ex) E (8.7) CTy = 1- v2 This discussion can be extended to derive the following stress strain relationships for the case of triaxial loading (Figure 8.6): 1 Ex = E [CTx - V(CTy + CTz)] 1 Ey = E [CTy - V(CTz + CTx )] (8.8) 1 Ez = E [CTz - V(CTx + CTy )] These formulas are valid for linearly elastic materials, and they can be used when the stresses induced are tensile or compres sive, by adapting the convention that tensile stresses are positive and compressive stresses are negative. Further generalization of stress-strain relationships for linearly elastic materials should take into consideration the relationships 158 Fundamentals of Biomechanics between shear stresses and shear strains"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003562_j.engappai.2007.08.007-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003562_j.engappai.2007.08.007-Figure1-1.png",
        "caption": "Fig. 1. Coordinated oper",
        "texts": [
            " (iii) In the other subspaces, the object tip\u2019s velocity is parallel to the tangential plane of the surface. But the tangential force caused by the deformation of surface is nonlinear and difficult to model. Therefore, adaptive fuzzy matrix is constructed to model the tangential force and suppress the inherent modelling errors as well as bounded disturbances. Simulation results are described in detail that show the effectiveness of the proposed control law. Consider a common rigid object held by m mobile manipulators with n degrees of freedom in a task space shown in Fig. 1, where the inertial reference frame is denoted by OXYZ, by which the position and orientation of the mobile manipulator end-effectors and object are referred; the object coordinate frame is denoted by OoX oY oZo and fixed at the center of mass of the object; the end-effector frame of the ith manipulator located at the grasp point is OeiX eiY eiZei. The following assumptions are needed. Assumption 2.1. All the end-effectors of the mobile manipulators are rigidly attached to the common object so that there is no relative motion between the object and the end-effectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002816_j.mechmachtheory.2004.06.003-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002816_j.mechmachtheory.2004.06.003-Figure3-1.png",
        "caption": "Fig. 3. Typical C2 overconstrained mechanisms.",
        "texts": [
            " Since the maximum number of linearly independent parallel revolute joints is 3, the lower limit on the number of prismatic joints is equal to 2. Since the maximum number of linearly independent prismatic joints is 3, the lower limit on the number of revolute joints is equal to 2. Because the revolute joints are parallel each other, the prismatic joints cannot be all perpendicular to the revolute joints. Otherwise, the resulting mechanism becomes a planar mechanism. Therefore, feasible joint assortments consist of 3R2P and 2R3P. Applying the concept of joint substitution, four-link C2 kinematic chains are derived in Table 2. Fig. 3 shows four example five- and four-link C2-mechanisms. There are six links and six joints in a basic F1 mechanism. We note that the maximum number of linearly independent intersecting revolute joints is three. It follows from rule 4 and the finite motion conditions that the joint screws of an F1mechanism should satisfy the following conditions. There are at least two and at most three successive revolute joints intersecting at a common point. We call such revolute joints R1 joints. The prismatic joints, if any, are perpendicular to the constraint force whereas the remaining revolute joints, called R2 joints, are parallel to each other and to the constraint force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002491_027836499401300404-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002491_027836499401300404-Figure6-1.png",
        "caption": "Fig. 6. The various vectors used in the equations.",
        "texts": [
            " To get algebraic constraints equations, we split the trajectory in elementary parts such that the change in the orientation will be small. As the orientation will affect only the vector CB, we will use a first- or secondorder approximation for this vector. Let Mi, M2 denote the extremities of one elementary part of the trajectory; \u2019ljJ1, 01, CPI the angles describing the orientation of the end effector at point M1; and ~2~2. CP2 the angles of the end effector at point M2. Between points M, and M2 (Fig. 6) at UQ Library on March 13, 2015ijr.sagepub.comDownloaded from 331 the position of point C is defined by equation (1), and the orientation angles can be written as: Using a first- or second-order approximation of CB leads to: where the vectors Ul, U2 are only dependent on the relative position of B and the angles V)1,01,01 and ~2~2.~2- Under this assumption we may now analyze the various constraints on an elementary part T of the trajectory. 3.1. Link Length Constraints By using equation (1) and a second-order approximation (23), we obtain the square of the link length p2 as a third-order polynomial Pp(A)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003891_s12283-009-0028-1-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003891_s12283-009-0028-1-Figure4-1.png",
        "caption": "Fig. 4 Experimental set-up for determining shaft stiffness",
        "texts": [
            "2 Determining shaft stiffness and damping parameters Separate stiffness constants for each of the three interconnecting springs were experimentally determined so that three shafts of varying stiffness could be employed in the model. To achieve this, three identical metal drivers were fitted with shafts of different stiffness (flexible, regular, and stiff) by a club professional with 30 years of experience. Each constructed club was measured to have a D1 swingweight. Once constructed, each club was rigidly secured in a vise so that the first 30 cm of the grip end was completely rigid (Fig. 4). This simulated the modeled club which was completely rigid for the first 30 cm. Markers were placed on the shaft so as to identify the segments defined by the mathematical club model. A 1 kg mass was suspended from the club, at the point where the shaft inserts into the hosel, resulting in shaft deflection. The deflection was video recorded and the coordinates of the markers were determined using the motional analysis software package HU-M-ANTM. From these coordinates, the relative angles between adjacent links were determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002691_1.1357163-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002691_1.1357163-Figure3-1.png",
        "caption": "Fig. 3 The coordinate system and geometry of the raceway in a ball bearing",
        "texts": [
            " As the ball bearing is operating without loading, the distance between two curvature centers of the inner and outer races can be given as A05ri1ro2D (2) where ri is the radius of curvature of the inner race, and ro is the radius of curvature of the outer race. The superscript \u2018\u20180\u2019\u2019 at the distance A represent zero loading. The contact angle under this circumstance, shown in Fig. 2, is a constant value, given as @7# a05cos21S 12 Pd 2A0D (3) 2.1.2 Contact Angle under Axial and Radial Loads. This study will try to establish the contact angle of all balls in a ball bearing under the loading conditions. Instead of a constant value, the contact angle of each ball in a bearing is considered to be variable, dependent upon the position angle. Figure 3 gives the coordinate system (x ,y ,z) defining the z-axis to be the axis of the shaft. In an adjacent coordinate system (x8,y8,z8), z8 is the central line of the raceway, and the x8-axis and y8-axis are parallel to the x-axis and y-axis, respectively. This new coordinate system is determined dependent upon the loading and the raceway being investigated. If the bearing is operating without any applied load in the axial or radial direction, the new coordinate system, (x8,y8z8) is transferred a very small distance such that it\u2019s origin point has the coordinates of ~0,0,z",
            " The origin point of the new coordinate system for the outer race also moves with an external load applied, to (jo,0,zo). As the geometry shows in Fig. 2, the coordinates for any point on the surface of the inner race can be written as ~xi ,yi ,zi!5~j i50,h i50,z i!1gW i1hW i (4) rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/07/20 where gW i is the distance between the z-axis and the curvature center of the inner race in vector form, and hW i is the radius of curvature of the inner race in vector form. The vector gW , according to Fig. 3 can be written as gW i5gi~~cos c!iW1~sin c! jW! (5) gi5di/21ri where c is the position angle between the x-axis and projection of the vector gW on the x-y plane. The vector hW , as shown in Fig. 3, can be written as hW i5hi~~cos u cos c!iW1~cos u sin c! jW1~sin u!kW ! (6) hi5ri then, Eq. ~4! can now be written as ~xi ,yi ,zi!5~~gi1hi cos u!cos c ,~gi1hi cos u!sin c ,hi sin u 1z i! (7) where z i in Eq. ~7!, according to Fig. 4, which is given as z i52~ri2D/2!sin a0 (8) JUNE 2001, Vol. 123 \u00d5 305 13 Terms of Use: http://asme.org/terms Downloaded F In Eq. ~8! ri is the radius of curvature of the inner race and a0 is the ball\u2019s contact angle under zero load. Here, the contact angles of the ball at the inner race and the outer race are assumed to be the same because the centrifugal force acting on the ball is ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003168_j.automatica.2006.01.009-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003168_j.automatica.2006.01.009-Figure3-1.png",
        "caption": "Fig. 3. DF-analysis in the complex plane.",
        "texts": [
            " 2, with yM,k+1= \u2212yM,k = \u2212y p M , is as follows (Atherton, 1975): q(y p M) = 2UM y p M [ ( \u2217 + 1) \u221a 1 \u2212 2 + j [( \u2217 \u2212 1) + ( \u2217 + 1)] ] . (6) A periodic solution can appear if the negative reciprocal of the DF (6) intersects the Nyquist plot of the harmonic response W(j ) (Atherton, 1975). The negative reciprocal of the DF (6) is: \u2212 1 q = y p M 4UM \u2212( \u2217 + 1) \u221a 1 \u2212 2 \u22172 (1 + ) + (1 \u2212 ) + y p M 4UM j [( \u2217 \u2212 1) + ( \u2217 + 1)] \u22172 (1 + ) + (1 \u2212 ) . (7) The locus (7) is a straight line backing out of the origin and forming a clockwise angle with respect to the negative real axis (see Fig. 3). From (7), angle can be expressed as a function of the controller parameters = arctan \u239b \u239c\u239d ( \u2217 \u2212 1) + ( \u2217 + 1) ( \u2217 + 1) \u221a 1 \u2212 2 \u239e \u239f\u23a0 . (8) Note that is ranging between 0 and /2. Then, the periodic motion may exist if at some frequency = the phase characteristic of the actuator-plant transfer function ranges between \u2212 and \u2212 3 2 . This is only possible if the overall relative degree of the actuator/process system is higher than two. If an intersection point exists then the frequency of the periodic solution is and the amplitude depends on the magnitude of W(j ) at the frequency "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002527_978-94-015-8348-0-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002527_978-94-015-8348-0-Figure9-1.png",
        "caption": "Figure 9: configuration for P3(0,1,0),B2 = ~",
        "texts": [
            " c is the maximal number of cusps, and d is the maximal number of nodes which can appear in a versal unfolding of the given singu larity. The reader is invited to peruse Figure 7 to see that the pictures are consistent with the tabled values of c, d. The three remaining monogerms of corank 1, namely the goose, butterfly and gulls all have codimension 2, so their versal unfoldings contain two unfolding parameters a, b. Here again one can determine critical curves and images for given values of a, b to obtain qualitative pictures of the changes in the critica! image illustrated in Figure 8, Figure 9 and Figure 10. In each case we have drawn a \"clock diagram\" in the (a, b)-plane giving a series of snapshots of the critica! image as (a, b) moves round a small circle centred at the origin. The curves coming into the origin correspond to the bifurcation curves in the moving lamina, that is they represent the loci of (a, b) giving rise to codimension 1 (multi)germs, i.e. lips, beaks or swallowtail types in the monogerm case, tacnode fold or cusp-plus-fold in the bigerm case, and triple fold in the trigerm case",
            ") 1\" straight-line mechanism of Hart mechanically interconnected with the Peaucellier-Lipkin inversor of 1864. Figure 1 Quadruplane inversor of Sylvester and Kempe (a generalization of Hart's inversor) Figure 3 A random 4-bar and a re flected similar one, built on tap Figure 7 jJ Two curve-cognates each representing the 2 .. straight-line mechanism of Hart(1877) Figure 2 8-bar linkage mechanism with bar A \"B\" moving perpendicular to the frame Figure 4 A o Hart's 2\"\" straight-line mechanism incorporated Figure 8 J c Hart's 2\"\" straight-line mechanism obtained by multiplication Figure 9 413 8-bar linkage mechanism with a rectilinear moving bar PR (the random contra-parallelogram, AS\u0102S, represents a sub-chain of the 8-bar) Figure 5 8-bar coupler cognate having a bar A \"B\" moving perpendicular 8-bar linkage mechanism containing a bar PR' moving in an invariable but oblique direction with the frame Figure 6 to the frame Figure 10 OB~nA.mA \",.,. 0.8\"4..t,.A\"' .$'/\",rrvw-\"\" ..,.;;\"\" o/ ~~mN'br# , In practice, only one equilateral dyad-linkage is needed to adjoin Hart's inversor in order to obtain an 8-bar with a translating link moving perpendicular to the frame, (figure 5)",
            " wbence equally the intersec tion (AoB x C0'C') of AoB and C0'C' traces a circle about the intersection of M and a line running parallel to AB but meeting the point (AoB x C0'C'). Tbe resulting six-bar containing the pentagon and the adjoined bar appears to be Hart's 2nd straigbt-line linkage mecbanism since among others B' traces a straigbt-line. Multiplying the six-bar with the factor A0DIA0B 1 in whicb D = AoB' x BoA' then results into an enlarged Hart's 2m1 straigbt-line mecbanism, also sbown in figure 9. This mecbanism tben consists of tbe pentagonal linkage AoEDCB0 and the bar AB. Naturally, tuming-joint D of tbe pentagon similarly traces a straigbt-line like B' did in the initial six bar. Tbe six-bar obtained this way, is to be set up by the initial four-bar AoABB0 and the additional linkage-dyad CDE. (Note tbat any four-bar contains sucb a unique point D. Tbe point plays a center-role in further generalization.) AoD. Wbence the factor equals DB\"IDB'. Thus, D Ao\"A\"B\"B0\" = (DB\"IDB').D A0' A'B'Bo', (7) Note that corresponding vertices of these two four-bars remain at the same ray joining the ray-center D",
            " However, in case the rectilinear motion is badly transmitted - as may be the case sometimes - one still bas the possibility to adjoin linkage parallelograms to sustain the motion. To avoid the then appearing overconstrainedness, one may simultaneously omit for example the superfluous bar Ao\"B0\". The result is a 10-bar linkage to be recognized in figure 4. 417 Hart's 2\"d straight-line mechanism occurs in pairs. That is to say, for each mechanism of this type, a curve cognate exists producing the same part of a straight-line. (figure 2 and also figure 9 of ref.[2].) Both cognates may further be generalized in a way as demonstrated in the figures 4 and 10. However, it is quite possible to let them also have the same (rectilinear) moving bar A\"B\". To attain this, one takes for both generalizations the same point B\" at the ray AJ) (and/or the same point A\" at DB0.). The two generalizations then appear to be each others' coupler cognate producing the identica} (rectilinear) motion for the common bar A\"B\". 5. Special Cases All 6-, 8- and 10-bar straight-line mechanisms of the focal type, have the advantage of a random choice for the dimensions of the initial four-bar AoABBo contained in them",
            " Now choose a sixth hip point, (z, y, z), tobe Ps(1, 2, 3) and pair it with an arbitrary sixth ankle point, (X, Y, Z), at Qs(2, 1, 1). Furthermore choose the leg length tobe 1 = 4. Substituting in Eq. 9, we get -7- 72t + 36t2 + 504t3 + 86t4 - 504t5 + 36t6 + 72t7 - 7t8 =o (10) This equation yields eight solutions but only four of them, (t1 -+ -0.4441447342254855, t2 -+ -0.0989246998462375, ta -+ 2.251518306850657, t4 -+ 10.10869885432393), 456 produce valid positions of the platform as shown in Fig. 5 - 8. Fig. 9 shows ali four positions in superposition. A simple mechanism, described in [15], can be devised to demonstrate BBM. Itis shown in Fig. 10 and consists of an inverted \"T\" made of wooden dowels glued together. A third dowel is cylindrically jointed and perpendicular to and bisected by the T-leg. Strings of equallength are attached to each end of the movable crossbar and connected to respective ends of the fixed one. When the movable crossbar is turned, while holding 457 the strings taut, its ends trace the curve of intersection between a sphere and cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure10-1.png",
        "caption": "Fig. 10. Coordinate systems applied for worm generation.",
        "texts": [
            " Elements of matrixM2g are determined by position vector 020g and direction cosines of coordinate axes of Sg (Fig. 8). The investigation of avoidance of interference may be accomplished analytically but it requires derivation of equations of tooth surfaces of many teeth and equations of their intersection with the head-cutter. The authors have used computer graphics as shown in Fig. 9. Avoidance of interference may require in some case the increase of the tilt of the head-cutter. Coordinate systems applied for derivation are shown in Fig. 10. Fixed coordinate systems Sn and Sm are rigidly connected to the frame of the generating machine. Movable coordinate systems Sd and S1 are rigidly connected to the cradle d of the generating machine and the worm, respectively. Schematics of worm generation are shown in Figs. 6 and 7. The worm is generated by a tilted head-cutter (Figs. 6 and 7). The blades of the head-cutter are of parabolic profile and deviate from the straight line profiles of the gear head-cutter (Fig. 11). Such mismatch is necessary for the localization of bearing contact of the gear drive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003125_physrevlett.61.106-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003125_physrevlett.61.106-Figure2-1.png",
        "caption": "FIG. 2. Solution of the diffusion equation at time /, and its approximation by two linear segments; ElU) is the thickness of the layer as measured from the surface of the gel.",
        "texts": [
            " In a highly viscous medium, inertial effects and kinetic energy terms can be ignored. The elastic forces are then balanced against the frictional forces, and the full mo tion of the beads is governed by the coupled differential equations -fdtn=8H{ro,rudjro,djru.. Mdn. These equations admit a uniformly expanding solution /\u2022o(x,/)=ro Cxo,/), a n d ri(x,f)\u2122*i. The expansion fac tor r*(xo,t) satisfies a simple diffusion equation dtr* *=(K/f)dfir*, and its behavior subject to the boundary conditions specified before is depicted in Fig. 2. As the figure demonstrates, this solution is adequately approximated by two linear segments: a swollen layer of thickness El(t) (i.e., r J U o , 0 - x 0 + ( \u00a3 - l ) { x o - - [ / o - - / 0 ) ] } for XQ> lo \u2014 l(t)) on top, and an undeformed gel lr* (XQ,0 =xo for jcn < lo~l(t)] at the bottom. The thickness of the swollen layer grows diffusively since l(t)~~(Dt)l/\\ w i t h / ) = # / / . The full set of coupled differential equations is too complicated to be studied analytically or numerically, and approximations must be made"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003001_j.ijimpeng.2003.10.038-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003001_j.ijimpeng.2003.10.038-Figure3-1.png",
        "caption": "Fig. 3. Linear approximation to Hertzian contact force relation.",
        "texts": [
            " According to Hertzian contact theory, the force deflection relationship for two elastic nonconforming bodies is F Fy \u00bc d dy 3=2 ; \u00f010\u00de where Fy is the force required to initiate yield and dy is the corresponding normal deflection at yield [7]. For yield initiating at mean contact pressure WyY , where Y is the uniaxial yield stress and Wy \u00bc 1:1 for spherical contact surfaces [11], the work done at initial yield Wy; can be obtained by integrating and setting d \u00bc dy: Wy \u00bc 2 5 Fydy: A linear approximation to Eq. (10) can be obtained which has equivalent work at yield. Setting Wy equal to the work done in a linear element, the average stiffness, ki; necessary to produce equal amounts of stored energy at F \u00bc Fy is obtained. See Fig. 3. Wy \u00bc 1 2 ki Fy ki 2 \u00bc 2 5 Fydy ) ki \u00bc 5Fy 4dy : Substituting for Fy and dy; ki \u00bc 5 4 pWyYiRi; \u00f011\u00de where Ri is the radius of ball i [11]. Using Eq. (11), Eq. (9) can be written as e2 R Y \u00bc e21 R1Y1 \u00fe e22 R2Y2 ; \u00f012\u00de where Y \u00bc \u00f0Y 1 1 \u00fe Y 1 2 \u00de 1; R \u00bc \u00f0R 1 1 \u00fe R 1 2 \u00de 1; and Yi; is the uniaxial yield stress of body i: Experimental impact data for collisions of dissimilar bodies have been measured in order to validate this theory. Collision tests were performed using 25:4 mm\u00f01 in:\u00de diameter solid spheres of two material types: (1) chrome steel (AISI 52100, ASTM A295), and (2) aluminum bronze (Alloy 630, ASTM B124)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure18-1.png",
        "caption": "Fig. 18. Lateral view of the blowhole phenomenon.",
        "texts": [
            " 16, point 1) is X H 0 ; Y H 0\u00f0 \u00de, the distance between it and the chamber is LH 1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0X H X H 0 \u00de2 \u00fe \u00f0Y H Y H 0 \u00de2 q \u00f035\u00de and the height difference between the twin rotors on the screw line H\u2013H can be expressed as DZ \u00bc jZ1 Z2j \u00f036\u00de Eqs. (35) and (36) are the length of the two sides of the leakiness triangle, making an approximate value of the blowhole area Ablowhole \u00bc 1 2 LH 1 DZ \u00f037\u00de Fig. 18, which provides a lateral view of these three examples, indicates no blowhole phenomenon between the chamber and the tooth profile tip in example 1 but does show a blowhole phenomenon for examples 2 and 3, whose identical design in the claw-shape of the rotor may affect pump efficiency. The calculated results of these three examples are shown in Table 2, and the area efficiency in example 1 is lower than that in examples 2 and 3. The result shows the length of line of action in example 1 is the shortest because the sealing line between the mating rotors is not continuous as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002929_bf01257946-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002929_bf01257946-Figure4-1.png",
        "caption": "Fig. 4. Singularity, Case 1.",
        "texts": [
            " I f the upper p la t fo rm is parallel to the base, then ZT1 = ZT2 ~- ZT3 = PZ\" whole Jacobian matr ix becomes 1 I(XT 2 -- XT3) OL 1 y OL I ] 7 1 [._ X OL2 Y \" Ok2 ] OL 3 OL 3 ] I(XT3 X OL4 Y \" OL4 \"] 1 _ TI)o_~T2+(YT3_ Tl)o--~r2 ] I(Xrl X ' OLs - Y \" oL5 q 1 _ r 2 ) o ~ r 3 + ( y r t Z2) o~r3j OL6 y OL6 ] (41) It is not hard to show that the first five columns of (41) are never dependent on each other. However, if the upper platform is not only parallel to the base but also rotates about its z-axis with \u00b190 \u00b0 (see Figure 4(a)), then the last column of 298 KAI LIU ET AL. (41) changes to \" a { OL1 OL1 ) - + 1 / a [ OL2 30L2 + a OL 3 v~ ox~-2 a OL 4 ,/30Xr2 a { OL5 \\b-x73 a ( OL 6 \\ f f273 since, in this case, XT3 -- XT1 = a, 30L6 _ _ v a-fT ) (42) Xr2 = \u00bd(Xrl + St3), v % Yrl - Y T 2 - 2 YT1 ~- YT3~ The last column (42) is still independent of the first five columns. If, further, Px = P r = O, then the upper platform is not only parallel to the base and rotates about its z-axis by +90 \u00b0, but also its z-axis is completely coincident with the fixed Z-axis as shown in Figure 4(b). In this case, the last column becomes 1 which is dependent on the third column [. 1 16.IT Pz 1 L2 That gives the following fact: Fact 1. If the position and orientation of upper platform is Xp_o = [0 0 Pz 0\u00b0 0\u00b0 90\u00b0] or Xp_o = [0 0 Pz 0\u00b0 0\u00b0 -90\u00b0] , then this configuration corresponds to a singularity. This kind of singularity occurs only when the three conditions below are simultaneously satisfied, that is, (1) The upper platform is parallel to the base; (2) The upper platform rotates about its z-axis by 90 \u00b0 or -90\u00b0; (3) The upper platform is cocentered with the base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002518_s0263574797000027-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002518_s0263574797000027-Figure4-1.png",
        "caption": "Fig . 4 . A Four-link Planar Robot .",
        "texts": [
            " Let us define an augmented objective function as E 5 E 0 1 m P (12) where E 0 is defined in (5) and m is the Lagrange multiplier which is positive . The objective function E is dif ferentiable , so the gradient  E  w can be easily computed . When m is suf ficiently large , the minimization of E is equivalent to the minimization of E 0 with inequality (9) . The proper choice of m depends on the problem at hand . For the purpose of illustration , we examine the inverse kinematics solutions of a four-link planar robot shown in Figure 4 . The forward kinematics function of the robot is G ( q ) 5 F L 1 c 1 1 L 2 c 1 2 1 L 3 c 1 2 3 1 L 4 c 1 2 3 4 L 1 s 1 1 L 2 s 1 2 1 L 3 s 1 2 3 1 L 4 s 1 2 3 4 G (13) and the corresponding Jacobian matrix is J ( q ) 5 3 2 L 1 s 1 2 L 2 s 1 2 2 L 3 s 1 2 3 2 L 4 s 1 2 3 4 2 L 2 s 1 2 2 L 3 s 1 2 3 2 L 4 s 1 2 3 4 2 L 3 s 1 2 3 2 L 4 s 1 2 3 4 2 L 4 s 1 2 3 4 L 1 c 1 1 L 2 c 1 2 1 L 3 c 1 2 3 1 L 4 c 1 2 3 4 L 2 c 1 2 1 L 3 c 1 2 3 1 L 4 c 1 2 3 4 L 3 c 1 2 3 1 L 4 c 1 2 3 4 L 4 c 1 2 3 4 4 T (14) where L i 5 1 . 0 is the length of the i th link for all i , s 1 5 sin ( q 1 ) , s 1 2 5 sin ( q 1 1 q 2 ) , s 1 2 3 5 sin ( q 1 1 q 2 1 q 3 ) , s 1 2 3 4 5 sin ( q 1 1 q 2 1 q 3 1 q 4 ) , and q i is the i th joint angle as shown in Figure 4 . The symbol c corresponds to cosine function . In the simulation study , we use the two-layer neural network as shown in Figure 2 with 40 neurons at hidden layer . The momentum coef ficient a is chosen as a 5 0 . 9 and the learning rate h is chosen as h 5 0 . 5 . The initial values of weights are selected as zero-mean random values with uniform distribution in [ 2 1 , 1 1] . We examine through simulation the neural network training on a specified domain spanned by 25 Cartesian positions h ( x , y ) 3 x 5 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.15-1.png",
        "caption": "Figure 3.15 Example 3.2.",
        "texts": [],
        "surrounding_texts": [
            "3.1 Definitions of Moment and Torque Vectors / 31 3.2 Magnitude of Moment / 31 3.3 Direction of Moment / 31 3.4 Dimension and Units of Moment / 32 3.5 Some Fine Points About the Moment Vector / 33 3.6 The Net or Resultant Moment / 34 3.7 The Couple and Couple-Moment / 39 3.8 Translation of Forces / 39 3.9 Moment as a Vector Product / 40 3.10 Exercise Problems / 44 3.1 Definitions of Moment and Torque Vectors A force applied to an object can translate, rotate, and/or de form the object. The effect of a force on the object to which it is applied depends on how the force is applied and how the ob ject is supported. For example, when pulled, an open door will swing about the edge along which it is hinged to the door frame (Figure 3.1). What causes the door to swing is the torque gen erated by the applied force about an axis that passes through the hinges of the door. If one stands on the free-end of a div ing board, the board will bend (Figure 3.2). What bends the board is the moment of the body weight about the fixed end of the board. In general, torque is associated with the rotational and twisting actions of applied forces, while moment is related to their bending effect. However, the mathematical definition of moment and torque is the same. Therefore, it is sufficient to use moment to discuss the common properties of moment and torque vectors. 3.2 Magnitude of Moment The magnitude of the moment of a force about a point is equal to the magnitude of the force times the length of the shortest dis tance between the point and the line of action of the force, which is known as the lever or moment arm. Consider a person on an exercise apparatus who is holding a handle that is attached to a cable (Figure 3.3). The cable is wrapped around a pulley and attached to a weight pan. The weight in the weight pan stretches the cable and produces a tensile force F in the cable. This force is transmitted to the person's hand through the handle. Assume that the magnitude of the moment of force F about point 0 at the elbow joint is to be determined. To determine the shortest distance between 0 and the line of action of the force, extend the line of action of F and drop a line from 0 that cuts the line of action of F at right angles. If the point of intersection of the two lines is R, then the distance d between 0 and R is the lever arm, and the magnitude of the moment M of force F about point o is: M=dF (3.1) 3.3 Direction of Moment The moment of a force about a point acts in a direction perpen dicular to the plane upon which the point and the force lie. For example, in Figure 3.4, point 0 and the line of action of force F lie on plane A. The line of action of moment M of force F about point o is perpendicular to plane A. The direction and sense of the mo ment vector along its line of action can be determined using the Moment and Torque 31 32 Fundamentals of Biomechanics right-hand-rule. As illustrated in Figure 3.5, when the fingers of the right hand curl in the direction that the applied force tends to rotate the body about point 0, the right hand thumb points in the direction of the moment vector. More specifically, extend the right hand with the thumb at a right angle to the rest of the fingers, position the finger tips in the direction of the applied force, and position the hand so that the point about which the moment is to be determined faces toward the palm. The tip of the thumb points in the direction of the moment vector. The line of action and direction of the moment vector can also be explained using a wrench and a right-treaded bolt (Figure 3.6). When a force is applied on the handle of the wrench, a torque is generated that rotates the wrench. The line of action of this torque coincides with the centerline of the bolt. Owing to the torque, the bolt will either advance into or retract from the board depending on how the force is applied. As in Figure 3.6, if the force causes a clockwise rotation, then the direction of torque is \"into\" the board and the bolt will advance into the board. If the force causes a counterclockwise rotation, then the direction of torque is \"out of\" the board and the bolt will retract from the board. In Figure 3.7, if point \u00b0 and force F lie on the surface of the page, then the line of action of moment M is perpendicular to the page. If you pin the otherwise unencumbered page at point 0, F will rotate the page in the counterclockwise direction. Us ing the right-hand-rule, that corresponds to the direction away from the page. To refer to the direction of the moments of copla nar force systems, it may be sufficient to say that a particular moment is either clockwise (cw) or counterclockwise (ccw). 3.4 Dimension and Units of Moment By definition, moment is equal to the product of applied force and the length of the moment arm. Therefore, the dimension of moment is equal to the dimension of force (ML/T2) times the dimension of length (L): [MOMENT] = [FORCE] [MOMENT ARM] = ~; L = ~;2 The units of moment in different systems are listed in Table 3.1. 3.5 Some Fine Points About the Moment Vector \u2022 The moment of a force is invariant under the operation of slid ing the force vector along its line of action, which is illustrated in Figure 3.8. For all cases illustrated, the moment of force about point 0 is: M=dF (ccw) where length d is always the shortest distance between point 0 and the line of action of F . Again for all three cases shown in Figure 3.8, the forces generate a counterclockwise moment. \u2022 Let F 1 and F 2 shown in Figure 3.9 be two forces with equal magnitude (Fl = F2 = F) and the same line of action, but acting in opposite directions. The moment Ml of force F 1 and the mo ment M2 of force F 2 about point 0 have an equal magnitude (Ml = M2 = M=dF), but opposite directions (Ml = -M2). \u2022 The magnitude of the moment of an applied force increases with an increase in the length of the moment arm. That is, the greater the distance the point about which the moment is to be calculated from the line of action of the force vector, the higher the magnitude of the corresponding moment vector. \u2022 The moment of a force about a point that lies on the line of action of the force is zero, because the length of the moment arm is zero (Figure 3.10). \u2022 A force applied to a body may tend to rotate or bend the body in one direction with respect to one point and in the opposite direction with respect to another point in the same plane. \u2022 The principles of resolution of forces into their components along appropriate directions can be utilized to simplify the cal culation of moments. For example, in Figure 3.11, the applied force F is resolved into its components Ex and F y along the x and y directions, such that: Fx = F cosO Fy = F sinO Since point 0 lies on the line of action of F x' the moment arm of F x relative to point 0 is zero. Therefore, the moment of F x about point 0 is zero. On the other hand, r is the length of the moment arm for force F relative to point O. Therefore, the moment of force F y about point 0 is: M = r F y = r F sin 0 (cw) Note that this is also the moment dF generated by the resultant force vector F about point 0, because d = r sinO. Moment and Torque 33 34 Fundamentals of Biomechanics 3.6 The Net or Resultant Moment When there is more than one force applied on a body, the net or resultant moment can be calculated by considering the vector sum of the moments of all forces. For example, consider the coplanar three-force system shown in Figure 3.12. Let d1, d2, and d3 be the moment arms of F l' F 2' and L relative to point O. These forces produce moments M1, M2, and M:3 about point 0, which can be calculated as follows: M1 = d1 F1 M2 = d2 F2 M3 = d3 F3 (cw) (cw) (ccw) The net moment Mnet generated on the body due to forces F l' F 2' and L about point 0 is equal to the vector sum of the mo ments of all forces about the same point: (3.2) A practical way of determining the magnitude and direction of the net moment for coplanar force systems will be discussed next. Note that for the case illustrated in Figure 3.12, the individual moments are either clockwise or counterclockwise. Therefore, the resultant moment must be either clockwise or counterclock wise. Choose or guess the direction of the resultant moment. For example, if we assume that the resultant moment vector is clock wise, then the clockwise moments M1 and M2 are positive and the counterclockwise moment M:3 is negative. The magnitude of the net moment can now be determined by simply adding the magnitudes of the positive moments and subtracting the negatives: (3.3) Depending on the numerical values of M}, M2, and M3, this equation will give a positive, negative, or zero value for the net moment. If the computed value is positive, then it is actually the magnitude of the net moment and the chosen direction for the net moment was correct (in this case, clockwise). If the value calculated is negative, then the chosen direction for the net mo ment was wrong, but can readily be corrected. If the chosen direction was clockwise, a negative value will indicate that the correct direction for the net moment is counterclockwise. (Note that magnitudes of vector quantities are scalar quantities that are always positive.) Once the correct direction for the net moment is indicated, the negative sign in front of the value calculated can be eliminated. The third possibility is that the value calculated from Eq. (3.3) may be zero. If the net moment is equal to zero, then the body is said to be in rotational equilibrium. This case will be discussed in detail in the following chapter. Example 3.1 Figure 3.13 illustrates a person preparing to dive into a pool. The horizontal diving board has a uniform thickness, mounted to the ground at 0, has a mass of 120 kg, and is e = 4 m in length. The person has a mass of 90 kg and stands at B which is the free-end of the board. Point A indicates the location of the center of gravity of the board. Point A is equidistant from points o and B. Determine the moments generated about point 0 by the weights of the person and the board. Calculate the net moment about point O. Solution: Let mi and m2 be the masses and WI and W2 be the weights of the person and diving board, respectively. WI and W2 can be calculated because the masses of the person and the board are given: WI = mi g = (90 kg)(9.8 m/s2) = 882 N W2 = m2 g = (120 kg)(9.8 m/s2) = 1176 N The person is standing at B. Therefore, the weight WI of the person is applied on the board at B. The mass of the diving board produces a force system distributed over the entire length of the board. The resultant of this distributed force system is equal to the weight W2 of the board. For practical purposes and since the board has a uniform thickness, we can assume that the weight of the board is a concentrated force acting at A, which is the center of gravity of the board. As shown in Figure 3.14, weights WI and W2 act vertically down ward or in the direction of gravitational acceleration. The diving board is horizontal. Therefore, the distance between 0 and B (t') is the length of the moment arm for WI and the distance be tween 0 and A (\u00a312) is the length of the moment arm for W2 \u2022 Therefore, moments MI and M2 due to WI and W2 about point o are: MI = e WI = (4 m)(882 N) = 3528 N-m (cw) e M2 = 2: W2 = (2 m)(1176 N) = 2352 N-m (cw) Since both moments have a clockwise direction, the net moment must have a clockwise direction as well. The magnitude of the net moment about point 0 is: Mnet = MI + M2 = 5880 N-m (cw) Moment and Torque 35 36 Fundamentals of Biomechanics (a) Example 3.2 As illustrated in Figure 3.1Sa, consider an athlete 1 wearing a weight boot, and from a sitting position, doing lower leg flexion/ extension exercises to strengthen quadricep muscles. The weight of the athlete's lower leg is WI = 50 N and the weight of the boot is W2 = 100 N. As measured from the knee joint at 0, the center of gravity (A) of the lower leg is located at a distance b a (b) f----I 0 A B 1 W2 2 ... 3 4 Figure 3.16 Forces and moment arms when the lower leg makes an angle () with the horizontal. Mo (N-m) 60 50 40 30 20 10 o +--r----r-+--- e Figure 3.17 Variation of moment with angle e. a = 20 cm and the center of gravity (B) of the weight boot is located at a distance b = 50 cm. Determine the net moment generated about the knee joint when the lower leg is extended horizontally (position 1), and when the lower leg makes an angle of 30\u00b0 (position 2),60\u00b0 (position 3), and 90\u00b0 (position 4) with the horizontal (Figure 3.1Sb). Solution: At position 1, the lower leg is extended horizontally and the long axis of the leg is perpendicular to the lines of action of WI and W2\u2022 Therefore, a and b are the lengths of the moment arms for WI and W2, respectively. Both WI and W2 apply clock wise moments about the knee joint. The net moment Mo about the knee joint when the lower leg is at position 1 is: Mo= aWI+ bW2 = (0.20)(50) + (0.50)(100) = 60N-m (cw) Therefore, the net moment about 0 is: Mo = dl WI + d2 W2 = a cos () WI + b cos () W2 = (aWl + bW2) cos () The term in the parentheses has already been calculated as 60 N-m. Therefore, we can write: Mo = 60 cos () For position 1: () = 0\u00b0 Mo =60N-m (cw) For position 2: () = 30\u00b0 Mo=S2N-m (cw) For position 3: () = 60\u00b0 Mo = 30N-m (cw) For position 4: () = 90\u00b0 Mo=O (cw) In Figure 3.17, the moment generated about the knee jOint is plotted as a function of angle (). Moment and Torque 37 Example 3.3 Figure 3.18a illustrates an athlete doing shoulder muscle strengthening exercises by lowering and raising a barbell (a) with straight arms. The position of the arms when they make an angle 0 with the vertical is simplified in Figure 3.18b. 0 represents the shoulder joint, A is the center of gravity of one arm, and B is a point of intersection of the centerline of the barbell and the extension of line OA. The distance between 0 and A is a = 24 cm and the distance between 0 and B is b = 60 cm. Each arm arm weighs WI = 50 N and the total weight of the barbell is W2 = 300N. Determine the net moment due to WI and W2 about the shoul der joint as a function of 0, which is the angle the arm makes with the vertical. Calculate the moments for 0 = 0\u00b0, 15\u00b0, 30\u00b0 , 45\u00b0 , and 60\u00b0. Solution: To calculate the moments generated about the shoul der joint by WI and W 2' we need to determine the moment arms dl and d2 of forces WI and W2 relative to O. From the geometry of the problem (Figure 3.18b), the lengths of the moment arms are: dl = a sinO d2 = b sinO Since the athlete is using both arms, the total weight of the bar bell is assumed to be shared equally by each arm. Also note that relative to the shoulder joint, both the weight of the arm and the weight of the barbell are trying to rotate the arm in the coun terclockwise direction. Moments MI and M2 due to W1 and W2 about point 0 are: Ml = dl WI = a WI sin 0 = (0.24)(50) sin 0 = 12 sin 0 W2 W2. (300) . . M2 = d2T = bT SinO = (0.60) 2 SinO = 90 SinO Since both moments are counterclockwise, the net moment must be counterclockwise as well. Therefore, the net moment Mo generated about the shoulder joint is: Mo = MI + M2 = 12 sinO + 90 sinO = 102 sinO N-m (ccw) To determine the magnitude of the moment about 0, for 0 = 0\u00b0, 15\u00b0, 30\u00b0, 45\u00b0, and 60\u00b0, all we need to do is evaluate the sines and carry out the multiplications. The results are provided in Table 3.2. (b) I\" Figure 3.18 An exercise to strengthen the shoulder muscles, and a simple model of the arm. b 38 Fundamentals of Biomechanics Example 3.4 Consider the total hip joint prosthesis shown in Figure 3.19. The geometric parameters of the prosthesis are such that \u00a31 = 50 mm, \u00a32 = 100 mm, (h = 45\u00b0, and fh = 90\u00b0. Assume that, when standing symmetrically on both feet, a joint reaction force of F = 400 N is acting at the femoral head due to the body weight of the patient. For the sake of illustration, consider three different lines of action for the applied force, which are shown in Figure 3.20. Determine the moments generated about points Band C on the prosthesis for all cases shown. Solution: For each case shown in Figure 3.20, the line of action of the joint reaction force is different, and therefore the lengths of the moment arms are different. From the geometry of the problem in Figure 3.20a, we can see that the moment arm of force F about points Band C are the same: d1 = \u00a31 cos(h = (50)(cos45\u00b0) = 35 mm Therefore, the moments generated about points Band Care: MB = Me = d1 F = (0.035)(400) = 14 N-m (cw) For the case shown in Figure 3.20b, point B lies on the line of action of the joint reaction force. Therefore, the length of the moment arm for point B is zero, and: MB =0 For the same case, the length of the moment arm and the moment about point Care: d2 = \u00a32 costh = (100)(cos45\u00b0) = 71 mm Me = d2 F = (0.071)(400) = 28 N-m (ccw) For the case shown in Figure 3.20c, the moment arms relative to Band Care: d3 = \u00a31 sin(h = (50)(sin45\u00b0) = 35 mm d4 = d3 + \u00a32 = (35) + (100) = 135 mm Therefore, the moments generated about points Band Care: MB = d3 F = (0.035)(400) = 14 N-m Me = d4 F = (0.135)(400) = 54 N-m (ccw) (ccw) 3.7 The Couple and Couple-Moment A special arrangement of forces that is of importance is called couple, which is formed by two parallel forces with equal mag nitude and opposite directions. On a rigid body, the couple has a pure rotational effect. The rotational effect of a couple is quan tified with couple-moment. Consider the forces shown in Figure 3.21, which are applied at A and B. Note that the net moment about point A is M = d F (cw), which is due to the force applied at B. The net moment about point B is also M=dF (cw), which is due to the force applied at A. Consider point C. The distance between C and B is b, arts! therefore, the distance between C and A is d - b. The net moment about C is equal to the sum of the clockwise moments of forces applied at A and B with moment arms d - band b. Therefore: M=(d-b)F+bF =dF (cw) It can be concluded without further proof that the couple has the same moment about every point in space. If F is the magni tude of the forces forming the couple and d is the perpendicular distance between the lines of actions of the forces, then the mag nitude of the couple-moment is: (3.4) The direction of the couple-moment can be determined by the right-hand-rule. 3.8 Translation of Forces The overall effect of a pair of forces applied on a rigid body is zero if the forces have an equal magnitude and the same line of action, but are acting in opposite directions. Keeping this in mind, consider the force with magnitude F applied at point PI in Figure 3.22a. As illustrated in Figure 3.22b, this force may be translated to point P2 by placing a pair of forces at P2 with equal magnitude (F), having the same line of action, but acting in op posite directions. Note that the original force at PI and the force at P2 that is acting in a direction opposite to that of the original force form a couple. This couple produces a counterclockwise moment with magnitude M = d F , where d is the shortest dis tance between the lines of action of forces at PI and P2. Therefore, as illustrated in Figure 3.22c, the couple can be replaced by the couple-moment. Provided that the original force was applied to a rigid body, the one-force system in Figure 3.22a, the three-force system in Figure 3.22b, and the one-force and one couple-moment system in Figure 3.22c are mechanically equivalent. 40 Fundamentals of Biomechanics y Ty 1. o ~~-------+------x Figure 3.24 The moment about 0 isM=r.. xF . 3.9 Moment as a Vector Product We have been applying the scalar method of determining the moment of a force about a point. The scalar method is satis factory to analyze relatively simple coplanar force systems and systems in which the perpendicular distance between the point and the line of action of the applied force are easy to calculate. The analysis of more complex problems can be simplified by utilizing additional mathematical tools. The concept of the vector (cross) product of two vectors was in troduced in Appendix B and will be reviewed here. Consider vectors A and Ji, shown in Figure 3.23. The cross product of A and B is equal to a third vector, c: C=AxB - - - (3.5) The product vector C has the following properties: \u2022 The magnitude of C is equal to the product of the magnitude of A, the magnitude of Ji, and sin (), where () is the smaller angle between A and ll. C = A B sin() (3.6) \u2022 The line of action of C is perpendicular to the plane formed by vectors A and B. \u2022 The direction and sense of C obeys the right-hand-rule. The principle of vector or cross product can be applied to de termine the moments of forces. The moment of a force about a point is defined as the vector product of the position and force vectors. The position vector of a point P with respect to another point 0 is defined by an arrow drawn from point 0 to point P. To help understand the definition of moment as a vector prod uct, consider Figure 3.24. Force F acts in the xy-plane and has a point of application at P. Force F can be expressed in terms of its components Fx and Fy along the x and y directions: F = Fx f + Fy j (3.7) The position vector of point P with respect to point 0 is repre sented by vector r.., which can be written in terms of its compo nents: (3.8) The components r x and r y of the position vector are simply the x and y coordinates of point P as measured from point O. The moment of force F about point 0 is equal to the vector product of the position vector r.. and force vector F: M=r x F - - - (3.9) Using Eqs. (3.7) and (3.8), Eq. (3.9) can alternatively be written as: M = (rx i + ry j) x (Fx i + Fy j) - - = rxFx (f x D + rxFy (f x j) (3.10) +ryFx (1 x D + ryFy (1 x D Recall that f x f = j x j = 0 since the angle that a unit vector makes with itself is zero, and sin 00 = O. f x j =!s. because the angle between the positive x axis and the poSitive y axis is 900 (sin 900 = 1). On the other hand, j xf = -!s.. For the la,st two cases, the product is either in the posItive z (counterclockwise or out of the page) or negative z (clockwise or into the page) direction. z and unit vector !s. designate the direction perpendicular to the xy-plane (Figure 3.25). Now, Eq. (3.10) can be simplified as: (3.11) To show that the definition of moment as the vector product of the position and force vectors is consistent with the scalar method of finding the moment, consider the simple case illus trated in Figure 3.26. The force vector F is acting in the positive y direction and its line of action is d distance away from point O. Applying the scalar method, the moment about a is: (ccw) (3.12) The force vector is acting in the positive y direction. Therefore: (3.13) If b is the y coordinate of the point of application of the force, then the position vector of point Pis: r=df+ b1 Therefore, the moment of F about point a is: M= r xF - - - = (d f + b D x (F D =dF(f x D+bF(1 x D = d F k (3.14) (3.15) Equations (3.12) and (3.15) carry exactly the same information, in two different ways. Furthermore, the y coordinate (b) of point P does not appear in the solution. This is consistent with the defi nition of the moment, which is the vector product of the position vector of any point on the line of action of the force and the force itself. In Figure 3.26, if C is the point of intersection of the line of action of force F and the x axis, then the position vector r' of point C with respect to a is: r' = d i - - (3.16) 42 Fundamentals of Biomechanics Therefore, fue moment of F about point 0 can alternatively be determined as: M=r.'F = (d D x (F D =dFk (3.17) For any two-dimensional problem composed of a system of coplanar forces in the xy-plane, the resultant moment vector has only one component. The resultant moment vector has a di rection perpendicular to the xy-plane, acting in the positive or negative z direction. The method we have outlined to study coplanar force systems using the concept of the vector (cross) product can easily be ex panded to analyze three-dimensional situations. In general, the force vector F and the position vector r. of a point on the line of action of F about a point 0 would have up to three components. With respect to the Cartesian coordinate frame: F = Fxi..+Fy1.+Fz1\u00a3 r. = rx i.. + ry 1. + rz 1\u00a3 The moment of F about point 0 can be determined as: M= r x F - - - = (rx i.. + ry j + rz!f) x (Fx i.. + Fy j + Fz 1\u00a3) - - = (ryFz - rzFy) i.. + (rzFx - rxFz) j + (rxFy - ryFx) 1\u00a3 (3.18) (3.19) (3.20) The moment vector can be expressed in terms of its components along the x, y, and z directions: (3.21) By comparing Eqs. (3.20) and (3.21), we can conclude that:"
        ]
    },
    {
        "image_filename": "designv10_8_0003126_j.mechmachtheory.2006.10.004-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003126_j.mechmachtheory.2006.10.004-Figure1-1.png",
        "caption": "Fig. 1. Basic structure of the 3-PRS manipulator.",
        "texts": [
            " Only by examination of both the Jacobian condition number, and the Jacobian\u2019s singular values, can a true understanding of the workspace characteristics of a given manipulator be achieved. As previously mentioned, the three mechanisms studied and compared in this paper are the 3-PRS, 3-RPS and Tricept mechanisms. These will now be discussed on a case by case basis by first describing each manipulator. A discussion on the manipulator\u2019s inverse displacement solution and Jacobian formulation will then follow. This mechanism, shown schematically in Fig. 1, consists of three identical kinematic chains. Each chain begins with an actuated prismatic joint attached to the base platform which may be inclined by angle c from the base platform. Note in Fig. 1, c = 90 . This is then followed by a passive revolute joint perpendicular to the direction of the prismatic joint. Finally, a passive spherical joint connects each chain to the moving platform. Conventionally, all of the mechanisms discussed in this paper have one translational and two rotational degrees of freedom. That is, a translation along the base frame\u2019s z-axis and rotations around the x- and y-axes depicted in Fig. 1. The kinematics for this manipulator have been previously presented in a variety of publications (i.e., [8,11,17]) and therefore only a brief review is provided here. Constraint equations were developed in [10] relating Giz to Gix and Giy (for i = 1,2,3). As the derivation of these constraint equations is very involved, they will not be presented here. Knowing the plane on which the end effector lies, the radius of the moving platform, and the constraint equations, the position of the spherical joints represented by points Ai may be determined. As presented in [11], the displacement of the actuated prismatic joint i is solved by examination of the vector loop representing branch i, depicted in Fig. 1 for branch i = 3. Two solutions for this displacement are obtained by solving for the squared length of the fixed-length link li jlij2 \u00bc jri bij2 \u00f08\u00de The smaller of the two solutions corresponds to a joint displacement where the spherical joint of that limb, denoted by Ai, has a higher z elevation than the revolute joint denoted by Bi. This solution is preferred in order to reduce the possibility of mechanical interference between the fixed length link and the actuated prismatic joint. Having solved for the manipulator\u2019s pose, velocity analysis is now possible. As discussed earlier, the first step in obtaining the desired Jacobian matrix, JP, is to formulate the 3 \u00b7 9 Jacobian in Eq. (4) according to the method introduced by Kim and Ryu [15]. According to Fig. 1, let ci + ri represent the location of point gi also located at spherical joint i. Equating the vector addition ci + bi + li to the weighted summation of vectors gi ci \u00fe bi \u00fe li \u00bc ki;1g1 \u00fe ki;2g2 \u00fe ki;3g3 \u00f09\u00de Finally, taking the first time derivative and simplifying sT bi sli _bi \u00bc ki;1sT li _g1 \u00fe ki;2sT li _g2 \u00fe ki;3sT li _g3 \u00f010\u00de where sbi and sli are unit vectors in the directions of bi and li, respectively. Eq. (10) may be written three times corresponding to each of the three limbs to formulate the manipulator Jacobians: Jq _q \u00bc Jx _x \u00f011\u00de where Jq \u00bc sT b1 sl1 0 0 0 sT b2 sl2 0 0 0 sT b3 sl3 2 64 3 75 3 3 \u00f012\u00de _q \u00bc _b1 _b2 _b3 T \u00f013\u00de Jx \u00bc k1;1sT l1 0 0 0 k2;2sT l2 0 0 0 k3;3sT l3 2 64 3 75 3 9 \u00f014\u00de _x0 \u00bc _g1 _g2 _g3 2 64 3 75 9 1 \u00f015\u00de and J \u00bc J 1 q Jx"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure11.28-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure11.28-1.png",
        "caption": "Figure 11.28 Problem 11.1.",
        "texts": [
            ") 1 2 Y2 = yo + Vo sm e t2 - 2 g t2 . 1 o = 10 + (vo sme)(2.5) - 2(9.8)(2.5)2 Solving this equation for Vo sin e: Vo sin e = 8.25 (ii) Noting that vosine over vocose is equal to tane, divide Eq. (ii) by Eq. (i): 8.25 tane = 2 = 4.125 Considering the inverse tangent of the value calculated above will yield: The speed of takeoff can now be determined from Eq. (i): 2 2 Vo = -- = = 8.5m/s cos e cos 76.40 11.12 Exercise Problems Problem 11.1 Consider a person throwing a ball upward into theairwithaninitialspeedofvo = lOm/s(Figure 11.28). Assume that at the instant when the ball is released, the person's hand is at a height ho = 1.5 m above the ground level. Neglecting the possible effects of air resistance, determine the maximum height hI that the ball reached, the total time t2 it took for the ball to ascend and descend, and the speed V2 of the ball just before it hit the ground. Note that this problem must be handled in two phases: ascend and descend. Also note that the speed of the ball at the peak was zero. Answers: hI = 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002844_mech-34344-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002844_mech-34344-Figure1-1.png",
        "caption": "Figure 1: 3-RRS mechanism",
        "texts": [
            " These advantages are usually paid with a more complex structure and the presence of singular configurations (translation singularities) in which the spherical constraint between platform and base fails. This paper presents a new spherical parallel manipulator, named 3-RRS wrist, belonging to the class of the not overconstrained and three-equal-legged SMs. The presented SM has a very reduced structural complexity and has no translation singularity. The 3-RRS wrist is obtained by imposing some manufacturing and mounting conditions on a parallel mechanism with three degrees of freedom (dof) that has three legs of type RRS (Fig. 1). Hereafter this mechanism will be called 3-RRS mechanism. In the next section a property of the rigid body motions will be demonstrated. Then, by exploiting this property, the mounting and manufacturing conditions that a 3-RRS mechanism has to encounter for being a spherical parallel manipulator will be enunciated. Finally the kinematic analysis of the 3-RRS wrist will be addressed and solved. For introducing the 3-RRS wrist the demonstration of the following statement is necessary: nloaded From: http://proceedings",
            "org/ on 02/02/2016 T zero and the linear homogeneous system (5) admits just the following solution q = 0 (8) Taking into consideration definition (4), Eq. (8) becomes as follows ( )P P C= \u00d7 \u2212\u03c9 (9) Finally, the dot product of Eq. (9) and (P \u2212 C) gives the following relationship ( )P P C\u22c5 \u2212 = 0 (10) Since the P point is any point of the rigid body, Eq. (10) states that any point of the rigid body moves on concentric spheres whose center is C, i.e., the rigid body accomplishes a spherical motion with center C. QED THE 3-RRS WRIST The number of degrees of freedom (dof number) of the 3-RRS mechanism (Fig. 1) can be computed with the Gr\u00fcbler equation: F = 6 (n \u2212 1) \u2212 j (6 \u2212 fj) (11) where F is the dof number of the mechanism, n is the number of links and fj is the dof number of the j-th kinematic pair. 3 Copyright \u00a9 2002 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Dow The 3-RRS mechanism (Fig. 1) is composed of eight links (n=8), three spherical pairs (fj=3) and six revolute pairs (fj=1). Substituting these data into Eq. (11) gives F=3. Therefore the 3- RRS mechanism has three dof, i.e., is not overconstrained. Figure 4 shows a 3-RRS mechanism encountering the following mounting and manufacturing conditions: (i) the revolute pair axes converge towards a single point; (mounting and manufacturing condition) (ii) the centers of the spherical pairs are not aligned; (manufacturing condition) (iii) the point the revolute pair axes converge towards does not lie on the plane located by the three spherical pair centers; (manufacturing condition) Henceforth a 3-RRS mechanism encountering these geometric conditions will be called 3-RRS wrist"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003431_ichr.2007.4813885-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003431_ichr.2007.4813885-Figure4-1.png",
        "caption": "Fig. 4. Left: Idea of this study. s1,s2,s3 are sensor data. In the blue region, humanoid robots walk stability. In the green region, humanoid robots are hit on disturbance. In the red region, humanoid robots fall. Right: Discriminant analysis for falling detection.",
        "texts": [
            " It is necessary to set an appropriate threshold to the degree of deviation to detect the falling because the degree of deviation rises sometimes even if the robot is not about to fall. However, in some cases the fall cannot be detected because there is no method of setting an appropriate threshold in this technique. It is possible to determine when a disturbance has been received by comparison with the steady state, as described in the previous paragraph. However, it is difficult to perform falling detection effectively. Figure. 4 shows a state in the sensor space where the humanoid robots is walking stably, a state where the robot has received a disturbance and a state where the the robot is falling. As shown in the figure, if the robot enters the disturbed state it can sometimes return to the stable state by applying appropriate feedback control, whereas in other cases it moves to the fall state. In order to perform fall detection before the robot has completely fallen, we propose to analyze the disturbed state. It is thought that the disturbed state is divided into two parts: one which returns to the stable state and one which leads to the fall state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002657_70.345948-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002657_70.345948-Figure7-1.png",
        "caption": "Fig. 7 . Nine DOF Cartesian path following.",
        "texts": [
            " A more complete collision detection procedure is being developed for spatial arm planning. The remaining examples illustrate applications to a spatial redundant 9 DOF arm. This consists of a PUMA 600 manipulator mounted on a platform providing additional linear, rotate and tilt joints. (See [ 3 3 ] for details of the CIRSSE dual-arm robotic testbed.) Fig. 6 shows the output sequence for joint path end-point planning to a specified task space positiodorientation in the presence of an obstacle. Fig. 7 shows the path sequence generated for a path following task incorporating a straight line translation coupled with a rotation of 180\u201d about the tip I- axis. Because of the manipulator joint limits, this can only be accomplished by switching the PUMA\u2019S pose from elbow-up to elbow-down at some intermediate point. As in the planar examples, the present algorithm accomplishes a smooth transition between these arm configurations. The final example (Fig. 8) illustrates a cyclic joint path sequence computed for the arm to follow a circular task space path while maintaining a fixed tool orientation (perpendicular to the plane of the circle)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.18-1.png",
        "caption": "Figure 12.18 Problem 12.1.",
        "texts": [
            " \u2022 Since the effects of nonconservative forces due to friction and air resistance are neglected, the solution of the problem is inde pendent of the shape of the track or how the skier covers the distance between the top and bottom of the track. The most im portant parameter in this problem affecting the takeoff speed of the skier is the total vertical distance between 1 and 2. This im plies that the problem could be simplified by noting that the skier undergoes a \"free fall\" between 1 and 2, which are hI =lsine distance apart. This is illustrated in Figure 12.17. Applying the principle of conservation of energy between 1 and 2 will again yield Eq. (iii). 12.13 Exercise Problems Problem 12.1 Figure 12.18 shows a person pushing a block of mass m on a surface that makes an angle e with the horizon tal. The coefficient of kinetic friction between the block and the inclined surface is J.L. If the person is applying a force with constant magnitude P and in a direction parallel to the incline, show that the accel eration of the block in the direction of motion can be express ed as: P . ax = - - g (J.L cose + sme) m Problem 12.2 Consider that a force with magnitude Fx that varies with displacement along the x direction is applied on an object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002467_s1388-2481(99)00148-4-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002467_s1388-2481(99)00148-4-Figure2-1.png",
        "caption": "Fig. 2. Structure of the screen-printing planar electrochemical sensor. Working electrode (WE): RuO2; counter electrode (CE): RuO2; reference electrode (RE): AgNAgCl.",
        "texts": [
            "5% NaCl, pH 7.4). Four different pastes were used to screen-print the sensors: DP 8011 (RuO2), DP 6160 (Ag), DP 6120 (Pd/Ag) and DP 5704 (dielectric), all from DuPont. The fundamental components of DP 8011 are a mixture of RuO2 particles and glass particles. After firing, the resulting film is composed of 30\u201340 vol% RuO2, while the rest (60\u201370%) is glass material with a composition of 65% PbO, 25% SiO2, and 10% Bi2O3. The resistance of the film is 10 V squarey1. The structure of the sensors is shown in Fig. 2. They were printed on 2=2 inch alumina ceramic substrates. The working and counter electrodes were formed with RuO2 paste. For the reference electrode, the Ag paste was used, and Pd/Ag paste was used for the bonding pads. Finally, in order to define the area of the electrode, a dielectric insulator layer was printed with DP 5704. The areas of working, counter and reference electrodes were 3, 4 and 1 mm2, respectively. The chloridation of the AgNAgCl reference electrode was accomplished by dipping for 1 min into a 1% FeCl3 solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003870_1.4001003-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003870_1.4001003-Figure1-1.png",
        "caption": "Fig. 1 Sketch of the two-stage nutation drive",
        "texts": [
            "4001003 Keywords: double circular-arc, spiral bevel gear, tooth profile, mathematical modeling, gear machining Introduction Nutation is the third movement of a gyroscope in addition to its elf-rotating motion and forward movement. This third movement s caused when the speed of the gyroscope is reduced, resulting in movement of the angle between the rotating axis of the gyrocope and the vertical plane. The principle of this rotation is used o create a kind of mechanical drive called the nutation drive. The utation drive can achieve a high reduction ratio with a compact tructure by the axial meshing of one pair of the external and nternal gears. A two-stage nutation drive system in Fig. 1 is comosed of an input shaft, external gears 1 and 3, internal gears 2 nd 4, and an output shaft. The external gear 1 meshing with the xed internal gear 2 is free to rotate about its axis, which is nclined to the axis of the input shaft. The input shaft is also an xis of the internal gear 2. The external gear 3 is fixed to the xternal gear and located inside the external gear 1. The external ear 3 engages with the internal gear 4 that is attached to the utput shaft and coaxial with it. The external gear 1 meshing with he internal gear 2 creates the first stage nutation drive",
            " One reason is that the tooth intensity will be weakened if the larger module is set that the length of the whole tooth depth will increase, especially in the situation with longer face width. The simulation was then verified in the software MASTERCAM, as shown in Fig. 16. From the running result of the program, it has verified the machining method we attempted. No interference or overcutting area occurs during the whole simulation process and machining. The pair of prototype of the spiral bevel gears using the above cutting process is presented in Fig. 17. Two pairs of bevel gears are required in the design of the nutation drive, as shown in Fig. 1. Since they have the same double circular-arc tooth profile and similarity in configuration except the number of teeth and pitch cone distance, only one pair of them is simulation results Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use F circular-arc spiral bevel gear Journal of Mechanical Design Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 discussed in the manufacturing process, and its manufactured double circular-arc spiral bevel gears is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002693_s0165-0114(02)00529-8-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002693_s0165-0114(02)00529-8-Figure3-1.png",
        "caption": "Fig. 3. Fuzzy variable of triangular type.",
        "texts": [
            " All the universes of discourse of S; S\u0307 and U are arranged from \u22121 to 1; thus, the range of nonfuzzy variables s; s\u0307 and u must be scaled to >t the universe of discourse of fuzzi>ed variable S; S\u0307 and U with scaling factors K1, K2 and K3, respectively, namely, S = K1 \u00b7 s(t); S\u0307 = K2 \u00b7 s\u0307(t); u(t) = K3 \u00b7 U: In the implementation, S\u0307 is approximated with (Sk \u2212 Sk\u22121)=T where T is the sampling period. For simplicity, a triangular type membership function is chosen for the aforementioned fuzzy variables, as shown in Fig. 3. The reasoning behind the fuzzy control rules for the FSMC, which will be presented later, is explained by the following analysis: By taking the time derivative of both sides of (7), we obtain s\u0307 = cTx\u0307 = cTAx + cTb (u) + cTb(Hx + Gxd + d): (20) Then, multiplying both sides of the above equation by s leads to ss\u0307 = scTAx + scTb (u) + scTb(Hx + Gxd + d): (21) Here, we assume that cTb\u00bf0. In (20), it is seen that s\u0307 increases as (u) increases and vice versa. In (21), it is seen that if s\u00bf0, then decreasing (u) will make ss\u0307 decrease and that if s\u00a10, then increasing (u) will make ss\u0307 decrease"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003318_14644207jmda80-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003318_14644207jmda80-Figure1-1.png",
        "caption": "Fig. 1 Experimental apparatus (a, angle of oblique impact)",
        "texts": [
            " Then, a method for constructing an FE ball model was proposed, based on the relationship between the material constants and the behaviour of the ball. The impact experiments were also conducted to obtain the dynamic properties of the golf ball. The results of the impact simulations of the ball model, as constructed by the proposed method, closely matched with the experimental results, and the method was verified by applying the process to other types of golf balls. BY IMPACT EXPERIMENT Impact experiments were conducted to identify the dynamic properties of the golf ball, as shown in Fig. 1. The ball was fired from an air gun in strainfree and non-rotational condition, so that a typical Proc. IMechE Vol. 220 Part L: J. Materials: Design and Applications JMDA80 # IMechE 2006 at Bibliothekssystem der Universitaet Giessen on June 15, 2015pil.sagepub.comDownloaded from golf impact would be realized, and collided with the end surface of the target, a circular bar of steel whose length is 1.80 m and diameter is 0.030 m. Normal and oblique impact experiments were conducted. The impact load histories, ball outer diameter deformation histories, and rebound velocity were obtained from the measured data for the normal impact tests"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure12.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure12.3-1.png",
        "caption": "Fig. 12.3 System with velocities",
        "texts": [],
        "surrounding_texts": [
            "From Eq. (10.19), describing the motion of the system are the Lagrange equations 12.3 Forced Vibration with Harmonic Excitation 181 The kinetic energy of the system is 2 1 .2 1 2\" 1 2 E = 2 mlql + 2 m2v2 = ~ 2 mivi i=l = ~ mlizr + ~ m2 [(izl + Liz2 COSq2)2 + (Liz2 Sinq2)2] 1 \u00b72 1 [.2 L2 \u00b72 2L\" 1 = 2m1q1 + 2m2 ql + q2 + qlq2cOSq2\u00b7 Thus we find (for small values of q2, i.e. q2 \u00ab 1) E 1 ( ).2 1 L2 \u00b72 L\" = 2 ml + m2 ql + 2 m2 q2 + m2 QlQ2\u00b7 The generalized forces Q i are determined from the virtual work of the forces acting in this system under an admissible virtual displacement, since defines these generalized forces (see Eq. 10.10) 6A = (Fo cos f2t - CQl - bizd 6Ql - m2gLQ2 6Q2 = Ql 6Ql + Q2 6Q2. We may calculate the following vectorial quantities"
        ]
    },
    {
        "image_filename": "designv10_8_0003827_j.engstruct.2008.05.011-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003827_j.engstruct.2008.05.011-Figure1-1.png",
        "caption": "Fig. 1b. Deflections in Frenet frame.",
        "texts": [
            " Assuming the habitual principles and hypotheses of the strength of materials [35] and considering the stresses associated with the normal cross-section (\u03c3 , \u03c4n, \u03c4b) (N/m2), the geometric characteristics of the section are: area A(s) (m2), shearing coefficients \u03b1n(s), \u03b1nb(s), \u03b1bn(s), \u03b1b(s) andmoments of inertia It(s), In(s), Ib(s), Inb(s) (m4). Longitudinal E(s) (N/m2) and transversal G(s) (N/m2) elasticity moduli give the elastic condition of the material. Applying the equilibrium of forces, the following equation is obtained:[D \u2212\u03c7 0 \u03c7 D \u2212\u03c4 0 \u03c4 D ][N Vn Vb ] + [qt qn qb ] = [0 0 0 ] . (2) The vectors involved in the equilibrium (Fig. 1a) are Internal forces Vt = Nt + Vnn + Vbb = \u222b A \u03c3dAt + \u222b A \u03c4ndAn +\u222b A \u03c4bdAb (N). Force load qt = qt t+ qnn+ qbb (N/m). The equation of moments is obtained applying the equilibrium law as well:[ 0 0 0 0 0 \u22121 0 1 0 ][ N Vn Vb ] + [ D \u2212\u03c7 0 \u03c7 D \u2212\u03c4 0 \u03c4 D ][ T Mn Mb ] + [ mt mn mb ] = [ 0 0 0 ] . (3) In this case, the vectors are: Internal momentsMt = T t+Mnn+Mbb = \u222b A (\u03c4bn\u2212 \u03c4nb) dAt+\u222b A \u03c3bdAn\u2212 \u222b A \u03c3ndAb (Nm). Moment loadmt = mt t+mnn+mbb (Nm/m). Fig. 1a. Internal forces and moments in Frenet frame. Once the constitutive relations are defined, kinematics law relates the rotations and displacements (Fig. 1b): \u2212 1 GIt 0 0 0 \u2212 Ib E(InIb \u2212 I2nb) \u2212 Inb E(InIb \u2212 I2nb) 0 \u2212 Inb E(InIb \u2212 I2nb) \u2212 In E(InIb \u2212 I2nb)  [ T Mn Mb ] + [D \u2212\u03c7 0 \u03c7 D \u2212\u03c4 0 \u03c4 D ][ \u03b8t \u03b8n \u03b8b ] \u2212 [ \u0398t \u0398n \u0398b ] = [0 0 0 ] . (4) Rotations components are given by \u03b8t = \u03b8t t+ \u03b8nn+ \u03b8bb (rad). Rotation load2t = \u0398t t+\u0398nn+\u0398bb (rad/m). Following the same procedure, the displacement equation is expressed: \u2212 1 EA 0 0 0 \u2212 \u03b1n GA \u2212 \u03b1nb GA 0 \u2212 \u03b1nb GA \u2212 \u03b1b GA  [N Vn Vb ] + [0 0 0 0 0 \u22121 0 1 0 ][ \u03b8t \u03b8n \u03b8b ] + [D \u2212\u03c7 0 \u03c7 D \u2212\u03c4 0 \u03c4 D ][u v w ] \u2212 [ \u2206t \u2206n \u2206b ] = [0 0 0 ] (5) where displacement components are denoted as \u03b4t = ut + vn + wb (m) and displacement load1t = \u2206t t+\u2206nn+\u2206bb (m/m) Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.20-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.20-1.png",
        "caption": "Figure 5.20 Free-body diagram.",
        "texts": [
            "4 Consider the weight lifter illustrated in Figure 5.18, who is bent forward and lifting a weight Woo At the position Applications of Statics to Biomechanics 99 shown, the athlete's trunk is flexed by an angle e as measured from the upright (vertical) position. The forces acting on the lower portion of the athlete's body are shown in Figure 5.19 by considering a section passing through the fifth lumbar vertebra. A mechanical model of the athlete's lower body (the pelvis and legs) is illustrated in Figure 5.20 along with the geometric parameters of the problem under consider ation. W is the total weight of the athlete, WI is the weight of the legs including the pelvis, W + Wo is the total ground reac tion force applied to the athlete through the feet (at C), F M is the magnitude of the resultant force exerted by the erector spinae muscles supporting the trunk, and F I is the magnitude of the compressive force generated at the union (0) of the sacrum and the fifth lumbar vertebra. The center of gravity of the legs in cluding the pelvis is located at B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002890_00006123-200110000-00003-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002890_00006123-200110000-00003-Figure12-1.png",
        "caption": "FIGURE 12. MEMS pressure sensors for medical applications. A, photograph of packages. B, schematic cross sectional depiction of a package with pressure sensor.",
        "texts": [
            " Typically, the sensing element consists of a flexible diaphragm that deforms because of a pressure differential across contact with Si underneath. (e) the cantilever is released by dipping the wafer in hydrofluoric acid, which etches all the SiO2 underneath and around the cantilever beam but does not etch the Si wafer or the polycrystalline silicon. Neurosurgery, Vol. 49, No. 4, October 2001 it. The extent of diaphragm deformation is converted to a representative electrical signal, which appears as the sensor output. Figure 12 presents an example of a pressure sensor manufactured by Motorola, Inc. (Schaumburg, IL), that could be integrated into a variety of diagnostic and therapeutic devices. The sensor chip consists of a thin Si diaphragm that is fabricated by bulk micromachining. Before the micromachining step, piezoresistors are patterned across the edges of the diaphragm region using microelectronics fabrication processing techniques. The sensor chip is bonded to a glass substrate to create a sealed vacuum cavity beneath the diaphragm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.17-1.png",
        "caption": "Fig. 6.17 Mechanical work performed by the actuator (a) against a constant load and (b) against a structure with pre-strain",
        "texts": [
            "27) By increasing the induced stroke from zero to the value ui, the actuator performs the work W = Fpui (6.28) 5 The above reported analysis of the work output of a solid-state actuator interfaced with a passive linear structure without pre-stress is a standard content of the literature dealing with solid-state actuation (e.g. [4]). Interestingly, in the cited contributions the other loading scenarios are \u2013 despite of their relevance \u2013 not discussed at all. 172 6 Design Principles for Linear, Axial Solid-State Actuators represented by the shaded area in Figure 6.17(a). In the case of Figure 6.6(b), the loop law requires u+up = us (6.29) while the values of the actuator and the structure strokes are related to the force in the circuit by the respective characteristics: 6.3 Theory of Single-Stroke Linear Solid-State Actuators 173 F + ka(u\u2212ui) = 0 (6.30) \u2212F + ksus = 0 (6.31) Solving the system (6.29)\u2013(6.31) for F and u gives u = ui \u2212 ks ka up 1+ ks ka ; F = ks 1+ ks ka ( ui +up ) (6.32) and the stroke work \u2013 represented by the shaded area in Figure 6.17(b) \u2013 reads W = \u222b ui 0 F (u\u0304i)du = \u222b ui 0 F (u\u0304i) du dui du\u0304i = 1 1+ ks ka \u222b ui 0 F (u\u0304i)du\u0304i (6.33) W = ksui( 1+ ks ka )2 ( up + ui 2 ) (6.34) As mentioned before, the pre-stress case (Figure 6.16(c)) is equivalent to the above treated pre-strain case. It is evident from the graph of Figure 6.17 that under the considered conditions no inherent limit to the actuator\u2019s stroke work exists. The amount of work performed by the actuator can be indefinitely increased by increasing the external load (force or pre-strain). 174 6 Design Principles for Linear, Axial Solid-State Actuators A linear solid-state actuator can be combined with passive components in such a way that the resulting system can be treated as a new linear solid-state actuator with modified properties. This requires: \u2022 the new system to interface with the mechanical environment through a single force and a single stroke as defined in Section 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002397_095440603762554668-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002397_095440603762554668-Figure2-1.png",
        "caption": "Fig. 2 Hatching scheme in the selective laser melting process",
        "texts": [
            " The laser beam can be carried through the optical bre, and the focused laser beam diameter is 0.8 mm on the powder bed. The rst solid layer is made by the movement of the beam on to the powder bed with a rapid melting and solidi cation process in the chamber continuously lled with argon gas. Then the platform is lowered by 0.1 mm, the next powder layer is deposited and another solid layer is made. By successive scanning and lowering of the platform a three-dimensional model is fabricated. The hatching pattern is shown in Fig. 2. One cycle of the hatching process for reducing distortion of the model and time is as follows: scanning only outline, scanning outline and hatching inside in the x direction, scanning only outline and scanning outline and hatching inside in the y direction. The hatching space is 0.75 mm and the layer thickness is 0.1 mm. Commercial pure titanium powder grade 1 was used in the experiment. The chemical compositions of the pure titanium are shown in Table 1. The powder has a very low amount of hydrogen (three times less the maximum of grade 1 titanium powder) to avoid the embrittlement effect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003594_j.snb.2009.11.068-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003594_j.snb.2009.11.068-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagrams of the micro -FI-AD biosensor chip and the experimental set-up of the -FI-AD system. (a) The top view diagram of the -FI-AD biosensor chip. The insert shows the enlarged details of the detection cell. The dimensions are: A, 100 m; B\u2013G, 300 m. (b) Dismantled view of the -FI-AD chip. (c) The experimental set-up of the -FI-AD system 1. working electrode modified with glucose oxidase; 2. Ag/AgCl reference electrode; 3. Pt counter electrode; 4. sampling probe capillary; 5. detection c te she t rating a",
        "texts": [
            " A platinum electroplating bath consisted of 5 mmol L\u22121 H2PtCl6 and 0.16 g L\u22121 (CH3COO)2Pb in a pH 4.0 BrittonRobinson buffer solution was freshly prepared before use. 2.2. Apparatus A CHI 810B electrochemical analyzer (CHI Instrument Co., Shanghai, China) was used for amperometric detection. A personal computer was employed to control the analyzer, automatic sample dispenser and collect data. A model PDC-32G-2 plasma cleaner/sterilizer (Harrick, New York, USA) was used for treatment of the surface of PC sheets. 2.3. Chip fabrication As schematically shown in Fig. 1a and b, the -FI-AD chip composed of an upper PC sheet with a channel network, a lower PC cover sheet with integrated three-electrode system, and a sampling probe made of fused-silica capillary. 2.3.1. Preparation of gold-electrode bases on a PC sheet The procedure used for fabrication of gold micro-electrode bases by photo-directed electroless gold plating was as described in our previous report [25]. Briefly, a PC sheet of 20 mm \u00d7 30 mm \u00d7 0.5 mm was exposed to UV lights emitted from a 30 W low-pressure mercury lamp for 3 h through a quartz glass photomask [26], the electrode pattern on the mask being transferred to the UV-exposed region of the PC sheet through surface photolysis",
            " After being rinsed with double distilled water (DDW) and dried with warm air, the plated gold bases were annealed at 142 \u25e6C for 3 h. 2.3.2. Channel formation and chip assembling A straight fused-silica capillary of 15 mm in length and 370 m o.d. was used as a template. It was hot embossed into a 2 mm-thick PC sheet (20 mm \u00d7 20 mm) at 138 \u25e6C and 1.0 MPa in a home-made thermal press system. Thus, a straight channel of 10 mm in length and 370 m in both width and depth was imprinted on the sheet at the position from one edge to the centre (Fig. 1a and b). Then, a 1.5 mm i.d. through hole was drilled at the terminal of the straight channel. The hole served as the detection cell where the integrated reference and counter electrodes were located after the channelstructured PC sheet was bonded to the electrode-plated PC sheet. The detailed structure of the detection cell is shown in the insert of Fig. 1a. A 15 mm long fused-silica capillary (100 m i.d., 370 m o.d.), functioning as the sampling probe, was connected to the straight channel by embedding 3 mm of the capillary into the channel inlet. Immediately after the PC sheet with integrated gold-electrode bases and the PC sheet with the channel structure and embedded sampling probe were treated with plasma generated at air pressure of \u22120.1 MPa, the channel-structured sheet was laid on the PC sheet Y. Wang et al. / Sensors and Actuators B 145 (2010) 553\u2013560 555 c c e 3 fi i b d t s 1 j s t t d 2 t r F w ell; 6",
            " Finally, the enzyme elecrode, and the channel network including the detection cell were insed with 25 mmol L\u22121 phosphate buffer (pH 7.0) and ready to r activating the carboxyl group of MPA by EDC and NHS. The black area represents iaturized salt bridge filled with saturated KCl solution; B: the off-chip micro Pt wire be used. When not in use, the enzyme electrode was stored at 4 \u25e6C with the channel being filled with 25 mmol L\u22121 phosphate buffer. 2.4. Micro flow-injection system The -FI-AD system, as illustrated in Fig. 1c, was composed of a microchip with sampling probe, a hydrostatic pressure generating tubing, an automatic sample dispense system and an electrochemical analyzer. The auto sample dispense system (see Fig. 1c) was the same as the previously reported [24,27]. Briefly, it consisted of 12 slotted sample vials mounted on a large ring gear and a slotted carrier vial on a pinion gear that was driven by a stepping-motor controlled with a computer via a program written in Lab-VIEW 7.5. 2.5. Operation procedure Before running the operation program, the channel network of the microchip was washed with a running buffer for 10 min. The sample vials on the auto sample dispense system were manually filled with 10 L of sample solutions, while the carrier vial was filled with 80 L of carrier solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003827_j.engstruct.2008.05.011-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003827_j.engstruct.2008.05.011-Figure2-1.png",
        "caption": "Fig. 2. Internal forces and deflections functions in global reference system.",
        "texts": [
            " It is important to note the strict order of the twelve functions in the equation. Forces produce moments, moments produce rotations and rotations produce displacements, in terms of the load applied. All functions are interconnected. This arranged format has permitted to obtain directly numerical results and matrices expressions [36]. The system (6) given in Box I is associated to the Frenet frame in natural coordinates of the curved line. It is possible to implement a change of basis and express the functions (Fig. 2) in a global coordinate system Pxyz which unit vectors are i, j and k:[ t n b ] = [ \u03c5tx \u03c5ty \u03c5tz \u03c5nx \u03c5ny \u03c5nz \u03c5bx \u03c5by \u03c5bz ][ i j k ] . The different coefficients of the basis change matrix represent the direction cosines. The differential system (6) given in Box I is transformed into global Cartesian coordinates in Box II. The components of internal forces, moments, rotations and displacements involved in Eq. (7) given in Box II are referred to the global absolute coordinate system. This new general expression of the differential system, which simulates the structural behaviour of the linear element, has a lower-triangular form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.29-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.29-1.png",
        "caption": "Figure 13.29 Double pendulum:",
        "texts": [
            " For example, the two-dimensional motion characteristics of the simple pendulum shown in Figure 13.28 can be fully described by 0 that defines the loca tion of the pendulum uniquely. Therefore, a simple pendulum has one degree of freedom. On the other hand, parameters 01 and O2 are necessary to analyze the coplanar motion of bar BC of the double pendulum shown in Figure 13.27, and therefore, a double pendulum has two degrees of freedom. Example 13.4 Double pendulum. Assume that arms AB and BC of the double pendulum shown in Figure 13.29 are undergoing coplanar motion. Let il = 0.3 m and \u00a32 = 0.3 m be the lengths of arms AB and Be, and (h and 02 be the angles arms AB and BC make with the vertical. The angular velocity and acceleration of arm AB are measured as WI =2 rad/s (counterclockwise) and al =0 relative to point A. The angular velocity and acceleration of arm BC is measu red as W2 =4 rad/s (counterclockwise) and a2 =0 relative to point B. Determine the linear velocity and acceleration of point B on arm AB and point C on arm BC at an instant when 01 = 30\u00b0 and 02 =45\u00b0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.27-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.27-1.png",
        "caption": "Figure 3.27 Example 3.5.",
        "texts": [
            " + rz 1\u00a3 The moment of F about point 0 can be determined as: M= r x F - - - = (rx i.. + ry j + rz!f) x (Fx i.. + Fy j + Fz 1\u00a3) - - = (ryFz - rzFy) i.. + (rzFx - rxFz) j + (rxFy - ryFx) 1\u00a3 (3.18) (3.19) (3.20) The moment vector can be expressed in terms of its components along the x, y, and z directions: (3.21) By comparing Eqs. (3.20) and (3.21), we can conclude that: Mz = rxFy - ryFx (3.22) The following example provides an application of the analysis outlined in the last three sections of this chapter. Example 3.5 Figure 3.27a illustrates a person using an exercise machine. The ilL\" shaped beam shown in Figure 3.27b repre sents the left arm of the person. Points A and B correspond to the shoulder and elbow joints, respectively. Relative to the per son, the upper arm (AB) is extended toward the left (x direction) and the lower arm (BC) is extended forward (z direction). At this instant the person is holding a handle that is connected by a ca ble to a suspending weight. The weight applies an upward (in the y direction) force with magnitude F on the arm at point C. The lengths of the upper arm and lower arm are a = 25 em and b = 30 em, respectively, and the magnitude of the applied force is F =200N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003933_j.engfailanal.2010.11.009-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003933_j.engfailanal.2010.11.009-Figure4-1.png",
        "caption": "Fig. 4. 3D model of the BW structure (total number of buckets: 23).",
        "texts": [
            " \u2013 The microstructure of the material in the zone of cracking. Based on the results of the calculated stress state and the measured welding residual stresses, a safety estimation of the critical welded joints is carried out utilizing the Goodman diagram [9,10]. There are two main reasons for identifying the BW body stress state: (1) Carrying out proof stress. (2) The selection of tension-metric measuring locations. The BW body stress state is calculated by applying the linear finite element method (FEM). The 3D model of the BW, Fig. 4, is set up by the synthesis of 3D models of all structural parts, Fig. 6. The model represents the continuum discretized by the 4-node linear tetrahedron elements [11] in order to create the FEM model (1,917,704 nodes and 6,418,422 elements). The analysis of the external load is performed in accordance with the code [12]. It is worth mentioning that during the identification of the circumferential and lateral force, according to the above mentioned DIN code, the effects of the bucket wheel (BW) eccentricity are neglected in relation to the system lines of the boom and the boom inclination relative to the vertical and horizontal plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003863_taes.2008.4560220-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003863_taes.2008.4560220-Figure4-1.png",
        "caption": "Fig. 4. Real-time architecture of platform.",
        "texts": [
            " In this section, we describe the experimental setup platform of the three-rotor helicopter including sensors and real-time architecture. The experimental results obtained using the proposed controller applied to the designed three-rotor aircraft are presented. We have built a three-rotor aircraft as shown in Fig. 2. The parameters of the three-rotor craft are m= 0:5 kg, l1 = 0:07 m, l2 = 0:24 m, l3 = 0:33 m. For simplicity we have developed a Simulink-based platform using MATLAB Simulink xPC target (see Fig. 4). We have used the commercial radio Futaba to transmit the signals to the three-rotor aircraft. The radio joystick potentiometers have been connected through the data acquisitions cards, Advantech PCL-818HG (16 channels A/D) and Advantech PCL-726 (6 channels D/A) to the PC (xPC target module). In order to measure the position (x,y,z) of the rotorcraft, we have used the 3D tracker system POLHEMUS. We have built a Simulink S-function for connecting the POLHEMUS via RS232 to the xPC target. The POLHEMUS system uses low-frequency magnetic transducing technology",
            " The developed IMU contains three gyroscopes (ADXRS150) arranged orthogonally and a dual-axis micromachined silicon accelerometer (ADXL203). Gyroscopes and accelerometers data are fused in order to provide accurate measurements SALAZAR-CRUZ ET AL.: REAL-TIME STABILIZATION OF A SMALL THREE-ROTOR AIRCRAFT 789 of the three angular rates ( _\u00c3, _\u03bc, _\u00c1) and two angular positions (\u03bc,\u00c1). The radio physical constraints are such that the control inputs have to satisfy the following inequalities 0:40 V< u < 4:70 V 0:40 V< \u00bf\u00c1 < 4:50 V 0:40 V< \u00bf\u03bc < 4:16 V 0:40 V< \u00bf\u00c3 < 4:15 V: (31) The real-time architecture of the platform is illustrated in Fig. 4. The rotorcraft evolves freely in a 3D space without any flying stand. The control goal is to perform the hover flight at the position (x,y,z) = (0,0,25) while stabilizing the orientation (\u00c3,\u03bc,\u00c1) = (0,0,0). The initial Euler angles and position are given by \u00c30 \u00bc 0\u00b1, \u03bc0 \u00bc 1\u00b1, \u00c10 \u00bc 0\u00b1, x0 \u00bc 0 cm, y0 \u00bc 0 cm, and z0 \u00bc 5 cm. Initial linear and angular velocities are set to zero. The control law parameters are listed in Table I. The saturation levels are chosen according to (55), and the bounds on control torques are set to one (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.23-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.23-1.png",
        "caption": "Figure 7.23 Hysteresis loop.",
        "texts": [
            " Therefore, the prod uct of stress and strain is equal to the work done on a body per unit volume of that body, or the internal work done on the body by the externally applied forces. For an elastic body, this work is stored as an internal elastic strain energy, and it is the release of this energy that brings the body back to its original shape upon unloading. The maximum elastic strain energy (per unit vol ume) that can be stored in a body is equal to the total area under the a-E diagram in the elastic region (Figure 7.21). There is also a plastic strain energy that is dissipated as heat while deforming the body. 7.12 Strain Hardening Consider the a-E diagram shown in Figure 7.23. Between 0 and A a tensile force is applied on the material and the material is deformed beyond its elastic limit. At A, the tensile force is removed, and the line AB represents the unloading path. At B the material is reloaded, this time with a compressive force. At C, the compressive force applied on the material is removed. Between C and 0, a second unloading occurs, and finally the material resumes its original shape. The loop OABCO is called the hysteresis loop, and the area enclosed by this loop is equal to the total strain energy dissipated as heat to deform the body in tension and compression"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003258_j.bspc.2007.06.003-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003258_j.bspc.2007.06.003-Figure3-1.png",
        "caption": "Fig. 3. Instrumented needle.",
        "texts": [
            " As already stated, the aim of this paper is to model the forces involved during the needle insertion from measurable informations in operating conditions. We consider that the tissues in which the needle is inserted are not equipped with particular fiducials that may allow to capture the organs motions. We suppose that the only informations at disposal are the position or the velocity of the needle tip and the interaction forces measured by a force sensor. To estimate needle insertion models we use a PHANToM haptic device from Sensable Technologies as an instrumented passive needle holder (see Fig. 3). Its encoders allow to measure the motions of the needle with a precision of 30 mm. The PHANToM end effector is equipped with an ATI Nano17 force sensor. All measurements are acquired at a frequency rate of 1 kHz, under real-time constraints imposed by the software implemented on Linux RTAI operating system. Finally, a needle holder is mounted on the force sensor so that needles of different sizes can be attached. Nevertheless, in the following experiments we will always use a 18-Gauge needle. For more details on the effect of the needle size and of its geometry, see [17] or [1]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.15-1.png",
        "caption": "Figure 4.15 Free-body diagram of the beam.",
        "texts": [
            "14 is hinged to the ground at A. A frictionless roller is placed between the beam and the ceiling at D to constrain the counter clockwise rotation of the beam about the hinge joint. A force that makes an angle f3 = 60\u00b0 with the horizontal is applied at B. The magnitude of the applied force is P = 1000 N. Point C rep resents the center of gravity of the beam. The distance between A and B is l = 4 m and the distance between A and Dis d = 3 m. The beam weighs W = 800 N. Calculate the reactions on the beam at A and D. Solution: Figure 4.15 illustrates the free-body diagram of the beam under consideration. The horizontal and vertical direc tions are identified by the x and y axes, respectively. The hinge joint at A constrains the translational movement of the beam both in the x and y directions. Therefore, there exists a reaction force RA at A. We know neither the magnitude nor the direc tion of this force (two unknowns). As illustrated in Figure 4.15, instead of a single resultant force with two unknowns (magni tude and direction), the reaction force at A can be represented in terms of its components RAx and RAy (still two unknowns). The frictionless roller at D functions as a \"stop.\" It prevents the counterclockwise rotation of the beam. Under the effect of the applied force ~ the beam compresses the roller, and as a reac tion, the roller applies a force RD back on the beam. This force is applied in a direction perpendicular to the length of the beam, or vertically downward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002322_3477.907567-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002322_3477.907567-Figure3-1.png",
        "caption": "Fig. 3. Four-link planar rotary manipulator arm.",
        "texts": [
            " The neural network defined in (14) is thus globally stable and convergent to the optimal solutions of the linear programs (11) and (12). The proof is complete. Computer simulations based on a four-link planar rotary manipulator and a seven-degree-of-freedom industrial redundant robot are conducted to demonstrate the effectiveness of the proposed neural network for minimization of infinity-norm of joint velocities in kinematic control of redundant manipulators. The following simulation is based on a four-link planar rotary manipulator arm as shown in Fig. 3 with lengths of m and m. The end-effector is to track a planar straight-line trajectory with end-effector velocity profiles as shown in Fig. 4. The initial configuration of the manipulator is rad. In this simula- tion, the differential equations (15)\u2013(17) are solved by using the fourth-order Runge\u2013Kutta method. The positive scalar constant is set to be 50 000. Fig. 5 shows joint motion trajectories of the redundant manipulator under infinity-norm joint velocity minimization. Fig. 6 delineates the transient behaviors of the joint velocities computed by neural networks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003912_s0022112073001849-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003912_s0022112073001849-Figure4-1.png",
        "caption": "FIGURE 4. Two profiles of equal area.",
        "texts": [
            " (19) For a particular choice of 6 and p, if p exceeds 2 we calculate K and h from (I I) and (13) respectively, with q5 equal to +6. If p is less than 2, equations (16) and (1 7) are used. The area of the cross-section is then calculated from ( 19). In figure 3 values of a have been plotted as a function of K for different angles of contact. As Neumann showed for zero contact angle, there is a maximum in the possible values a may attain. Below this maximum two profiles exist having for the same area a two different heights K. As an example, the profiles are shown in figure 4 for a contact angle of 30\" corresponding to the points A and B in figure 3. It will also be seen that, if we have an equilibrium shape, then by drawing the horizontal surface from which the drop hangs at a different level we automatically obtain an equilibrium solution for a different area and contact angle. From figure 3 we see that, as liquid is added to the drop, the height K increases until the maximum cross-sectional area is reached. Addition of more liquid would then result in a situation for which no equilibrium is possible, and so liquid would certainly separate from the drop"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002859_1350650021543960-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002859_1350650021543960-Figure3-1.png",
        "caption": "Fig. 3 High-pressure, high shear stress viscometer for 1.0GPa pressure",
        "texts": [],
        "surrounding_texts": [
            "The low-shear viscosity measurements were performed with falling body viscometers that have been previously described [4, 10]. Viscosity may be measured over a range of viscosity of nine orders of magnitude by interchanging sinkers of varying weight and geometry. The in\u00afuence of geometry upon falling velocity has previously been analysed [11]. The sinker is reset by inverting the viscometer, avoiding the heating of the sample that accompanies the use of a solenoid to reset. The shear stress, t, applied to the liquids in these experiments is less than 100Pa, so that it is de\u00aenitely the limiting low shear viscosity, m, that is measured. The high shear stress measurements were performed in a new pressurized Couette rheometer (see F ig. 3). This instrument is similar to one previously described [12], except as noted in the following. The sample is sheared between a rotating inner cylinder and a stationary outer cylinder with a radial clearance of 2.1, 3.9 or 4:2 mm and Proc Instn Mech Engrs Vol 216 Part J: J Engineering Tribology J05501 # IMechE 2002 at UQ Library on June 21, 2015pij.sagepub.comDownloaded from a working diameter of 2.0 or 2.4 mm, depending upon the particular cylinder set. The torque required to restrain the outer cylinder is measured by a full strain gauge bridge bonded to a thin (0.2 mm) aluminium alloy tube. Pressure is measured by a manganin resistance gauge that has been calibrated against a Harwood cell to 1 GPa. The electrical signals for both the pressure measurement and the torque measurement are passed through the pressure vessel using commercial (Omega) stainless steel sheathed, compacted magnesium oxide insulated and sealed multiconductor wire. This instrument differs from others fabricated in this laboratory by not using a separate low-viscosity pressurizing medium. The sample is instead pressurized directly by an intensi\u00aeer attached to the viscometer as shown in F ig. 3. To improve repeatability, the cylinder set is held in a relative axial position by a spring-loaded driveshaft at one end of the inner cylinder and a ball bearing at the other end. Temperature is maintained by pumping heated air through passages not shown in the \u00aegure. The increase in pressure afforded by this new Couette rheometer makes shear thinning observable for the \u00aerst time in these very low molecular weight liquids. Pressure of the order of 1 GPa raises the limiting stress to greater than 30 MPa, exposing the non-Newtonian behaviour."
        ]
    },
    {
        "image_filename": "designv10_8_0002898_0890-6955(95)00091-7-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002898_0890-6955(95)00091-7-Figure2-1.png",
        "caption": "Fig. 2. D - H parameters between two flames [8] : 0 . = turn around axis z . - t , d. = movement along axis z._,;",
        "texts": [
            " The other rotational axis is located at the rotational table. (3) RRLLL: The workpiece is supported by a double turn table, i.e. the work table has two rotational axes: Positioning accuracy improvement in five-axis milling by post processing 225 (a) having a rotational table on the tilting one; (b) having a tilting table on the rotational one. 2. MODELING OF FIVE-AXIS MACHINE TOOLS The transformation of axes from one link to another can be described completely by four kinematics parameters, called D - H parameters (see Fig. 2). Let us assume that the transformation between frame (n - 1) and frame (n) is given by A,: A,, = R(Z,O,,). T(O,O,d,,). T( ot~,O,O).(X,a,,) (1) a~ = movement along axis x.; an = turn around x.. 226 R. Md. Mahbubur et al. If the joints are prismatic then \u00ae. is constant and d. is variable. In the case of a revolute joint, O. is variable and the others are constants. The total transformation is denoted by the matrix T. If the A,. matrix describes transformation with respect to the base coordinate system, then Tto t -- Am"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.6-1.png",
        "caption": "Figure 14.6 Force applied by the high bar on the gymnast's arms (measured in Newtons) versus angle f3 in degrees.",
        "texts": [
            " At position 3, the tendency of the gymnast is to move away from the center of rotation and what is holding the gymnast in the circular path of motion is the \"pulling\" effect of the high bar. At position 4, forces acting in the radial direction are T4 applied by the high bar and Wn4 = Wsin(45)componentofthegymnast's weight. From the geometry of the problem, Wn4 is centrifugal. Assuming that L is centripetal and applying the equation of motion: Similarly at position 5: LFns = manS: T4 - Wn4 = man4 T4 = Wn4 + man4 T4 = m g sin(45) + m an4 T4 = (60)(9.8)(sin45) + (60)(33.41) Ts = mg+mans Ts = (60)(9.8) + (60)(39.19) = 2939 N In Figure 14.6, these results are used to plot a force applied by the high bar on the arms of the gymnast versus angular position (measured in terms of angle f3 in Figure 14.3) graph. Note that between positions 1 and 2, the high bar has a pushing effect on the arms. In other words, the force applied by the high bar on the arms is compressive. Just after position 2, the force applied by the high bar is zero, and thereafter it has a pulling or tensile effect on the arms. (e) The equation of motion in the tangential direction is: or Forces acting in the tangential direction for different positions of the gymnast's center of gravity are shown in Figure 14"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002899_bit.260420805-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002899_bit.260420805-Figure2-1.png",
        "caption": "Figure 2. A 3-mL miniaturized probe: Union Cross fitting (Swagelok, Solon, OH) adapted for aeration, mixing, and light detection. Temperature is kept constant at 28\u00b0C with a water bath.",
        "texts": [
            " The voltage was recorded with a data-acquisition software (Unkelscope, Cambridge, MA) for 1 h via a DAS-8PGA A/D board (Keithley-Metrabyte, Taunton, MA). The measurement error is Y.3 mV. This particular set-up gave a current (mV) to light (photons/s) conversion of 1.25 X lo5 photons/mV. s. TESCIONE AND BELFORT: CONSTRUCTION AND EVALUATION OF A METAL BIOSENSOR 947 Cells were grown and prepared as described above, but centrifuged in 3-mL quantities. Approximately 2.5 mL of a resuspended sample was added manually to a Union Cross fitting (Swagelok, Solon, OH), adapted as shown in Figure 2, and the luminescence measured as described above. The fitting was adapted for these light measurement studies. It had a total capacity of 3 mL. A glass disk was glued into the right-hand-side fitting of the cross, the \u201cprobe\u201d or minisensor. The fiber optic was fitted with ferrules into this fitting. The glass disk protected it from contact with the culture. The effective volume that the fiber optic saw in the probe was approximately 1.4 mL. The whole probe was kept in a 28\u00b0C water bath. A miniature stir bar provided mixing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002527_978-94-015-8348-0-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002527_978-94-015-8348-0-Figure10-1.png",
        "caption": "Figure 10: Spherocylindrical Mechanism & Swept Surfaces",
        "texts": [
            " c is the maximal number of cusps, and d is the maximal number of nodes which can appear in a versal unfolding of the given singu larity. The reader is invited to peruse Figure 7 to see that the pictures are consistent with the tabled values of c, d. The three remaining monogerms of corank 1, namely the goose, butterfly and gulls all have codimension 2, so their versal unfoldings contain two unfolding parameters a, b. Here again one can determine critical curves and images for given values of a, b to obtain qualitative pictures of the changes in the critica! image illustrated in Figure 8, Figure 9 and Figure 10. In each case we have drawn a \"clock diagram\" in the (a, b)-plane giving a series of snapshots of the critica! image as (a, b) moves round a small circle centred at the origin. The curves coming into the origin correspond to the bifurcation curves in the moving lamina, that is they represent the loci of (a, b) giving rise to codimension 1 (multi)germs, i.e. lips, beaks or swallowtail types in the monogerm case, tacnode fold or cusp-plus-fold in the bigerm case, and triple fold in the trigerm case",
            " The first one represents the inversor mechanism (figure 1), while the 2nd one represents a special case of Kempe's focal mechanism (figures 2 and 9), ref.[3,4]. Hart's inv~rsor has further been generalized, which lead to the so-called quadruplane inversor of Sylvester and Kempe (figure 3). The result though, may stiH be recognized as a six-bar linkage mechanism of Watt's form.(ref.[S]) The generalization of the focal type, however, does lead to an eight-bar but then contain ing a rectilinear translating bar. (figure 4, see also figure 10 of ref.[4]) 4ll A. J. Lenartic and B. B. Ravani (eds.), Advances in Robot Kinematics and Computationed Geometry, 411-420. \u00a9 1994 Kluwer Academic Publishers. 412 Eight-bar linkages with such a rectilinear translating bar, may also be obtained from a design based on Harts' inversor. (figure 5, see also figure 10 of ref.[6].) 1\" straight-line mechanism of Hart mechanically interconnected with the Peaucellier-Lipkin inversor of 1864. Figure 1 Quadruplane inversor of Sylvester and Kempe (a generalization of Hart's inversor) Figure 3 A random 4-bar and a re flected similar one, built on tap Figure 7 jJ Two curve-cognates each representing the 2 .. straight-line mechanism of Hart(1877) Figure 2 8-bar linkage mechanism with bar A \"B\" moving perpendicular to the frame Figure 4 A o Hart's 2\"\" straight-line mechanism incorporated Figure 8 J c Hart's 2\"\" straight-line mechanism obtained by multiplication Figure 9 413 8-bar linkage mechanism with a rectilinear moving bar PR (the random contra-parallelogram, AS\u0102S, represents a sub-chain of the 8-bar) Figure 5 8-bar coupler cognate having a bar A \"B\" moving perpendicular 8-bar linkage mechanism containing a bar PR' moving in an invariable but oblique direction with the frame Figure 6 to the frame Figure 10 OB~nA.mA \",.,. 0.8\"4..t,.A\"' .$'/\",rrvw-\"\" ..,.;;\"\" o/ ~~mN'br# , In practice, only one equilateral dyad-linkage is needed to adjoin Hart's inversor in order to obtain an 8-bar with a translating link moving perpendicular to the frame, (figure 5). The mechanism contains a contra-parallelogram and two identica! dyad chains, remaining parallel during the motion. The same procedure may be applied at the quadruplane inversor of Sylvester and Kempe. 414 Then, the equilateral dyad PR'D' adjoined to the 6-bar, remains parallel to the identical dyad OQ0'Q' giving a rectilinear translating bar PR' moving straight with respect to the fixed link OOo'",
            " We conclude that the general approach as developed in the underlying manuscript, really represents a generalized method simultaneously interconnecting ali linearizers known to mankind. [1] Hart,H.: A parallel motion, Proc.London Math.Soc.6(1875),p.l37-9 [2] Dijksman,E.A.: Six-Bar Cognates of a Stephenson Mechanism, Joumal of Mecha nisms,Vol.6(1970),Nr.1 ,p.31-57,(page 40) [3] Hart,H.: On some cases ofparallel motion, Proc.London Math.Soc.8(1877),p.286-289. [4] Dijksman,E.A.: Kempe's (Focal) Linkage Generalized, particularly in connection with Hart's second straight-line mechanism,Mechanism and Machine Theory,Vol.l0(1974),Nr.6,p.445460,(figure 10) [5] Kempe,A.B.: On a general method of producing exact rectilinear motion by linkworks, Proc. Royal Soc.London,23(1875),p.565-77. [6] Dijksman,E.A.: Overconstrained Linkages to be derived from perspectivity and rejlection, Proc.71h World Congress on TMM,Sevilla, Spain,Vol.l(l987),p.69-73(figure 10) [7] Kempe,A.B.: How to draw a straight-line-III,Nature,16(1811)p.l21 [8] Kempe,A.B.: On conjugate Four-piece Linkages,Proceedings of the London Mathematical Society,9(1878)p.l33-147 [9] Wunderlich,W.: On Burmester's focal mechanism and Hart's straight-line motion, Joumal of Mechanisms, Vol.3 (1968), Nr.2, p.79-86. [10] Ruzinov,L.D.: Design of Mechanisms by Geometric Transformations, (translated from the Russian into English), Iliffe Books Ltd., London,(l968). On the Reduction of Parameters in Kinematic Equations K",
            " Furthermore choose the leg length tobe 1 = 4. Substituting in Eq. 9, we get -7- 72t + 36t2 + 504t3 + 86t4 - 504t5 + 36t6 + 72t7 - 7t8 =o (10) This equation yields eight solutions but only four of them, (t1 -+ -0.4441447342254855, t2 -+ -0.0989246998462375, ta -+ 2.251518306850657, t4 -+ 10.10869885432393), 456 produce valid positions of the platform as shown in Fig. 5 - 8. Fig. 9 shows ali four positions in superposition. A simple mechanism, described in [15], can be devised to demonstrate BBM. Itis shown in Fig. 10 and consists of an inverted \"T\" made of wooden dowels glued together. A third dowel is cylindrically jointed and perpendicular to and bisected by the T-leg. Strings of equallength are attached to each end of the movable crossbar and connected to respective ends of the fixed one. When the movable crossbar is turned, while holding 457 the strings taut, its ends trace the curve of intersection between a sphere and cylinder. Roles of the BBM design constants, a and p, and the motion parameter, t, as they pertain to the mechanism, are indicated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003421_0167-6911(89)90036-4-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003421_0167-6911(89)90036-4-Figure1-1.png",
        "caption": "Fig. 1. Partial distributed sliding mode of v, + uv~ = 0, on v = exp( - x2).",
        "texts": [],
        "surrounding_texts": [
            "Consider a dynamical system described by a feedback-controlled FOQPDE: ~v~__~ ~ ~v \"~- ' ~ - S i ( v , x , t, u) = b(v , x, t, u) , i = 1 (2.1a) y = h ( v , x, t) (2.1b) 0167-6911/89/$3.50 \u00a9 1989, Elsevier Science Publishers B.V. (North-Holland) where y is the sca lar -valued ou tpu t funct ion, x represents the vector of local spat ia l coord ina te funct ions x i def in ing po in ts on an open set in R\", t denotes time, while u = u(v, x, t) is a d is t r ibu ted feedback cont ro l law taking values in R. The funct ion v is the unknown scalar funct ion, regarded as the d i s t r ibu ted ' s t a te ' of the cont ro l led system. F o r each smooth solut ion v of (2.1), the X, 's are the smooth componen t s of a t ime-varying con t ro l -pa ramet r i zed vector field X, which is assumed to be local ly nonzero and def ined on an open set of R\". The funct ion b : R n + 3 - + R and the funct ion h : R\" \u00f7 3 __, R are local ly smooth funct ions of their arguments . Cond i t ion y = 0 is assumed to local ly def ine an isola ted smooth man i fo ld solut ion v = ~ ( x , t), i.e., h(q>(x, t) , x, t)=-O. The graph of v is assumed to be a smooth t ime-varying surface with local ly nonzero grad ien t except poss ib ly on a set of measure zero. This surface is addressed as the sliding manifold, or the sliding surface, and is local ly def ined as S = {(v , x, t ) ~ R \" + 2 : v=dp(x, t ) } . Al l our cons idera t ions and results are of a local charac te r on a given open set N of R \"+2 descr ibed by the local coord ina te funct ions (v, x, t). The pro jec t ion of such an open set N on to R \"+1 is labe led as M and such a set is equ ipped with local coord ina tes (x , t). Fo r a given smooth feedback funct ion u = u(v, x, t), and a cor respond ing solut ion v of (2.1), the vector field c o l [ S i r , x , t , u ) , 11 is a smooth vector field local ly def ined on M. Definition 1 [1]. G iven an n-d imens iona l surface y in M and a (not necessar i ly smooth) funct ion ~p : y ~ R, the Cauchy data, or the initial condition, of the F O Q P D E (2.1) is cons t i tu ted by the pa i r (~p, y). The n-d imens iona l submani fo ld F in N, represented by the graph of q, on ~,, is called the initial submanifold. Given a smooth feedback funct ion u, an init ial subman i fo ld F is noncharacteristic at the po in t ( x 0, to) in 4', if the vector c o l [ X ( v 0 , Xo, to, U(Vo, x0, to ) ) , 1] in R \"+1 is not tangent to ), at the po in t ( x o, to), with v 0 = \u00a2k(x 0, to). It will be assumed th roughout that for a given smooth d is t r ibu ted feedback cont ro l u(v, x, t) and a given Cauchy da t a ( represented by the noncharacteristic ini t ial cond i t ion subman i fo ld F in R\"+2), the g raph of the solut ion v of (2.1) is local ly smooth, with nonzero g rad ien t everywhere on the open set N where we car ry our cons idera - tions, except, possibly, on a set of measure zero. This a ssumpt ion is sat isf ied in several classical physical examples . (See, for instance, A r n o l d [1], p. 62.) Ava i l ab le to the cont ro l le r is a distributed variable structure feedback switching law: (u+(v , x, t) for y > 0, (2.2) u = ( [ u _ ( v , x, t) f o r y < 0 , with u+(v, x, t) > u-(v , x, t), locally. Defini t ion 2. A d i s t r ibu ted s l iding regime is said to local ly exist on an open set -/ff of the man i fo ld S if and only if the total derivative of the ou tpu t funct ion of the con t ro l led system (2.1)-(2.2) satisfies (see [10]): d y l im d y < 0 and l im - ~ - > 0. (2.3) y ~ +0 d t y ~ - 0 TO simpl i fy no ta t ion we in t roduce the vector z = col(v, x, t) of local coord ina te funct ions and the con t ro l -pa ramet r i zed vector field = c o l [ b ( z , u), X ( z , u), 1] referred to as the characteristic direction field of (2.1). The Lie derivative of a scalar funct ion h(z) with respect to the vector field ~, for a given feedback cont ro l inpu t u = u(z), is de no t e d by L~z.u(z))h or s imply by L~h. In local coord ina tes : L~h = ( S h / S v ) b ( z , u) + ( S h / S x ) X ( z , u) + ah/at. Theorem 1. For a given Cauchy data (~p, \"t) defining an initial submanifold 1\" with nonempty intersection with N, a distributed sliding regime locally exists for system (2.1)-(2.2) on an open set .Ap (-'= N ~ S) of S, if and only if the phase flows corresponding to the controlled characteristic direction field of (2.1), which arise from the initial submanifold q~, exhibit such a local sliding regime on JV\" under the influence of the switching law (2.2). Proof. Suppose a distributed sliding mode locally exists for (2.1)-(2.2) on an open set JV\" of S. Then, the total time derivatives of y, at any point z in N, belonging to the graph of the solution of the controlled equation, can be computed in terms of the directional derivatives along the controlled characteristic direction field ~. These derivatives are given by: f o r y > O: d y = [ S h / b v ] d v / d t + [ Sh /Sx ] d x / d t + [ Sh/Ot ] dt = [Sh /Sv ]b (v , x, t, u +) + [ S h / 3 x ] X ( v , x, t, u +) + [Sh/St] = L ~ ( , . , + ( , ) ) h < O; f o r y < O: d y = [ S h / S v ] d v / d t + [ a h / O x ] d x / d t + [ ah /a t l dt = [Sh /Sv]b (v , x, t, u - ) + [ S h / S x ] X ( v , x, t, u - ) + [Sh/St] = L~(..u-(.))h > O. In other words, the controlled dynamical system described by the following set of ordinary differential equations: dz d-7 = ~ ( ' ' u), (2.4a) y = h ( z ) , (2.4b) (also known as the controlled characteristic equation (2.1)), with initial conditions taking values in F, exhibits a local sliding regime on the open set .,4 r of the sliding manifold S, determined by y = 0, when u is governed by the switching law (2.2). Sufficiency follows easily by assuming that a sliding mode exists for the controlled characteristic system and hypothesizing, at the same time, that a distributed sliding mode does not exist. By reversing the arguments presented above, a contradiction is easily established. [] Local sliding regimes, on subsets of S, of the distributed controlled system (2.1), (2.2) are, hence, completely characterized in terms of the local sliding motions - on the same manifold S - of the finite dimensional time-varying system (2.4) controlled by a switching law of the form (2.2). Theorem 2. A distributed sliding regime exists on an open set ~ of S for system (2.1), (2.2) if and only if there is an open neighborhood N of S in R n+ 2 where ~uL~h * O. (2.5) Proof. If L,h does not depend locally on u then, changing the control u from u+(z) to u - ( z ) at points z of LAP does not have any effect on the sign of L,h. Therefore, there exists an open set N in R n+2, containing ~,r, where the existence conditions (2.3) are violated and a sliding regime can not locally exist on sV'. To proof sufficiency, suppose L~h(z) explicitly depends on u, locally around sV in N. Let e - ( z ) be a smooth, locally strictly positive function of z. Then, by virtue of the implicit function theorem, the equation L , h ( z , u ) = e - ( z ) locally has a unique smooth solution u = u-*(z ) such that = t - ( z ) > O. Similarly, by the same arguments, given a smooth locally strictly negative function e+(z), a smooth control law u = u ~ ( z ) locally exists such that = < 0 . Hence, conditions (2.3) are locally valid around N and a sliding regime exists on the open set dV\" of S for the found distributed variable structure feedback control law: u + ( z l = u + ' ( z ) for h ( z ) > 0, u = u - ( z ) u -~(z ) for h ( z ) < O. [] Definition 3. For all initial states z located on the open set X of S, the unique distributed control function, uEQ(z), locally constraining the distributed trajectories to the sliding manifold S, in the region of existence ~V of the sliding motion, is known as the distributed equivalent control. (i.e., the equivalent control turns the open set ~4 r of S into a ocal integral manifold of the characteristic controlled direction field defined on ~ for some given initial Cauchy data defined on JV'). The resulting characteristic dynamics, ideally con- 180 H. Sira-Ramirez / Distributed sliding mode control strained to S, will be addressed as the characteristic ideal sliding dynamics. (See the original concept in Utkin [10] for ODE's . ) A coordinate-free description of such dynamics in S is: dz d-7 = ~ ( z ' uEQ(z)) , h(z ) = 0 . (2.6) The direction field ~(z, uEQ(z)) will be referred to as the equivalent direction field. Given an arbitrary smooth, noncharacteristic initial n-dimensional submanifold F of the zero output manifold v = ~(x , t), every integral manifold of the equivalent direction field, ~(z, uEQ(z)), is evidently a local solution, specified by v = q~(x, t), of the PDE representing the distributed ideal sliding dynamics: i~v ~ ~v ~ + ~-- -X, (v , x , t, uEQ(v, x, t)) i= 1 iSx~ A necessary and sufficient condit ion for an open set ~V\" of S to qualify as a local ( n + l ) - dimensional integral manifold of the controlled trajectories (2.6) is that the gradient of h be locally poin twise o r thogona l to the s m o o t h equivalent direction field ~(z, uEQ(z)), i.e., L,<:,uEo~z>)h(z ) = 0 for z ~ ,A r. (2.8) For an exposition of the results available for the assessment of the existence of sliding regimes in systems of the general form (2.4), the reader is refered to Sira-Ramirez [7] and to [8,9] for other classes of systems. 3. Example Consider the controlled system described by - v + e x p ( - x ) for-a<x<a, (3.1b) Y = 0 elsewhere. Let w be a given positive constant. The distributed variable structure control law u = w s i g n [ - v + e x p ( - x 2 ) ] , excercised along each possible characteristic, creates a distributed sliding regime on the manifold y = 0 when the controlled motions start from, say, the initial submanifold defined by: r = ((v, x ) :v where (exp[- 2 ] ~(x)= I for --a+~<x<a+~, 0 elsewhere with ~ a given positive constant satisfying ~ > 2a. Figures 1 and 2 depict the nature of the sliding regime creation process on y = 0 by means of the distributed controlled motions of (3.1)."
        ]
    },
    {
        "image_filename": "designv10_8_0002585_tec.2003.811740-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002585_tec.2003.811740-Figure1-1.png",
        "caption": "Fig. 1. Cross-section of induction motor for ME condition.",
        "texts": [
            " Different inductances of induction motor can be calculated based on the multiple coupled circuit model using winding functions, air-gap length and mean radius inverse functions. Obviously, the winding functions of the stator winding and rotor rings of the motor do not change in eccentric conditions compared to the symmetrical condition. However, the inverse functions of the air-gap length and the mean radius will change with respect to the symmetrical case. It is intended to calculate these two functions analytically, which express the geometrical model of the motor. Fig. 1 shows the geometrical model of induction motor for unsymmetrical condition. Referring to Fig. 1, the length and the mean radius of the air-gap inverse functions are as follows: (1) In order to describe the geometrical model of the motor, versus the rotor circumferential angle and the rotation angle in mechanical degree must be calculated. The length of at an angle is obtained by intersection of the rotor circle equation and line, while the rotor has angle with respect to the mechanical reference (stator axes). In order to determine the rotor circle equation in stator frame, the following equation can be written by referring to Fig",
            " In the remaining part, it is shown that if the air-gap mean radius is ignored and instead one term of expansion of series (8) is included, a precise geometrical model is obtained without change of computation time. Therefore: (15) Fig. 5 compares the relative error of this model with mode . As seen, the error of the proposed model is 2 to 3 times lower than other models. IV. INDUCTANCES OF INDUCTION MOTOR FOR ECCENTRICITY CONDITIONS Generally, MMF of the air-gap produced by current of winding at angle in respect to the stationary stator reference is given by (16) Where is the winding function of winding . Referring to Fig. 1, the differential of magnetic flux due to winding which crosses the corresponding air-gap over angle is: (17) Where is the air-gap length, and is the mean radius of the air-gap. The differential of flux-linkage between winding and is calculated as follows: (18) where is the turns function of winding . Taking into account the rotor mechanical angle: (19) If the center lines of stator and rotor are in parallel and the rotor bars are assumed in parallel to the stator center line and symmetric around the center line and symmetric around the rotor cylinder, (19) will be written as: (20) It is noted that generally cannot be replaced by in (20) and this assumption is valid for symmetrical and uniform air-gap"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure20-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure20-1.png",
        "caption": "Fig. 20. Face-gear drive with conical worm: bearing contact at the beginning of the cycle of meshing.",
        "texts": [],
        "surrounding_texts": [
            "The finite element analysis has been performed for a face-worm gear drive with conical worm of common design parameters represented in Table 1. For the analysis the model of the whole worm (Fig. 17) and the whole face-gear (Fig. 18) have been substituted by a model of five-pair of teeth in meshing (Fig. 19) in order to save computational time. Elements C3D8I of first order have been used for the finite element mesh. The total number of elements is 55 672 with 68 671 nodes. The material used is steel with Young\u2019s modulus E \u00bc 206800 N/mm2 and Poisson\u2019s ratio 0.29. The torque applied to the face-gear is 50 Nm. Figs. 20\u201322 show how the bearing contact looks at the beginning, at the middle, and at the end of a cycle of meshing. The results obtained by finite element analysis confirm the longitudinal path of contact and the avoidance of edge contact. Fig. 23 shows the variation of bending and contact stresses on the face-gear from the beginning of the contact to the end of contact on one tooth of the face-gear. The stresses are represented as unitless parameters in function of the worm rotation rm1 \u00bc r1 rmax1 ; \u00f013\u00de rm2 \u00bc r2 rmax2 \u00f014\u00de where r1 and r2 are the bending and contact stresses of Mises and rmax1 and rmax2 are the maximum bending and contact stresses of Mises on the face-gear. In the example developed, rmax1 \u00bc 168 N/mm2 and rmax2 \u00bc 1090 N/mm2. The load is always shared by three pairs of teeth, therefore the contact ratio is 3."
        ]
    },
    {
        "image_filename": "designv10_8_0002890_00006123-200110000-00003-Figure17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002890_00006123-200110000-00003-Figure17-1.png",
        "caption": "FIGURE 17. Schematic illustration of a smart tool for minimally invasive surgery. The sensors would enable the surgeon to distinguish different types of tissue, and the ultrasonic cutting elements and cauterizer would enable precision cuts with minimal nonspecific damage.",
        "texts": [
            " For example, the incorporation of pressure sensors, strain gauges, or biochemical sensors into surgical instruments could enable \u201csmart instruments\u201d that would be able to distinguish different types of tissue with regard to both tissue density and biochemical makeup. Furthermore, the incorporation of MEMS sensors and actuators into surgical instruments could allow for precision cutting or local manipulation of tissue with unprecedented control, thereby minimizing tissue damage. A possible example of such smart tools is illustrated in Figure 17. The use of sensors and actuators that modify, limit, and amplify selected surgeon-generated motions could significantly enhance the surgeon\u2019s precision, accuracy, and speed. This enhancement could be accomplished by the use of systems that, among other things, filter out undesirable repetitive motion (e.g., tremors) while enhancing desirable motion (e.g., precision) and even amplifying other motions (e.g., extension of an instrument such as a microdissection tool under enhanced control). The availability of such smart instruments should also enhance the capabilities of minimally invasive neurosurgical procedures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003784_jssc.200900494-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003784_jssc.200900494-Figure1-1.png",
        "caption": "Figure 1. Selection of appropriate elution solvent for cartridges. C18 cartridge, conditions: sample loaded: 50 mL of 0.2 ppm of Chlorpyrifos and Phosalone standard solutions (A). MWCNT cartridge, conditions: sample loaded: 500 mL of 0.02 ppm of Chlorpyrifos and Phosalone standard solutions (B). Elution solvent volume 4 mL; HPLC mobile phase, water/methanol (20:80 v/v); pH 5 5; flow rate 5 1 mL/min; column, C18 (250 4.6 mm, 10 mm); l5 288.5 nm; room temperature.",
        "texts": [
            "com Effects of some parameters including the type and volume of elution solvent, pH of sample and flow rate of sample through cartridges on extraction efficiency were investigated using C18 and MWCNT cartridges as sorbents. In order to determine the most appropriate elution solvent, five different solvents such as n-hexane, methanol, ethyl acetate, dichloromethane and acetonitrile were investigated for both C18 and MWCNT cartridges. It was found that dichloromethane gave the best recovery among these solvents (Fig. 1). For the determination of suitable volume of elution solvent different volumes (1, 2, 3, 4, 5 and 6 mL) of dichloromethane were used for elution of retained pesticides from cartridges. The appropriate volumes of dichloromethane were 4 mL for C18 and 3 mL for MWCNT cartridge (Fig. 2). Sample pH plays an important role in the SPE procedure because the pH of solution determines the state of analyte in solution as ionic or molecular form, and thus determines the extraction recovery of target analytes",
            "571.5 Tap water C18 5 95.072.0 95.271.9 NDb) NDb) 10 96.571.8 97.271.8 MWCNT 5 97.571.5 98.471.4 NDb) NDb) 10 98.571.2 100.071.0 Conditions as in Table 1. a) Data are shown as mean7SD (n 5 3) b) ND, not detected. Figure 6. Typical chromatograms of pesticides using C18 cartridge: unspiked river water (Shahpour Bridge) sample (A), spiked river water (Shahpour Bridge) sample with 5 mg/ mL of two pesticides (B) and standard mixture of Chlorpyrifos and Phosalone (5 mg/mL) (C). HPLC conditions as in Fig. 1. & 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.jss-journal.com levels (5 and 10 mg/mL) to the real water samples. The recovery percentage of each pesticide was obtained as follows: %R \u00bc A1 A2 A3 100 \u00f02\u00de where A1, A2 and A3 are peak area of spiked, unspiked water sample and standard, respectively. The pesticide contents in water sample and their recoveries for both cartridges are listed in Table 4. Figures 6 and 7 represent typical chromatograms of spiked and unspiked river water (Shahpour Bridge) and standard water samples after extracting using C18 and MWCNT cartridges"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003537_annals.1389.024-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003537_annals.1389.024-Figure6-1.png",
        "caption": "FIGURE 6. Mechanics of the spoke\u2013cp axis. Most of the t-force that develops in an intact flagellum during the beat cycle will be directed across the spoke\u2013cp axis. The components of that force-bearing axis are shown here in isolation. We know almost nothing of the mechanics of this structure that is so strategically positioned to interact with the t-force. Questions that need to be addressed are: (A) Is the spoke shaft extensible and how are its properties changed by the four calmodulin units located on the shaft? (B) Does the spoke head form a bond to the cp projections and, if it does, how mechanically strong is the linkage? (C) Are the cp projections flexible and elastic? How much axonemal distortion is possible without detaching the spoke head from the cp projections? All of these factors will impact the distribution of t-force between the spoke\u2013cp axis and the dynein, and may be the key to understanding the control of the amplitude of the beat.",
        "texts": [
            " This also means that most, or all, of the t-force that develops acts across the central axis as well. Since the radial spokes from doublets 1 and 5\u20136 appear to interact with the cp projections this raises the question of the role of the spoke\u2013cp axis in the distribution of the t-force, as illustrated in FIGURE 4. There are many unanswered questions regarding the role of the spoke\u2013cp axis in managing the t-force. In the context of the Geometric Clutch mechanism this is a crucial issue; the points of major interest are illustrated in FIGURE 6. The flexibility of the cp projections could play a role in governing the distribution of t-force between the dyneins and the spokes. The more the t-force that is carried by the spoke\u2013cp axis, the less t-force the dynein motors will experience; thus, a greater curvature will develop before dynein disengagement occurs. This puts the spokes and cp apparatus in an ideal regulatory position. Release of the spoke head attachments to the cp projections would cause dramatic redistribution of t-force from the spokes to the dyneins",
            " Therefore, the most fundamental issue to be addressed is: 4. Do the spokes form physical attachments to the cp projections, and if they do, how much force can that attachment hold? This is a most fundamental interaction and is a crucial determinant of how the axoneme distributes t-force. We know from the work of Warner and Satir that the spokes readily tilt and the spoke heads translocate to new positions on the cp apparatus as the axoneme bends.42 Remarkably, we know almost nothing else about the spoke head\u2013cp interaction. FIGURE 6 illustrates the components of the spoke\u2013cp axis and properties of that axis that need to be discovered. In a typical bending wave of a sea urchin sperm, the spokes of doublet 1 must experience a t-force of approximately 7pN/ spoke immediately after switching.27 Before the dyneins bridges release, the t-force experienced by the spokes on doublet 1 may even be higher, but will depend on how much the t-force is resisted by the attached dynein bridges. How does the spoke head attachment to the cp projections handle the t-force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003194_0278364904038366-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003194_0278364904038366-Figure2-1.png",
        "caption": "Fig. 2. Top view of the swimming machine (AV) at the University of Minnesota. Only the 30 cm spanned Joukowski foil is submerged in water. The system has four degrees of freedom with only the heaving and pitching motions of the Joukowski foil being directly actuated. The floating mechanism enables the pitching pulley to move independently of the heaving motor.",
        "texts": [
            " The functions \u03c9i(\u03b6 ), i = 1, \u00b7 \u00b7 \u00b7 , 4 and \u03c95(\u03b6, \u03b6k(t)) are given in Appendix A.1. Once the complex potential has been defined, the velocity (u, v) of the fluid particle at location z is given by (Streitlien 1994; Li and Saimek 1999) d\u03c9 dz = d\u03c9 d\u03b6 dF d\u03b6 \u22121 = u\u2212 iv, (3) which, using eq. (2) can be written as d\u03c9 dz = Q1(\u03b6, \u03b61(t), . . . , \u03b6nk (t))   U V \u03b3c \u03b31 ... \u03b3nk   . for some Q1(\u03b6, \u03b61(t), . . . , \u03b6nk (t)) \u2208 1\u00d7(nk+4). Let q = [\u03b1,R, \u03c6, \u03b8] \u2208 4 be the generalized coordinate vector of the AV consisting of the longitudinal, radial, heaving and pitching coordinates (Figure 2). Let M(q) \u2208 4\u00d74 be the positive definite inertia matrix of the AV in these coordinates. The sum of the kinetic energies of the AV and of the surrounding water is then given by T = L 2 \u03c1 \u222b Sv d\u03c9 dz ( d\u03c9 dz ) dA+ 1 2 q\u0307TM(q)q\u0307 (4) where \u03c1 is the density of the water, and L is the out-of-plane dimension (the height) of the foil. The integral in the first term is taken over the complete water area outside the foil and outside any free vortices on the 2D plane. Notice that the foil\u2019s velocities, U , V and , can be expressed linearly with respect to the velocities of the generalized coordinates q\u0307"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002397_095440603762554668-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002397_095440603762554668-Figure1-1.png",
        "caption": "Fig. 1 Experimental equipment of the selective laser melting system",
        "texts": [],
        "surrounding_texts": [
            "F igure 1 shows the SLM system used for the experiment. Initially a powder bed with a thickness of around 0.1 mm is deposited on to the stainless steel base plate attached to the piston. The powder bed is scanned by a pulsed neodymium-doped yttrium aluminium garnet (Nd\u2013YAG) laser head (LUXSTAR), which is attached to an x\u2013y table. The average power of 50 W and the maximum peak power of 3 kW are suf cient energy to melt metallic powder, and the pulsed laser allows many combinations of interaction time and peak power. The laser beam can be carried through the optical bre, and the focused laser beam diameter is 0.8 mm on the powder bed. The rst solid layer is made by the movement of the beam on to the powder bed with a rapid melting and solidi cation process in the chamber continuously lled with argon gas. Then the platform is lowered by 0.1 mm, the next powder layer is deposited and another solid layer is made. By successive scanning and lowering of the platform a three-dimensional model is fabricated. The hatching pattern is shown in Fig. 2. One cycle of the hatching process for reducing distortion of the model and time is as follows: scanning only outline, scanning outline and hatching inside in the x direction, scanning only outline and scanning outline and hatching inside in the y direction. The hatching space is 0.75 mm and the layer thickness is 0.1 mm. Commercial pure titanium powder grade 1 was used in the experiment. The chemical compositions of the pure titanium are shown in Table 1. The powder has a very low amount of hydrogen (three times less the maximum of grade 1 titanium powder) to avoid the embrittlement effect. The powder is made by the induction melting gas atomizing process, which leads to spherical particles. The particle diameter distribution is under 45 mm and the average particle size is 25 mm. The apparent density of the powder is around 64 per cent of the real density."
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.20-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.20-1.png",
        "caption": "Figure 4.20 A concurrent force system.",
        "texts": [
            "8 N (-+) Finally, consider the translational equilibrium of the beam in the y direction: RAy - WI - W2 + Ty = 0 RAy = WI + W2 - Ty RAy = 600 + 400 - 500 = 500 N (t) Now that we determined the scalar components of the reaction Statics: Analyses of Systems in Equilibrium 63 force at A, we can also calculate its magnitude: If a is the angle R A makes with the horizontal, then: a = tan- I (RAY) = tan- I ( 500 ) = 53\u00b0 RAx 376.8 \u2022 The weights of the beam and load on the beam have a com mon line of action. As illustrated in Figure 4.20a, their effects can be combined and expressed by a single weight W = WI + W2 = 1000 N that acts at the center of gravity of the beam. In ad dition to W, we also have R A and T applied on the beam. In other words, we have a three-force system. Since these forces do not form a parallel force system, they have to be concurrent. Therefore, the lines of action of the forces must meet at a single point, say P. As illustrated in Figure 4.20b, if we slide the forces to point P and express them in terms of their components, we can observe equilibrium in the x and y directions such that: In the x direction: In the y direction: RAx = Tx RAy+Ty = W \u2022 The fact that R A and T have an equal magnitude and they both make a 53\u00b0 angle with the horizontal is due to the symmetry of the problem with respect to a plane perpendicular to the xy plane that passes through the center of gravity of the beam. 4.9 Cable-Pulley Systems and Traction Devices Cable-pulley arrangements are commonly used to elevate wei ghts and have applications in the design of traction devices used in patient rehabilitation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.34-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.34-1.png",
        "caption": "Figure 3.34 Problem 3.5.",
        "texts": [
            "33, the fixed and free ends of the beam are identified as A and C, respectively. Point B corresponds to the center of gravity of the beam. Assume that the beam shown has a weight W = 100 N and a length l = 1 m. A force with magnitude F = 150 N is applied at the free-end of the beam in a direction that makes an angle () = 45\u00b0 with the horizontal. Determine the magnitude and direction of the net moment de veloped at the fixed-end of the beam. Answer: MA = 56 N-m (ccw) Problem 3.5 Consider the L-shaped beam illustrated in Figure 3.34. The beam is mounted to the wall at A, the arm AB extends in the z direction, and the arm BC extends in the x direction. A force F is applied in the z direction at the free-end of the beam . (a) If the lengths of arms AB and BC are a and b, respectively, and the magnitude of the applied force is F, observe that the position vector of point C relative to point A can be written as r.. = b i.. +a ~ and the force vector can be expressed as F = F ~, where L j, and ~ are unit vectors indicating positive x, y, and z directions, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure7-1.png",
        "caption": "Fig. 7 Some 3-DOF single-loop kinematic chains involving a PPR virtual chain",
        "texts": [
            " From the geometric condition of legs based on the reciprocity condition a3 , we obtain that the axes of all the R joints within the leg and the virtual chain should be parallel to a plane perpendicular to the axis of the . Considering that the axes of all the R joints within a serial kinematic chains of class b4 is always parallel to a line, one can obtain 3-DOF single-loop kinematic chains composed of a PPR virtual chain and a leg with a 1- -system. The 3-DOF single-loop kinematic chains we ob- 1116 / Vol. 127, NOVEMBER 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 tained are, respectively, composed of two serial kinematic chain of classes b4 see Figs. 7 e and 7 f . In Fig. 7, joints marked by a same number, 1 or 2, comprise one serial kinematic chain with specific characteristics. The axes of the R joints in each of the 3-DOF single-loop kinematic chains are always parallel to two different lines which further determine one plane. The leg-wrench system is a 1- -system which is composed of all whose axes are perpendicular to the axes of all the R joints. The 3-DOF single-loop kinematic chains we obtained fall into the following four classes see Fig. 7, for example : a Single-loop kinematic chains formed by a serial chain of class b2 and a serial chain of class b3 Figs. 7 a and 7 b . b Single-loop kinematic chains formed by one serial chain of class b4 Fig. 7 c . c Single-loop kinematic chains formed by a serial chain of class b1 and a serial chain of class b3 Fig. 7 d . d Single-loop kinematic chains formed by two serial chain of class b4 Figs. 7 e and 7 f . In the representation of the types of 3-DOF single-loop kinematic chains involving a virtual chain Fig. 1 , PPR-equivalent parallel kinematic chains, PPR-equivalent PMs and their legs, X denotes a P or an R joint, PP N denotes two successive P joints whose directions are parallel to the virtual plane. XXX N denotes three successive X joints in which the axes of all the R joints are perpendicular to the virtual plane and the directions of all the P Transactions of the ASME 3 Terms of Use: http://asme",
            " Theoretically, any six R and P joints the twists of which are linearly independent together with a PPR virtual chain constitute a 3-DOF single-loop kinematic chain. 7.3 Type Synthesis of Legs for PPR-Equivalent Parallel Kinematic Chains. The type of a leg for PPR-equivalent parallel kinematic chains can be represented by a chain of characters representing the type of joints from the base to the moving platform in sequence. By removing the virtual chain in a 3-DOF single-loop kinematic chain involving a virtual chain, one leg for PPR-equivalent PMs can be obtained. For example, by removing the virtual chain in an RRR N RR IV kinematic chain Fig. 7 d , an RRR N RR I leg Fig. 8 d can be obtained. Figure 8 shows some legs for PPR-equivalent parallel kinematic chains and their leg-wrench systems. The leg-wrench system of the RRR NRa leg Fig. 8 b is a 1- 0-1- -system. Its basis can be represented by a rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 whose axis is perpendicular to the axes of all the R joints within a same leg and a 0 whose axis intersects the axes of the Ra joint and is parallel to the axes of the R joints within RRR N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003570_tsmc.1980.4308518-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003570_tsmc.1980.4308518-Figure8-1.png",
        "caption": "Fig. 8. Motion in space with locked joint.",
        "texts": [
            " (8) If the motion in space is to be studied, one may use the approach in [12] as follows. a) Set F2, F3, and F4 equal to zero in (Al)-(A9) in the Appendix, and call the resulting equations space equations (SEQ). b) From SEQ and the constraints (8) compute, as in [12], the forces of constraint rF =rF(X, U) (9) where vector U consists of gravity and torque actuators u2 and U3 at the hip, as shown in the Appendix. The resulting system is shown in Fig. 7(b). Equations (9) and (1): X=f(X, U,rI0, 0,0) describe the motion of the system. Case 2-Locked Joint in Space (Fig. 8(a)) Suppose the right leg is turned 90\u00b0 and is prevented from further rotation by the appendage. Further, it is pressed against the appendage by some of the component muscles of u2. This is a very simple case by which the locking mechanism is explained. The actual locking mechanisms of the body are, of course, much more complex and interesting. For example, the knee joint lock is a screw structure [17]-[20]. The present model also demonstrates one important feature of the lock: it is possible to maintain the constraint by the action of a subset of muscles involved while other muscles that are instrumental in bringing the limb to the locked position may rest [13], [19]. When the lock is in effect, in addition to F1, the forces F2 are also active F2= (F6G6)T. (10) In addition to the four constraints of (8), the following two constraints hold: X2- k2sin92- (d2+ e)coso2-x1 - (1I - k1 - e)sinO1 =0 Y2-k2cos02+ (d2+ e)sino2-Yl - (11- k - e)cos91 =0. (I 1) Analogous to Case 1, one may compute Fl =F(X, U) F2=F2(X. U). (12) The system model is shown in Fig. 8(b). The transition from unlocking to locking and vice versa are analogous to Cases 3 and 6 below. Since (8) are always satisfied a simpler alternative for the locking constraint (11) is possible. Equations (8) and (11) may be combined to derive a single constraint for the locking condition: 01- 02 = 7r~1 22 If this formulation is used, the corresponding force has one component Y2: F6= Y2sin02 G6= Y2cos 02 Case 3- One Leg Landing (Fig. 9(a)) The model descends to the ground on point A, and this point is immobilized instantaneously both in x and y directions, at the point of contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003225_j.euromechsol.2005.02.004-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003225_j.euromechsol.2005.02.004-Figure9-1.png",
        "caption": "Fig. 9. Kinematic structure of Isoglide 4 T3R1-v1.1 (a) and its associated graph (b).",
        "texts": [
            " 8 is fully-isotropic (Carricato and Parenti-Castelli, 2002) and it was developed by the Department of Mechanical Engineering at the University of California (Kim and Tsai, 2002) under the name of PCM and by the Department of Mechanical Engineering at the University of Laval under the name of Orthogonal Tripteron (Gosselin et al., 2004). Kim and Tsai (2002) have shown that Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s mobility criterion does not work for this parallel mechanism. Example 2. The parallel mechanism C \u2190 A1\u2013A2\u2013A3\u2013A4 in Fig. 9 is obtained by parallel concatenation of 4 elementary legs A1 (1A \u2261 0\u20132A\u2013 \u00b7 \u00b7 \u00b7\u20136A), A2 (1B \u2261 0\u20132B\u2013 \u00b7 \u00b7 \u00b7\u20135B), A3 (1C \u2261 0\u20132C\u2013 \u00b7 \u00b7 \u00b7\u20136C) and A4 (1D \u2261 0\u20132D\u2013 \u00b7 \u00b7 \u00b7\u20136D). We can see by inspection that: (RA1 ) = (vx,vy,vz,\u03c9x,\u03c9y), (RA2) = (vx,vy,vz,\u03c9y), (RA3 ) = (vx,vy,vz,\u03c9y,\u03c9z), (RA4 ) = (vx,vy,vz,\u03c9y,\u03c9z) and SAi = 5, i = 1,3,4 and SA2 = 4. The spatiality of the mobile platform given by Eq. (47) is SC 6/1 = dim(RA1 \u2229RA2 \u2229RA3 \u2229RA4) = 4, that is four relative independent velocities (vx,vy,vz and \u03c9y) exist between the mobile and reference platforms. The mechanism has 15 revolute and 4 prismatic joints ( \u2211m i=1 fi = 19). The number of joint parameters that lost their independence in the parallel robotic manipulator in Fig. 9 given by Eq. (57) is r = rC = 5 + 4 + 5 + 5 \u2212 4 = 15. The mobility of the parallel robotic manipulator given by Eq. (62) is MC = 19 \u2212 15 = 4. Four variables qi of the prismatic joints connecting each leg to the reference element are used to command the position and the orientation of the mobile platform. The parallel robotic manipulator T3R1-type presented in Fig. 9 represents a solution of a family of modular parallel robotic manipulators with 2\u20136 degrees of freedom and decoupled motions, proposed by the author of this paper, and developed under the name \u201cIsoglide\u201d, by the research team MMS (Mechanisms, Machines and Systems) of the French Institute of Advanced Mechanics. Example 3. The parallel manipulator in Fig. 10 (Gogu, 2004) is a parallel mechanism D \u2190 E1\u2013E2\u2013E3 with three complex legs. A planar parallelogram loop is serially concatenated in each leg. We can see by inspection that: (RE1) = (vx,vy,vz,\u03c9y), (RE2) = (vx,vy,vz,\u03c9z), (RE3) = (vx,vy,vz,\u03c9x) and SEi = 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002591_978-94-017-0657-5_3-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002591_978-94-017-0657-5_3-Figure5-1.png",
        "caption": "Figure 5. Manipulator with a misaligned X actuator.",
        "texts": [
            " For all the cases, the average stiffness becomes higher around the Z actuator. From the distribution point of view, Arrangement III is better than the others. In practice, it may be difficult to fabricate and assemble a perfect orthogonal frame. In this section, we illustrate a method for compensating manufacturing and assembling errors of the linear actuators by one example. We assume that the X actuator is twisted by a small angle /),.8 about the Z axis, and the other actuators are mounted perfectly along the Y and Z axes as shown in Fig. 5. When the X and Z actuators are held stationary, the dotted line in Fig. 6 denotes the possible locus of B2 \u2022 Hence, if the revolute joint axes of the X limb remain parallel to the prismatic joint as shown in Fig. 6 (a), the x, y, and z motions of the moving platform will be coupled. The coupling problem can be solved by adjusting the revolute joint axes such that they are all parallel to the X axis as shown in Fig. 6 (b). It should be noted that the three revolute joint axes in each limb should be parallel to one another, otherwise, this manipulator may not move or generate pure translational motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002710_70.681244-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002710_70.681244-Figure1-1.png",
        "caption": "Fig. 1. Parallel manipulator.",
        "texts": [
            "ndex Terms\u2014 Direct kinematic problem, guaranteed computations, interval arithmetic, nonlinear equations, parallel manipulator. I. INTRODUCTION PARALLEL manipulators have been increasingly studied since the introduction of the concept by McGough in 1947 [1], [2]. Solving the direct kinematic problem for this type of systems is known to be difficult, to the point that it has become a benchmark example for both symbolical and numerical computation [3]\u2013[6]. Consider the parallel manipulator shown in Fig. 1, with six limbs articulated with universal joints at the base and spherical joints on the mobile plate. Such a system is often called a Stewart\u2013Gough platform [7], [8]. The position of the mobile plate is controlled by acting on the lengths of the limbs. The direct kinematic problem, i.e., the computation of all possible positions of the mobile plate from the knowledge of the lengths of its limbs and geometry of the base and mobile plate, is not completely solved, except for some special geometric configurations [1], [5], [9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002576_s0094-114x(97)00101-8-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002576_s0094-114x(97)00101-8-Figure3-1.png",
        "caption": "Fig. 3. Coordinate systems for the bevel gear generation mechanism.",
        "texts": [
            " 2, the tooth surface of the imaginary generating gear can be represented as follows: Q 360 \u00ff fc fe 2 ; 2 S 2e sin fe 2 ; 3 and R2 x2 y2 z2 8<: 9=; S cosQ x1 \u00ffS sinQ y1 z1 8<: 9=;; 4 where fe is the cradle angle and is one of the machine settings for the Gleason hypoid grinder; fe is the eccentric angle and is also a machine setting; e is the machine eccentric constant, and e = 8 inches for the Gleason No. 463 hypoid grinder; S, is the basic radial distance setting; Q, is the basic cradle angle setting; and x1, y1 and z1 are the surface coordinates of the cupshaped grinding wheel represented in Equation (1). As shown in Fig. 3 [20], coordinate systems S2(x2, y2, z2), S3(x3, y3, z3), S4(x4, y4, z4), S5(x5, y5, z5), and S6(x6, y6, z6) are rigidly attached to the cradle, machine frame, sliding base, work head, and workpiece, respectively. Therefore, the locus of the imaginary generating gear represented in the workpiece coordinate system S6 can be obtained by applying the following coordinate transformation matrix equation: R6 M65 M53 M32 R2; 5 where M65 1 0 0 \u00ffDx 0 cos xw \u00ffsin xw 0 0 sin xw cos xw 0 0 0 0 1 26664 37775; M53 cos gm 0 sin gm \u00ffEs sin gm 0 1 0 \u00ffEv \u00ffsin gm 0 cos gm Es cos gm 0 0 0 1 26664 37775; M32 cos xc sin xc 0 0 \u00ffsin xc cos xc 0 0 0 0 1 0 0 0 0 1 26664 37775; xc, is the cradle rotational angle; xw, is the work spindle rotational angle; gm, is the machine root angle; Dx, is the increment of machine center to back; Es, is the sliding base setting; and Ev, is the vertical o set setting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003722_02640410601113239-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003722_02640410601113239-Figure5-1.png",
        "caption": "Figure 5. Plane between two consecutive club positions (adapted from Neal & Wilson, 1985).",
        "texts": [
            " This was especially important as it is the velocity vector of the clubface just before impact (together with clubface orientation) that is critical to postimpact ball flight, and any swing plane is simply a method to ensure correct size and direction of this vector. The position of the club in two consecutive frames generated four sets of three-dimensional coordinates (handle and clubface markers in each frame). As the definition of a plane requires only three sets of coordinates, it was possible to generate a simple \u2018\u2018plane of best fit\u2019\u2019 for the four sets of coordinates from the two consecutive frames (Figure 5). Therefore, 100 separate planes of best fit could be created from each set of normalized frames for the downswing. Horizontal angle (a) and angle to target (b) line could then be computed from the equations of these planes in an identical manner as that described for the single plane for the whole downswing, and the time-course of these angles could be examined for consistency or change. It was noted that when the club was moving very slowly at the start of the downswing, the planes of best fit generated were very inconsistent for most golfers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.22-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.22-1.png",
        "caption": "Figure 4.22 Pulley and load.",
        "texts": [
            "9 Cable-Pulley Systems and Traction Devices Cable-pulley arrangements are commonly used to elevate wei ghts and have applications in the design of traction devices used in patient rehabilitation. For example, consider the simple ar rangement in Figure 4.21 where a person is trying to lift a load through the use of a cable-pulley system. Assume that the per son lifted the load from the floor and is holding it in equilibrium. The cable is wrapped around the pulley, which is housed in a case that is attached to the ceiling. Figure 4.22 shows free-body diagrams of the pulley and the load. r is the radius of the pulley and 0 represents a point along the centerline (axle or shaft) of the pulley. When the person pulls the cable to lift the load, a force is applied on the pulley that is transmitted to the ceiling via the case housing the pulley. As a reaction, the ceiling ap plies a force back on the pulley through the shaft that connects the pulley and the case housing the pulley. In other words, there 64 Fundamentals of Biomechanics exists a reaction force R on the pulley. In Figure 4.22, the reaction force at 0 is represented by its scalar components Rx and Ry. The cable is wrapped around the pulley between A and B. If we ignore the frictional effects between the cable and pulley, then the magnitude T of the tension in the cable is constant every where in the cable. To prove this point, let's assume that the mag nitude of the tensile force generated in the cable is not constant. Let TA and TB be the magnitudes of the tensile forces applied by the cable on the pulley at A and B, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure10.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure10.15-1.png",
        "caption": "Figure 10.15. Gas injection system for metallo-organic precursors. The precursor is evaporated through the capillary (1) pointing to the deposition spot. The reservoir (2) holds the precursor and is heated and cooled, respectively, by the Peltier element (3). It shifts the heat between reservoir and thermal mass (4); the temperature can be controlled by a sensor (5). The GIS hole can be positioned and oriented towards the substrate using the mobile platform (6).",
        "texts": [
            " The diameter of the capillary has to be chosen small enough to allow the vacuum system of the SEM to reach the system\u2019s operating pressure, but wide enough to allow sufficient precursor flux. If the diameter chosen is too wide, the vacuum pumps will evacuate the reservoir to a considerable extent, until operating pressure is reached. 10.4.3.2 Heating/Cooling Stages In order to overcome the above disadvantages of constant evaporation stages, gas injection systems, using Peltier elements for heating and cooling the precursor reservoir, have been developed. In Figure 10.15, a gas injection system for metallo- Nanostructuring and Nanobonding by EBiD 325 organic precursors is shown. The precursor fills the reservoir, which is sealed by a rubber o-ring between reservoir and cap. A steel capillary with length 40 mm and an inner diameter of 0.6 mm is connected to the reservoir. Heating and cooling, respectively, of the reservoir can be achieved by shifting heat between the thermal mass and the reservoir. In order to control the temperature of the reservoir, a temperature sensor has been built between the reservoir and the Peltier element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002501_icpr.1996.546041-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002501_icpr.1996.546041-Figure2-1.png",
        "caption": "Figure 2. The geometry of a screw: Every motion can be modeled as a rotation with angle 0 about an axis at c'with direction rand a subsequent translation d along the axis.",
        "texts": [
            " As the screw axis is a line in space it depends on four parameters which together with the rotation angle 8 and the translation along the axis d (pitch) constitute the six degrees of freedom of a rigid transformation. In the following we will solve the problem Compute d as well as the screw_axis gzven by its direction and moment pair ( I , & ) from R and t'. The direction i i s parallel t o the rotation axis. The pitch d is the projection of translation on the rotation axis, therefore equal trz In order to recover the moment & we introduce a point c'on the screw axis being the projection of the origin on the axis (Fig. 2). The coordinate system is shifted to this point and then transformed. The resulting translation is then d r + ( I - R)Z. The so called pitch d = pi? Using the Rodrigues formula RZ= E++ s in (e ) ix c'+ (1 - cos ~ ) l ' x ( i ' x 4 and Z T r = 0 it follows that [l] (9) 1 0 - 2 2 c'= -(F- (Z9jT-t cot - I x q. This point and hence the screw axis is not defined if the angle 0 is either 0 or 180. Otherwise the moment vector reads then - 1 B 2 2 ?6 = z x I = - ( T x r+ i x ( t 'x 0 cot -). (10) We proceed then with the computation of the corresponding quaternion: 4 Gzven the screw parameters ( 8 , d , I , 6) compute the correspondzng dual quaternzon d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.11-1.png",
        "caption": "Figure 3.11 Component of F .",
        "texts": [
            " \u2022 The moment of a force about a point that lies on the line of action of the force is zero, because the length of the moment arm is zero (Figure 3.10). \u2022 A force applied to a body may tend to rotate or bend the body in one direction with respect to one point and in the opposite direction with respect to another point in the same plane. \u2022 The principles of resolution of forces into their components along appropriate directions can be utilized to simplify the cal culation of moments. For example, in Figure 3.11, the applied force F is resolved into its components Ex and F y along the x and y directions, such that: Fx = F cosO Fy = F sinO Since point 0 lies on the line of action of F x' the moment arm of F x relative to point 0 is zero. Therefore, the moment of F x about point 0 is zero. On the other hand, r is the length of the moment arm for force F relative to point O. Therefore, the moment of force F y about point 0 is: M = r F y = r F sin 0 (cw) Note that this is also the moment dF generated by the resultant force vector F about point 0, because d = r sinO"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002795_0932-4739-00854-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002795_0932-4739-00854-Figure1-1.png",
        "caption": "Fig. 1. Cross sectional diagram of filter feeding in choanoflagellates, showing some of the measures used in this paper. H is the mid-point of the cell above a boundary, A is the radius of the cell protoplast and L the length of the flagellum. \u03bb is the wavelength and \u03b2 the amplitude of the wave. Grey lines show direction of fluid flow, grey spheres indicate the manner and sites of bacterial capture and ingestion.",
        "texts": [
            " Balancing forces over a control volume and using slender body theory allows estimates of pressure drop across the collar of the three species of choanoflagellate to be made. The magnitude of pressure drop (\u2206p) was found to be consistent with previous publications, suggesting that \u2206p may be a constraining parameter for filter feeders. Key words: Choanoflagellates; Fluid Flow; Pressure Drop; Slender Body Theory; Viscous Eddies; Food particle filtration. they may be responsible for the majority of the grazing pressure exerted on the bacterial standing stock (Fenchel 1982). The basic mechanism of filter feeding, common to all choanoflagellates, is illustrated in Figure 1. The round or ovoid protoplast (cell), typically 10\u201320 \u00b5m in length, is modified at the distal end into a crown, or collar like structure. The radially symmetrical collar is formed from a palisade of identical microvilli, the number and length of 0932-4739/02/38/04-313 $ 15.00/0 The Choanoflagellida, or choanoflagellates, are single celled heterotrophic nanoflagellates of the phylum Choanozoa (Cavalier-Smith 1993). These organisms are widely distributed geographically and representatives of the group can be found in most aquatic habitats",
            " Higdon describes the choanoflagellate by a limited number of parameters. The spherical cell body radius (A), and the radius (a) and length (L) of the smooth cylindrical flagellum are used to geometrically model the flagellate. The cell body is situated at a height (H) above the surface to which the cell is attached. The flagellar motion is defined as a sinusoidal wave in terms of the amplitude (\u03b2), the wavelength (\u03bb) and the total number of waves (N) occurring over the length of the flagellum (see Fig. 1). Using these parameters, Higdon determined the velocity field and power consumption for a cell with varying L/A, a/A and H/A ratios. Varying these ratios allowed Higdon to determine the theoretical optimal configuration of cellular dimensions and flagellar waveform. The present paper attempts to verify, or refute, the optima identified by Higdon (1979b), by comparing them to measurements on the cellular parameters and flagellar waveforms of three species of choanoflagellates. Liron and Blake (1981) also employed \u2018stokeslets\u2019 to determine the occurrence, number and shape of viscous eddies generated by point forces near solid boundaries"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002468_s0003-2670(02)00334-3-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002468_s0003-2670(02)00334-3-Figure1-1.png",
        "caption": "Fig. 1. Single-chip electrode set.",
        "texts": [
            " The N-tris(hydroxymethyl)methyl-2-aminoethanesulfonic acid (TES) was provided by Dojindo Labs (Kumamoto, Japan). The -aminopropyltriethoxysilane ( -APTES) was provided by Shinetsu Chemical Industries of Tokyo, Japan. The Nafion\u00ae was provided by Aldrich (Milwaukee, WI, USA), in the form of a 5% (w/w) solution. The PFCP was polymerized from ethylene, and a PFCP solution was prepared in perfluorocarbon (C8F18) [3]. All reagents were of analytic grade. The single-chip electrode set we used to construct our Ag/AgCl QREs and glucose sensors is shown in Fig. 1 [2,3]. It consists of a WE (7.18 mm2 in area) made of platinum, a Ag/AgCl QRE (1.39 mm2 in area) made of silver/silver chloride, and a CE (3.55 mm2 in area) made of platinum, all fabricated on a single quartz substrate. The WE and CE consist of a 300 nm thick platinum layer on a 100 nm thick titanium layer. The reference electrode was formed by depositing a 300 nm thick silver layer on a 100 nm thick titanium layer, and then chlorinating the silver layer surface with a 50 mM concentration of iron chloride (pH 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.30-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.30-1.png",
        "caption": "Figure 4.30 Free-body diagram of the beam.",
        "texts": [
            " For example, consider the translational equilibrium of the beam in the y direction: Now, consider the rotational equilibrium of the beam about A (a) (b) (c) w w w and assume that counterclockwise moments are positive: M-lP=O M=l P Note that the reactive moment with magnitude M is a \"free vector\" that acts everywhere along the beam. Example 4.5 Consider the uniform, horizontal beam shown in Figure 4.29. The beam is fixed at A and a force that makes an angle fJ = 30\u00b0 with the horizontal is applied at B. The magnitude of the applied force is P = 100 N. C is the center of gravity of the beam. The beam weighs W = 50 N and has a length l = 2 m. Determine the reactions generated at the fixed end of the beam. Solution: The free-body diagram of the beam is shown in Figure 4.30. The horizontal and vertical directions are indicated by the x and y axes, respectively. Px and Py are the scalar components of the applied force P. Since we know the magnitude and direction of.E., we can readily calculate Px and Py: Px = P cosfJ = (100)(cos60) = 50.0 N (+x) Py = P sin fJ = (100)(sin 60) = 86.6 N (+y) In Figure 4.30, the reactive force R A at A is represented in terms of its scalar components RAx and RAy. We know neither the mag nitude nor the direction of RA (two unknowns). We also have a reactive moment at A with magnitude M acting in a direction perpendicular to the xy-plane. While drawing the free-body diagram, we assumed that this moment is counterclockwise with respect to the xy-plane. In this problem, we have three unknowns: RAx, RAy, and M. To solve the problem, we need three conditions. First, consider the translational equilibrium of the beam in the x direction: -RAx + Px = 0 RAx = Px = 86"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002488_j.1460-2687.2001.00073.x-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002488_j.1460-2687.2001.00073.x-Figure1-1.png",
        "caption": "Figure 1 Schematic of deformed shape of thin-walled shell after snap-through buckling. Contact region previously was \u00afattened but after a critical de\u00afection, snap-through occurs in the form of an inverted spherical cap.",
        "texts": [
            " Hubbard, Department of Mechanical & Aeronautical Engineering, University of California-Davis, Davis, CA 95616, USA. E-mail: mhubbard@ucdavis.edu Deformation of a thin elastic spherical shell Updike & Kalnins (1970, 1972) developed a thin shell analysis for deformations, stresses, pressure and resultant force in an elastic spherical shell that is compressed against a \u00afat surface. With increasing compression the shell wall undergoes a sequence of three distinct patterns of deformation, two of which are illustrated in Fig. 1: (a) an initial stage of small de\u00afection in which the shell \u00afattens against the surface with de\u00afection d; (b) after the de\u00afection exceeds a critical value dc, buckling or snap-through of the cap occurs into the interior of the shell with central de\u00afection x; (c) at even larger de\u00afections circumferential buckling of the inverted cap occurs into a set of three or four lobes. Only the \u00aerst two of these patterns are considered herein. The de\u00afection at which the \u00aerst stage of buckling occurs depends on the ratio of shell radius to wall thickness R/h, the elastic modulus E and any internal pressurization pg",
            " Steele (1988) showed that although signi\u00aecant circumferential strain can develop in the knuckle, this region contains only a small part of the volume of the deformed region if the shell is thin; hence circumferential knuckle stretching \u00d3 2001 Blackwell Science Ltd \u00b7 Sports Engineering (2001) 4, 49\u00b161 51 makes only a higher order contribution to the total strain energy of deformation. As the thickness of the shell increases, the knuckle region increases in size and signi\u00aecance. Thus for this second phase of deformation we assume a deformed con\u00aeguration that consists of the original or undeformed shell with an inverted spherical cap of opposite curvature (see Fig. 1). For the related problem of shell indentation by a concentrated force acting at the crown, Steele (1988) obtained the de\u00afection x at the crown of the shell as x h 2d h K\u0302 F b 2 ; 2 where K\u0302 8 3p 2 3 1\u00ff m2 q 1:19 for m 0:3: 3 This expression was obtained by relating the strain energy of bending in the knuckle to the work done by the force at the crown. The analysis can be improved by including the geometric nonlinearity in edge bending (Ranjan & Steele 1980; Steele 1989). This has the effect of reducing the shell stiffness by 20% and it can be included in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003382_bi00328a001-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003382_bi00328a001-Figure4-1.png",
        "caption": "FIGURE 4: Proposed stable states of galactose oxidase. Of the four possible states only the E.Cu*,, state is active. Furthermore, the existance of any transient states which might occur during turnover is not addressed in this model. See text for further discussion.",
        "texts": [
            " Several facts support the hypothesis that the enzyme can exist in active and inactive states. Even though, as isolated, galactose oxidase has been shown to be nearly 100% in the Cu(I1) form, we speculate that this is a necessary requirement but not sufficient for galactose oxidase to be catalytically active. The fact that, in the absence of oxidants, catalytic lags are observed upon addition of substrate to solutions of galactose oxidase suggests that turnover may be autocatalytic. That is, some small portion of the enzyme might already exist in the active Cu*,, state (see Figure 4), and turnover by active enzyme elevates inactive Cu, enzyme to active Cu*,, enzyme. However, as turnover continues, enzyme can still drop into the C U * ~ state which is also inactive as indicated by the fact that galactose oxidase can be essentially shut off during turnover by adjusting the solution potential to about 240 mV vs. SHE. Oxidants, then, have their effect on steady-state catalytic activity because they maintain a high ratio of Cu*, to C U * ~ during turnover. Furthermore, we hypothesize that the CU*,,/CU*,~ E'\" is higher than the Cu,,/Curd E'\""
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002852_s0022112005006373-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002852_s0022112005006373-Figure2-1.png",
        "caption": "Figure 2. Conventions used and geometrical properties of the disks.",
        "texts": [
            " In this latter case, a few theoretical analyses have attempted to extract the physical mechanisms (Stong 1968; Crane 1988; Bocquet 2003) and recently, three of us have published the first quantitative experimental results on the first bounce (Clanet, Hersen & Bocquet 2004). This study has motivated extensive numerical simulations (Nagahiro & Hayakawa 2005; Yabe et al. 2005). Here, we first complete our previous results by showing the skipping stone domain in a general phase diagram. Then, we extend the study to several skips and determine the origin of the dissipation responsible for the end of the skipping. The conventions used throughout the article are presented in figure 2: a model stone of thickness h and radius R has a translation velocity U and spinning velocity \u2126 \u2261 \u2126n, where n is the unit vector normal to its surface. The orientation of the . stone is defined by the attack angle \u03b1 such that cos \u03b1 \u2261 n \u00b7 ez, where ez is the unit vector normal to the unperturbed water surface. The direction of motion of the stone is defined by the impact angle \u03b2 such that cos \u03b2 \u2261 U \u00b7 ex , where ex is the unit vector tangent to the water surface. An experimental setup has been designed to control independently \u2126 , U , \u03b1 and \u03b2 . The collision of the stone with water is recorded using a high-speed video camera (Kodak HS4540). Most of the experiments are conducted with an aluminium stone, that is with the stone (s) to water (w) density ratio: \u03c1s/\u03c1w \u2248 2.7. The geometrical characteristics of the stones are presented in figure 2. 3.1. A single skip 3.1.1. Chronophotography Chronophotography of a typical collision sequence is presented in figure 3. The collision time \u03c4 is measured on such graphs as the time during which the stone is in contact with water: as an example we measure \u03c4 \u2248 32 ms in figure 3. We also observe that under these conditions of large spin velocity, the attack angle \u03b1 remains constant during the whole impact process. Finally, the cavity created is not symmetrical: it exhibits a larger curvature close to the impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002706_tac.2002.802750-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002706_tac.2002.802750-Figure1-1.png",
        "caption": "Fig. 1. General n-trailer system.",
        "texts": [
            " This work was supported by the Swedish Foundation for Strategic Research through the Center for Autonomous Systems at the Royal Institute of Technology (KTH). The author was with the Division of Optimization and Systems Theory, Royal Institute of Technology, Stockholm SE 10044, Sweden. He is now with the SISSA-ISAS, International School for Advanced Studies, 34014 Trieste, Italy (e-mail: altafini@sissa.it). Publisher Item Identifier 10.1109/TAC.2002.802750. II. KINEMATIC MODEL FOR THE GENERAL n-TRAILER AND FRENET FRAMES Suppose we have a general n-trailer system with m (m n) of the trailers hooked at a distance Mi from the preceding axle; see Fig. 1. Assume that each body is composed of one single axle. The nonholonomic constraints on the points Pi (below called nonholonomic points) originate from the assumption of rolling without slipping of the wheels. If we call n1; . . . ; nm, nj < nj+1, nm < n the indices of the axles having nonnull off-hitching (Mn 6= 0) we can group together the axles between two consecutive kingpin hitchings: f0; 1; . . . ; n1g; . . . ;fnj 1+1; nj 1+2; . . . ; nj 1; njg; . . . ;fnm+ 1; nm + 2; . . . ; n 1; ng. We do not consider the case of two consecutive axles having off-hitching"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003433_1.2164476-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003433_1.2164476-Figure1-1.png",
        "caption": "FIG. 1. Schematic diagram of laser cladding process.",
        "texts": [
            " In this article, an analytical model is presented to compute the attenuation of the laser energy by powder stream based on classic physical optics theories, and to compute the heating of the powder particles by the radiation of the laser beam according to the heat equilibrium principle. The effects of the powder feeding rate and the powder feeding angle on the temperature distribution and the laser intensity distribution are studied for a practical case under a given stream spread and speed of powder particles. II. INTERACTION BETWEEN THE LASER BEAM AND THE POWDER STREAM Figure 1 shows the laser cladding process studied in this article. The origin of the coordinates, O, is fixed at the laser spot center, the nozzle has an obliquity, , with the horizontal surface, and the half spreading angle of the powder stream is . O is a virtual feeding origin for the convenience of computing, which has the distances of S and H from the origin O in the horizontal and vertical directions, respectively. The nozzle can be adjusted to give different feeding angles. To develop a model of interaction between the laser beam and powder stream, the following assumptions are made: 1 The laser beam has no divergence or convergence in the interaction region; 2 The powder particles are spherical; 3 The particle concentration in the powder stream is a Gaussian distribution in the direction perpendicular to the nozzle centerline; 4 The effect of gravity and drag exerted by the surrounding gas on the powder flight is neglected and all the particles have the same constant velocity; and 5 The intraparticle temperature gradient is neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003694_jst.65-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003694_jst.65-Figure2-1.png",
        "caption": "Figure 2. Measurement setup of the rowing simulator: instrumented single scull placed inside the Cave.",
        "texts": [
            "com & 2008 John Wiley and Sons Asia Pte Ltd Sports Technol. 2008, 1, No. 6, 257\u2013266258 Research Article J. von Zitzewitz et al. actual length (lR) of the unwound rope can be measured for a given winch diameter (dW). Furthermore, three incremental wire potentiometers (4 cts/mm) lead from the ground and from the sculling rigger to the oar. With this sensor configuration, the spatial orientation of the oar, as well as the oar displacement in the direction of its longitudinal axis, can be measured (Figure 2). The position of the boat seat (xS) is measured by a further incremental wire potentiometer (4 cts/mm). In general, a model for virtual rowing is driven by measured variables, which reflect the rower\u2019s performance. The model output controls the displays presented to the user. In our setup, a haptic, visual, and acoustic display are integrated. Our model inputs are the three oar angles y (in the horizontal plane), d (in the vertical plane), and f (around the longitudinal oar axes), and the seat position xS (Figure 3) summarized in the vector k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003257_tmag.2006.875352-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003257_tmag.2006.875352-Figure4-1.png",
        "caption": "Fig. 4. Three-phase SRG: (a) with neutral connected; (b) without neutral.",
        "texts": [
            " The prime mover moment applied to the SRG causes the variation of the phase inductance . If the rotation speed is close to the resonant frequency 0018-9464/$20.00 \u00a9 2006 IEEE of the RLC circuit, the oscillation makes a start. The generator has no need for any additional energy source (e.g., an accumulator or a battery) to produce electrical power. Two main circuits for the implementation of an autonomous ac three-phase generator that is based on SRG are considered. There is a Y\u2013Y connection with neutral [Fig. 4(a)] and a Y\u2013Y connection with isolated neutral [Fig. 4(b)]. The connection of the capacitor bank in Fig. 4(b) could be changed to due to the linear properties of the capacitors. The SRG has no magnetic coupling between its phases [9]. This property suggests us to consider the three-phase autonomous reluctance generator as a set of magnetically and electrically decoupled circuits with a balanced load. Therefore, all theoretical approaches that were employed for single-phase SRG are also valid for the three-phase SRG with neutral. As a result, the numerical simulations of the three-phase switched reluctance generator and the single-phase switched reluctance generator are similar [see (1)]",
            " 5(b) and 6(b)] and the experimental results [Figs. 5(a) and 6(a)] for the three-phase SRG validate our theoretical approaches. Fig. 6(c) shows results of the numerical simulation of the phase current, while the representation of the phase inductance in the form of the sum of zero, first, and second Fourier harmonics is utilized. The present connection is commonly used for rejecting the third and higher harmonics from a current and voltage waveforms [10]. The set of (2) completely describe the behavior of the circuit in Fig. 4(b). The results of numerical simulations and experiments are shown in Figs. 7 and 8. It is seen that the waveform of the phase current has no third and higher harmonics. Furthermore, the theoretical and experimental results are in good agreement (2) It is seen that the third harmonic has a strong influence on the phase current waveform in the single-phase generator and the three-phase generator with neutral. The third harmonic has a demagnetization influence in the aligned position of the rotor, as is seen in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002491_027836499401300404-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002491_027836499401300404-Figure1-1.png",
        "caption": "Fig. 1. A 6-DOF para.llel manipulator",
        "texts": [
            ", given two different postures for the end effector, is the straight line joining these two postures in the parameters space fully inside the workspace? This algorithm is based on the analysis of the algebraic inequalities describing the constraints on the workspace and provides a technique for computing those parts of the trajectory that lie outside the workspace. This method is exact if the orientation of the end effector is kept constant along the trajectory and approximate if the orientation is allowed to vary. 1. Introduction A general 6-DOF parallel manipulator is shown in Figure 1, which has six linear adjustable actuators connecting a mobile platform and a base platform. As the length of the actuators change, an end effector attached to the mobile platform can be moved in 6-DOF space. Each link is connected to the base platform through a universal joint and to the mobile platform through a ball-and-socket joint. The workspace of a parallel manipulator is limited owing to three types of constraints: 1. Limited range for the link lengths. The minimum length of link will be denoted p\u2019 fni and the maximum length p\u2019max 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure3.6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure3.6-1.png",
        "caption": "Figure 3.6. a. SOLIM learns an inverse model of the system behavior. b. Step 1: SOLIM mapping : d am g p , step 2: system response : a ms p g , step 3: approximation by updating mw",
        "texts": [
            " SOLIM learning is divided into an approximation and a self-organization part. The approximation part locally learns the output support vector that has been most responsible for the measurement, and the new selforganization rule locally rearranges the neighboring vectors around this output support vector. The task of the SOLIM network is to learn a continuous, smooth inverse model m G P of a system behavior s P G , such that the difference between the desired system output dg and the measured system output mg is minimized (Figure 3.6a). Learning Controller for Microrobots 67 p . c. Step 4: self-organization in output space by arranging all neighbors of mw n . The structure of the SOLIM network is similar to the structure of extended SOM [18] (Figure 3.7). The network N consists of N nodes , , ,i i i i in Bg p c . Each node in associates an input support vector i Gg with an output support vector i Pp and thus forms a kind of look-up table. In addition, each node in has an associated support vector ic in topology space C and a set iB of nodes b i kn that defines its neighborhood. The following steps are performed during operation in the context of a learning controller, i.e., during the learning of a model of an inverse system behavior (Figure 3.6b, Figure 3.6c, and Figure 3.7). These steps are explained in more detail in the following sections. Mapping. A desired system output is mapped to actuation parameters d am g p . System response. The actuation parameters ap are applied to the system and the system output is measured a ms p g . Approximation. The pair m ag p describes the system behavior. Using mg as map input yields a winning node mw n that has the highest influence with respect to mg . Therefore, the corresponding output support vector mw p is updated such that the mapped output of mg is approximately ap "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.1-1.png",
        "caption": "Fig. 6.1 Actuator force and stroke",
        "texts": [
            "3 Theory of Single-Stroke Linear Solid-State Actuators 159 As mentioned before, a single-stroke actuator interfaces with its mechanical environment (or host mechanical system) through two scalar variables, the actuator force and the actuator stroke. The actuator force F has the nature of an internal axial reaction or a zero moment couple. It is defined as positive if the actuator exerts a tension load on the host system (i.e. if it is subjected to compression loading by external forces). The actuator stroke u is the relative displacement of the actuator\u2019s end points and is positive if their relative distance increases (see Figure 6.1).1 Mathematically, the actuator can be described by a parametric relationship be- tween force and stroke: f (F,u,\u03b1) = 0 (6.1) The parameter \u03b1 represents the actuator input quantity \u2013 usually of non-mechanical nature 2 \u2013 which allows controlling the actuator by modifying the force which the actuator makes available for a given stroke or, conversely, the stroke provided by the actuator for a given force. 1 In the following, we will apply the word stroke also to passive mechanical components to denote, in general, a positive or negative elongation, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002442_02783640122068218-Figure17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002442_02783640122068218-Figure17-1.png",
        "caption": "Fig. 17. Outline of biped robot.",
        "texts": [
            " The relationship between clearance of the swing leg tip and shank mass ratio is shown in Figure 16. We note that the shank mass ratio value of about 0.3 is optimum in terms of the stable and robust walking gait. From the parameter study described above, it seems that the simulation results are consistent with walking characteristics of a human being. To validate the simulation results stated above, we manufactured the biped robot similar to the analytical model shown in Figure 5b. The structure of the robot is schematically illustrated in Figure 17. The robot has three legs whose outer legs are connected by a shaft at the hip to prevent a rolling motion. The shaft and the inner leg are connected serially by a 100 W AC servomotor through one-tenth reduction gears. The thigh and shank of each leg are connected by a passive joint with a knee stopper. An optical encoder of 1000 pulses is mounted at each knee joint. To equalize the total mass and moment inertia of each leg, the inner leg is made of an aluminum alloy frame with a 40-by-80 mm cross section, while a couple of the outer legs are made of a 30-by-80 mm frame",
            " Since the available small gyroscope sensors are too sensitive to impact disturbances at the collision with the ground, the absolute shank angle is estimated from the relative angles measured by the optical encoders at the knee and the hip motor. If the relative angle at at RUTGERS UNIV on August 11, 2015ijr.sagepub.comDownloaded from the hip and knee is denoted by \u03b1 and \u03b2, respectively, as shown in Figure 15, \u03b83 will be estimated by \u03b83 = 1 2 \u03b1 + \u03b2. (10) However, the estimation formula (10) is valid only when both thighs are symmetrical with respect to a vertical line, as shown in Figure 17. The estimation accuracy becomes worse when\u03b1 is small, as understood from the stick figures in Figure 6a. In the following experiment and numerical simulation, we used eq. (10) to estimate \u03b83. At the beginning of the experiment, it seemed to be very difficult for the biped robot to walk. After identifying the equivalent values of mass, mass center position, and moment of inertia of each link, including the motor and gears and equivalent viscous damping coefficient at each joint, we simulated the self-excited biped locomotion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002751_0094-114x(95)00121-e-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002751_0094-114x(95)00121-e-Figure5-1.png",
        "caption": "Fig. 5. Undercut in an elliptical gear.",
        "texts": [
            " When the same parameters given in the previous examples are used, the module of the rack cutter is 5.0 ram, which is smaller than the limiting value of the gear module calculated from equation (32), i.e. m = 9.22 mm. Therefore, undercutting of the generated elliptical gear tooth will not occur. However, suppose that another rack cutter with module m = 15 mm is used to generate an elliptical gear of the same pitch ellipse, and that the number of teeth of the elliptical gear is 15. Then the proposed computer program and computer graphics yield the tooth profile of an elliptical gear shown in Fig. 5. It is clear that undercutting has occurred in this case. This verifies the equations developed above. For the special case where the major semi-axis a and the minor semi-axis b are equal, and are equal to R, the elliptical gear will regress to a spur gear, and m = 2R/n and p = R can thus be obtained. Substituting these values into equation (32) yields the following expression for the minimum number of teeth: 2 n - - sin2\u00a2, ~ (33) 890 Shinn-Liang Chang et al. S U M M A R Y A complete mathematical model o f elliptical gears, including fillets, bo t tom lands, and working surfaces o f the tooth profile, has been developed in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure5-1.png",
        "caption": "Fig. 5. Blade and generating cones applied for generation of face worm gear: (a) blade; (b, c) generating cones for concave and convex sides.",
        "texts": [
            " The tilt of the head-cutter allows to avoid interference of the head-cutter with teeth that neighbor to the space being generated. Fig. 4 illustrates schematically the generation of the face-gear. The tool is mounted at the cradle c of the generating machine (Fig. 4) and performs rotation about the tool axis. The face-gear R2 and the cradle c are held at rest and the tooth surface of the face-gear is generated as the copy of the tool surface. Indexing of face-gear has to be provided for generation of each space of the gear. Blades of the gear head-cutter are shown in Fig. 5(a). The angles ag of blade profile are of different magnitude for the convex and concave sides of the space of the face worm gear. Circular arc profiles of the blade fillet are provided for the generation of the fillet of the gear. The generation of the worm is performed by a tilted head-cutter mounted on the cradle d of the generating machine (Fig. 6). The worm and the cradle d perform related rotations determined as x\u00f0w\u00de x\u00f0d\u00de \u00bc N2 N1 \u00f01\u00de where N2 and N1 are the number of teeth and threads of the face-gear and the worm",
            " Circle C that lies in P and passes through A1, P and A2 is of radius q determined by using the coordinates of A1, P and A2. The axis zg of the generating tool is perpendicular to plane P and passes through point Og that is the center of circle C. The orientation of plane P is determined with respect to plane T of the drawings (Fig. 8(b)). The installment of the generating tool with respect to coordinate system S2 rigidly connected to face worm gear is determined by direction cosines of coordinate system Sg of the generating tool and position vector 020g. The blade of the gear head-cutter is a straight line (Fig. 5(a)) and profile angle ag is determined from the condition that the straight line is a tangent to the cross-section of the face-gear at point P. The surface of the head-cutter is illustrated in Fig. 5(a). It may be represented as a combination of a cone in the working part and a torus of the fillet part. The gear tooth surface is generated as a copy of the tool surfaces and is represented in S2 by the matrix equation r2 ug; hg \u00bc M2grg ug; hg : \u00f07\u00de Here ug; hg are the surface coordinates of the head-cutter represented by vector function rg ug; hg . Matrix M2g describes the coordinate transformation from the tilted head-cutter to coordinate system S2. Elements of matrixM2g are determined by position vector 020g and direction cosines of coordinate axes of Sg (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.38-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.38-1.png",
        "caption": "Figure 4.38 Example 4.7.",
        "texts": [
            "2 x W2 = a W2 i - b ~2 If Statics: Analyses of Systems in Equilibrium 71 The translational equilibrium of the beam would yield: RAx = 0 RAy = WI + W2 + P RAz = 0 The rotational equilibrium of the beam would yield: a WI MAx = --2- -a W2 +aP MAy = 0 MAz = b W2 _ bP 2 \u2022 Note the similarities between this and the shoulder example in the previous chapter (Example 3.5). 4.11 Systems Involving Friction Frictional forces were discussed in detail in Chapter 2. Here, we shall analyze a problem in which frictional forces play an important role. Example 4.7 Figure 4.38 illustrates a person trying to push a block up an inclined surface by applying a force parallel to the incline. The weight of the block is W, the coefficient of maximum friction between the block and the incline is IL, and the incline makes an angle e with the horizontal. Determine the magnitude P of the minimum force the person must apply in order to overcome the frictional and gravitational effects to start moving the block in terms of W, IL, and e. Solution: Note that if the person pushes the block by applying a force closer to the top of the block, the block may tilt (rotate in the clockwise direction) about its bottom right edge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002491_027836499401300404-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002491_027836499401300404-Figure5-1.png",
        "caption": "Fig. 5. Examples of trajectory verification. On the left, the frontier of the workspace where there is no link interference is drawn in thick lines; on the right is drawn a 3D trajectory. The forbidden parts of the trajectory are drawn in dashed lines (computation time: 13.5 ms and 200 ms).",
        "texts": [],
        "surrounding_texts": [
            "329\n2.3.1. Distance Betrveen the Lines\nThe distance l12 between the lines associated with links 1\nand 2 can be written as:\nBecause\nthe inequality l12 2 < d leads to a second-order inequality P~ (a) > 0. The intervals .~d on A included in [0,1] such that PI (A) is positive define the parts of the trajectory for which the distance between the lines is less than or equal to d.\nLet Q~, Q2 be the points on lines 1,2 belonging to their common perpendicular. If these points belong to the links for some values of A in Id, then there is link interference. We define al, a2 by:\nConsequently, point Qi belongs to link i if ai is in [0,1]. Using equation (10), o;],o;2 can easily be obtained as:\nwhere the r, s, t are constants. Let 7~ be the intervals included in [0,1] such that 7~ is positive or equal to 0 (i.e., ai > 0) and IFi be the intervals in [0,1 ] where P~~ - Pd(A) is negative or equal to 0 (i.e., az < 1). We may remark that all these intervals can be easily obtained from the above equations. The set ID of intervals of A in [0,1] where the distance between the links is the distance between the lines and is less than d is therefore:\n- - - -\nIf Id is an empty set, the distance between the lines (which is a lower bound of the distance between the links) is always greater than d, and therefore link interference cannot occur. If Id is not empty and ID is empty, we cannot state whether the distance between the links is less than d, as this distance is always greater or equal to the distance between the lines. The distance between the links is therefore different from the distance between the lines.\n2.3.2. Distance Between the Points Bi and Their Projections\nThe distance l from point Bj to line 2 can be written as:\nThe inequality l < d leads to a second-order inequality n2 _ Pl \u2019 (.-B) 2: 0, and interference will occur if the projection Q of Bl on line 2 belongs to link 2. We define 01 such that A2Qi = ,QtA2B2, and the above condition will be fulfilled if (3\u00a1 belongs to [0,1]. Equations (2) and (1) lead to:\nLet Tgj be the intervals included in [0,1 such that\nThe set of intervals\nI~j , i, j E [ 1, b], i ~ j defines the components of the :\ntrajectory for which interference occurs between links i and j.\n2.3.3. Distance Between the Points A2 and Their Projections\nThe distance lA~ from point A1 to line 2 is:\nThe components of the trajectory for which link interference occurs are defined by the intervals such that 1 A2 - d < 0, which is equivalent to a second-order\nI\n~2 inequality PA\u2019 (A) > 0 under the condition that the projection ~1 of ~4i on line 2 belongs to link 2. We define /-l1 such that A2Qi = pIA2B2 and ~1 belongs to link 2 if ~C1 is in [0,1 ]. Equations (2) and (1) lead to:\nwhere the a, b, f are constants. Let IAi denote the in-\ntervals included in [0,1 such that Pi A2 > 0 (IA12 < c0,\nP2 2 > 0 (W >_ 0), ~ - Q(A) :::; 0 (~1 :::; 1). The set of intervals IA; , i, j E [ 1, 6], I # j defines the components\ni , _\nof the trajectory on which interference between links i and j occurs.\n2.3.4. Distance Between Points Ai and Bj The distance between points A2 and B} can be written as:\nat UQ Library on March 13, 2015ijr.sagepub.comDownloaded from",
            "330\nwhich is a second-order polynomial in A. We denote by IAi B~ the intervals of A included in [0,1] such that PAiB/\u00c0) - d2 S; 0. These intervals define the parts of the trajectory for which the distance from Bj to Ai is less than d. An analysis of this inequality (Merlet 1993b) enables us to establish the following rule:\nRule 7: Let a be the angle between the vectors Aimi + CBj, MiM2. If the distance between the points A2 and Bj is greater than d when the endeffector location is M1 and M2, then the distance between these points will be less than d for some C on the line joining M] and M2 if and only if:\nThe union had of all the forbidden intervals for A for each constraint describes the parts of the trajectory that are outside the workspace. We get:\n2.4. Computation Time\nThe above algorithms have been implemented in a workspace computation program. This program is written in C on a Sun Sparc2 workstation. The computation time for verifying the link lengths constraints is approximately 1.6 ms if the trajectory is correct and 2 ms if some points are outside the workspace. A computation time of 1.34 to 1.72 ms is necessary for checking link interference between a pair of links. As for the mechanical limits on the passive joints, the computation time for one face of one pyramid is approximately 0.3 ms.\nIf we check all the constraints, the computation time for a trajectory is approximately 29 ms. Such a time seems to be adequate with a real-time computation.\n2.5. Examples\nWe have performed trajectory verification for a prototype of a parallel manipulator developed by Arai et al. (1990) at the Mechanical Engineering Laboratory in Tsukuba (Figs. 4 and 5).\n3. Trajectory With a Varying Orientation In the case of a constant orientation we have seen that the constraints can be expressed under the form of algebraic equations in the variable A. If we now introduce a varying orientation, we have no more algebraic constraints,\nthe base joints (computation time: 1. 99 ms and 3.16b ms j.\nas A will appear in the sines and cosines of the rotation matrix.\nTo get algebraic constraints equations, we split the trajectory in elementary parts such that the change in the orientation will be small. As the orientation will affect\nonly the vector CB, we will use a first- or secondorder approximation for this vector. Let Mi, M2 denote the extremities of one elementary part of the trajectory; \u2019ljJ1, 01, CPI the angles describing the orientation of the end effector at point M1; and ~2~2. CP2 the angles of the end effector at point M2. Between points M, and M2 (Fig. 6)\nat UQ Library on March 13, 2015ijr.sagepub.comDownloaded from",
            "331\nthe position of point C is defined by equation (1), and the orientation angles can be written as:\nUsing a first- or second-order approximation of CB leads to:\nwhere the vectors Ul, U2 are only dependent on the relative position of B and the angles V)1,01,01 and ~2~2.~2- Under this assumption we may now analyze the various constraints on an elementary part T of the trajectory.\n3.1. Link Length Constraints\nBy using equation (1) and a second-order approximation (23), we obtain the square of the link length p2 as a third-order polynomial Pp(A). As for the constant orientation case, the analysis of the polynomial PP(~) - Pmax2, ~PP(~) - Prrun enables us to compute the intervals of A in [0,1 such that the link length is greater than its maximum value or lower than its minimal value.\n3.2. Constraints on the Passive Joints\nUsing a second-order approximation of CB (23) together with equation ( 1 ), the constraint equation (7) leads to a second-order inequality. Analysis of this inequality yields the intervals on A such that some point of the link lies outside the pyramid. By considering all the set of faces of every pyramid, we get those parts of the trajectory that do not satisfy the joints constraints. A similar analysis can be done for the passive joints of the mobile plate. The following simplification rules can be established (Merlet 1993b):\nRule 8: Let ni be the external normal to the face i of the pyramid describing the constraints on the base joint. Let U1, U2 be the vectors of the second-order approximation of CB. If, at the extreme points of T, the vector AB lies inside the pyramid with respect to face and if U2.n;T > 0, then the constraint on the joint is satisfied on the whole T. Rule 9: If, at the extreme points of T, the vector AB lies inside the pyramid with respect to face i, this constraint will not be satisfied at some points of T if and only if:\n3.3. Link Interference\n3.3.1. Distance Between the Lines\nLet ll~ denote the distance between lines 1 and 2. By using equation (1) and a first-order approximation (22), the inequality ll~ < d can be written as a fourth-order polynomial in A P(A) > 0.\nIf the common perpendicular points Ql, Q2 of lines 1\nand 2 belong to the links, we get link interference. We define a], a2 such that A1Q1 = 0: 1 Al HI, A2Q2 = a2A2B2 and we get:\nwhere r, s, t are constants. We compute the intervals of [0,1] where P(A) > 0 (i.e., lt2 < c~, P(az) > 0 {i.e., ai > 0), P(c~z) - Pd :::; 0 (i.e., aj < 1). All these intervals can be easily derived from the analysis of the various polynomials. The intersection ID of all these intervals defines the components of T for which link interference occurs. If Id is empty, the distance between the lines (which is a lower bound of the distance between the links) is always greater than d. Consequently, the distance between the links is also always greater than d. If Id is not empty and ID is empty, we cannot conclude that the distance between the lines is less than d, but the distance between the links is greater than the distance between the lines.\n3.3.2. Distance Between the Points Bi and Their\nProjections\nThe distance l from point Bl to line 2 is given by equation (14). Using equations (1) and (23), the inequality\nr)2\n1 <_ d leads to a fourth-order inequality PB\u2019 (a) > 0. Link interference will occur if this inequality is satisfied and if the projected point Q, of B1 on line 2 belongs to link 2. We get\nQi will belong to link 2 if 01 is in [0,1]. Let Tgj be the\nintervals included in [0,1] such that PB~ > 0 (1 < dj,\nat UQ Library on March 13, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.69-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.69-1.png",
        "caption": "Figure 8.69 The free-body diagram.",
        "texts": [
            " The nail is firmly clamped to the bench and a downward force with magnitude F = 1000 N is applied. Determine the stresses generated at section bb of the nail which is located at a horizontal distance d = 6 em measured from the point of application of the force on the nail. The geometry of the nail at section bb is a square with sides a = 15 mm. Solution: The nail is hypothetically cut into two parts by a plane passing through section bb, and the free-body diagram of the proximal part of the nail is shown in Figure 8.69. The transla tional equilibrium of the nail in the vertical direction requires the presence of a compressive force at section bb with a magnitude equal to the magnitude F = 1000 N of the external force applied on the nail. The rotational equilibrium condition requires that there is a clockwise internal bending moment at section bb with magnitude: M = d F = (0.06)(1000) = 60 N-m The compressive force at section bb gives rise to an axial stress O'a. The nail has a square geometry at section bb, and its cross sectional area is: A = a2 = (0.015)2 = 2.25 X 10-4 m 2 Therefore, the magnitude of the axial stress at section bb due to the compressive force is: F 1000 6 O'a = - = 4 = 4.4 x 10 Pa = 4.4 MPa A 2.25 x 10- The area moment of inertia I of the nail at section bb is: I = a4 = (0.015)4 = 4.2 X 10-9 m4 12 12 The bending moment M at section bb gives rise to a flexural stress O'b. The flexural stress is maximum on the medial and lat eral sides of the nail, which are indicated as M and L in Figure 8.69. The maximum flexural stress is: M a (60)(0.015) 6 O'bmax = 2T = 2(4.2 x 10-9) = 107.1 x 10 Pa = 107.1 MPa The flexural stress O'b varies linearly over section bb. It is com pressive on the medial half of the nail, zero in the middle, and tensile on the lateral half of the nail. The distribution of normal stresses O'a and CTb due to the compressive force F and bending Multiaxial Deformations and Stress Analyses 191 moment M at section bb are shown in Figures 8.70a and 8.70b, respectively. The combined effect of these stresses is shown in Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.32-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.32-1.png",
        "caption": "Figure 3.32 A bench test.",
        "texts": [
            " Point o represents the knee joint, A is the center of gravity of the lower leg, W is the total weight of the lower leg, F is the magnitude of the force applied by the pad on the lower leg in a direction perpendicular to the long axis of the lower leg, a is the distance between 0 and A, and b is the distance between 0 and the line of action of F measured along the long axis of the lower leg. (a) Determine an expression for the net moment about 0 due to Wand F. (b) If a = 20 cm, b = 40 cm, () = 30\u00b0, W = 60 N, and F = 200 N, calculate the net moment about O. Answers: (a) Mo = bF - aWcosO (b) Mo = 69.6 N-m (ccw) Problem 3.3 Figure 3.32 illustrates a bench experiment designed to test the strength of materials. In the case illustrated, an in tertrochanteric nail that is commonly used to stabilize fractured femoral heads is firmly clamped to the bench such that the distal arm (BC) of the nail is aligned vertically. The proximal arm (AB) of the nail has a length a and makes an angle () with BC As illustrated in Figure 3.32, the intertrochanteric nail is sub jected to three experiments by applying forces F 1 (horizontal, toward the right), F 2 (aligned with AB, toward A), and L (vertically downward). Determine expressions for the moment Moment and Torque 45 generated at B by the three forces in terms of force magnitudes and geometric parameters a and (). Answers: Ml=aF1sin()(cw) M2 =0 Ma=aF3cos()(Ccw) Problem 3.4 The simple structure shown in Figure 3.33 is called a cantilever beam and is one of the fundamental mechanical ele ments in engineering"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003739_j.eswa.2010.03.049-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003739_j.eswa.2010.03.049-Figure9-1.png",
        "caption": "Fig. 9. Cart-pole system.",
        "texts": [
            " 0 if and only if z! 0 which implies that S2 ! 0. Therefore, it can be concluded that the stabilization of both subsystems can be achieved. In order to verify the theoretical considerations and show the correct operation of the proposed control method, a cart-pole system is simulated and comparisons between the proposed method and the existing decoupled methods (DSMC and SIDFLC) are demonstrated. All simulations were carried out by Matlab/Simulink. The dynamic behavior of the cart-pole system shown in Fig. 9 can be described by the following nonlinear equations: _x1\u00f0t\u00de \u00bc x2\u00f0t\u00de _x2\u00f0t\u00de \u00bc f1\u00f0x; t\u00de \u00fe b1\u00f0x; t\u00deu\u00f0t\u00de \u00fe d1\u00f0t\u00de _x3\u00f0t\u00de \u00bc x4\u00f0t\u00de _x4\u00f0t\u00de \u00bc f2\u00f0x; t\u00de \u00fe b2\u00f0x; t\u00deu\u00f0t\u00de \u00fe d2\u00f0t\u00de \u00f023\u00de where tion of the pole. f1\u00f0x; t\u00de \u00bc mtg sin\u00f0x1\u00de mpL sin\u00f0x1\u00de cos\u00f0x1\u00dex2 2 L 4 3 mt mp cos2\u00f0x1\u00de b1\u00f0x; t\u00de \u00bc cos\u00f0x1\u00de L 4 3 mt mp cos2\u00f0x1\u00de f2\u00f0x; t\u00de \u00bc 4 3 mpLx2 2 sin\u00f0x1\u00de \u00fempg sin\u00f0x1\u00de cos\u00f0x1\u00de 4 3 mt mp cos2\u00f0x1\u00de b2\u00f0x; t\u00de \u00bc 4 3 4 3 mt mp cos2\u00f0x1\u00de \u00f024\u00de where x1\u00f0t\u00de is the angular position of the pole from the vertical axis, x2\u00f0t\u00de is the angular velocity of the pole with respect to the vertical axis, x3\u00f0t\u00de is the position of the cart, x4\u00f0t\u00de is the velocity of the cart, mt is the total mass of the system (which includes the mass of the pole, mp, and the mass of the cart, mc\u00de, and L is the half-length of the pole"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.32-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.32-1.png",
        "caption": "Figure 7.32 Stress-strain diagram for the bone.",
        "texts": [
            "050 Determine the tensile stresses and strains developed in each specimen, plot a stress-strain diagram for the bone, and deter mine the elastic modulus (E) for the bone. Solution: The cross-sectional area of each specimen is A = 4 mm2 or 4 x 10-6 m2. When the applied load is zero, the gage length is 5 mm, which is the original (undeformed) gage length, lo. Therefore, the stress and strain developed in each specimen can be calculated using: F l -lo a=- A \u20ac=-- lo The following table lists stresses and strains calculated using the above formulas: F (N) a x 106 (Pa) i(mm) \u20ac(mm/mm) 0 0 5.000 0.0 240 60 5.017 0.0034 480 120 5.033 0.0066 720 180 5.050 0.0100 In Figure 7.32, the stress and strain values computed are plotted to obtain a a-\u20ac graph for the bone. Notice that the relationship between the stress and strain is almost linear, which is indicated in Figure 7.32 by a straight line. Recall that the elastic modulus of a linearly elastic material is equal to the slope of the straight line representing the a-\u20ac rela tionship for that material. Therefore: a 180 x 106 9 E = - = = 18 x 10 Pa = 18 GPa \u20ac 0.0100 Example 7.4 Figure 7.33 illustrates a fixation device consist ing of a plate and two screws, which can be used to stabilize fractured bones. During a single leg stance, a person can apply his/her entire weight to the ground via a single foot. In such situations, the total weight of the person is applied back on the person through the same foot, which has a compressive effect on the leg, its bones, and joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure2.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure2.12-1.png",
        "caption": "Figure 2.12 Intensity afforce (pressure) applied on the snow by a pair of boots is higher than that applied by a pair of skis.",
        "texts": [
            " The principles behind the concept of pressure have many ap plications. Note that the larger the area over which a force is applied, the lower the magnitude of pressure. If we observe two people standing on soft snow, one wearing a pair of boots and the other wearing skis, we can easily notice that the person wearing boots stands deeper in the snow than the skier. This is simply because the weight of the person wearing boots is dis tributed over a smaller area on the snow, and therefore applies a larger force per unit area of snow (Figure 2.12). It is obvious that the sensation and pain induced by a sharp object is much more severe than that produced by a force that is applied by a dull object. A prosthesis that fits the amputated limb, or a set of den tures that fits the gum and the bony structure properly, would feel and function better than an improperly fitted implant or re placement device. The idea is to distribute the forces involved as uniformly as possible over a large area. 2.14 Frictional Forces Frictional forces occur between two surfaces in contact when one surface slides or tends to slide over the other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003126_j.mechmachtheory.2006.10.004-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003126_j.mechmachtheory.2006.10.004-Figure2-1.png",
        "caption": "Fig. 2. Basic structure of the 3-RPS manipulator.",
        "texts": [
            " This mechanism has been previously studied in a variety of publications including [12]. This mechanism also consists of three identical limbs. However, the order of the joints is different from that of the previously presented manipulator. In the 3-RPS manipulator, a passive revolute joint connects each limb to the base platform. This is then followed by the actuated prismatic joint whose direction is always perpendicular to the passive revolute joint at the base. Finally, the passive spherical joint connects each limb to the end effector. This architecture is depicted in Fig. 2. Similarly to the 3-PRS mechanism, the limbs of the 3-RPS mechanism are confined to move on a single plane. As such, the constraint equations relating the designated independent degrees of freedom (G1z , G2z , and G3z ) to the dependent degrees of freedom (Gix and Giy ) are the same. These constraint equations are presented in detail in [10]. The only difference from the inverse displacement solution of the 3-PRS mechanism is in the final step. That is, after solving for the position of the spherical joints (Ai), the following vector loop (see Fig. 2) may be formulated: li \u00bc ri bi \u00f016\u00de and solved for the displacement of the actuated prismatic joint i, that is jlij. Only the positive solution for this equation is used. Due to similarity in the constraint equations for the 3-PRS and 3-RPS mechanisms, the development of the dimensionally homogeneous Jacobian J is also very similar. Consider Eq. (9) again. The vector bi is a known constant in the architecture of the 3-RPS mechanism where the magnitude of vector li is now a variable. With this in consideration, taking the first time derivative of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure4.9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure4.9-1.png",
        "caption": "Figure 4.9. The size of the ROI is defined depending on the size of the contour. 100 pixels are added to the maximum dimension",
        "texts": [
            " Frame-by-frame tracking is achieved by continuous minimization, whereby the minimized contour of the current frame is used as the start contour for the following frame. In addition to the high robustness against additive noise and due to the consideration of the gray level probability distribution, a transformation space enables a high robustness against clutter, since only certain shapes of the contour are allowed. As for the cross-correlation approach, an ROI is used to decrease the image acquisition time. The size of the ROI changes with the dimension of the contour (Figure 4.9), and the position is shifted with the center of gravity. Thus, the ROI is automatically defined for each frame. Real-time Object Tracking Inside an SEM 117 Because region-based tracking is a frame-by-frame minimization, a first initialization step is needed to estimate the first ROI. Therefore, the target object has to be recognized in the first input image, which can be done by cross-correlation as described in Section 4.4. The initial shape of the contour can be defined manually or, if available, from a CAD model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.33-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.33-1.png",
        "caption": "Figure 13.33 Circular motion of C as observed from point B.",
        "texts": [
            " + sin 01 i Therefore, the velocity and acceleration vectors of point B with respect to the XY coordinate frame and in terms of Cartesian unit vectors are: ll.B = \u00a3 1 WI (cos 01 \u00a3 + sin 01 D !lB = -\u00a31 W12 (sin 01 \u00a3 - cos 01 D If we substitute the numerical values of \u00a31 = 0.3 m, 01 = 30\u00b0, ll.B = 0.52\u00a3 + 0.301 (i) !lB = -0.60 \u00a3 + 1.041 (ii) Motion of point C as observed from point B: The motion of point C as observed from point B is similar to the motion of point B as observed from point A. Point C ro tates with a constant angular velocity of W2 in a circular path of radius \u00a32 about point B (Figure 13.33). Therefore, the deriva tion of velocity and acceleration vectors for point C relative to the xy coordinate frame follows the same procedure outlined for the derivation of velocity and acceleration vectors for point B relative to the XY coordinate frame. The magnitudes of the tangential velocity and normal acceleration vectors of point C relative to Bare: VC/B = \u00a32 W2 aC/B = \u00a32 W22 If !12 and h are unit vectors in the normal and tangential direc tions to the circular path of C when arm BC makes an angle 02 with the vertical, then: ll"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002890_00006123-200110000-00003-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002890_00006123-200110000-00003-Figure2-1.png",
        "caption": "FIGURE 2. Schematic cross sectional depiction of a piezoresistive pressure sensor. The pressure difference across the sensing diaphragm causes it to deform and strain, which in turn changes the electrical resistance of the patterned resistors. The bond pads are used to connect the sensor to an electrical circuit, which is used to measure the change in electrical resistance and hence the applied pressure on the diaphragm.",
        "texts": [
            " These initial pressure sensors were subject to both chronic and catastrophic measurement errors, however, because of the degradation of the epoxy bonds, among other factors. In the late 1960s and early 1970s, methods of fabricating thin Si diaphragms\u2014initially by mechanical milling and subsequently by chemical etching techniques\u2014were perfected (3, 7, 17, 40, 60\u201362, 72). These advances, along with concurrent improvements in microelectronics fabrication, enabled the development of high-quality Si pressure sensors in which the strain gauge resistors were integrated into the Si diaphragm (73), as illustrated in Figure 2. The first highvolume pressure sensor was marketed by National Semiconductor Corporation (Santa Clara, CA) in 1973, and by that time, piezoresistive pressure sensor technology had become a low-cost, batch-fabricated manufacturing technology. Miniature Si pressure sensors for implant and indwelling applications were developed in 1971 (5). During evaluation, it was found that the performance of the sensors could vary significantly with the techniques used to mount the Si chips in the housing packages"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.1-1.png",
        "caption": "Figure 7.1 Loading modes.",
        "texts": [
            " The extent of deformation will be dependent upon many factors including the magnitude, direction, and duration of the applied force, the material properties of the object, the geom etry of the object, and environmental factors such as heat and humidity. In general, materials respond differently to different loading configurations. For a given material, there may be different me chanical properties that must be considered while analyzing its response to, for example, tensile loading as compared to loading that may cause bending or torsion. Figure 7.1 is drawn to illus trate different loading conditions, in which an L-shaped beam is subjected to forces F l' F 2' and L. The force F 1 subjects the arm AB of the beam to tensile loading. The force F 2 tends to bend the arm AB. The force L has a bending effect on arm BC and a twisting (torsional) effect on arm AB. Furthermore, all of these forces are subjecting different sections of the beam to shear loading. 7.2 Uniaxial Tension Test The mechanical properties of materials are established by subjec ting them to various experiments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure13-1.png",
        "caption": "Fig. 13. Cross section of switched PM motor.",
        "texts": [
            " These PM SI FUON: ELECTRICAL MACHINES FOR VARIABLE-FREQUENCY DRIVES I133 motors have the additional advantage that their mass and volume can be made considerably less than either induction or commutator motors of similar maximum torqut: rating [401. VI. SWITCHED OR TRAPEZOIDAL PM MOTORS The other major class of PM motor drives is alternatively known as trapezoidally excited motors, or brushless dc motors, or simply as switched motors [41 I. They have stator windings that are supplied in sequence with nearrectangular pulses of current. A cross section of one type of motor is shown in Fig. 13. In most respects, this switched motor is identical in form with the synchronous PM motor of Fig. 8. For this two-pole motor, the rotor magnets extend around approximately 180\" peripherally. The stator windings are generally similar to those of an induction or synchronous motor except that the conductors of each phase winding are distributed uniformly in slots over two arcs of 60' (or somewhat less in some designs). The windings of this type of motor are connected in a star comfiguriAon. The electrical supply system is designed to provide a current which can be switched sequentially to pairs of the three stator terminals. In the condition shown in Fig. 13, current has just been switched into phase a and out of phase c. For the next 60' of rotation, two 120\" arcs of uniform current distribution are so placed with respect to the magnets to produce counter-clockwise torque. As the magnet edge crosses the line between sectors b and c', the current continues through phase c but is switched to enter through phase b. The sequence of switching actilons can be simply triggered by use of signals from position sensors (e.g., Hall generators) mounted on the shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure9.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure9.15-1.png",
        "caption": "Figure 9.15. NMT module",
        "texts": [
            " The change in resistance, and consequently the differential voltage of the Wheatstone bridge, can be converted into a force signal by performing a calibration described below (Section 9.2.4.2). The beam is also furnished with a tip. The pyramidal tip has a height of 17 \u03bcm; the tip radius is 10 nm; the maximum applicable load is 20 mN; the measurement resolution is 1 \u03bcN [30]. 286 Iulian Mircea and Albert Sill Nanoindentation tests also require very sensitive displacement sensors and positioners. A device that can play both roles is the NMT module [31]. In Figure 9.15, such a module is shown. In principle, it is a motorized table driven by a very precise linear motor. The motor can carry loads up to 2 kg with a maximum stroke of up to 70 mm with a resolution of 2 nm. The NMT module is equipped with a very precise displacement sensor with a resolution of 10 nm, has small dimensions (e.g., module type NMT-20: 50 \u00d7 26 \u00d7 10mm3), and is vacuum compatible [31]. Before performing nanoindentation tests, calibrations of the piezoresistive AFM are necessary: the stiffness calibration and the electrical calibration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003912_s0022112073001849-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003912_s0022112073001849-Figure5-1.png",
        "caption": "FIGURE 5. The variation of the profile.",
        "texts": [
            " We therefore determine the change SE, in the energy when small changes SK and Sh are made in K and A. We suppose that the equilibrium profile x(y) is replaced by x + ss(y), and that 8, SK and Sh are all of the same order of magnitude. If we put then from (1) we find F(y, x, xu) = (1 + x;)& + XY, (24) The condition for constant volume is We shall suppose that the perturbation s(y) vanishes for values of y in the range (0, yo), that is, the profile is undisturbed in a region close to the apex (see figure 5). Later the consequences of allowing yo to tend to zero will be examined. Thus, the condition (26) becomes 0 = hSK+&8K2COte+\u20ac Sdy+o(\u20ac3) , (27) (28) s: and we have \u201c(Yo) = 0 and h + Sh = X ( K + 8K) + \u20ac S ( K + SK), \u20ac S ( K ) = 6h-6KCOt8fO(\u20ac2). which is equivalent to (29) (30) We also need the expansions of the profile x(y) near C and 0, which are K-ZJ = (h-x)tan8+O(h-x)2, (31) (32) x = (2y/p)4 + O(y%). The value of SE, can now be evaluated from (25) as far as terms 0(e2). In simplifying the expressions obtained, we use the equilibrium condition given by (3), the value of a from (19) and the condition in (27)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure15.19-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure15.19-1.png",
        "caption": "Figure 15.19 Oblique central impact of two pool balls.",
        "texts": [
            " For a two-dimensional collision problem, the conservation of linear momentum principle must be applied in two coordinate directions. In addition, the nature of the collision must be known. For example, if the collision is perfectly elastic, then the total kinetic energy of the system is also conserved. If the collision is perfectly inelastic, then the velocities of the objects after the collision are equal. The following example will illustrate some of the concepts in volved in two-dimensional collision problems. Example 15.8 Figure 15.19 illustrates an instant during a pool game. What the pool player wishes to do is to hit the stationary target ball (ball 2) by the cue ball (ball 1) so as to move the target ball toward and into the corner pocket. Consider that the cue ball is given a velocity of VIi = 5 m/ s toward the target ball, and that a line connecting the center of mass and the geometric center of the corner pocket make an angle () = 45\u00b0, as shown in Figure 15.20. The rectangular coordinates x and yare chosen in such a way that they respectively coincide with the line of impact (perpendicular to the contacting surfaces), and the plane of contact (tangential to the contacting surfaces)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003115_41.184822-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003115_41.184822-Figure4-1.png",
        "caption": "Fig. 4. Approximation of electrical power output and process laws.",
        "texts": [
            " 6 w eq\u2019 ef P m Pe P v t vd U4 M D id iq xd xd \u2019 Tdo \u2019 Ta Ka Tg ZQ xt xe NOTATIONS Rotor phase angle of generator Rotor speed of generator Transient induced voltage Excitation voltage Mechanical power input Electrical power output Reactive power Terminal voltage d-Axis components of terminal voltage q-Axis components of terminal voltage Inertia constant Damping coefficient d-Axis components of armature current q-Axis components of armature current d-Axis synchronous reactance d-Axis transient reactance Time constant of d-axis circuit AVR (automatic voltage regulator) time constant AVR gain GOV (governor) time constant GOV gain Transformer reactance V, Infinite bus voltage ua AVR control input ug GOV control input up PSS (power system stabilizer) control input. A 6 = 6 - a, A w = w - w,, Aef = ef - ef,, A P m = P m - Pm,, A P = P m - Pe, AVt = Vt - Vto, Here, \u201c0\u201d denotes the value of variables on the desired equilibrium point. In this numerical example, nonlinearities of the electric power output is modeled by three linear systems shown in Fig. 4. The model is composed of three fuzzy process laws. System 1 represents the system that the excitation of AVR is increased (L\u2019), system 2 that the excitation is decreased (L2> and system 3 that the rotor phase angle 6 of generator exists near the unstable equilibrium point (L3) . We assume a three-phase short circuit fault at the point F in Fig. 3. As soon as the fault is cleared at the time tc s, the transmission by two lines is switched to that by one line, and the proposed control method is applied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.17-1.png",
        "caption": "Figure 4.17 Resultant forces acting on the beam.",
        "texts": [
            " We can now correct it by writing: RAy = 555 N (t) The corrected free-body diagram of the beam is shown in Figure 4.16. Since we already calculated the components of the reaction force at A, we can also determine the magnitude and direction of the resultant reaction force EA at A. The magnitude of R A is: RA = J(RAx)2 + (RAy)2 = 747 N If a is the angle R A makes with the horizontal, then: a = tan-1 (RAY) = tan-1 (555) = 500 RAx 500 The modified free-body diagram of the beam showing the force resultants is illustrated in Figure 4.17. Example 4.3 The uniform, horizontal beam shown in Figure 4.18 is hinged to the wall at A and supported by a cable attached to the beam at B. At the other end, the cable is attached to the wall such that it makes an angle f3 = 53\u00b0 with the horizontal. Point C represents the center of gravity of the beam, which is equidistant from A and B. A load that weighs W2 = 400 N is placed on the beam such that its center of gravity is directly above C. If the length of the beam is l = 4 m and the weight of the beam is Wi = 600 N, calculate the tension T in the cable and the reaction force on the beam at A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003334_s11071-007-9306-2-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003334_s11071-007-9306-2-Figure2-1.png",
        "caption": "Fig. 2 Geometry in angular contact ball bearing",
        "texts": [
            " Thus, the displacements of the bearing center are defined in the inertial coordinate system and include not only the radial displacements x, y and axial displacement z but also the rotations about the x and y-axes, \u03b8x and \u03b8y , respectively. The displacement vector can be written as {U} = {x y z \u03b8x \u03b8y }T. (1) The rolling element is located with the displacement vector of the inner race center of curvature in the local rolling element coordinate system. For the j th ball, the displacement vector can be expressed as {uj } = {urj uzj u\u03d5j }T. (2) Figure 2 shows the various parameters used. With the small motion assumption, the relationship between {uj } and {U} is as follows: {uj } = [Tj ]{U}, (3) where [Tj ] is the transformation matrix [8, 9] [Tj ] = [ cos\u03d5j sin\u03d5j 0 \u2212zp sin\u03d5j zp cos\u03d5j 0 0 1 rp sin\u03d5j \u2212rp cos\u03d5j 0 0 0 \u2212 sin\u03d5j cos\u03d5j ] . (4) The angular location of the j th rolling element, \u03d5j , can be obtained from \u03d5j = 2\u03c0(j \u2212 1) N + \u03c9ct + \u03d50. (5) The varying compliance frequency or the ball passage frequency can be described as the cage speed times the number of balls"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.7-1.png",
        "caption": "Figure 3.7 The magnitude and direction of moment of F about O.",
        "texts": [
            " When a force is applied on the handle of the wrench, a torque is generated that rotates the wrench. The line of action of this torque coincides with the centerline of the bolt. Owing to the torque, the bolt will either advance into or retract from the board depending on how the force is applied. As in Figure 3.6, if the force causes a clockwise rotation, then the direction of torque is \"into\" the board and the bolt will advance into the board. If the force causes a counterclockwise rotation, then the direction of torque is \"out of\" the board and the bolt will retract from the board. In Figure 3.7, if point \u00b0 and force F lie on the surface of the page, then the line of action of moment M is perpendicular to the page. If you pin the otherwise unencumbered page at point 0, F will rotate the page in the counterclockwise direction. Us ing the right-hand-rule, that corresponds to the direction away from the page. To refer to the direction of the moments of copla nar force systems, it may be sufficient to say that a particular moment is either clockwise (cw) or counterclockwise (ccw). 3.4 Dimension and Units of Moment By definition, moment is equal to the product of applied force and the length of the moment arm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002598_s0003-2670(98)00061-0-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002598_s0003-2670(98)00061-0-Figure3-1.png",
        "caption": "Fig. 3. Voltammograms of DA and AA electrocatalytic oxidation at PNR modified electrode. (a) 0.1 mol l\u00ff1 HAc\u00b1NaAc buffer; (b) a 2.5 10\u00ff5 mol l\u00ff1 DA 2.5 10\u00ff3 mol l\u00ff1 AA (1st cycle); (c) the same as (b) (5th cycle); Scan rate: 50 mV s\u00ff1; Potential range: \u00ff0.2 to 0.5 V.",
        "texts": [
            " The surface concentration (\u00ff ) of electro-active species can be calculated from IP n2F2A\u00ff /4RT. \u00ff is the total surface concentration of electrode reaction active-substance (mol cm\u00ff2), A is the electrode area (cm2), IP is expressed in amperes and n, F, R, and T have their usual signi\u00aecance. From this, \u00ff 1.2 10\u00ff7 mol cm\u00ff2. PNR \u00aelm-modi\u00aeed electrodes possess strong electrocatalytic action for DA. We tested this catalytic reaction in different electrolyte systems at different pH values. The best choice of supporting electrolyte system is 0.1 mol l\u00ff1 HAc\u00b1NaAc (pH 4.6). Fig. 3(c) shows the voltammograms of DA catalytically oxidized at PNR \u00aelm electrodes (EPaDA 265 mV) in the presence of AA. In the potential range\u00ff0.2\u00b10.5 Vand a scan rate of 50 mV s\u00ff1, the peak currents (IPaDA) are in good linear relationship with DA concentrations in the range 5.0 10\u00ff6\u00b12.0 10\u00ff4 mol l\u00ff1 (Fig. 4 (a)). The linear regression equation is: IpaDA mA 0:05 1:34 105CDA mol l\u00ff1 with correlation coef\u00aecients of 0.9996 (n 7). In 0.1 mol l\u00ff1 HAc\u00b1NaAc solution, PNR \u00aelm modi\u00aeed electrodes also possess a strong electrocatalytic action for AA (EPa 186 mV). When AA was added, the PNR oxidation current of p2 peak greatly increased and the reduction current of p2 peak decreased (Fig. 3(b)). The increase and decrease of the redox peaks were dependent on the AA concentration. This is a main property of electrocatalyzing reaction by mediators. In addition, the catalytic currents were decreased with increasing cyclic scan numbers. A stable current value was obtained after \u00aeve cycles. If the solution was shaken slightly, the current was the same as that of the \u00aerst cycle. So, we could use the peak current of the \u00aerst cycle for analysis. The catalytic peak currents (IPaAA) of the \u00aerst cycle are in linear relationship with the AA concentration in the range 2",
            " This indicates that the adsorptive ability of AA is larger than its oxidation product. During the cyclic scan, part of the AA oxidation product may be deadsorbed. That is why the catalytic currents decreased with increasing cyclic scan num- ber. In contrast, the catalytic currents of DA at PNR \u00aelm-modi\u00aeed electrodes do not have this character. Its catalytic currents are stable. From the difference between the two electrode processes we can determine both, DA and AA concentrations in the same solution (see below). Fig. 3 shows the voltammograms of DA and AA catalytically oxidized simultaneously at PNR \u00aelm electrodes. We can determine both concentrations by using the different stability of the catalytic currents. That is, the catalytic currents for DA (IPaDA) are stable and that of AA(IPaAA) are decreased by increasing the cycle number. In the \u00aerst cycle, IPaAA was large, which made IPaDA unclear (Fig. 3(b)). We measured IPaAA in the \u00aerst cycle as the signal used (IPaAA1) for determining AA concentration. By cycling continuously, IPaAA was decreased and the IPaDA (which was stable) appeared clearly [Fig. 3(c)]. We measured IPaDA in the 5th cycle as the signal (IPaDA1) for determining DA concentration. By adding standard solutions of AA and DA simultaneously, we repeated the above procedure by measuring the \u00aerst cycle signal as IPaAA2 and the 5th cycle signal as IPaDA2. Using the values of IPaAA1, IPaAA2, IPaDA1 and IPaDA2 both, AA and DA concentrations can be calculated. The dopamine hydrochloride injection (DHI) solution (standard content of DA 10 mg ml\u00ff1, 2 ml per injection) was diluted to 10 ml with water, 25 ml was piped into each of the series of 10 ml volumetric \u00afasks and made up to volume with 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003029_a:1020128408706-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003029_a:1020128408706-Figure1-1.png",
        "caption": "Figure 1. Examples of shaded maneuverability domains (convex and non-convex) and of the corresponding optimal Hamiltonian H \u2217.",
        "texts": [
            " X\u2032 \u2208 D(X, t) u \u2208 (X, t) (14) Thus H \u2217 = H \u2217 (P,X, t) and it is called either \u2018optimal Hamiltonian\u2019 or \u2018generalized Hamiltonian\u2019 or sometimes just \u2018Hamiltonian\u2019 by the different authors. All this is of course very confusing and thus we will use \u2018control Hamiltonian\u2019 for the scalar function H (P,X,u, t) of (13) and \u2018optimal Hamiltonian\u2019 for the scalar function H \u2217 (P,X,t) of (14). Notice that the optimal Hamiltonian H \u2217 is independent of the closure and the \u2018convexisation\u2019 of the maneuverability domain D (Figure 1) and then this closure and this convexisation must be justified ([15], pp. 243\u2013245) but fortunately we will not meet this difficulty in our analysis. We now need some vocabulary: (A) A couple (Xo, to), (Xf, tf ) is \u2018connectable\u2019 if an admissible trajectory X(t) allows to join these two points. (B) A connectable couple is a \u2018limit couple\u2019 if non-connectable couples exist in any of its vicinities. (C) The trajectory X(t) corresponding to a limit couple is a \u2018limit trajectory.\u2019 (D) If all couples of a limit trajectory X(t) are limit couples, that trajectory is an \u2018extremal trajectory",
            " (16) Notice that (15) is equivalent to {(X, t) \u2208 B}\u21d2|H \u2217(P,X, t)| |P|g(t), almost always. (17) Bi-canonical systems have major interests: (A) The convexisation and the closure of the maneuverability domain is \u2018justified\u2019 (i.e. the admissible trajectories obtained after convexisation and closure are limits of suitable sequences of trajectories that were admissible before the convexisation and the closure). The convexisation of the maneuverability domain is also called \u2018relaxation of the control,\u2019 it corresponds to a fast alternate use of X\u2032\u2217 A and X\u2032\u2217 B in Figure 1, as a sail boat that tacks about and goes against the wind. When (15) and (16) are not satisfied, the optimal Hamiltonian is not almost always a \u2018Lipschitz function\u2019 of P and X (but notice that discontinuities with respect to the time t are not dangerous) and we can obtain the following effect: Maneuverability domain before closure: 2 \u221a|x | < dx/dt 1 + 2 \u221a|x | . Starting from xo = 0 at to = 0, we will remain above x = t2, but after closure the trajectory x = 0 will become admissible. . .. Similar difficulties arise for the convexisation when (15) and (16) are not satisfied ([15], p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003466_027836498300200302-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003466_027836498300200302-Figure3-1.png",
        "caption": "Fig. 3. Approach lengths (A) for point Q in the workspace of the simple 61Z robot (B).",
        "texts": [
            " For defining the end contours, we need to store a set of intermediate radial coordinates between the radial boundaries of the workspace. Interior points in the workspace for joints with full or partial mobility can be eliminated in the following way. A Z-R cross section of the workspace can be used and the points examined to see if other points exist within a full neighborhood around it. Those points with a full neighborhood around them are judged to be interior points and can be eliminated. Table I shows the effects of the reduction schemes on the amounts of information for the workspace Wk(P) of the robot in Fig. 3, which has full mobility at each joint and a Ao of 30\u00b0. The polar coordinate system and point-reduction techniques make it practical to utilize sweeping operations to determine the workspace for a general n-R manipulator. The workspace of a CincinnatiMilacron T3 robot, with limited joint mobility (Table 2) and Ao = 12\u00b0 is shown in Fig. 2. In our study, we also found that changes in parameter &reg;ok alone can have a drastic influence upon the resulting workspace (Hansen 1983). at NORTH DAKOTA STATE UNIV LIB on May 29, 2015ijr",
            " APPROACH ANGLE The limits of movement or orientations of a hand around a given point define the range of approach angles to that point. These angles are the possible approach directions to that point. If a point can be approached from any angle, then the point is classified as being in the primary part of the workspace (Gupta and Roth 1982). A point that can only be approached from a limited range of angles is in the secondary part of the workspace. In our studies, we always have the last revolute axis coincide with the hand\u2019s z-axis in order to have the twist of the hand an independent variable. The simple 6-R robot in Fig. 3B can be studied for the approach angles to points in its workspace. The nonzero-link parameters are -a, =c~3 =a4 =cx~ =90\u00b0, ~ = 0.5, s4 = 0.4, and h = 0.1. The robot has a workspace bounded by concentric spheres of radii R;-handR4+h.R;isa2-s4andRaisa2+s4, where a2 ~ s4 + f~. The concentric spheres of radii R; and Ro define the workspace of the wrist point H (Fig. at NORTH DAKOTA STATE UNIV LIB on May 29, 2015ijr.sagepub.comDownloaded from 27 Fig. 4. Graph of service coefficient 8 versus radial distance R of point Q",
            " To determine the approach length L, the hand\u2019s z-axis is aligned with the aforementioned straight line, and the hand is moved out from point Q until the limit of such at NORTH DAKOTA STATE UNIV LIB on May 29, 2015ijr.sagepub.comDownloaded from 28 movement is reached. Then L = maximum (QP). A set of these straight-line approach lengths can be developed at point Q by using permissible approach angle directions (note that L = 0 if an approach-anglelimit direction is used). Using this procedure, we can evaluate the capability of the mainpulator to perform tasks such as drilling, insertion, and so on at critical points of the workspace or workstation. The 6-R robot in Fig. 3B is used for a simple illustration. The symmetry of the workspace in Fig. 3B allows us to use any arbitrary cross section of the workspace through the origin. A line is extended from any given point Q at some angle A from the radial line extended through Q from the origin. The maximum approach length L from the hand point P to Q can be given by where Ro,i is either Ra or Ri, depending on which sphere is intersected. R is the radial distance from the origin to Q, and h is the hand length. Only positive values of L are true in (Eq. 6), and these lengths must also lie entirely in the region bounded by the R, and Ro spheres. Figure 3A shows the approach lengths to a point at different angles. The approach lengths of general robots can be . investigated by using the numerical technique described in Section 4 to move the hand out from a given point at a specified orientation until a limit is reached. Figure 6 shows a typical summary of approach lengths versus approach angles in two planes. 4. Arm Movement The problem of determining the joint angles or variables for a given manipulator to produce some required hand position or motion is the first step in manipulator motion control (Pieper and Roth 1969)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure12-1.png",
        "caption": "Fig. 12. Conical worm thread surfaces in 3D space.",
        "texts": [
            " The cradle d and the head-cutter are considered in derivations as one rigid body. Rotations of the head-cutter and cradle d are considered in derivations as rotation of one rigid body. Rotation of the head-cutter about its axis provides the desired velocity of cutting and does not effect the process of generation. Eq. (10) is the equation of meshing. The cross product in equation of meshing is the normal to the surface head-cutter represented in S1. Vector or1=ow1 is equivalent to the vector of relative velocity in meshing of the head-cutter and the worm. Fig. 12 represents in 3D space the worm thread surface R1. The generation of R1 needs separate generation of both sides of thread surfaces because the plunging motion (see Eq. (8)) may require different parabola coefficients for each side. Multi-thread worm requires separate generation of each of the thread. The purpose of simulation of meshing and contact is determination of bearing contact and transmission errors of a misaligned face worm gear drive. The procedure of simulation is computerized and is performed by application of developed computer programs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.55-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.55-1.png",
        "caption": "Figure 8.55 Definitions of the parameters involved.",
        "texts": [],
        "surrounding_texts": [
            "\u2022 For a specimen subjected to torsion, the maximum shear stress before fracture is the torsional strength of that specimen. In this case, the torsional strength of the femur is 56.9 MPa. \u2022 The torsional stiffness is the ratio of the applied torque and the resultant angular deformation. In this case, the torsional stiffness of the femur is (180 N-m) I (200 x Jr /1800 ) = 515.7 N-ml rad. \u2022 The torsional rigidity is the torsional stiffness multiplied by the length of the specimen. In this case, the torsional rigidity of the femur is (509.9 N-m/rad)(0.37 m) = 190.8 N-m2 /rad. \u2022 The maximum amount of torque applied to a specimen before fracture is defined as the torsional load capacity of the specimen. In this case, the torsional load capacity of the femur is 180 N-m. \u2022 The total area under the torque versus angular displacement diagram represents the torsional energy storage capacity of the specimen or the torsional energy absorbed by the specimen. In this case, the torsional energy storage capacity of the femur is !(180 N-m)(20\u00b0 x Jr 11800 ) = 31.4 N-m-rad. \u2022 Torsional fractures are usually initiated at regions of the bones where the cross-sections are the smallest. Some particularly weak sections of human bones are the upper and lower thirds of the humerus, femur, and fibula; the upper third of the radius; and the lower fourth of the ulna and tibia. Example 8.5 Consider the solid circular cylinder shown in Figure 8.43a. The cylinder is subjected to pure torsion by an externally applied torque, M. As illustrated in Figure 8.43b, the state of stress on a material element with sides parallel to the longitudinal and transverse planes of the cylinder is pure shear. For given M and the parameters defining the geometry of the cylinder, the magnitude Txy of the torsional shear stress can be calculated using the torsion formula provided in Eq. (8.26). Using Mohr's circle, investigate the state of stress in the cylinder. Solution: Mohr's circle in Figure 8.44a is drawn by using the stress element of Figure 8.43b. On surfaces A and B of the stress element shown in Figure 8.43b, there is only a negative shear Multiaxial Deformations and Stress Analyses 179 stress with magnitude i xy . Therefore, both A and B on the i-a diagram lie along the i axis where a = O. Furthermore, the ori gin of the i-a diagram constitutes the midpoint between A and B, and hence, the center, C, of the Mohr's circle. The distance be tween C and A is equal to i xy , which is the radius of the Mohr's circle. Mohr's circle cuts the horizontal axis at two locations, both at a distance ixy from the origin. Therefore, the principal stresses are such that al = ixy (tensile) and a2 = ixy (compres sive). Furthermore, i xy is also the maximum shear stress. The point where a = al on the i-a diagram in Figure 8.44a is labeled as D. The angle between lines CA and CD is 90\u00b0, and it is equal to half of the angle of orientation of the plane with normal in one of the principal directions. Therefore, the planes of maximum and minimum normal stresses can be obtained by rotating the element in Figure 8.43b 45\u00b0 (clockwise). This is illustrated in Figure 8.44b. The lines that follow the directions of principal stresses are called the stress trajectories. As illustrated in Figure 8.45 for a circular cylinder subjected to pure torsion, the stress trajectories are in the form of helices making an angle 45\u00b0 (clockwise and counter clockwise) with the longitudinal axis of the cylinder. As dis cussed previously, the significance of these stress trajectories is such that if the material is weakest in tension, the failure occurs along a helix such as bb in Figure 8.45, where the tensile stresses are at a maximum. 8.12 Bending Consider the simply supported, originally straight beam shown in Figure 8.46. A force with magnitude F applied downward bends the beam, subjecting parts of the beam to shear, tension, and compression. There are several ways to subject structures to bending. The free-body diagram of the beam in Figure 8.46 is shown in Figure 8.47a. The number of parallel forces acting on the beam are three. F is the applied load, and Rl and R2 are the reaction forces. The type of bending to which this beam is subjected is called a three-point bending. The beam in Figure 8.47b, on the other hand, is subjected to a four-point bending. The stress analyses of structures subjected to bending start with static analyses that can be employed to determine both external reactions and internal resistances. For two-dimensional prob lems in the xy-plane, the number of equations available from statics is three. Two of these equations are translational equilib rium conditions ('L F x = 0 and 'L F y = 0) and the third equation guarantees rotational equilibrium ('L Mz = 0). The internal re sistance of structures to externally applied loads can be deter mined by applying the method of sections, which is based on the 180 Fundamentals of Biomechanics fact that the individual parts of a structure that is itself in static equilibrium must also be in equilibrium. This concept makes it possible to utilize the equations of equilibrium for calculating internal forces and moments, which can then be used to deter mine stresses. Stresses in a structure subjected to bending may vary from one section to another and from one point to another over a given section. For design and failure analyses, maximum normal and shear stresses must be considered. These critical stresses can be determined by the repeated application of the method of sections throughout the structure. Consider the simply supported beam shown in Figure 8.48a. Assume that the weight of the beam is negligible. The length of the beam is i, and the two ends of the beam are labeled as A and B. The beam is subjected to a concentrated load with magnitude F, which is applied vertically downward at point C. The distance between A and Cis i1. The free-body diagram of the beam is shown in Figure 8.48b. By applying the equations of equilibrium, the reaction forces at A and B can be determined as RA = (1 - i1/i)F and RB = (i1li)F. To determine the internal reactions, the method of sections can be applied. As shown in Figure 8.48c, this method is applied at sections aa and bb because the nature of the internal reactions Multiaxial Deformations and Stress Analyses 181 on the left-hand and right-hand sides of the concentrated load are different. Once a hypothetical cut is made, either the left hand or the right-hand segment of the beam can be analyzed for the internal reactions. In Figure 8.48c, the free-body diagrams of the left-hand segments of the beam are shown. For the vertical equilibrium of each of these segments, there must be an internal shear force at the cut. The magnitude of this force at section aa can be determined as V = RA by applying the equilibrium condition L Fy = O. This force acts vertically downward and is constant between A and C. The magnitude of the shear force at section bb is V = F - RA = RB, and since F is greater than RA, it acts vertically upward. The sign convention adopted in this text for the shear force is illustrated in Figures 8.49 and 8.50. An upward internal force on the left-hand segment (or the downward internal force on the right-hand segment) of a cut is positive. Otherwise the shear force is negative. Therefore, as illustrated in Figure 8.48d, the shear force is negative between A and C, and positive between C and B. In addition to the vertical equilibrium, the segments must also be checked for rotational equilibrium. As illustrated in Figure 8.48c, this condition is satisfied if there are internal resisting moments at sections aa and bb. By utilizing the equilibrium condition L M = 0, the magnitudes of these counterclockwise moments can be determined for sections a a and b b as M = x RA and M = XRA - (x - .el)F, respectively. Note that M is a function of the axial distance x measured from A. The function relating M and x between A and C is different than that between C and B. These functions are plotted on an M versus x graph in Fig ure 8.48e. The moment is maximum at C where the load is ap plied. As illustrated in Figures 8.49 and 8.50, the sign convention adopted for the moment is such that a counterclockwise moment on the left-hand segment (or the clockwise moment on the right hand segment) of a cut is positive. It can also be demonstrated that shear force and bending mo ment are related through the following equation: V=_dM dx (8.30) If the variation of M along the length of the structure is known, then the shear force at a given section of the structure can also be determined using Eq. (8.30). The procedure outlined above is also applied to analyze a sim ply supported beam subjected to a distributed load of w (force per unit length of the beam), which is illustrated in Figure 8.48f through j. The procedure for determining the internal shear forces and resisting moments in cantilever beams subjected to Figure 8.49 Positive shear forces and bending moments. Figure 8.50 Negative shear forces and bending moments. 182 Fundamentals of Biomechanics y (.) I \u00b7 r ' :zs:\u00b7\u00b7\u00b7\u00b7f\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7I\u00b7\u00b7\u00b7\u00b7n x concentrated and distributed loads is outlined graphically in Figure 8.51. When a structure is subjected to bending, both normal and shear stresses are generated in the structure. For example, consider the beam shown in Figure 8.52. The beam is bent by a downward force. If the beam is assumed to consist of layers of material, then the upper layers of the beam are compressed while the layers on the lower portion of the beam are subjected to tension. The extent of compression or the amount of contraction is maximum at the uppermost layer, and the amount of elongation is max imum on the bottom layer. There is a layer somewhere in the middle of the beam where a transition from tension to compres sion occurs. For such a layer, there is no tension or compression, and therefore, no deformation in the longitudinal direction. This stress-free layer that separates the zones of tension and compres sion is called the neutral plane of the beam. The line of intersec tion of the neutral plane with a plane (transverse) cutting the longitudinal axis of the beam at right angles is called the neutral axis. The neutral axis passes through the centroid. Centroids of symmetrical cross-sections are located at their geometric centers (Figure 8.53). The above discussion indicates that when a beam is bent, it is subjected to stresses occurring in the longitudinal direction or in Multiaxial Deformations and Stress Analyses 183 a direction normal to the cross-section of the beam. Furthermore, for the loading configuration shown in Figure 8.52, the distribu tion of these normal stresses over the cross-section of the beam is such that it is zero on the neutral axis, negative (compressive) above the neutral axis, and positive (tensile) below the neutral axis. For a beam subjected to pure bending, the following equa tion can be derived from the equilibrium considerations of a beam segment: My ax = --- I (8.31) This equation is known as the flexure formula, and the stress ax is called the flexural stress. In Eq. (8.31), M is the bending moment, y is the vertical distance between the neutral axis and the point at which the stress is sought, and I is the area moment of inertia of the cross-section of the beam about the neutral axis. The area moments of inertia for a number of simple geometries are listed in Table 8.1. Table 8.1 Area (A), area moment of inertia (I) about the neutral axis (NA),first moment of the area (Q) about the neutral axis, and maximum normal(O\"max) and shear ('max) stresses for beams subjected to bending and with cross-section as shown. bh2 fBNA A=bh Q=S Mh bh3 O\"max= 21 1=12 3V >--b~ Tmax=2A Q_2rq3 -0-NA A=11'rq2 - 3 Mrq 4 O\"max= 1 1 _'!I!:..tL - 4 4V Tmax=3A Q=rq(rq2 + r;2) @ A=7r(rq2 - r;2) Ti Mrq NA 7r{rq 4- r ;41 O\"max= 1 1= 4 2V Tmax=T The stress distribution at a section of a beam subjected to pure bending is shown in Figure 8.54. At a given section of the beam, both the bending moment and the area moment of inertia of the cross-section are constant. According to the flexure formula, the flexural stress a x is a linear function of the vertical distance y measured from the neutral axis, which can take both positive and negative values. At the neutral axis, y = 0 and a x is zero. For points above the neutral axis, y is positive and ax is negative, 184 Fundamentals of Biomechanics indicating compression. For points below the neutral axis, y is negative and ax is positive and tensile. At a given section, the stress reaches its absolute maximum value either at the top or the bottom of the beam where y is maximum. It is a common practice to indicate the maximum value of y with e, eliminate the negative sign indicating direction (which can be found by inspection), and write the flexure formula as: Me amax = -1- (8.32) For example, for a beam with a rectangular cross-section, width b, height h, and bending moment M, e = hj2 and the magnitude of the maximum flexural stress is: Mh amax = 12 with b h3 1=- 12 Note that while deriving the flexure formula, a number of as sumptions and idealizations are made. For example, it is as sumed that the beam is subjected to pure bending. That is, it is assumed that shear, torsional, or axial forces are not present. The beam is initially straight with a uniform, symmetric cross section. The beam material is isotropic and homogeneous, and linearly elastic. Therefore, Hooke's law (ax = EEx) can be used to determine the strains due to flexural stresses. Furthermore, Poisson's ratio of the beam material can be used to calculate lateral contractions and/ or elongations. When the internal shear force in a beam subjected to bending is not zero, a shear stress is also developed in the beam. The distribution of this shear stress on the cross-section of the beam is such that it is maximum on the neutral axis and zero on the top and bottom surfaces of the beam. The following formula is established to calculate shear stresses in bending: VQ Txy =-- 1 b (8.33) In Eq. (8.33), V is the shear force at a section where the shear stress Txy is sought, 1 is the moment of inertia of the cross-sectional area about the neutral axis, and b is the width of the cross-section. As shown in Figure 8.SS,let Yl be the vertical distance between the neutral axis and the point at which Txy is to be determined. Then Q is the first moment of the area a bed about the neutral axis. The first moment of area abed can be calculated as Q = Ay, where A is the area enclosed by a bed and y is the distance between the neutral axis and the centroid of area abed. Note that both A and yare maximum at the neutral axis, and A is zero at the top and bottom surfaces. Therefore, Q is maximum at the neutral axis, and zero at the top and bottom surfaces. Maximum Q's for different cross-sections are listed in Table 8.l. The shear stress distribution over the cross-section of a beam is shown in Figure 8.56. The shear stress is constant along lines Multiaxial Deformations and Stress Analyses 185 parallel to the neutral axis. The shear stress is maximum at the neutral axis, where Yl = 0 and Q is maximum. Maximum shear stresses for different cross-sections can be obtained by substi tuting the values of I and Q into Eq. (8.19), which are listed in Table 8.1. For example, for a rectangular cross-section: 3V Tmax = 2 b h Consider a cubical material element in a beam subjected to shear force and bending moment as illustrated in Figure 8.57. On this material element, the effect of bending moment M is represented by a normal (flexural) stress ax, and the effect of shear force V is represented by the shear stress Txy acting on the surfaces with normals in the positive and negative x (longitudinal) directions. As shown in Figure 8.57b, for the rotational equilibrium of this material element, there have to be additional shear stresses (Tyx) on the upper and lower surfaces of the cube (with normals in the positive and negative Y directions) such that numerically Tyx = Txy. The occurrence of Tyx can be understood by assuming that the beam is made of layers of material, and that these layers tend to slide over one another when the beam is subjected to bending (Figure 8.58). There are various experiments that may be conducted to analyze the behavior of specimens subjected to bending forces. Some of these experiments will be introduced within the context of the following examples. Example 8.6 Figure 8.59 illustrates an apparatus that may be used to conduct three-point bending experiments. This appara tus consists of a stationary head (A) to which the specimen (B) is attached, two rings (C and D), and a mass (E) with weight W applied to the specimen through the rings. For a weight W = 1000 N applied to the middle of the specimen and for a support length of e = 16 cm (the distance between the left and the right supports), determine the maximum flexural and shear stresses generated at section bb of a specimen. The specimen has a square (a = 1 cm) cross-section, and the distance between the left support and section bb is d = 4 cm (Figure 8.60a). Solution: The free-body diagram of the specimen is shown in Figure 8.60a. The force (W) is applied to the middle of the speci men. The rotational and translational equilibrium of the speci men requires that the magnitude R of the reaction forces gener ated at the supports must be equal to half of W. That is, R = 500 N. The specimen has a square cross-section, and its neutral axis is located at a vertical distance a /2 measured from both the top and bottom surfaces of the specimen. The normal (flexu ral) stresses generated at section bb of the specimen depend on 186 Fundamentals of Biomechanics Figure B.60a. the magnitude of the bending moment M at section bb and the area moment of inertia I of the specimen at section bb about the neutral axis. At section bb, the magnitude of the flexural stress is maximum (CTmax ) at the top (compressive) and the bottom (ten sile) surfaces of the specimen: Ma CTmax = T 2' The internal resistances at section bb of the specimen are shown in Figure 8.60b. For the rotational equilibrium of the specimen: M = d R = (0.04)(500) = 20 N-m The area moment of inertia of a square with sides a is: I = a4 = (0.01)4 = 8.33 X 10-10 m4 12 12 Substituting M and I into the flexure formula will yield: ( 20 ) 0.01 6 CTmax = 8.33 X 10-10 2 = 120 x 10 Pa = 120 MPa The shear stress generated at section bb of the specimen is a function of the shear force Vat section bb, and the first moment Q and the area moment of inertia I of the cross-section of the specimen at section bb. The shear stress is maximum \u00abmax) along the neutral axis, such that: VQ <max = Ta For the vertical equilibrium of the specimen (Figure 8.60b), the magnitude V of the internal shear force at section bb must be equal to the magnitude R of the reac.tion force; V = R = 500 N. The first moment of the cross-sectional area of the specimen about the neutral axis is: Q = a3 = (0.01)3 = 0 125 X 10-6 m3 88' Therefore, the maximum shear stress occurring at section bb along the neutral axis is: (500)(0.125 x 10-6) 6 <max = (8.33 x 10-10)(0.01) = 7.5 x 10 Pa = 7.5 MPa Remarks: Note that magnitudes and directions of internal shear force and bending moment are different at different sections of the specimen. At a given section, the internal shear force and bending moment are functions of the horizontal distance be tween the left support (or the right support) and the section. This is illustrated in Figure 8.61a for a section that lies some where between the left support and where the load W is applied Multiaxial Deformations and Stress Analyses 187 on the specimen. If the distance between the left support and the section is x, then the magnitude of the internal bending moment at the section is:"
        ]
    },
    {
        "image_filename": "designv10_8_0003453_tsmc.1983.6313183-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003453_tsmc.1983.6313183-Figure1-1.png",
        "caption": "Fig. 1. Position and orientation vectors of the hand.",
        "texts": [
            " In this paper, generation of joint trajectories using Z-splines and quartic splines are presented and compared to the quadratic polynomial trajectory and modified cubic spline trajectory. Path errors due to the approximations are analyzed. Fortran programs are written to perform these calculations. Experimental results are obtained for an il lustrative example. II. REPRESENTATION OF T H E M O T I O N The motion of a manipulator can be described in terms of the positions and orientations of the hand. As shown in Fig. 1, a coordinate frame (n,s,a) attached onto the hand is located at p . The frame, which specifies the position and orientation of the hand, can be represented by a 4 X 4 matrix [1]: # ( , ) - ( * ( ' ) *(<) \u00ab(0 P ( * ) \\ ( 1 ) 1 \u03bf \u03bf \u03bf \u03b9 / v ' where \u03c1 is the position vector of the hand; n, s, and a are 0018-9472/83/1100-1094$01.00 \u00a91983 IEEE LIN AND CHANG: JOINT TRAJECTORIES OF MECHANICAL MANIPULATORS 1095 the unit normal, unit slide and unit approach vectors, respectively. The motion of the manipulator discussed in this paper will be specified by a sequence of Cartesian knots {Hl9 Hl9- \u00b7 \u00b7 , / / \u201e } "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002305_j.1460-2687.1999.00015.x-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002305_j.1460-2687.1999.00015.x-Figure1-1.png",
        "caption": "Figure 1 Kinematical properties of the lower leg and foot at the time just before the collision between the foot and the ball. The linear velocity of the contact point on the foot is approximately the product of the angular velocity of the shank and the distance between the knee joint and the contact point. The reason for this is that the linear velocity of the knee joint is close to zero at the time of impact (see text for further explanation).",
        "texts": [
            " Although the foot doesn't follow the path of the ball after the collision due to its linked connection with the shank and thigh, the collision could still be seen as a one-dimensional collision and the velocity of the ball is normally described according to the following expression: Vball mlf Vfoot 1 e mlf mball 1 \u00d3 1999 Blackwell Science Ltd \u00b7 Sports Engineering (1999) 2, 121\u00b1125 121 Correspondence address: Thomas Bull Andersen, MSc, Laboratory for Functional Anatomy, Biomechanics and Motor Control, Institute of Medical Anatomy C, University of Copenhagen, Blegdamsvej 3, DK-2200 Copenhagen N, Denmark. Tel.: +45 35 32 72 34; Fax: +45 35 32 72 17. E-mail: ta@ami.dk where Vball is the velocity of the ball after impact, mlf is the mass of the lower leg and foot, Vfoot is the velocity of the foot before impact, e is the coef\u00aecient of restitution and mball is the mass of the soccer ball (Fig. 1). The critical variables affecting the velocity of the standardized ball after the collision are the coef\u00aecient of restitution, the velocity of the foot before impact and the effective striking mass. By \u00aelming and computer analysing the kick it is possible to determine the velocities of the foot and the ball. The problem in the literature has been to estimate the effective striking mass, mlf. The effective striking mass has been estimated to be 1 kg in some studies and up to 4 kg in others (Plagenhoef 1971; Togari 1972; Asami & Nolte 1983)",
            " The 16 mm \u00aelms were transferred to video using a \u00aelm projector with a built-in video camera (Elmo TRV16G/CCD). The co-ordinates of the markers and 122 Sports Engineering (1999) 2, 121\u00b1125 \u00b7 \u00d3 1999 Blackwell Science Ltd the centre of the ball were digitized on a computer using the video based Ariel Performance Analysis System (APAS). Displacement data were \u00aeltered using a digital fourth-order Butterworth low-pass \u00aelter with zero degree phase lag (Winter 1990). Optimal cut-off frequencies (6\u00b110 Hz) were determined by use of residual analysis (Winter 1990). Collision between foot and ball Figure 1 shows the kinematic properties of the leg and the ball at the time of impact. Our experiments showed that the linear velocity of the knee joint was close to zero at the time of impact (between 0.06 and 0.56 m s)1). The linear velocity of the foot was between 15.18 and 20.09 m s)1 at the time of impact. This justi\u00aees that the system before impact can be described as having only the angular momentum of the lower leg and foot about the knee joint since the velocity of the ball is zero before impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure2.17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure2.17-1.png",
        "caption": "Figure 2.17 Problem 2.3.",
        "texts": [
            " Determine the magnitude and direction of the net force applied by the workers on the block. Answer: 283 N, northeast. Problem 2.2 As illustrated in Figure 2.16, consider two workers who are trying to move a block. Assume that both workers are applying equal magnitude forces of 200 N. One of the workers is pushing the block toward the northeast, while the other is pulling it in the same direction. Determine the magnitude and direction of the net force applied by the workers on the block. Answer: 400 N, northeast. Problem 2.3 Consider the two forces, F 1 and F 2' shown in Figure 2.17. Assume that these forces are applied on an object in the xy-plane. The first force has a magnitude Fl = 15 Nand is applied in a direction that makes an angle a = 30\u00b0 with the positive x axis, and the second force has a magnitude F2 = 10 N and is applied in a direction that makes an angle fJ = 45\u00b0 with the negative x axis. (a) Calculate the scalar components of F 1 and F 2 along the x and y directions. (b) Express F 1 and F 2 in terms of their components. Force Vector 27 28 Fundamentals of Biomechanics (c) Determine an expression for the resultant force vector, FR' (d) Calculate the magnitude of the resultant force vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.8-1.png",
        "caption": "Figure 14.8 Free-body diagram of the ski jumper before takeoff.",
        "texts": [
            " At the end of the track, the direction normal to the track coincides with the vertical and the direction tangential to the track coincides with the horizontal. Consider a 70 kg ski jumper who is decelerating at a rate of 1.5 m/ S2 due to air resistance. If the friction on the track is neg ligible and the ski jumper reaches the end of the track with a horizontal velocity of v = 20 m/ s, determine the forces applied on the skier by the air resistance and the track. Solution: The free-body diagram of the ski jumper at the very end of the track (just before takeoff) is shown in Figure 14.8. The forces acting on the ski jumper are W due to gravity, R} due to air resistance, and the reaction force R2 applied by the track on the skis. Note that R2 is applied in the vertical direction or direction normal to the track. It is assumed that R} due to air resistance is applied in the horizontal direction or direction tangent to the track. At the circular end region of the track, the ski jumper undergoes a motion in a circular path with radius r = 50 m. The speed of the ski jumper at the very end of the track is v = 20 m/ s"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure4.9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure4.9-1.png",
        "caption": "Fig. 4.9 Datasheet of an industrial moving coil actuator. Courtesy of BEI Kimco Magnetics",
        "texts": [
            "24) substituting lw = 2\u03c0r2N and N = (r3 \u2212 r1)l2k f f /Aw: 4.7 Finite Element Analysis 119 120 4 Design Analysis of Moving Coil Actuators Jmax = 1 r \u221a \u0394T NuL\u03bbair 2k3 f f \u03b40 (1+ \u03b3\u0394T )kr2(kr3 \u2212 kr1)kl2 (4.25) The FEA mesh of the analyzed actuator is shown in Figure 4.6. The results illustrating the magnetic flux densities and Maxwell tensor stresses are presented in Figures 4.7 and 4.8 . The present section presents an analysis of data from different manufacturers of moving coil actuators. A typical datasheet is illustrated in Figure 4.9. Similarly as described in Section 3.8, moving coil actuators can be considered to be cooled by means of natural convection. The Nusselt number can be written[5] as: NuD = 129.20\u00d7D1/4 0.0026 < D < 0.124 m NuD = 217.25\u00d7D1/3 0.124 \u2264 D < 5.75 m (4.26) Different manufactured industrial moving coil actuators have been studied. Their output mechanical quantities compared to the maximum quantities previously stated are shown in Figures 4.10 and 4.11. The maximum quantities have been calculated using design factors q f = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003107_bf02657500-FigureI-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003107_bf02657500-FigureI-1.png",
        "caption": "Fig. I - - Schematic ~llustratLon of laser beam (electron beam), substrate geometry, and coordinate system.",
        "texts": [
            " For example, when the depth of the molten area was around 200 to 300/xm (Figures 12(a) to 12(c)), the convections were quite pronounced. For a shallower depth of melting (below about 100 ~zm) no con- vections could be traced. Furthermore, originally CuA12 precipitants, such as the one marked by a circle in Figure 12(d), have melted and resolidified without considerable dimensional changes. Still some diffusion has occurred, and this point will be discussed later in more detail. In Figure 13(a) we show a secondary electron image of an XY cross section of a laser molten region. This figure is just similar to the image shown in Figure 7(a) and reveals the same characteristics. Here, however, we have analyzed the Cu concentration along a line starting from the point marked A to the point marked B. This Cu concentration profile, i.e., the Cu concentration vs the distance from point A, is shown in Figure 13(b). Pronounced Cu peaks in Figure 13(b) appear at the points where one observes transitions in the microstructure bands of Figure 13(a). The occurrence of different microstructures has already been described in connection with Figure 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.13-1.png",
        "caption": "Figure 8.13 Transformation of stress tensor components.",
        "texts": [
            " The bar is subjected to externally applied forces that cause various modes of deformation within the bar. Let P be a point within the struc ture. Assume that a small cubical material element at point P with sides parallel to the sides of the bar is cut out and analyzed. As illustrated in Figure 8.12, this material element is subjected to a combination of normal (o-x and o-y) and shear (rxy) stresses in the xy-plane. Now, consider a second element at the same mate rial point but with a different orientation than the first element (Figure 8.13). One can assume that the second material element is obtained simply by rotating the first in the counterclockwise direction through an angle (). Let x' and y' be two mutually per pendicular directions representing the normals to the surfaces of the transformed material element. The stress distribution on the transformed material element would be different than that of the first. In general, the second element may be subjected to normal stresses (0-x' and 0-y') and shear stress (r x'y') as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure9.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure9.3-1.png",
        "caption": "Figure 9.3. Schematic representation of a bar under axial load: a. initial length of the bar; b. bar elongated under an axial load",
        "texts": [],
        "surrounding_texts": [
            "The basic concepts of the mechanics of materials can be explained by looking at a cylindrical bar under axial forces [5]. An axial force is oriented parallel to the axis of the structural element. If the bar with an initial length L is loaded under the axial load P, it will be stretched, so the length will be L + , where is the elongation of the bar. Furthermore, if a cross-sectional area A is considered, the stress in the bar can be defined by [5]: P A , (9.3) The strain is given by: L , (9.4) Hook\u2019s Law expresses the linear relationship between stress and strain [5]: E , (9.5) where E is the modulus of elasticity of the material. It is also called Young\u2019s modulus."
        ]
    },
    {
        "image_filename": "designv10_8_0002910_9.273337-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002910_9.273337-Figure4-1.png",
        "caption": "Fig. 4. Final cost function \\ f - ~ ( . r )",
        "texts": [
            " At each point in T o , the right-hand side - of (73) is computed and this in each iteration T = 1: . . . . T. The minimizing control is stored at the end as the final value of the controller function. On our workstation, IBM RS 6000, this problem took roughly two minutes of computing time and 50 kB storage. A final stability test along the lines of Section W E verified that the computed controller practically asymptotically stabilizes the system from G\u2018 to N(O.l). and E = 21 points in Design Results The computed cost function WF(.r) is shown in Fig. 4. The origin is in the center of the figure. The two relative maxima are at the points [-T. 01 and [T. 01, i.e., the hanging position of the pendulum. Toward the boundary of the computing region WT(..C) increases steeply, as a result of the last two terms in e, and finally reaches the upper bound 7 = 80. The piecewise constant controller is shown in Fig. 5. There are certain regions where the control function looks relatively smooth and an approximation of the piecewise constant function by a continuous function might be possible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003218_978-94-011-2526-0_1-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003218_978-94-011-2526-0_1-Figure4-1.png",
        "caption": "Fig. 4 Orientation structure",
        "texts": [
            " 2), denoted as 6-4 structure, and the position analysis reduces to find all possible closure configurations of the structure. A careful inspection of Fig. 2 shows that the 6-4 structure can be analyzed by considering first a statically determined substructure, called positioning substructure, which is responsible for the positioning of reference point Q (see Fig. 3). Once the position of point Q has been determined, the orientation of the platform W can be found by referring to the structure of Fig. 4, which represents the most general fully-parallel constraint defining the relative orientation of two bodies having a point in common. Thus position and orientation of the platform can be solved separately. Determination of point Q Dosition. The geometrical dimensions of the base are given; hence the coordinates of points Pi, i=1,3, in an arbit rary reference coordinate system WA fixed to the base are known (see Fig. 3). For a given input the leg lengths Hi, i=1,3, are also known. The closure equations of the positioning substructure are: ( 1",
            " The last two equations of system (3) are linear in 0 and ~; the determinant D of their coefficient matrix is given by the expression: (6) which is not equal to zero because points Pl, Pz, and Ps are supposed to be not aligned. Then the unknowns 0 and ~ can be linearly determined. By substituting the values of 0 and ~ in the first equation of system (3), two roots can be found for o. Hence, according to (2), two possible positions of the point Q are obtained. (If the roots were complex conjugate the manipulator would not have any real closure). Determination of platform orientation. The geometry of the orienta tion structure (see Fig. 4) is given. In particular, the lengths Lj of the legs AjBj, j=1,3, are known, and the positions of points Q, Al, A2, and As are given in WA. Moreover, the positions of points Q, B1, B2, and Ba are given in an arbitrary reference system WB fixed to the platform. Let WOA be a second reference system fixed to the base with origin in Q and its z axis, namely ZOA, directed from Q to Al; axis XOA can have arbitrary direction on a plane orthogonal to ZOA. Let MA be the 4x4 matrix for coordinate transformation from WOA to WA",
            " The values of 8, and 82 corresponding to the closures of the structure can be determined by imposing that distances A2Bz and A3B3 equal the leg lengths L2 and La respectively. To this respect, let consider the 3x3 rotation matrix R for the coordinate transformation from system WOB to system WOA: I C1C2-U\u00b7S1S2 -C1S2-U\u00b7S,C2 V\u00b7S1 I R = s,CZ+U\u00b7C,S2 -S,Sz+u\u00b7c,Cz -v\u00b7c, V\u00b7S2 v\u00b7cz U (7) written according to the Denavit-Hartenberg notation, where cj=cos8j, sj=sin8j, u=cosa, v=sina, and a is the angle between the axes ZOA and ZOB. With reference to Fig. 4, it can be found: cosa = --------- sina = (1-cos2a)i (8) where all right hand side quantities of (8) can be determined. The closure equations for the orientation structure, written in reference system WOA, are: (9) where Ajo is the position vector of point Aj in WOA and ~jO is the position vector of point Bj in WOB. By developing equations (9) it can be obtained: Each equation in system (10) is cosine-sine linear in 8, and 82; i.e., any term, if dependent on 8j (j=1,2), contains either cos8j or sin8j"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003751_s0022112007009949-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003751_s0022112007009949-Figure1-1.png",
        "caption": "Figure 1. (a) Sketch of a section of the magnetic filament tail showing the position, Yn, radius an, and the unit vector tn for bead n. The vector tn points from the particle\u2019s centre to the attachment point of the link. (b) Sketch of two neighbouring particles of the filament. The link exerts a force Fn\u22121",
        "texts": [
            " In the particle-based approach, the magnetic swimmer is treated as a series of N +1 rigid spheres, where the first N beads are paramagnetic and comprise the filament tail. Bead N + 1 is a large, non-paramagnetic sphere and provides a representation of the artificial swimmer\u2019s red blood cell cargo (Dreyfus et al. 2005). Each bead n = 1 . . . N + 1 centred at Y n has local body axes (tn, pn, qn) and is of radius an, where an = a for the paramagnetic spheres n = 1 . . . N and aN+1 = R for the large sphere (figure 1a). In the experiments, the ratio R/a \u2248 6.0 (Dreyfus et al. 2005). The unit vector tn is defined such that the locations of points on the surface of sphere n where the two links are attached are Y n \u00b1 an tn. Additionally, magnetic beads comprising the tail have magnetic permeability \u00b5. The permeability of the surrounding medium is taken to be that of free space \u00b50. In the experiments, the paramagnetic beads are of radius a =0.5 \u00b5m and a typical frequency of the applied field is \u03c9 = 62.8 rad s\u22121 (Dreyfus et al",
            " Both N(s) and M(s) vary with arclength 0 s l and balance the applied forces per unit length K and torques per unit length \u03c4 . In (2.9), t denotes the vector tangent to the centreline of the link. The moment M is related to the deformation of the link through the constitutive law M = \u03ba t \u00d7 dt ds + C t d\u03a8 ds , (2.10) where \u03ba is the bending modulus, C the twist modulus, and \u03a8 the twist angle. Consider the link connecting beads n \u2212 1 and n. This link begins (s = 0) at the point Y n\u22121 + an\u22121 tn\u22121 on the surface of bead n \u2212 1 and ends (s = l) at Y n \u2212 an tn on the surface of bead n as shown in figure 1(b). At the points of contact, the centreline of the link is taken to be perpendicular to the surfaces of the spheres corresponding to the clamped-end boundary conditions t = tn\u22121 at s = 0 and t = tn at s = l. The link is inextensible and there is the constraint (Y n \u2212 Y n\u22121) \u2212 an tn \u2212 an\u22121 tn\u22121 = \u222b l 0 t ds (2.11) on the components of the vector pointing from the attachment site on bead n \u2212 1 to that on bead n. Associated with this constraint are the force on bead n \u2212 1, Fn\u22121 elas = \u03bb1 tn\u22121 + \u03bb2 pn\u22121 + \u03bb3qn\u22121 and the equal and opposite force on bead n, Fn elas = \u2212Fn\u22121 elas "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure4.7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure4.7-1.png",
        "caption": "Fig. 4.7 Shear force acting on an element",
        "texts": [],
        "surrounding_texts": [
            "The problem is solved (indirectly) by finding the stress function T which satisfies within the ellipse y2 z2 a2 + b2 = 1 the differential equation (4.14), and on the ellipse satisfies the boundary condition T = O. The function is { y2 z2 } T = m a2 + b2 - 1 , The stress components are (Eq. 4.13) 2z 2y IJxy = 2GrJm b2 ' IJxz = -2GrJm a2 The shear stress T is the resultant of IJ xy and IJ xz, and so y2 z2 T = 4GrJm a4 + b4 with the maximum value on the boundary at the ends of the minor axis, that is, at the points nearest the axis of the torsional rotations. 4.1 Solid Cross Sections 75 From Eq. (4.6), we determine by integration the function 7jJ(y, z) a 2 _ b2 7jJ = - Z--b2 yz. a + The lines of constant values of the warping are shown in Fig. 4.2. From these results, we can deduce the following relations MT Tmax = WT ' {} D Corresponding values of the polar moment of inertia J T and the section modulus W T may be determined for cross sections of different kinds: 1. Equilateral triangle Let the boundary of a torsion member be an equilateral triangle with h = V3a/2. Proceeding as for the elliptical cross section, we find MT Tmax = WT ' {} 1 3 WT = 20 a , V3 4 JT = -a . 80 (4.24) 76 4. Torsion of Prismatic Bars 2. Narrow rectangular cross section Consider a bar subjected to torsion. Let the cross section of the bar be a solid rect angle with width b and depth h, where b \u00ab h. From the different analogies (e.g. the soap-film analogy, originally proposed by L. Prandtl.),2 we may conclude that except for the region near z = \u00b1h/2 the stress components a xy and a xz are ap- f-b-j I y 1 Fig. 4.4 z Narrow rectangle proximately independent of z, and a xy ~ 0, a xz ~ T(Y) = 2G1'Jy. Thus, from Eq. (4.13), we determine T~T(y)= b; {l- (2:r}, and furthermore 1 3 Jr=3\"hb. (4.25) (4.26) (4.27) We note, however, that near the ends, of course, these results, which are valid only for narrow cross sections, do not apply. The exact theory for the rectangle is then required. The simple parabolic approximate form of T (Eq. 4.26) will give a good approx imation, since it differs from the true solution only in the small end zones. We may generalize Eq. (4.27) by introducing correction factors 0: and (3, as functions of the ratio h/b (see Table 4.1), to give 1 2 1 3 WT = 0: 3\" hb, Jr = (3 3\" hb . (4.28) 2 Analogies exist where physically different problems have similar mathematical descrip tions. In this case solutions - or experimental findings - from one problem may be trans ferred to the other - analogous - problem. The most known analogy to the torsion problem of prismatic bars is that of a membrane (soap film) fixed on a closed boundary, having the same shape as the cross section of the torsion bar, where pressure is applied to one side of the membrane. We therefore refer e.g. to the textbook of Boresi, Schmidt & Sidebottom, Advanced Mechanics of Materials, 5th. Edition, John Wiley & Sons, N.Y. etc., 1993. 4.2 Thin-Walled Closed Cross Sections 77 4.2 Thin-Walled Closed Cross Sections In the preceding section, we have discussed torsion of prismatic bars with solid cross sections. In the following sections, we now will examine this problem with thin-walled cross sections. We maintain the assumptions of St. Venant's theory about the displacement com ponents (Eqs. 4.1, 4.2), and furthermore - for the moment - assume unrestrained warping 'IjJ(y, z) in the x direction. In Section 3.2, we discussed beams of thin walled cross sections subject to shear forces. From this section, we take the modi fied description of thin-walled cross sections, with cross-sectional centerline (mid dle line), and additional rectangular coordinates (, along the centerline and 'f/, per pendicular to (. Thus, the thin-walled cross section is described by the coordinates y((), z(() of the centerline, and thickness J(() ofthe profile. for the shear stresses, and u=u(x,() (4.29) (4.30) for the displacements, constant in the 'f/ direction. We note that assumptions (4.29) coincide with the assumptions (3.37) for the shear stresses due to shear forces (Sec tion 3.2). Defining now the shear flow t( () as J 8/2 t(() = O\"xC, d'f/, (4.31) -8/2 we obtain with (4.29h t(() = T(()J((). (4.32) From the equilibrium (in axial direction) of a small element cut from the thin-walled tube (Fig. 4.6), we see that t = T( ()8( () = const. , (4.33) provided there are no axial stresses (J xx' Thus, the largest shear stress occurs where the thickness is smallest, and vice versa. Of course, if the thickness is uniform, then the shear stress T is constant around the tube. In order to relate the shear flow to the torque M T acting on the tube, consider an element of length d( in the cross section: The total shear force acting on the element is t de, and the moment of this force about any point 0 is dMT = a(()td(, (4.34) in which a( () is the distance from 0 to the tangent to the centerline. The total torque then is MT = t f a(()d( = 2Amt, (4.35) where the integral represents double the area Am enclosed by the centerline of the tube. From this equation, we find MT t = T(()8(() = 2Am ' (4.36) and finally, 4.3 Thin-Walled Open Sections 79 Tmax = (4.37) Bredt's first formula. To determine a relation between torque M T and twist {}, we start from assump tion (4.30), and (4.38) With these displacements, we find ) 1 { dux } ex((( =\"2 d( + {}a(() , (4.39) and thus from Hooke's law (4.40) Integrating this expression over the entire length of the centerline yields f T(() d( = c{ f dux + {} f a(() d(}. (4.41) The first integral of the right hand side vanishes (continuity of u x), and thus with Eq. (4.36), we finally arrive at 2 {f d( }-l Jr = 4Am 8(() , (4.42) Bredt's second formula. If in Eq. (4.41) the integrals are not taken over the entire length of the centerline, e.g. for the first integral of the right hand side J( dux = ux(() - ux(O) = {}{'l,b(() - 'l,b(O)} , (4.43) o Bredt's second formula is replaced by a slightly different relation (4.44) from which the distribution of the warping along the centerline may be calculated. 80 4. Torsion of Prismatic Bars Fig. 4.8 Thin-walled open section"
        ]
    },
    {
        "image_filename": "designv10_8_0002706_tac.2002.802750-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002706_tac.2002.802750-Figure2-1.png",
        "caption": "Fig. 2. Frenet frames associated with the nonholonomic points P .",
        "texts": [
            " Under the assumption that the path is sufficiently smooth and that the curvature has an upper bound, a particularly useful local frame to describe the lateral dynamics of the path following problem decoupled from the longitudinal one is the so-called Frenet frame i.e., a frame moving on the path having origin on the orthogonal projection of the point of interest. In [2], the tracking criterion introduced consists in considering n+ 1 frames simultaneously, one for each nonholonomic point. Each of the curvilinear frames (see Fig. 2) is represented by two coordinates (s ; ) where s is the line integral along the path to follow, up to the actual projection of the point Pi on the path itself and is the orientation of the frame with respect to the inertial frame. In the Frenet frame, the point Pi is represented by the signed distance zi between the point itself and its orthogonal projection and by the relative orientation angle ~ i. The decoupling property of the Frenet frame has already been used by several authors for the path following problem (see [10] and [12])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.11-1.png",
        "caption": "Figure 4.11 A concurrent, three-force system.",
        "texts": [
            " \u2022 Three10rce systems: If there are only three forces acting on a body and if the body is in equilibrium, then the forces must form either a parallel or a concurrent system of forces. Furthermore, for either case, the forces form a coplanar force system. A parallel three-force system is illustrated in Figure 4.10. If two of the three forces are known to be parallel to one another, then we can readily assume that the third force is parallel to the other two and establish the line of action of the unknown force. A concurrent three-force system is illustrated in Figure 4.11. In this case, the lines of action of the forces have a common point of intersection. If the lines of action of two of three forces act ing on a body are known and if they are not parallel, then the line of action of the third force can be determined by extending the lines of action of the first two forces until they meet and by drawing a straight line that connects the point of intersection and the point of application of the unknown force. The straight line thus obtained will represent the line of action of the un known force. To analyze a concurrent force system, the forces forming the system can be translated to the point of intersection (Figure 4.11b). The forces can then be resolved into their compo nents along two perpendicular directions and the translational equilibrium conditions can be employed to determine the un knowns. In such cases, the rotational equilibrium condition is satisfied automatically. \u2022 Statically determinate and statically indeterminate systems: For two-dimensional problems in statics, the number of equilibrium equations available is three. Therefore, the maximum number of unknowns (forces and/ or moments) that can be determined by applying the equations of equilibrium is limited to three"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002591_978-94-017-0657-5_3-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002591_978-94-017-0657-5_3-Figure6-1.png",
        "caption": "Figure 6. Top view of a misaligned actuator.",
        "texts": [
            " From the distribution point of view, Arrangement III is better than the others. In practice, it may be difficult to fabricate and assemble a perfect orthogonal frame. In this section, we illustrate a method for compensating manufacturing and assembling errors of the linear actuators by one example. We assume that the X actuator is twisted by a small angle /),.8 about the Z axis, and the other actuators are mounted perfectly along the Y and Z axes as shown in Fig. 5. When the X and Z actuators are held stationary, the dotted line in Fig. 6 denotes the possible locus of B2 \u2022 Hence, if the revolute joint axes of the X limb remain parallel to the prismatic joint as shown in Fig. 6 (a), the x, y, and z motions of the moving platform will be coupled. The coupling problem can be solved by adjusting the revolute joint axes such that they are all parallel to the X axis as shown in Fig. 6 (b). It should be noted that the three revolute joint axes in each limb should be parallel to one another, otherwise, this manipulator may not move or generate pure translational motion. A new 3-DOF translational parallel manipulator, behaving like a conventional X-Y-Z Cartesian machine, is conceived. It is shown that the x, y, and z motions of the manipulator are decoupled. Some design considerations with regard to the location of the Z actuator and a method for compensating the misalignment of the actuators are discussed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.31-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.31-1.png",
        "caption": "Figure 13.31 Tangential velocity and normal acceleration of B.",
        "texts": [
            " Magnitudes of linear velocity in the tangential direc tion and linear acceleration in the normal direction of point B can be determined using: VB = \u00a31 WI aB=\u00a3l W12 The magnitude of the tangential component of the acceleration vector is zero since WI is constant or since ell = O. Therefore, VB and a B are essentially the magnitudes of the resultant linear velo city and acceleration vectors. To express these quantities in vec tor forms, let n1 and t1 represent the normal and tangential directions to the circular path of point B when arm AB makes an angle lh with the horizontal (Figure 13.31). Also let 111 and h be unit vectors in the positive n1 and tl directions, such that the positive 111 direction is outward (i.e. from A toward B) and positive h direction is pointing in the direction of motion (i.e. counterclockwise). The normal (centripetal) acceleration is al ways directed toward the center of motion, and is acting in the negative 111 direction: l:!.B = VB h = \u00a31 WI il f!.B = -a B 111 = -\u00a3 1 W1 2 111 Note that directions defined by unit vectors 111 and h change continuously as point B moves along its circular path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.9-1.png",
        "caption": "Figure 3.9 Opposite moments.",
        "texts": [
            " Therefore, the dimension of moment is equal to the dimension of force (ML/T2) times the dimension of length (L): [MOMENT] = [FORCE] [MOMENT ARM] = ~; L = ~;2 The units of moment in different systems are listed in Table 3.1. 3.5 Some Fine Points About the Moment Vector \u2022 The moment of a force is invariant under the operation of slid ing the force vector along its line of action, which is illustrated in Figure 3.8. For all cases illustrated, the moment of force about point 0 is: M=dF (ccw) where length d is always the shortest distance between point 0 and the line of action of F . Again for all three cases shown in Figure 3.8, the forces generate a counterclockwise moment. \u2022 Let F 1 and F 2 shown in Figure 3.9 be two forces with equal magnitude (Fl = F2 = F) and the same line of action, but acting in opposite directions. The moment Ml of force F 1 and the mo ment M2 of force F 2 about point 0 have an equal magnitude (Ml = M2 = M=dF), but opposite directions (Ml = -M2). \u2022 The magnitude of the moment of an applied force increases with an increase in the length of the moment arm. That is, the greater the distance the point about which the moment is to be calculated from the line of action of the force vector, the higher the magnitude of the corresponding moment vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002421_robot.1999.770007-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002421_robot.1999.770007-Figure2-1.png",
        "caption": "Figure 2: The kinematic parameters.",
        "texts": [],
        "surrounding_texts": [
            "1 Introduction\nBiped locomotion is a popular research area in robotics due to the high adaptability of a walking robot in an unstructured environment. When attempting to automate the motion planning process for a biped walking robot, one of the main issues is assurance of dynamic stability of motion. This can be categorized into three general groups [l]: body stiG bility, body path stability, and gait stability. A Zero Moment Point (ZMP), a point where the total forces and moments acting on the robot are zero, is usually used as a basic component for dynamically stable motion.\nStable walking using a compensative inverted pendulum was achieved e.g. by the robot [2] with eight control variables (called degrees of freedom, DOF) and an upper body acting like an inverted pendulum. Other approaches for stable locomotion, with or without ZMP use, have been considered as well (see, e.g. [5],[6],[7]). In a more recent achievement, Honda\u2019s hu-\nmanoid robot P2 [8] showed the ability to walk forward, backward, right, left, up and down a staircase, and on the uneven terrain.\nNow suppose the biped robot has a sensor (say, vision) that allows it to detect an object in front of it, and suppose it walks in a scene with obstacles. In principle, this should allow the robot to operate in the scene the way humans do, avoiding the obstacles while maintaining stable motion. When encountering an obstacle on its way, depending on the obstacle\u2019s size and shape, a way of recuperating from the disturbance is to step over the obstacle, or step on it, or try to pass around it. Foot placement during this operation should be planned so as to preserve dynamical stability. If feasible, such a behavior would produce dynamically stable real time motion in an unstructured environment with unknown obstacles.\nAttempting such an approach is the topic of this work. The work builds and further extends the methodology presented in [3], which allows a biped robot to maintain dynamically stable motion under force disturbances. Some details are skipped due to the lack of space; for those, refer to [4].\n2 The Model of Biped Locomotion\nThe robot consists of seven body parts [5]: one hip, two thighs, two calves, and two feet. Body parts have certain masses, which all affect the dynamics and the walking pattern. There is a total of twelve DOF - six at the hip, two at knee, and four at ankle, Figures 1,2 . Similar to the human knee, robot knee joints are able to turn only about 04 axis; each joint between the hip and thigh has three DOF. The ankle joint turns about 05 axis and 0s axis.\nThe robot is assumed to be equipped with sensors (say, a vision) capable of sensing obstacles on its way and assessing their dimensions and distances to them. Only obstacles directly in front of the robot are considered. Each obstacle is a parallelepiped: it can be\n0-7803-51 80-0-5/99 $10.00 0 1999 IEEE 375",
            "small enough to step over it by raising a leg, or small and wide enough to step on/off it, or tall enough so that side steps are necessary to pass around it.\nTwo major phases in walking dynamics are hypothesized [5]: single support phase and double support phase. During the single support phase, one leg is on the ground, and the other leg is in the swinging motion. As soon as the swinging leg reaches the ground, the system is in the double support phase, Figure 3. Denote T2 the time period of deploy phase, T3 - of swing phase, T4 - of heel contact phase, and 2Tl - of support phase. The time period of a single walking cycle within which all body parts return to their original configuration is 4Tl.\n, support b ' angk ~ o u ~ s ~ u p p o t t ~ a s e I Single xme\nI h p h I Swtng ' w a n t a u I ' ~bploy ' Swing : ~ e e i c ~ n t a c t ' I 1 i\n3 Zero Moment Point and Locomotion LaLsrr T2 T3\nI ZMP is defined as a point on the walking surface\nin which the total forces and moments acting on the robot are zero [l]. If at a given moment of motion all the forces acting on the robot (gravity, reaction forces, and inertia forces) are balanced so that ZMP lies within the current robot footprint, the robot's POsition at this moment is dynamically stable. If this is true throughout the motion, and the trajectory of the robot's center of mass (COM) is smooth and lies be-\nlRigMLeg suppoct\nFigure 3: Phases of a single walking cycle.",
            "Variation in step length. With the robot dimensions under the model used, a normal motion step (single walking cycle) is of length 28 inches. When sensing an obstacle that is to be negotiated, the robot may decide to step on or over it, and this may require the robot first positioning itself at a specific position relative to the obstacle. This can be done by modifying the step length appropriately. Due to the effects of dynamics and related computational difficulties, it is not easy to compute the trajectory for an arbitrary step \u201con the fly\u201d; instead, a small number of \u201c typ ical\u201d step lengths that together cover a large set of situations are developed and \u201ccanned\u201d. Relative to the normal step length, this includes a half step (14 inches), quarter step (7 inches), and zero step (0 inch) lengths options. By aplying an appropriate scheme for the dynamics of swing leg and hip position trajectories, a stable walk for those walking patterns is obtained.\nVariation in the swine lee: height. With normal walk pattern, the robot can negotiate obstacles up to 1 inch high. To step over higher obstacles, the leg needs to be raised higher than normal. This changes the whole swing leg trajectory (according to the model, the COM of a swinging leg trajectory has parabolic shape [5]). Similar to the above, five trajectories that take care of the motion dynamic stability are precomputed and stored - for the obstacle heights (height ranges) 1, 2,3 ,4 , and 5 inches. (Bigger heights seem to be feasible; no attempt was made to maximize the step height for stepping on/over obstacles). After obtaining from the sensors the height and width of the obstacle that is to be negotiated, and after deciding to negotiate it by stepping on or over it, the robot chooses and executes the appropriate leg height trajectory.\nForward-side step and side step. When the obstacle is too high to step over or on it, the robot will attempt to pass around it. The (local) direction of passing around an obstacle (left or right) is decided upon beforehand; in our experiments (see below) it has been \u201cleft\u201d. If at the moment of such a decision the robot still has room for forward motion, it can be combined with side motion, producing a forward-side step. Otherwise, a side step, which has no forward component and is perpendicular to the prior direction of motion, is executed; in our scale, the side step is 6 inches long.\nTo keep the motion smooth, depending on the swinging leg at the moment of a (left) forward-side step, it may be either left or right leg that starts the maneuver. If it is the left leg, the forward-side step is simply build of the two components as above; after its execution the robot torso ends up 6 inches to the left. Because of the possible entanglement between two legs, the same cannot be done with the right leg starting the maneuver. In this case, after the step execution the right foot end up right in front of the left foot; the next step by the left leg will complete the forward-side step maneuver. Again, tied to this operation is the adjustment of the swing leg COM and hip position trajectories so as to satisfy dynamics stability.\nStepping on/off obstacles. If the obstacle is wide and flat enough to step on, sometimes it is more efficient to negotiate it by stepping on it rather than going around it. Similar to the stepping over o p tion above, five dynamically stable trajectories, for the foot heights from 1 to 5 inches, are precomputed and stored. Once the height of such an obstacle is known, the swing leg COM and hip position trajectories are chosen from the set. The walking pattern of stepping off the obstacle is similar. Depending on the length of the obstacle, stepping on the obstacle may be followed by few normal steps, then perhaps a reduced length step, and finally stepping off step.\nThe flowchart of the overall decision making algorithm capable of negotiating a sequence of obstacles of the types described above is shown in Figure 5. Darkened boxes indicate the final action in the current cycle, after which a new step is initiated and the control goes to the top of the flowchart. The algorithm for selecting the walking pattern utilizes nested if-else commands.\n5 Simulated Examples\nDescribed here are the results of computer simulated experiments with two-legged locomotion in the"
        ]
    },
    {
        "image_filename": "designv10_8_0003933_j.engfailanal.2010.11.009-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003933_j.engfailanal.2010.11.009-Figure3-1.png",
        "caption": "Fig. 3. BW boom head with excavating device.",
        "texts": [],
        "surrounding_texts": [
            "The extremely dynamic and stochastic nature of external loads and very heavy duty operation may lead to a whole range of failures of BWE and stacker\u2013reclaimer (BWSR). In some cases, the failure consequences can be catastrophic [1\u20133], Fig. 1. Even when they are not disastrous [4\u20136], the consequences lead to very high financial losses [7] which, in fact, represent costs of losses in production [8]. After the first erection, a trial operation of BWE SRs 1300, Figs. 2 and 3, is performed by excavating distracted overburden because there were no operational and technological conditions for a \u2018\u2018full\u2019\u2019 exploitative investigation. The capacity of the machine was proved during the trial operation and no defects were found. However, after only 1800 h of operation, problems occurred in the operation of the reducer, as well as cracks and deformations of the BW body, Figs. 4 and 5. The occurrence of cracks in the welded butt joints positioned circumferentially (diameters D1, D2 and D3), Fig. 5, brought about a complete . All rights reserved. ax: +381 11 3370364. separation of individual parts of the structure and complete loss of the BW shape. Arc-shaped cracks occurred in the weld metal (WM) and HAZ, with lengths corresponding to: 270 (diameter D1), 130 (diameter D2) and 190 (diameter D3). In order to diagnose the cause of cracks occurrence in BW body structure, the following had to be performed: Calculation of the stress state of the BW body structure. Experimental procedure, which, given the nature of the failure, includes: \u2013 Chemical composition and mechanical properties of parent metal (PM). \u2013 Tensile properties, hardness and impact toughness of welded joints. \u2013 Tendency towards cracks occurrence. \u2013 Welding residual stress. \u2013 Working stress. \u2013 The microstructure of the material in the zone of cracking. Based on the results of the calculated stress state and the measured welding residual stresses, a safety estimation of the critical welded joints is carried out utilizing the Goodman diagram [9,10]."
        ]
    },
    {
        "image_filename": "designv10_8_0003306_j.bioeng.2006.06.003-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003306_j.bioeng.2006.06.003-Figure5-1.png",
        "caption": "Fig. 5. Scheme of the lysine biosensor. 1, PVC electrode body; 2, connector piece; 3, conducting composite (or biocomposite); 4, lysine oxidase membrane; 5, dialysis membrane; 6, circular copper piece; 7, solder; 8, O-ring. \u2018\u2018Reprinted Saurina et al. (1999), with permission from Elsevier.\u2019\u2019",
        "texts": [
            " Lysine biosensors were constructed in three different configurations: (A) the lysine oxidase membrane was attached to a graphite\u2013methacrylate composite electrode for the oxidative electrochemical detection of hydrogen peroxide at +1000 mV; (B) the lysine oxidase membrane was attached to a peroxidase-modified graphite\u2013methacrylate biocomposite electrode for reductive electrochemical detection of oxidised peroxidase; (C) the lysine oxidase membrane was attached to a peroxidase-modified graphite\u2013methacrylate biocomposite electrode which was used for hydroquinone-mediated detection. The sensitivity was higher in the (A) and (C) configurations although they were affected by other amino acids acting as interferents. These types of biosensors permit rapid analysis of lysine in contrast to time consuming chromatographic techniques. A scheme of the lysine biosensor is shown in Fig. 5. Figures of merit of these biosensors are given in Table 1. Conductive polymers have been extensively employed in the construction of biosensors because these materials facilitate the electron transfer between the enzyme active site and the electrode surface. Enzymes entrapped within polypyrrole (PPy) films prepared by electropolymerization from aqueous solutions have been commonly used to prepare electrodes. Thus, Brahim et al. (2002a) developed a glucose biosensor based on GOx entrapment within a composite pHEMA/PPy membrane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002882_313-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002882_313-Figure4-1.png",
        "caption": "Figure 4. Cross sectional scheme of the micropump built with four PCBs.",
        "texts": [
            " To build the pump, four double-sided 70 \u00b5m copper-plated PCBs (with a total thickness of 800 \u00b5m) were mechanically and wetchemically structured. The foil was clamped into a special handling system (structured rings) to allow the processing (structuring, coating, cleaning and positioning) of the foil. After mounting the heater into the actuator chamber, all parts were cleaned. Subsequently the PCBs and the foil were coated with adhesive and stacked into a positioning system. Finally the PCB stack is put into a thermopress to cure the adhesive. Figure 4 schematically shows a cross section of the micropump. By switching on the heater, it dissipates electric power and causes an increase of temperature in the chamber. That forces the chamber pressure to rise and subsequently leads to a movement of the membrane decreasing the pump chamber\u2019s volume. The resulting over-pressure closes the inlet valve and opens the outlet valve simultaneously driving the fluid out of the chamber to the outlet. Cooling down the heater lets the actuator membrane return to its initial position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.21-1.png",
        "caption": "Figure 8.21 Analyses of the material element in Figure 8.20.",
        "texts": [
            " Therefore, point A on the Mohr's circle represents the orienta tion of the material element for which the normal stresses are max imum and minimum, and the material element in Figure 8.18b represents the state of principal stresses. Example 8.3 Consider the material element shown in Figure 8.20. In the xy-plane, the element is subjected to compressive stress ax and shear stress i xy . Using Mohr's circle, determine the principal stresses, maximum shear stress, and the principal planes. Solution: Mohr's circle in Figure 8.21a is drawn by using the plane stress element in Figure 8.20. There is a negative (com pressive) normal stress with magnitude ax and a negative shear stress with magnitude ixy on surface A of the material element in Figure 8.20. Therefore, point A on Mohr's circle has coordinates -a x and -ixy . Surface B on the stress element has only a negative shear stress with magnitude i xy . Therefore, point B on the i-a diagram lies along the i-axis at a ixy distance above the origin 166 Fundamentals of Biomechanics (positive)",
            " The center C of Mohr's circle can be determined as the point of intersection of the line connecting A and B with the a-axis. The radius of the Mohr's circle can also be determined by utilizing the properties of right triangles. In this case: r= ( ax )2 + T2 2 xy Once the radius of the Mohr's circle is established, it is easy to find the principal stresses a1 and a2 and the maximum shear stress Tmax: ax a1 = r - 2 (tensile) ax a2 = r + 2 (compressive) Tmax = r To determine the angle of rotation, fh, of the plane for which the stresses are maximum and minimum, we need to read the angle between lines CA and CD in Figure 8.21a, which is equal to 201. From the geometry of the problem: 2lh = 1800 - tan-1 (~: ) As illustrated in Figure 8.21b, to construct the material element for which normal stresses are maximum and minimum, cal culate angle 01 and rotate the material element in Figure 8.20 through an angle 01 in the clockwise direction. 8.6 Failure Theories To ensure both safety and reliability, a structure must be de signed and a proper material must be selected so that the strength of the structure is considerably greater than the stresses to which it will be subjected when it is put in service. For example, if a material is subjected to tensile loads only, then the strength of the material must be judged by its ultimate strength (or yield strength)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure13-1.png",
        "caption": "Figure 13. Se t t ing of b o u n d a r y condi t ions in a f ini te-element mode l wi th th ree pairs of tee th .",
        "texts": [
            " The performed stress analysis is based on the finite-element method [8] and application of a general computer program [9]. The development of finite-element models of helical gears has been accomplished according to the ideas presented in previous papers [3,4]. 1076 F . L . LITVlN et al. A model of three teeth has been considered as it is shown in Figure 12. This model is generated automatical ly as a function of number of elements in profile and longitudinal direction. Setting of boundary conditions is accomplished automatical ly and are shown in Figure 13. The following ideas are applied, (i) Nodes on the two sides and bo t tom part of the portion of the gear rim are considered as fixed (Figure 13a). (ii) Nodes on the two sides and the bo t tom part of the pinion rim form a rigid surface (Figures 13a and 13b). (iii) A reference node N (Figure 13b) 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, rotation about the pinion axis, while all other degrees of freedom are fxed. Application of a torque T in rotational motion at the reference point N allows to apply such torque to the pinion model. The contact algorithm of the finite-element analysis computer program [9] requires definition of contacting surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.4-1.png",
        "caption": "Figure 8.4 A rectangular bar subjected to tensile forces in the x and y directions and a material element under biaxial stresses.",
        "texts": [
            "5) This formula can be used to calculate the Poisson's ratio of a material if the elastic and shear moduli are known. 8.2 Biaxial and Triaxial Stresses As discussed in the previous section, when an object is subjected to uniaxial loading, strains can occur in all three directions. The strains in the lateral directions can be calculated by utilizing the definition of Poisson's ratio. Poisson's ratio also makes it possible to analyze situations in which there is more than one normal stress acting in more than one direction. Consider the rectangular bar shown in Figure 8.4. The bar is sub jected to biaxial loading in the xy-plane. Let P be a point in the bar. Stresses induced at point P can be analyzed by constructing a cubical material element around the point. A cubical material element with sides parallel to the sides of the bar itself is shown in Figure 8.4, along with the stresses acting on it. ax and ay are the normal stresses due to the tensile forces applied on the bar in the x and y directions, respectively. If Ax = a band Ay = be are the areas of the rectangular bar with normals in the x and y directions, respectively, then ax and ay can be calculated as: Fx Fx ax = - =- Ax a b F F a-....L-....L y- A -be y Multiaxial Deformations and Stress Analyses 157 The effects of these biaxial stresses are illustrated graphically in Figure 8.5. Stress CTx elongates the material in the x direction and causes a contraction in the y (also z) direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.41-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.41-1.png",
        "caption": "Figure 4.41 Center of gravity of the paper is located at the intersection of lines aa and bb (suspension method).",
        "texts": [
            " The center of gravity of an object is such that if the object is cut into two parts by any vertical plane that goes through the center of gravity, then the weight of each part would be equal. There fore, the object can be balanced on a knife-edge that is located directly under its center of gravity or along its gravity line. If an object has a symmetric, well-defined geometry and uniform composition, then its center of gravity is located at the geomet ric center of the object. There are several methods of finding the centers of gravity of irregularly shaped objects. One method is by\" suspending\" the object. For the sake of illustration, consider the piece of paper shown in Figure 4.41. The center of gravity of the paper is located at C. Let 0 and Q be two points on the paper. If the paper is pinned to the wall at 0, there will be a non-zero net clockwise moment acting on the paper about point o because the center of gravity of the paper is located to the right of O. If the paper is released, the moment about 0 due to the weight W of the paper will cause the paper to swing in the clockwise direction first, oscillate, and finally come to rest at a position in which C lies along a vertical line aa (gravity line) passing through point 0 (Figure 4.41b). At this position, the net moment about 0 is zero because the length of the moment arm of W relative to 0 is zero. If the paper is then pinned at point Q, the paper will swing in the counterclockwise direction and soon come to rest at a position in which C is located directly under Q, or along the vertical line bb passing through Q (Figure 4.41c). The point at which lines aa and bb intersect will indicate the center of gravity of the paper, which is point C. Note that a piece of paper is a plane object with negligible thick ness and that suspending the paper at two points is sufficient to locate its center of gravity. For a three-dimensional object, the object must be suspended at three points in two different planes. Another method of finding the center of gravity is by \"balanc ing\" the object on a knife-edge. As illustrated in Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002858_0191-8141(92)90061-z-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002858_0191-8141(92)90061-z-Figure2-1.png",
        "caption": "Fig. 2. Developable surtaccs. (a) General case in which a curve is formed from the intersection of generators; (b) special case of a conical surface.",
        "texts": [
            " As can be readily demonstrated by flexing a sheet of paper, a limited range of fold forms is capable of being produced by isometric bending. All developable surfaces are ruled surfaces which means that straight lines (generators) can be drawn on them and have the additional property that adjacent generators, if extended far enough, will intersect one another (Hilbert & CohnVossen 1952). In the general case of a developable surface, successive points of intersection of generators define a curve in space (Fig. 2a). The curve can consist of a single point (Fig. 2b) as in the case of conically-folded surfaces. If this point is situated at infinite distance the surface becomes cylindrical. From a geological point of view this curve made up of the intersection points of generators is important be- cause it marks the maximum extent of the isometrically folded sheet. In other words, the isometric folding model is not capable of explaining the structure of an infinitely-extensive sheet; only of compartments within it bounded by some form of discontinuity. At all points lying along any generator line of a developable surface, unlike other classes of ruled stirfaces, the orientation of the surface is constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure7-1.png",
        "caption": "Fig. 7. Installment of the worm with respect to the cradle d.",
        "texts": [
            " Circular arc profiles of the blade fillet are provided for the generation of the fillet of the gear. The generation of the worm is performed by a tilted head-cutter mounted on the cradle d of the generating machine (Fig. 6). The worm and the cradle d perform related rotations determined as x\u00f0w\u00de x\u00f0d\u00de \u00bc N2 N1 \u00f01\u00de where N2 and N1 are the number of teeth and threads of the face-gear and the worm. The rotation of the head-cutter is provided for obtaining the desired velocity of cutting (grinding) and is not related with the meshing of cradle d and the worm. Fig. 7 illustrates the installment of the worm with respect to the cradle d. The process of generation of the worm simulates its meshing with the face-gear. The face-gear is represented in Fig. 7 as cradle d that carries the head-cutter. The worm head-cutter and cradle d may be considered as rigidly connected each to other in the process of meshing of cradle d with the worm. The surface of the head-cutter simulates the tooth surface of the face worm gear. The process of worm generation provides for the gear drive: (i) localization of bearing contact, and (ii) a parabolic function of transmission error. Localization of contact is achieved by deviation of profiles of blades of worm head-cutter with respect to the blades of gear head-cutter (see Section 3). Parabolic function of transmission errors is provided by variation of distance Em\u00f0w1\u00de (Fig. 7) during the worm generation where w1 is the angle of worm rotation performed during the process of worm generation. The derivation of face-gear tooth surface of new design is based on the following procedure: (i) Derivation of face-gear tooth surfaces R 2 of existing design generated by a hob. (ii) Determination of pitch point P of existing design. (iii) Determination of circle C of surface R 2 that passes through point P and two other points of R 2. The radius of circle C is the radius of the head-cutter to be used for generation of face-gear tooth surface of new design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002957_s0263574703005216-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002957_s0263574703005216-Figure5-1.png",
        "caption": "Fig. 5. The manipulator with optimised link lengths given in the first row of Table 1; \u201c. . \u201d is for 1 =1200, 4 =960, =119.38810, \u201c- - -\u201c is for 1 =300, 4 =240, =98.49690, and \u201c. . ..\u201dis for 1 =3000, 4 =2400, c=52.15350.",
        "texts": [
            "1 while the others were kept constant. The range of initial values for the parameters was \u2264L0, L1, L2 \u22642.0 and =0.8. Different initial values resulted in different solutions satisfying the objective function and the synthesis constraints. Sets of optimised link lengths are given in Table I. The variation of the transmission angle and the condition number of the Jacobian matrix for the solution number 1 given in Table I are depicted in Figure 4. The three configurations of the resulting five bar parallel manipulator are shown in Figure 5. The results given in Table I are in agreement with \u201cFiveBar Grashof Criteria\u201d proposed by Ting,35 which states that when Lmax +Lmin 1 +Lmin 2 >Lother 1 +Lother 2, the mechanism has at most two cranks. This is also required by Constraint V given above; while L1 and L4 are making full rotations, the transmission angle is satisfying Constraint IV, as shown in the top plot of Figure 4. Other linkages satisfying the \u201cFive-Bar Grashof Criteria\u201d can be obtained by introducing appropriate constraints into the optimisation procedure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.4-1.png",
        "caption": "Figure 3.4 Direction of the moment vector.",
        "texts": [
            " To determine the shortest distance between 0 and the line of action of the force, extend the line of action of F and drop a line from 0 that cuts the line of action of F at right angles. If the point of intersection of the two lines is R, then the distance d between 0 and R is the lever arm, and the magnitude of the moment M of force F about point o is: M=dF (3.1) 3.3 Direction of Moment The moment of a force about a point acts in a direction perpen dicular to the plane upon which the point and the force lie. For example, in Figure 3.4, point 0 and the line of action of force F lie on plane A. The line of action of moment M of force F about point o is perpendicular to plane A. The direction and sense of the mo ment vector along its line of action can be determined using the Moment and Torque 31 32 Fundamentals of Biomechanics right-hand-rule. As illustrated in Figure 3.5, when the fingers of the right hand curl in the direction that the applied force tends to rotate the body about point 0, the right hand thumb points in the direction of the moment vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002548_s0957-4158(96)00045-1-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002548_s0957-4158(96)00045-1-Figure3-1.png",
        "caption": "Fig. 3. A two-degree-of-freedom manipulator.",
        "texts": [
            " In view of the SMC, Eqn (25), the proposed FSMC can now be formulated as follows: ui(t) = [-- kdi(s, , csi) - { [cix2i(t) + f i ( x , t) - C,X2id (t) -- X2id (t)[ + }3~(X, t)[} sgn (a,(e(t))) --fif~(x, t)]/[(1 -- ~b(x, t))bg(x, t)]. (37) It is noted that ki\" sgn (tri(e(t))) in Eqn (25) is replaced by k d i ( s , cs3. Unlike conventional SMC that has fixed feedback gains, the FSMC has varying feedback gains which are properly adjusted according to the commanded fuzzy rules. 5. AN ILLUSTRATIVE EXAMPLE Consider the two-degree-of-freedom manipulator as shown in Fig. 3. The manipulator has one rotational and transitional joint in the (x, y) plane. The dynamic equations of this configuration follow directly from an application of Lagrange's equation. By assuming Y t/m,t, , / \\ 208 SEUNG-BOK CHOI and JUNG-SIK KIM normal ized unit mass and unit length of the arm, and neglecting the gravity force, we obtain the following dynamic equat ions [12]: t'(t) = r(t)O 2 (t) - 0 .2 (0 / (2 + 2m) + F(t)/(1 + m) (38a) if(t) = ( - 2(1 + m)r(t) + l)i'(t)0.(t)/((5/6) - r(t) + (1 + m)r 2 (t)) + T(t)/((5/6) - r(t) + (1 + m)r 2 (t)) + d(t), (38b) where an unknown but bounded external torque dis turbance d(t) and a variable pay load m bounded as 0 ~< mmi n ~< m ~< mma x are imposed to demons t ra te the effectiveness and robustness of the proposed control scheme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure6-1.png",
        "caption": "Fig. 6. Schematic of worm generation.",
        "texts": [
            " The face-gear R2 and the cradle c are held at rest and the tooth surface of the face-gear is generated as the copy of the tool surface. Indexing of face-gear has to be provided for generation of each space of the gear. Blades of the gear head-cutter are shown in Fig. 5(a). The angles ag of blade profile are of different magnitude for the convex and concave sides of the space of the face worm gear. Circular arc profiles of the blade fillet are provided for the generation of the fillet of the gear. The generation of the worm is performed by a tilted head-cutter mounted on the cradle d of the generating machine (Fig. 6). The worm and the cradle d perform related rotations determined as x\u00f0w\u00de x\u00f0d\u00de \u00bc N2 N1 \u00f01\u00de where N2 and N1 are the number of teeth and threads of the face-gear and the worm. The rotation of the head-cutter is provided for obtaining the desired velocity of cutting (grinding) and is not related with the meshing of cradle d and the worm. Fig. 7 illustrates the installment of the worm with respect to the cradle d. The process of generation of the worm simulates its meshing with the face-gear. The face-gear is represented in Fig",
            " 7 and 10. We emphasize that the shortest distance Em between the worm and the cradle is executed in the cycle of meshing as a parabolic function Em w1\u00f0 \u00de \u00bc E0 \u00fe aplw 2 1 \u00f08\u00de where E0 is the normal value of the center distance; apl is the parabola coefficient of the plunge aplw 2 1. The plunge aplw 2 1 enables to provide a predesigned parabolic function of transmission errors of the gear drive (see Section 5). We remind that the worm is generated by the head-cutter that is installed on the cradle d (Fig. 6) whereas the worm and the cradle d perform related rotations. The worm thread surface is determined as the envelope to the family of head-cutter surfaces as follows: r1 uw; hw;w1\u00f0 \u00de \u00bc M1dMdwrw uw; hw\u00f0 \u00de; \u00f09\u00de or1 ouw or1 ohw or1 ow1 \u00bc f uw; hw;w1\u00f0 \u00de \u00bc 0: \u00f010\u00de Here rw uw; hw\u00f0 \u00de is the vector function that determines the surface of the head-cutter in coordinate system Sd of the cradle d; uw; hw\u00f0 \u00de are the surface parameters of the generating tool (the head-cutter or the grinder); w1 is the generalized parameter of motions;M1d andMdw describe the coordinate transformation from Sd to S1 and Sw to Sd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003371_1.2768079-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003371_1.2768079-Figure4-1.png",
        "caption": "Fig. 4 Initial and final positions of curvature centers",
        "texts": [
            " From this figure, the distance between the center of curvature of the inner and left-outer race can be written as A = ro + ri \u2212 D = BD 6 where B= fo+ f i\u22121. From the right hand side of Fig. 2, = ro \u2212 ro 2 \u2212 go 2 2 7 thus, the contact angle can be expressed as OCTOBER 2007, Vol. 129 / 80107 by ASME of Use: http://www.asme.org/about-asme/terms-of-use U o p r C r F s 8 Downloaded Fr f = arccos A \u2212 Pd/2 \u2212 A 8 nder external applied loads or imposed rotations and translations f the inner ring Fig. 3 , the raceway curvature centers reach final ositions, as schematically presented in Fig. 4. In this figure, the ight- and left-outer raceway groove curvature centers Cor and ol are fixed in space, whereas inner centers Cir and Cil moves elative to these fixed points. ig. 3 Coordinate system, external applied loads, and correponding rotations and translations 02 / Vol. 129, OCTOBER 2007 om: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms Quasistatic Analysis Contact Geometry. Following the general approach used by Harris 9 and using Fig. 4, the distance between the groove curvature centers and the final position of the ball center O can be written as mk = fm \u2212 0.5 D + mk \u2212 hmk 9 where are normal contact deformations, h the lubricant film thickness at the ball-ring raceway contacts, k=r or k= l for right or left contact, and m= i or m=o for inner or outer race, respectively. Equations 10 and 11 can be written from Fig. 5 as Fig. 5 Inner raceway curvature centers in global system Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use W t c e T t T H l T b w t J Downloaded Fr OGCir = \u2212 f i \u2212 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002489_jp2:1994100-FigureI-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002489_jp2:1994100-FigureI-1.png",
        "caption": "Fig. I. Alignment geometry in the (~,z) plane for (a) constrained extension [Sect. 3.I]; (b) imposed extension experiment by Mitchell et al. [Sect. 3.2]; (c) simple shear [Sect. 3.3]. no and n are",
        "texts": [],
        "surrounding_texts": [
            "arises from the normalization of P(R). Including this term, the free energy is:\n~' =\nTr[1\u00b0 1\u00b0~ l~~ ii -in ~~~~~\n(4) kBT 2 ~ \" ~ \"\net[~]\nThe resultant elastic free energy will depend on the nematic order at formation through 1\u00b0 and\non the nematic order in the current state through l~~, that is F~i \" Fei(Q\u00b0, Q). In turn Q will = = =depend on the imposed I through both magnitude Q and direction n of the current nematic order. It is the purpose of this paper to specify how Q and n depend on the imposed strain. As a result of applying I, minimizing the free energy will yield new Q and n, differing from Q\u00b0 and n\u00b0, and hence a new equilibrium shape I. Thus the current director, n, is in general not\ncoincident with the initial n\u00b0, except if I has the same principal frame as n\u00b0 and is a uniaxial\nextension. In this latter case ljj = I, ii =\nI/fi and\n~' = ~~ l~ + 2\n~~ is) kBT li\nAllowing I in is) to relax to its equilibrium (I.e. zerc-stress) value, that is taking 0F~i/0A =\no, gives the spontaneous shape change Am = (ljjl\u00a7/I(li)~~~ due to a change in the current\nnematic order with respect to its initial state [3]. One particular case of this is essential. If one heats the nematic rubber so that the current state is isotropic, its step length tensor is = 16,k. The spontaneous distortion is then Am =\nill /lj)~/~, which will in general be less than one, a flattening, if the crosslinking state was prolate uniaxial. This is a useful experiment since it is a direct measure of the chain anisotropy and is pivotal in what follows. The inverse experiment would be the cooling the initially isotropic rubber down to the nematic state with Q\n\" Q\u00b0. This gives the spontaneous distortion\nlc = I /lrr > I, an elongation of the sample that can be easily measured. In general we envisage performing elasticity experiments at the formation temperature, or at lower temperatures where Am > 1, I.e. further chain ordering causes a spontaneous elongation of the sample. Returning the value of Am to (5) gives the elastic free energy as a function of I and 1\u00b0: F~i IQ)\n\"\nF~j ii ,1,1\u00b0) which represents an addition to the Landau-de Gennes free energy of the nematic ordi$qiJirtic in the current order parameter Q if the crosslinking is done in the isotropic state, quartic and quadratic in Q if the crosslinking was performed in the nematic state see [3] for a detailed discussion. The free energy F~i(I ,1,1\u00b0) then is minimized with respect to Q in\norder to totally solve the problem. ~\nWe are interested here in the case where an imposed deformation I has principal axes not coincident with n\u00b0, thereby creating an equilibrium state with n at some angle 6 with respect to n\u00b0. In separate papers we shall consider applied (uniaxial) stress and electric fields, both of which lead to novel counter intuitive effects. We shall determine 6 as a function of the magnitude of deformation and the orientation of the frame of the imposed deformation A,j with respect to n\u00b0. To do this we shall proceed essentially as above, minimizing F~i with\nrespect to any free components of and with respect to Q and 6, which characterize Q.\nWe consider several types of deformations in increasing order of complexity taking two principal axes of distortion to define the (z, z) plane. For these distortions we show below that the director rotates about the axis and remains in the (z, z) plane, therefore one can effectively operate with (2 x 2) anisotropic matrices. Each type of deformation produces characteristic\ninstabilities. Some produce \"soft elasticity\" phenomenon hitherto unknown in rubber theories",
            "initial and current directors respectively; unit vectors u (u, v for simple shear) define the principal\naxes of deformation.\nand which we discuss in a separate paper. We list here each type of deformation and analyze them later in separate sections.\n(A) Uniaxial extension at an angle a with respect to I (coincident with the initial director\nn\u00b0), figure la. In terms of the unit vector u of the direction of extension, the deformation\ntensor at a constant volume is A~ = (1/@)6,j + (A lilt)1t,ltj. This is simple conceptually but difficult to apply in practice since biaxial stresses are needed to create uniaxial deformation in a misaligned but naturally uniaxial system. The simplicity of I however allows one to see the hallmark of instabilities occurring in more complex geometrfis. We find a jump in the\ndirector at a critical strain applied at a = x/2. For a < x/2, the director moves continuously\naway from n\u00b0 as I increases.\n(B) Extension applied at an angle a with respect to n\u00b0, but normal transverse relaxation\npermitted (giving in general a biaxial I). Relaxation via simple shear strains is prohibited by symmetry, figure 1b. This geometry iithat employed experimentally by Mitchell et al. [ll]. We again find a discontinuity in the direction of n with I, but now over a range of a around x/2. As one reduces a below x/2 eventually these transitions terminate at a critical point.\nThere is mechanical hysteresis where the transitions are discontinuous.",
            "(C) Simple shear at an angle a with respect to the initial director, figure lc. In terms\nof unit vectors along the direction of shear, u, and along the gradient, v, the deformation is l~ = 6,j + lltiuj. At a critical a, dependent only on the initial network anisotropy, the rotation of n with I is continuous until a critical value of I is attained. This critical I likewise depends only on initial anisotropy.\n3, Results.\nHenceforth we use a coordinate system (z,z,y) based on u e rotated by a about \u00a7 from the original (principal) frame of1\u00b0. This will be a principal frame, for instance, for imposed\nuniaxial strain and a simple frame in which to consider shear. The tensors 1\u00b0 and l~~ have\nto be rotated by angles a. and A = a\n6 from their principal frames. Second rank (2 x 2)\ntensors, for instance 1\u00b0, will be characterized by their mean 1\u00b0 = (1( +1\u00a7)/2 and anisotropy\n61\u00b0 =\n(lj -1[)/2 of their principal values and similarly for l~~ and I. Details of calculations\nare to be found in the following section 4.\n3.I UNIAXIAL EXTENSION. Using the expressions for 1\u00b0 and l~~ given by equation (2) with the corresponding orientation of the director in each case, and taking the uniaxial form\n1 =\n~ $~ one obtains for the elastic part of the free energy (with ly = lilt) \" o I/ '\nwhere the coefficients of the angularly varying terms depend simply on 1\u00b0, and angle a. The\nvariation of F~i with the relative orientation of the current director, A, is through the Cl and\nC2 terms. Taking the minimal free energy, at 0F/0A = o, and inserting A, 6A, 1\u00b0 and 61\u00b0, one\nobtains for the equilibrium orientation:\ntan 2A =\n~(A( I)@sin 2a\n~~~ ~ ~~~~~ ~/~) + (If 1)(12 + 1/1) cos 2a (7)\nwhere lc = (lj/1\u00a7)~/~ specifies the anisotropy of the initial strand conformation.\nThe rotation 6 of n is shown as a function of the imposed I at constant a in figure 2a.\nFigure 2b shows 6(a) for various (fixed) I. When I is imposed at an angle a = x/2 an internal\nbarrier prevents any rotation of n until I > i~. The system then breaks symmetry and jumps\nto 6 = x/2. For smaller a < x/2 there is no degeneracy in the direction of rotation and the\ndirector is continuously dragged around towards o.\nOne would expect that the discontinuous jump in the director orientation is due purely to\na symmetry argument that there is a degeneracy at a = x/2. In fact we shall see in the next\nsubsection that the reason for such discontinuity is more subtle and it may persist for some\nregion of finite a < x/2. The discontinuity in 6(a) is seen in a different guise in some of the other geometries, below.\nThe curves for different o cross and this is more easily seen in figure 2b where, for a given I < lc, the 6(a) curves have maxima, which disappear with a singularity at the critical\nextension =\nlc."
        ]
    },
    {
        "image_filename": "designv10_8_0002939_j.mechmachtheory.2005.11.005-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002939_j.mechmachtheory.2005.11.005-Figure9-1.png",
        "caption": "Fig. 9. Right and left configurations of SCARA robot with wrist at (600, 400, 130) mm.",
        "texts": [
            " For this simulation experiment, the robot configuration described by the joint variable vector f 0:1201 1:6380gT radians would be preferred over the configuration described by the joint variable vector {1.2960 1.6404}T radians to achieve the wrist position (600, 400, 130) mm since it involves a smaller total joint displacement. The distribution of individ- uals in the population at the initial generation and generation numbers 5, 10 and 70 of the real-coded GA using niching strategy 2 for simulation experiment no. 5 is shown in Fig. 8(a)\u2013(d). A 3D modeler was developed in MATLAB to visualize the multiple configurations obtained through the inverse kinematics solution. Fig. 9 shows the robot at the wrist position (600, 400, 130) mm in both the right and left configurations, respectively. Chapelle and Biduad [15] and Chapelle [16] use evolutionary symbolic regression for the solution of the 2D inverse kinematics problem. The results converge towards the exact analytical expression for one joint and approximate the second joint solution with a small average error. This regression would have to be repeated for each multiple inverse kinematics solution. The current work evaluates the multiple inverse kinematics solutions of the SCARA robot simultaneously by using the forward kinematic equations of the robot and solving Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003152_j.ijmachtools.2004.11.006-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003152_j.ijmachtools.2004.11.006-Figure9-1.png",
        "caption": "Fig. 9. Generating swept volumes of different cutter types: (a) APT-like cutter (if B like cutter (if B2 T ;2 CD2 T ;2 %F2 T ;2 and B2 T ;1 CD2 T ;1 OF2 T ;1), the profile only exists o envelope is illustrated as blue), (d) ball-end mill; (e) flat-end mill.",
        "texts": [
            " The commonly used end mill 2 T ;2 CD2 T ;2 OF2 T ;2), the profile exists on the lower conical surface, (b) APTn the toroidal surface and upper conical surface, (c) fillet-end mill (swept cutters, such as fillet-end mill, ball-end mill and flat-end mill have been modeled in the figures. In the part (c) of every figure, the ingress and egress boundary surfaces are illustrated. These boundary surfaces are generated by splitting the cutter surfaces with the earlier described swept profiles at initial and final cutter configurations. This procedure is necessary to close the swept volume, and subsequently to obtain a topological valid swept volume described in B-rep. Fig. 9 shows the closed swept volumes generated by different end mill cutters using the B-Rep model in the CasCadew [29] environment. Note that the swept volumes in Fig. 9(a) and (b) are different for a generalized cutter, which is discussed in the solution analysis in Section 5. In general, the swept volume must afterwards be checked, to ensure topological validity and to avoid non-manifold and twisting structures. A general discussion for formulating the swept profile on five-axis tool motions has been presented in this paper. The explicit formulations are derived by introducing the moving frame and rigid body motions. The cases of common cutters, which were derived from the geometric definition of a generalized cutter, are also addressed in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003891_s12283-009-0028-1-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003891_s12283-009-0028-1-Figure2-1.png",
        "caption": "Fig. 2 a Dynamic loft is the change in nominal club loft that results from clubhead deflection. b Dynamic close also occurs as a result of clubhead deflection and is a close in the face of the clubhead relative to the intended clubhead direction",
        "texts": [
            " These procedures are not trivial as the clubhead would experience high frequency movement (due to ball impact) at the precise time when the swings\u2019 representative clubhead speeds were measured. Although it is generally accepted that the orientation of the clubhead relative to the ball is altered by the shaft bending near impact, few studies have attempted to quantify the effects. Mather and Cooper [3] stated that depending on the geometry of the shaft, a lead deflection of 5 cm can result in a 5 increase in the loft of the club. They refer to this added loft as dynamic loft (Fig. 2a). Horwood [4] explained that increasing the lead deflection at impact would increase the dynamic loft at impact and result in a higher ball trajectory. Dynamic close also occurs as a result of clubhead deflection and is a close in the face of the clubhead relative to the intended clubhead direction (Fig. 2b). Although not explicitly reported by any of the previously mentioned researchers, bending in the toe-up/ toe-down direction may also alter ball flight. The purpose of this paper was to gain an understanding of the role that shaft stiffness plays during the golf swing. This was accomplished through the use of mathematical modeling and optimized computer simulation techniques. 2 Methods 2.1 Model description A representative mathematical model of a golfer was constructed using a six-segment (torso, arm, and four club segments), 3D, linked system (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003014_1.2895905-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003014_1.2895905-Figure1-1.png",
        "caption": "Fig. 1",
        "texts": [
            " However, this is assumed since the final diagonal matrix is of the same rank as the original A matrix. Therefore, T must be of full rank. Before discussing the use of the orthogonal complement, an example is presented to illustrate decoupling with the congruency transformation. Example of Decoupling With the Congruency Transformation. Consider the following system of two particles connected by a rigid, massless rod. Sliding mass ml is constrained to move along the horizontal axis n2, and the mass m 2 must stay on the constant radius arc with respect to m a in the n 1 - n 2 plane, as shown in Fig. 1. Using the generalized coordinates qa and q2, the matrix A is assembled using Ja and J2 for each of the masses. This gives and - rsq2 ] (28) which can be combined according to Eq. (17) to obtain - m a m 2 -m2rcq2] A = -m2rcq2 --mzr 2 ] . (29) Equation (19) is used to form the congruency transformation for A as T = [10 - m z r c q 2 / ( m l + m 2 ) ] \" 1 (30) For this system the resultant applied force vectors for each mass are and The above matrices can then be assembled using Eq. (18a) to yield the following dynamical equations: [ - - m l - m 2 0 ] 0 m2 r2 -- mZr2c2q2/(m 1 + m2) fi [ 0 0 = _m~racq2sq2u~/(ml + m2) + -magrsq2 The complete set of equations of motion are Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002865_ac050198b-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002865_ac050198b-Figure2-1.png",
        "caption": "Figure 2. Screen-printed carbon paste electrode. (A) Fabrication process: 1. polyester (PE) substrate; 2, silver connectors and electrode site; 3, carbon paste electrodes; and 4, insulator. (B) SPCE with sample well: 1, SPCE; 2, 100-\u00b5L sample well block. and (C) SPCE with capillary sample cell: 1, SPCE; 2, capillary fluidic path formed on double-sided tape; and 3, cover plate.",
        "texts": [
            ") potentiostat was used to run cyclic voltammograms (CVs) and measure current-time responses (chronoamperometry). For the Y-NaR-immobilized GCE, glassy carbon working electrode (d ) 3 mm, BAS), platinum wire counter electrode (coil), and Ag/AgCl reference electrode (3 M KCl, BAS) were used, and buffer solution in a 5-mL cell was continuously stirred by magnetic bar during the amperometric experiments. For the Y-NaRimmobilized SPCE, carbon paste working electrode (d ) 3 mm), carbon paste counter electrode, and Ag/AgCl reference electrode printed all in one plate as shown in Figure 2 were clamped with a well-type 100-\u00b5L cell, and nitrate-containing solutions were dropped in the well for stationary amperometric experiments. All potentials in the text are referenced to the Ag/AgCl electrode. Ion chromatography (IC, Dionex 500, Sunnyvale, CA) and spectrophotometry (DR 2000, HACH, Loveland, CO) were used for the comparative determination of nitrate in real samples. The IC system was equipped with an AS 40 automated sampler, a GP 40 gradient pump, an Ionpac AS14A analytical column (4 \u00d7 250 mm) with an AG 14A guard column (4 \u00d7 50 mm), an ASRS-Ultra II self-regenerating suppressor in external water flow mode using high pressurized reservoir containing ultrapure deionized water, and an ED40 electrochemical detector and operated at a flow rate of 1 mL/min with 0",
            " The spectrophotometric measurement was made with the cadmium reduction method using the reagent NitraVer from HACH. A spectrophotometric cell was filled with 25 mL of sample after filtering it through the 0.47-mm circle size glass microfiber filters (GF/C, Catalog No. 1822 047, Whatman), adding one NitraVer nitrate reagent (powder pillow) into the cell, and placing it into a spectrophotometer to read the absorbance at 500 nm. Preparation of SPCE. A semiautomatic screen-printing machine (LS-150 type, Newlong Seimitsu Kogyo Co., Ltd.) and a set of stencils (Daeshin Co.) patterned for the electrodes shown in Figure 2 were used to prepare SPCEs. The substrate of the SPCE is a 0.5-mm-thick flexible polyester (PE, Korea 3M, Seoul, Korea) plate, which was cut in to a 10 cm \u00d7 15 cm piece and thermally treated at 150 \u00b0C for 6 h before printing to prevent further thermal shrinkage in the following process. Silver paste (LS-506J type, Asahi Chemical Research Lab. Co., Ltd.), carbon paste (TU-15ST-S type, Asahi Co.), and insulator ink (Seoul Chemical Research Laboratory, Shiheung, Korea) were sequen- (26) Lu, G.; Lindqvist, Y",
            " 2000, 39, 1180. (33) Mellor, R. B.; Ronnenberg, J.; Campbell, W. H.; Diekmann, S. Nature 1992, 355, 717. (34) D\u0131\u0301az Garc\u0131\u0301a, M. E.; Sanz-Medel, A. Anal. Chem. 1986, 58, 1436. (35) Can\u0303abate D\u0131\u0301az, B.; Schulman, S. G.; Segura Carretero, A.; Ferna\u0301ndez Gutie\u0301rrez, A. Anal. Chim. Acta 2003, 489, 165 (and references therein). 4468 Analytical Chemistry, Vol. 77, No. 14, July 15, 2005 tially screen-printed on the thermally pretreated PE plate, using the stencils corresponding to each layer pattern shown in Figure 2, and dried at 150 \u00b0C for 10 min after each printing process. The overall dimension of an individual SPCE strip was 8 mm \u00d7 34 mm. The diameter of the round-shaped working electrode was 3 mm. The Ag/AgCl reference electrode was prepared by oxidative treatment of the dried silver paste using 3 M FeCl3 solution. Y-NaR Immobilized Electrodes. The GCE electrodes were polished first with 1- and 0.3-\u00b5m alumina polishing powder on a polishing pad (Buehler), followed by sonication for 5 min in a water/ethanol solution (50 v/v %) and were air-blow dried",
            "3,8,21 The effect of interfering substances (nitrite, sulfate, chloride, phosphate, chlorate) was also measured. As reported previously,6 the Y-NaRimmobilized GCE exhibits a large interfering response to chlorate (10.0 nA/\u00b5M) and a response to nitrite to some extent (2.5 nA/ \u00b5M). Analytical Chemistry, Vol. 77, No. 14, July 15, 2005 4471 Having developed the GCE-based nitrate monitoring biosensor, we extended the technology to the fabrication of disposable SPCE with built-in sample cell for in situ monitoring of nitrate in the field. Figure 2 has shown the fabrication procedures for SPCE and its capillary cell structure. The SPCE-based biosensor was used with a portable potentiostat device, and -900 mV was applied to the working electrode. The sample introduced into the sample well or capillary cell dissolved the enzyme-containing reagent layer in short time, bringing about an abrupt change in impedance and current between the working and counter electrodes. The sample and mixed reagents then underwent the diffusion-controlled nitrate reduction reaction, resulting in the reduction current proportional to the concentration of nitrate in a given time period. The current profiles in Figure 9 sequentially display the events occurring at the SPCE-based biosensor, and the calibration curve in the inset is plotted with the currents measured at 180 s after injecting the sample into the well (Figure 2b). The calibration equation obtained after subtracting the background current of the SPCE modified with inactivated enzyme in PVA layer (mean 4600 nA) was within the linear detection range of 15-250 \u00b5M (0.9-15.5 ppm, r2 ) 0.996, n ) 40, RSD < 2.8%). The sensitivity of the electrode was 5.5 nA/\u00b5M with a detection limit of 5.5 \u00b5M (0.3 ppm, S/N ) 3). The detection limit of SPCE was comparable to or higher than those from other methods, which ranges from 0.05 to 20 \u00b5M in the literature.1 The sensitivity of the Y-NaR-immobilized SPCE was \u223c75% that of the same enzyme-immobilized GCE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003363_ac702146u-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003363_ac702146u-Figure1-1.png",
        "caption": "Figure 1. Schematic of the amperometric enzyme immunosensor based on the poly-o-ABA-modified electrode.",
        "texts": [
            "5 \u00b5m R-alumina on filter paper, and then sonicated prior to use two times with isopropyl alcohol and one time with double-distilled water. The BDD thin film was cut into 1 \u00d7 1 cm2, soaked in freshly prepared piranha solution (H2SO4/H2O2 (30% v/v) 3:1) for 30 min (safety note: the piranha solution should be handled with extreme caution), and rinsed with double-distilled water. The working area was controlled by a silicone rubber gasket of 5 mm diameter. The schematic of the poly-o-ABA-modified immunosensor is shown in Figure 1. The electrode was electropolymerized with 50 mM o-ABA in 1 M H2SO4 by 10 cycles of cyclic voltammetry with a scan rate of 40 mV s-1 and the potential range of 0-0.97 V. The poly-o-ABA-modified electrode was subsequently coated with 50 \u00b5L of NHS/EDAC solution (1/1 mg in 100 \u00b5L of 100 mM PBS buffer, pH 7.22) for 30 min, and then the supernatant was removed. A drop of 50 \u00b5L of 40 ppm GaMIgG was applied to each poly-o-ABA-modified electrode. After 120 min of incubation, the solution was removed, and 50 \u00b5L of 1 M ethanolamine solution was drop cast onto each poly-o-ABA-modified immunosensor and incubated for 30 min",
            " The N1s spectrum in Figure 3B shows the presence of poly-o-ABA. The spectrum is the same N1s spectrum of polyaniline because the o-ABA is one of an aniline derivative. The ratio of the C1s peak of COOH groups to N1s of poly-o-ABA (COOH/N) is about 1:1. This result confirmed the postulation of poly-o-ABA formation that one COOH group and one N come from a monomer of o-ABA. Immunosensor. Determination of MIgG, the target protein, using a sandwich-type immunoassay by a disposable poly-o-ABAmodified BDD was developed. The scheme is shown in Figure 1. In this approach, comparison was also made between poly-o-ABAmodified BDD and GC immunosensors treated with the same conditions. The sandwich immunoassay involved immobilization of the primary antibody GaMIgG, capture of the target MIgG, association of GaMIgG-ALP, and finally using AAP as substrate. The ALP enzymatically generated AA is an electroactive species that can produce an electrochemical oxidation signal. The electrochemical signal is related to the quantity of MIgG. The enzymatic reaction of ALP and electrochemical oxidation of AA are shown in eqs 4 and 5, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003225_j.euromechsol.2005.02.004-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003225_j.euromechsol.2005.02.004-Figure10-1.png",
        "caption": "Fig. 10. Kinematic structure of Orthoglide (a) and its associated graph (b).",
        "texts": [
            " Four variables qi of the prismatic joints connecting each leg to the reference element are used to command the position and the orientation of the mobile platform. The parallel robotic manipulator T3R1-type presented in Fig. 9 represents a solution of a family of modular parallel robotic manipulators with 2\u20136 degrees of freedom and decoupled motions, proposed by the author of this paper, and developed under the name \u201cIsoglide\u201d, by the research team MMS (Mechanisms, Machines and Systems) of the French Institute of Advanced Mechanics. Example 3. The parallel manipulator in Fig. 10 (Gogu, 2004) is a parallel mechanism D \u2190 E1\u2013E2\u2013E3 with three complex legs. A planar parallelogram loop is serially concatenated in each leg. We can see by inspection that: (RE1) = (vx,vy,vz,\u03c9y), (RE2) = (vx,vy,vz,\u03c9z), (RE3) = (vx,vy,vz,\u03c9x) and SEi = 4. The spatiality of the mobile platform in parallel mechanism D given by Eq. (58) is SD 7/1 = dim(RE1 \u2229 RE2 \u2229 RE3) = 3. The same three relative independent velocities (vx,vy,vz) exist between the mobile and reference platforms as in Example 1. The mechanism has 18 revolute and 3 prismatic joints ( \u2211m i=1 fi = 21). Spatiality of the elementary open chain associated with each planar parallelogram closed loop is three, that is the three closed loops serially concatenated in the complex legs cancel the independence of t = 3 \u00d7 3 = 9 joint variables. The l total number of joint parameters that lost their independence in the parallel robotic manipulator in Fig. 10 given by Eq. (60) is r = rD = 4 + 4 + 4 \u2212 3 + 9 = 18. The mobility of the parallel robotic manipulator given by Eq. (61) is M = 21 \u2212 18 = 3. Three variables qi of the prismatic joints connecting each leg to the reference element are used to command the position of the mobile platform as in Example 1. The parallel mechanism presented in Fig. 10 was developed at IRCCyN under the name Orthoglide (Wenger and Chablat, 2000). Delta robot (Clavel, 1988; Pierrot et al., 1990) and University of Maryland parallel manipulator (Tsai and Stamper, 1996) represents other examples of parallel robots with complex legs integrating parallelogram closed loops serially concatenated. The mobility of these parallel robots can be easily obtained by using Eq. (61). Tsai (2000) have shown that Chebychev\u2013Gr\u00fcbler\u2013 Kutzbach\u2019s mobility criterion does not work for these parallel mechanisms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003438_j.isatra.2008.03.002-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003438_j.isatra.2008.03.002-Figure2-1.png",
        "caption": "Fig. 2. Membership function of state variables.",
        "texts": [
            " The dynamics of the system can be expressed as equations [16] x\u03071 = x2 x\u03072 = g sin x1 \u2212 mlx2 2 cos x1 sin x1/(mc + m) l(4/3 \u2212 m cos2 x1/(mc + m)) + cos x1/(mc + m) l(4/3 \u2212 m cos2 x1/(mc + m)) u + \u2206 where x1 and x2 are the angular position and velocity of the pole. g = 9.8 m/s2 is the acceleration due to gravity, mc = 1 kg is the mass of cart, m = 0.1 kg is the mass of pole, l = 0.5 m is the half-length of pole, u is the applied force. The control objective is to maintain the system to track the desired trajectory ym = (\u03c0/30) sin(t). The Gaussian type membership functions for system state x1 and x2 are constructed as in Fig. 2. The initial states are x = [\u2212\u03c0/60, 0] T and step size 0.01 s. A certain disturbance \u2206 = 0.01 \u2217 sin(5t) is added to verify the robustness for the controller. The stabilizing function \u03b11 is \u03b11 = \u22128z1 with z1 = x1 \u2212 ym and we obtain the control law u = \u2212z1 \u2212 4z2 \u2212 \u03c82 4 \u00b7 0.8 \u03be2\u03be T 2 z2 \u2212 \u03b8\u03022\u03c62 tanh ( \u03b8\u03022\u03c62z2 0.5 ) with z2 = x2 \u2212 \u03b11 and \u03b32 = 0.8. The adaptive law for \u03c82 and \u03b8\u03022 are \u03c8\u03072 = 70 [ 1 4 \u00b7 0.82 \u03be2\u03be T 2 z2 2 \u2212 0.03(\u03c82 \u2212 0.2) ] \u02d9\u0302 \u03b82 = 8[\u03c62 \u2016z2\u2016 \u2212 0.03(\u03b8\u03022 \u2212 0.2)]. For comparison, the indirect adaptive fuzzy control (IAFC) [16] u I = 1/g\u0302(x |\u03b8g)[\u2212 f\u0302 (x |\u03b8 f )+ y\u0308m + kTe] under the same conditions is also demonstrated",
            "5x1 + (1 + x2 1)x2 + \u22061(t) x\u03072 = x1x2 2 + (3 + cos(x1x2))u + \u22062(t). The control objective is to maintain the system to track the desired angle trajectory, ym = \u03c0/5(sin(t) + 0.3 sin(3t)) and to regulate a constant set-point value ym = 0. A certain disturbance \u22061 = sin(x1), \u22062 = 2x1 sin(t) is added to verify the robustness for the controller. Moreover, a Gaussian noise with mean zero and variance 0.001 is injected at the output of the system. The membership functions for system state x1 and x2 are constructed as in Fig. 2. The initial states are x(0) = [0.2, 0] T and step size 0.01 sec. The stabilizing function \u03b11 is \u03b11 = \u22124z1 \u2212 \u03c81 4 \u00b7 0.8 \u03be1\u03be T 1 z1 \u2212 \u03b8\u03021\u03c61 tanh ( \u03b8\u03021\u03c61z1 0.5 ) with z1 = x1 \u2212 ym . The adaptive law for \u03c81 and \u03b8\u03021 are \u03c8\u03071 = 90 [ 1 4 \u00b7 0.82 \u03be1\u03be T 1 z2 1 \u2212 0.03(\u03c81 \u2212 0.2) ] \u02d9\u0302 \u03b81 = 8[\u03c61 \u2016z1\u2016 \u2212 0.03(\u03b8\u03021 \u2212 0.2)] and we obtain the control law u = \u2212z1 \u2212 4z2 \u2212 \u03c82 4 \u00b7 0.8 \u03be2\u03be T 2 z2 \u2212 \u03b8\u03022\u03c62 tanh ( \u03b8\u03022\u03c62z2 0.5 ) with z2 = x2 \u2212 \u03b11 and \u03b32 = 0.8. The adaptive law for \u03c82 and \u03b8\u03022 are \u03c8\u03072 = 70 [ 1 4 \u00b7 0.82 \u03be2\u03be T 2 z2 2 \u2212 0",
            " Above equation can be expressed in the form of (18) by noting that x1 = q, x2 = q\u0307, x3 = \u03c4 x\u03071 = x2 x\u03072 = \u2212 B D x2 \u2212 N D sin x1 + 1 D (x3 + \u03c4d) x\u03073 = \u2212 Km M x2 \u2212 H M x3 + u M . The control objective is to maintain the system to track the desired angle trajectory, ym = \u03c0/5(sin(0.5t) + 0.5 sin(1.5t)) and to regulate a constant set-point value ym = 0. A Gaussian noise with mean zero and variance 0.001 is injected at the output of the system. The membership functions for system state x1, x2 and x3 are constructed as in Fig. 2. The initial states are x(0) = [0.4, 0.2,\u22120.2] T and step size 0.01 s. The stabilizing function \u03b11 and \u03b12 are \u03b11 = \u22128z1 \u03b12 = \u2212z1 \u2212 4z2 \u2212 \u03c82 4 \u00b7 0.8 \u03be2\u03be T 2 z2 \u2212 \u03b8\u03022\u03c62 tanh ( \u03b8\u03022\u03c62z2 0.4 ) with z1 = x1 \u2212 ym and z2 = x2 \u2212 \u03b11. The adaptive law for \u03c82 and \u03b8\u03022 are \u03c8\u03072 = 75 [ 1 4 \u00b7 0.82 \u03be2\u03be T 2 z2 2 \u2212 0.05(\u03c82 \u2212 0.5) ] \u02d9\u0302 \u03b82 = 5[\u03c62 \u2016z2\u2016 \u2212 0.05(\u03b8\u03022 \u2212 0.5)] and we obtain the control law u = \u22124z2 \u2212 4z3 \u2212 \u03c83 4 \u00b7 0.8 \u03be3\u03be T 3 z3 \u2212 \u03b8\u03023\u03c63 tanh ( \u03b8\u03023\u03c63z3 0.4 ) with z3 = x3 \u2212 \u03b12 and \u03b32 = 0.8. The adaptive law for \u03c83 and \u03b8\u03023 are \u03c8\u03073 = 60 [ 1 4 \u00b7 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure9.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure9.2-1.png",
        "caption": "Figure 9.2 Strain rate (E) dependent viscoelastic behavior.",
        "texts": [
            "3) states that stress, a, is not only a function of strain, E, but is also a function of the strain rate, E = dE / d t, where t is time. A more general form of Eq. (9.3) can be obtained by including higher-order time derivatives of strain. Equation (9.3) indicates that the stress-strain diagram of a viscoelastic material is not \"--------- f Figure 9.1 Linearly elastic material behavior. 198 Fundamentals of Biomechanics (j unique but is dependent upon the rate at which the strain is developed in the material (Figure 9.2). L..-______ \u20ac 9.2 Analogies Based on Springs and Dashpots In Section 7.8, while covering Hooke's law, an analogy was made between linearly elastic materials and linear springs. An elastic material deforms, stores potential energy, and recovers defor mations in a manner similar to that of a spring. The elastic mod ulus E for a linearly elastic material relates stresses and strains, whereas the constant k for a linear spring relates applied forces and corresponding deformations (Figure 9.3). Both E and k are measures of stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002939_j.mechmachtheory.2005.11.005-Figure14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002939_j.mechmachtheory.2005.11.005-Figure14-1.png",
        "caption": "Fig. 14. Multiple configurations of PUMA robot at wrist position (600, 149.09, 200) mm.",
        "texts": [
            " The fitness values of the feasible multiple solutions obtained using niching strategy 2, Dq, for the simulation experiments are given in Table 2 and can be used for multiplicity resolution. Fig. 13(a)\u2013(d) show the distribution of individuals in the population at the initial, two intermediate and generation number 260 of the realcoded GA for the simulation experiment no. 1. For this simulation experiment, the robot configuration described by the joint variable vector f 0:0014 0:4304 0:1152gT radians would be preferred over the other three possible configurations to achieve the wrist position (600, 149.09, 200) mm since it involves a smaller total joint displacement. Fig. 14 shows the robot at the wrist position (600, 149.09, 200) mm using the 3D modeler developed in MATLAB in all possible configurations. Chapelle and Bidaud [17,18] restrict the characteristic points in the learning base of the genetic programming approach to only one of the multiple inverse kinematics problem solutions. The authors claim that this can be done by automatic elimination of the points which tend to increase the fitness and/or with an initial knowledge of the right points field given by the observation of the robotic system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.11-1.png",
        "caption": "Figure 12.11 A block is pushed from position 1 to 2.",
        "texts": [
            " As compared to the applications of the equations of motion, these methods are easier to apply and are particularly useful when the information provided or to be determined is in terms of velocities rather than accelerations. Definitions of im portant concepts introduced in this chapter and various meth ods of analyses in kinetics are summarized in Table 12.3. The following examples will demonstrate some of the applications of these methods. Example 12.2 A 20 kg block is pushed up a rough, inclined surface by a constant force of P = 150 N that is applied parallel to the incline (Figure 12.11). The incline makes an angle e = 30\u00b0 with the horizontal and the coefficient of friction between the incline and the block is f-L = 0.2. If the block is displaced by .e = 10 m, determine the work done on the block by force P , by the force of friction, and by the force of gravity. What is the net work done on the block? Solution: The free-body diagram of the block is shown in Figure 12.12. W is the weight of the block, f is the frictional force at the bottom surface of the block, and N is the reaction force applied by the incline on the block"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003138_s1474-6670(17)30474-3-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003138_s1474-6670(17)30474-3-Figure3-1.png",
        "caption": "Fig. 3. Configurations of the four-rotor rotorcraft. (a) Pitch, (b) roll and (c) yaw control inputs.",
        "texts": [
            " In this type of helicopters the front and the rear motors rotate counter clockwise while the other two rotate clock wise. Pitch movement is obtained by increasing the speed of the rear motor while reducing the speed of the front motor. The roll movement is obtained similarly using the lateral motors. The yaw movement is obtained by increasing the speed of the front and rear motors while decreasing the speed of the lateral motors. Note that when the yaw and roll angles are set to zero, the 4-rotor helicopter reduces to a PVTOL (,;ee figure 3). In our experiment the roll and yaw angles are controlled manually by an experienced pilot. The remaining controls, i.e. the collective input (or throttle input) and the pitch control, are controlled using the control strategy presented in the previous sections. In the four-rotor helicopter, the throttle input is the sum of the thrusts of each 1ll0tOr. The two control signals are transmitted by a Futaba Skysport 4 radio. The control signals are referred as throttle control input ill. pitch control input U,2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.5-1.png",
        "caption": "Fig. 6.5 Spring element with (a) stroke and force indications, (b) ideal stroke and (c) force generators with integrated sensors",
        "texts": [
            " The small triangle near the top of each symbol allows distinguishing positive and negative forces in the graph: a compression (positive) force is represented by a current flowing toward the triangle, whereas a tension (negative) force \u201cflows\u201d in the opposite direction (from the triangle towards the other terminal). A positive stroke (elongation) is represented by a positive voltage measured from the terminal with the triangle to the other one, while a negative voltage represents a negative stroke (shortening). According to this convention, the circuits of Figure 6.3, which look similar, represent two different mechanical systems (see Figure 6.4). Further, we will introduce symbols for ideal stroke and force sensors, to provide the graphs with the corresponding indications (see Figure 6.5(a)). The attribute \u201cideal\u201d refers to the fact that the force in the stroke sensor as well as the stroke of 162 6 Design Principles for Linear, Axial Solid-State Actuators the force sensor is assumed to be zero. The sensors work like a voltmeter and an ammeter, respectively and are provided with a plus mark to relate the sign of the measured quantity to the displayed value (if, for instance, the force \u201cflows\u201d towards the plus sign, the sensor outputs a positive value. In the case of Figure 6.5(a) the stroke and force sensors are expected to provide values of opposite signs. Stroke 6.3 Theory of Single-Stroke Linear Solid-State Actuators 163 and force sensors can be integrated into the symbols of ideal generators as shown in Figures 6.5(b) and 6.5(c). In such cases the plus mark is omitted with the convention that the measurement direction conforms with the positive direction of the force or stroke generation as identified by the triangle in the generator symbol. If necessary, the spring symbol can be completed by the indication of the stiffness value (see Figure 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002727_bi961868y-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002727_bi961868y-Figure2-1.png",
        "caption": "FIGURE 2: Catalytic cycle of LPO in the oxidation of p-substituted phenols, including the effect of fluoride. X represents the heme substitution, and RH represents the protein amino acid responsible for the radical species.",
        "texts": [
            " In fact, the reaction of Compound III with the substrate forms CompI(IV,P\u2022+) which activates the normal cycle of the enzyme involving CompII(IV,RH), CompII(III,R\u2022), and the resting state. In the period between the two linear phases the continuous change in the slope is due to a change in the composition of enzymatic species in solution. Since there is accumulation of Compound III, the Soret band moves from 412 to 424 nm. The catalytic behavior is in accord with the enzymatic cycle represented in Figure 2. It differs from those of classical peroxidases such as HRP for the greater importance assumed by the formation of Compound III and for the possibility to have two intermediates with an oxidative equivalent above the native enzyme in the LPO-H2O2 system. In order to confirm the cycle in Figure 2 the same experiment as that reported in Figure 1A was performed, but the order of introduction of the reagents was changed. In particular, the substrate p-cresol was introduced as the last reactant. In this way, the enzyme in the presence of hydrogen peroxide forms Compound III and then, introducing the substrate, the conditions become similar to those of the second phase of the experiment represented in Figure 1A. In fact, in this experiment a straight line with a slope similar to, but slightly smaller than, that in the second phase of the previous experiment was obtained",
            " The LPO-F- complex obtained in the decomposition of Compound III is in the high-spin state and has an optical spectrum similar to that of the native enzyme (\u03bbmax 412 nm). Thus, it is possible to prevent the accumulation of Compound III during the kinetic experiments using fluoride as decomposition agent. Figure 3 shows the effect of fluoride in the time course of the oxidation of p-cresol with H2O2 catalyzed by LPO, together with the indication of the enzyme Soret band during the different phases of the reaction. The halogen ion affects the reaction in a concentration dependent manner. The presence of fluoride modifies the kinetic mechanism as shown in Figure 2. One effect of fluoride is to reduce the slope of the first phase of the reaction because, on binding to LPO, it reduces the concentration of free enzyme. The effect of fluoride on the second phase is to increase the slope because it reduces the lifetime of the low reactive Compound III species. Moreover, above 25 mM fluoride there is no appreciable accumulation of Compound III. Also, using fluoride it is not possible to simplify the cycle, because when the concentration of fluoride is raised to prevent the accumulation of Compound III the halogen binds to LPO inhibiting the formation of CompI(IV,P\u2022+)",
            " In addition, the velocity of the inactivation process depends strongly on the substrate (with phenols having high redox potential the inactivation is fast). (c) The oxidation of phenols by LPO depends strongly on the substrate redox potential. In fact, when the phenolic E\u00b0 is high, the kinetic parameters (kcat and kcat/KM) are small and there is a fast inactivation of the enzyme to Compound III. Moreover, at pH 5, the enzyme seems to be a very poor catalyst in the oxidation of p-substituted phenols bearing an amino group. The explanation of these differences starts from the catalytic cycle. It is represented in Figure 2 and differs from those of the other peroxidases for the presence of two intermediates bearing a radical delocalized on an amino acid residue. The cycle resembles that of CCP, which delocalizes a radical on a tryptophan residue (Trp191) to form Compound ES (Bosshard et al., 1991; Anni & Yonetani, 1992; Ortiz de Montellano, 1992) but, during turnover, the radical reacts faster than the ferryl group, so that CCP uses only one intermediate having an oxidizing state above the resting enzyme. The reaction of Compound I through the ferryl group was observed only using equimolar quantities of reducing agent (not during turnover) and in particular conditions (Coulson et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.38-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.38-1.png",
        "caption": "Figure 5.38 Forces acting on the lower leg.",
        "texts": [
            " The biceps femoris has prox imal attachments on the pelvic bone and the femur, and distal attachments on the tibia and fibula. There is also the popliteus muscle that has attachments on the femur and tibia. The pri mary function of this muscle is knee flexion. The other muscles of the knee are sartorius, gracilis, gastrocnemius, and plantaris. Example 5.6 Consider a person wearing a weight boot, and from a sitting position, doing lower leg flexion/ extension ex ercises to strengthen the quadriceps muscles (Figure 5.37). Forces acting on the lower leg and a simple mechanical model of the leg are illustrated in Figure 5.38. WI is the weight of the lower leg, Wo is the weight of the boot, F M is the magnitude of the ten sile force exerted by the quadriceps muscle on the tibia through the patellar tendon, and F I is the magnitude of the tibiofemoral joint reaction force applied by the femur on the tibial plateau. The tibiofemoral joint center is located at 0, the patellar tendon is attached to the tibia at A, the center of gravity of the lower leg is located at B, and the center of gravity of the weight boot is located at C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure3.20-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure3.20-1.png",
        "caption": "Fig. 3.20 Element of a non-prismatic beam",
        "texts": [
            " Considering first plane bending of rectangular cross sections, we may start with the same assumptions that have been made for calculating the shear stresses of con stant rectangular cross sections, and of symmetric general cross sections, respec tively, Eqs. (3.3), (3.13), and (3.25). We note that for changing widths assumption (3.25) has to be replaced by (3.34) again. 3.5 Stresses in Non-prismatic Beams 61 In the same way as we did for prismatic beams, we cut a small element of length dx out of the non-prismatic beam (Fig. 3.20) with Integrating over the relevant surfaces, the equilibrium of the forces in x direction yields 1 a {jh(X)/2 } o-xz(z) = b ax o-bdz . (3.56) z Introducing here Eq. (3.13), we arrive at 1 a {N jh(X)/2 M(x) jh(X)/2 } o-xz(z) = b ax A(x) b zdz + J(x) b zdz (3.57) z z and finally QSy 1 {N(AA*)'+M(SJY)'}, o-xz(z) = Jb + b (3.58) where j h(X)/2 A*(x, z) = bdz, j h(X)/2 Sy(x, z) = zbdz (3.59) z z are the zeroth and the first moment, respectively, of the shaded portion of the cross sectional area with respect to the y axis, which are now functions of x and z"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002518_s0263574797000027-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002518_s0263574797000027-Figure3-1.png",
        "caption": "Fig . 3 . Object Modeling Method .",
        "texts": [
            " Of course smaller balls can more accurately describe the set occupied by the links and obstacles , but it would also require more balls and computations . We recommend to use balls with dif ferent radii to cover dif ferent shapes of links and objects so that more accurate converge is possible without increasing complexity . This object modeling method is called the ball-covering modeling method . Similar method was proposed as the spherical representation in the study of human body modeling . 2 0 To illustrate the idea stated above , a planar redundant robot is considered as shown in Figure 3 . Suppose that there are N l balls covering links and N o balls covering http://journals.cambridge.org Downloaded: 03 Jul 2014 IP address: 138.37.211.113 obstacles . Let the pairs ( R l i , Z l i ) and ( R o j , Z o j ) be the radii and centers of two balls among all balls covering the links and obstacles , where i 5 1 , 2 , . . . , N l and j 5 1 , 2 , . . . , N o . Radii R l i and R o j are preselected , therefore they are fixed . The center position vector Z l i depends on joint angles , hence Z l i can be written as Z l i ( q ) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.33-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.33-1.png",
        "caption": "Figure 7.33 Example 7.4.",
        "texts": [
            "033 0.0066 720 180 5.050 0.0100 In Figure 7.32, the stress and strain values computed are plotted to obtain a a-\u20ac graph for the bone. Notice that the relationship between the stress and strain is almost linear, which is indicated in Figure 7.32 by a straight line. Recall that the elastic modulus of a linearly elastic material is equal to the slope of the straight line representing the a-\u20ac rela tionship for that material. Therefore: a 180 x 106 9 E = - = = 18 x 10 Pa = 18 GPa \u20ac 0.0100 Example 7.4 Figure 7.33 illustrates a fixation device consist ing of a plate and two screws, which can be used to stabilize fractured bones. During a single leg stance, a person can apply his/her entire weight to the ground via a single foot. In such situations, the total weight of the person is applied back on the person through the same foot, which has a compressive effect on the leg, its bones, and joints. In the case of a patient with a frac tured leg bone (in this case, the femur), this force is transferred from below to above (distal to proximal) the fracture through the screws of the fixation device"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002307_a:1026567812984-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002307_a:1026567812984-Figure4-1.png",
        "caption": "Figure 4. Screw motion about the line axis l (ts : longitudinal displacement by d and Rs : rotation angle \u03b8 ) (a) the motor relating two axis lines, (b) motor applied to an object. Note that the indicated vectors in the figures will be represented in Subsection 4.3 as bivectors.",
        "texts": [
            " Also note that the dual of a scalar is the pseudoscalar P and the duals of the first three basis bivectors are the next three ones that is for example (\u03b32\u03b33) \u2217 = I\u03b32\u03b33 = \u03b34\u03b31. According to Clifford [9] a basic geometric interpretation of a motor can be seen as the necessary operation to convert the rotation axis of a rotor into another one. Each rotor can be geometrically represented as a rotation plane with the rotation axis normal to this plane. Thus, one rotor can be spanned using a scalar and the bivector basis \u03b32\u03b33, \u03b33\u03b31, \u03b31\u03b32 and the dual one by a pseudoscalar and \u03b34\u03b31, \u03b34\u03b32, \u03b34\u03b33. Figure 4(a) depicts a motor action in detail where the rotor axes are now considered as rotation lines. In the Figure let us first turn the orientation of the axis of one rotor Ra parallel to the other one Rb by applying the rotor Rs . Then slide it the distance d along the connecting axis into the position of the axis of the second rotor. These operations can be seen together as forming a twist about a screw with the line axis l and the relation called pitch which equals to |ts | = d \u03b8 for \u03b8 6= 0. The Fig. 4(b) shows an action of a motor on a real object. In this case the motor relates the rotation axis line of the initial position of the object to the rotation axis line of its final position. Note that in both figures the angle and sliding distance indicate how the rigid displacement takes place around and along a screw line axis l respectively. We said in Subsection 3.1 that a rotor relates two vectors. Now, in the case of a motor it relates the rotation axes of two rotors. A motor is specified only by its direction and position of the screw axis line, twist angular magnitude and pitch",
            " If we want to express the motor using only rotors in dual spinor representation we proceed as follows M = TsRs = ( 1+ I ts 2 ) Rs = Rs + I ts 2 Rs . (37) Let us consider carefully the dual part of the motor. This is the geometric product of the bivector ts and the rotor Rs . Since both are expressed in terms of the same bivector basis their geometric product will be also expressed in this basis and this can be seen as a new rotor R\u2032s . Thus, we can further write M = Rs + I ts 2 Rs = Rs + I R\u2032s (38) In this equation the line axes of the rotors are differently oriented in space, see Fig. 4(a). That means that they represent the general case of non-coplanar rotors. If the sliding distance ts is zero then the motor will degenerate to a rotor M = TsRs = ( 1+ I ts 2 ) Rs = ( 1+ I 0 2 ) Rs = Rs . (39) In this case the two generating axis lines of the motor are coplanar, thus the motor is called a degenerated one. Finally, the bivector ts can be expressed in terms of the rotors using previous results R\u2032s R\u0303s = ( ts 2 Rs ) R\u0303s, (40) therefore, ts = 2R\u2032sR\u0303s . (41) Figure 4 shows that t is a distance bivector relating the two rotation axes of the rotors Ra and Rb, and ts is a bivector representing a displacement along the motor axis line. According to Fig. 4(b) the distance t considered here as a bivector can be computed in terms of the bivectors tc and ts as follows t = t\u22a5 + t\u2016 t = (tc \u2212 Rs tc R\u0303s)+ (t \u00b7 n)n = (tc \u2212 Rs tc R\u0303s)+ dn = tc \u2212 Rs tc R\u0303s + ts = tc \u2212 Rs tc R\u0303s + 2R\u2032s R\u0303s . (42) So far the motor was studied from a geometrical point of view, next its more relevant algebraic properties are given. A general motor can be expressed as M\u03b1 = \u03b1M (43) where \u03b1 \u2208 R and M is a unit motor as in previous sections. In this section we deal further with unit motors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002972_60.50825-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002972_60.50825-Figure3-1.png",
        "caption": "Fig. 3 Vector Diagram of the PM Motor",
        "texts": [
            " According to this principle, the stator currents are transformed into a frame of reference which is moving with the rotor flux, so that a direct and a quadrature component of the stator current vector can be defined which serve as non-interacting inputs for controlling the magnitude of the flux and the torque respectively. This may be deduced from a vector diagram describ ing the motor voltage equation (1) for steady state condit ions (8) \u00b0 \ufffd j6 r ( ) where \ufffdf JW'o/f e 9 is the back-emf vector leading the permanent magnet fl ux vector in space by 90\u00b0, we = p.u r and p is the nUr;]ber of pole pairs in the per'[lanent magnets. The cor responding vector diagram is drawn in Fig. 3, where the d-q rotor frame is rotating at constant speed wr\u2022 Equa tion (8) is next decomposed into the rotor coordinate frame through the d-q or Park transformation to result in: 'is vd + jVq is id + jiq (10) Vq Rs iq +weLsid + Ef vd Rsid - W eLs i q The d-q variables are obtained froll' the phase variables through the Park transformation defined by taking phase-a axis as a reference and 6r as the instantaneous rotor position. l- , i q d J - \ufffd [Sin a r - 3 cos e r Isin a r sin(a r-1200) coste r-1200) I sin(S r-1200) L Sin(a r+1200) (11) The expression for the electric torque is - \ufffd \u2022 ",
            " Flux weakening in a permanent magnet motor has a similar effect as the direct field weakening in a separately excited dc motor. This Is done by Intro ducing a negative current component in the d-axls to create a d-axls flux in opposition to that of the rotor flux resulting in a decreased airgap flux. This arma ture reaction effect is used to enlarge the operating speed range of the PM motor and to relieve the current regulator from saturation that occurs at high speeds. As shown in the vector diagram of Fig. 3, the amplitude of the terminal voltage, vs1' at id = 0 exceeds the permi ss i b 1 e max i mum vol tage, Vmax' By appropriately cantrall ing id ' the ampl itude of the ter m inal voltage vs2 is reduced to equal. Vmax' The optimal control procedure Is thus as follows: for iq\ufffd \ufffd iqma\ufffd at.any speed, o\ufffd\ufffdrate with i *.= I c and ld - O. I\u00b7or lye> \\,jioldX' ene CIJrr2tlt c?\"Ject3ry s hould be along the voltage-limit ellipse as shown in Fig. 7a. The value iqmax that sets the boundary bet ween normal and flux-weakening operation is found from equation (14) by setting id = 0, and solving for Iq; ",
            " ,\ufffd\ufffd\ufffd -'0 l\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7 ,\u00b7 \u00b7\u00b7 \u00b7 \u00b7 \u00b7 \u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7,\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7 .............................\u2022 ... ; ............ . \u2022........................ J\ufffd\ufffd\ufffd -'5 \ufffd--------\ufffd----------\ufffd--------\ufffd------\ufffd\ufffd4 o (c) ,0 Fig. 7 Current Reference Generation in the Flux Weakening Mode 20 Iqc (A) demagnetization limit of the permanent magnets. This is accomp\ufffdished b\ufffd insuring :h\ufffdt iqC \ufffdnd id* are clamped to theIr restrIcted range. 1 qcmax - Ismax and I dmax Idmax' Th I s fl ux weakeni ng procedu re maximi zes tne torque capability of the motor in the extended speed range. Figure 3 shows the steady state response of the drive to a constant torque command under the optimal control strategy, the speed being hel d at 1500 rpm. It can be seen that for the hysteresis controller, the phase current in Fig. 3a is constrained to follow the reference value within the hysteresis band. Neverthe less, as discussed in [8J, because of the independence in the control of the three phases, the current ripple can reach double the hysteresis band value due to the appearance of free-wheelin\ufffd periods when a zero voltage switching state (v7 or v8 1n Fig. 5) is commanded to the inverter. The switching frequency is variable and depends on the hysteresis oand and the operating conditions. The results of Fig. 8b for the space-vector controller shOll that the free-wheeling periods are eli minated and the switching frequency is hi3her than for the simple hysteresis controller, therefore this method acts as three hysteresis controllers with dependent control and guarantees an exact control of the phase currents within the tolerance band"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003864_s0094837300003286-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003864_s0094837300003286-Figure11-1.png",
        "caption": "FIGURE 11. Changes in magnitude of the forward thrust F and the transverse thrust T in the tail of Squalus acanthias, across one stroke. A, the ventral hypochordal lobe; B, the dorsal lobe of the tail. The data are derived from those in Figure 10, with T estimated as v2 (the square of the transverse speed of the tail) with F estimated as tr cot 0. The dotted lines in the descending portions of the curves show the negative thrust at the end of the stroke that must be assumed if the water is still relative to the fish. The solid lines show a corrected curve, allowing for the momentum of the water; see text.",
        "texts": [
            ") Using the data from Gray's photographs we may make the following extremely simple attempt to estimate the relative values of F and T for sharks. First we can measure di rectly the speed of transverse movement of the available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0094837300003286 Downloaded from https://www.cambridge.org/core. Stockholm University Library, on 02 Dec 2018 at 01:56:22, subject to the Cambridge Core terms of use, HETEROCERCAL TAIL 27 tail, both at the center of effort of the dorsal lobe and at the ventral hypochordal lobe. From this we can draw graphs (Figure 11) showing change in F and T during the stroke from the estimations F = v2 cot 6 and T = v2, v2 being a direct measure of T' in equations (1 to 5 ) , above. From this exercise, some interesting points emerge. First, it will be seen that in Squalus acanthias (and indeed prob ably in all sharks), at the end of each beat the dorsal and ventral lobes of the tail reach angles of inclination exceeding 90\u00b0. This has two results: (a) it places each lobe in the correct orientation to start the next stroke with a low angle of inclination, and (b) potentially produces a reversed thrust F, moving the fish backwards (Figure 11). The latter, of course, is an artifact of the assumption that the water is perfectly still with respect to the fish. In fact, basic hydrodynamic considerations show that when the tail is decelerating at the end of the stroke, the displaced water behind the tail has a greater transverse momentum than that in front of the tail and thus a forward thrust is maintained. In the absence of direct mea- surement of the forward and transverse acellerations of the tail throughout the stroke, we may estimate the magnitudes of the forward and transverse thrust during these latter phases of the stroke, as in Figure 11. With this, we may estimate that, on average across the whole stroke, the forward and transverse thrust in the dorsal lobe of the tail are in the proportion F/T = 1.85. In the ventral hypochordal lobe F/T is estimated as 1.50 averaged over the whole stroke. It will be obvious that the relative magni tudes of F and T will be changed if the angle of inclination changes in a different pattern during the beat of the tail. We can simulate this in a simple way by moving the curves shown in Figure 11 to the right (increasing average F / T ) or the left. Changes may also be effected by modification of the change in transverse speed of the tail during the beat, although Gray (1933) and most other authors believe that it is always symmetrical. Referring back to our simple model, we can calculate a series of \"balanced\" values of the (dorsal) thrust angle and angle of rotation for different hypothetical ratios of F/T (Table 1). Because it seems reasonable that the upper limit on the angle of rotation would be 45\u00b0, we can also place upper limits on the angles of thrust and therefore, given the relationship between the angle of thrust and the heterocercal angle (Figure 4 ) , upon the latter also",
            " Therefore, if this curve is generally applicable, from Table 1 we can see that for all values of the thrust angles that are less than 26\u00b0 (heterocercal angle of 33\u00b0) a available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0094837300003286 Downloaded from https://www.cambridge.org/core. Stockholm University Library, on 02 Dec 2018 at 01:56:22, subject to the Cambridge Core terms of use, 28 THOMSON completely balanced thrust is possible. At thrust angles greater than 26\u00b0 the thrust will be out of balance at the portion of the stroke at which F/T approaches its peak (Table 2, Figure 11), and the deviation will be such as to give a line of thrust directed behind the center of gravity of the fish. Any such devia tion must be compensated for either by exter nal factors (see ventral hypochordal lobe, below) or by corresponding adjustment dur ing the rest of the stroke (leading, in that case, to a symmetrical \"wobble\" in swimming). Ventral hypochordal lobe.\u2014The develop ment of the ventral hypochordal lobe in sharks varies widely and without discontinuity from the condition exemplified by the nurse shark Ginglyostoma, where it is absent, to the large epipelagic sharks such as Lamna, Isurus and Rhincodon, where it makes up more than 30% of the total caudal fin surface",
            " The tip of the ventral hypochordal lobe moves transversely through a complete arc, exactly like the dorsal lobe of the tail but out of phase. As it flexes along its long axis, it produces its own changing angles of inclination and, being at a different point along the length of the fish from the center of effort of the dorsal lobe, the center of effort of the ventral hypochordal lobe has its own (smaller) transverse velocity. The average ratio F/T, as developed from the Squalus acanthias data, is lower in the ventral hypochordal lobe than in the dorsal lobe (1.50 as compared with 1.85). However, as Figure 11 and Table 2 show, the maximum value of F/T is larger (2.68). The absolute magnitude of the thrust is less because of the smaller arc of transverse movement and cor responding lower velocities and also the lesser surface area of the ventral hypochordal lobe. The peak value of F/T = 2.68 gives a maxi- available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0094837300003286 Downloaded from https://www.cambridge.org/core. Stockholm University Library, on 02 Dec 2018 at 01:56:22, subject to the Cambridge Core terms of use, HETEROCERCAL TAIL 29 mum thrust angle of only 21\u00b0 for maintenance of a totally balanced thrust from the ventral hypochordal lobe"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.11-1.png",
        "caption": "Figure 6.11. Force feedback using piezoresistors. a. Microgripper with two integrated force sensors; b. double cantilever beam with stress concentrating structure (from [33], courtesy of Shaker Verlag).",
        "texts": [
            " To enable a simple and fast exchange of the grippers\u2019 end-effectors without additional electrical connections, two strain gages have been glued on each of the two actuators\u2019 housings, Figure 6.10b. If an object is gripped, the strain caused by the deformation of the actuators\u2019 housing can be measured. Taking into account the change of the stiffness of this system, the gripping force can be calculated. This method has the drawback of low accuracy. Several different microgrippers for the assembly of microparts were developed by [33] (Figure 6.11a). The grippers were manufactured using plasma-enhanced dry etching of silicon and deep UV lithography of SU-8. The joints of the grippers were designed as flexure hinges; they are actuated by shape memory alloys. A double cantilever beam structure for stress concentration was integrated into the Force Feedback for Nanohandling 187 gripper jaws, and piezoresistors were implanted in the areas with the highest mechanical stress (Figure 6.11b). The tensile and compression stresses during gripping cause a change of the resistance of the piezoresistors. A noticeable nonlinearity of the sensor\u2019s output presumably results from the wires to the piezoresistors. As the wires are made of a sputtered gold layer, they deflect together with the flexures and thus change their resistivity analogously to the piezoresistors due to mechanical stress. The goal of the work described in [43] was the development of grippers with integrated sensors for gripping and contact force measurement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002929_bf01257946-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002929_bf01257946-Figure1-1.png",
        "caption": "Fig. 1. Stewart platform geometry.",
        "texts": [
            " This immediately suggests several approaches for avoiding the singularity in machining applications by suitable path planning. In Section 5, we describe the approach in the study of the dynamics of the Stewart platform and give the initial result. The detailed dynamic equations and the complete result will be given in our future papers. 2. Summary of Kinematics and Inverse Kinematics In this paper, interest focuses on the Stewart platform configuration which consists of a semi-regular hexagonal lower platform, an equilateral triangular upper platform, and six identical linear actuators, as shown in Figure 1. Fix an inertia frame (X, Y, Z) at the center of the lower platform with the Z-axis pointing vertically upward. Fix another moving coordinate system ( x , y , z ) at the center of gravity of the upper platform with the z-axis normal to the platform, pointing outward. In the sequel, these two coordinate systems are called the BASE frame and the TOP frame, respectively. The physical dimensions of the lower and upper platform and the coordinates of their vertices in terms of the BASE frame or the TOP frame are shown in Figure 2",
            " Since there is no explicit expression available for the forward kinematics, deriving the dynamic equations directly in link space would be very difficult. On the other hand, deriving the equations of motion for the Stewart platform in Cartesian space will be easier. This is exactly the reverse of the serial-link situation. To obtain the kinetic and potential energies, we will divide the Stewart platform into two different parts: the upper platform (with mass mu) and the six legs (each with mass ml). Note that a perfect study will also require a decomposition in two of each leg - the lower part, and the upper moving part, see Figure 1. This would give the exact expression of the different energies. However, these expressions are very complicated and very difficult to use. So, as a compromise solution, we will consider that each leg can be modeled by its center of mass (Gi) and that the mass is concentrated on there. Note that G i is time-varying due to the extension of link i. The assumption that G i is fixed at the center of each leg is not accurate enough for our purposes. To determine the moving point Gi, note that: (i) The center of m a s s Gli of the lower part is not in the middle of this body (see Figure 1) due to the great mass of the DC motor. Let us denote by ll, the length, ml, the mass, of this part and ~5, the distance BiGli. (ii) On the contrary, the upper part of each linear actuator is uniform. Thus, its center of mass G2i is in its 'middle point'. Let us denote by l 2 the length and m2 the mass of this second part. (iii) Finally, denote by -ffi the unitary vector (BiTj/11 BiTj II) wherej -- (i + 1)/2 if i is odd, and j = i /2 if i is even. One then easily obtains B ~ . G i - l m 2 [ ( 6 m l l l O "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003933_j.engfailanal.2010.11.009-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003933_j.engfailanal.2010.11.009-Figure5-1.png",
        "caption": "Fig. 5. Location of cracks in BW body structure.",
        "texts": [
            " 2 and 3, is performed by excavating distracted overburden because there were no operational and technological conditions for a \u2018\u2018full\u2019\u2019 exploitative investigation. The capacity of the machine was proved during the trial operation and no defects were found. However, after only 1800 h of operation, problems occurred in the operation of the reducer, as well as cracks and deformations of the BW body, Figs. 4 and 5. The occurrence of cracks in the welded butt joints positioned circumferentially (diameters D1, D2 and D3), Fig. 5, brought about a complete . All rights reserved. ax: +381 11 3370364. separation of individual parts of the structure and complete loss of the BW shape. Arc-shaped cracks occurred in the weld metal (WM) and HAZ, with lengths corresponding to: 270 (diameter D1), 130 (diameter D2) and 190 (diameter D3). In order to diagnose the cause of cracks occurrence in BW body structure, the following had to be performed: Calculation of the stress state of the BW body structure. Experimental procedure, which, given the nature of the failure, includes: \u2013 Chemical composition and mechanical properties of parent metal (PM)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.8-1.png",
        "caption": "Figure 5.8 Three-muscle system.",
        "texts": [
            " Therefore, the joint reaction force F J corresponds to the resultant of the distributed force system (pressure) applied through the synovial fluid. \u2022 The most critical simplification made in this example is that the biceps was assumed to be the single muscle group responsi ble for maintaining the flexed configuration of the forearm. The reason for making such an assumption was to reduce the sys tem under consideration to one that is statically determinate. In reality, in addition to the biceps, the brachialis and the brachio radialis are also primary elbow flexor muscles. Consider the flexed position of the arm shown in Figure 5.8a. The free-body diagram of the forearm is shown in Figure 5.8b. F MI, F M2, and F M3 are the magnitudes of the forces exerted on the forearm by the biceps, the brachia lis, and the brachioradialis muscles with attachments at A}, A2, and A3, respectively. Let (h, (h, and (h be the angles that the biceps, the brachialis, and the brachioradialis muscles make with the long axis of the lower arm. As compared to the single-muscle system that consisted of two unknowns (F M and F J ), the analysis of this three-muscle system is quite complex. First of all, this is not a simple parallel force system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002352_1.2830138-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002352_1.2830138-Figure4-1.png",
        "caption": "Fig. 4 Radial stiffness, 7014 bearing, Fz = 540/V, Fx = Fn Fy = 0K = 0, = 0",
        "texts": [
            " The computer solution has been for mulated to allow mixed boundary conditions to be solved, based on the load and deflection initial conditions. Stiffness and deflections are calculated while the equilibrium of the balls and the bearing is established. The solution of these equations is accomplished in a computer program that is both accurate and robust\u2014showing strong resistance to instability. Output of these computer solutions shows that the bearing stiff ness is a function of boundary condition, loads, and rotational speed, as shown in Fig. 4. As rotational speed increases, the bearing stiffness decreases significantly for this constant preload example. This decrease in stiffness could play a crucial role in spindle response at larger cutting speeds. To demonstrate this, the bearing program has been coupled to the spindle model described below. Spindle dynamic response is generated using a lumped mass discretization of a Timoshenko beam. This derivation provides a simple, yet accurate representation of a spindle of arbitrary geometry and loading",
            " Equation (25) represents the complete eigenvalue solution of the discrete spindle coupled to the bearing load-deflection analy sis. ([ /] - L02[M,]-[a])-{X] = {0] (25) Cutting Loads. Evaluation of natural frequency is based upon small excitations about an equilibrium position. For linear bearing stiffness and linear beam deflection, this equilibrium position is the undeformed spindle, but when non-linear bearing stiffness is included, the static equilibrium position affects the bearing stiffness, and hence, the spindle response. The effect of loading on bearing stiffness is shown earlier in Fig. 4. When machine tool spindles are subjected to exterior loads, such as cutting loads, spindle-bearing response can change, and hence the effect of such loads must be considered. Cutting loads may be divided into static and dynamic compo nents. The dynamic loads, due to dynamic motion of the cutting tool, are assumed to provide system excitation. Static load cre ates a deformed equilibrium in bearing and spindle position. To determine the influence coefficient matrix of a loaded spindle, the technique is to first solve load-equilibrium equations with static loads"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.3-1.png",
        "caption": "Figure 13.3 Pendulum.",
        "texts": [
            " Note that angular quantities (), w, and a differ dimensionally from their linear counterparts x, v, and a by a length factor. The units of angular quantities in different unit systems are the same. Angular displacement is measured in radians (rad), angu lar velocity is measured in radians per second (rad / s) or s -I, and angular acceleration is measured in radians per second squared (rad/ s2) or S-2. 13.6 Definitions of Basic Concepts To be able to define concepts common in angular motions, con sider the simple pendulum illustrated in Figure 13.3. The pen dulum consists of a mass attached to a string. The string is fixed to the ceiling at one end and the mass is free to swing. Assume that l is the length of the string and it is attached to the ceiling at O. If the mass is simply released, it would stretch the string and Angular Kinematics 277 278 Fundamentals of Biomechanics come to a rest at B that represents the neutral or equilibrium posi tion of the mass. If the mass is pulled to the side, to position A, so that the string makes an angle (}o with the vertical and is then released, the mass will oscillate or swing back and forth about its neutral position in a circular arc path of radius f"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure1.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure1.1-1.png",
        "caption": "Fig. 1.1 Section surface and related stress vector s",
        "texts": [
            " The purpose of the majority of structures or structural members designed by engineers is to transmit these forces; and it is of great importance for the designer to know the manner in which the force is transmitted in each member, because it may be that the mode of internal distribution of the force - conditioned by the shape and dimensions of the member - is such that failure of the material of which the member is made may occur at some point or points in the member. It is necessary, therefore, to consider how a force is transmitted through an element of material. Consider a solid body under the action of a system of forces in equilibrium, e.g. distributed forces f, and concentrated forces F i, i = 1,2, ... ,n, respectively, act ing on the outer surface of this body, and concentrated reactions acting at the two supports as sketched in Fig. 1.1. When we cut this body into two pieces, passing an arbitrary surface through it, each of the two pieces will be in equilibrium if an additional force is applied to it. In the uncut body this force must be transmitted through the imaginary surface, and it is plausible to assume that each area element L1A makes its contribution L1F. The limit of the quotient L1F / L1A for vanishing L1A is called the stress L1F dF 8(n) = }lr::.o L1A = dA (1.1) in the element, where the orientation of area dA is designated by the unit vector n"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003570_tsmc.1980.4308518-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003570_tsmc.1980.4308518-Figure3-1.png",
        "caption": "Fig. 3. Three link biped in the plane.",
        "texts": [
            " As will be shown via a simpler example, this model satisfies all conditions that are essential for effective control of locomotion [2,p.360]. It allows for rapid or slow locomotion with the option of deliberately violating certain constraints and maintaining others. Of course, the constraints that are permanently maintained (L'l) cannot be violated unless excessive external forces are applied (crash and collision injury). With this background, a planar three-link model is discussed below which is subjected to constrained motion on surfaces with dry friction. The example (Fig. 3) discussed below is an extended version of the three-link biped model [12] in the frontal plane. The equations of this model are derived in the Appendix. It is intended to demonstrate all four types of constraint. In order to demonstrate locking, a simple mechanism in the form of an appendage is added to the torso that prevents rotation of the right leg around the body beyond 90 degrees. The torso and the associated forces that act on it are shown in Fig. 4. The right and left legs are shown in Figs",
            " Suppose a new basis W is selected in the (n-r) dimensional space of the constrained system and that it is (23) If (23) is substituted in (18) and use is made of (20) and (21), one obtains (Z) a__CTF(4I(Z) awW=f4(W,W)+f5(W,W)U+ az F (24) aZT premultiplying both sides of (24) by a , and computing W, one obtains W=(aZTwIaz) [f6+f7U+ awT CF]. (25) It is easy to show that aZT aCTaw____=z0.waz (26) Therefore, (25) does not contain F and hence with W= W constitutes the state equations of the reduced system. The computation of (26) is carried out below for a simple example. Suppose in Fig. 3, point A is at the origin of the coordinate system and is fixed, and suppose point D is free. Let the objective be to eliminate the forces of constraint F1 and G,. The constraints are C =Xi- k sin l = 0 C2=Yl-kIcos91 =0. (27) Let W= (x2,x3,y2,y3, l192, and 93)T. Equation (21) becomes X = k sin0l Y= k cos91 X2 =X2 Y2 =Y2 X3 = X3 Y3 =Y3 0a3 = 0a3' (28) From the above equation one derives 0 0 aZT 0 aw k, cosO 0 L 0 0 0 0 0 -k,sinO, 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003573_s0022-0728(84)80371-x-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003573_s0022-0728(84)80371-x-Figure5-1.png",
        "caption": "Fig. 5. Cyclic vo l tammograms at a silver electrode in phosphate buffer so lut ion containing 0.1 M NaC104 (pH 7.0), w i thout (-- - - - - ) and wi th 0 .37 mM cy tochrome c ( ), in the presence o f 2 mM purine. Scan rate: (a) and (-- - - --) 10, (b) 20, (c) 50 m V s -1 .",
        "texts": [
            " The adsorption at the S atoms of PySSPy was further supported by the fact that 4-mercaptopyridine also acted as a promoter for cytochrome c at potentials at which no oxidation of 4-mercaptopyridine to PySSPy took place. The adsorption behaviour of PySSPy on Ag and Au electrodes together with that of 4-mercaptopyridine is currently under further investigation, and details will be reported later. In the presence of purine, the SERS measurement interestingly suggested the possibility of another mechanism for the enhancement of the rate of heterogeneous electron-transfer of cytochrome c. At an Ag electrode, purine also acted as a promoter for cytochrome c (Fig. 5); the electrochemical behaviour was similar to that obtained at a PySSPy-modified Ag electrode. The SERS signals of purine at an Ag electrode were observed, which were similar to those obtained at an Au electrode [9], indicating that purine is adsorbed onto the Ag electrode. When purine was added to a cytochrome c solution, the SERRS signals of cytochrome c at the Ag electrode changed gradually to show the SERS signals due to purine, but purine did not fully displace the adsorbed cytochrome c; even after the addition of large, excess amounts of purine and then standing for more than 1 h at --0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002745_j.ab.2004.11.017-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002745_j.ab.2004.11.017-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of one-compartment spectroelectrochemical cell.",
        "texts": [
            " Metal complexes [Os(4,4 0-dimethyl-2,2 0- dipyridyl)2(imidazole)Cl](PF6)2 [11], potassium octacyano tungstate (IV) (K4[W(CN)8]) [12], potassium hexacyano osmate (III) (K4[Os(CN)6]) [13], and potassium octacyano molybdate (IV) (K4[Mo(CN)8]) [14] were synthesized according to the literature. BODs (EC 1.3.3.5, 3.31 U mg 1) from Myrothecium verrucaria and Trachderma tsunodae were a gift from Amano Enzyme (Japan) and purchased from Takara Shuzo (Japan), respectively. All other chemicals used were of reagent grade. Electrolysis cell A quartz cuvette for UV-vis spectroscopy (10 \u00b7 10 \u00b7 42 mm) was used as an electrolysis cell. As shown in Fig. 1, a Pt mesh (100 mesh, 10 \u00b7 20 mm) was attached at the bottom and two frosted sides of the cuvette and used as the working electrode. A lead wire was attached to the working electrode for electric contact. A Pt wire (1 mm diameter) as the auxiliary electrode was immersed into solution to a depth of about 1 mm. An Ag|AgCl|sat.KCl (Hokuto Denko, Japan) was used as the reference electrode, to which all potentials are referred, unless otherwise stated. These electrodes were fixed with a silicon cap on the top of the cell"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.57-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.57-1.png",
        "caption": "Figure 4.57 Problem 4.10.",
        "texts": [
            " RAx = Px (-x) RAy = 0 RAz = Py (-z) MAx = bPz (+y) MAy = aPx (-y) MAz = bPx (-z) Problem 4.9 Figure 4.56 illustrates a person who is trying to pull a block on a horizontal surface -using a rope. The rope makes an angle () with the horizontal. If W is the weight of the block and JL is the coefficient of maximum friction between the bottom surface of the block and horizontal surface, show that the magnitude P of minimum force the person must apply in order to overcome the frictional and gravitational effects (to start moving the block) is: JLW P=---- cos () + JL sin () Problem 4.10 Figure 4.57 illustrates a person trying to push a block up on an inclined surface by applying a horizontal force. c B \u2022 ~'1 p 80 Fundamentals of Biomechanics The weight of the block is W, the coefficient of maximum friction between the block and the incline is /hI and the incline makes an angle 0 with the horizontal. Determine the magnitude P of minimum force the person must apply in order to overcome the frictional and gravitational ef fects (to start moving the block) in terms of W, /h, and O. Answer: sinO + /h cosO W P=----- cos 0 - /h sin 0 Chapter 5 Applications of Statics to Biomechanics 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002442_02783640122068218-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002442_02783640122068218-Figure5-1.png",
        "caption": "Fig. 5. Analytical model of three-degree-of-freedom walking mechanism.",
        "texts": [
            " Thus, the swing motion would change so that the shank motion delays at about 90 degrees from the thigh motion. Through this feedback, it is also expected that the kinetic energy of the swing leg increases and that the reaction torque (\u2212T ) will make the support leg rotate in the forward direction in a region where \u03b83 > 0. The self-excitation of the swing leg based on the asymmetrical matrix is explained in detail below. Figure 2 depicts the two-DOF swing leg model whose first joint is stationary. To make Figure 2 compatible with Figure 5b, the upper and lower links are termed the second and third links, respectively. To generate a swing motion like a swing leg, only the second joint is driven by the torque T2, which is given by the negative position feedback of the form T2 = \u2212k\u03b83. (1) From the fundamental study of the asymmetrical stiffness matrix-type self-excitation (Ono and Okada 1994a), it is known that damping plays an important role in inducing the at RUTGERS UNIV on August 11, 2015ijr.sagepub.comDownloaded from self-excited motion",
            " Since the exciting force acts only during half the period and the input energy is consumed at the plastic knee collision, the divergence rate becomes small compared with Figure 3. The next question is whether the biped mechanism, which combines the two-DOF swing leg discussed in Section 2 and the single-DOF support leg, can generate a biped locomotion that satisfies the conditions (1), (4), and (5). Since it is difficult to derive this solution analytically, we numerically show that the nonlinear biped system excited by the asymmetrical feedback exhibits a stable biped locomotion that satisfies the three conditions as a limit cycle of the system. Figure 5a shows the representative postures of a biped mechanism during half of the period of biped locomotion. From an aspect of the difference of the basic equation, one step process can be divided into two phases: (1) from the start of the swing leg motion to the collision at the knee (the first phase) and (2) from the knee collision to the touchdown of the straight swing leg (the second phase). We assume that the change of the support leg to the swing leg occurs instantly and that the end of the second phase is the beginning of the first phase. The self-excitation feedback of (1) is applied only during the first phase. We assume that the support leg is kept straight because of internal reaction torque at the knee for simplifying the forward dynamic simulation. The validity of this assumption will be examined later. Under the assumption of a straight support leg, the analytical model during the first phase is represented as a three-DOF link system, as shown in Figure 5b. Viscous damping is applied to the knee joint of the swing leg. The equation of motion in this system during the first phase is written as  M11 M12 M13 M22 M23 sym M33    \u03b8\u03081 \u03b8\u03082 \u03b8\u03083   (6) +   0 C12 C13 \u2212C12 \u03b33 C23 \u2212 \u03b33 \u2212C13 \u2212C23 \u2212 \u03b33 \u03b33    \u03b8\u03071 \u03b8\u03072 \u03b8\u03073   +  K1 K2 K3   =  \u2212T2 T2 0   , where the elementsMij , Cij , andKi of the matrices are shown in Appendix A. T2 is the feedback input torque given by eq. (1). When the shank becomes straight in line with the thigh at the end of the first phase, it is assumed that the knee collision occurs plastically",
            "2 and that a lighter shank is better in terms of both velocity and efficiency. The relationship between clearance of the swing leg tip and shank mass ratio is shown in Figure 16. We note that the shank mass ratio value of about 0.3 is optimum in terms of the stable and robust walking gait. From the parameter study described above, it seems that the simulation results are consistent with walking characteristics of a human being. To validate the simulation results stated above, we manufactured the biped robot similar to the analytical model shown in Figure 5b. The structure of the robot is schematically illustrated in Figure 17. The robot has three legs whose outer legs are connected by a shaft at the hip to prevent a rolling motion. The shaft and the inner leg are connected serially by a 100 W AC servomotor through one-tenth reduction gears. The thigh and shank of each leg are connected by a passive joint with a knee stopper. An optical encoder of 1000 pulses is mounted at each knee joint. To equalize the total mass and moment inertia of each leg, the inner leg is made of an aluminum alloy frame with a 40-by-80 mm cross section, while a couple of the outer legs are made of a 30-by-80 mm frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure5.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure5.3-1.png",
        "caption": "Figure 5.3. Focusing on two different depths: a. eyes are focused on level F1; b. eyes are focused on level F2",
        "texts": [
            " The control of the eye muscles is closely linked to disparity detection. If the eyes have to focus on a new fixation point, the required eye movement can be calculated (or at least estimated fairly accurately) based on the actual measured disparities. For example, if a point is fixed, which lies further away (but in the same cyclopean line of sight), then the vergence signals, which control the movement of the eyes, are determined by the measured disparities of the new fixation point relative to the actual fixation point. Figure 5.3 shows an example of this. In Figure 5.3a, the eyes are focused on the level F1. Points on this level have disparity 0. The points on the more distant level F2 have a negative disparity d(F2). The greater the extent of this disparity, the further do the eyes have to turn outwards in order to focus on the level F2 (Figure 5.3b). Through the changes in the fixation level, the disparities in the new level become 0. The disparity region is shifted; it is always relative to the fixation point. In Figure 5.3a, F2 always has a negative disparity to F1. In Figure 5.3b, F1 always has a positive disparity to F2. 134 Marco J\u00e4hnisch As referred to above, the disparity search area for the algorithmical processing of stereoscopic images has a limited extent. Disparities outside of this search area cannot be detected. Because the value range of the arising disparities in a stereoscopic image pair is not known in advance, the question arises as to how the search area can be selected. One possible answer is to make the search area sufficiently large such that the probability of disparities lying outside the area is reduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.25-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.25-1.png",
        "caption": "Fig. 6.25 The elliptical region of the fish-mouth actuator spring",
        "texts": [
            " Several simplified analytical models were formulated and compared to another as well as to FEM analysis results. The most accurate proved to be the so-called circle-arc model, in which the elliptical regions of the spring were approximated by circle arcs and supposed to keep a circular shape after bending [2]. This model provides the expression of the stroke amplification ratio \u03b3s = 1\u22122\u03bc arctan ( 1 \u03bc ) \u03bc \u2212 (\u03bc2 \u22121)arctan ( 1 \u03bc ) (6.96) where \u03bc = a b (6.97) is the axis ratio of the spring ellipse (see Figure 6.25). The expression (6.96) can be simplified for large aspect ratios by Taylor approximation as \u03b3s \u22123 4 \u03bb (6.98) which provides for \u03bb \u2265 2 the amplification factor with an (overestimation) error less than 7%. The spring\u2019s primary stiffness is essentially related to the bending stiffness of the elliptical regions. Here simple models on the basis of the Bernoulli-Euler beam theory supply a useful basis for the design analysis. As far as the secondary stiffness 190 6 Design Principles for Linear, Axial Solid-State Actuators is concerned it could be necessary to take into account membrane deformations of the composite spring to properly evaluate its behavior"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.60-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.60-1.png",
        "caption": "Figure 8.60 The free-body diagrams.",
        "texts": [
            " This appara tus consists of a stationary head (A) to which the specimen (B) is attached, two rings (C and D), and a mass (E) with weight W applied to the specimen through the rings. For a weight W = 1000 N applied to the middle of the specimen and for a support length of e = 16 cm (the distance between the left and the right supports), determine the maximum flexural and shear stresses generated at section bb of a specimen. The specimen has a square (a = 1 cm) cross-section, and the distance between the left support and section bb is d = 4 cm (Figure 8.60a). Solution: The free-body diagram of the specimen is shown in Figure 8.60a. The force (W) is applied to the middle of the speci men. The rotational and translational equilibrium of the speci men requires that the magnitude R of the reaction forces gener ated at the supports must be equal to half of W. That is, R = 500 N. The specimen has a square cross-section, and its neutral axis is located at a vertical distance a /2 measured from both the top and bottom surfaces of the specimen. The normal (flexu ral) stresses generated at section bb of the specimen depend on 186 Fundamentals of Biomechanics Figure B.60a. the magnitude of the bending moment M at section bb and the area moment of inertia I of the specimen at section bb about the neutral axis. At section bb, the magnitude of the flexural stress is maximum (CTmax ) at the top (compressive) and the bottom (ten sile) surfaces of the specimen: Ma CTmax = T 2' The internal resistances at section bb of the specimen are shown in Figure 8.60b. For the rotational equilibrium of the specimen: M = d R = (0.04)(500) = 20 N-m The area moment of inertia of a square with sides a is: I = a4 = (0.01)4 = 8.33 X 10-10 m4 12 12 Substituting M and I into the flexure formula will yield: ( 20 ) 0.01 6 CTmax = 8.33 X 10-10 2 = 120 x 10 Pa = 120 MPa The shear stress generated at section bb of the specimen is a function of the shear force Vat section bb, and the first moment Q and the area moment of inertia I of the cross-section of the specimen at section bb. The shear stress is maximum \u00abmax) along the neutral axis, such that: VQ <max = Ta For the vertical equilibrium of the specimen (Figure 8.60b), the magnitude V of the internal shear force at section bb must be equal to the magnitude R of the reac.tion force; V = R = 500 N. The first moment of the cross-sectional area of the specimen about the neutral axis is: Q = a3 = (0.01)3 = 0 125 X 10-6 m3 88' Therefore, the maximum shear stress occurring at section bb along the neutral axis is: (500)(0.125 x 10-6) 6 <max = (8.33 x 10-10)(0.01) = 7.5 x 10 Pa = 7.5 MPa Remarks: Note that magnitudes and directions of internal shear force and bending moment are different at different sections of the specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure11-1.png",
        "caption": "Fig. 11 3-\u201ePP\u2026NRa PPR-equivalent parallel kinematic chains",
        "texts": [
            " A set of two RRR NRa legs with 1- 0-1- -system and one RR B RRR A legs with a 1- -system can be used to construct a 2- RRR NRa - RR B RRR A PPR-equivalent parallel kinematic chain Fig. 10 . It is learned from Table 2 that among the combinations of sets of leg-wrench systems, there is only one combination, the combination of three 1- 0-2- , in which all the leg-wrench system are of the same type. From Table 1, there is one type of leg, PP NRa, with a 1- 0-2- wrench system. Thus there is only one 3-legged PPR-equivalent parallel kinematic chain, 3- PP NRa Fig. 11 , with identical type of legs. For an m-legged PPR-equivalent parallel kinematic chain, if the total of the orders, i=1 m ci, of all of its leg-wrench systems is greater than 3, it is an overconstrained hyperstatic kinematic chain. The number of overconstraints redundant constraints of the PPR-equivalent parallel kinematic chain is i=1 m ci\u22123 . It is noted that there exist no constraint singularities 24 for PPR-equivalent parallel kinematic chains of families 1, 2, 4, 5, 6, 9, 10, 11, and 12. For a PPR-equivalent PM, constraint singularities occur at configurations in which the order of the wrench system of the PPR-equivalent parallel kinematic chain is less than 3",
            " 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not parallel to the axes of the R joints within RRR N. It can be proved that the set of actuated joints is valid since the validity condition Eq. 4 of the actuated joints is satisfied. Based on the above validity condition of actuated joints, a number of PPR-equivalent PMs have been identified. Due to the large amount of PPR-equivalent PMs and space limitation, only several PPR-equivalent PMs are presented Figs. 12 b and 14\u201316 . It is noted that for the PMs corresponding with the sole PPRequivalent parallel kinematic chain, 3- PP NRa Fig. 11 , with identical type of legs, the three P joints located on the base do not constitute a valid set of actuated joints. Thus, there are no 3-DOF PPR-equivalent PMs with identical types of legs. From these PPR-equivalent PMs obtained, a number of variations can be obtained using the techniques listed in the Appendix. For instance, Fig. 17 shows a 2-RP U-UP U PPR-equivalent PM. This PM is obtained from the 2- RP R NRa-RA RP R BRA PPR- NOVEMBER 2005, Vol. 127 / 1119 3 Terms of Use: http://asme.org/terms Downloaded F equivalent PM shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003684_j.matdes.2008.06.037-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003684_j.matdes.2008.06.037-Figure4-1.png",
        "caption": "Fig. 4. Experimental gear wheels: (a) unmodified spur gear and (b) tooth width-modified spur gear.",
        "texts": [
            " After applying two different teeth loadings (8 and 13 Nm) on the gear teeth, the hertz surface pressures generated on the gear tooth surfaces for the width-modified and unmodified gear tooth contact regions reached the values shown in Fig. 3. As can be seen in Fig. 3, the values of Hertz surface pressure formed on the modified gear teeth were not completely equilibrated. This arises from the radius of curvature of the gear teeth. The tooth profile of the modified and unmodified spur gears can be seen in Fig. 4. Polymer gears used in this study as driving gears were made of Polyamide 66 GFR30. This material has glass fiber reinforcement and heat aging resistance. It is also an injection molding-grade material designed for machinery components and housings with high stiffness and dimensional stability. The specification material properties of the gear pairs used in this study are summarized in Tables 1 and 2, respectively. Wear tests of the gear pairs and the experimental gear tooth were carried out on a FZG (Forschungsstelle f\u00fcr Zahn\u00e4der und Getriebebau) test machine (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.29-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.29-1.png",
        "caption": "Figure 3.29 Vector product method (Example 3.5).",
        "texts": [
            " At the shoulder joint, the feeling is such that there is an upward force of F, a torque with magnitude Mx that Moment and Torque 43 is trying to twist the upper arm in the yz-plane, and a moment Mz that is trying to rotate or bend the upper arm in the xy-plane. If the person is able to hold the arm in this position, then he/ she is producing sufficient muscle forces to counterbalance these applied forces and moments. Solution 2: Vector product method. The definition of moment as the vector product of the position and force vectors is more straightforward to apply. The position vector of point C (where the force is applied) with respect to point A (where the shoulder joint is located) and the force vector shown in Figure 3.29 can be expressed as follows: r.=ai+b1\u00a3 F =F 1 The cross product of r. and F will yield the moment of force F about point A: M= r x F - - - = (a i + b 1\u00a3) x (F D =aF(fxD+bF(1\u00a3xD =aFk-bFi - - = (0.25)(200) 1\u00a3 - (0.30)(200) i =50k-60i - - The negative sign in front of 60 i indicates that the x component of the moment vector is acting in the negative x direction. Fur thermore, there is no component associated with the unit vector j, which implies that the y component of the moment vector is zero. Therefore, the moment about point A has the following components: Mx = 60N-m My = 0 Mz = 50N-m ( - x direction) (+z direction) These results are consistent with those obtained using the scalar method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.6-1.png",
        "caption": "Figure 5.6 Rotational (F Mn) and stabilizing or sliding (F Mt) components of the muscle force.",
        "texts": [
            " \u2022 The angle (angle of pull) between the line of action of the muscle force and the long axis of the bone upon which the mus cle force is exerted is critical in determining the effectiveness of the muscle force. When the lower arm is flexed to a right angle, the muscle tension has only a rotational effect on the forearm about the elbow joint, because the line of action of the muscle force is at right angles with the longitudinal axis of the forearm. For other flexed positions of the forearm, the muscle force can have a translational (stabilizing or sliding) component as well as a rotational component. Assume that the linkage system shown in Figure 5.6a illustrates the position of the forearm relative to the upper arm. n des ignates a direction perpendicular (normal) to the long axis of the forearm and t a direction tangent to it. Assuming that the line of action of the muscle force remains parallel to the long axis of the humerus, F M can be decomposed into its rectangu lar components F Mn and F Mt. In this case, F Mn is the rotational (rotatory) component of the muscle force because its primary function is to rotate the forearm about the elbow joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003225_j.euromechsol.2005.02.004-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003225_j.euromechsol.2005.02.004-Figure11-1.png",
        "caption": "Fig. 11. Kinematic structure of Isoglide 4 T3R1-v3.1 (a) and its associated graph (b).",
        "texts": [
            " 10 was developed at IRCCyN under the name Orthoglide (Wenger and Chablat, 2000). Delta robot (Clavel, 1988; Pierrot et al., 1990) and University of Maryland parallel manipulator (Tsai and Stamper, 1996) represents other examples of parallel robots with complex legs integrating parallelogram closed loops serially concatenated. The mobility of these parallel robots can be easily obtained by using Eq. (61). Tsai (2000) have shown that Chebychev\u2013Gr\u00fcbler\u2013 Kutzbach\u2019s mobility criterion does not work for these parallel mechanisms. Example 4. Fig. 11 presents Isoglide4-v.3.1 which can be considered a parallel robotic manipulator T3R1-type with two complex legs D \u2190 E1\u2013E2. Two revolute joints connect the mobile platform 9 to the complex legs. Leg E1 integrates three elementary open kinematic chains connecting the fixed base to an intermediate mobile platform 5. These three elementary open kinematic chains form a complex chain similar to the parallel mechanism with elementary legs presented in Example 1. Two closed loops are parallel concatenated in leg E1",
            " The same four relative independent velocities (vx,vy,vz and \u03c9y) exist between the mobile and reference platforms as in Example 2. The mechanism has 19 revolute and 4 prismatic joints ( \u2211m i=1 fi = 23). The two planar parallelogram loops serially concatenated in the complex leg E2 cancel the independence of 2 \u00d7 3 = 6 joint variables. The two closed loops parallel concatenated in leg E1 cancel the independence of 4 + 4 + 4 \u2212 3 = 9 joint variables (see Example 1). The total number of joint parameters that lost their independence in Isoglide4-v.3.1 (Fig. 11) given by Eq. (60) is r = rD = (4 + 4) \u2212 4 + 6 + 9 = 19. The mobility of the parallel robotic manipulator given by Eq. (61), is M = 23 \u2212 19 = 4. The four independent joint parameters necessary to describe the motion of any link of the mechanism are the joint variables qi of the four prismatic joints. In this paper we have presented new formulae for mobility and spatiality of parallel robotic manipulators. General (full-cycle) mobility is defined and calculated by using 12 spatiality theorems demonstrated via the theory of linear transformations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003295_0301-679x(91)90024-4-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003295_0301-679x(91)90024-4-Figure1-1.png",
        "caption": "Fig 1 Ball-and-disc machine with microscope and video camera",
        "texts": [],
        "surrounding_texts": [
            "In the present investigation the central film thickness stabilized between 0.35 and 0.45 of the base oil film thickness after about 40 cycles, which in this case means about three minutes of running.\nWilson -~ used a method based on electrical capacitance to study the film thickness in spherical and cylindrical roller bearings. His results agree with those found by Aihara and Dowson 2 and Pooh 1, a decreasing film thickness which tends to stabilize after two hours of running time. Wilson also measured a temperature rise of about 20\u00b0C during the two hours of running. The decreasing film thickness can thus be explained partly by the viscosity decrease due to increasing temperature.\nCameron and Gohar 4 applied optical interferometry to the study of film thickness in EHD contacts. The advantage of this method is that it can visualize the film thickness variations within the contact whereby the other methods eg electrical capacitance and magnetic reluctance give the mean value of the film thickness in the contact. Optical interferometry has been used in several investigations of EHD contacts lubricated with oil and in some investigations of EHD contacts lubricated with grease.\nKageyama et a l 5 have studied a grease lubricated point contact under conditions of pure sliding with optical interferometry. As before 1-3, the results showed a decreasing film thickness with time. After about five minutes of running the film thickness decreased to below the smallest detectable level using the optical interferometry method. Thus any possible equilibrium limit was not found in their investigation.\nZhu and Neng ~' also used optical interferometry to study EHD line and point contacts under rolling conditions. Their experimental results concerning point contact agree mainly with those found by Kageyama et a l 5 but Zhu and Neng% after about five minutes of running, detected an equilibrium film thickness of about ten per cent of the initial film thickness. The film thickness with the line contact situation stabilized at about 80 per cent of the initial value.\nOne problem when studying grease lubricated contacts using optical interferometry is the evaluation of the results. With lubricating oil the contact is stable due to a continuous supply of homogeneous oil which gives plenty of time for evaluation. When using grease, without continuous supply, the film thickness changes with time. Sudden film fluctuations have also been observed in this investigation. This makes it difficult to evaluate the film thickness in real time.\nThis paper suggests a way to overcome the problem of evaluating the varying film thickness using a video camera. Results from an EHD point contact lubricated with six different greases evaluated with the described method are also presented.\nLubricants tested\nData on the greases investigated in this paper are given in Table 1. The six greases are all of the most common NLGI grade 2, measured at 25\u00b0C, and consist of base oil and soap without any additives. The greases have been worked 60 strokes in a standard grease worker before the penetration measurements.\n180\nThe base oils are: one mineral oil of naphthenic type, B1; and one synthetic base oil, B2, which mainly consists of polyalphaolefin. The viscosities, -%, the temperature-viscosity coefficients 13, and the pressureviscosity coefficients ~, at 20\u00b0C, are given in Table 2.\nThe soap thickeners are of three types: lithium; lithium complex; and sodium. One difference between them is the size and shape of the soap structures. The lithium and lithium complex soap structures are known to be comparably small7; if there is a difference between them the lithium complex fibres are smaller. The diameter of the lithium fibres is 0.1 to 0.2 ~xm and the length 5-20 fxm. The sodium soap structure is larger with a fibre diameter of 1-10 ixm and a length of 10-15 Ixm. The size of the structures should be compared with the measured central film thickness, 0.2 Ixm. The greases were unworked at the beginning of the tests.\nExperimental details\nIn this investigation the film thickness in an EH D point contact was measured using optical interferometry. The apparatus used was connected to a video camera for documentation and evaluation of the results. The apparatus has been used without the video camera in investigations of lubricating oils by Isaksson ~.\nThe central parts of the apparatus, shown in Fig l, were a steel ball with a diameter of 50 mm and a surface roughness of 0.04 ~m rms, and a glass disc, diameter 100 mm, with a surface roughness of 0.009 ~m rms. The steel ball was mounted in a conical seat. The mounting made replacement of the ball easy and gave a tolerance of radial run out, for the contact radius of the ball, of less than 5 p~m.\nWith a lever and a weight the steel ball was loaded against the glass disc, radially 35 mm from the disc centre. The 2.0 kg weight used in this investigation",
            "gave a loading force of 60 N thus giving a maximum Hertzian pressure of 0.38 GPa and a contact radius of 0.30 mm. The glass disc was mounted in a steel disc supported by a large ball bearing. The glass disc, as well as the steel ball, were connected via chain drives to variable-speed drives, driven by electric motors. Separate drives for the ball and the disc enabled continuously variable Velocity conditions from the pure rolling condition to different degrees of sliding, with a maximum rolling velocity of 1 m s- l . By adjusting the speed of the ball and the disc, using the separate drives, sliding at the beginning of the test was avoided. In this investigation the rotating speeds were adjusted to give pure rolling at a velocity of 0.055 m s -].\nThe glass disc was made semi-transparent with a 200/~ chromium layer on the side facing the steel ball, and the contact between the glass disc and the ball was illuminated with white light led through a fibre-optic bundle and a prism. The light was reflected both from the chromium layer and from the steel ball, which gave interference patterns of different colours depending on the distance between the reflecting surfaces, up to a maximum distance of 1 Ixm.\nThe contact between the ball and the disc was magnified 40 times with a microscope and recorded with a video camera by putting the camera lens close to, and in line with, the eyepiece of the microscope. The video camera was a commercial model (VHS) giving 25 pictures per second with a shutter speed of one thousandth of a second. With a rolling speed of 0.055 m s -1, about 3.7 Hertzian contact diameters passed between every exposure on the video tape. The contacting surfaces moved roughly one tenth of the Hertzian contact diameter during each exposure. The video camera also copied a stop watch with minutes, seconds and tenths of a second to the recorded picture which made the evaluation easier.\nWhen the contact was lubricated with grease, without continuous supply, the changes in film thickness and\nthus in colours between every picture made the video recorded results unreliable at rolling velocities exceeding 0.1 m s -1. This was owing to the low frame speed of 25 s 1. By studying the colours carefully the thickness of the lubricating film in every part of the contact could be revealed. The film thickness was evaluated with Eq (1) using the following colours and corresponding wavelengths: red, 630 nm; orange, 600 nm; green, 530 nm; and blue, 470 nm.\nh = qX/2n (1)\nTo be able to calculate the refractive index of the lubricant, its pressure dependence has to be known. The refractive index-pressure variation was calculated by first calculating the density variation with Eq (2), which gives a good approximation up to pressures of 1 GPa, and then by using the Lorenz-Lorentz relation, Eq (3), with k = 0.35 m 3 kg -t (Ref 9).\np = Po 1 + 1 + 1. ( p i n a P a ) (2)\n(n 2 - 1)/(n 2 + 2) = pk (3)\nBefore each test, the steel ball and the glass disc were cleaned with toluene and covered with a layer of fresh grease on the contacting parts of the surfaces. The steel ball and the glass disc were accelerated to their right speeds, the video camera was started, and then the ball was loaded against the disc thus starting the test. All tests were made at a temperature of 20\u00b0C.\nResults\nThe results are presented in Fig 2, showing the film thickness in the centre of the contact during a specific cycle of the glass disc, together with a comprehensive description of the grease behaviour. The diagram has little value without the description because many differences between the greases, observed on the video\nTRIBOLOGY INTERNATIONAL 181",
            "recorded pictures, are not seen in Fig 2. Observations not shown in Fig 2 are sudden variations of the film thickness inside the contact which disturb locally the normal horseshoe shape of the contact, like the example shown in Figs 3 and 4, or momentary lifts of the whole film thickness with remaining horseshoe shape as shown in Figs 5 and 6. Because of difficulties in reproducing the video recorded picture in print, the contacts shown in Figs 3 and 5 are elucidated with sketches shown in Figs 4 and 6 respectively.\nWith a rolling velocity of 0.055 m s ~ the glass disc completes a cycle, one revolution, every four seconds. During the first cycle the conditions are comparable to tests with a continuous grease supply. After the first cycle progressive lubricant starvation can be seen.\nIn Fig 2 results from measurements with the base oils are also presented, made under fully flooded conditions. When lubricated with grease, the central film thickness, during the first cycle of the glass disc, is consequently higher than the film thickness obtained with the base oils. These results agree with those found by Dalmaz and Nantua ~\u00b0 in their investigation of a point contact lubricated with a continuous supply of grease.\nGreases G1, G2 and G3 have an initial film thickness of 0.60 ~m and G4, G5 and G6 an initial film thickness of 0.51 I~m. The base oil of G1, G2 and G3, namely B1, has a significantly larger pressure-viscosity\n182\ncoefficient than B2 at 20\u00b0C, as shown in Table 2. This explains the difference in initial film thickness. The viscosity, -%, of the base oils are nearly equal at 20\u00b0C but the viscosity of B1 increases more in the inlet\nJune 91 Vol 24 No 3"
        ]
    },
    {
        "image_filename": "designv10_8_0003770_j.jsv.2008.04.024-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003770_j.jsv.2008.04.024-Figure4-1.png",
        "caption": "Fig. 4. Bearing and added mass: type and location of sensors.",
        "texts": [
            " The mass M was increased to 18 kg but was partially supported by a vertical spring; thereby, the radial static load applied to the bearing remains unchanged. This configuration is explored in Section 6. It is clear at this step that a complete quasi-periodic route to chaos cannot be reached with these settings: the maximum value of f pb remains below f x even for higher values of M; this indicates that the excitation frequency is not supposed to reach the second chaotic region. The bearing is centrally located in the housing M and the measurements are made on the outer diameter of the housing as shown in Fig. 4. The two piezo-accelerometers are attached to the mass; their directions are ARTICLE IN PRESS B. Mevel, J.L. Guyader / Journal of Sound and Vibration 318 (2008) 549\u2013564 555 chosen to be vertical and horizontal. One optical sensor is located facing the bearing. It is sensitive to the variation of light reflected by the balls. The two piezo-accelerometers describe the motion of the bearing in its plane. The optical sensor generates a pulse at each pass of one ball with respect to a fixed point of the rig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003626_1.35445-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003626_1.35445-Figure4-1.png",
        "caption": "Fig. 4 First four elastic modes of the morphing UAV at 65deg.",
        "texts": [
            " The whole idea is to sensibly reduce the total number of parameter vertices N, each related to an LTI model, to attain a practical affineLPVmodelwhich can be described exclusively by the vertex values i. The affine LPV model can be scheduled by t , which is a convex combination of these vertices i. The outcome of this modeling process are N sets of dimensional aeroelastic stability derivatives upon which the morphing LPV models are generated. Five structural models with different inboard wing folding angles were employed, that is, 0, 45, 65, 90, and 125 deg. As an example, the first four mode shapes of the morphing UAV for 65 deg are displayed in Fig. 4. For this modeling process, the flight condition parameters are 1) Mach numbers M 0:5, 0.6, 0.7, 0.8, 0.85, 0.9, and 0.95; 2) altitudeH varying from 5 to 50 kft with discrete increments, each 5 kft; and 3) wing folding angle 0, 45, 65, 90, and 125 deg. In this way, a total of 350 operating points are generated, that is, 70 flight conditions for each one of the wing folding angles. This set of dimensional aeroelastic derivatives form the coefficients of the differential equations that will describe the motion of the morphing UAV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure11.19-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure11.19-1.png",
        "caption": "Figure 11.19 Horizontal component of the velocity remains constant through the motion. Velocity vector is always tangent to the trajectory of motion.",
        "texts": [
            "30) take the following special forms for projectile motion: x = Xo + (vo cos 0) t . 1 2 Y = yo + (vo sm 0) t - 2. g t Vx = Vo cosO Vy = Vo sin 0 - g t (11.31) (11.32) (11.33) (11.34) Here, if the origin of the xy coordinate frame is chosen to coin cide with the initial position of the ball, then Xo = 0 and yo = o. Note from Eq. (11.33) that the magnitude of the horizontal com ponent of the velocity vector is not a function of time. There fore, Vx = Vxo remains constant throughout the projectile motion (Figure 11.19). The magnitude of the vertical component of the velocity vector is a linear function of time. It is positive (upward) initially, decreases in time as the object ascends, and drops to zero at the peak. After reaching the peak, the vertical compo nent of the velocity vector changes its direction from upward to downward, while its magnitude increases until it lands on the ground. At any instant during the flight, the resultant velocity vector is tangent to the trajectory of the projectile motion. Another important aspect of the projectile motion is that if both the takeoff and landing occur at the same elevation, then the motion is symmetric with respect to a plane that passes through the peak and cuts the plane of motion at right angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003899_s10472-009-9125-x-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003899_s10472-009-9125-x-Figure3-1.png",
        "caption": "Fig. 3 Illustration of Algorithm 1 a triangular configuration (Ti), b computation of the target point",
        "texts": [
            " Here, the motion of each robot is controlled by the first-order linear differential equation for the distance from the centroid of Ti, and for the internal angle of Ti, respectively (see Section 3.2). This section describes the local interaction algorithm that enables three neighboring robots to generate Ei from an arbitrary Ti (see Algorithm 1), and proves the convergence of the algorithm. 3.1 Algorithm description The algorithm consists of a function \u03d5interaction whose arguments are pi and Ni at each activation. Consider a robot ri and its two neighbors s1 and s2 located within ri\u2019s SB. As shown in Fig. 3a, three robots are configured into Ti whose vertices are pi, ps1, and ps2, respectively. As illustrated in Fig. 3b, ri finds the centroid pct of the triangle pi ps1 ps2 with respect to its local coordinates, and measures the angle \u03c6 between the line connecting two neighbors and ri\u2019s horizontal axis. Using pct and \u03c6, ri calculates the target point pti as described in Line 3 and Line 4 of Algorithm 1. Each robot computes the target point at each instant in time by their current observation of neighboring robots. Algorithm 1 Local Interaction constant du := uniform distance FUNCTION \u03d5interaction({ps1, ps2}, pi) 1 (pct,x, pct,y) := centroid(ps1, ps2, pi) 2 \u03c6 := angle between ps1 ps2 and ri\u2019s local horizontal axis 3 pti,x := pct,x + du cos(\u03c6 + \u03c0/2)/ \u221a 3 4 pti,y := pct,y + du sin(\u03c6 + \u03c0/2)/ \u221a 3 5 pti := (pti,x, pti,y) To assist the explicit understanding of the proposed local interaction, we explain how the positions of three robots converge into Ei"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.66-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.66-1.png",
        "caption": "Figure 8.66 A bench test.",
        "texts": [
            " y Lx - ~ A ~a\" -- Tyx - __ Tyx 188 Fundamentals of Biomechanics Once the radius of the Mohr's circle is established, principal stresses and maximum shear stress can be determined as 0\"1 = r O\"x/2 (tensile), 0\"2 =r + O\"x/2 (compressive),and rmax =r. To deter mine the angle of rotation, (h, of the plane for which the stresses are maximum and minimum, we need to read the angle between lines CA and CD (in this case, it is 21h counterclockwise), divide it by two, and rotate the stress element in Figure 8.63b in the clockwise direction through an angle {h. This is illustrated in Figure 8.64b. Analyses of the material element in Figure 8.63c are illustrated graphically in Figure 8.65 . Example 8.8 Figure 8.66 illustrates a bench test that may be used to subject bones to bending. In the case shown, the distal end of a human femur is firmly clamped to the bench and a horizontal force with magnitude F = 500 N is applied to the head of the femur at point P. Determine the maximum normal and shear stresses generated at section aa of the femur that is located at a vertical distance h = 16 cm measured from point P. Assume that the geometry of the femur at section aa is circular with inner radius ri = 6 mm and outer radius r 0 = 13 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002957_s0263574703005216-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002957_s0263574703005216-Figure2-1.png",
        "caption": "Fig. 2. (a) Geometric model of the manipulator for a0 =00, (b) representation of two possible forward kinematics solutions.",
        "texts": [
            " The input motions of the active joints can be independent from each other or be provided via a set of gears maintaining a specified phase angle between the two active joints in order to generate an infinite number of different motions from the output point C.5 Analytical expressions for the coordinates of the output point C, where the end effector is mounted, are obtained for the provided joint inputs 1 and 4, and the specified link lengths L0, L1, L2, L3, L4 and the angle 0. 7 It must be noted that for a parallel RRRRR manipulator L1 =L4 and L2 =L3. The angle 1 and the radial distance Ri describe the center of mass Gi of the ith link. Referring to Figure 2(a), the coordinates of B and D, which are the x and y components of the r 1 and r 4 vectors, can be considered as the coordinates of the centers of two circles of radii L2 and L3. The centres of two circles are expressed as functions of the inputs provided by the actuators fixed to the ground. It is well known that the intersection of the two circles gives a maximum of two solutions, which are the possible locations of point C. Referring to Figure 2(b), the analytical expressions for these two solutions are obtained using the following algorithm; r 1 =L1 cos 1 i +L1 sin 1 j , r 4 =(L0 +L4 cos 4)i +L4 sin 4 j , (1) q =r 4 r 1 = x\u0304i +y\u0304j , (2) x\u0304=r4x r1x, y\u0304=r4y r1y, q= x\u03042 + y\u03042, (3) and the coordinates of C1 and C2 are; x1 =xB +Qx\u0304 y\u0304 L2 2 q2 Q2, y1 =yB +Qy\u0304 x\u0304 L2 2 q2 Q2, (4) x2 =xB +Qx\u0304 y\u0304 L2 2 q2 Q2, y2 =yB +Qy\u0304 x\u0304 L2 2 q2 Q2, (5) and Q= L2 2 +q2 L2 3 2q2 , (6) So, it is now possible to determine the position of the output point for given joint inputs",
            "35 The mechanism will not move unless a special precaution is taken to pass through the change-position configuration. (iv) The transmission angle , which is the angle between L2 and L3 of Figure 1, must be 50\u00b0\u2264 \u2264130\u00b0, ideally be 90\u00b0, for effective force transmission from two coupler links to the output point C. Especially when its deviation from 90\u00b0 is greater than 500, it causes unacceptable higher acceleration and jerk, and objectionable noise at high speeds. It must also be continuous between the desirable ranges.1,5 Referring to Figure 2(a), it is mathematically expressed as; cos =1 q2 2L2 2 (15) (v) For the sake of generality, it is required that the links connected to the active joints make unlimited rotations. This constraint is based on the \u201cthe theorem of full rotatability of linkages\u201d.34,35 which states that if the sum of the longest link length L0 and link Lk is smaller than the sum of the lengths of the rest of the mechanism links, the link Lk will make unlimited rotations. For the manipulator at hand, the links connected to the active joints /actuators are link 1 and link 4. Therefore, the full rotatability constraint for the mechanism in Figure 2(a) requires L0 +L1 <L2 +L3 +L4 and L4 +L4 < L1 +L2 +L3. However, for a parallel five-bar manipulator, these two conditions reduce to L0 <2L2. When L0 +L1 =L2 +L3 +L4 and L0 +L4 = L1 +L2 +L3, the centerlines of all links are collinear, the mechanism is a change-point mechanism. On the other hand, when L0 +L1 >L2 +L3 +L4 and L0 +L4 >L1 +L2 +L3, the mechanism is a double-rocker mechanism; the active joints cannot make a full rotation.35 Each of the active joints can move between two limit positions shown in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003669_bf03256551-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003669_bf03256551-Figure3-1.png",
        "caption": "FIG. 3. A VSCMG System with Pyramid Configuration at . 0, 0, 0, 0 T",
        "texts": [
            " This torque, being in the null space of the matrix , has no effect on the output torque and hence the stability analysis of the adaptive control laws developed earlier still holds. The parameters used for the simulations are shown in Table 1. Notice that the initial wheel speeds of the VSCMGs are set to 30,000 RPM, a value that is an order of magnitude larger than the speed of conventional CMGs, since the flywheels of VSCMGs used for IPACS in general need to spin very fast so that they are competitive against traditional chemical batteries. We assume a standard four-VSCMG pyramid configuration, as shown in Fig. 3. The nominal values of the axis directions at are (49) (50) The (unknown) actual axis directions at used in the present example are assumed as 0 At0 n t1,0 n , t2,0 n , t3,0 n , t4,0 n 0.5774 0 0.8165 0 0.5774 0.8165 0.5774 0 0.8165 0 0.5774 0.8165 As0 n s1,0 n , s2,0 n , s3,0 n , s4,0 n 0 1 0 1 0 0 0 1 0 1 0 0 0, 0, 0, 0 T G*n YG\u0302G (51) (52) which are obtained by slightly perturbing the nominal axis directions. This choice of perturbation leads to orthogonality of the axes for the uncertain matrices as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure2-1.png",
        "caption": "Fig. 2 Screw",
        "texts": [
            " With the introduction of the concept of virtual chain, a PM can be named according to the type of its virtual chain. In this way, the motion pattern of a PM is thus clearly shown by its name. For example, in a PPR-equivalent PM, the moving platform can rotate about an axis which translates along a plane which is parallel to the directions of the two P joints. The concept of virtual chain is also one of the key issues for the method for the type synthesis proposed in the following sections. 3.1 Screw and Reciprocal Screws A normalized screw is defined by see Fig. 2 $ = s s r + hs if h is finite 0 s if h = 1 where s is a unit vector along the axis of the screw $, r is the vector directed from any point on the axis of the screw to the origin of the reference frame O-XYZ, and h is called the pitch. Two screws, $1 and $2, are said to be reciprocal if they satisfy the following condition: 1114 / Vol. 127, NOVEMBER 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 $1 $2 = $1 T$2 = 0 2 where = 0 I3 I3 0 3 where I3 is the 3 3 identity matrix and 0 is the 3 3 zero matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.41-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.41-1.png",
        "caption": "Figure 5.41 Patella increases the length of the lever arm.",
        "texts": [
            " Since the normal component of F M is a sine function of 110 Fundamentals of Biomechanics angle (), a larger angle between the patellar tendon and the long axis of the tibia indicates a larger rotational effect of the muscle exertion. This implies that for large () ,less muscle force is wasted to compress the knee joint, and a larger portion of the muscle tension is utilized to rotate the lower leg about the knee joint. \u2022 One of the most important biomechanical functions of the patella is to provide anterior displacement of the quadriceps and patellar tendons, thus lengthening the lever arm of the knee extensor muscle forces with respect to the center of rotation of the knee by increasing angle () (Figure 5.41a). Surgical removal of the patella brings the patellar tendon closer to the center of rotation of the knee joint (Figure 5.41b), which causes the length of the lever arm of the muscle force to decrease (d2 < d1). Losing the advantage of having a relatively long lever arm, the quadri ceps muscle has to exert more force than normal to rotate the lower leg about the knee joint. \u2022 The human knee has a two-joint structure composed of the tibiofemoral and patellofemoral joints. Note that the quadriceps muscle goes over the patella, and the patella and the muscle form a pulley-rope arrangement. The higher the tension in the mus cle, the larger the compressive force (pressure) the patella exerts on the patellofemoral joint"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003889_09544062jmes849-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003889_09544062jmes849-Figure1-1.png",
        "caption": "Fig. 1 Example of the meshing of the tooth and its foundation",
        "texts": [
            " This stretching exploits three-dimensional surface geometry matrices by finding nearest available coordinate point so that any curve fitting or interpolation is not required. The meshing process is parameterized and needs only the following values: the amount of elements in mesh width, length, height, and foundation depth directions. In addition, the generated element mesh can be modified using weighting functions. This allows mesh density to be varied in certain areas for purposes of accuracy. An example of tooth meshing is shown in Fig. 1. Both pinion and gear tooth meshes can be modified independently. For example, mesh density in tooth foundation is formed with an exponential equation causing the mesh to be denser just below the tooth. This is a critical location of concentrations of deformation and stress. The foundation mesh is created utilizing elliptical shapes to create element mesh boundaries. The form of the semi-elliptical foundation can be varied using the semi-axis of the ellipse as variables. Axes af and bf present the semi-axes of the ellipse"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002823_02640410500127876-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002823_02640410500127876-Figure2-1.png",
        "caption": "Figure 2. Geometry of the experiment. The four open circles show locations of markers used to record (x,y) coordinates on the forearm and rod. V denotes the velocity of a point on the rod 60 cm from the handle end.",
        "texts": [
            " Internal rotation of the upper arm plays an important role in many swinging styles, but it did not play any significant role in the present study. Given that the hand, forearm and upper arm can each rotate in various planes, there are many different ways to swing a rod. The present study was restricted in its scope to just one of those ways (or two if we include the case where the upper arm remained at rest), but it was one where each rod could be swung at near maximum possible speed. Swing speed was recorded using the arrangement shown in Figure 2. Each participant was asked to sit or stand at a selected location and to swing each rod as fast as possible so that the rod would impact a pillow located anteriorly. The height of the pillow was adjusted so that the forearm would be approximately horizontal at impact. Each swing was recorded at 240 frames per second using two Qualisys infrared cameras located approximately 3 m apart in a plane parallel to the sagittal plane and about 4 m from the sagittal plane. Two cameras were used to obtain three-dimensional images, although subsequent analysis showed that motion of the forearm and rod out of the sagittal plane was negligible in all cases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002791_s0957-4158(99)00052-5-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002791_s0957-4158(99)00052-5-Figure7-1.png",
        "caption": "Fig. 7. Slope angle a.",
        "texts": [
            " The evaluation function is given Eep x kep1 min x 2Bfkx\u00ff x k2g kep2 T 0 Cepdt4 min 9 where B denotes a set of e ective interpolated con\u00aegurations with the best evaluation in GA operation, x denotes the nearest interpolated con\u00aeguration to the x, and Cep denotes a constraint. In the EP layer, the intermediate postures x of biped locomotion evolute toward ones in the best trajectories of GA layer. The constraints in GA and EP are given Cga o Constraint is satisfied: Cep c Constraint is not satisfied: 10 where c denotes the penalty vector whose components are positive. If the constraint is not satis\u00aeed, the second term of evaluation function Eqs. (8) and (9) gives a penalty vector c. We generate a reference trajectory on the \u00afat \u00afoor and slope shown in Fig. 7. The simulation conditions are shown in Tables 1 and 2. Figs. 8, 11 and 14 show one step motion of biped locomotion robot on the slope obtained by the energy minimizing evaluation function Eq. (8). Figs. 9, 12 and 15 show the positions of ZMP. The large circles and small circle display the positions of ZMP during single support period and double support period respectively. During single support period, ZMP must exist in the rectangular domain drawn by a solid line, and during double support period, ZMP must exist in the hexagonal domain drawn by a dashed line"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure3.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure3.5-1.png",
        "caption": "Fig. 3.5 Small element of a beam with distribution of stresses",
        "texts": [
            " As a second assumption, we take Fig. 3.4 z a(x,z) Normal and shear stresses of a beam with rectan gular cross section the distribution of the shear stresses to be uniform across the width of the beam. Thus - inconsistent with Hooke's law - we replace Eq. (3.2) by O\"xy = 0, a xz = T(Z). (3.25) These assumptions will enable us to completely determine the distribution of the shear stresses. A small element of length dx may be cut out between two adjacent cross sec tions and between two planes parallel to the neutral surface (see Fig. 3.5). Integrating over the relevant surfaces, the equilibrium of the forces in x direction yields J~ J~ 00\" - a(x, z)bdz + {O\"(x, z) + ox dX} bdz - T(z)bdx = 0, z z 3.2 Shear Stresses 45 from which (3.26) z z The partial differential of IJ can be determined from Eq. (3.13) OIJ _ !....- { N M(X)} _ dM ~ _ Q ax - ax A + J Z - dx J - J Z , (3.27) since N as well as the width and height of the rectangular cross section are assumed to be constant. Introducing this relation into Eq. (3.26), we find Q l! T(Z) = Jb /2 zdA"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002848_tia.2003.816480-Figure17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002848_tia.2003.816480-Figure17-1.png",
        "caption": "Fig. 17. Thermal FLUX3D of the tested motor.",
        "texts": [
            " The Joule losses are distributed in correlation with the motor stator resulting MMF. Matlab is chosen to define the motor topology and to determine the thermal impedance values. Simulink is chosen to determine the temperature gradients by solving the equivalent thermal scheme determined in Matlab. This scheme permits to consider only one tooth or several teeth (linear motor) connecting between themselves. C. 3-D Finite-Element Thermal Model FLUX3D software permits us to elaborate the thermal 3-D finite-element model, presented in Fig. 17. The five different steps are usual: geometry description; 3-D mesh; physical description; solving process; and, finally, results exploitation. The main problems come from the physical description for mainly three reasons. First, heterogeneous volumes like coils (which contain copper, mica and air in unknown geometrical configuration) have to be modeled with an equivalent homogenous material and, consequently, an equivalent conductivity must be computed. Second, air convection coefficients, particularly in the air gap or around the windings, are difficult to evaluate",
            " \u2022 The temperatures of the stator and the windings, issued from the lumped scheme as well as FLUX3D simulations with convection boundary conditions, present some discrepancies with the measurements. This can be explained by the fact that the convection factors are evaluated using empiric formula, so that there is an uncertainty on the computation of the thermal fluxes at the stator surface. \u2022 Concerning the rotor, some differences between the geometry modeled in the lumped scheme and the real one presented in Fig. 17 explain that the simulated temperature is higher than the experimental ones. Indeed, the nonactive parts of the motor are not considered in the lumped scheme so that the rotor convection coefficients are undervalued. This paper has presented two different models of iron losses. The first use a lumped scheme and the second a 2-D FEM simulation. There is a relatively good agreement between the two results, but they differ with experimental results. The authors think that the determination of the ac components of the rotor flux density is a key issue"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure13-1.png",
        "caption": "Fig. 13. Tangency of contacting surfaces.",
        "texts": [
            " The generation of R1 needs separate generation of both sides of thread surfaces because the plunging motion (see Eq. (8)) may require different parabola coefficients for each side. Multi-thread worm requires separate generation of each of the thread. The purpose of simulation of meshing and contact is determination of bearing contact and transmission errors of a misaligned face worm gear drive. The procedure of simulation is computerized and is performed by application of developed computer programs. The meshing of misaligned gear tooth surfaces is based on continuous tangency of contacting tooth surfaces (Fig. 13). Surfaces R1 and R2 of the worm and face worm gear and their normals are represented in a fixed coordinate system Sf . The continuous tangency of R1 and R2 is represented by equations: r \u00f01\u00de f u1; h1;/1\u00f0 \u00de r \u00f02\u00de f u2; h2;/2\u00f0 \u00de \u00bc 0; \u00f011\u00de n \u00f01\u00de f u1; h1;/1\u00f0 \u00de n \u00f02\u00de f u2; h2;/2\u00f0 \u00de \u00bc 0: \u00f012\u00de We have changed for the purpose of simplicity the designations of variables of Eqs. (11) and (12) in comparison with previous designations. The solution of Eqs. (11) and (12) is an iterative process and enables to determine the paths of contact on tooth surfaces of the face-gear and the worm and functions of transmission errors [8,9]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002352_1.2830138-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002352_1.2830138-Figure1-1.png",
        "caption": "Fig. 1 Bearing geometry and loading",
        "texts": [
            " The following limitations are placed on the model, (1) Friction is ignored, as are cage forces, lubrication, and thermal expansion. (2) Gyroscopic moments act along the rolling axis of the ball only, and therefore do not affect contact deformation. (3) Bearing rings are considered rigid, and the outer ring is assumed stationary. Inner ring deformation will be addressed below. Inner ring motion is expressed in terms of a five degree of freedom coordinate system located at the bearing centroid (Fig. 1). The displacement vector {S} describes the three linear and two rotational motions, [Sx 8y 6Z yx yy] T, while the loading is represented by {F} = [Fx F, Fz Mx My] T. In order to find ball load equilibrium, displacements and loads of the inner ring must be transformed to the ball coordinate system at the inner ring groove center. The groove center displacement is {u} = [ur uz 6}T, and the loading is {Q} = [QrQzM]T. {S} = [Jty] r{\u00ab} {\u00a5\u201e\\ = [R<nT{Q} W>] = COS (j) 0 0 sin (/> 0 0 0 \u2014zp sin (f> 1 rp sin 4> 0 - s i n 4> zp cos (j> \u2014rpcos 4> cos 4> (1) (2) For the ball load equilibrium, the geometry and loading of the ball and the raceways are analyzed (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure14-1.png",
        "caption": "Fig. 14. Rotors and chamber.",
        "texts": [
            " 13c, we can verify our drawings by calculating the equation of the line of action and then draw it out onto the screw rotor surface where it adheres. Our results then verify the accuracy of the rotor design. The performance and sealing properties will be discussed in the following sections. When area efficiency increases, the pump exhaust also increases. Therefore, one common method for estimating pump performance is to calculate the area efficiency by integration. That is to say, if the rotor tooth profile consists of multiple segment curves, each segment must be integrated and then summed to give the area of the rotor. As shown in Fig. 14, where A is the area of the rotor and Ac is the area of carryover, the formula for the area efficiency g is g \u00bc 2\u00f0pq2 1 A Ac\u00de pq2 1 \u00fe 4rq1 \u00f032\u00de The area of carryover in example 1 is shown in Fig. 14 and those of examples 2 and 3 are in Fig. 15. When we calculate the area efficiency, we must subtract the area of carryover. 1 parameter values for these three examples le 1 Pitch radius: r = 50 First segment is circular arc: q1 = 70, C1 = (0,0), a1 = 90 Second segment is circular arc: q2 = 30, C2 = (0,40), a2 = 36.87 Third segment is circular arc: q3 = 80, C3 = (30,0), a3 = 53.13 le 2 Pitch radius: r = 50, a = 12.87 First segment is circular arc: q1 = 70, C1 = (0,0), a1 = 77.13 Second segment is circular arc: q2 = 30, C2 = (0,40), a2 = 36"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.13-1.png",
        "caption": "Figure 6.13. Tactile microgripper. a. Comparision to a match (from [50], courtesy of Georg Greitmann); b. cross.section of sensor and actuator finger",
        "texts": [
            " With that size, they are often already too large for integration into ever smaller grippers and end-effectors. Thus, piezoresistive strain gages are more and more directly integrated into areas with high mechanical stress by ion implantation. This work was pioneered by M. Tortonese, who developed the first piezoresistive AFM cantilever at IBM Almaden Research Center [54]. One of the first examples of the transfer of this technology to microrobotics is the tactile, silicon-based microgripper developed at ETH Zurich [50] (Figure 6.13a). The gripper is made of two fingers \u2013 a bimorph actuator and a piezoresistive force sensor \u2013 which both serve as end-effectors at the same time (Figure 6.13b). The length of the fingers is 1.5 mm, their width between 80 \u03bcm and 240 \u03bcm, and their thickness is 12 \u03bcm. Objects with a size up to 400 \u03bcm can be 190 Stephan Fahlbusch gripped. Two different types of this gripper were developed. One version had four piezoresistors connected into a full Wheatstone bridge and one smaller version had only two piezoresistors. An analog PI controller was implemented to allow for force-controlled gripping of microparts. A similar force sensor was developed at the Mechanical Engineering Laboratory, Japan, in co-operation with Olympus [51]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.34-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.34-1.png",
        "caption": "Figure 4.34 Free-body diagram of the beam.",
        "texts": [
            " 68 Fundamentals of Biomechanics the positive 2 direction. Therefore: Ml = b P = (0.30)(120) = 36 N-m (+2) As illustrated in Figure 4.33c, to translate the force from B to A, place another pair of forces at A with equal magnitude and opposite directions. This time, the downward force at Band the upward force at A form a couple, and again, they can be replaced by a couple-moment (Figure 4.33d). The magnitude of this couple-moment is M2 = a P and it acts in the positive x direction. Therefore: M2 = a P = (0.20)(120) = 24 N-m (+x) Figure 4.34 shows the free-body diagram of the beam. P is the magnitude of the force applied at C which is translated to A, and Ml and M2 are the magnitudes of the couple-moments. RAx, RAy, and RAz are the scalar components of the reactive force at A, and MAx, MAy, and MAz are the scalar components of the reactive moment at A. Consider the translational equilibrium of the beam in the x direction: The translational equilibrium of the beam in the y direction re quires that: LFy=O: RAy = P = 120N (+y) For the translational equilibrium of the beam in the 2 direction: Therefore, there is only one non-zero component of the reactive force on the beam at A and it acts in the positive y direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002848_tia.2003.816480-Figure19-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002848_tia.2003.816480-Figure19-1.png",
        "caption": "Fig. 19. FLUX3D temperature color-shaded plots (K).",
        "texts": [
            " For the FLUX3D simulations, the temperature on the outside stator yoke is imposed, based on measurements. This implies a correction of the convection and conductivity in the lumped model, which is not applied right now. The convection factor in the air gap is imposed for FLUX3D. Similar coefficient is introduced for the lumped model. The lumped thermal scheme gives the temperature gradient distribution of Fig. 18. FEM simulations permit to obtain the color shaded plots of temperature shown in Fig. 19. Fig. 20 shows the infrared camera image of the motor at rated point and for an ambient temperature of 24 C. Fig. 21 summarize the key temperature gradients and Fig. 22 the ratio of different gradients versus measurements. The following comments can be made. \u2022 FLUX3D simulation with Dirichlet boundary conditions gives very satisfying results in the stator and in the winding. It is due to the fact that the real temperature is imposed at the external stator surface. \u2022 The temperatures of the stator and the windings, issued from the lumped scheme as well as FLUX3D simulations with convection boundary conditions, present some discrepancies with the measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002442_02783640122068218-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002442_02783640122068218-Figure1-1.png",
        "caption": "Fig. 1. Three-degree-of-freedom walking mechanism on a sagittal plane.",
        "texts": [
            " In Section 2, we explain a biped mechanism model and the self-excitation of swing motion of a two-DOF swing leg. In Section 3, the analytical model of a three-DOF biped mechanism and the analytical method are discussed. In Section 4, we show calculated results of stable biped locomotion on level ground and describe various characteristics of the self-excited walking obtained from the simulation study. Then, in Section 5, we explain the manufactured biped robot and experimental results for verification of the theoretical results. Figure 1 shows a biped mechanism to be treated in this study. Here we focus only on the biped locomotion in the sagittal plane. The biped mechanism does not have an upper body and consists of only two legs that are connected in a series at the hip joint through a motor. Each leg has a thigh and a shank connected at a passive knee joint that has a knee stopper. By the knee stopper, an angle of the knee rotation is restricted like the human knee. The legs have no feet, and the tip of the shank has a small roundness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003191_tia.1986.4504785-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003191_tia.1986.4504785-Figure6-1.png",
        "caption": "Fig. 6. Orientation of rotor two-phase axes with respect to magnetic axis of phase as.",
        "texts": [
            " However, from (9), this expression reduces to X3ms-Xlmss=3Lmls sin ds (14) The flux which links the two coils due to rotor current components is computed in a similar manner. However, in this case the rotation of the rotor with respect to the stationary coils requires a change in variables. For this purpose it is conventional to replace the actual currents in the rotor bars by equivalent two-phase currents which produce the same fundamental MMF distribution. The location of the magnetic axes of these two-phase currents with respect to phase as is shown in Fig. 6. The flux which links the n, and n3 coils due to currents in the rotor is [5] Xir=Lm1,iq rr COS (Or+E)-Lm I r id, sin (Or+ ) (15) X3r=LmIriqr4 COS (Or-E)-Lmlridr sin (Or-e) (16) where Lmir represents the maximum mutual coupling between one of the two sensing coils and one of the two equivalent d-q currents. Upon subtracting (16) from (15) the following result can be obtained X3r-Xlr= -2Lmir sin C(i r sin Or+ idrr COS Or). (17)mr qr dr However, from the d-q equations of transformation, it is possible to relate the rotor d-axis current in the rotor reference frame to the stator stationary reference frame by the transformation equation iIs= (i r sin Or+ i dr COS Or)",
            " Machines wound with \"fractional-slot\" windings, that is, windings with unequal numbers of coils per group, can also be utilized with suitable selection of coils used for flux sensing. It does not appear that the technique is practical for concentric coil configurations since the voltages induced in each coil of the group are in time phase. In general, the principle in applying the flux-sensing scheme is to select the outer two coils of one phase belt as the flux-sensing coils such that the angle e in Fig. 6 is as large as possible. Implementation of the flux signal and calculation of the electromagnetic torque, according to the flow diagram of Fig. 7, in analog circuitry is straightforward. In practice, it has not been found necessary to filter or further manipulate the air-gap voltage signal in any way. Noise has not been observed to be a problem. All of the analog components needed to compute airgap flux, and electromagnetic torque can be readily installed on a small rack-mounted printed circuit card"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002591_978-94-017-0657-5_3-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002591_978-94-017-0657-5_3-Figure2-1.png",
        "caption": "Figure 2. Plan view of a serial manipulator made up of three compliant joints.",
        "texts": [
            " Since the revolute joints are free to rotate, external force can only be transmitted in a direction parallel to the common joint axis of each limb and this force will produce a moment about each revolute joint. Assume that all links are rigid, and the major source of compliance comes from the flexibility of the revolute joints. The deflection between two members of a revolute joint can be modeled as an infinitesimal rotation about an axis perpendicular to the axis of revolution. We call such an axis of deflection a virtual axis of compliance. In this regard, we may consider each limb together with the moving platform as a serial manipulator having three virtual axes of compliances as shown in Fig. 2. From the result of Kim and Tsai (2002), a compliance mapping can be written as 8p=C f (4) where 8p = [8Px,8py,8pJ T , and C is a diagonal compliance matrix whose diagonal elements are given by (5) C 2 2 2 ii = CilPn + C;2P;2 + C;3PiJ where cij is an angular compliance constant, and Pij = Ilpijll denotes the distance between a virtual axis of compliance and the end-effector, P. Multiplying Eq. (5) by C- I , we obtain the stiffness mapping as f =K Op (6) where K = C- I is called the stiffness matrix of the manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002876_j.engappai.2004.12.004-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002876_j.engappai.2004.12.004-Figure1-1.png",
        "caption": "Fig. 1. Definition of body-fixed coordinate system.",
        "texts": [
            " (1) and (2) a vehicle\u2019s six degrees of freedom rigid-body equations can be expressed as: M_m \u00fe C\u00f0m\u00dem \u00feD\u00f0m\u00dem \u00fe g\u00f0g\u00de \u00bc s; (3) _g \u00bc J\u00f0g\u00dem; where g is the position and orientation of the vehicle in earth fixed frame, m the linear and angular velocity of the vehicle in body fixed frame, M the inertia matrix, C\u00f0m\u00de the matrix consisting of Coriolis and centripetal terms, D\u00f0m\u00de the matrix consisting of damping or drag terms, g\u00f0g\u00de the vector of forces and moments due to gravitation and s the vector of control inputs. The matrix J\u00f0g\u00de converts velocity in a body fixed frame, m; to velocity in an earth fixed frame, _g: For the 1In this derivation bold face characters will be used for vectors. body-fixed velocity, m \u00bc \u00bduvwpqr T; the coordinate system is chosen as in Fig. 1 with the surge u pointing towards the bow of the craft, the sway v to starboard, and the heave w pointing down. The rotations around the surge, sway and heave axes, respectively, roll p, pitch q and yaw r, obey the rules for a right-hand-side coordinate system. The Earth-fixed system has elements, respectively, pointing north, east and towards the centre of the earth and again three rotations about these axes. A detailed derivation of these non-linear equations of motion can be found in Fossen (1994)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.10-1.png",
        "caption": "Figure 6.10. Gripping force sensor based on strain gages. a. Actuator integrated into the gripper; b. strain gages glued on the actuators\u2019 housings (from [42], courtesy of Shaker Verlag).",
        "texts": [
            " Fiber optical sensors for process control in microsystem assembly were developed by [41]. Two different solutions for integrated sensors were realized, and the usability of these sensors to measure gripping forces has been shown in principle (Figure 6.9). Using a grayscale picture, the presence of a gripped object and information about an increase or decrease of the gripping force could be gained. However, quantitative measurements were not possible. 186 Stephan Fahlbusch Hence, a gripping force sensor based on strain gages was developed for the same gripper by [42], Figure 6.10a. To enable a simple and fast exchange of the grippers\u2019 end-effectors without additional electrical connections, two strain gages have been glued on each of the two actuators\u2019 housings, Figure 6.10b. If an object is gripped, the strain caused by the deformation of the actuators\u2019 housing can be measured. Taking into account the change of the stiffness of this system, the gripping force can be calculated. This method has the drawback of low accuracy. Several different microgrippers for the assembly of microparts were developed by [33] (Figure 6.11a). The grippers were manufactured using plasma-enhanced dry etching of silicon and deep UV lithography of SU-8. The joints of the grippers were designed as flexure hinges; they are actuated by shape memory alloys"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003431_ichr.2007.4813885-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003431_ichr.2007.4813885-Figure7-1.png",
        "caption": "Fig. 7. The compass model of single mass. \u03b1 is an angle between two support legs. \u03b21 and \u03b22 are an angle between each support leg and ground. L1 and L2 are each length of support leg.",
        "texts": [
            " An analytical solution of z is obtained by Eq. (4). Here the Ukemi motion can be generated online by using the analytical solution \u23a7\u23aa\u23a8 \u23aa\u23a9 x(t) = x(0) cosh \u03c9t + x\u0307(0) \u03c9 sinh\u03c9t, z(t) = kx(0) cosh \u03c9t + k x\u0307(0) \u03c9 sinh\u03c9t + zc. (5) x(0), x\u0307(0) are the position and the velocity when the fall is detected. \u03c9 is the angular frequency of the motion equation. To balance the humanoid robot\u2019s body after the Ukemi motion the position of the hands must be determined. So, the compass model of single mass shows humanoid robots like Fig. 7. The collision of humanoid robots and ground is assumed to be a completely inelastic collision, and the expression of the momentum is given as follows: \u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 M (v+ x \u2212 v\u2212x ) = Px, M (v+ z \u2212 v\u2212z ) = Pz, IG (\u03c9+ \u2212 \u03c9\u2212) = \u2212L2Pz cos \u03b22 \u2212 L2Px sin\u03b22. (6) (v\u2212x , v\u2212 z , \u03c9\u2212), (v+ x , v+ z , \u03c9+) are the velocity in the horizontal direction of center of gravity, the velocity in perpendicular direction, and the angular velocity before and after the robot collides; Px, Pz are the horizontal impulse, and IG is the inertia around center of gravity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002327_s0094-114x(97)00056-6-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002327_s0094-114x(97)00056-6-Figure1-1.png",
        "caption": "Fig. 1. Typical rotor con\u00aeguration and coordinate system.",
        "texts": [
            " The in\u00afuence of coupled bending and torsion motions in the presence of a gear box and the e ect of axial torque on the bending sti ness are ignored while determining the response under torsional excitation. In this paper, it is shown that the coupled bending torsion motion due to gears has signi\u00aecant in\u00afuence on the rotor dynamics of turbo\u00b1alternator systems and induce large amplitude whirls in bending due to torsional excitation, as under short circuit conditions. The e ect of axial torque is shown to have no signi\u00aecant in\u00afuence. 2. FINITE ELEMENT FORMULATION A rigid disk in Y\u00b1Z plane is shown in Fig. 1. The displacements V, W and the corresponding slopes B, G for lateral motion and the spin speed O with torsional velocity a\u00c7 are as denoted. The kinetic energy of the disk for lateral motion is given by [8] Td 1 2 md _Vd 2 _Wd 2 1 2 IdD _Bd 2 _Gd 2 \u00ff 1 2 IdP O _ad Bd _Gd \u00ff Gd _Bd 1 2 IdP O _ad 2 1 Following Lagrangian approach, we can obtain Md f qdg O Gd f _qdg fFd s g 2 where Md md 0 md 0 0 IdD 0 0 0 IdD 0 0 0 0 Idp 26666664 37777775 sym Gd 0 0 0 0 0 0 0 0 \u00ffIdp 0 0 0 0 0 0 26666664 37777775 skew sym and fqdgT fVdWdBdGdadg Figure 2 shows a 2 noded shaft element with 10 degrees of freedom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003474_1.383649-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003474_1.383649-Figure2-1.png",
        "caption": "FIG. 2. Base plane zones of contact with nonfluctuating total length of lines of contact. Zone of contact in upper sketch satisfies (L/A)= 2. Zone of contact in lower sketch satisfies (FL/A A): 3.",
        "texts": [
            " 1, by multiplying the total mesh loading W o by the Fourier-series coefficients of 1/Kr(x). According to Eqs. (22) and (23), for M = 1 this expression is where \u2022r is given by Eqs. (24) and (25). (26) 1. D/scuss/on The spherical Bessel functions in Eq. (26) depend on two dimensionless parameters, L/A and FL/AA, which will appear repeatedly throughout the remainder of the paper. The parameter L/A is the profile or transverse contact ratio whereas FL/AA is the axialcontact ratio. \u2022.\u00f8 According to Fig. 2 of Ref. 1, L/A is the length L of the path of contact divided by the tooth spacing A, both measured on a line defined by the intersection of a plane normal to the gear axes (transverse plane s,o ) and the plane of contact. Furthermore, according to Eq. (D5) of Ref. 1, we have A = L/tan\u00bd,. If we denote by A, the tooth spacing in the axial direction measured in the plane of contact (axial pitch 6) then from Fig. 2 of Ref. I we see that tan\u00bd, =A/A,,. (27) 1760 J. Acoust. Soc. Am., Vol. 66, No. 6, December 1979 William D. Mark' Vibratory excitation ofgear systems. II 1760 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 137.189.170.231 On: Tue, 23 Dec 2014 12:59:41 which is the ratio of the face width to the axial pitch, i.e., the axial contact ratio (Ref. 6, p. 211). For helical gears, the axial contact ratio can be interpreted as the average number of teeth in contact across their full depth D, as illustrated in the upper right-hand corner of Fig",
            " (32) and (33), we see that if L/ix is an integer, we have aw,=0 for n= 1,2,3,... in this case also; moreover, since (n\u2022rFL\u2022 sin(n?rFL/Aix) (34) Jo \\ AIX / = n\u2022rFL /AiX ' it follows that if FL/AiX is an integer, we also have aw,=0 for the tooth-meshing harmonics n= 1, 2,3, .... Thus, in the helical gear case when Krc(y, z) is assumed to be a constant, we require that either L/iX or FL/AiX be an integer for the vanishing of the tooth deformation contribution to the tooth-meshing harmonics. These integral contact ratio criteria can be-understood with the aid of Fig. 2, which illustrates the zone of con- 1761 J. Acoust. Soc. Am., Vol. 66, ,No. 6, December 1979 William D. Mark: Vibratory excitation f gear systems. II 1761 Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 137.189.170.231 On: Tue, 23 Dec 2014 12:59:41 tact, as shown in Fig. 2 of Ref. 1, but for cases of integral transverse and axial contact ratios (L/z\u2022)--2 and (FL/AA)=3. From Fig. 2, we see that if either contact ratio is an integer, there is no fluctuation in the total length of lines of contact within the zone of contact as the gears rotate. Consequently, if the local tooth-pair stiffness per unit length of line of contact K rc(y, z) is a constant, then when either the transverse or the axial contact ratio is a constant, there is no variation in the total stiffness of the mesh as the gears rotate. Hence, functions j,(x) have the asymptotic form j,,(x)=x cos[x- (m + (36) It follows from Eqs",
            "231 On: Tue, 23 Dec 2014 12:59:41 Wo/K v the transverse contact ratio L/A characterizes to a first approximation the spur gear design parameters insofar as the overall behavior of the envelope of the static transmission error spectrum is concerned. For example, from Eq. (137), we can see that doubling L/\u2022x while holding Wo/\u2022 \u2022 fixed will tend to a first a\u2022proximation to decrease the level of any specified toothmeshing harmonic component p =n/N (') or band of rotational harmonies by about 6 dBf 'x From Eq. (C8) of Ref. 1, we have L =Dcscqb. Furthermore, from Fig. 2 of Ref. I we can see that N (')A =27rRlo' ), where R(o') is the base cylinder radius of gear (.). Hence, we can express th,e transverse contact ratio in terms of fundamental design parameters by L/A =DN (') csc\u2022b/27rRg \u00b8 , (1 48) where D is the true active tooth depth illustrated in Fig. 4 of Ref. 1, \u2022b is the pressure angle, and N ( '\u2022 is the number of teeth on gear (-). In particular, from Eq. (148) and the above comments, we see for spur gears that doubling the number of teeth while holding D, R(o' ), qb, and Wo/K \u2022 constant would tend to a first approximation to decrease the level of any specified toothmeshing harmonic component or band of rotational harmonics by about 6 dBf '\u2022 This result is in agreement with the general belief that fine-pitch gears are quieter than those with coarse pitch",
            " (132), we can see that doubling either FL/AA or L/A while holding Wo/\u2022 v fixed will tend to a first approximation to decrease the level of any specified tooth-meshing harmonic component p =n/N (') or band of rotational harmonics by about 6 dB. \u2022'x From Eqs. (A4) and (C4) of Ref. 1, we have (L/A) =tan\u2022b =cos\u2022b tan,p, where \u2022bb and \u2022b are the base cylinder and pitch cylinder helix angles respectively, and qb is the pressure angie. Hence, using N(')A =27rRlo') and the above expression for L/A, we may express the transverse contact ratio in terms of fundamental design paramete rs by FL _ FN (') cos\u2022b tan\u2022 (149) AA 2 \u2022rR\u2022' ) ' where F is the face width illustrated in Fig. 2 of Ref. 1. Thus, from Eqs. (148) and (149) and the above comments, we see that doubling the number of teeth while holding F, D, qb, \u2022b, R(o'), and Wo/tT \u2022 constant would tend to a first approximation to decrease the level of any specified tooth-meshing harmonic component or band of rotational harmonics by about 12 dB in the case of helical gearsf 'x Doubling the face width while holding the other parameters constant would tend to dectease specific harmonic components or band levels by about 6 dB"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003711_ac070325z-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003711_ac070325z-Figure1-1.png",
        "caption": "Figure 1. Schematic drawing of the structure of the microplate differential calorimeter. A full microplate consists of 48 combinations of reference wells and sample wells.",
        "texts": [
            " In analogy with the implementation of enzymatic assays in microplate array format (96, 384, 1536 wells) and an optical detection system,12,13 we report on an innovative concept where the microplate array format is used for the calorimetric detection of low molecular analytes. The calorimeter is based on microplate differential calorimetry (MiDiCal) technology14 that applies an array of 96 wells (with a maximal volume of 20 \u00b5L) allowing the simultaneous quantification of 48 samples. The transduction principle is based on the differential measurement of the heat generated between two wells, located at the cold and the hot junctions of a thermopile (Figure 1). In one well the reaction heat of the biochemical reaction between substrate and enzyme is monitored and compared to that of the reference well where no specific biochemical reaction takes place. This will suppress the thermal noise associated with the dilution of the sample in the buffer. Since total assay volume in the microplate differential calorimeter is low there is no considerable need for immobilization of enzymes to reduce the analysis cost. Ascorbic acid is chosen as model component for the calorimetric detection because of its importance in the human diet"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure6-1.png",
        "caption": "Fig. 6. Design region of the parameter.",
        "texts": [
            " (3) by coordinate transformation from coordinate system S1 to coordinate system S2 which yields r \u00f02\u00de 2 as follows: r \u00f02\u00de 2 \u00bcM21r \u00f01\u00de 2 \u00bc R cos\u00f0a 2/ 2u\u00de 2r\u00bdcos /\u00fe cos\u00f02/\u00fe u\u00de R sin\u00f0a 2/ 2u\u00de \u00fe 2r\u00bdsin /\u00fe sin\u00f02/\u00fe u\u00de 1 2 64 3 75 \u00f04\u00de where the superscript of r \u00f02\u00de 2 indicates the segment 2 of the claw-shape in Fig. 3. Subsequently, the equation of meshing can be represented as follows: f \u00bc or \u00f02\u00de 2 ou k ! or \u00f02\u00de 2 o/ \u00bc 0 \u00f05\u00de where k is the unit vector in the z direction. Substituting Eq. (4) into Eq. (5) yields the following: f \u00bc R\u00bdsin\u00f0a / 2u\u00de \u00fe sin\u00f0a u\u00de \u00fe r sin\u00f0/\u00fe u\u00de \u00bc 0 \u00f06\u00de Here, we must consider Eqs. (4) and (6), and then the conjugate curve will be generated. Finally, the complete claw-shape can be yielded. As shown in Fig. 6, the mathematical model of the circular arc can be represented in the coordinate system S1 as follows: ri;1 \u00bc cxi \u00fe qi cos h cyi \u00fe qi sin h 1 2 64 3 75; hi 1 < h < hi; i \u00bc 1\u20133 \u00f07\u00de where h0 = 0 and Ci = (cxi,cyi) are the centre of the three circular arcs represented in coordinate system S1. Additionally, the conjugate segment can be obtained by coordinate transformation as follows: ri;2 \u00bcM21ri;1 \u00f08\u00de Substituting Eq. (7) into Eq. (8) to yield the following: ri;2 \u00bc qi cos\u00f0h 2/\u00de cxi cos 2/\u00fe cyi sin 2/ 2r cos / qi sin\u00f0h 2/\u00de cxi sin 2/\u00fe cyi cos 2/\u00fe 2r sin / 1 2 64 3 75 \u00f09\u00de The conjugate segment must also satisfy the equation of meshing as following: X xi;1 Nxi;1 \u00bc Y yi;1 Nyi;1 ; i \u00bc 1\u20133 \u00f010\u00de where (X,Y) are the Cartesian coordinates of the instantaneous centers: X \u00bc r cos / Y \u00bc r sin / \u00f011\u00de and (Nxi,1,Nyi,1) indicates the normal vector of the instant contact point on the transverse tooth profile of rotor 1: Ni;1 \u00bc oyi;1 oh i oxi;1 oh j \u00bc Nxi;1i\u00fe N yi;1j \u00bc qi cos hi\u00fe qi sin hj; i \u00bc 1\u20133 \u00f012\u00de Substituting Eqs. (7), (11) and (12) into Eq. (10) yields the following equation of meshing: f \u00bc cyi cos h cxi sin h\u00fe r sin\u00f0h /\u00de \u00bc 0; i \u00bc 1\u20133 \u00f013\u00de Solving Eq. (13) and substituting the solution into Eq. (9) then gets the conjugate curve. As shown in Fig. 6, the rotor profile consists of three circular arcs whose centers and radii are C1, C2 and C3 and q1, q2 and q3, respectively. r is the pitch radius. From Wang, Fong and Fang [1], we know that the conditions of no carryover can be shown as follows: q2 P q1 r q2 P q3 r \u00f014\u00de r P ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cx2 2 \u00fe cy2 2 q r P ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cx2 3 \u00fe cy2 3 q \u00f015\u00de Therefore, to make the circular arc join smoothly to point Q, we use the following trigonometry method: \u00f0q3 q2\u00de 2 \u00bc \u00f0q1 q2\u00de 2 \u00fe \u00f0q3 r\u00de2 2\u00f0q1 q2\u00de\u00f0q3 r\u00de cos h1 \u00f016\u00de in which q1, q2, r, h1 are known"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003152_j.ijmachtools.2004.11.006-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003152_j.ijmachtools.2004.11.006-Figure8-1.png",
        "caption": "Fig. 8. Tool motion along a pre-defined trajectory in five-axis and corresponding swept profiles: (a\u2013c) APT-like cutter; (d\u2013f) fillet-end mill; (g\u2013i) ball-end mill; (j\u2013l) flat-end mill. (a) Cutter geometric definition; (b) cutter motion track and swept profiles (red lines); (c) generated swept volume.",
        "texts": [
            " Moreover, for the same parameter configurations, the distribution of the parameter vT varies by angular velocity u. In contrast with the parametric description, Fig. 7 shows 3D closed swept profiles on the boundary surfaces of a generalized cutter. On a segment of the cutter configurations, the swept profiles are varied according to the different orientation angles and machine motions. One can find the different distribution of profile curves on the boundary surfaces. The difference becomes larger when the cutter changes its tool orientations by larger angles during the motion configurations. Fig. 8 shows the generated swept profiles of different end mill cutters by implementing five-axis motions along a predefined trajectory. The control points of these cutters are defined to move along the Y-axis with a constant cutting direction and cutting velocity. The commonly used end mill 2 T ;2 CD2 T ;2 OF2 T ;2), the profile exists on the lower conical surface, (b) APTn the toroidal surface and upper conical surface, (c) fillet-end mill (swept cutters, such as fillet-end mill, ball-end mill and flat-end mill have been modeled in the figures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002321_jsvi.2000.2950-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002321_jsvi.2000.2950-Figure2-1.png",
        "caption": "Figure 2. Drive unit.",
        "texts": [
            " One test linear bearing consists of one pro\"le rail and one carriage with recirculating balls. Preloads of test linear bearings are light or medium. The preloading for the test linear bearings was made by inserting balls slightly larger than the ball groove space between the pro\"le rail and the carriage. Table 1 shows the test linear bearing speci\"cation. The test linear bearings in this study and those of a previous sound study [10] are identical. All test linear bearings were lubricated with mineral oil (ISO VG56). Figure 2 shows the drive unit which was developed for sound and vibration measurement of linear motion rolling bearings [11]. The drive unit consists of a motor, a coupling, support bearings, a sliding screw, sliding guides, a pusher, and a concrete bed. The pro\"le rail of a test linear bearing is \"xed on the concrete bed by bolts. The carriage of the test linear bearing is driven through a coupling, support bearings, a sliding screw, sliding guides and a pusher from a motor. Therefore, when the motor rotates at a constant speed, the carriage of the test linear bearing can be driven at a constant linear velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure7.13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure7.13-1.png",
        "caption": "Figure 7.13. Mechanical drawing of the nanohandling robot station",
        "texts": [
            " 218 Volkmar Eichhorn and Christian Stolle Following the generic concept of the automated microrobot-based nanohandling station (AMNS) introduced in Chapter 1, a robot station was developed that can be integrated into an SEM and can use different end-effectors for the non-destructive characterization and reliable three-dimensional handling of CNTs. Either the tip of a piezoresistive AFM probe for the mechanical characterization of CNTs or an electrothermal nanogripper [43] for CNT handling is applied. A mechanical drawing of the experimental setup of the nanohandling robot station is shown in Figure 7.13. The setup is mounted on a base plate and contains two different manipulators. There is a three-axes micromanipulator MM3A [56] that is equipped with an end-effector holder and is used for the coarse positioning between end-effector and CNT sample. The micromanipulator offers a theoretically possible resolution of 5 nm for the two rotational axes and 0.25 nm for the linear axis. A nanopositioning piezo stage with three degrees of freedom carries the CNT sample. The resolution of the nanopositioning stage [57] is limited by the 16-bit D/A converter of the control module and amounts to 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003138_s1474-6670(17)30474-3-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003138_s1474-6670(17)30474-3-Figure1-1.png",
        "caption": "Fig. 1. The PVTOL aircraft(front view)",
        "texts": [
            " Section 3 gives the control of the vertical displacement while the pitch and horizontal displacement control are presented in Sedion 4. Real-Time experimental results are given in section 5. The conclusions are finally given in section 6. The PVTOL system equations are given by i: = - sin( B)t!) + c cost B)U2 Y = cos(B)u,) +csin(B)u,2- 1 jj = Uz (1 ) where x is the horizontal displacement, y is the vertical displacement and B is the angle the PV TOL makes with the horizontal line. Ul is the collective input and 'U2 is the couple as shown in figure 1. The parameter c is a small coeffi cient which characterizes the coupling between the rolling moment and the lateral acceleration of the aircraft. The term -1 is the normalized gravitational acceleration. Let us use the following change of coordinates proposed in (Olfati-Saber, 1999). x = x - csin(B) f} = y+dcos(B) -1) (2) The system dynamics considering these new coor dinates becomes :1: = - sin(B)u) y = cOS(B)Ul - 1 jj = U,2 where \u00b7ftl = Ul - cFP. DISPLACEMENT (3) The vertical displacement f} will be controlled by forcing the altitude to behave as a linear system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure4.6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure4.6-1.png",
        "caption": "Fig. 4.6 Element of thin-walled tube",
        "texts": [
            " Thus, the thin-walled cross section is described by the coordinates y((), z(() of the centerline, and thickness J(() ofthe profile. for the shear stresses, and u=u(x,() (4.29) (4.30) for the displacements, constant in the 'f/ direction. We note that assumptions (4.29) coincide with the assumptions (3.37) for the shear stresses due to shear forces (Sec tion 3.2). Defining now the shear flow t( () as J 8/2 t(() = O\"xC, d'f/, (4.31) -8/2 we obtain with (4.29h t(() = T(()J((). (4.32) From the equilibrium (in axial direction) of a small element cut from the thin-walled tube (Fig. 4.6), we see that t = T( ()8( () = const. , (4.33) provided there are no axial stresses (J xx' Thus, the largest shear stress occurs where the thickness is smallest, and vice versa. Of course, if the thickness is uniform, then the shear stress T is constant around the tube. In order to relate the shear flow to the torque M T acting on the tube, consider an element of length d( in the cross section: The total shear force acting on the element is t de, and the moment of this force about any point 0 is dMT = a(()td(, (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure15-1.png",
        "caption": "Fig. 15. Illustration of: (a) the volume of the 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 analysis using CAD computer programs in an interactive way is time expensive, requires skilled users for application of computer programs and has to be done for every case of development of gear geometry, position of meshing and installment desired. The developed approach is free of all these disadvantages and is summarized as follows: Step 1: It is possible to represent analytically the volume of the tooth using the equations of the surfaces and the portions of the corresponding rim. Fig. 15(a) shows the designed body for one tooth model of the face-gear. Step 2: Six surfaces (Fig. 15(b)) determined analytically divide the volume in six parts and control the discretization of these tooth subvolumes into finite elements. Step 3: Analytical determination of node coordinates is performed automatically by choosing the desired number of elements in longitudinal and profile directions (Fig. 15(c)). All the nodes of the finite element analysis are determined analytically and the points of the intermediate surfaces of the tooth belong to the real gear tooth surfaces. Step 4: Discretization of the model by finite elements (using the nodes determined previously) is accomplished as shown in Fig. 15(d). Step 5: The boundary conditions for the face-gear and the worm are set automatically under the following conditions: (i) Nodes on the bottom of the worm rim are considered as fixed (Fig. 16(a)). (ii) Nodes on the two sides and the bottom part of the face-gear rim form a rigid surface (Fig. 16(b)). Such rigid surface is a three-dimensional structure that may perform translational and rotation but cannot be deformed. (iii) Considering the face-gear rim rigid surfaces the variables of motions of the face-gear (its translation and rotation) are associated with a single point M located on the axis of the face-gear chosen as the reference point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003214_cdc.2005.1583480-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003214_cdc.2005.1583480-Figure1-1.png",
        "caption": "Fig. 1. Tiltrotor-based mechanism",
        "texts": [
            " Moreover, the involved equations of motion are highly coupled and nonlinear. Gary Gress [4] discovered that the tiltrotor-based mechanism can provide hover stability of a small UAV by using the gyroscopic nature of two tilting rotors. In this paper, we propose an alternative configuration/system, called BIROTAN1 (BI-ROtors with tilting propellers in TANdem) where the center of mass of the UAV is located below the tilting axes, resulting in a significant pitching moment. We have constructed two prototypes of a birotor rotorcraft as shown in Figure 1(b), inspired by G. Gress\u2019s mechanism. The experimental results showed that this aerodynamical configuration is very promising. This configuration is adapted for the miniaturization of the UAV, and it results in a simple 1This work was supported by the ONERA (French aeronautics and space research centre), the DGA (French Arms Procurement Agency of the Ministry of Defence) and the French Picardie Region Council. mechanical realization. Unlike the full-scale tiltrotors, the propellers can tilt in two directions providing also stability and control in hover",
            " However, one can expect some robustness properties of the control law in view of the study developed in [6]. The analysis presented here has shown that hover control of a two-propeller VTOL aircraft is possible using two tilting rotors. The pitch stability is increased by combining the opposed lateral tilting with the longitudinal tilting of the two rotors. The resulting oblique tilting appears to be effective and practical. Indeed, the experimental results obtained on prototypes constructed by our team (see Figure 1(b)) are very promising. In this paper, we have also developed a 6-DOF model of the birotor aircraft and synthesized a nonlinear controller which leads to a satisfactory control. To the authors knowledge, no other control law has been derived for a small tiltrotor-based rotorcraft model. [1] G. K. Yamauchi, A. J. Wadcock, and M. R. Derby, \u201cMeasured aerodynamic interaction of two tiltrotors,\u201d in AHS 59th Annual Forum, Phoenix, Arizona, May 2003. [2] D. Wyatt, \u201cEagle eye pocket guide,\u201d Bell Helicopter Textron Inc, Printed in USA, June 2004"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure4-1.png",
        "caption": "Fig. 4. Schematic illustration of the head-cutter, the cradle c, and the face worm gear.",
        "texts": [
            " The determination of conjugation of tooth surfaces of proposed gear drive required the application of theory of enveloping that is the subject of differential geometry and theory of gearing represented in the works by Zalgaller [17], Zalgaller and Litvin [18], Favard [2], Korn and Korn [6], Litvin [8,9], and other works. The generation is performed by a tilted head-cutter with straight line profiles of blades (Fig. 3). The tilt of the head-cutter allows to avoid interference of the head-cutter with teeth that neighbor to the space being generated. Fig. 4 illustrates schematically the generation of the face-gear. The tool is mounted at the cradle c of the generating machine (Fig. 4) and performs rotation about the tool axis. The face-gear R2 and the cradle c are held at rest and the tooth surface of the face-gear is generated as the copy of the tool surface. Indexing of face-gear has to be provided for generation of each space of the gear. Blades of the gear head-cutter are shown in Fig. 5(a). The angles ag of blade profile are of different magnitude for the convex and concave sides of the space of the face worm gear. Circular arc profiles of the blade fillet are provided for the generation of the fillet of the gear",
            " (iii) Determination of circle C of surface R 2 that passes through point P and two other points of R 2. The radius of circle C is the radius of the head-cutter to be used for generation of face-gear tooth surface of new design. (iv) Determination of profile of blade of head-cutter considering the cross-section of R 2 at pitch point P. (v) Derivation of surface of head-cutter applied for generation of surface R2 of new design. (vi) Determination of installment of the head-cutter on the cradle c (Fig. 4). (vii) Determination of surface R2 of the new design as the copy of the gear head-cutter surface. The described procedure is applied for derivation of both tooth sides. 2 of existing design Surface R 2 is determined in coordinate system S2 rigidly connected to the face-gear as follows [10]: r 2 \u00bc r 2 uh; hh;wh\u00f0 \u00de; \u00f02\u00de or 2 ouh or 2 ohh or 2 owh \u00bc f uh; hh;wh\u00f0 \u00de \u00bc 0: \u00f03\u00de Here Eq. (2) represent the family of hob surfaces in S2; Eq. (3) is the equation of meshing; uh; hh\u00f0 \u00de are the parameters of hob surface; wh is the generalized parameter of motion in the process of generation of surface R 2 of existing design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003024_i2003-00334-5-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003024_i2003-00334-5-Figure2-1.png",
        "caption": "Fig. 2 \u2013 The buckled shapes studied in this paper can be created by cutting out this circular strip, of radius R, length L = 2\u03c0R, and width w. Rotate the two ends around r\u03021 \u00d7 r\u03022 so that the two gray arrows point 180\u25e6 away from one another, and place them over the lower line so that the arrows coincide. The paper will assume the undulating shape from fig. 3 with \u221a g0 = 2. Moving the ends to other horizontal distances \u03bb along the line, or choosing other points along the strip for arclength L, allows one to explore a two-parameter family of periodic strip solutions.",
        "texts": [
            " 1, but it does allow one to calculate a basic undulating shape that appears as an ingredient of the buckling cascade. To form a rough correspondence between the two problems, choose L/\u03bb \u2261 \u221a g0 to be the amount the membrane in fig. 1(c) has been stretched at the left edge. If a strip of length L is given metric (5) and no constraint is applied, then the minimum energy configuration is easy to find. The material can relax completely by forming a ring of radius R, which curls round and round in a circle. Thus one can obtain some intuition about the problem by cutting out the paper figure in fig. 2 and pulling the ends apart. Let r\u03021(\u03b8) and r\u03022(\u03b8) be two unit vectors attached to the circular strip, where r\u03021 points around the circumference, and r\u03022 points along the radius. Then the lowest-energy deformations of the paper strip are described by two functions \u03c8\u0307(\u03b8) and \u03c6\u0307(\u03b8) that describe the rate of rotation around axes r\u03021 (twisting) and r\u03022 (bending), respectively. The directions of the unit vectors are determined by \u2202r\u03021 \u2202\u03b8 = \u03c6\u0307(\u03b8) r\u03023 + r\u03022, (7a) \u2202r\u03022 \u2202\u03b8 = \u03c8\u0307(\u03b8) r\u03023 \u2212 r\u03021, (7b) r\u03023 = r\u03021 \u00d7 r\u03022",
            " The solutions of eqs. (13) are indexed by four constants: the initial values \u03c6\u0307(0) and h(0), the normalized strip length L/R, and p. The initial value \u03c8\u0307(0) vanishes because \u03c8\u0307(\u03b8) is odd. By varying \u03c6\u0307(0) and p, it is possible to ensure that r\u03021(L/R) = x\u0302 and r\u03022(L/R) = y\u0302. The remaining constant h(0) can then be employed to vary the wavelength \u03bb. Thus the solutions can be indexed by \u03bb and L, which can be varied independently within certain ranges. To observe these solutions, one can cut out the strip in fig. 2, pick various strip lengths L, and force the strip at these points to lie at distance \u03bb from the origin. Closed-form solution. \u2013 In a special case, eqs. (7) and (13) have a closed-form solution [7]. Set C1 = C2, and take \u03c6\u0307 = \u03c9 cos \u03b1\u03b8, \u03c8\u0307 = \u03c9 sin \u03b1\u03b8. (14) g0 = L/\u03bb = 4/3, and the results are compared with the corresponding solution of eqs. (13). (c) Ends of the strip are held such that \u221a g0 = L/\u03bb = 1.13 and are compared with the corresponding solution of eqs. (13). For given L/\u03bb = \u221a g0, there is a special wavelength \u03bb = 4\u03c0R( \u221a g0 \u2212 1) g0 (15) for which u can be expressed purely in terms of trigonometric functions",
            " (1), and compared both the shape and energy of the resulting solution with the analytical predictions. The results are displayed in fig. 4(a). The closed-form solution available when C1 = C2 is almost indistinguishable from the numerical solution of eqs. (13) when C1 = 2C2/3. The direct minimization of eq. (1) deviates slightly from the exact solution, probably because of incomplete convergence and finite-size effects in the numerics. As a final check of our understanding, we cut strips similar to those in fig. 2 from sheets of polycarbonate, pinned their ends as described in the caption, and used a scanning profilometer to find the shape of their centerlines. In figs. 4(b) and (c) we compare solutions of eqs. (13) to the measured shapes. Note that once L/R and \u03bb/R are determined, the shape is completely specified and there are no free parameters. Agreement between predicted and experimental shapes is satisfactory It is possible that the lowest-energy state for the simple metric in eq. (5) involves a cascade of oscillations on many scales, but we have not yet obtained detailed evidence"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.41-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.41-1.png",
        "caption": "Figure 7.41 Problem 7.4.",
        "texts": [
            " For the conditions indicated below, determine the correct symbol relat ing tensile stresses 0\"1 and 0\"2 and tensile strains El and E2. Note that //>// indicates greater than, // <\" indicates less than, //=\" in dicates equal to, and //?\" indicates that the information provided is not sufficient to make a judgement. (a) If Al > A2 and Fl = F2, then 0\"1 >=? < 0\"2 and E1 >=? < E2 (b) If El > E2, Al = A z, and Fl = Fz, then 0\"1 >=? < o\"z and El >=? < E2 Answers: Given at the end of the chapter. Problem 7.4 Figure 7.41 illustrates a bone specimen with a cir cular cross-section. Two sections, A and B, that are fo = 6 mm distance apart are marked on the specimen. The radius of the specimen in the region between A and B is ro = 1 mm. This specimen was subjected to a series of uniaxial tension tests until fracture by gradually increasing the magnitude of the ap plied force and measuring corresponding deformations. As a Stress and Strain 149 150 Fundamentals of Biomechanics (J (MPa) 300 -rn-rn-rnrrrrrrrrrrrr-rn-rn 200 +H+H-++If-H-H\"D+\"I+++t+H+H 100+H+H~f-H-H+H+++t+H+H O~~~~~~LU+W~ o 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.72-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.72-1.png",
        "caption": "Figure 8.72 Problem 8.3.",
        "texts": [
            " The bar is subjected to biaxial forces in the x and y directions such that F x = 4 x 106 Nand that Ex is tensile while F y is compressive. Assuming that the bar material is linearly elastic, determine: (a) average normal stresses O'x, O'y, and O'z developed in the bar, (b) average normal strains Ex, Ey, and Ez, and (c) dimension, e', of the bar in the x direction after deformation. (a) O'x = 10 CPa, O'y = 1 GPa, O'z = 0 (b) Ex = 0.1030, Ey = -0.0400, Ez = -0.0027 (c) e' =22.06 cm Problem 8.3 Consider the solid circular cylinder shown in Figure 8.72. The cylinder has a length e = 10 cm and radius ro = 2 cm. The cylinder is made of a linearly elastic material with shear modulus G = 10 GPa. If the cylinder is subjected to a twisting Multiaxial Deformations and Stress Analyses 193 torque with magnitude M = 3000 N-m, calculate: (a) the polar moment of inertia, J, of the cross-section of the cylinder, (b) the maximum angle of twist, f), in degrees, (c) the maximum shear stress, r, in the transverse plane, and (d) the maximum shear strain, y, in the transverse plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003856_isma.2009.5164788-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003856_isma.2009.5164788-Figure1-1.png",
        "caption": "Figure 1: Quadrotor Schematic",
        "texts": [
            "00 \u00a92009 IEEE ISMA09-1 The equations of motion of the quadrotor are [4]: 2.1. General Theory of Nonlinear Inverse Dynamics The objective of this section is to review the techniques that can be applied to develop a nonlinear controller for the quadrotor system. The technique is based on the construction of a nonlinear inverse dynamic controller described in [6], for a system of the form: The inertial position of the quadrotor center of mass is de noted by x, y and z. The thrust control is denoted by Ul along the body attached frame ez (see Figure 1). The three body axis mo ments are denoted by U2, U3 and U4 defined in body attached frame (ex, ey , ez ). The vehicle mass and gravitational acceleration are denoted by m and 9 respectively. Note that we have normailized U 1 by the vehicle mass and U2, U3 and U4 by the vehicle moment of inertia. (18) (19) (20) Ljh(x) L g Lj-1 h(x) _ 1 - L g Lj-1 h (x) a(x) (3(x) where L'h(x) is called the Lie derivative of L~-lh(x) along the vector field f. Note that by choosing the control u in (17) as 2.2. Application of Nonlinear Inverse Dynamics to the Quadro tor Aircraft and provided that the integer p exists and L gLj-l h(x) i= 0 in the neighborhood of Xo, equation (13) can easily obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003770_j.jsv.2008.04.024-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003770_j.jsv.2008.04.024-Figure1-1.png",
        "caption": "Fig. 1. (a) Bearing geometry and (b) modelling.",
        "texts": [
            " [7], an experiment was carried out in this paper to confirm our predictions of routes to chaos in ball bearings. The experiment is based on a test rig specially dedicated and an experimental procedure to generate projection of attractors. This paper presents the main results of this experiment. The following bearing modelling was derived in Ref. [7] to study the routes to chaos and here provides guidelines to design the experimental set-up. The resolution of the following equations allows us to calculate the mass displacements permitting comparisons with experiments. As shown in Fig. 1, an ideally radially loaded ball bearing is considered. The two rings are rigid bodies and so the raceways may be represented by two circles. The balls are assumed to be massless, the inner ring has no translation but rotates around its axis z and the outer ring has two translations xe and ye in its plane but no rotation about its axis z. The equation of motion of the outer ring is Mx00e \u00f0t\u00de \u00fe Cx0e\u00f0t\u00de \u00fe XZ j\u00bc1 f j\u00f0t\u00de cos\u00f0yj\u00f0t\u00de\u00de \u00bc F (1) My00e \u00f0t\u00de \u00fe Cy0e\u00f0t\u00de \u00fe XZ j\u00bc1 f j\u00f0t\u00de sin\u00f0yj\u00f0t\u00de\u00de \u00bc 0 (2) where yj\u00f0t\u00de \u00bc y\u00f0t\u00de \u00fe \u00f0j 1\u00de2p=N is the angular position of the jth ball, y\u00f0t\u00de is the angular position of the rotating frame associated with the ball retainer and f j\u00f0t\u00de is the load associated with the jth ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002421_robot.1999.770007-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002421_robot.1999.770007-Figure1-1.png",
        "caption": "Figure 1: Model of the walking robot.",
        "texts": [],
        "surrounding_texts": [
            "1 Introduction\nBiped locomotion is a popular research area in robotics due to the high adaptability of a walking robot in an unstructured environment. When attempting to automate the motion planning process for a biped walking robot, one of the main issues is assurance of dynamic stability of motion. This can be categorized into three general groups [l]: body stiG bility, body path stability, and gait stability. A Zero Moment Point (ZMP), a point where the total forces and moments acting on the robot are zero, is usually used as a basic component for dynamically stable motion.\nStable walking using a compensative inverted pendulum was achieved e.g. by the robot [2] with eight control variables (called degrees of freedom, DOF) and an upper body acting like an inverted pendulum. Other approaches for stable locomotion, with or without ZMP use, have been considered as well (see, e.g. [5],[6],[7]). In a more recent achievement, Honda\u2019s hu-\nmanoid robot P2 [8] showed the ability to walk forward, backward, right, left, up and down a staircase, and on the uneven terrain.\nNow suppose the biped robot has a sensor (say, vision) that allows it to detect an object in front of it, and suppose it walks in a scene with obstacles. In principle, this should allow the robot to operate in the scene the way humans do, avoiding the obstacles while maintaining stable motion. When encountering an obstacle on its way, depending on the obstacle\u2019s size and shape, a way of recuperating from the disturbance is to step over the obstacle, or step on it, or try to pass around it. Foot placement during this operation should be planned so as to preserve dynamical stability. If feasible, such a behavior would produce dynamically stable real time motion in an unstructured environment with unknown obstacles.\nAttempting such an approach is the topic of this work. The work builds and further extends the methodology presented in [3], which allows a biped robot to maintain dynamically stable motion under force disturbances. Some details are skipped due to the lack of space; for those, refer to [4].\n2 The Model of Biped Locomotion\nThe robot consists of seven body parts [5]: one hip, two thighs, two calves, and two feet. Body parts have certain masses, which all affect the dynamics and the walking pattern. There is a total of twelve DOF - six at the hip, two at knee, and four at ankle, Figures 1,2 . Similar to the human knee, robot knee joints are able to turn only about 04 axis; each joint between the hip and thigh has three DOF. The ankle joint turns about 05 axis and 0s axis.\nThe robot is assumed to be equipped with sensors (say, a vision) capable of sensing obstacles on its way and assessing their dimensions and distances to them. Only obstacles directly in front of the robot are considered. Each obstacle is a parallelepiped: it can be\n0-7803-51 80-0-5/99 $10.00 0 1999 IEEE 375",
            "small enough to step over it by raising a leg, or small and wide enough to step on/off it, or tall enough so that side steps are necessary to pass around it.\nTwo major phases in walking dynamics are hypothesized [5]: single support phase and double support phase. During the single support phase, one leg is on the ground, and the other leg is in the swinging motion. As soon as the swinging leg reaches the ground, the system is in the double support phase, Figure 3. Denote T2 the time period of deploy phase, T3 - of swing phase, T4 - of heel contact phase, and 2Tl - of support phase. The time period of a single walking cycle within which all body parts return to their original configuration is 4Tl.\n, support b ' angk ~ o u ~ s ~ u p p o t t ~ a s e I Single xme\nI h p h I Swtng ' w a n t a u I ' ~bploy ' Swing : ~ e e i c ~ n t a c t ' I 1 i\n3 Zero Moment Point and Locomotion LaLsrr T2 T3\nI ZMP is defined as a point on the walking surface\nin which the total forces and moments acting on the robot are zero [l]. If at a given moment of motion all the forces acting on the robot (gravity, reaction forces, and inertia forces) are balanced so that ZMP lies within the current robot footprint, the robot's POsition at this moment is dynamically stable. If this is true throughout the motion, and the trajectory of the robot's center of mass (COM) is smooth and lies be-\nlRigMLeg suppoct\nFigure 3: Phases of a single walking cycle.",
            "Variation in step length. With the robot dimensions under the model used, a normal motion step (single walking cycle) is of length 28 inches. When sensing an obstacle that is to be negotiated, the robot may decide to step on or over it, and this may require the robot first positioning itself at a specific position relative to the obstacle. This can be done by modifying the step length appropriately. Due to the effects of dynamics and related computational difficulties, it is not easy to compute the trajectory for an arbitrary step \u201con the fly\u201d; instead, a small number of \u201c typ ical\u201d step lengths that together cover a large set of situations are developed and \u201ccanned\u201d. Relative to the normal step length, this includes a half step (14 inches), quarter step (7 inches), and zero step (0 inch) lengths options. By aplying an appropriate scheme for the dynamics of swing leg and hip position trajectories, a stable walk for those walking patterns is obtained.\nVariation in the swine lee: height. With normal walk pattern, the robot can negotiate obstacles up to 1 inch high. To step over higher obstacles, the leg needs to be raised higher than normal. This changes the whole swing leg trajectory (according to the model, the COM of a swinging leg trajectory has parabolic shape [5]). Similar to the above, five trajectories that take care of the motion dynamic stability are precomputed and stored - for the obstacle heights (height ranges) 1, 2,3 ,4 , and 5 inches. (Bigger heights seem to be feasible; no attempt was made to maximize the step height for stepping on/over obstacles). After obtaining from the sensors the height and width of the obstacle that is to be negotiated, and after deciding to negotiate it by stepping on or over it, the robot chooses and executes the appropriate leg height trajectory.\nForward-side step and side step. When the obstacle is too high to step over or on it, the robot will attempt to pass around it. The (local) direction of passing around an obstacle (left or right) is decided upon beforehand; in our experiments (see below) it has been \u201cleft\u201d. If at the moment of such a decision the robot still has room for forward motion, it can be combined with side motion, producing a forward-side step. Otherwise, a side step, which has no forward component and is perpendicular to the prior direction of motion, is executed; in our scale, the side step is 6 inches long.\nTo keep the motion smooth, depending on the swinging leg at the moment of a (left) forward-side step, it may be either left or right leg that starts the maneuver. If it is the left leg, the forward-side step is simply build of the two components as above; after its execution the robot torso ends up 6 inches to the left. Because of the possible entanglement between two legs, the same cannot be done with the right leg starting the maneuver. In this case, after the step execution the right foot end up right in front of the left foot; the next step by the left leg will complete the forward-side step maneuver. Again, tied to this operation is the adjustment of the swing leg COM and hip position trajectories so as to satisfy dynamics stability.\nStepping on/off obstacles. If the obstacle is wide and flat enough to step on, sometimes it is more efficient to negotiate it by stepping on it rather than going around it. Similar to the stepping over o p tion above, five dynamically stable trajectories, for the foot heights from 1 to 5 inches, are precomputed and stored. Once the height of such an obstacle is known, the swing leg COM and hip position trajectories are chosen from the set. The walking pattern of stepping off the obstacle is similar. Depending on the length of the obstacle, stepping on the obstacle may be followed by few normal steps, then perhaps a reduced length step, and finally stepping off step.\nThe flowchart of the overall decision making algorithm capable of negotiating a sequence of obstacles of the types described above is shown in Figure 5. Darkened boxes indicate the final action in the current cycle, after which a new step is initiated and the control goes to the top of the flowchart. The algorithm for selecting the walking pattern utilizes nested if-else commands.\n5 Simulated Examples\nDescribed here are the results of computer simulated experiments with two-legged locomotion in the"
        ]
    },
    {
        "image_filename": "designv10_8_0003126_j.mechmachtheory.2006.10.004-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003126_j.mechmachtheory.2006.10.004-Figure3-1.png",
        "caption": "Fig. 3. Basic structure and vector model of the Tricept manipulator.",
        "texts": [
            " The last manipulator analysed in this study is the Tricept mechanism which has been studied in a variety of works (see for instance [13,18]), most likely as a result of its large commercial success. The most unique feature of this mechanism with four limbs is that the fourth leg, having 3-DOF, is entirely composed of passive joints. Each of the actuated limbs has 7-DOF and therefore the 3-DOF passive leg is used to constrain the system to those 3-DOF contained within it. This assembly is schematically depicted in Fig. 3. The order of joints composing the passive leg may be interchanged in order to minimise undesired motions of the end effector, or \u2018parasitic\u2019 motions as defined in [11]. For instance, if the Tricept mechanism is to be implemented as a translational manipulator, as most research papers do, large motions in the x- and y-directions are possible if the passive prismatic joint follows the passive universal joint attached near the base platform. However, by reversing the joints, as depicted in Fig. 3, these motions become limited by the distance between the universal joint and the end effector platform, i.e., the magnitude of vector d depicted in Fig. 3. Furthermore, in this work, these translational displacements along the x- and y-axes are considered to be parasitic motions whereas rotations around x and y are desired (see Fig. 3). Note that these parasitic motions may be eliminated by letting the intersection of the two revolute axes composing the universal joint, lie on the plane defined by the centres of the spherical joints attached to the moving platform, i.e., making jdj = 0. Therefore, to allow a fair comparison to the 3-PRS and 3-RPS manipulators, the order of joints composing the central, passive limb is chosen as prismatic-universal (PU), as opposed to the UP limb commonly used in most works where this mechanism is treated as a translational device"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003881_j.aca.2010.11.053-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003881_j.aca.2010.11.053-Figure1-1.png",
        "caption": "Fig. 1. The diagram of the magnetic glassy carbon e",
        "texts": [
            " At last, the aldehyde grafted microspheres were separated by magnet and redispersed in 0.8 mL PBS (pH = 7.0) containing 0.4 mg mL\u22121 Tyr and left to react at 4 \u25e6C for 48 h with occasionally stirring. The resulted Tyr conjugated magnetic materials were denoted as TyrFe3O4@mSiO2 and Tyr-Fe3O4@SiO2, respectively. 4@SiO 2 m i w r 1 w F f s e ( o m F 3 3 m v .5. Preparation of the magnetic loaded phenol biosensor MGCE (3 mm in diameter) was purchased from Jiangfen Instruents, Inc., China. The inner structure of the electrode was shown n Fig. 1a. The MGCE was firstly polished to a mirror finish ith 0.3 and 0.05 m alumina slurry followed by thoroughly insing with deionized water. After sonicating successively in :1 nitric acid, acetone and ethanol, the electrodes were rinsed ith deionized water and dried at room temperature. The Tyre3O4@mSiO2 modified electrode (Tyr-Fe3O4@mSiO2/MGCE) was abricated by dropping 3 L of the 0.5 mg mL\u22121 Tyr-Fe3O4@mSiO2 uspension on the surface of the MGCE and followed with water vaporation. For comparison, the Tyr-Fe3O4@SiO2/MGCE and the Tyr-Fe3O4@mSiO2)-PVA/GMCE obtained by further coating of 3 L f 2% PVA on the Tyr-Fe3O4@mSiO2/MGCE were prepared",
            " 4a shows the cyclic voltammograms (CVs) of the Tyre3O4@SiO2/MGCE and the Tyr-Fe3O4/mSiO2/MGCE in 0.1 M air aturated pH 6.0 PBS with and without the addition of 50 M henol. Without addition of phenol, only low background curents were observed. Upon the addition of phenol to the uffer solution, the CVs of Tyr-Fe3O4@SiO2/MGCE and the Tyre3O4@mSiO2/MGCE both gave peak shaped catalytic reduction aves, which were caused by the reduction of quinone species iberated from the enzymatic reaction of Tyr on the electrode surace [15]. The catalytic scheme is shown in Fig. 1b. The current n the Tyr-Fe3O4@mSiO2/MGCE was much higher than that on the yr-Fe3O4@SiO2/MGCE. The increase of the current response was ssumed to be attributed to two possibilities. Firstly, although the esopores cannot be used for Tyr immobilization, they may actully adsorb small molecules [25], phenol in this case, which could acilitate the enzymatic reaction. In addition, the porous structure ncreases the surface roughness, which facilitates the immobilizaion of enzyme by increasing amount and better maintaining the nzyme activity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003684_j.matdes.2008.06.037-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003684_j.matdes.2008.06.037-Figure7-1.png",
        "caption": "Fig. 7. Meshing point and positions of the intermediate points on the gear flank.",
        "texts": [
            " The experiments were carried out under dry conditions. The wear depth in the profile of the newly modified gears and unmodified spur gears were measured and the change in profile was determined. The experimental plastic spur gear tooth initial profile was recorded before the experiment and the profile after the experiment was compared by measuring the wear depths to determine the profile changes. To allow for more sensitive measurements, the tooth height was divided into a total of 16 spaces (E,1,2,3,4,D,5,6,7,8,P,9,10,B,11, 12,A) (Fig. 7). The SM350 Vertical Profile Optical Projector apparatus was used to measure the profiles. The experimental gears were produced at a normal room temperature of 20\u201323 C. In this study, width modification was used to equalize the maximum Hertz surface pressure on a single spur gear tooth meshing with the maximum pressure on a double tooth spur gear meshing. An increase in the wear depth was observed because of the effect of high sliding velocity at the tooth root and the tooth tip of the unmodified plastic spur gears (Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure1-1.png",
        "caption": "Fig. 1 PPR virtual chain",
        "texts": [
            " There is usually more than one kinematic chain corresponding to a same motion pattern. The simplest kinematic chain, which can express the motion pattern well, is called the virtual chain for the motion pattern. For example, several kinematic chains, such as a chain composed of one E joint and a serial chain composed of three R joints with parallel axes, all correspond to a planar motion. The E chain is called the virtual chain for the planar motion. The virtual chain for the motion pattern of the PMs to be synthesized in this paper is the PPR virtual chain Fig. 1 in which the moving platform can rotate about an axis which translates along a plane 9,15 . In a PPR virtual chain, the axis of the R joint is not perpendicular to the directions of the two P joints. For convenience, the axis of the R joint within the PPR virtual chain is called a virtual axis, the plane which is parallel to the directions of the two P joints within the PPR virtual chain is called a virtual plane. In the PPR-equivalent PMs proposed in 9,15 , the axis of rotation is limited to be parallel to the plane along which it translates",
            " 7, for example : a Single-loop kinematic chains formed by a serial chain of class b2 and a serial chain of class b3 Figs. 7 a and 7 b . b Single-loop kinematic chains formed by one serial chain of class b4 Fig. 7 c . c Single-loop kinematic chains formed by a serial chain of class b1 and a serial chain of class b3 Fig. 7 d . d Single-loop kinematic chains formed by two serial chain of class b4 Figs. 7 e and 7 f . In the representation of the types of 3-DOF single-loop kinematic chains involving a virtual chain Fig. 1 , PPR-equivalent parallel kinematic chains, PPR-equivalent PMs and their legs, X denotes a P or an R joint, PP N denotes two successive P joints whose directions are parallel to the virtual plane. XXX N denotes three successive X joints in which the axes of all the R joints are perpendicular to the virtual plane and the directions of all the P Transactions of the ASME 3 Terms of Use: http://asme.org/terms Downloaded F joints are parallel to the virtual plane. RR I denotes two successive R joints whose axes intersect at the same point on the virtual axis, Ra denotes an R joint whose axis is collinear with the virtual axis, RA denotes an R joint whose axis is parallel to the virtual axis, XX B and XXX B denote, respectively, two or three successive X joints in which there is at least one R joint and the axes of all the R joints, within a 3-DOF single-loop kinematic chain or a leg for PPR-equivalent parallel kinematic chains, are parallel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003904_10402001003693109-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003904_10402001003693109-Figure1-1.png",
        "caption": "Fig. 1\u2014Tribological contact of interest.",
        "texts": [
            " Samples were developed further (Roberts (6)) by adding carbon black to the specimens before curing. This improved light absorption and therefore reduced light reflections not occurring at the contact surface, leading to improved image quality. Later, Roberts and Tabor (5) and Richards and Roberts (7) introduced an Abbe prism to replace the flat glass disc. The illuminating beam was thus moved to a nonnormal incidence to the contact area, so the amount of scattered light received by the detector was greatly reduced. This is shown schematically in Fig. 1. Using this method, film thickness measurements down to \u223c10 nm where achieved. The Abbe prism consists of a block of glass in the form of a right-angled prism with 30-60-90\u25e6 triangular faces. A beam of light enters face AB, is refracted and undergoes total internal reflection from faces AC and BC, and enters the contact about three quarters of the way from A along the face AC. Here, a por- tion of the light is reflected from the glass surface and the remainder passes through any lubricant film to be reflected back from the ball surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003694_jst.65-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003694_jst.65-Figure3-1.png",
        "caption": "Figure 3. Definition of oar angles and oar forces; the oar angle measured at the oar lock (yL) can differ from the blade angle (y) due to oar bending.",
        "texts": [
            " The position of the boat seat (xS) is measured by a further incremental wire potentiometer (4 cts/mm). In general, a model for virtual rowing is driven by measured variables, which reflect the rower\u2019s performance. The model output controls the displays presented to the user. In our setup, a haptic, visual, and acoustic display are integrated. Our model inputs are the three oar angles y (in the horizontal plane), d (in the vertical plane), and f (around the longitudinal oar axes), and the seat position xS (Figure 3) summarized in the vector k. The outputs are the oar forces in the horizontal and the vertical plane FO \u00bc \u00f0FOy;FOd \u00deT for the haptic display, as well as the boat velocity _xB represented by appropriate animations and sounds on the visual and the acoustic display, respectively. Furthermore, the oar angles are directly mapped to visual and acoustic dimensions shown as a virtual oar to the user. In our model, the virtual oar length (l) the rower\u2019s mass (mR), and further parameters are adjustable according to the boat type and the user"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002844_mech-34344-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002844_mech-34344-Figure4-1.png",
        "caption": "Figure 4: 3-RRS wrist",
        "texts": [
            " 1) can be computed with the Gr\u00fcbler equation: F = 6 (n \u2212 1) \u2212 j (6 \u2212 fj) (11) where F is the dof number of the mechanism, n is the number of links and fj is the dof number of the j-th kinematic pair. 3 Copyright \u00a9 2002 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Dow The 3-RRS mechanism (Fig. 1) is composed of eight links (n=8), three spherical pairs (fj=3) and six revolute pairs (fj=1). Substituting these data into Eq. (11) gives F=3. Therefore the 3- RRS mechanism has three dof, i.e., is not overconstrained. Figure 4 shows a 3-RRS mechanism encountering the following mounting and manufacturing conditions: (i) the revolute pair axes converge towards a single point; (mounting and manufacturing condition) (ii) the centers of the spherical pairs are not aligned; (manufacturing condition) (iii) the point the revolute pair axes converge towards does not lie on the plane located by the three spherical pair centers; (manufacturing condition) Henceforth a 3-RRS mechanism encountering these geometric conditions will be called 3-RRS wrist. In the following paragraphs of this section it will be shown that the 3-RRS wrist is a spherical parallel manipulator when the three revolute pairs adjacent to the base are actuated. With reference to Fig. 4, the points Ai, i=1,2,3, are the spherical pair centers and the point C is the point the revolute pair axes converge towards. The point C is fixed in the base. Moreover, Sb is a reference system fixed in the base and Sp is a reference system fixed in the platform. nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Te Figure 5 shows the i-th leg, i=1,2,3, of the 3-RRS wrist. According to Fig. 5, w1i and \u03b81i are respectively the axis unit vector and the joint coordinate of the revolute pair adjacent to the base and w2i and \u03b82i are respectively the axis unit vector and the joint coordinate of the revolute pair not adjacent to the base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.55-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.55-1.png",
        "caption": "Figure 4.55 Problems 4.7 and 4.8.",
        "texts": [
            " Determine the tensions TI and T2 in the cables, weights WI and W2, and angle ex that cable 1 makes with the horizontal, so that the leg remains in equilibrium at the position shown. Answers: Tl = WI = 223.6 N T2 = W2 = 282.8 N ex = 26.6\u00b0 Problem 4.6 Consider the uniform, horizontal cantilever beam shown in Figure 4.54. The beam is fixed at A and a force that makes an angle f3 = 63\u00b0 with the horizontal is applied at B. The Statics: Analyses of Systems in Equilibrium 79 magnitude of the applied force is P = 80 N. C is the center of gravity of the beam and the beam weighs W = 40 N and has a length l = 2 m. Problem 4.7 Consider the L-shaped beam illustrated in Figure 4.55. The beam is welded to the wall at A, the arm AB extends in the positive z direction, and the arm BC extends in the negative y direction. A force P is applied in the positive x direction at the free-end (B) of the beam. The lengths of arms AB and BC are a and b, respectively, and the magnitude of the applied force is P. Assuming that the weight of the beam is negligibly small, de termine the reactions generated at the fixed end of the beam in terms of a, b, and P. Answers: The non-zero force and moment components are: RAx = P (-x) MAy = aP (-y) MAz = bP (-z) Problem 4.8 Reconsider the L-shaped beam illustrated in Figure 4.55. This time, assume that the applied force P has components in the positive x and positive zdirectionssuch that P = Pxi+Pyj. Determine the reactions generated at the fixed end of the beam in terms of a, b, Px , and Py. RAx = Px (-x) RAy = 0 RAz = Py (-z) MAx = bPz (+y) MAy = aPx (-y) MAz = bPx (-z) Problem 4.9 Figure 4.56 illustrates a person who is trying to pull a block on a horizontal surface -using a rope. The rope makes an angle () with the horizontal. If W is the weight of the block and JL is the coefficient of maximum friction between the bottom surface of the block and horizontal surface, show that the magnitude P of minimum force the person must apply in order to overcome the frictional and gravitational effects (to start moving the block) is: JLW P=---- cos () + JL sin () Problem 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure2.21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure2.21-1.png",
        "caption": "Figure 2.21 An experimental method to determine the coefficient of friction.",
        "texts": [
            " What is the minimum horizontal force required to move the block toward the right? Answer: Slightly greater than 300 N. Problem 2.6 As shown in Figure 2.20, consider a block that weighs W. Owing to the effect of gravity, the block is sliding down a slope that makes an angle () with the horizontal. The co efficient of kinetic friction between the block and the slope is Ilk. Show that the magnitude of the frictional force generated be tween the block and the slope is f = Ilk W cos (). Problem 2.7 Figure 2.21 shows a simple experimental method to determine the coefficient of static friction between surfaces in contact. This method is applied by placing a block on a hori zontal plate, tilting the plate slowly until the block starts sliding over the plate, and recording the angle the plate makes with the horizontal at the instant when the sliding occurs. This critical angle \u00ab()c) is called the angle of repose. At the instant just before the sliding occurs, the block is in static equilibrium which will be discussed in later chapters"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003912_s0022112073001849-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003912_s0022112073001849-Figure3-1.png",
        "caption": "FIGURE 3. Area a as a function of height K.",
        "texts": [
            " After straightforward manipulation we find in this region x = 4E($p) - 2 W p ) - 2E($p, $1 + q + p , $), (17) where E($p) and I<($p) are the complete elliptic integrals. grating. With the condition that xu is infinite when y is zero we obtain The cross-sectional area may be obtained by multiplying (3) by xy and inte- u -px+xy- joxdy = -(1+x2)-4, Y and if y is put equal to K we find a-Kh+pA-sinO = 0. (19) For a particular choice of 6 and p, if p exceeds 2 we calculate K and h from (I I) and (13) respectively, with q5 equal to +6. If p is less than 2, equations (16) and (1 7) are used. The area of the cross-section is then calculated from ( 19). In figure 3 values of a have been plotted as a function of K for different angles of contact. As Neumann showed for zero contact angle, there is a maximum in the possible values a may attain. Below this maximum two profiles exist having for the same area a two different heights K. As an example, the profiles are shown in figure 4 for a contact angle of 30\" corresponding to the points A and B in figure 3. It will also be seen that, if we have an equilibrium shape, then by drawing the horizontal surface from which the drop hangs at a different level we automatically obtain an equilibrium solution for a different area and contact angle. From figure 3 we see that, as liquid is added to the drop, the height K increases until the maximum cross-sectional area is reached. Addition of more liquid would then result in a situation for which no equilibrium is possible, and so liquid would certainly separate from the drop. However, if the maximum cross-section were exactly attained and liquid were withdrawn, the figure shows that it is possible for the drop height K to continue to increase, since points such as B represent an equilibrium. Obviously in practice this region would be very difficult to enter, since a slight excess of liquid above the maximum would cause the drop to break, while an amount less than the maximum would make it impossible to reach points like B by removal of liquid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002321_jsvi.2000.2950-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002321_jsvi.2000.2950-Figure10-1.png",
        "caption": "Figure 10. Details of \"nite element model.",
        "texts": [
            " The overall view and the details of the \"nite element model of the test linear bearing are shown in Figures 9 and 10, respectively. To model the carriage block and the end caps, an eight-node solid element was chosen in COSMOS/M. In the model, the mass m b of each ball in the load zone. l L , the spring constant K C caused by the elastic contact between the carriage and each ball, the spring constant K R caused by the elastic contact between the pro\"le rail and each ball were considered. To simplify the analysis, we assumed that the ball interval is equal and one ball is located in the center of the load zone as shown in Figure 10. In addition, we assumed that K C is equal to K R because the raceway groove radii of the carriage and those of the pro\"le rail in the test linear bearing are identical. Based on these assumptions, K C and K R can be expressed as K C \"K R \"2 l L k Z L , (8) where Z@ L is the number of balls in the load zone in one circulation when one ball is located in the center of the load zone. In the analysis using FEM, we used the material constants, Z@ L , m b , K C and K R for test linear bearings as shown in Table 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002761_robot.1989.100120-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002761_robot.1989.100120-Figure1-1.png",
        "caption": "Fig 1. Five Coordinate Frames for the Space Vehicle / Manipulator System.",
        "texts": [
            " (rad) Rotation matrix from the inertia frame to the manipulator base frame. Rotation matrix from the inertia frame to the k-th body frame (The vehicle frame for k = 0, the k-th link frame of the manipulator for k = 1,. . . , n ) . Jacobian matrix of the position of the center of mass of k-th body (k = 1,. . . , n) in the manipulator base frame. (m) i x i identity matrix. z-y-x Euler angles. ( radls) 2.2 Kinematics of Space Vehicle/Manipulator Systems The basic equations of kinematics of space vehicle/manipulator system is developed in this subsection. Fig. 1 shows a model of space vehicle/manipulator system. Five kinds of frames, the inertia frame, the vehicle frame, the manipulator base frame, the k-th link frames, and the manipulator endeffector frame, are represented by I , V , B , I ( , and E respectively. The link frames of the manipulator are defined by Denavit-Hartenberg convention [7]. The vehicle frame is assumed to be fixed a t the center of mass of the vehicle. Supposing zero linear and angular momentum a t initial time, the linear and angular momentum conservations are represented by n ( ' I k ' w k + m k I r k x I T k ) = 0, (2) k=O The vehicle and manipulator motions are described by the following 81 and 8 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure4.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure4.3-1.png",
        "caption": "Fig. 4.3 Equilateral triangle",
        "texts": [],
        "surrounding_texts": [
            "The problem is solved (indirectly) by finding the stress function T which satisfies within the ellipse y2 z2 a2 + b2 = 1 the differential equation (4.14), and on the ellipse satisfies the boundary condition T = O. The function is { y2 z2 } T = m a2 + b2 - 1 , The stress components are (Eq. 4.13) 2z 2y IJxy = 2GrJm b2 ' IJxz = -2GrJm a2 The shear stress T is the resultant of IJ xy and IJ xz, and so y2 z2 T = 4GrJm a4 + b4 with the maximum value on the boundary at the ends of the minor axis, that is, at the points nearest the axis of the torsional rotations. 4.1 Solid Cross Sections 75 From Eq. (4.6), we determine by integration the function 7jJ(y, z) a 2 _ b2 7jJ = - Z--b2 yz. a + The lines of constant values of the warping are shown in Fig. 4.2. From these results, we can deduce the following relations MT Tmax = WT ' {} D Corresponding values of the polar moment of inertia J T and the section modulus W T may be determined for cross sections of different kinds: 1. Equilateral triangle Let the boundary of a torsion member be an equilateral triangle with h = V3a/2. Proceeding as for the elliptical cross section, we find MT Tmax = WT ' {} 1 3 WT = 20 a , V3 4 JT = -a . 80 (4.24) 76 4. Torsion of Prismatic Bars 2. Narrow rectangular cross section Consider a bar subjected to torsion. Let the cross section of the bar be a solid rect angle with width b and depth h, where b \u00ab h. From the different analogies (e.g. the soap-film analogy, originally proposed by L. Prandtl.),2 we may conclude that except for the region near z = \u00b1h/2 the stress components a xy and a xz are ap- f-b-j I y 1 Fig. 4.4 z Narrow rectangle proximately independent of z, and a xy ~ 0, a xz ~ T(Y) = 2G1'Jy. Thus, from Eq. (4.13), we determine T~T(y)= b; {l- (2:r}, and furthermore 1 3 Jr=3\"hb. (4.25) (4.26) (4.27) We note, however, that near the ends, of course, these results, which are valid only for narrow cross sections, do not apply. The exact theory for the rectangle is then required. The simple parabolic approximate form of T (Eq. 4.26) will give a good approx imation, since it differs from the true solution only in the small end zones. We may generalize Eq. (4.27) by introducing correction factors 0: and (3, as functions of the ratio h/b (see Table 4.1), to give 1 2 1 3 WT = 0: 3\" hb, Jr = (3 3\" hb . (4.28) 2 Analogies exist where physically different problems have similar mathematical descrip tions. In this case solutions - or experimental findings - from one problem may be trans ferred to the other - analogous - problem. The most known analogy to the torsion problem of prismatic bars is that of a membrane (soap film) fixed on a closed boundary, having the same shape as the cross section of the torsion bar, where pressure is applied to one side of the membrane. We therefore refer e.g. to the textbook of Boresi, Schmidt & Sidebottom, Advanced Mechanics of Materials, 5th. Edition, John Wiley & Sons, N.Y. etc., 1993. 4.2 Thin-Walled Closed Cross Sections 77 4.2 Thin-Walled Closed Cross Sections In the preceding section, we have discussed torsion of prismatic bars with solid cross sections. In the following sections, we now will examine this problem with thin-walled cross sections. We maintain the assumptions of St. Venant's theory about the displacement com ponents (Eqs. 4.1, 4.2), and furthermore - for the moment - assume unrestrained warping 'IjJ(y, z) in the x direction. In Section 3.2, we discussed beams of thin walled cross sections subject to shear forces. From this section, we take the modi fied description of thin-walled cross sections, with cross-sectional centerline (mid dle line), and additional rectangular coordinates (, along the centerline and 'f/, per pendicular to (. Thus, the thin-walled cross section is described by the coordinates y((), z(() of the centerline, and thickness J(() ofthe profile. for the shear stresses, and u=u(x,() (4.29) (4.30) for the displacements, constant in the 'f/ direction. We note that assumptions (4.29) coincide with the assumptions (3.37) for the shear stresses due to shear forces (Sec tion 3.2). Defining now the shear flow t( () as J 8/2 t(() = O\"xC, d'f/, (4.31) -8/2 we obtain with (4.29h t(() = T(()J((). (4.32) From the equilibrium (in axial direction) of a small element cut from the thin-walled tube (Fig. 4.6), we see that t = T( ()8( () = const. , (4.33) provided there are no axial stresses (J xx' Thus, the largest shear stress occurs where the thickness is smallest, and vice versa. Of course, if the thickness is uniform, then the shear stress T is constant around the tube. In order to relate the shear flow to the torque M T acting on the tube, consider an element of length d( in the cross section: The total shear force acting on the element is t de, and the moment of this force about any point 0 is dMT = a(()td(, (4.34) in which a( () is the distance from 0 to the tangent to the centerline. The total torque then is MT = t f a(()d( = 2Amt, (4.35) where the integral represents double the area Am enclosed by the centerline of the tube. From this equation, we find MT t = T(()8(() = 2Am ' (4.36) and finally, 4.3 Thin-Walled Open Sections 79 Tmax = (4.37) Bredt's first formula. To determine a relation between torque M T and twist {}, we start from assump tion (4.30), and (4.38) With these displacements, we find ) 1 { dux } ex((( =\"2 d( + {}a(() , (4.39) and thus from Hooke's law (4.40) Integrating this expression over the entire length of the centerline yields f T(() d( = c{ f dux + {} f a(() d(}. (4.41) The first integral of the right hand side vanishes (continuity of u x), and thus with Eq. (4.36), we finally arrive at 2 {f d( }-l Jr = 4Am 8(() , (4.42) Bredt's second formula. If in Eq. (4.41) the integrals are not taken over the entire length of the centerline, e.g. for the first integral of the right hand side J( dux = ux(() - ux(O) = {}{'l,b(() - 'l,b(O)} , (4.43) o Bredt's second formula is replaced by a slightly different relation (4.44) from which the distribution of the warping along the centerline may be calculated. 80 4. Torsion of Prismatic Bars Fig. 4.8 Thin-walled open section"
        ]
    },
    {
        "image_filename": "designv10_8_0002890_00006123-200110000-00003-Figure15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002890_00006123-200110000-00003-Figure15-1.png",
        "caption": "FIGURE 15. Examples of neural probes fabricated by micromachining technology. (a) photograph showing a probe through the eye of a needle. (b) schematic depiction of the probe shown in (a). (c) schematic depiction of a multishank probe.",
        "texts": [
            " For example, rather than provide a fixed electrical current pattern to a specific region of the brain to compensate for a pathological movement, a \u201csmart prosthesis\u201d could record electrical activity from the surrounding brain and modify electrode stimulation on the basis of the surrounding brain data obtained. This type of input could perhaps even help the surgeon direct the initial placement of the electrode. Furthermore, integration of locomotive actuators on the electrodes could enable the creation of a \u201csmart neural prosthesis\u201d that would propel itself to a more optimal recording and stimulation location. Figure 15 shows examples of microelectrode arrays that have been fabricated using MEMS technology to link the central nervous system to microelectronic circuitry (32, 51\u2013 53). These neural probes were designed for multichannel sensing and stimulation in the cerebral cortex. The micromachined Si substrate supports an array of metallic film conductors that are insulated above and below by dielectric films. Openings in the upper layer along the probe shank-defined stimulating or recording sites, which are inlaid with gold or iridium oxide for interfacing with brain tissue"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002655_j.bios.2004.08.035-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002655_j.bios.2004.08.035-Figure2-1.png",
        "caption": "Fig. 2. Representation of the multi-biosensor flow cell. It consists of four black Perspex cells where sealed printed electrodes can be inserted. Each cell is supplied with high intensity LED of 650 nm, to activate light-dependent electron transfer.",
        "texts": [
            " Impurities were removed during the initial stabilization under the constant potential (10 min). The flow cell device is a box parallelepiped\u2014shaped with a size of 20 cm \u00d7 15 cm \u00d7 13 cm and weight of 1 kg depending on the number of flow cells. The device consists of four black Perspex flow cells where sealed printed electrodes can be inserted. Each cell is supplied with a high-intensity LED of 650 nm, suitable to activate light reaction in Photosystem II. Each cell has three flow ways for fluid movements, two flow input and one flow output (www.biosensor.it) as shown in Fig. 2. The duration of light pulses was set to 5 s every 10 min at the light intensity of about 130 mol photons m\u22122 s\u22121. The volume of the flow-cell was adjusted by a silicon spacer (0.5 mm) (Krejici Eng. Czech Rep). The electrode was continuously washed with the measuring buffer (see above) plus an electron acceptor. The flow of the buffer (0.2 ml min\u22121) can be driven by a set of mini pumps (Krejici Eng. Czech Rep) or alternatively by the 402-syringe pump (www.gilson.com); this type of pump allows to maintain the biological material fixed over the electrode avoiding leaking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure12.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure12.4-1.png",
        "caption": "Fig. 12.4 System with forces (left) and virtual displacements (right)",
        "texts": [],
        "surrounding_texts": [
            ">:l' 2' >:l uQi m2Lizl + m2L iz2 uQi Introducing this into the Lagrange equations, we find ( (ml + m2) m2L2) q + (b 0) q + (C 0 ) q = (FO cos f2t) . m2L m2L 0 0 0 m2gL 0 We first determine the eigenfrequencies and the modes of vibration for an un damped system. 182 12. Systems of Several Degrees of Freedom From Eq. (12.10), we conclude I e - w5(ml + m2) -W5m 2L 1=0 -W5m2L m2gL - W5 m 2L2 with the frequency equation"
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.54-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.54-1.png",
        "caption": "Figure 8.54 Normal (flexural) stress distribution over the cross-section of the beam.",
        "texts": [
            "1 Area (A), area moment of inertia (I) about the neutral axis (NA),first moment of the area (Q) about the neutral axis, and maximum normal(O\"max) and shear ('max) stresses for beams subjected to bending and with cross-section as shown. bh2 fBNA A=bh Q=S Mh bh3 O\"max= 21 1=12 3V >--b~ Tmax=2A Q_2rq3 -0-NA A=11'rq2 - 3 Mrq 4 O\"max= 1 1 _'!I!:..tL - 4 4V Tmax=3A Q=rq(rq2 + r;2) @ A=7r(rq2 - r;2) Ti Mrq NA 7r{rq 4- r ;41 O\"max= 1 1= 4 2V Tmax=T The stress distribution at a section of a beam subjected to pure bending is shown in Figure 8.54. At a given section of the beam, both the bending moment and the area moment of inertia of the cross-section are constant. According to the flexure formula, the flexural stress a x is a linear function of the vertical distance y measured from the neutral axis, which can take both positive and negative values. At the neutral axis, y = 0 and a x is zero. For points above the neutral axis, y is positive and ax is negative, 184 Fundamentals of Biomechanics indicating compression. For points below the neutral axis, y is negative and ax is positive and tensile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002721_a:1019687400225-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002721_a:1019687400225-Figure8-1.png",
        "caption": "Figure 8. Definition of the form of the links of the PA-10 robot.",
        "texts": [
            "15 meter, the total mass of the robot (including the base) is 35 kg, it can manipulate a load up to 10 kg. Owing to the great load to the robot mass ratio, the accuracy of the rigid model is moderate and especially for high load masses. The aim of our experiments is to show that the elastic model can improve this accuracy. The parameters defining frames Rai, specifying the shape of the links, are shown in Table II. The corresponding numerical values are obtained from the manufacturer data sheets. Notice that links 1, 3, 5, and 7 are identical, and links 2, 4, and 6 are also identical (Figure 8). It is to be noted that Bi is aligned with Oi for links 1, 3, 5, and 7, whereas Oi is aligned with Ai for links 2, 4, and 6. The nominal flexible parameters are given in Table III. The values of the first moments and mass of the base are not given since they have no effect on the calibration model. Also, we recall that link 7 is represented by a lumped mass (L7 = 0). The gravity acceleration vector g in the base frame R0 is given as: 0g = {0 0 \u22129.81]T (m \u00b7 s\u22122). The position error between the rigid direct model and the flexible model is about 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.44-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.44-1.png",
        "caption": "Figure 8.44 Analyses oj the material element in Figure 8.43.",
        "texts": [
            " The cylinder is subjected to pure torsion by an externally applied torque, M. As illustrated in Figure 8.43b, the state of stress on a material element with sides parallel to the longitudinal and transverse planes of the cylinder is pure shear. For given M and the parameters defining the geometry of the cylinder, the magnitude Txy of the torsional shear stress can be calculated using the torsion formula provided in Eq. (8.26). Using Mohr's circle, investigate the state of stress in the cylinder. Solution: Mohr's circle in Figure 8.44a is drawn by using the stress element of Figure 8.43b. On surfaces A and B of the stress element shown in Figure 8.43b, there is only a negative shear Multiaxial Deformations and Stress Analyses 179 stress with magnitude i xy . Therefore, both A and B on the i-a diagram lie along the i axis where a = O. Furthermore, the ori gin of the i-a diagram constitutes the midpoint between A and B, and hence, the center, C, of the Mohr's circle. The distance be tween C and A is equal to i xy , which is the radius of the Mohr's circle. Mohr's circle cuts the horizontal axis at two locations, both at a distance ixy from the origin. Therefore, the principal stresses are such that al = ixy (tensile) and a2 = ixy (compres sive). Furthermore, i xy is also the maximum shear stress. The point where a = al on the i-a diagram in Figure 8.44a is labeled as D. The angle between lines CA and CD is 90\u00b0, and it is equal to half of the angle of orientation of the plane with normal in one of the principal directions. Therefore, the planes of maximum and minimum normal stresses can be obtained by rotating the element in Figure 8.43b 45\u00b0 (clockwise). This is illustrated in Figure 8.44b. The lines that follow the directions of principal stresses are called the stress trajectories. As illustrated in Figure 8.45 for a circular cylinder subjected to pure torsion, the stress trajectories are in the form of helices making an angle 45\u00b0 (clockwise and counter clockwise) with the longitudinal axis of the cylinder. As dis cussed previously, the significance of these stress trajectories is such that if the material is weakest in tension, the failure occurs along a helix such as bb in Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.36-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.36-1.png",
        "caption": "Figure 4.36 Free-body diagram of the beam.",
        "texts": [
            " Now that we determined the components of the reactive force and moment at A, we can also Statics: Analyses of Systems in Equilibrium 69 calculate the magnitudes of the resultant force and moment at A: RA = J RAx2 + RAy2 + RAz2 = RAy = 120 N MA = J MAx2 + MAl + MAz2 = 43.3 N-m The second method of analyzing the same problem utilizes the vector properties of the parameters involved. For example, the force applied at C and the position vector of point C relative to A can be expressed as (Figure 4.35): P = - P i = -120 i r.. = -b \u00a3 + a If = -0.30 \u00a3 + 0.20 If Here, f, j, and If are unit vectors indicating positive x, y, and z directions, respectively. The free-body diagram of the beam is shown in Figure 4.36 where the reactive forces and moments are represented by their scalar components such that: First, consider the translational equilibrium of the beam: RA + P = 0 (RAx \u00a3 + RAy i + RAz If) + (-120 D = 0 RAx \u00a3 + (RAy -120) j + RAz If = 0 For this equilibrium to hold: RAx = 0 RAy = 120 N (+y) RAz = 0 As discussed in the previous chapter, by definition, moment is the cross (vector) product of the position and force vectors. Therefore, the moment Me relative to A due to force P applied at Cis: Me=r.. xP = (-0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure16-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure16-1.png",
        "caption": "Fig. 16. Schematic illustration of: (a) boundary condition for the worm, and (b) boundary conditions for the face-gear.",
        "texts": [
            " Step 3: Analytical determination of node coordinates is performed automatically by choosing the desired number of elements in longitudinal and profile directions (Fig. 15(c)). All the nodes of the finite element analysis are determined analytically and the points of the intermediate surfaces of the tooth belong to the real gear tooth surfaces. Step 4: Discretization of the model by finite elements (using the nodes determined previously) is accomplished as shown in Fig. 15(d). Step 5: The boundary conditions for the face-gear and the worm are set automatically under the following conditions: (i) Nodes on the bottom of the worm rim are considered as fixed (Fig. 16(a)). (ii) Nodes on the two sides and the bottom part of the face-gear rim form a rigid surface (Fig. 16(b)). Such rigid surface is a three-dimensional structure that may perform translational and rotation but cannot be deformed. (iii) Considering the face-gear rim rigid surfaces the variables of motions of the face-gear (its translation and rotation) are associated with a single point M located on the axis of the face-gear chosen as the reference point. Point M has only one degree of freedom (rotation about the face-gear axis) and all the other degrees of freedom are fixed. The torque T is applied directly to the face-gear at its reference point M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003233_j.clinbiomech.2005.10.007-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003233_j.clinbiomech.2005.10.007-Figure1-1.png",
        "caption": "Fig. 1. Free body diagram of the inverted pendulum model. This idealized pendulum moves in the global XY-plane, has a massless shaft of length r, a load m at its tip (equal to body mass for a given subject), and an inclination angle h. In the absence of joint moments, there are only horizontal and vertical ground reaction forces (GRF) at the pivot (Fh and Fv, respectively). Because contralateral GRF transmitted to the mass are not included, this model is valid only during single support.",
        "texts": [
            " Subtracting coordinates of the average CoP from those of the instantaneous CoM, and projecting the resulting vector onto the global XY-plane (X anterior, Y vertically upward), provided a telescoping inverted pendulum with variable length r, and a mass m at its tip equal to body-mass for each subject. Radial and angular kinematics of this CoP\u2013CoM pendulum were calculated using central difference techniques, and used in forward and inverse dynamics as detailed below. Finally, more conventional inverse dynamics were performed in Visual3D to provide lower extremity joint powers. Our CoP\u2013CoM pendulum was similar to inverted pendulums in the literature (Pai and Patton, 1997; Buczek et al., 2000). In the absence of joint powers, there were no moments at the stationary pivot (Fig. 1). Summing forces in Cartesian coordinates, we obtained expressions for Newton s second law, where ax and ay are accelerations of the pendulum CoM. X F x \u00bc max \u00f01\u00de X F y \u00bc may \u00f02\u00de Using the following relationships, we transformed to polar coordinates, with r being the length of the pendulum, and h being its angle of inclination with respect to the horizontal. x \u00bc r cos h \u00f03\u00de y \u00bc r sin h \u00f04\u00de Double differentiating these expressions, and substituting for accelerations in Eqs. (1) and (2), we were left with equations for the horizontal (Fh) and vertical (Fv) reaction forces at the pivot (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure14-1.png",
        "caption": "Fig. 14. Cross section of reluctance motor.",
        "texts": [
            " Both switched and synchronous PM motors are capable of very fast dynamic response in high-performance drive applications. Because of the high resistivity of the magnet material, the motor does not have any significant intemal time delay [35]. The response can be made essentially as rapid as the supply inverter can apply the appropriate phase currents. This rapid response can be achieved with a control system which is considerably simpler than the vector control discussed for induction motors. VII. SYNCHRONOUS-RELUCTANCE MOTORS Figure 14 shows a cross section of a simple two-pole synchronous reluctance motor [MI. The stator is identical with that of an induction or synchronous machine. A sinusoidally distributed rotating field is produced by a threephase set of sinusoidal stator currents in the windings. The rotor is shaped with a small air gap in the direct (d) axis and a large gap in the quadrature (4) axis. In addition, the rotor of this motor is made of iron laminations separated by nonmagnetic material to increase the reluctance to flux in the quadrature axis",
            " Power Factor The importance of the saliency ratio is emphasized by noting that the maximum power factor obtainable from the reluctance motor is equal to (A - l ) / (A + 1) requiring a ratio of A =I1 to reach a power factor of 0.85 [l]. To the extent that such high values of saliency are achieved, the performance of the reluctance motor can be made remarkably similar to that of an induction motor. The motor would be designed for continuous operation near the condition of maximum power factor. The rated torque would be in the range 0.54.6 of the maximum torque and the load angle 6 would be less than 45\". B . Configurations The type of rotor shown in Fig. 14 can achieve an unsaturated saliency ratio in the range 6 1 2 [45]-[47]. The effective saliency ratio will be decreased as the iron is magnetically saturated. This rotor can be made in a four- or six-pole configuration using appropriately bent laminations. A variety of altemate structures have been proposed.[48], [491 Reluctance motors can be operated in a switched mode similar to that discussed for PM motors. Uniformly distributed stator windings are used and pulses of current are supplied to the windings in sequence [50]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure1.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure1.11-1.png",
        "caption": "Fig. 1.11 Axes and deformation directions",
        "texts": [
            " Using the tetragonal crystal system [19]:\u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239d S1 S2 S3 S4 S5 S6 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u23a0 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 s11 s12 s13 0 0 0 s12 s11 s13 0 0 0 s13 s13 s33 0 0 0 0 0 0 s44 0 0 0 0 0 0 s44 0 0 0 0 0 0 s66 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u00d7 \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239d T1 T2 T3 T4 T5 T6 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u23a0 + \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 0 0 d31 0 0 d31 0 0 d33 0 d15 0 d15 0 0 0 0 0 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 \u00d7 \u239b \u239dE1 E2 E3 \u239e \u23a0 (1.13) Analogously: \u239b \u239dD1 D2 D3 \u239e \u23a0= \u23a1 \u23a3 0 0 0 0 d15 0 0 0 0 d15 0 0 d31 d31 d33 0 0 0 \u23a4 \u23a6\u00d7 \u239b \u239c\u239c\u239c\u239c\u239c\u239c\u239d T1 T2 T3 T4 T5 T6 \u239e \u239f\u239f\u239f\u239f\u239f\u239f\u23a0 + \u23a1 \u23a3 \u03b511 0 0 0 \u03b511 0 0 0 \u03b533 \u23a4 \u23a6\u00d7 \u239b \u239dE1 E2 E3 \u239e \u23a0 (1.14) 1.1 Actuator Principles 15 The deformation directions are shown in Figure 1.11. It is important to note that all the parameters used in (1.12) have to be considered in the different deformation directions. Depending on the electrical field application and the deformation of interest, piezoelectric actuators can be employed using different modes: \u2022 Longitudinal mode d33. See Figure 1.12(a). Expression (1.13) turns into: S3 = 6 \u2211 i=1 (s3iTi)+d33E3 (1.15) \u2022 Transverse mode d31. See Figure 1.12(b). Expression (1.13) turns into: S1 = 6 \u2211 i=1 (s1iTi)+d31E3 (1.16) 16 1 Actuator Principles and Classification \u2022 Shear mode d15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002466_s004220050558-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002466_s004220050558-Figure4-1.png",
        "caption": "Fig. 4. The trigger signal of the push-o is the stance leg angle reaching a critical value uPO . The push-o phase ends at heel contact. uPO is smaller than the trailing leg angle at beginning of the next step UTL",
        "texts": [
            " By increasing the sti ness of one of the muscles in a period where it can perform positive work, an additional activation force is obtained. A proper muscle activation pattern is needed to initiate this sti ness increase and to achieve a continuous cyclic motion. A very simple but e ective method is state triggering (Van der Linde, 1998b). Muscle activation dynamics is neglected, so the sti ness change is instantaneous. For the bipedal model, the trigger events are chosen intuitively as follows. The push-o trigger signal is chosen to be the stance leg angle reaching a critical value uPO (Fig. 4) on tPO. In orbit the trailing leg angle at the beginning of the step n Un TL equals the trailing leg angle at the beginning of the step n 1 Un 1 TL . Therefore, uPO cannot be chosen larger than UTL. During the push-o phase the stance leg plantar \u00afexor sti ness (Fig. 2b) will be increased by dCLEG. The push-o phase ends when the swing leg hits the ground. The hip activation is triggered at the beginning of the swing phase. During the activation period the swing leg hip extensor, and the stance leg hip extensor (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure5.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure5.11-1.png",
        "caption": "Figure 5.11. A schematic representation of a neuron",
        "texts": [
            " The following section deals in short with the functioning of the neurons which make up biological vision systems. The neurons in a neuronal network are connected to each other in a complicated way. If they receive sufficient stimulation, they are able to fire off so-called action potentials (APs) which are transmitted to the next neuron, where they may cause another fire-off. A neuron normally receives APs from several other (precursor) neurons and then transmits its APs to several other (successor) neurons. A neuron is schematically represented in Figure 5.11. The number of precursor neurons from which the neuron receives APs, and which therefore influence its response, is known as the \u201creceptive field\u201d. The APs arriving from the neurons of the receptive field have varying impacts on the behavior of the neuron; they are weighted. This weighting can also be negative; that is, having an inhibiting effect on the neuron. Whether a neuron fires off an AP to its successors or not depends on the weighted sum of the incoming potential. In fact, the exact firing behavior of a neuron is not just dependent on the weightings, but in addition on the timing at which the APs arrive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003558_physreve.80.011917-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003558_physreve.80.011917-Figure1-1.png",
        "caption": "FIG. 1. A cartoon of a \u201cbacterium\u201d as modeled by an anisotropic rod. For the wild types, the movements of the flagella not shown of the bacterium create a stress field which exerts an average force the drag force on the center-of-mass of the bacterium along its long axis and by Newton\u2019s third law, there is a reaction force the thrust force exerted on the fluids through its surface. Thus, the resulting active stress tensor for the effective medium bacteria +fluid is that of a force dipole, which is proportional the uniaxial order parameter Qij. For the tumblers, there are opposite forces exerted on both ends of the rod in the direction perpendicular to its long axis. The resulting active stress for tumblers is the biaxial order parameter.",
        "texts": [
            " To describe the local orientation of the bacteria, we employ a nonhydrodynamic variable, the symmetrictraceless alignment tensor Qij x , t , which, as expected, decays to zero in finite time in the isotropic phase. We first develop the phenomenological equations for an equilibrium two-component nematic liquid crystal in its isotropic phase. We then add to these equations the forces and torques arising from the active sources propelling the bacteria. Each bacterium is modeled as an anisotropic rod with force generators that create a stress field that exerts an average force on and an average torque about the center-of-mass of a bacterium see Fig. 1 . By Newton\u2019s third law, there must also be an equal and opposite force exerted on the fluid by the bacterium at its surface. The resulting active stress for the effective medium is obtained simply by adding up these forces for a collection of bacteria. In agreement previous studies 32,37 , we find that the active stress is proportional to the alignment tensor. We assume that the active particles, as well as the solvent molecules, are conserved t A = \u2212 \u00b7 gA, 1 t S = \u2212 \u00b7 gS. 2 These two equations imply the conservation of the total mass density = A+ S: t =\u2212 \u00b7g, where g gA+gS is total mo- mentum density",
            " For the moment, we will ignore the stochastic parts of the active forces and focus on the part with fixed value in the body frame, which we will continue to denote simply as f\u0303 i . In Appendix B, we will derive the contribution to the continuum equation noise for a particular model for stochastic active forces. We model the active particles as rigid biaxial rods with orthonormal sets of body axes 1,i , 2,i , and 3,i locked to the particle , where we take 3,i to be along the longest axis of the particle and 1,i to be along the shortest see Fig. 1 . We consider two cases. Case 1 : Wild type. The active force points on average along the long or \u201cthree\u201d axis. In this case, we can set dij =W\u0303 3,i 3,j , where W\u0303 has units of energy force times distance and we obtain the microscopic contribution ij A x,t = W\u0303 3,i 3,j x \u2212 x 16 to the active stress, which on course-graining can be expressed in the incompressible limit, when x = is a constant, as 011917-4 ij A x,t = Wc x,t Qij x,t + 1 3 ijWc x,t , 17 where W W\u0303 /mA, mA is the mass of an active particle, c x , t = A x / is its concentration field, and Qij x,t 1 nA x,t 3,i 3,j \u2212 1 3 ij x \u2212 x t 18 is the standard nematic order parameter 49 , where nA x , t = A x /mA is the number density of the active particles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003371_1.2768079-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003371_1.2768079-Figure6-1.png",
        "caption": "Fig. 6 Axis definition",
        "texts": [
            " The analysis which folow is that of Jones 10 applied on a double arched ball bearing. he equations for the inertia forces and moments on the ball j can e written as Fxj = 0 17 Fyj = 0 18 Fzj = mb 1 2 d\u0304m mj 2 19 M\u0304xj = 0 20 M\u0304yj = J Rj mj sin j 21 M\u0304zj = \u2212 J Rj mj cos j sin j 22 ith d\u0304m the pitch diameter when dynamic effects have acted on he ball defined by d\u0304m = dm + 2 fo \u2212 0.5 D + ol cos ol \u2212 2 fo \u2212 0.5 D cos f 23 ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms From Fig. 6, x = R cos cos 24 y = R cos sin 25 z = R sin 26 Internal Kinematics. Figure 7 shows the contact of the ball with the left-inner race. Assume that the ball is fixed in the plane of the paper. Let the inner race rotate with angular velocity i. According to Hertz, the radius of the elastically deformed surface in the plane of the major axis of the pressure ellipse is Ril = 2f iD 2f i + 1 27 From Fig. 7, a point Xil ,Yil on this race has the linear velocity due to the term i cos il: V1il = \u2212 i cos il d\u0304m 2 cos il \u2212 r\u0304il 28 where OCTOBER 2007, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002352_1.2830138-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002352_1.2830138-Figure7-1.png",
        "caption": "Fig. 7 Uniform spindle with resultant loads",
        "texts": [
            "F = 0 Ry + R2 + \u00a3 P,\u2022 = 0 f = i \u00a3M\u201e = 0 Rrlr + MRl + R2-lf n + MR2+ X ( / W i +M,) = 0 (10) ( = i Thus, the reaction forces are: *i = [ I (Pi(h ~ If) -M,)~ MRI - MR2]/L 1=1 n Ri = [ I (Pidr - /,) + M,) + MRl + MR2]/L (11) i=\\ The spindle is next transformed to a uniform shaft by the addition of applied shears and moments at each diameter step. For example, at the first element (Fig. 6) a shear and a moment are created in the uniform shaft: MH) (-Pi) Mal = l(j-j\\-Px{ai-lx)-Mx) (12) Equation (13) shows the shear and moment near the cutting tool tip, and the final transformed shaft is shown in Fig. 7. The moment of inertia / of the uniform shaft is selected as the largest inertia. K(\u201e-i> = -l(^~ - 7 W 1 + R2+lPi) Vn-l W ,= 1 MD(\u201e_\u201e = -l(~- - - W ( a \u00bb - , - lr) + \u0302 (fl,,-! - //) \\ A i - l in) 11-\\ + I {Ptian-y - /,) + M,) + MRl + MR2] (13) 1=1 MAY 1998, Vol. 120 / 389 Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/19/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ! IT \\kr\\ I I #H KA^ I, I*/1 (f\u00ab-l|IJL 4=Ui I I Fig. 5 Spindle discretization \u2022\u2022T\u2014-rif i l\u2014TT'\"\"f 3S1 \u00a3K A/ /\u201em, I \u00ab"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002557_20.124038-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002557_20.124038-Figure2-1.png",
        "caption": "Figure 2. Contours of magnitude of B with rotor 12 degree from aligned position.",
        "texts": [
            " Performing a variation on the new functional, we have 6II' = SII + 1 SA (& - I)~) dI'+ rL This is required to be zero for all variations of A, $,. and $S. The first surface term in the above equation simply reiterates tlie constraint of ( G ). The second and third identify X as being equal to That is, B . fi on the interface I'r; 111. RESULTS The new scheme has been implemented in three dimension and was used to model an switched reluctance motor which has been modelled previously using conventional Finite Elemeiits [4]. Figure 2 shows a computer generated t h e e dimensional view of the model with the rotor 12 degree away from the aligned position. The figure also shows a contour plot of the magnitude of I3. Figure 3 illustrates how tlie nodes of the stator and rotor region need not be joined at the interface. Figure 4 below shows liow tlie flux linkage for one stator pole obtained with the new schemes compares with earlier 2D results. The higher flux linkage exhibited iii tlie three dimensional results are caused by the end turns of the coil giving rise to higher flux densities at tlie end of the poles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure15.23-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure15.23-1.png",
        "caption": "Figure 15.23 A system of three forces acting on the body.",
        "texts": [
            " Note that the linear and angular quantities are analogous to each other in such pairs as x and (), v and w, a and (x, m and I, F and M, and p and L. Impulse and Momentum 335 336 Fundamentals of Biomechanics translational motion characteristics. The size and shape (i.e., in ertial effects) must be taken into consideration if the object is undergoing a rotational motion. Now that we have defined the basic concepts behind the rotational motion of rigid bodies, we can integrate our knowledge about translational and rotational motions to investigate their general motion characteristics. Consider the rigid body illustrated in Figure 15.23. Let m be the total mass of the body, and C be the location of its mass center. There are three coplanar forces acting on the body. Force F3 is not producing any torque about C because its line of action is passing through C (i.e., its moment arm is zero). Forces F 1 and F 2 are producing clockwise moments about C with magnitudes Ml =dlFl and M2 =d2F2, respectively. As illustrated in Figure 15.24, the three-force system can be reduced to a one-force and one-moment system such that L \u00a3 = F 1 + F 2 + F 3 is the net or the resultant force acting on the body and Me = Ml + M2 is the resultant of the couple-moments as measured about e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003077_3-540-53135-1_6-Figure21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003077_3-540-53135-1_6-Figure21-1.png",
        "caption": "Fig. 21. Schematic presentation of the mechanical model of an oriented and crystalline fiber: a chain spring in series coupling with a shear spring",
        "texts": [
            " The equation for the elastic tensile curve of the fibril with well-oriented chains is c 1 g = -- + (sin 2 qg) [1 - exp ( - o/go) ] ec 2- (17) where (s in 2 fPo) is the initial value of the orientation parameter before loading. The equation for the compliance shows that the elastic response of a fibril is equal to that of a serial arrangement of two springs, viz. a \"chain spring\" with modulus ec and a \"shear spring\" with modulus 2g0/(sin 2 cO). The chain spring provides the chain stretching contribution, ec = cy/ec, while the shear spring imparts the rotational contribution to the fiber strain cos ~ -- cos q~o ~r cos ~Po ~\u00a2 = e\" (chain) + E (shear) Simple series model This mechanical model is depicted in Fig. 21. The Eqs. (15) and (17) have been confirmed for aromatic polyamide fibers by a variety of experiments. Figure 22 shows the dynamic compliance versus the orientation parameter measured during extension of medium and high-modulus PpPTA fibers. It confirms the linear relation (15) and yields e\u00a2 = 240 G Nm -z and go = 2 G Nm -2. It has been shown that the tensile curves of the second and higher extensions of an aramid fiber are well described by Eq. (17) [143]. A relation between the strain and the dynamic modulus has been derived, which agrees welt with the experimental results [151, 152]",
            " Presumably this is caused by the combination of the rigid nature of the chains, the high crystallinity of the structure and the hydrogen bonding between the chains. By investigating the structural changes during creep and stress relaxation Northolt et al. [191, 192] arrived at a model for viscoelastic extension of well-oriented fibers. In these fibers the dynamic compliance, S, was found to be linearly related to the orientation parameter (sin 2 q0) according to Eq. (15). Thus by measuring S during creep and stress relaxation the change of the orientation distribution can be monitored. The modified series model shown in Fig. 21 has been extended to include the viscoelastic behaviour. To this end the simple assumption is made that the time-dependent part of the creep strain arises solely from the rotation of the chains towards the direction of the fibre axis as a result of the shear deformation of the crystallites. This yields for the fiber extension as a function of the time t during creep caused by a stress Co ~\u00b0 2 ~(t) -~ - - + (( sin2 q~o) -- ( sin2 q~(t))). e e (18) At any time the orientation parameter is given by the equation for the dynamic compliance (15) and we obtain G0 e(t) -~ - - + go[So - S(t)]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002756_tec.2003.822299-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002756_tec.2003.822299-Figure2-1.png",
        "caption": "Fig. 2. Balanced operation of SMSEIG: (a) Phasor diagram. (b) Phasor diagram showing detailed angular relationships.",
        "texts": [
            " Provided that the generator impedance angle lies between and rad, can be synthesized with the proper magnitude and phase angle as to yield perfect phase balance in the induction generator, as illustrated in Figs. 2(a) and (b). Under this condition, the induction generator operates with balanced phase currents and phase voltages and its performance is similar to a three-phase SEIG with balanced excitation capacitances and balanced load impedances. The currents , and can be adjusted easily by varying the capacitances , and . Fig. 2 also suggests that the SMSEIG is best suited for supplying high power factor (e.g., resistive) loads. The circuit configuration of the SMSEIG involves a threephase induction machine with asymmetrically connected stator windings and externally connected impedances. To determine the steady-state performance of the SMSEIG, a method that accounts for the winding asymmetry as well as the variable nature of the frequency and magnetizing reactance is proposed. The procedure is outlined as follows. \u2022 Set up and solve the \u201cinspection equations\u201d using the method of symmetrical components",
            " Performance of the SMSEIG can subsequently be obtained from the equations presented in Section III.A. The negative-sequence voltage must vanish for the threephase SEIG to operate with perfect phase balance [4]. Equating in (10) to zero, we obtain (16) Since lossless capacitances are used, . From (16), the values of and that give balanced operation are sin (17) sin (18) From (8) sin (19) Under balanced conditions, the following angular relationships in the SMSEIG may be deduced from the phasor diagram shown in Fig. 2(b): From the current phasor triangles, it can be shown that the line current and the stator phase current are related by sin (20) The phase angle between the line current and C-phase current in Fig. 2(b) is sin sin sin (21) If the load power factor angle is defined as positive when the line current lags the load voltage , then (22) Since when the phase voltages are balanced, the load admittance , referred to the base frequency, is given by sin (23) Equations (17)\u2013(19), and (23) give the conditions for perfect phase balance in the SMSEIG. Equations (17)\u2013(19) may be simplified when the load is purely resistive. Since the load power factor angle is now rad, it can be shown that the generator impedance angle is tan rad (24) The induction generator thus operates with an output power factor of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003864_s0094837300003286-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003864_s0094837300003286-Figure3-1.png",
        "caption": "FIGURE 3 . Simple rectangular plane used as a model to develop the account of tail action described in the text. A, long axis held horizontal: plan view (above) and side elevation. B , long axis elevated at hetero cercal angle: plan view (above) and side elevation. C, long axis held horizontal but model rotated along long axis: side elevation (above) and rear elevation (below). D, model both raised by heterocercal angle and rotated along long axis: side elevation (at left) and rear elevation (at right). For explanation of symbols, see text.",
        "texts": [
            " It is now apparent, however, that a funda mental objection to both the standard model and these modifications of it is that they are based on an incomplete assessment of the balance of forces acting within the tail fin. The key to understanding the situation actually is contained in Grove and NewelFs, Affleck's, and Aleev's papers but has not gained full attention. It is crucial to notice that the orientation of the whole tail at the heterocercal angle neces sarily directs the principal forward thrust produced by the tail action downwards by this angle. We may demonstrate the situation by considering a simple model (Fig. 3A-D). Take a rectangular plane as a model of the tail. If the plane is moved transversely through the water at an angle of inclination 0, there will be produced an oblique resultant force moving the tail with respect to the water (see Gray 1933 and Lighthill 1969) for detailed discussion). This force can be resolved as a forward (F ) and a transverse (T) thrust (Figure 3A). The relative magnitudes of F and T will depend on the value of 6 (F/T = cot 6). If the model is oriented with its long axis horizontal, the forward thrust will be directed horizontally. If it is raised at an angle (the heterocercal angle) from the horizontal, then the forward thrust F will be directed downwards; T remains transverse (Figure 3B). If the model is oriented horizontally but rotated along its long axis by angle rot (the angle of rotation), then the orientation of the forward thrust F will remain unchanged (i.e. direct along the long axis of the model); however, the transverse thrust T will produce a resultant that can be resolved into directly transverse (T\") and vertical (B) components (Figure 3C). The magnitudes T' and B are given by: T = T cos rot (1) B-T tan rot or B = T sine rot. (2) It will be noted that B is oriented perpen dicular to the long axis of the model. There fore, if the model is horizontal, B is vertical. If the model is again inclined at the hetero cercal angle het (Figure 3D) then B is inclined upward and forward at angle het from the vertical and can be resolved again to give a new vertical component B' = B cos het and an additional forward thrust C = B sine het. Therefore: B' = (T sine rot) (cos het) (3) and C = (T sine rot) (sinehet). (4) available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0094837300003286 Downloaded from https://www.cambridge.org/core. Stockholm University Library, on 02 Dec 2018 at 01:56:22, subject to the Cambridge Core terms of use, HETEROCERCAL TAIL 23 The absolute values of F and T will be diminished as the model is rotated along its long axis, because of the effective reduction of the frontal surface area of the fins",
            " The dorsal lobe of the tail, excluding the subterminal lobe, seems to act as a single unit, the notochordal mass and longitudinal hypochordal lobe having the same angle of rotation and dorsal thrust angle. The subterminal lobe acts separately, with its own angle of rotation and the ventral hypochordal lobe (here present) acts separately with its own angles of ventral elevation, thrust and rotation. We will therefore continue the analysis, below, in terms of these three units. Analysis We may now proceed to a discussion of the major factors modifying the simple model of tail action given above. The ratio F/T.\u2014As shown in Figure 3A, the relationship between F and T is given by the angle of inclination of the tail. However, the angle of inclination changes during each stroke of the tail. We cannot readily obtain the values of this angle from our pictures taken from directly behind the fish. Luckily how ever, Gray (1933) has given us an elegant study of the forces produced by the tail fin in fishes. Among the data he presents is a sequence of pictures of a shark (Squalus acan- thias), taken from directly above, from which such measurements can be taken"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure5.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure5.1-1.png",
        "caption": "Figure 5.1. Schematic diagram of the stereoscopic effect: F \u2013 fixed point; P \u2013 a point with equal disparity to F; Q \u2013 a point with a different disparity",
        "texts": [
            "1, an overview of the principles of stereoscopic image approaches is provided. In Section 5.2.2, the principles of stereoscopic imaging for SEMs are shown and in 5.2.3, the mathematical basics are presented. Section 5.2.4 gives an introduction to the subject of biological vision systems. The stereoscopic principle is described here with the help of the human visual system. This enables depth perception by using two eyes, which observe the surroundings from slightly different perspectives. This shift allows the brain to reconstruct the depth data. Figure 5.1 shows a schematic representation of the principle function. The eyes focus on a fixed point (point F), which thus impacts on the middle of the retinas of both eyes. The optical axes intersect at point F. If the retinal projections of point P are considered, which is at the same distance from the observer, it can be seen that relative to F, point P appears to be equally shifted in both the left and the right eye. On the other hand, point Q is placed in front of F and therefore results in dissimilar shifts in the left and right eyes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002528_978-3-662-04117-8-Figure13.22-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002528_978-3-662-04117-8-Figure13.22-1.png",
        "caption": "Figure 13.22: Experimental plant",
        "texts": [
            " As can be derived from the peak in the transient of the velocity, the time-optimal control is a very dynamic control concept by which the steady state is reached only after 125 ms. In the simulation the time-optimal controller alone is able to reach a steady state without any offset. This, of course, is possible be cause friction or any other disturbances were not implemented in the simulation model. For validation, the time-optimal controller was implemented at subsystem 3 of the experimental plant whose structure is shown in figure 13.22. The algorithm of the time-optimal controller was realized in the programming language C and implemented on a PC (for features see table 8.1) equipped with an AD/DA-board to read the actual and reference values of the web-force F23 and the velocity V3 from the plant's control system. During the operation of the plant, the controller accesses the data of the approximated control surface stored in the RAM of the PC. The actual value of fJ.M3GRNN is then determined from the control surface and transferred back to the control system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure4-1.png",
        "caption": "Fig. 4 PPR virtual chain",
        "texts": [
            " To facilitate the type synthesis of PPR-equivalent parallel kinematic chains, the conditions for a parallel kinematic chain to be a PPR-equivalent parallel kinematic chain can be described as: 1 Each leg of the parallel kinematic chain and a same virtual chain constitute a 3-DOF single-loop kinematic chain. 2 The wrench system of the parallel kinematic chain is the same as that of the virtual chain in any one general configuration. Condition 1 for PPR-equivalent parallel kinematic chains guarantees that the moving platform can undergo at least the PPRmotion, while condition 2 for PPR-equivalent parallel kinematic chains guarantees further that the DOF of the moving platform is 3. For a PPR virtual chain Fig. 4 , the wrench system is a 1- 0-2- -system, which is composed of a all the whose axes are perpendicular to the axis of the R joint and b all the 0 whose axes are perpendicular to the directions of the P joints and copla- rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 nar with the axis of the R joint, and c other which are linear combinations the above and 0. One set of basis wrenches of the 1- 0-2- -system is 01, 2, and 3. In any general configuration, the wrench system of a PPRequivalent parallel kinematic chain Fig. 3 a is the same as that of its virtual chain, i.e., a 1- 0-2- -system Fig. 4 . As the wrench system of a parallel kinematic chain is the union linear combination of those of all its legs in a general configuration 22 , the wrench system of any leg in a PPR-equivalent parallel kinematic chain is a subsystem of its wrench system. Here and throughout this paper, the wrench system of a leg is called a leg-wrench system. In the type synthesis of PMs, one is only interested in the leg-wrench systems in which there is a set of basis wrenches with 0- and/or -pitches. It is then concluded that any leg-wrench system with order ci 0 of a PPR-equivalent parallel kinematic chain is a 1- 0-2- -system, 1- 0-1- -system, 2- -system, 1- 0-system or 1- -system in a general configuration Fig",
            " For legs with ci=0, one is interested in legs with simple structures: RUS, PUS, and UPS legs. 1 By assembling two or more legs for PPR-equivalent parallel kinematic chains shown in Table 1, we obtain parallel kinematic chains in which the moving platform can undergo a PPRequivalent motion Fig. 9 . The geometric relation between different legs has also been shown in the notation of legs we proposed in Sec. 7. To guarantee that the DOF of the moving platform is three, the wrench system of the parallel kinematic chain must be a 1- 0-2- -system Fig. 4 . NOVEMBER 2005, Vol. 127 / 1117 3 Terms of Use: http://asme.org/terms Downloaded F It is found that not arbitrary set of m, where m 2, legs can be used to construct an m-legged PPR-equivalent parallel kinematic chain since the union of their leg-wrench systems may be not a 1- 0-2- -system. For example, a set of three RRR NRa legs Fig. 8 b cannot be used since the union of the their leg-wrench systems is a 1- 0-1- -system. Due to the large number of PPR-equivalent parallel kinematic chains and space limitation, only the families of 3-legged PPRequivalent parallel kinematic chains, which are denoted by the valid combination of sets of leg-wrench systems, are listed Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure9.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure9.4-1.png",
        "caption": "Fig. 9.4 System with two degrees of freedom",
        "texts": [
            "5) From this relation, we find the general condition {F - cl /1 - (f /IF } f = 0, (9.6) 9.2 Bifurcation Problems with Finite Degrees of Freedom lSI which has the same trivial solution as before, and a second solution I Ferit = clJl - (f /l)2, I (9.7) indicating an unstable equilibrium at the bifurcation point (see Fig. 9.3). F Ferit / stable ~(f) f Fig. 9.3 Load-deflection curve of the rigid bar Next, we consider a system of two pin-jointed rigid bars subjected to an ax ial compressive load F (see Fig. 9.4a). Again, the question is whether there can b) t c2h be equilibrium in the deflected form (Fig. 9.4b). As in the previous example, for small disturbances h, 12, each bar is in compressive direct loading of magnitude F. Therefore, each bar exerts a force F towards the joint and for equilibrium, we find F h + (F - c2l) 12 = 0 (9.8) These are homogeneous equations which are satisfied by f 1 = 12 = 0 correspond ing to the straight form, and also when the determinant of the coefficients vanishes F - C2 l I =0 F - 2c2 l (9.9) The characteristic equation F2 - F(CI + 2C2)l + CIC2l2 = 0 (9.10) 152 9. Stability of Equilibrium has the solution F1,2 = ~ { C1 + 2C2 \u00b1 V ci + 4c~ }, and more specifically (C1 = 2C2 = c) Fcritl = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002352_1.2830138-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002352_1.2830138-Figure3-1.png",
        "caption": "Fig. 3 Ball contact loads and centrifugal force",
        "texts": [
            " The inner ring groove center and ball center motion are defined by the contact angle a and the center lengths /. These are found geometrically, given the initial center length l0, the unknown ball displacement v, and the unknown inner ring displacement u. The contact deformation is then the change in the center length. O'I li l0i Og le l0i (3) Contact loads are calculated with Hertzian theory for spherical contact where K is the load-deflection parameter and is found using the method described by Harris (1990). Qi = Kt6}n Qe = Ke6ln (4) Examining Fig. 3, load equilibrium at the ball is the solution of two nonlinear equations for the unknown displacement of the ball center (ur, vz). A Newton-Raphson solution is used to solve this system numerically at each ball. Qi cos a, - Qe cos ae + Fc Qi sin a, \u2014 Qe sin ae (5) Global force equilibrium is established in terms of inner ring loads and the transformed ball reaction forces. An iterative solu tion of these equations is made using the Newton-Raphson tech nique. Bearing stiffness is found using the Jacobian matrix, giving the complete load-deflection relationship"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.37-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.37-1.png",
        "caption": "Figure 8.37 Under pure torsion, principal normal stresses( L1, L2) occur on planes whose normals are at 45\u00b0 with the centerline.",
        "texts": [
            " The transverse and longitudinal stresses are denoted with Tt and Te, respectively, and the equilibrium of the material element requires that Tt and Te are numerically equal. \u2022 A shaft subjected to torsion not only deforms in shear but is also subjected to normal stresses. This can be explained by the fact that the straight line AB deforms into a helix AB', as illustrated in Figure 8.30. The length l before deformation is in creased to length .e' after the deformation, and an increase in length indicates the presence of tensile stresses along the direc tion of elongation. \u2022 Consider the material element in Figure 8.37. The normals of the sides of this material element make an angle 45\u00b0 with the centerline of the shaft. It can be illustrated by proper coordinate transformations that the only stresses induced on the sides of such an element are normal stresses (tensile stress 0\"1 and com pressive stress 0\"2). The absence of shear stresses on a material element indicates that the normal stresses present are the prin cipal (maximum and minimum) stresses, and that the planes on which these stresses act are the principal planes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003600_tnn.2008.2008329-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003600_tnn.2008.2008329-Figure7-1.png",
        "caption": "Fig. 7. The 3-D mesh plot of the statistic performance function.",
        "texts": [
            " In the simulation, it is assumed that the unknown dynamic model is designed as (35) By solving LMI (9), it can be obtained that For DNN model (6), we select In the adaptive laws (24)\u2013(26), we select In the reference model (17), , , and . For sliding hyperplane , we select When the control input (23) and the adaptive laws (24)\u2013(26) are applied, the state of the identified nonlinear system (35) is shown in Fig. 3 and the state of DNNs (6) is shown in Fig. 4. Fig. 5 is the state of the dynamic reference model. Fig. 6 shows the sliding hyperplane . Finally, Fig. 7 shows the 3-D mesh plot of the integrated performance function. Figs. 3\u20137 demonstrate that a satisfactory tracking performance, identification capability, and robustness are achieved. On the other hand, in order to show the extensive applicability of the proposed method, we consider the following system: where and are set to and , respectively, and For this system, are the interval functions defined as follows: elsewhere where , . Other parameters are the same as in the previous design. Based on new B-spline models, the 3-D mesh plot of the integrated performance function is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.15-1.png",
        "caption": "Figure 6.15. Schematic drawing of a two-axes PVDF micro force sensor",
        "texts": [
            " A commercial five-axes IC wafer probe was used as a micromanipulation system at Michigan State University, USA, to automate the assembly of micromirrors. The mirrors usually lie on the substrate\u2019s surface after production and have to be brought into an upright position where they are locked mechanically. A two-axes PVDF-based force sensor was developed to measure the forces during the lift process [2]. For each axis of the sensors, two PVDF films are connected in parallel, and the two axes are assembled in series and rotated by 90\u00b0 (Figure 6.15). The entire sensor has a length of more than 4 cm and a height of 192 Stephan Fahlbusch more than 1 cm. It was calibrated by measuring its deflection under a light microscope; the stiffness required to calculate the force was determined from the Young\u2019s modulus and the geometry of the sensor. More and more applications in micro- and especially nanotechnology hit the lightoptical microscope\u2019s resolution limit of about 400 nm. Smaller objects, such as carbon nanotubes or nanowires with dimensions of several hundreds of nanometers down to only a few nanometers, cannot be resolved individually with a lightoptical microscope"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure12.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure12.1-1.png",
        "caption": "Figure 12.1 shows a large body m 1 able to move horizontally, a motion described by ql but restrained by a spring of stiffness Cl. Connected to ml is another body m2, which moves with relative motion q2, so that the force in the connecting spring is C2q2. To the body m 1 an external independent force F 0 sin Dt is applied horizon tally. Then from Newton's law the following system of differential equations",
        "texts": [
            "10) has been derived from a system of n equations: there remain n - 1 independent equations which establish the relative magnitudes of the ampli tudes iii- For example, suppose iil is chosen as the one arbitrary constant: the n - 1 ratios ii2j(jl, ... , iii/iil may be determined from the equations (12.9) after substi tution of each value of w5. For each natural frequency the different values of the iii / iil corresponding to that frequency describe the mode of vibration. Thus with the lowest eigenfrequency, the system oscillates in its first mode; and so forth. Let us consider the forced vibration of a typical undamped two DOF system such as shown in Fig. 12.1. The equations of motion of this system are (see Eqs. 12.1) mlih + Clql - C2q2 = Fa sin nt (12.11) m2(ih + ih) + C2Q2 = o. As with a system having a single DOF, the steady-state forced vibration will have a circular frequency agreeing with the excitation ql = iil sin nt , q2 = ii2 sin nt . Introducing these into the above equations, we find (-mln2 + cd iil -C2 ii2 = Fo -m2n2 iil +( -m2 n2 + C2) ii2 = 0, two equations for the two unknown amplitudes ii l, ii2; with the solutions iil = Fa (C2 - m2n2 )/D ii2 = Fa m2 n 2 / D , where D is the Lagrangian determinant of the free system, that is D= I Cl - ml n 2 -C2 I -m2n2 C2 - m2 n2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003414_ma00197a027-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003414_ma00197a027-Figure2-1.png",
        "caption": "Figure 2. Model for nucleation and substrate completion on a nonideal serrated surface. Note that the serration is on a molecular level. The first (u = 1) stem is put down at a cost in free energy of 2(21/2)bo~8,1 where us < u. Note that for a stem with a square cross section a. = 2bo. Each stem added to the substrate after the first incurs a free energy cost qfold + 2(21/2)bou,1, where us represents the nonideality of the substrate.",
        "texts": [
            " 7, 1989 Chain-Folded Systems with Lattice Strain 3047 Table I11 Summary of Results for the Serrated Edge Model with Lattice S t r a i d property non-steady-state nucleation, L = 0 (suppressed backward reaction) steady-state nucleation, L = 1 (fully active backward reactiodb k T a o ( W e-4(21/z)b~a.a./(AG3kT i = C ola(l/ao)[ 2 ( 2 1 ~ 2 ) b o u , l u ] [ K] I. nucleation rate i (nuclei cm-' s-'); i = Coofl(l/ao) also AG, and AT, AG, AG - 21/2a,/bo = (Ahr ) (AT, ) /T , AG, and A T , same as for L = 0 2. f l (events s-l) and K k T 2(2ll2) boas 3. initial lamellar thickness, cm \"The results given hold for the \"square\" model depicted in Figure 2 where a. = 2bo. This is a good approximation when a, = 2bo. The factor 2ll2 becomes 5'/*/2 when a0 = bo. The prefactors '21, '211, OZIII are in cm s-l deg-'. The prefactors *ZI and lZIII are in cm s deg-2, and '211 is in cm s-l deg+. b A factor [l - exp(-aobo6AG,/kr] appears in the derivation for g for the case z = 1. Because a, is small, 6 is large; accordingly this factor is essentially unity at normal undercoolings and this table reflects this approximation. Experiments are expected to correspond to regime 11",
            " matching point is that g,,,, has been set as the standard, and gnu, for t = 0 and c = 1 set equal to this q ~ a n t i t y . ~ Therefore, the absolute value of gnuc(c=O) is the same as gnuc(t=l), so that for g, pe=o/pt=l E 1. It is readily seen that the differences are minimal, showing that the forward reactions dominate all properties such as GI, GII, GnI, and 1,* that depend on the flux across the nucleation barrier. 111. Nucleation on a Nonideal Serrated Surface The serrated surface model is depicted in Figure 2. Note that the serration is on a molecular level. We shall follow the procedures devised for treating the flat surface model in essentially the same sequence, with both the c = 1 and t = 0 results being summarized in Table 111. We begin with a discussion of the thermodynamic behavior induced by the effect of as as a prelude to constructing A& and thence the rate constants. The origin of the lattice strain is the same as in the case of the flat surface model, i.e., it is caused by repulsions of chain folds that cause a general expansion of the lattice",
            " ~ + ~ ~ ~ 1 ~ z ~ ~ ~ u . l ~ / ~ ~ (23c) When compared with eq 22b, the ratios Ao/B1 and A / B show that detailed balance holds. From eq 23a one finds properties of the model, we treat the limiting case where there is no term in u whatsoever. Thermodynamics of Bulk and Surface States. It is necessary to emphasize at the outset that because of the different geometry of the chains on the serrated surface, AG,, Tm\u2019, AT,, and T, differ from those for the flat surface model. (Note the definitions of a. and bo in Figure 2.) For simplicity, we take the stem to be square and note that then a. = 2bo. Observe that bo plays the role of a layer thickness. The lattice strain energy is calculated as 2- (21/2)bousl divided by 2b021 = 21/2u,/b0, which is also equal to 2(21/2)u,/ao. This is essentially the \u201cburied\u201d interfacial surface free energy divided by the volume of a stem and as before has the units of free energy per unit volume. As each stem is added to the surface during substrate completion, it incurs an interfacial energy of 21/2bo~sl for each of the sides in contact with the substrate because of the strain in the substrate; by this accounting a \u201cburied\u201d stem experiences a us effect totalling 2(21/2)bo~,2 or 21/2aOu,l",
            " By introducing a minimal degree of flat surface character into the model by inserting a term 2y0ul for the first stem in eq 22b, where y o is a small vertical distance (\u201cblunted corner\u201d) associated with a utype surface, the infinities in i and 6 are avoided even when u, - 0. For example, 6 in eq 28 then becomes k T l ( 2 - (21/2)boa, + 2y0u). The unique properties of the serrated model as given by eq 30 are still retained with this modification for a wide range of us values provided that you is rather smaller than boa,. Equation 30 holds irrespective of whether 6 = 0 or E = 1 (Table 111). In the serrated surface model with chains possessing a square cross section such that a. = 2bo as depicted in Figure 2, the nearest point of \u201cadjacent\u201d reentry during substrate completion is actually a rather distant secondnearest neighbor. In this version of the model, the interaction between two adjacent stems on the substrate would be quite weak. In the version of the model where the shape of the molecular cross section is adjusted so that a. = bo (which corresponds more closely, for instance, to the 200 front in polyethylene) the interactions between adjacent stems on the substrate are somewhat more like those occurring between normal nearest neighbors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002528_978-3-662-04117-8-Figure8.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002528_978-3-662-04117-8-Figure8.1-1.png",
        "caption": "Figure 8.1: Backlash model",
        "texts": [
            " Its appearance is quite common in control systems with mechanical connections (e.g. gears). In contrast to other nonlinearities in electro-mechanical control systems, e.g. friction or eccentricities, backlash acts as a structure switching nonlinearity. This means that during time periods when the two com ponents of the backlash containing mechanical parts do not engage, the whole system is split into two decoupled subsystems. This causes special problems in the control of such systems. A model of backlash is shown in figure 8.1. In this chapter we address the problem of identification of backlash. There are nu merous contributions in literature that deal with the problem of controlling sys tems containing backlash. Tao and Kokotovic [7, 8] propose an inverse backlash model to compensate the backlash nonlinearity. However, this concept assumes that backlash is located at either the input or the output of the system, and that the available control signal is able to provide both very high and stepwise amplitudes. In the control concepts in [1, 2, 4, 5] it must be known in advance, if a system contains backlash and if so, its magnitude",
            " The parameter TN is the normalizing time constant, mw is an additional disturbance torque. The signal fiow graph is valid if we assume that the motor is so inert that variations in the position CPl occur slower than the twisting speed of the shaft. This means that the shaft does not transfer torque before the backlash comes into engagement. Without restrictions in the following derivat ions we can set the ge ar transmission ratio i = 1. Using this common two-mass system description, it must be noted that the complicated mathematical characteristic of backlash, described in figure 8.1, now simplifies to a deadzone characteristic. This is because the two components of the part containing backlash only get into the state of disengagement, if the shaft is not twisted, i.e. if ICPl - CP21 < aB\u00b7 This feature is very important with respect to the identification with a neural network. We only use the neural network as part of our observer structure to learn an unknown static nonlinear function. Considering the characteristic in figure 8.1 we detect that this characteristic is contradictory to the mathematical definition of a function. Thus, such a backlash nonlinearity cannot be approximated by a neural network directly. However, in an elastie two~mass system of figure 8.3, baeklash only appears as a deadzone which in fact is a mathematical function and thus ean be learned by a neural network. To apply the method of the systematic observer design introduced in chapter 5, we have to use the plant's state space representation. During the first steps of our considerations, we neglect the second nonlinear characteristic, friction F("
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure7-1.png",
        "caption": "Figure 7. Contact lines L~_I and Lc~ corresponding to meshing of rack-cutter }-~c with pinion and worm surfaces ~1 and ~ , respectively.",
        "texts": [
            " The relation between v~ and ~(w) is defined as v2 = ~(~)rp~, (4) where rpw is the radius of the worm pitch cylinder. Worm surface E~ is generated as the envelope to the family of rack-cutter surfaces Ec. STEP 4. The discussions above enable to verify simultaneous generation of pinion tooth surface E1 and worm thread surface E~, by rack-cutter surface E~. Each of the two generated surfaces E1 and Ew are in line contact with rack cutter surface Ec. However, the contact lines L d and L ~ do not coincide, but intersect each other as shown in Figure 7. Here, L~I and Low represent the lines of contact between Ec and El , Ec and E~, respectively. Lines L d and L ~ are obtained for any chosen values of related parameters of motion between E~, El , and E~ at the same t ime in the process of enveloping. Point N of intersection of lines L~w and L~I (Figure 7) is the common point of tangency of surfaces Ec, El , and Ew. GENERATION OF AN INVOLUTE PINION TOOTH SURFACE BY A CRINDING WORM. Direct derivation of generation of surface Ez by the grinding worm surface E~ may be accomplished as follows. (a) Consider tha t worm surface E~ and pinion tooth surface E1 perform rotat ion between their crossed axes with angular velocities w(~) and w(z). I t follows from discussions above tha t E~ and E1 are in point contact and N is one of the instantaneous points of contact of E,, and E1 (Figure 7). (b) The concept of direct derivation of Ez by E~ is based on the two-parameter enveloping process. The process of such enveloping is based on application of two independent sets of parameters of motion. Topology of Modified Surfaces 1069 (i) One set of parameters relates the angles of rotat ion of the worm and the pinion as Cw N1 - - z ~1 Nw ' ( 5 ) wherein N~ is the number of worm threads and N1 is the number of the pinion teeth. Usually, N~ - 1. (ii) The second set of parameters relates the displacement s~ of the worm (Figure 8), that is collinear to the axis of the pinion, and a small rotat ional angle ~1 of the pinion about the pinion axis as S w - p , ( 6 ) where p is the screw parameter of the pinion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure21-1.png",
        "caption": "Fig. 21. Face-gear drive with conical worm: bearing contact at the middle point of the cycle of meshing.",
        "texts": [],
        "surrounding_texts": [
            "The finite element analysis has been performed for a face-worm gear drive with conical worm of common design parameters represented in Table 1. For the analysis the model of the whole worm (Fig. 17) and the whole face-gear (Fig. 18) have been substituted by a model of five-pair of teeth in meshing (Fig. 19) in order to save computational time. Elements C3D8I of first order have been used for the finite element mesh. The total number of elements is 55 672 with 68 671 nodes. The material used is steel with Young\u2019s modulus E \u00bc 206800 N/mm2 and Poisson\u2019s ratio 0.29. The torque applied to the face-gear is 50 Nm. Figs. 20\u201322 show how the bearing contact looks at the beginning, at the middle, and at the end of a cycle of meshing. The results obtained by finite element analysis confirm the longitudinal path of contact and the avoidance of edge contact. Fig. 23 shows the variation of bending and contact stresses on the face-gear from the beginning of the contact to the end of contact on one tooth of the face-gear. The stresses are represented as unitless parameters in function of the worm rotation rm1 \u00bc r1 rmax1 ; \u00f013\u00de rm2 \u00bc r2 rmax2 \u00f014\u00de where r1 and r2 are the bending and contact stresses of Mises and rmax1 and rmax2 are the maximum bending and contact stresses of Mises on the face-gear. In the example developed, rmax1 \u00bc 168 N/mm2 and rmax2 \u00bc 1090 N/mm2. The load is always shared by three pairs of teeth, therefore the contact ratio is 3."
        ]
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure4.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure4.1-1.png",
        "caption": "Fig. 4.1 Stresses in an elliptical cross section",
        "texts": [],
        "surrounding_texts": [
            "The problem is solved (indirectly) by finding the stress function T which satisfies within the ellipse y2 z2 a2 + b2 = 1 the differential equation (4.14), and on the ellipse satisfies the boundary condition T = O. The function is { y2 z2 } T = m a2 + b2 - 1 , The stress components are (Eq. 4.13) 2z 2y IJxy = 2GrJm b2 ' IJxz = -2GrJm a2 The shear stress T is the resultant of IJ xy and IJ xz, and so y2 z2 T = 4GrJm a4 + b4 with the maximum value on the boundary at the ends of the minor axis, that is, at the points nearest the axis of the torsional rotations. 4.1 Solid Cross Sections 75 From Eq. (4.6), we determine by integration the function 7jJ(y, z) a 2 _ b2 7jJ = - Z--b2 yz. a + The lines of constant values of the warping are shown in Fig. 4.2. From these results, we can deduce the following relations MT Tmax = WT ' {} D Corresponding values of the polar moment of inertia J T and the section modulus W T may be determined for cross sections of different kinds: 1. Equilateral triangle Let the boundary of a torsion member be an equilateral triangle with h = V3a/2. Proceeding as for the elliptical cross section, we find MT Tmax = WT ' {} 1 3 WT = 20 a , V3 4 JT = -a . 80 (4.24) 76 4. Torsion of Prismatic Bars 2. Narrow rectangular cross section Consider a bar subjected to torsion. Let the cross section of the bar be a solid rect angle with width b and depth h, where b \u00ab h. From the different analogies (e.g. the soap-film analogy, originally proposed by L. Prandtl.),2 we may conclude that except for the region near z = \u00b1h/2 the stress components a xy and a xz are ap- f-b-j I y 1 Fig. 4.4 z Narrow rectangle proximately independent of z, and a xy ~ 0, a xz ~ T(Y) = 2G1'Jy. Thus, from Eq. (4.13), we determine T~T(y)= b; {l- (2:r}, and furthermore 1 3 Jr=3\"hb. (4.25) (4.26) (4.27) We note, however, that near the ends, of course, these results, which are valid only for narrow cross sections, do not apply. The exact theory for the rectangle is then required. The simple parabolic approximate form of T (Eq. 4.26) will give a good approx imation, since it differs from the true solution only in the small end zones. We may generalize Eq. (4.27) by introducing correction factors 0: and (3, as functions of the ratio h/b (see Table 4.1), to give 1 2 1 3 WT = 0: 3\" hb, Jr = (3 3\" hb . (4.28) 2 Analogies exist where physically different problems have similar mathematical descrip tions. In this case solutions - or experimental findings - from one problem may be trans ferred to the other - analogous - problem. The most known analogy to the torsion problem of prismatic bars is that of a membrane (soap film) fixed on a closed boundary, having the same shape as the cross section of the torsion bar, where pressure is applied to one side of the membrane. We therefore refer e.g. to the textbook of Boresi, Schmidt & Sidebottom, Advanced Mechanics of Materials, 5th. Edition, John Wiley & Sons, N.Y. etc., 1993. 4.2 Thin-Walled Closed Cross Sections 77 4.2 Thin-Walled Closed Cross Sections In the preceding section, we have discussed torsion of prismatic bars with solid cross sections. In the following sections, we now will examine this problem with thin-walled cross sections. We maintain the assumptions of St. Venant's theory about the displacement com ponents (Eqs. 4.1, 4.2), and furthermore - for the moment - assume unrestrained warping 'IjJ(y, z) in the x direction. In Section 3.2, we discussed beams of thin walled cross sections subject to shear forces. From this section, we take the modi fied description of thin-walled cross sections, with cross-sectional centerline (mid dle line), and additional rectangular coordinates (, along the centerline and 'f/, per pendicular to (. Thus, the thin-walled cross section is described by the coordinates y((), z(() of the centerline, and thickness J(() ofthe profile. for the shear stresses, and u=u(x,() (4.29) (4.30) for the displacements, constant in the 'f/ direction. We note that assumptions (4.29) coincide with the assumptions (3.37) for the shear stresses due to shear forces (Sec tion 3.2). Defining now the shear flow t( () as J 8/2 t(() = O\"xC, d'f/, (4.31) -8/2 we obtain with (4.29h t(() = T(()J((). (4.32) From the equilibrium (in axial direction) of a small element cut from the thin-walled tube (Fig. 4.6), we see that t = T( ()8( () = const. , (4.33) provided there are no axial stresses (J xx' Thus, the largest shear stress occurs where the thickness is smallest, and vice versa. Of course, if the thickness is uniform, then the shear stress T is constant around the tube. In order to relate the shear flow to the torque M T acting on the tube, consider an element of length d( in the cross section: The total shear force acting on the element is t de, and the moment of this force about any point 0 is dMT = a(()td(, (4.34) in which a( () is the distance from 0 to the tangent to the centerline. The total torque then is MT = t f a(()d( = 2Amt, (4.35) where the integral represents double the area Am enclosed by the centerline of the tube. From this equation, we find MT t = T(()8(() = 2Am ' (4.36) and finally, 4.3 Thin-Walled Open Sections 79 Tmax = (4.37) Bredt's first formula. To determine a relation between torque M T and twist {}, we start from assump tion (4.30), and (4.38) With these displacements, we find ) 1 { dux } ex((( =\"2 d( + {}a(() , (4.39) and thus from Hooke's law (4.40) Integrating this expression over the entire length of the centerline yields f T(() d( = c{ f dux + {} f a(() d(}. (4.41) The first integral of the right hand side vanishes (continuity of u x), and thus with Eq. (4.36), we finally arrive at 2 {f d( }-l Jr = 4Am 8(() , (4.42) Bredt's second formula. If in Eq. (4.41) the integrals are not taken over the entire length of the centerline, e.g. for the first integral of the right hand side J( dux = ux(() - ux(O) = {}{'l,b(() - 'l,b(O)} , (4.43) o Bredt's second formula is replaced by a slightly different relation (4.44) from which the distribution of the warping along the centerline may be calculated. 80 4. Torsion of Prismatic Bars Fig. 4.8 Thin-walled open section"
        ]
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure7.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure7.11-1.png",
        "caption": "Figure 7.11. Comparison of standard AFM tips and CNT-based supertips",
        "texts": [
            " The quality of information strongly depends on the size and shape of the AFM probes used. Commercially available AFM probes are usually made of micromachined silicon cantilevers with integrated pyramidal tips. Such tips have a typical radius of about 10 nm. Conventional AFM probes are, therefore, unable to penetrate highaspect-ratio structures and to exactly profile surfaces with a complex topography. CNT-based supertips with superior characteristics (stability, resolution, lifetime, etc.) can overcome the limitations of micromachined silicon tips (Figure 7.11). Supertips, however, cannot only be used as the main sensing component ultimately responsible for the quality of AFM imaging. Their extremely small size and their high conductivity also make them suitable to function as ultra fine nanoelectrodes able to electrically contact nanoscale structures in nanoelectronics. Characterization and Handling of Carbon Nanotubes 213 In order to realize the above-mentioned applications and to make use of carbon nanotubes in nanotechnology products, a complete and correct charaterization of carbon nanotubes must be achieved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003933_j.engfailanal.2010.11.009-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003933_j.engfailanal.2010.11.009-Figure6-1.png",
        "caption": "Fig. 6. 3D models of the main BW substructures.",
        "texts": [
            " Based on the results of the calculated stress state and the measured welding residual stresses, a safety estimation of the critical welded joints is carried out utilizing the Goodman diagram [9,10]. There are two main reasons for identifying the BW body stress state: (1) Carrying out proof stress. (2) The selection of tension-metric measuring locations. The BW body stress state is calculated by applying the linear finite element method (FEM). The 3D model of the BW, Fig. 4, is set up by the synthesis of 3D models of all structural parts, Fig. 6. The model represents the continuum discretized by the 4-node linear tetrahedron elements [11] in order to create the FEM model (1,917,704 nodes and 6,418,422 elements). The analysis of the external load is performed in accordance with the code [12]. It is worth mentioning that during the identification of the circumferential and lateral force, according to the above mentioned DIN code, the effects of the bucket wheel (BW) eccentricity are neglected in relation to the system lines of the boom and the boom inclination relative to the vertical and horizontal plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.14-1.png",
        "caption": "Figure 4.14 Example 4.2.",
        "texts": [
            " A frictionless knife-edge, point support, fulcrum, or roller can provide a support only in the di rection perpendicular (normal) to the surfaces of contact. Such supports cannot provide reaction forces in the direction tangent to the contact surfaces. Therefore, if there were active forces on the beam applied along the long axis (x) of the beam, these sup ports could not provide the necessary reaction forces to maintain the horizontal equilibrium of the beam. Example 4.2 The uniform, horizontal beam shown in Figure 4.14 is hinged to the ground at A. A frictionless roller is placed between the beam and the ceiling at D to constrain the counter clockwise rotation of the beam about the hinge joint. A force that makes an angle f3 = 60\u00b0 with the horizontal is applied at B. The magnitude of the applied force is P = 1000 N. Point C rep resents the center of gravity of the beam. The distance between A and B is l = 4 m and the distance between A and Dis d = 3 m. The beam weighs W = 800 N. Calculate the reactions on the beam at A and D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003795_978-3-540-85640-5_14-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003795_978-3-540-85640-5_14-Figure4-1.png",
        "caption": "Fig. 4. Illustration of the path following problem.",
        "texts": [
            " 3, where x denotes the robot state vector [xR yR \u03b8]T and xd is the desired state vector; xR and yR are robot position observed in the world coordinate system. Based on this input-output linearized system, path following and orientation tracking problems are analyzed with respect to the robot translation and rotation control in the following subsections. The influence of actuator saturation is also accounted to keep the decoupling between the translation and rotation movements. As one high-level control problem, path following is chosen in our case to deal with the robot translation control. The path following problem is illustrated in Fig. 4. P denotes the given path. Point Q is the orthogonal project of R on the path P . The path coordinate system xtQxn moves along the path P and the coordinate axes xt and xn direct the tangent and normal directions at point Q, respectively. \u03b8P is the path tangent direction at point Q. Based on the above definitions, the path following problem is to find proper control values of the robot translation velocity vR and angular velocity \u03b1\u0307 such that the deviation distance xn and angular error \u03b8\u0303R = \u03b1 \u2212 \u03b8P tend to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure3-1.png",
        "caption": "Fig. 3. Modification shape of the claw-shape.",
        "texts": [
            " 1, the claw profile consists of an arc, an Archimedean and an epitrochoid that is generated by the tip point of the claw. Hence, its contact type is point to curve. Followings explains the existing disadvantages of the current design and propose our ideas on the improvement: (1) As shown in Fig. 1, there is a larger gas carryover at the claw-shape. This means a larger gas may be carried from high-pressure port back to low-pressure port. Thus, the pump performance may be reduced. In this paper, we propose a new claw-shape whose concept design is shown in Fig. 3. This new design of claw-shape is similar to Kashiyama patent [16] as shown in Fig. 4. Kashiyama developed twin-screw compressor with square-threaded rotor for the vacuum system and distinguished from the conventional one by the extra large wrap angle except the tooth profile. The transverse sections of Kashiyama\u2019s profiles are formed by cycloid and involute curves and may not be conjugate at all. However, our design on claw-shape is completely conjugate. (2) As shown in Fig. 2, there is a gas carryover phenomenon between two mating rotors",
            " 5, where point g is an important location (related to parameters R and a) for the claw-shape, R is the distance from point g to Of, and a is the angle measured from the xf axial to point g. Point g can be represented in the coordinate system S1 as r \u00f0g\u00de 1 \u00bc R cos a R sin a 1 2 64 3 75 \u00f01\u00de As shown in Fig. 5, two rotors rotate with a constant gear ratio in opposite directions about parallel axes so that point g can generate a locus. The locus of the tooth profile r \u00f01\u00de 2 in coordinate system S2 is then obtained by coordinate transformation: r \u00f01\u00de 2 \u00bcM21r \u00f0g\u00de 1 \u00bcM2f Mf 1r \u00f0g\u00de 1 \u00f02\u00de where the superscript of r \u00f01\u00de 2 indicates the segment 1 of the claw-shape in Fig. 3 and M2f \u00bc cos / sin / 2r cos / sin / cos / 2r sin / 0 0 1 2 64 3 75 Mf 1 \u00bc cos / sin / 0 sin / cos / 0 0 0 1 2 64 3 75 In order to derive the conjugate profile of segment 1, we can copy the same profile as r \u00f01\u00de 2 on the rotor 1 and use u instead of /, which is written as: r \u00f01\u00de 2 \u00bc r \u00f01\u00de 2x r \u00f01\u00de 2y 1 2 64 3 75 \u00bc R cos\u00f0a 2u\u00de 2r cos u R sin\u00f0a 2u\u00de \u00fe 2r sin u 1 2 64 3 75 \u00f03\u00de In order to avoid the tooth interference during the meshing of claw-shape, we should find out the angle a and u first. Then, a and u can be found by solving equations r \u00f01\u00de 2x \u00bc r and r \u00f01\u00de 2y \u00bc 0 simultaneously. So, to give the parameters values R and r, then a and u can be solved. The equation of the claw-shape (segment 2 in Fig. 3) can be determined from Eq. (3) by coordinate transformation from coordinate system S1 to coordinate system S2 which yields r \u00f02\u00de 2 as follows: r \u00f02\u00de 2 \u00bcM21r \u00f01\u00de 2 \u00bc R cos\u00f0a 2/ 2u\u00de 2r\u00bdcos /\u00fe cos\u00f02/\u00fe u\u00de R sin\u00f0a 2/ 2u\u00de \u00fe 2r\u00bdsin /\u00fe sin\u00f02/\u00fe u\u00de 1 2 64 3 75 \u00f04\u00de where the superscript of r \u00f02\u00de 2 indicates the segment 2 of the claw-shape in Fig. 3. Subsequently, the equation of meshing can be represented as follows: f \u00bc or \u00f02\u00de 2 ou k ! or \u00f02\u00de 2 o/ \u00bc 0 \u00f05\u00de where k is the unit vector in the z direction. Substituting Eq. (4) into Eq. (5) yields the following: f \u00bc R\u00bdsin\u00f0a / 2u\u00de \u00fe sin\u00f0a u\u00de \u00fe r sin\u00f0/\u00fe u\u00de \u00bc 0 \u00f06\u00de Here, we must consider Eqs. (4) and (6), and then the conjugate curve will be generated. Finally, the complete claw-shape can be yielded. As shown in Fig. 6, the mathematical model of the circular arc can be represented in the coordinate system S1 as follows: ri;1 \u00bc cxi \u00fe qi cos h cyi \u00fe qi sin h 1 2 64 3 75; hi 1 < h < hi; i \u00bc 1\u20133 \u00f07\u00de where h0 = 0 and Ci = (cxi,cyi) are the centre of the three circular arcs represented in coordinate system S1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.32-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.32-1.png",
        "caption": "Figure 13.32 Expressing unit vectors !.h and h in terms of Cartesian unit vectors!. and L",
        "texts": [
            " That is, 111 and h define a set of local coordinate directions that vary in time. By employing proper coordinate transformations, we can express these unit vectors in terms of Cartesian unit vectors i. and j. Cartesian coordinate directions, which are global as opposed to local, are not influenced by the motion of point B. The coordinate transformation can be done by expressing unit vectors 111 and h in terms of Cartesian unit vectors i. and j. It can be observed from the geometry of the problem that (Figure 13.32): 111 = sin Olf - cos 01 i h = cos 01 i. + sin 01 i Therefore, the velocity and acceleration vectors of point B with respect to the XY coordinate frame and in terms of Cartesian unit vectors are: ll.B = \u00a3 1 WI (cos 01 \u00a3 + sin 01 D !lB = -\u00a31 W12 (sin 01 \u00a3 - cos 01 D If we substitute the numerical values of \u00a31 = 0.3 m, 01 = 30\u00b0, ll.B = 0.52\u00a3 + 0.301 (i) !lB = -0.60 \u00a3 + 1.041 (ii) Motion of point C as observed from point B: The motion of point C as observed from point B is similar to the motion of point B as observed from point A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure1-1.png",
        "caption": "Figure 1. Hobbing process.",
        "texts": [],
        "surrounding_texts": [
            "ELSEVIER\nAvailable online at www.sciencedirect.com MATHEMATICAL\nCa S C I E N C m D, n z \u00a2 T \u2022 COMPUTER MODELLING\nMathematical and Computer Modelling 42 (2005) 1063-1078 www.elsevier.com/locate/mcm\nTopology of Modif ied Surfaces of Involute Helical Gears with Line Contact\nDeve loped for Improvement of Bearing Contact , Reduct ion of Transmiss ion\nErrors, and Stress Analys is\nF. L. LITVIN Gear Research Center\nD e p a r t m e n t of Mechanical and Indust r ia l Engineer ing Univers i ty of Illinois at Chicago\n842 West Taylor Street , Chicago, IL 60607-7022, U.S.A.\nI . G O N Z A L E Z - P E R E Z * A N D A . F U E N T E S D e p a r t m e n t of Mechanica l Engineer ing\nPoly technic Univers i ty of Ca r t agena\nCampus Mural la del Mar, C / D o c t o r Fleming, s / n - 30202, Car tagena , Murcia , Spain ignacio, g o n za l ez@ u p c t , es\nK . H A Y A S A K A A N D K . Y U K I S H I M A Gear R&D Group, Research Deve lopment Center\nYamaha Motor Co., LTD 2500 Shingai, Iwata, Shizuoka 438-8501, J a p a n\n(Received August 2004; accepted October 2004)\nA b s t r a c t - - T h e main defects of misaligned helical gear drives with parallel axes are: edge contact, noise, and not favorable conditions of bearing contact. One of the greatest concern of manufacturing of helical gear drives (with parallel axes) is the edge contact of tooth surfaces that is caused by misalignment. At present, a t tempts to avoid edge contact are based on providing chamfers of the tooth surfaces of the gears that may be obtained by modification of the profile of the cutting hobs. The zones of tooth surfaces with chamfers and zones with conventional screw involute surfaces are not connected smoothly, in many cases the magnitude of required chamfers is not determined analytically, and the edge contact is not avoided. The finishing process of helical gears with chamfers is a complicated one. The existing design has to be complemented with TCA (tooth contact analysis). These are the reasons why a new topology of modified helical gear tooth surfaces with involute and crowned zones is proposed. An involute zone is provided in the central area of gear tooth surfaces that will allow line contact if misalignment does not occur. Zones at the top, bottom, front, and back sides of tooth surfaces are crowned and allows localization of the bearing contact when misalignments occur. Crowned zones with smooth connections to the involute zone are obtained as the result of profile and longitudinal crowning. The function of transmission errors is provided at each cycle of meshing as the sum of three branches. Two branches of a parabolic function at the extremes of the cycle of meshing are in tangency with the middle branch of zero transmission errors. The generation of gear\n*Author to whom all correspondence should be addressed. The authors express their deep gratitude to Yamaha Motor Co., the Spanish Ministry of Science and Technology (Project Reference DPI2004-00764 financed jointly by FEDER), and the Seneca Foundation (Project Reference PPC/01446/03) for the financial support of the research projects.\n0895-7177/05/$ - see front matter @ 2005 Elsevier Ltd. All rights reserved. doi: 10.1016/j.mcm.2004.10.028\nTypeset by .AMS-TEX",
            "1064 F . L . LITVIN et aI.\ntooth surfaces is accomplished by a grinding worm. This has required the solution of two problems, (i) determination of the worm thread surface that is conjugated to the theoretical pinion\ntooth surface, and (ii) generation by the grinding worm of a crowned pinion tooth surface.\nSimulation of meshing of misaligned gear drives is accomplished by application of TCA program developed by the authors. The formation of the bearing contact is analyzed considering more than one cycle of meshing. Existence of areas of severe contact stresses is avoided. The developed approach is illustrated with numerical examples. @ 2005 Elsevier Ltd. All rights reserved.\nK e y w o r d s - - G e a r design, Tooth contact analysis, Transmission errors, Stress analysis.\n1. I N T R O D U C T I O N\nCrowning of gear tooth surfaces is important for design of misaligned gears for improvement of the bearing contact and reduction of noise [1].\nAmong of different cutting methods of gear teeth like hobbing, milling, or shaping, hobbing is the most broadly applied due to its high productivity and low cost [2]. Figure la shows a hob for standard cutting and Figure lb illustrates the three motions required for the generating process: two rotational motions of the pinion blank and the hob, and the feed motion of the hob. Heat t reatment of gear tooth surfaces (performed after rough cutting) is required in many applications of gear drives. Then, a finishing process becomes necessary for elimination of distortions of tooth surfaces. Among the existing finishing processes, grinding is the preferable one due to its high accuracy [2]. Grinding by a worm-shape tool (see below) is an extension of the finishing of process of gears.\nThere is a tendency at present in application of hobs with a modified shape, for instance, of hobs that may produce a chamfer, cutting out the tip of the gear tooth (Figure 2). For this reason, the hob tooth is designed with a ramp. It is expected that the tool designer is familiar with the tooth element proportions and the applied design parameters such as the module, helix angle, shape of the chamfer, etc.\nChamfers on the top, front, and back sides of gear teeth are provided to avoid edge contact that may occur on the respective tooth part due to gear misalignment. Existence of chamfers complicates the finishing process, but this inconvenience has to be accepted.\nProviding of chamfers should not be considered as the indulgence of ignoring of possible existence of singularities in the zone between the chamfers and involute part of tooth surfaces.\nThe authors propose application for the finishing process of a worm-shape tool (Figure 3) that enables to obtain a modified regular tooth surface, avoid areas of severe contact stresses, and",
            "Topology of Modified Surfaces\n1065\nabsorb t r ansmiss ion errors, if they occur. I t is sufficient to modify the geometry of only one member of the ma t ing gears, usually, of the pinion.\nThe basic idea of the proposed finishing process by the gr inding worm is appl ica t ion of modified\nroll for the too th generat ion. The mot ions applied for genera t ion are,"
        ]
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure1.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure1.1-1.png",
        "caption": "Figure 1.1. Generic concept of the automated microrobot-based nanohandling station",
        "texts": [
            " The vacuum chamber of an SEM is for many applications the best place for a nanohandling robot. It provides an ample work space, very high resolution up to 1 nm, and a large depth of field (see Chapter 2 for more information). Quite a few research groups have recently been investigating different aspects of nanohandling in SEM, e.g., [78, 88, 89, 93, 94, 102, 108, 116, 121, 128, 129]. However, real-time visual feedback from changing work scenes in the SEM 10 Sergej Fatikow containing moving microrobots is a challenging issue, which is thoroughly analyzed in Chapter 4. Figure 1.1 presents a generic concept of the automated microrobot-based nanohandling station (AMNS), first introduced in [130] and further gradually developed at the University of Karlsruhe and the University of Oldenburg [120\u2013127]. Positioning with nanometer precision is the first precondition for the development of an AMNS. Typically, the microrobots are driven by piezoactuators with resolutions down to sub-nm ranges. The travel range is comparatively large with several tens of millimeters for stationary microrobots and with almost no limitation for mobile microrobot platforms [128, 131, 132]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002691_1.1357163-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002691_1.1357163-Figure4-1.png",
        "caption": "Fig. 4 A ball in contact with the outer and inner rings under the loads that are in the radial and axial direction",
        "texts": [
            "org/ on 05/07/20 where gW i is the distance between the z-axis and the curvature center of the inner race in vector form, and hW i is the radius of curvature of the inner race in vector form. The vector gW , according to Fig. 3 can be written as gW i5gi~~cos c!iW1~sin c! jW! (5) gi5di/21ri where c is the position angle between the x-axis and projection of the vector gW on the x-y plane. The vector hW , as shown in Fig. 3, can be written as hW i5hi~~cos u cos c!iW1~cos u sin c! jW1~sin u!kW ! (6) hi5ri then, Eq. ~4! can now be written as ~xi ,yi ,zi!5~~gi1hi cos u!cos c ,~gi1hi cos u!sin c ,hi sin u 1z i! (7) where z i in Eq. ~7!, according to Fig. 4, which is given as z i52~ri2D/2!sin a0 (8) JUNE 2001, Vol. 123 \u00d5 305 13 Terms of Use: http://asme.org/terms Downloaded F In Eq. ~8! ri is the radius of curvature of the inner race and a0 is the ball\u2019s contact angle under zero load. Here, the contact angles of the ball at the inner race and the outer race are assumed to be the same because the centrifugal force acting on the ball is ignored. Similarly, the coordinates of any point on the outer surface as shown in Fig. 2, are given as: ~xo ,yo ,zo",
            "org/ on 05/07/20 here, the two elastic deformations, dr and da , can be readily obtained from the experimental measures of the displacement gauge. Then Eq. ~9! can be rewritten as: ~xo ,yo ,zo!5~~go1ho cos u!cos c1jo ,~go1ho cos u! 3sin c ,ho sin u1zo! (13) the two tori with point i and point o as the center of two circles and ri and ro as the radius of two circles for the inner and outer races respectively, would intersect at two points. If c1 , c2 are the two intersecting points of these two circles, referring according to the illustration in Fig. 4, the contact angle a can be written as: a5p2u2b (14) The angle b, by the sine theorem, is given as: sin b ro 5 sin m A (15) then the angle b is obtained as: b5sin21S ro sin m A D (16) where A is the distance between two curvature centers, i and o. Based on the cosine theorem, the angle m satisfies the expression: cos m5 ri 21ro 22A2 2riro (17) In most practical applications, the bearing has the same radius of curvature for both the inner and the outer races (ro5ri). Consequently, Eq. ~16! can be further simplified to: b5cos21S A 2ro D (18) According to Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.17-1.png",
        "caption": "Figure 5.17 Normal and shear components of the joint reaction force.",
        "texts": [
            " (i) and (ii): FMx = (50)(cos300) = 43 N (+x) FMy = (50)(sin300) = 25 N (-y) From Eqs. (v) and (vi): F J x = 43 N ( - x) The resultant of the joint reaction force can be computed either from Eq. (iii) or (iv). Using Eq. (iii): Remark: F - F J x _ 43 = 86 N J - cos,8 - cos 60\u00b0 \u2022 The extensor muscles of the head must apply a force of 50 N to support the head in the position considered. The reaction force developed at the atlantooccipital joint is about 86 N. \u2022 The joint reaction force can be resolved into two rectangu lar components, as shown in Figure 5.17. FJn is the magnitude of the normal component of F J compressing the articulating joint surface, and F J t is the magnitude of its tangential compo nent having a shearing effect on the joint surfaces. Forces in the muscles and ligaments of the neck operate in a manner to counterbalance this shearing effect. Example 5.4 Consider the weight lifter illustrated in Figure 5.18, who is bent forward and lifting a weight Woo At the position Applications of Statics to Biomechanics 99 shown, the athlete's trunk is flexed by an angle e as measured from the upright (vertical) position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003847_icsma.2008.4505621-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003847_icsma.2008.4505621-Figure1-1.png",
        "caption": "Fig 1. Top view of quadrotor.",
        "texts": [
            " The OS4 project [4] was started in March 2003, with an aim to develop devices for searching and monitoring hostile indoor environments. The X4 Flyer project of Australian National University [5], aims at developing a quadrotor for indoor and outdoor applications. The control system of the vehicle is based on classical control methodology. 2. CONSTRUCTION AND ASSUMPTIONS The A quadrotor simply consists of four dc motors on which propellers are mounted. These motors are arranged at the corners of a X-shaped frame, where all the arms make an angle of 90 degrees with one another. As shown in Figure 1, two of the rotors or propellers spin in one direction and the other in the opposite direction. The motors labeled as MI and M3 spin in the clockwise direction with velocity and other two in the opposite direction. Each spinning propeller generates vertically upward lifting force. All the motion of machine is a consequence of this force. The mathematical model developed in this text is based on certain basic assumptions as given below: * Quadrotor body is rigid. * Propellers are rigid. * There is no air friction on quadrotor body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.15-1.png",
        "caption": "Figure 12.15 The free-body diagram of the ski jumper.",
        "texts": [
            " The length of the track is l = 25 m and the track makes an angle () = 45\u00b0 with the horizontal. If the skier starts at the top of the track with zero initial speed, determine the takeoff speed of the skier at the bottom of the track using (a) the work-energy theorem, (b) the conservation of energy principle, and (c) the equation of motion along with the kinematic relationships. Assume that the effects of friction and air resistance are negligible. Solution (a): Work-energy method The free-body diagram of the ski jumper is shown in Figure 12.15. The forces acting on the ski jumper are the gravitational force W and the reaction force applied by the track on the skis in a direc tion perpendicular to the track. The x direction is chosen to co incide with the direction of motion and y is perpendicular to the track. Therefore, the weight of the ski jumper has components along the x and y directions, such that Wx = W sin () = mg sin () and Wy = W cos () = mg cos (). On the other hand, N acts in the y direction. Note that Wx is the driving force for the skier"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003403_s10544-008-9214-3-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003403_s10544-008-9214-3-Figure2-1.png",
        "caption": "Fig. 2 (a) A picture of the ECC MDEA 5037 Au chip (b) An optical micrograph showing the three electrode electrochemical cell and the individual disc (insert) of the micro-disc array",
        "texts": [
            "1 Design and fabrication of MDEAs Micro-disc electrode arrays (MDEAs) are single electrodes formed from a single contiguous layer of electrode material with electrolyte exposures that occur through an array of micron-dimensioned openings formed through an insulator. The geometric area of the exposed electrode is therefore divided amongst an array of micron-dimensioned electrodes (50 \u03bcm diameter) each connected one to the other but separated from the electrolyte by a passivating layer (0.5 \u03bcm thick) of silicon nitride (Si3N4). Figure 2 gives pictures and optical micrographs of the ECCMDEA 5037 device used in this work and show the hexagonal packing arrangements of the individual discs of the array. The working electrodes are thus hexagonal arrays of recessed microdiscs, fabricated by photolithographic techniques, with each micro-disc residing at the bottom of a cylindrical cavity etched through the Si3N4 passivation layer. The ECC MDEA 5037 is a dual electrochemical cell on a chip, with a large area counter electrode and reference electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.5-1.png",
        "caption": "Figure 8.5 Method of superposition.",
        "texts": [
            " A cubical material element with sides parallel to the sides of the bar itself is shown in Figure 8.4, along with the stresses acting on it. ax and ay are the normal stresses due to the tensile forces applied on the bar in the x and y directions, respectively. If Ax = a band Ay = be are the areas of the rectangular bar with normals in the x and y directions, respectively, then ax and ay can be calculated as: Fx Fx ax = - =- Ax a b F F a-....L-....L y- A -be y Multiaxial Deformations and Stress Analyses 157 The effects of these biaxial stresses are illustrated graphically in Figure 8.5. Stress CTx elongates the material in the x direction and causes a contraction in the y (also z) direction. Strains due to CTx in the x and y directions are: CTX Exl =- E CTx Eyl = -v Exl = -v E Similarly, CTy elongates the material in the y direction and causes a contraction in the x direction (Figure 8.5b). Therefore, strains in the x and y directions due to CTy are: CTy Ey2 = E CTy Ex2 = -v Ey2 = -v E The combined effect of CTx and CTy on the plane material ele ment is shown in Figure 8.5c. The same effect can be repre sented mathematically by adding the individual effects of CTx and CTy. The resultant strains in the x and y directions can be determined as: CTx CTy Ex = Exl + Ex2 = E - v E CTy CTx Ey = Eyl + Ey2 = E - v E (8.6) If required, these equations can be solved simultaneously to ex press stresses in terms of strains: CTx = (Ex + V Ey) E 1 - v2 (Ey + v Ex) E (8.7) CTy = 1- v2 This discussion can be extended to derive the following stress strain relationships for the case of triaxial loading (Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003638_1.2900714-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003638_1.2900714-Figure3-1.png",
        "caption": "Fig. 3 Housing shape modifications",
        "texts": [
            " The oil sump is a parallelepiped with one face made of Plexiglas in order to visualize the oil flows around the pinions Fig. 2 . A variety of lubricants and gears with several immersion depths can be used in the test rig but the results presented in this paper are limited to spur steel gears Table 1 . The internal dimensions of the housing are 380 260 100 mm3, which, for all the gear configurations, lead to axial and radial clearances above 27 mm sufficient to minimize enclosure effects on churning losses. As shown in Fig. 3, some movable walls can be inserted in the gearbox, thus making it possible to modify the radial and axial distances between a wall and a gear face or top land. The minimum axial clearance that is possible is 1 mm while the minimum radial clearance is 5 mm. Thermocouples are used for measuring the ambient and the lubricant temperatures; they are also used to ensure that thermal equilibrium is attained. In order to carry out experiments with various lubricant temperatures, several heating covers have been placed on the external bottom face of the housing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002738_s0301-679x(01)00107-4-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002738_s0301-679x(01)00107-4-Figure2-1.png",
        "caption": "Fig. 2. Thermal EHL results of the finite line contact for Ue=6.0\u00d710 11, Ry=4 mm and x=1.5. (a) Surface of pressure P; (b) pressure contours in the end region; (c) surface of film thickness H; (d) film thickness contours in the end region; (e) surface of temperature T at Z=0.6; (f) temperature contours at Z=0.6 in the end region.",
        "texts": [
            " The number of nodes employed for the solution of the three-dimensional energy equations is 11 across the film, and 6 in both za and zb directions within solids a and b, respectively. The properties of the lubricant and solids used in the analysis are shown in Table 1. The lubricant properties coincide with those of the oil Shell Turbo 33, which is a typical lubricant for EHL problems. The properties for both solids coincide with those of steel. For all the results the film thickness is given by H=105\u00d7h/Rx. The thermal results obtained for the finite line contact of Ue=6.0\u00d710 11, Ry=4 mm and x=1.5 are illustrated in Fig. 2. In Figs 2(a) and (c) the surfaces of pressure P and film thickness H are plotted over the calculating domain. Within the film the highest temperature occurs in the layer of Z=0.6, therefore in Fig. 2(e) the surface of temperature T is plotted over this layer. Corresponding to the results shown in Figs 2(a), (c) and (e), contour maps of P, H and T are shown over the end region in Figs 2(b), (d) and (f), respectively. Because of side-leakage, the lubricating characteristics between the middle and the end of the roller are significantly different. That is, the lubricating situation in the end region is much worse than that in the middle region. Note that along the direc- tion of entrainment, in the end region the maximum pressure and the highest film temperature are much higher than in the middle region, but the minimum film thickness is much lower"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure2.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure2.1-1.png",
        "caption": "Figure 2.1. Two subsequent zoom-and-center steps during magnification of the object with diameter s . The left image has a lower magnification compared to the right one, i.e., kn > kn+1. In the right image, the parameters used in Equation 2.2 are shown. The inner square is used as the area of movement for the object with a diameter s .",
        "texts": [
            " Hence, the number of zoom-and-center (ZAC) steps should be minimized. It is therefore of considerable interest to calculate how many ZAC steps are at least necessary, until an object is sufficiently magnified, starting from a defined imaged area. For determining the number of steps, the following approach is sensible: the imaged area should be square-shaped with an edge length nk ; the minimum edge length of the next ( 1nk ) magnification step can then be determined by the following equation: 1 Pixel n Pos n Pixel u k H s u k A . (2.1) In Figure 2.1, the single terms are illustrated. The term H s represents the minimum desired image size, consisting of the structural size s of the object and the hull factor H. The structural size s is the size of an object (e.g., diameter of a carbon nanotube, CNT) or the distance between object and tool in a handling process. The hull factor H determines the image size compared to the object size needed for the handling process. After every zoom step, the object is centered again. The actuator performing this positioning step has an accuracy of Posu , which has to be added to the hull"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003366_tbme.2007.908069-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003366_tbme.2007.908069-Figure1-1.png",
        "caption": "Fig. 1. States of scissors and a plate at time t and t + dt of a cutting process. At time t, the plate is locally deformed. During time period dt, a small area of the plate h dx is cut.",
        "texts": [
            " DiMaio and Salcudean developed a force model for needle insertion based on the finite-element method [19]. Okamura et al. developed a force model for needle insertion based on experimental data [20]. When you cut an object with a pair of scissors, the force that you feel between your fingers includes two main components: friction forces of the contact of the blades and the forces of cutting of the object. In this section, we do not model the friction forces. However, we show in Section IV that friction forces can be measured by opening or closing empty scissors, and be summed into the model. Fig. 1(a) shows the interaction between a pair of scissors and a thin plate with thickness at the time when the plate is locally deformed. A Cartesian frame is defined at the pivot of the scissors such that the -axis is along the symmetry line of the scissors. The plate is located along and it does not move during cutting. We assume that the pivot of the scissors does not change orientation during cutting. For now, we also assume that the pivot of the scissors does not move. The opening angle of the scissors is defined by and the position of the edge of the crack made by the scissors is defined by . The blades locally deform an area of the plate around the crack edge. The deformation can take various forms including bending, stretching, compression, or a combination thereof. During deformation, the upper edge of the crack tip is displaced from to , where is a displacement length (see Fig. 1). In response to deformation of the plate, the force is applied to the upper blade along the normal to the blade\u2019s edge at point . is calculated by (1) where is a nonlinear function of the tip displacement, obtained by measurement or material properties. The torque caused by at the pivot is calculated by (2) where is the angle between the blade\u2019s edge and the centerline of the blade. ( is not zero because scissors\u2019 blades are slightly tapered as shown in Fig. 1.) The force felt by the user at the handle is calculated by (3) where is the distance between the pivot and the handle. The curve of the blade edge has a significant effect on the torque response of the scissors. Here, we define the curve of the edge of the upper blade in the Cartesian frame as (4) where is a point on the edge of the blade and is a nonlinear function. We obtain by fitting an analytical curve to the edge of the upper blade as shown in Fig. 2. We extract the blade edge from a real image of the blade. Considering (4), the displacement length caused by a blade with curve is obtained by (5) Fig. 1 shows two sequential time steps: and of a scissor cutting process. During , the opening angle of the scissors is changed from to , and the crack tip position is moved from to . The area of crack extension is . A fracture mechanics energy-based approach is used to estimate the torque and the crack tip position during cutting. Based on the principle of conservation of energy (6) where is the external work applied by the scissors, is the change in elastic potential energy stored in the plate, and is the irreversible work of fracture",
            " The high-frequency torque fluctuations are formed as a sequence of deformation and rupture phases. The average torque during 2 to 3 is predicted by (12). We now consider the case that the blades of the scissors slice through the plate to cut it. First, the scissor blades are closed and deform the plate. Then the pivot of the scissors are moved along -axis and cut the plate. The force caused by deformation force (22) at the pivot along is calculated by (18) where is the angle between the upper blade edge and the -axis (see Fig. 1). The torque applied to the upper blade is calculated by (2), considering as the distance between the crack edge and the pivot. Sharp cutting starts when the torque reaches the sharp cutting torque level calculated by (15) and continues as long as the pivot moves toward the plate. The torque and force applied to the pivot remain constant during cutting if the opening angle of the scissors does not change. A series of cutting experiments were performed to validate the analytical model. A two-degree-of-freedom robot holding a pair of scissors (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.8-1.png",
        "caption": "Figure 3.8 Moment is invariant under the operation of sliding the force along its line of action.",
        "texts": [
            "4 Dimension and Units of Moment By definition, moment is equal to the product of applied force and the length of the moment arm. Therefore, the dimension of moment is equal to the dimension of force (ML/T2) times the dimension of length (L): [MOMENT] = [FORCE] [MOMENT ARM] = ~; L = ~;2 The units of moment in different systems are listed in Table 3.1. 3.5 Some Fine Points About the Moment Vector \u2022 The moment of a force is invariant under the operation of slid ing the force vector along its line of action, which is illustrated in Figure 3.8. For all cases illustrated, the moment of force about point 0 is: M=dF (ccw) where length d is always the shortest distance between point 0 and the line of action of F . Again for all three cases shown in Figure 3.8, the forces generate a counterclockwise moment. \u2022 Let F 1 and F 2 shown in Figure 3.9 be two forces with equal magnitude (Fl = F2 = F) and the same line of action, but acting in opposite directions. The moment Ml of force F 1 and the mo ment M2 of force F 2 about point 0 have an equal magnitude (Ml = M2 = M=dF), but opposite directions (Ml = -M2). \u2022 The magnitude of the moment of an applied force increases with an increase in the length of the moment arm. That is, the greater the distance the point about which the moment is to be calculated from the line of action of the force vector, the higher the magnitude of the corresponding moment vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003933_j.engfailanal.2010.11.009-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003933_j.engfailanal.2010.11.009-Figure8-1.png",
        "caption": "Fig. 8. Measuring forces in the tie-rods of BWB SRs 1200.",
        "texts": [],
        "surrounding_texts": [
            "The analysis of the external load is performed in accordance with the code [12]. It is worth mentioning that during the identification of the circumferential and lateral force, according to the above mentioned DIN code, the effects of the bucket wheel (BW) eccentricity are neglected in relation to the system lines of the boom and the boom inclination relative to the vertical and horizontal plane. Therefore, based on the model containing the above mentioned effects, Fig. 7, the in-house software RADBAG has been developed and validated [13,14], Figs. 8 and 9. This software enables the definition of the effect of resistance-to-excavation in any position of the bucket wheel boom (BWB). Functioning of the BWE is characterized by the phenomenon of an outstandingly dynamic character. The basic cause of this phenomenon is the fact that the buckets repeatedly get into contact with soil i.e., the changeability of the number of buckets to catch the soil. In this particular case, dynamic characteristics of the external load (f), shown below in Fig. 10, have the values provided in Table 1: Coefficient of non-uniformity knun \u00bc fmax fmin and Coefficient of dynamism kdyn \u00bc 2 fmax fmax \u00fe fmin The stress\u2013strain state is identified for the group of load cases including possible combinations: (a) intensity of force resisting excavation; (b) value of coefficients of radial (kN) and lateral (kB) component of force resisting excavation; (c) direction of the radial component; (d) position of the tooth the load is being applied on. (a) The intensity of the force resisting excavation is determined for two cases: the nominal and the limit parameters of the BW drive. (b) According to the results of the researches provided in [15], the load analysis is performed for kN = 0.6 and kB = 0.25. (c) Depending on the excavating conditions, the radial component can be directed to the BW or to the pit face. (d) During the excavation of soft or relatively soft stones, the distribution of the tangential component of the force resist- ing excavation over the bucket and teeth is very uneven. According to the results of experimental investigations, periodically up to 90% of the tangential component of the force resisting excavation affects one bucket. That load can even be concentrated on one tooth only."
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.39-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.39-1.png",
        "caption": "Figure 4.39 Free-body diagram of the block.",
        "texts": [
            " Determine the magnitude P of the minimum force the person must apply in order to overcome the frictional and gravitational effects to start moving the block in terms of W, IL, and e. Solution: Note that if the person pushes the block by applying a force closer to the top of the block, the block may tilt (rotate in the clockwise direction) about its bottom right edge. Here, we shall assume thatthere is no such effect and that the bottom surface of the block remains in full contact with the ground. The free-body diagram of the block is shown in Figure 4.39. x and y correspond to the directions parallel and perpendicular to the incline, respectively. P is the magnitude of the force ap plied by the person on the block in the x direction, f is the frictional force applied by the ground on the block in the neg ative x direction, N is the normal force applied by the ground on the block in the positive y direction, and W is the weight of the block acting vertically downward. The weight of the block has components in the x and y directions that can be de termined from the geometry of the problem (see Figure A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure9.8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure9.8-1.png",
        "caption": "Figure 9.8. Schematic representation of a cross-section of an indentation pile-up (from [9], with kind permission of the Japanese Journal of Applied Physics, Institute of Pure and Applied Physics)",
        "texts": [
            " Myiake et al. [9] analyzed the influence of the pile-up on the results obtained by nanoindentation experiments. They conducted such experiments by means of a commercial AFM (atomic force microscopy) system, equipped with a rectangular stainless steel AFM cantilever with a diamond tip, on reference specimens (fused silica and single-crystal silicon). For the determination of the contact area, they analyzed the data by means of the Oliver and Pharr method and by direct measurement of this area with an AFM. Figure 9.8 shows a schematic representation of a cross-section of an indentation with pile-up. They found that the results obtained by the Oliver and Pharr procedure were overestimated. Therefore, it can be concluded that for very precise results, it is very useful to measure the contact area of the residual imprint after the indentation tests. As we have seen, the only difference in calculating the Young\u2019s modulus by instrumented indentation for indenters with a different shape is the factor introduced by Oliver and Pharr [7] in Equation 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure8-1.png",
        "caption": "Fig. 8 Some legs for PPR-equivalent parallel kinematic chains",
        "texts": [
            "3 Type Synthesis of Legs for PPR-Equivalent Parallel Kinematic Chains. The type of a leg for PPR-equivalent parallel kinematic chains can be represented by a chain of characters representing the type of joints from the base to the moving platform in sequence. By removing the virtual chain in a 3-DOF single-loop kinematic chain involving a virtual chain, one leg for PPR-equivalent PMs can be obtained. For example, by removing the virtual chain in an RRR N RR IV kinematic chain Fig. 7 d , an RRR N RR I leg Fig. 8 d can be obtained. Figure 8 shows some legs for PPR-equivalent parallel kinematic chains and their leg-wrench systems. The leg-wrench system of the RRR NRa leg Fig. 8 b is a 1- 0-1- -system. Its basis can be represented by a rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 whose axis is perpendicular to the axes of all the R joints within a same leg and a 0 whose axis intersects the axes of the Ra joint and is parallel to the axes of the R joints within RRR N. The leg-wrench systems of the RA RRR BRA leg Fig. 8 e and the RR B RRR A leg Fig. 8 f are both a 1- -system. The axis of the basis wrench is perpendicular to the axes of all the R joints within a same leg. All the legs for PPR-equivalent PMs obtained are listed in Table 1. For legs with ci=0, one is interested in legs with simple structures: RUS, PUS, and UPS legs. 1 By assembling two or more legs for PPR-equivalent parallel kinematic chains shown in Table 1, we obtain parallel kinematic chains in which the moving platform can undergo a PPRequivalent motion Fig. 9 . The geometric relation between different legs has also been shown in the notation of legs we proposed in Sec. 7. To guarantee that the DOF of the moving platform is three, the wrench system of the parallel kinematic chain must be a 1- 0-2- -system Fig. 4 . NOVEMBER 2005, Vol. 127 / 1117 3 Terms of Use: http://asme.org/terms Downloaded F It is found that not arbitrary set of m, where m 2, legs can be used to construct an m-legged PPR-equivalent parallel kinematic chain since the union of their leg-wrench systems may be not a 1- 0-2- -system. For example, a set of three RRR NRa legs Fig. 8 b cannot be used since the union of the their leg-wrench systems is a 1- 0-1- -system. Due to the large number of PPR-equivalent parallel kinematic chains and space limitation, only the families of 3-legged PPRequivalent parallel kinematic chains, which are denoted by the valid combination of sets of leg-wrench systems, are listed Table 2. Using Tables 1 and 2, PPR-equivalent parallel kinematic chains of different families can be obtained. Let us take PPR-equivalent parallel kinematic chains of family 3 Table 2 as an example"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002518_s0263574797000027-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002518_s0263574797000027-Figure12-1.png",
        "caption": "Fig . 12(b) . Obstacle Avoidance Joint Solutions at 15 Tool Tip Positions .",
        "texts": [
            " With the joint angle and link parameters defined in Table III , the positional forward kinematics is expressed as follows : X 5 C 1 [ d 6 ( C 2 3 C 4 S 5 1 S 2 3 C 5 ) 1 S 2 3 d 4 1 a 3 C 2 3 1 a 2 C 2 ] 2 S 1 [ d 6 S 4 S 5 1 d 2 ) (15) Y 5 S 1 [ d 6 ( C 2 3 C 4 S 5 1 S 2 3 C 5 ) 1 S 2 3 d 4 1 a 3 C 2 3 1 a 2 C 2 ] 1 C 1 ( d 6 S 4 S 5 1 d 2 ) (16) Z 5 d 6 ( C 2 3 C 5 2 S 2 3 C 4 S 5 ) 1 C 2 3 d 4 2 a 3 S 2 3 1 a 2 S 2 (17) A set of 15 points on a straight line , as shown in Figure 11(a) and listed in Table IV , is used for training . The first run of training is in the environment without obstacles . We use a neural network with 45 neurons at the hidden layer . In order to obtain the elbow-up solution , q 0 is chosen as (0 8 , 2 90 8 , 90 8 , 0 8 , 0) T . It took 1765 iterations to reduce the kinematics error E 0 to below 0 . 001 . The joint solutions are plotted in Figure 11(b) . The robot links of the solution are almost in a plane . When there is an obstacle in the work space as shown in Figure 12(a) , the obstacle avoidance solution took 3826 iterations to reduce the kinematics error to below 0 . 001 . The joint solutions are plotted in Figure 12(b) . http://journals.cambridge.org Downloaded: 03 Jul 2014 IP address: 138.37.211.113 The robot links are no longer in a plane , rather they are twisted to avoid the obstacle . A neural network technique has been introduced in this paper to solve the inverse kinematics problem of redundant robot manipulators with obstacle avoidance capabilities . The solution technique requires only the knowledge of robot forward kinematics including the corresponding Jacobian . Both obstacle free and obstacle avoidance cases were studied "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003218_978-94-011-2526-0_1-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003218_978-94-011-2526-0_1-Figure3-1.png",
        "caption": "Fig. 3 POSitioning substructure",
        "texts": [
            " Finally, a numerical example confirms the new theoretical results. Kinematic model. When a set of actuator displacements is given the manipulator becomes a statically determined structure (see Fig. 2), denoted as 6-4 structure, and the position analysis reduces to find all possible closure configurations of the structure. A careful inspection of Fig. 2 shows that the 6-4 structure can be analyzed by considering first a statically determined substructure, called positioning substructure, which is responsible for the positioning of reference point Q (see Fig. 3). Once the position of point Q has been determined, the orientation of the platform W can be found by referring to the structure of Fig. 4, which represents the most general fully-parallel constraint defining the relative orientation of two bodies having a point in common. Thus position and orientation of the platform can be solved separately. Determination of point Q Dosition. The geometrical dimensions of the base are given; hence the coordinates of points Pi, i=1,3, in an arbit rary reference coordinate system WA fixed to the base are known (see Fig. 3). For a given input the leg lengths Hi, i=1,3, are also known. The closure equations of the positioning substructure are: ( 1.1) (1. 2) (1. 3) Provided the three points Pi, i=1,3, are not aligned, the following expression is introduced: (2) where 0, ~, and a are parameters to be determined. Equations (1), after some algebra, become: { 02(P2-P,)2+~2(PS-P1)2+02[(P2-P1)X(P3-P1)]2+ 2-0-~-(P2-P,)-(P3-Pl) = H12 a-(P2-p,)2 + ~-(P2-Pl)-(P3-P,) = [H,2_H2 2+(P2-P,)2]/2 a-(P2-p,)-(Ps-P,) + ~-(Pa-p,)2 = [H12-Ha 2+(Pa-P, )2]/2 (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002791_s0957-4158(99)00052-5-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002791_s0957-4158(99)00052-5-Figure1-1.png",
        "caption": "Fig. 1. Zero Moment Point (ZMP).",
        "texts": [
            " To generate natural motion is equal to \u00aending the motion which minimizes the total energy consumption which is required for all actuators in the robot system. Then, we consider the conditions for stable walking. Biped locomotion robots must be controlled under the possibility of falling down. So the reference trajectory of biped locomotion robots must be generated without falling down. From these reasons, we must consider many kinds of conditions for continuous walking without falling down. The moment is generated by the \u00afoor reaction force and torque. Fig. 1 shows the concept of Zero Moment Point, where p is the point that Tx=0 and Ty=0. Tx, Ty represent the moments around x axis and y axis generated by reaction force Fr and reaction torque Tr, respectively. The point p is de\u00aened as the Zero Moment Point (ZMP). When the ZMP exists within the domain of the support surface, the contact between the ground and the support leg is stable. pzmp x zmp, yzmp, 0 2 S 1 where pzmp denotes a position of ZMP. S denotes a domain of the support surface. This condition indicates that no rotation around the edges of the foot occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002898_0890-6955(95)00091-7-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002898_0890-6955(95)00091-7-Figure5-1.png",
        "caption": "Fig. 5. Coordinate system for LLLRR type machine.",
        "texts": [],
        "surrounding_texts": [
            "The transformation of axes from one link to another can be described completely by four kinematics parameters, called D - H parameters (see Fig. 2). Let us assume that the transformation between frame (n - 1) and frame (n) is given by A,: A,, = R(Z,O,,). T(O,O,d,,). T( ot~,O,O).(X,a,,) (1) a~ = movement along axis x.; an = turn around x.. 226 R. Md. Mahbubur et al. If the joints are prismatic then \u00ae. is constant and d. is variable. In the case of a revolute joint, O. is variable and the others are constants. The total transformation is denoted by the matrix T. If the A,. matrix describes transformation with respect to the base coordinate system, then Tto t -- Am.Ts.A L (3) where AL contains the tool length L. The position of the tool tip is described by 4 \u00d7 4 homogeneous matrix: Trot = ny Gy ay py (4) Gz az Pz 0 0 where [ax, ay, az] T is the tool direction and [Px, Py, Pz] T is the tool tip position in the base coordinate system (see Figs 3-5, Table I), and where cos (iMJT) is the cosine of angle (dot product) between the iM and JT axes. Ttot = Am.Ts.A L -cosCcosB -sinC -cosCsinB -cosC.sinB-L + X | -sinCcosB cosC -sinCsinB sinC.sinBL + Y-am Trot / / sinB 0 - c o s B - c B . L - ~ Z \" ~ - d m [ o 0 0 1 (6) (7) The direction cosine of the tool is given by 228 R. Md. Mahbubur et aL ail \"-cosCsinBav = -sinCsinB a - cosB =I arctan(a ) [ Xp+COsCsin., ] - _ ly, + inCsin L-aq L Zp+cBL+dm ] (8) (9) (I0) 2.2. Zero reference model The machine zero point is the point where the joint displacements are zero. The displacement in the reference coordinate system is given by Tmt= Am'AI~2~3~4~5\" ~ (11) where A i is the transformation matrix in the reference coordinate system and is described by the Rodrigues equation and To is the transformation at the machine zero position. 2.2.1. Rotation around an arbitrary axis. If the rotational axes are not perpendicular to each other (although they should be), then there exists rotation around an arbitrary axis in the space; the dot product of two orthogonal axes is not zero [for example, cos(90) = 0, but cos(89.99) ~ 0]. Though the variation is small, we cannot neglect it because small variations in angular error gives a large tool tip deviation from the desired position depending on the length of tool and the spindle pivot distance. Let us now think about three-dimensional rotations of a point P around a line with a direction cosine of l, m and n. P* is the new position of P after rotation O. The rotation matrix is given by the Rodrigues equation [7, 8]: R = I F v 0 + c 0 lmvO-nsO lnv0+ms0 0 ImvO+nsO m2v0+c0 mnvO- /sO 0 lnv0-ms0 mnvO +/sO n2v0 + cO 0 0 0 0 1 (12) where v\u00ae is 1 - cosO, sO is sin\u00ae and cO is cos\u00ae. p . = [ R 0 0 0 (I-R)P~].p (13) Where P* and P are the final and initial points, respectively, and I is the identity matrix. P~ is the point where the axis of rotation passes. 2.2.1.1. Revolute joint. If the joint is revolute then we need five parameters to describe the rotation completely: two for the direction cosine, two for rotation center offsets, one for the rotation angle (\u00ae). 2.2.1.2. Prismatic joint. For the prismatic joint, we need three independent parameters to describe it completely. Here the displacement is d and the direction cosine is [1, m, n] from which two are required. The transformation is given by Positioning accuracy improvement in five-axis milling by post processing 229 0 0 1 O d . m 0 1 (14) 0 0 Now the final transformation is given by Ttot = Am'A t'A2\"A3\"Aa'As'To (15) To is the transformation at the zero position and Ai is the transformation based on the Rodrigues equation. 2.2.2. Error model offive-axis machine tools. Joint axes orientations are varied with the degree of misalignment. If we find the value of l and n in the reference coordinate system then m is given by m = l ~ 1 2 - n 2 (16) The location of the actual joint varies with the location of the plane. In the modeling of the zero position, the machine zero position and the coordinate system are defined before defining the unit vector of each axis. The unit vector from Fig. 4. is defined as follows (Table 2): [l,m,n] are the direction cosines of individual axis in the reference coordinate system. The rows 0-4 are for the five axes of the machine. The above model is for the ideal case. According to Table 2, the X-axis should pass through the point Po [Po~, Poy, Poz] with a direction cosine [1,0,0]. If Pot is the real point [Po#:Por] through which the X-axis passes then aPo = Oi + (Pyor-eyo) j + (Pzor-Pzo)k (17) where APoy=(Py:Poy) and APo~--(Po=--Poz) are small deviations in the position of the origin in the base Y- and Z-directions, respectively. The actual direction cosine of joint one is given by Uo = [ ~l =m~-n~,mo, no I (18) Extending the idea to all joints results in Table 3 where the unknown direction and position values can be found by the calibration process. 230 R. Md. Mahbubur et al. Table 3 describes the real machine geometry with either arbitrary rotation or a displacement axis. [P,, p , Pz] r is the transformation at the zero position. [P~, Pyr, Pzr] 7 is the actual location (offsets) of the axis. If we know the direction cosine of the actual axis and the offsets we can find the tool tip and the orientation of the tool axis vector for a given displacement of joints using Equation (13) and Equation (14). We shall try to find the direction cosine of Table 3 by measuring the real machine and find the tool tip in the base coordinate system. [ l O O P x 0 1 0 P y A,,= 0 0 1 P ~ 0 0 0 1 - 1 0 0 0 ] =/o ,oo / /o o_1 L O 0 0 1 J Tto~ = Am'AI'A2\"A3\"A4\"As'To Trot = (19) (20) - c o s C c o s B -s inC -cosCsinB -cosCsinB-L + X + P, -sinCcosB cosC -sinCsinB -sinCsinBLz + Y + Py sinB 0 -cosB -cosBL z + Z + Pz 0 0 0 1 (21) (22) where A~, A2, A3, A4, A5 all are based on Rodrigues equation, To is transformation with respect to reference coordinate system when all joints displacements are zero."
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.12-1.png",
        "caption": "Figure 12.12 Free-body diagram of the block.",
        "texts": [
            "2 A 20 kg block is pushed up a rough, inclined surface by a constant force of P = 150 N that is applied parallel to the incline (Figure 12.11). The incline makes an angle e = 30\u00b0 with the horizontal and the coefficient of friction between the incline and the block is f-L = 0.2. If the block is displaced by .e = 10 m, determine the work done on the block by force P , by the force of friction, and by the force of gravity. What is the net work done on the block? Solution: The free-body diagram of the block is shown in Figure 12.12. W is the weight of the block, f is the frictional force at the bottom surface of the block, and N is the reaction force applied by the incline on the block. The x and y directions are chosen in such a manner that the motion occurs in the pos itive x direction, and there is no displacement of the block in the y direction. Force P is applied in the same direction as the displacement of the block. Therefore, the work done by L to displace the block by a distance of .e along the incline is: (i) The weight W of the block has components along the x and y directions, such that Wx = W sin e and Wy = W cos e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002599_imece2004-59224-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002599_imece2004-59224-Figure5-1.png",
        "caption": "Figure 5. A model of one-stage gearbox dynamics",
        "texts": [
            " In this case, it is assumed that the driven gear can still continue rotating during this short term due to the rotation inertia. A dynamic model coupling both torsional and lateral motions is ideal for investigating the vibration response properties of a gearbox system. For simplification, we assume that the gearbox casing is rigid so that the vibration propagation along the casing is linear. Thus, the vibration response properties of gears in lateral directions are consistent with those on the gearbox casing. Figure 5 shows the model developed by Bartelmus [12]. The system is driven by electric motor torque M1 and loaded with torque M2. The motor shaft and the shaft that the pinion mounts on are coupled with a flexible coupling named input coupling. The output coupling is applied to couple the shaft of the load and the shaft that the gear mounts on. The shafts, which the pinion and the gear mount on, are mounted on the bearings. The bearings are mounted on the gearbox casing, which is considered as the rigid casing for simplification"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003684_j.matdes.2008.06.037-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003684_j.matdes.2008.06.037-Figure5-1.png",
        "caption": "Fig. 5. Schematic view of the gear test rig. 1: DC motor; 2, 3: gears box; 4, 5, 6: shaft; 7: circulating gears; 8: pinion and gears (test gears); 9: coupling; 10, 11: load coupling; 12: washer; 13: support tube.",
        "texts": [
            " Polymer gears used in this study as driving gears were made of Polyamide 66 GFR30. This material has glass fiber reinforcement and heat aging resistance. It is also an injection molding-grade material designed for machinery components and housings with high stiffness and dimensional stability. The specification material properties of the gear pairs used in this study are summarized in Tables 1 and 2, respectively. Wear tests of the gear pairs and the experimental gear tooth were carried out on a FZG (Forschungsstelle f\u00fcr Zahn\u00e4der und Getriebebau) test machine (Fig. 5). The FZG test machine is a power-circulating test machine which is a test gear tooth wear apparatus [19,22,23]. The closed loop was changed with 7.5 kW DC electric motor driving vehicle. Gear loading was generated by FZG closed loop geared system. In this closed loop, number 5 shaft was fixed with a pin and a twisting moment was generated in number 6 shaft by applying a gear loading with an arm. Initially, the gears were run for 10 min at a pinion rotation speed of 200 rpm and a low contact load (3 N/mm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002791_s0957-4158(99)00052-5-Figure21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002791_s0957-4158(99)00052-5-Figure21-1.png",
        "caption": "Fig. 21. Representation of joint angle.",
        "texts": [
            " The control system of the biped locomotion robot is shown in Fig. 18. This biped locomotion robot is controlled by using PD control so as to follow the reference trajectory obtained in the previous section. This biped locomotion robot has been able to walk under the condition of which one step is 0.30 m per 5.0 s. The walking of biped locomotion robot is shown in Figs. 19 and 20. Figs. 21\u00b134 show the joint angles (deg.) in walking. Cyclic walking pattern has been realized. The places of joint angles are shown in Fig. 21. This biped locomotion robot can walk continuously without falling down. The obtained natural motion trajectory can be applied successfully to the practical biped locomotion robot. This paper proposed a hierarchical evolutionary algorithm to generate natural motion for biped locomotion robot on the slope so as to minimize total energy. We consider total energy of actuators to generate more natural motion. Human walking is very e cient and smooth. Humans can make use of gravity e ectively. The smooth motion is caused by good energy e ciency therefore the walking with less energy consumption is suitable for the biped locomotion robots, and looks like more natural motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.18-1.png",
        "caption": "Figure 4.18 Example 4.3.",
        "texts": [
            " We can now correct it by writing: RAy = 555 N (t) The corrected free-body diagram of the beam is shown in Figure 4.16. Since we already calculated the components of the reaction force at A, we can also determine the magnitude and direction of the resultant reaction force EA at A. The magnitude of R A is: RA = J(RAx)2 + (RAy)2 = 747 N If a is the angle R A makes with the horizontal, then: a = tan-1 (RAY) = tan-1 (555) = 500 RAx 500 The modified free-body diagram of the beam showing the force resultants is illustrated in Figure 4.17. Example 4.3 The uniform, horizontal beam shown in Figure 4.18 is hinged to the wall at A and supported by a cable attached to the beam at B. At the other end, the cable is attached to the wall such that it makes an angle f3 = 53\u00b0 with the horizontal. Point C represents the center of gravity of the beam, which is equidistant from A and B. A load that weighs W2 = 400 N is placed on the beam such that its center of gravity is directly above C. If the length of the beam is l = 4 m and the weight of the beam is Wi = 600 N, calculate the tension T in the cable and the reaction force on the beam at A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002691_1.1357163-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002691_1.1357163-Figure1-1.png",
        "caption": "Fig. 1 The cross section of a single-row ball bearing",
        "texts": [
            " The following assumptions are made for the derivation of the contact angle of a ball in a bearing: 1 No configuration change or elastic deformation of the inner or outer races except at the ball contact area; 2 No lubrication and thermal effect; 3 No centrifugal force effect; 4 No misalignment in the bearing system. 001 by ASME Transactions of the ASME 13 Terms of Use: http://asme.org/terms Downloaded F 2.1.1 Contact Angle without Loading. The geometry of a ball bearing without loading is show in Fig. 1. The total clearance, which consists of the clearances between a ball and the inner race and between a ball and the outer race, is given as: Pd5do2di22D (1) where do is the raceway diameter of the outer race, and di is the raceway diameter of the inner race. D is the ball diameter. As the ball bearing is operating without loading, the distance between two curvature centers of the inner and outer races can be given as A05ri1ro2D (2) where ri is the radius of curvature of the inner race, and ro is the radius of curvature of the outer race"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.2-1.png",
        "caption": "Figure 6.2. Forces acting on a gripped part",
        "texts": [
            " However, it has to be ensured Force Feedback for Nanohandling 171 that the microgripper grips the parts well enough to prevent slipping, while at the same time not damaging them. The gripping force acts from the gripper on the gripped part. It has to counteract a total load resulting from several single forces and torques, including static holding forces as well as dynamic and process-related loads. The required magnitude of the gripping force depends on the geometries of gripper and part as well as \u2013 in the case of force-fit gripping \u2013 the friction coefficient between gripper jaw and part. The forces occurring during force-fit gripping are shown in Figure 6.2. The gripping force FG acts on the part as normal force and, thus, generates the friction force FR. According to Coulomb\u2019s Law, the friction force acts against the direction of motion and, thus, against the weight G of the part. If the gripped part is not moving, the following equation applies: GR FnFG , (6.8) with the static friction coefficient \u03bc between gripper jaw and part and the number of gripper jaws n. Resolving this equation for the required gripping FG force leads to: n gmFG , (6.9) with the mass m of the part and the gravity g"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002491_027836499401300404-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002491_027836499401300404-Figure2-1.png",
        "caption": "Fig. 2. The various vectors used in the equations.",
        "texts": [
            "comDownloaded from 327 . ~, 0, ~: three angles defining the orientation of the end effector . R: rotation matrix relating the relative frame to the fixed frame. . pi: length of link i 2. Trajectory With a Fixed Orientation In this section we will assume that the orientation of the end effector is kept constant all along the trajectory. Let us define the start and goal points of the trajectory as 1B;[1, lbf2 and let C be a point on the trajectory (i.e., a point lying on the segment lllllVl2). Any such point (Fig. 2) can be defined as: 2.1. Limitation on the Link Lengths The length of a link for any point on the trajectory between M, and 112 (Fig. 2) is the Euclidean norm of vector AB. We have: where CB = RCBr is a constant vector. The square of the link length p is given by: Using equation (1), this equation can be rewritten as a second-order equation: We consider now the equation _a~2 + bA + c - p~,~2. Because a > 0, the equation will be positive for all A if this equation has no root. Consequently, in that case the link length will be greater than pmax on the whole trajectory. Assume now that the equation has two roots ~ 1, ~2 sorted by value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002528_978-3-662-04117-8-Figure4.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002528_978-3-662-04117-8-Figure4.2-1.png",
        "caption": "Figure 4.2: Examples of localized basis functions",
        "texts": [
            "2 A continuous bounded and non-negative function B : IRP ---+ IRo+ is a localized basis function if it has a global maximum at .x. = ~ and ij, fOT all elements x p of the P-dimensional vectoT.x., it meets fOT xp and lim B(.x.) 0 11;,:11-+00 This definition will allow uniform representation of different neural network and fuzzy approaches. Examples for localized basis functions are Gaussian radial basis functions, Parzen windows, and triangular windows. In [5] even rectangular windows are included. In figure 4.2 some symmetric candidates for these basis functions are shown. As mentioned above, a weighted sum of localized basis functions has shown good ability of function approximation. To identify a universal and convergent func tion approximator, two properties have to be verified: First, a universal function approximator has to be able to approximate any nonlinearity as defined above arbitrarily dose by proper choice of design parameters and, second, the inherent approximation error between the nonlinearity and the approximator output has to converge to its global minimum",
            "2, an RBF network can be represented as a weighted sum of basis functions resulting in an estimate of the nonlinearity, wh ich corresponds to equation (4.2). This not only enables local adaptation of weights but also provides extrapolation as far as A(;r:) > .0. is ensured [1, 14]. A common choice of activation function is the Gaussian radial basis function ( 4.4) introducing a smoothing parameter (J, which provides different shapes. This rep resentation is used in correspondence with the Gaussian standard deviation [15], where a function Cn correlated to the n-th weight is defined to be the squared length of the vector ;r: - Kn (see also figure 4.2): p 2]xp - Xn,p? (4.5) p=l For this constellation, the topology of an RBF network can be outlined as given in figure 4.3. Alternatively, the Manhattan distance could be employed for Cn : p Cn := L Ixp - Xn,pl (4.6) p=l The General Regression Neural Network (GRNN) has evolved from the RBF network to improve function approximation with a minimal number of weights. Given a finite number of sampies of a continuous function, regression means the calculation of the most probable output for a specific input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002695_bulm.1999.0160-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002695_bulm.1999.0160-Figure1-1.png",
        "caption": "Figure 1. An idealized algal cell. \u03b8 increases in the anti-clockwise sense and h denotes the displacement of the centre of gravity from the centre of the cell, C, so that h = h(x\u0302 sin \u03b8 \u2212 y\u0302 cos \u03b8) relative to Cartesian coordinates, Cxy. The horizontal, x , and the vertical, y, directions are fixed relative to the laboratory. Wc is the swimming velocity of the microorganisms relative to the water.",
        "texts": [
            " They were able to calculate the statistical moments required for the coefficients of the Fokker\u2013Planck equation for the cells\u2019 orientational probability density function. These coefficients are needed in the new continuum model developed by Pedley and Kessler (1990). Numerical simulation of bioconvection in two dimensions has been carried out by Childress and Peyret (1976) and by Harashima et al. (1988). Both studies were for purely up-swimming (negatively gravitactic) micro-organisms. For simplicity, algal cells such as Chlamydomonas (whose shapes closely approximate a spheroid) are idealized here as spheres of radius a. Figure 1 shows such a cell placed in a shear flow. Since algal cells are small with typical body diameters of 10\u201320\u00b5m, and swim at speeds of 100\u00b5m s\u22121, the Reynolds number associated with swimming is very small and inertia can be neglected. Thus a typical cell swims in a direction p at an angle \u03b8 to the vertical determined by a balance between the gravitational torque, Tg, due to its being bottom heavy, and a viscous torque, T\u00b5, due to fluid-velocity gradients, \u2207u, across its body and rotation of the cell, i",
            " We retain the simpler form for J in equation (5) because it contains the essential features that we wish to model and because improvements appear to lead to quantitative adjustments rather than qualitative changes (Ghorai, 1997). Typical values for these parameters are given in Table 1, which is based on estimates given by Kessler (1986) for a suspension of Chlamydomonas nivalis. The vorticity evolves according to the equation \u2202\u03b6 \u2202t +\u2207 \u00b7 (\u03b6u) = \u03bd\u22072\u03b6 \u2212 1\u03c1g\u03d1 \u03c1 \u2202n \u2202x . (6) Here \u03bd is the kinematic viscosity and equation (6) is derived under the Boussinesq approximation, neglecting all effects of the cells on the fluid except their negative buoyancy, because the suspension is dilute. From Fig. 1, we have p \u2261 (px , py) = (\u2212 sin \u03b8, cos \u03b8), where \u03b8 is the solution of equation (2). If the shear is sufficiently small so that |B\u03b6 | \u2264 1, then the steady-state orientation is obtained by setting the left-hand side of equation (2) equal to zero. When |B\u03b6 | \u2264 1, we find that p\u0304 = (\u2212\u03ba, (1\u2212 \u03ba2)1/2), |\u03ba| \u2264 1, (7) where \u03ba = B\u03b6 . If the vorticity is large ( |B\u03b6 | > 1), the cell tumbles but swims on average in a fixed direction at an angle to the vertical (Kessler, 1985b). When the vorticity is large, the average swimming direction p\u0304 is approximated by integrating the swimming direction over the tumbling period (Ghorai and Hill, 1999)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure11.31-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure11.31-1.png",
        "caption": "Figure 11.31 Problem 11.4.",
        "texts": [
            "3 Based on the assumption that the air resistance is negligible, it is suggested that the overall motion character istic of a long jumper may be analyzed by assuming that the center of gravity of the athlete undergoes a projectile motion (Figure 11.30). Consider an athlete who jumps a horizontal distance of 9 m after reaching a maximum height of 1.5 m. What was the takeoff speed Vo of the athelete? Discuss how the athlete can improve his/her performance. Answer: Vo = 7.28 m/s Linear Kinematics 251 252 Fundamentals of Biomechanics Problem 11.4 The ski jumper shown in Figure 11.31, leaves the ramp with a horizontal speed of Vo and lands on a slope that makes an angle fJ = 45\u00b0 with the horizontal. Neglecting air resistance (the effect of which may be quite signi ficant), determine the takeoff speed vo, landing speed VI, and the total time t}, that the ski jumper was airborne if the skier touched down at a distance d = 50 m from the ramp measured parallel to the slope. Answers: vo = 13.2 mis, VI =29.6 mis, tI =2.7 s Problem 11.5 Assume that in another trial, the ski jumper in the previous problem manages to maintain the takeoff speed at Vo = 13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003870_1.4001003-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003870_1.4001003-Figure4-1.png",
        "caption": "Fig. 4 Meshing coordinate systems between the crown and external spiral bevel gears",
        "texts": [
            " The pitch cone angle of the internal bevel gear is larger than 90 deg, and the pitch cone angle of the external bevel gear is less than 90 deg. As aforementioned, the generation of the double circular-arc profile bevel gears can be seen as an enveloping process by a crown gear, whose tooth depth is the same along the generatrix of a pitch cone. Thus, the design and manufacture of the spiral bevel gears can be investigated on the crown gear. To establish the meshing theory of double circular-arc spiral bevel gears and obtain the tooth equation, five coordinate systems are established in Fig. 4 to describe the meshing 21 between the crown and external bevel gears. Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use n c o g b t r t r r t r g c p T T T T F i J Downloaded Fr The fixed coordinate system Sm im , jm ,km represents the origial location of the external and internal spiral bevel gears attached oordinate system Si ii , ji ,ki i=1,2 in Figs. 4 and 5. The crown-origin coordinate system S0 i0 , j0 ,k0 represents the riginal location of the crown gear rotatable coordinate system SC. The coordinate system SC iC , jC ,kC is attached to the crown ear and rotates about the axis kC of the center of the crown gear y angular speed C, with C representing the rotational angle of his gear. The coordinate system S1 i1 , j1 ,k1 attached to the external spial bevel gear in Fig. 4 rotates about the axis k1 of the center of he external gear by angular speed 1, with 1 representing the otational angle of this gear. The coordinate system S2 i2 , j2 ,k2 attached to the internal spial bevel gear in Fig. 5 rotates about the axis k2 of the center of he internal gear by angular speed 2, with 2 representing the otational angle of this gear. In both Figs. 4 and 5, the matrix transformation from the crown ear attached coordinate system SC to the bevel gear attached oordinate systems S1 and S2 can be obtained, and the detail exressions of the each transformation matrix are given as follows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003870_1.4001003-Figure16-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003870_1.4001003-Figure16-1.png",
        "caption": "Fig. 16 Simulation machining of the spiral bevel gears",
        "texts": [
            "org/ on 01/28/201 yas = e cot cos a + a + la sin a + xa = e cot cos \u2212 a \u2212 a + la sin \u2212 a + ya = e cot sin \u2212 a + a + la cos \u2212 a + 35 The internal surface can be obtained as = \u2212 s /sin 2 s = \u2212 fs = xf 2 + yf 2 \u2212 xfs 2 + yfs 2 xfs = e cot sin f \u2212 f \u2212 lf cos f + yfs = e cot cos f + f \u2212 lf sin f + xf = e cot cos \u2212 f \u2212 f \u2212 lf sin \u2212 f + yf = e cot sin \u2212 f + f \u2212 lf cos \u2212 f + 36 To facilitate the operation during the generation process mentioned above, the standard module is set at the small end. One reason is that the tooth intensity will be weakened if the larger module is set that the length of the whole tooth depth will increase, especially in the situation with longer face width. The simulation was then verified in the software MASTERCAM, as shown in Fig. 16. From the running result of the program, it has verified the machining method we attempted. No interference or overcutting area occurs during the whole simulation process and machining. The pair of prototype of the spiral bevel gears using the above cutting process is presented in Fig. 17. Two pairs of bevel gears are required in the design of the nutation drive, as shown in Fig. 1. Since they have the same double circular-arc tooth profile and similarity in configuration except the number of teeth and pitch cone distance, only one pair of them is simulation results Transactions of the ASME 6 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure3.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure3.11-1.png",
        "caption": "Fig. 3.11 Thin-walled square cross sec tion, functions zo, and S",
        "texts": [],
        "surrounding_texts": [
            "We determine the cross-sectional area and moment of inertia to be 3.2 Shear Stresses 51 A = 2c5(b + h) = 56.103 mm2 1 h2 1 J = - c5h3 + bc5 - = -6 c5h2 (h + 3b) = 648.107 mm4. 6 2 We first analyze the shear stress of a closed cross section. Due to the symmetry of the section with respect to the xz plane, we know that T vanishes at y = O. We therefore only need to examine one half of the section, e.g. the left half - with the shear force Q acting in z direction. The distribution of the shear stress T is obtained by multiplying S (() by the factor Q 6Q Jc5 c52 h2 (h + 3b) with the maximum value of 3 Q h+2b Q Q Tmax = 4: c5h h + 3b = 0.594 c5h = 1.847 A . The resultant of all shear stresses on the cross section is clearly a vertical force, because the horizontal stresses in the flanges - in both parts of the section - cancel one another and produce no resultant. The shear stresses in the web have a resultant T2 , which can be found by integrating over the whole domain (2, as follows T2 = J T(()c5 d( = ~ J S(() d( = ~ 112 c5h2 (h + 3b) = ~ , (2 (2 which establishes the fact that the resultant of the shear stresses is equal to the vertical load We now assume that the square cross section is a welded structure, with a long weld in the webs at z = O. We further assume that due to some carelessness during the welding process one of the welds, the right one (say), breaks, and that the closed cross section turns over to an open one. In the second part of this example, we 52 3. The Theory of Simple Beams I iQ ~t5h(h + 4b) t , - - d----{' - - - - - - . Y z ~t5h(h + 4b) Fig. 3.12 Thin-walled open square cross section, function S are now interested in the influence of this change on the distribution of the shear stresses. The distribution of the function zrS (() is the same as before, but due to the differ ent starting points of the integration over (, however, we get a different distribution of the first moment S ((), which is no longer symmetric with respect to the xz plane. It follows from these considerations that the distribution of the shear stress T has changed drastically compared with the solution of the closed cross section. The symmetry has been lost and the maximum value of the stress has increased by a factor of2. iQ T3 .- t tTl , <: T21 , - - d----{------. t I Y Y I Z YD ~z tTl Fig. 3.13 - Thin-walled open square T3 cross section Moreover, if we calculate the resultants of the shear stresses in the different regimes of (, with Tl = ~ 418 rSh3 = 0.0469 Q T2 = ~ 214 rSh2 (5h + 12b) = 1.0938Q T3 = ~ ~ rShb(h + 2b) = 0.3299 Q, we have to realize that the horizontal stresses in the flanges no longer cancel one another. Instead, in addition to the resultant of the vertical stresses 3.3 Shear Center of Thin-Walled Open Sections 53 we end up with a twisting moment about the x axis, which does not exist as an ex ternal moment, thus indicating that the assumption that the beam axis is coincident with the x axis has to be modified. This inconsistency may help us to determine the shear center of a non-symmetric cross section."
        ]
    },
    {
        "image_filename": "designv10_8_0002844_mech-34344-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002844_mech-34344-Figure6-1.png",
        "caption": "Figure 6: 3-RS structure",
        "texts": [
            " The inverse position analysis of the 3-RRS wrist is the determination of the actuated joint coordinate values compatible with a given platform orientation. In the implementation of these two problems the base point C can be also considered fixed in the platform since the platform accomplishes spherical motions with center C. Since the actuated joint coordinates have to assume given values, the revolute pairs adjacent to the base can be considered locked. If the actuated revolute pairs are locked, the 3-RRS wrist becomes the 3-RS structure shown in Fig. 6. Therefore the DPA reduces to find the possible assembly configurations of the 3-RS structure. The closure equations of the 3-RS structure can be written as follows [Rbp p(Ai \u2212 C) + b(C \u2212 Bi)] 2 = hi 2, i=1,2,3 (12) where Rbp is the rotation matrix that transforms the vector components measured in Sp into the vector components measured in Sb and the left-hand superscript p or b added to a vector indicates the reference system, Sp or Sb respectively, the vector is measured in. Expanding Eqs. (12) yields the following relationships (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003573_s0022-0728(84)80371-x-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003573_s0022-0728(84)80371-x-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms at a PySSPy-modified silver electrode in phosphate buffer solution containing 0.1 M NaC104 (pH 7.0) without ( - - - - - - ) and with 0.37 mM cytochrome c ( ). No promoter in the solution. Scan rate: (a) and ( - - - - - - ) 10, (b) 20, (c) 50 mV s -1 .",
        "texts": [
            " 6 cm 3 ). The angle of incidence of the laser light was ca. 60 \u00b0, and the scattered light was collected at 90 \u00b0 to the incidence light. A spectral band-pass width of ca. 5 cm -1 was used. A scan rate of 2.5 cm -1/s was usually used; when necessary, a scan rate of 0.5 cm -1/s was also used, but the Raman spectra observed were almost the same as those obtained at 2.5 cm -1/s, except for the improved S/N ratio, to some extent. The electrolyte solutions were purged with nitrogen prior to all measurements. Figure 1 shows the cyclic voltammograms of cytochrome c at a PySSPymodified Ag electrode in a phosphate buffer solution without PySSPy in the solution. Although the current--potential curves are somewhat asymmetrical in the reduction and reoxidation currents because dissolution of the silver electrode at positive potentials limits the usable potential region, the enhancement of the electron-transfer kinetics of cytochrome c at a PySSPy-modified 343 Ag e lec t rode is clearly observed. The fo rmal po ten t ia l es t imated f ro m the midpo in t be tween the anodic and ca thodic peak potent ia ls , (Epa + Epc)/2, was ca",
            " This is p robab ly because desorp t ion of c y t o c h r o m e c f rom the e lec t rode occur red at highly negative potent ia ls . At potent ia l s m or e posi t ive than --0.5 V, the SERS signals again became illdef ined. C o t t o n et al. r epo r t ed [15] tha t at - -0 .2 V tu n a f e r r o c y t o c h r o m e c, 344 Which was formed at --0.6 V at an Ag electrode, was reoxidized to give SERS signals of ferricytochrome c. However, from the redox potentials for both tuna heart and horse heart cytochrome c [16] (see also Fig. 1), E \u00b0' = ca. 0.01 V, reoxidation of adsorbed ferrocytochrome c at --0.2 V is unlikely. In the present experiment, when the electrode potential was changed from --0.5 to --0.2 V, the SER8 spectra obtained using both the 514.5 and 457.9 nm lines showed that the adsorbed cytochrome c was rather in the reduced (ferro) form at --0.2 V (Fig. 2). The decrease of the SERS signals at potentials more positive than --0.5 V thus resulted from desorption from the electrode and/or a change in the orientation, at the electrode, of cytochrome c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure12-1.png",
        "caption": "Fig. 12. Screw rotor for example 2.",
        "texts": [
            " For an easy comparison, the tooth profiles in examples 1 and 2 though are quite identical; the only difference between them is at the claw-shape. In example 3, the curve of shortened epicycloid is added to the tooth profile. In this paper, we mainly focus on the issue that different claw-shapes may affect its pump performance. Due to the same claw-shape design in example 1 and the patents, we will represent example 1 as the patent design. Figs. 8\u201310 represent the design results and locus of examples 1, 2 and 3, respectively. Figs. 11\u201313 illustrate the screw rotors in examples 1, 2 and 3, respectively. As shown in Fig. 11c, Fig. 12c and Fig. 13c, we can verify our drawings by calculating the equation of the line of action and then draw it out onto the screw rotor surface where it adheres. Our results then verify the accuracy of the rotor design. The performance and sealing properties will be discussed in the following sections. When area efficiency increases, the pump exhaust also increases. Therefore, one common method for estimating pump performance is to calculate the area efficiency by integration. That is to say, if the rotor tooth profile consists of multiple segment curves, each segment must be integrated and then summed to give the area of the rotor",
            " The calculated results of these three examples are shown in Table 2, and the area efficiency in example 1 is lower than that in examples 2 and 3. The result shows the length of line of action in example 1 is the shortest because the sealing line between the mating rotors is not continuous as shown in Fig. 11d. Figs. 11\u201313 illustrate the inappropriateness of the design in example 1. In Fig. 11b, if we move the screw rotor to a certain angle, an obvious clearance may appear, indicating that the design of this example is inferior. However, in Fig. 12d and Fig. 13d, the lines of action are continuous; there is no clearance between the mating rotors in Fig. 12b and Fig. 13b. Thus, the designs in examples 2 and 3 are better than that in example 1. In contrast to the design in example 2, using a curve with shortened epicycloid for the tooth profile in example 3 can improve pump performance. By comparison of these two examples, it shows that their area efficiencies are approximate but the line of action in example 3 is shorter than that in example 2. Therefore, example 3 could be thought better than example 2. According to the discussion above, we know the design of claw-shape in example 1 cannot form a well gas sealing between the twin-screw rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002791_s0957-4158(99)00052-5-Figure17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002791_s0957-4158(99)00052-5-Figure17-1.png",
        "caption": "Fig. 17. biped locomotion robot (mm).",
        "texts": [
            " These \u00aegures show that all the positions of ZMP are in the domain of support surface and then the biped locomotion robot is stable. Furthermore, Figs. 10, 13 and 16 show the total powers of actuators. The \u00aegures show that desired powers of actuators are very low. By giving the large number of penalty value, the trajectory which satis\u00aees constraints is generated easily, and the energy-optimized trajectory has successfully been found (Figs. 11\u00b116). In trial, we produced the biped locomotion robot shown in Fig. 17. This robot Fig. 10. Total power (\u00ff58). has 13 joints, and has a three-dimensional mechanism. The main scales of biped locomotion robot are shown in Fig. 17. The weight of this biped robot is 24 kg. For the reduction of weight, the body is made of aluminum materials. The inclinometers and force sensors are mounted in the waist plate and foot plate respectively. Each joint is driven by the actuator that consists of a DC servomotor and a reduction spiral gear, and each of the actuators and gears are mounted in the link structure. This structure is strong against falling down of the robot and it looks smart and more similar to a human. In this section, we apply the `case 2' trajectory calculated in the previous section to the practical biped locomotion robot shown in Fig. 17. The control system of the biped locomotion robot is shown in Fig. 18. This biped locomotion robot is controlled by using PD control so as to follow the reference trajectory obtained in the previous section. This biped locomotion robot has been able to walk under the condition of which one step is 0.30 m per 5.0 s. The walking of biped locomotion robot is shown in Figs. 19 and 20. Figs. 21\u00b134 show the joint angles (deg.) in walking. Cyclic walking pattern has been realized. The places of joint angles are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure8-1.png",
        "caption": "Fig. 8. (a) Points A1, P, and A2 that belong to surface R 2 generated by the hob; (b) plane P in 3D space, determined by the condition that P passes through A1, P, and A2.",
        "texts": [
            " We may represent R 2 in two parameter form by using the theorem of implicit function system existence as follows [6,8,9,17,18]: Consider that point M u0h; h 0 h;w 0 h satisfies equation f h \u00bc 0 and an inequality of ouh \u00fe of ohh 6\u00bc 0 \u00f04\u00de is observed at M, say because of =ohh 6\u00bc 0. Therefore equation f h \u00bc 0 may be solved in the neighborhood of M by function hh \u00bc hh uh;wh\u00f0 \u00de; hh 2 C1: \u00f05\u00de Then surface R 2 may be represented locally as r 2 uh; hh uh;wh\u00f0 \u00de;wh\u00f0 \u00de \u00bc R 2 uh;wh\u00f0 \u00de: \u00f06\u00de Pitch point P is the point of tangency of the cone of the worm and the pitch cone of the existing design (Fig. 8). Determination of P requires application of Eqs. (2) and (3) and parameters Em and L of installment of the worm. The generating tool is installed in a plane (designated by P) that is determined by three chosen points of surface R 2 generated by a hob. These points are designated as A1, P and A2 (Fig. 8(a)) where P is the pitch point, A1 and A2 are the points of R 2 that are generated by the middle point of the axial profile of the hob. Plane P is shown in 3D (Fig. 8(b)). Circle C that lies in P and passes through A1, P and A2 is of radius q determined by using the coordinates of A1, P and A2. The axis zg of the generating tool is perpendicular to plane P and passes through point Og that is the center of circle C. The orientation of plane P is determined with respect to plane T of the drawings (Fig. 8(b)). The installment of the generating tool with respect to coordinate system S2 rigidly connected to face worm gear is determined by direction cosines of coordinate system Sg of the generating tool and position vector 020g. The blade of the gear head-cutter is a straight line (Fig. 5(a)) and profile angle ag is determined from the condition that the straight line is a tangent to the cross-section of the face-gear at point P. The surface of the head-cutter is illustrated in Fig. 5(a). It may be represented as a combination of a cone in the working part and a torus of the fillet part. The gear tooth surface is generated as a copy of the tool surfaces and is represented in S2 by the matrix equation r2 ug; hg \u00bc M2grg ug; hg : \u00f07\u00de Here ug; hg are the surface coordinates of the head-cutter represented by vector function rg ug; hg . Matrix M2g describes the coordinate transformation from the tilted head-cutter to coordinate system S2. Elements of matrixM2g are determined by position vector 020g and direction cosines of coordinate axes of Sg (Fig. 8). The investigation of avoidance of interference may be accomplished analytically but it requires derivation of equations of tooth surfaces of many teeth and equations of their intersection with the head-cutter. The authors have used computer graphics as shown in Fig. 9. Avoidance of interference may require in some case the increase of the tilt of the head-cutter. Coordinate systems applied for derivation are shown in Fig. 10. Fixed coordinate systems Sn and Sm are rigidly connected to the frame of the generating machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002582_202-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002582_202-Figure7-1.png",
        "caption": "Figure 7. The airflow and resulting forces acting on a golf ball moving to the left without backspin (a) and with backspin (b).",
        "texts": [
            " They found good agreement between their results, using finite element analysis, and the measured launch conditions of different ball types struck by professional golfers. The benefit of such a golf ball, which has high spin rates for the high-lofted irons and relatively low spin rates for the driver, is that it would allow the good golfer control around the greens without loss in the drive distance. After the golf ball leaves the clubhead its motion is governed by the force of gravity and the aerodynamic forces that are exerted on it by the air. This section will look at the various aerodynamic measurements that have been carried out on golf balls. Figure 7(a) shows the basic features of the air flow pattern around a golf ball. The separation point is the position where the boundary layer, which is the thin air layer dragged by the surface of the ball, separates from the surface. In the figure shown, the boundary layer separates just downstream of the sphere\u2019s mid-section. The wake that is created is a region of relatively low pressure and the resulting pressure difference between the forward and rearward regions results in a pressure drag on the body",
            " The corresponding decrease in the size of the wake is very evident in the photographs they present. The effect of dimples on a golf ball is further highlighted by Fox and McDonald (1992) who obtained samples of golf balls without dimples. The average drive distance of these balls in tests was only 125 yards compared to 215 yards for dimpled golf balls. A spinning golf ball travelling through the air will have, in addition to drag, a force perpendicular to the ball\u2019s velocity, commonly referred to as lift. Figure 7(b) shows the airflow pattern around a spinning golf ball, in this case equivalent to a golf ball travelling to the left with backspin. As is shown in the figure, the boundary layer is dragged around by the spinning ball and the separation point is delayed on the upper surface while occurring earlier on the lower surface. The photographs of Aoki et al (1999) clearly show the separation point shifting downstream at the top of the spinning ball and shifting upstream at the bottom. The resulting differences in the air flow speeds over the top and bottom surfaces will result in a net upward force, or lift, being exerted on the golf ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure6-1.png",
        "caption": "Figure 6. For illustration of axodes of worm, pinion, and rack-cutter.",
        "texts": [
            " ( 2 ) Here, v (~) and v (1) are the velocities of the worm and the pinion at M; it is the unit vector directed along the common tangent to the helices; # is the scalar factor. Equation (2) indicates tha t the relative velocity at point M is collinear to the unit vector it. Grinding w o r m ~ ~ M .i~.~ Helical pinion DETERMINATION OF WORM THREAD SURFACE. Generation of worm thread surface Ew is based on the imaginary meshing of three surfaces: the to-be-derived worm thread surface E~, the pinion tooth surface El , and the rack-cutter tooth surface E~. Figure 6 shows the axodes of these three surfaces wherein the shortest distance between pinion and worm axodes is extended. Plane Yl represents the axode of the rack-cutter. Surface E,, is obtained using the following steps. STEP 1. Tooth surface Ec of a rack-cutter with straight profiles is considered as given. STEP {2. Translational motion of rack-cutter surface Ec, tha t is perpendicular to the axis of the pinion, and rotational motion of the pinion provide surface E1 as an envelope to the family of surfaces of E~. Velocity Vl (Figure 6) is applied to rack-cutter while the pinion is rotated with angular velocity co (1). The relation between vl and w (1) is defined as Vl = w ( 1 ) r p l , (3) where rpl is the radius of the pinion pitch cylinder. STEP 3. An additional motion of surface Ec with velocity Vaux along direction t-t of skew rackcutter teeth (Figure 6) is performed and this motion does not affect surface El . Vector equation 1068 F.L. LITVIN et al. v2 = v1 +Va,x allows to obtain velocity v~ of rack-cutter Ec in the direction tha t is perpendicular to the axis of the worm. Then, we may represent the generation of the worm surface Ew by the rack-cutter Ec considering tha t the rack-cutter performs translational motion v2 while the worm is rotated with angular velocity w( ' ) . The relation between v~ and ~(w) is defined as v2 = ~(~)rp~, (4) where rpw is the radius of the worm pitch cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002685_s0003-2670(00)00953-3-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002685_s0003-2670(00)00953-3-Figure4-1.png",
        "caption": "Fig. 4. Cyclic voltammograms of the three bilayers of PVP\u2013Os/HRP modified electrode (a) in the absence of H2O2 and (b) in presence of 2 mM H2O2. Condition: in 0.01 M phosphate buffer (pH=7.0) containing 0.1 M KCl, scan rate 5 mV/s.",
        "texts": [
            " The increase of deposited layers led to the increase of amount of electroactive groups, which may increase the sensitivity of the response. On the other hand, the thicker layers may increase electron-hopping distance and hinder the diffusion of supporting elec- trolyte, which is indispensable for the redox electron transfer. 3.3. Electrocatalytic reduction of H2O2 at the multilayer film electrode containing HRP and PVP\u2013Os The catalytic reduction of hydrogen peroxide at the multilayer films containing HRP can be seen clearly in Fig. 4. In the absence of H2O2, the peroxidase contributes no response and only a typical oxidation and reduction peak of mediator (PVP\u2013Os) is observed (Fig. 4 (a)). After adding hydrogen peroxide to the above solution, a dramatic change was produced in the cyclic voltammograms, with an increase in cathodic currents and a concomitant decrease in anodic currents. At slow scan speeds (5 mV/s) the anodic peak disappears almost completely and the cathodic peak increase largely (Fig. 4 (b)). Comparison of the voltammograms with and without the adding of H2O2 illustrates that the PVP\u2013Os can effectively mediate electron transfer between peroxidase in the multilayer films and the gold electrode surface. The reason may be the configuration of PVP\u2013Os could be easily adjusted, and when it is adsorbed onto enzyme modified substrate, segments of redox polymers may fold along the enzyme and penetrate these, thus, easily mediate electron transfer from the electrode surface to active center of the enzyme [37]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.42-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.42-1.png",
        "caption": "Figure 5.42 Static analysis of the forces acting on the patella.",
        "texts": [
            " The higher the tension in the mus cle, the larger the compressive force (pressure) the patella exerts on the patellofemoral joint. We have analyzed the forces involved around the tibiofemoral joint by considering the free-body diagram of the lower leg. Having determined the tension in the patellar tendon, and as suming that the tension is uniform throughout the quadriceps, we can calculate the compressive force applied on the patello femoral joint by considering the free-body diagram of the patella (Figure 5.42a). Let F M be the uniform magnitude of the tensile force in the patellar and quadriceps tendons, Fp be the magni tude of the force exerted on the patellofemoral joint, a be the angle between the patellar tendon and the horizontal, y be the angle between the quadriceps tendon and the horizontal, and \u00a2 be the unknown angle between the line of action of the com pressive reaction force at the joint (Figure 5.42b). We have a three-force system and for the equilibrium of the patella it has to be concurrent. We can first determine the common point of intersection Q by extending the lines of action of patellar and quadriceps tendon forces. A line connecting point Q and the point of application of F p will correspond to the line of action of F p. The forces can then be translated to Q (Figure 5.42c), and the equilibrium equations can be applied. For the equilibrium of the patella in the x and y directions: LFx=O: LFy=O: F p cos \u00a2 = F M (cos Y - cos a) Fp sin\u00a2 = FM (sin a - sin y) These equations can be solved simultaneously for angle \u00a2 and the magnitude F p of the compressive force applied by the femur Applications of Statics to Biomechanics 111 on the patella at the patellofemoral joint: Fp = (COS y - cosa) FM cos\u00a2 -1 ( sin a - sin y ) \u00a2 = tan cosy - cosa 5.10 Mechanics of the Ankle The ankle is the union of three bones: the tibia, the fibula, and the talus of the foot (Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002518_s0263574797000027-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002518_s0263574797000027-Figure11-1.png",
        "caption": "Fig . 11(b) . Joint Solutions at 15 Positions .",
        "texts": [
            " However , if we only consider the position of the end point of an attached tool , the PUMA 560 arm as shown in Figure 10 will become a redundant robot since the tool tip in the three-dimensional Cartesian space is related to five joint angles (a two degree redundancy) . With the joint angle and link parameters defined in Table III , the positional forward kinematics is expressed as follows : X 5 C 1 [ d 6 ( C 2 3 C 4 S 5 1 S 2 3 C 5 ) 1 S 2 3 d 4 1 a 3 C 2 3 1 a 2 C 2 ] 2 S 1 [ d 6 S 4 S 5 1 d 2 ) (15) Y 5 S 1 [ d 6 ( C 2 3 C 4 S 5 1 S 2 3 C 5 ) 1 S 2 3 d 4 1 a 3 C 2 3 1 a 2 C 2 ] 1 C 1 ( d 6 S 4 S 5 1 d 2 ) (16) Z 5 d 6 ( C 2 3 C 5 2 S 2 3 C 4 S 5 ) 1 C 2 3 d 4 2 a 3 S 2 3 1 a 2 S 2 (17) A set of 15 points on a straight line , as shown in Figure 11(a) and listed in Table IV , is used for training . The first run of training is in the environment without obstacles . We use a neural network with 45 neurons at the hidden layer . In order to obtain the elbow-up solution , q 0 is chosen as (0 8 , 2 90 8 , 90 8 , 0 8 , 0) T . It took 1765 iterations to reduce the kinematics error E 0 to below 0 . 001 . The joint solutions are plotted in Figure 11(b) . The robot links of the solution are almost in a plane . When there is an obstacle in the work space as shown in Figure 12(a) , the obstacle avoidance solution took 3826 iterations to reduce the kinematics error to below 0 . 001 . The joint solutions are plotted in Figure 12(b) . http://journals.cambridge.org Downloaded: 03 Jul 2014 IP address: 138.37.211.113 The robot links are no longer in a plane , rather they are twisted to avoid the obstacle . A neural network technique has been introduced in this paper to solve the inverse kinematics problem of redundant robot manipulators with obstacle avoidance capabilities "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002564_s0021-9290(00)00228-1-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002564_s0021-9290(00)00228-1-Figure2-1.png",
        "caption": "Fig. 2. Plan view of release and subsequent trajectory. The camera axis is oriented perpendicular to the desired throwing line x, but the actual trajectory neither begins above, nor does its vertical plane remain parallel to, the desired throwing line.",
        "texts": [
            "91 m tall } 14 throws) was at college level. Each was asked to produce three sets of relatively high initial angle, normal and relatively low initial-angle throws, respectively, all at maximum effort, and each used the standard rotary throwing technique. A 200 Hz video (ExpertVision, Santa Rosa, California) motion analysis system was used to determine initial release angle, speed, height and horizontal distance for each throw as described below. A straight desired throwing line (the x-axis of a second coordinate system; see Fig. 2) was laid out on the ground bisecting the throwing circle with origin also at the center of the inner board edge. The single camera was levelled and placed at a distance c0 (approximately 2.5 m) from, and with its axis perpendicular to, this line so that its field of view encompassed release and the beginning of flight (Fig. 2). Initial 2-D calibration of the camera relied on a calibration object in the xy plane. Throwers were instructed to throw so that both the release position and initial velocity vector lay in this plane. Even with assistance and feedback, however, the throwers found it very difficult to (and never did) release the shot exactly in the desired plane or in the correct direction. The implications of this on scaling are discussed further below. Camera data were first processed, using the (naive) 2-D assumption that the throw occurred in the xy plane",
            " Thus, an alternate scaling method using this data was developed to produce more accurate estimates for release conditions. The basic idea is to include parameters in the model which account for the major error sources due to scaling, and to use video and range data to estimate release conditions and error sources simultaneously, thus removing their effects from the calculated release conditions. This technique is an example of using accurate non-image-related information to correct out-of-plane errors (Sih et al., 2001). Consider Fig. 2. Initial calibration determines a nominal scale factor s0 (meters per pixel), which applies only to motion in the calibration plane. However, the general throw was neither released in the desired xy plane, nor was its x0y0 flight plane parallel to it. Therefore, the correct scale factor s varies with distance c from the camera throughout flight according to s \u00bc cs0=c0 \u00bc \u00f0c0 \u00fe z0 \u00fe vxt tan f\u00des0=c0; \u00f03\u00de where vx is the x velocity and t is the time since release. Combining parameters yields s \u00bc s1 \u00fe kt; \u00f04\u00de where s1 and k are interpreted as initial scale factor at release and (constant) time rate of change of scale factor throughout flight, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003562_j.engappai.2007.08.007-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003562_j.engappai.2007.08.007-Figure5-1.png",
        "caption": "Fig. 5. Coordinated 3-DOF mobile manipulators working on the surface.",
        "texts": [
            " 0 as t!1. The boundedness of the internal force errors can be seen from the following equation derived from (63) and (27) as \u00f01\u00fe Kf \u00deeI \u00bc Z1\u00f0xo\u00deL \u00feTM1\u00f0xo\u00de \u20acxo Z\u03021\u00f0xo\u00deL \u00feT\u00bdW\u0302 T M FM \u20acxod . \u00f0113\u00de Since ro! 0, \u20acxo! \u20acxod , the right-hand side of (113) is bounded, the size of eI can be adjusted by choosing the proper gain matrices KI such that eI ! 0, then lI ! lId . & To verify the effectiveness of the proposed control algorithm, let us consider two coordinated 3-DOF mobile manipulators system shown in Fig. 5. Each mobile manipulator is subjected to the following constraints: _xi cos yi \u00fe _yi sin yi \u00bc 0. Using Lagrangian approach, we can obtain the standard form with qvi \u00bc \u00bdxi yi yi T, qai \u00bc \u00bdy1i y2i y3i T, qi \u00bc \u00bdqvi qai T, and Avi \u00bc \u00bdcos yi sin yi 0:0 T. The dynamics of the ith mobile manipulator is given by (1) as Mi\u00f0qi\u00de \u20acqi \u00fe Ci\u00f0qi; _qi\u00de _qi \u00fe Gi\u00f0qi\u00de \u00bc Bi\u00f0qi\u00deti \u00fe JT eif ei, where Mi, Ci, Gi and Bi are omitted here for space limit. The position of end-effector can be given by xei \u00bc xfi \u00fe \u00f0l2 cos y2i \u00fe l3 cos\u00f0y2i \u00fe y3i\u00de\u00de cos\u00f0y1i \u00fe yi\u00de, yei \u00bc yfi \u00fe \u00f0l2 cos y2i \u00fe l3 cos\u00f0y2i \u00fe y3i\u00de\u00de sin\u00f0y1i \u00fe yi\u00de, zei \u00bc l1 \u00fe l2 sin y2i \u00fe l3 sin\u00f0y2i \u00fe y3i\u00de, aei \u00bc \u00f0y2i \u00fe y3i\u00de sin\u00f0y1i \u00fe yi\u00de, bei \u00bc \u00f0y2i \u00fe y3i\u00de cos\u00f0y1i \u00fe yi\u00de, gei \u00bc yi \u00fe y1i, where aei, bei and gei are roll angle, the pitch angle and yaw angle for the ith end-effector",
            " To avoid such a phenomenon, a sat-function is used to replace the sgn-function. The sat-function is given by sat\u00f0r\u00de \u00bc 1 if r4e; 1 if ro e; 1 e r otherwise; 8>><>: where e \u00bc 0:01 in the simulation. The parameters are m1i \u00bc 2:0 kg, m2i \u00bc 1:3 kg, m3i \u00bc 1:74 kg, l1i \u00bc l2i \u00bc l3i \u00bc 1:0m, mpi \u00bc 1 kg, and mo \u00bc 1 kg, Iwi \u00bc Ipi \u00bc 1:0, di \u00bc 0, li \u00bc 2ri \u00bc 1:0. Assume that we have no knowledge about the system, that is, M1, V 1, G1 and f t are unknown. A deformable working surface is assumed in Cartesian space as Fig. 5, the desired trajectory for the object in x-axis and y-axis are chosen as xe \u00bc 1:5\u00fe 0:2 cos\u00f0pt\u00de and ye \u00bc 1:5\u00fe 0:2 sin\u00f0pt\u00de. The surface is oriented normal to the z-axis and located at ze \u00bc 22:125 cm. For a certain deformation in z-direction, the stiffness of Ke \u00bc 1:0Ncm 1 and the dampness of Ce \u00bc 0:1N s cm 1 are assumed to be unknown. The contact force of the object is calculated by f m \u00bc 1:0 \u00f022:125 zm\u00de 0:1 _zm, if zmo22:125 cm. The task of object requires the exertion of f d z \u00bc 10:0N contact force normal to the working surface while tracking a smooth trajectory tangent to the surface and lI \u00bc 5:0N in the grasped object"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002844_mech-34344-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002844_mech-34344-Figure5-1.png",
        "caption": "Figure 5: The i-th leg of the 3-RRS wrist",
        "texts": [
            " In the following paragraphs of this section it will be shown that the 3-RRS wrist is a spherical parallel manipulator when the three revolute pairs adjacent to the base are actuated. With reference to Fig. 4, the points Ai, i=1,2,3, are the spherical pair centers and the point C is the point the revolute pair axes converge towards. The point C is fixed in the base. Moreover, Sb is a reference system fixed in the base and Sp is a reference system fixed in the platform. nloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/02/2016 Te Figure 5 shows the i-th leg, i=1,2,3, of the 3-RRS wrist. According to Fig. 5, w1i and \u03b81i are respectively the axis unit vector and the joint coordinate of the revolute pair adjacent to the base and w2i and \u03b82i are respectively the axis unit vector and the joint coordinate of the revolute pair not adjacent to the base. The point Bi is the foot of the perpendicular through Ai to the axis of the revolute pair not adjacent to the base. The point Di is the foot of the perpendicular through Bi to the axis of the revolute pair adjacent to the base. The geometric parameters ai, bi, di and hi are the lengths of the segments AiC, BiC, BiDi and AiBi respectively. Moreover, the link adjacent to the base is named 1i and the link adjacent to the platform is named 2i. Since the points Ai, Bi and C are fixed in the link 2i (see Fig. 5) the lengths ai, bi and hi are constant. Therefore when the revolute pairs adjacent to the base are actuated and the platform moves the three points Ai, i=1,2,3, fixed in the platform, are constrained to move on concentric spheres whose center is C and whose radii are respectively ai, i=1,2,3. This condition and the manufacturing conditions (ii) and (iii) lead to the conclusion that the 3-RRS wrist's platform always satisfies the hypotheses of statement (1). Hence, the 3-RRS wrist's platform can exclusively accomplish spherical motions with center C, i.e., the 3-RRS wrist is a spherical parallel manipulator. The position analysis consists in the solution of two 4 rm Copyright \u00a9 2002 by ASME s of Use: http://www.asme.org/about-asme/terms-of-use Dow problems: the direct position analysis (DPA) and the inverse position analysis (IPA). The direct position analysis of the 3-RRS wrist is the determination of the platform orientations compatible with given values of the actuated joint coordinates \u03b81i, i=1,2,3, (Fig. 5). The inverse position analysis of the 3-RRS wrist is the determination of the actuated joint coordinate values compatible with a given platform orientation. In the implementation of these two problems the base point C can be also considered fixed in the platform since the platform accomplishes spherical motions with center C. Since the actuated joint coordinates have to assume given values, the revolute pairs adjacent to the base can be considered locked. If the actuated revolute pairs are locked, the 3-RRS wrist becomes the 3-RS structure shown in Fig",
            " Therefore the DPA reduces to find the possible assembly configurations of the 3-RS structure. The closure equations of the 3-RS structure can be written as follows [Rbp p(Ai \u2212 C) + b(C \u2212 Bi)] 2 = hi 2, i=1,2,3 (12) where Rbp is the rotation matrix that transforms the vector components measured in Sp into the vector components measured in Sb and the left-hand superscript p or b added to a vector indicates the reference system, Sp or Sb respectively, the vector is measured in. Expanding Eqs. (12) yields the following relationships (see Fig. 5) ai 2 + bi 2 + 2 b(C \u2212 Bi) \u22c5 [Rbp p(Ai \u2212 C)] = hi 2 i=1,2,3 (13) Equations (13) are linear in the entries of the Rbp matrix. Therefore, if the Rbp rotation matrix entries are expressed by using the three Rodrigues parameters [11], Eqs. (13) will become a three quadratic equation system in three unknowns: the values of the three Rodrigues parameters. In the literature, two procedures [12-13] have been presented for solving a three quadratic equation system in three unknowns. Both these procedures show that the Sylvester eliminant of such a system is an univariate eight degree polynomial with real coefficients",
            " The N matrix definition (23.1) leads to the following expression for det(N) det(N) = n1\u22c5(n2\u00d7n3) (24) where ni = (Ai \u2212 C) \u00d7 w2i, i=1,2,3 (25) Therefore, the rotation singularities occur whenever the 3-RRS wrist configuration satisfies the following singularity condition n1\u22c5(n2\u00d7n3) = 0 (26) Condition (26) is verified when the three vectors ni, i=1,2,3, are all parallel to a single plane. Since the three vector ni, i=1,2,3, are respectively perpendicular to the three planes of the triangles AiBiC, i=1,2,3, (see Fig. 5), condition (26) is verified when the intersection of these three planes is a straight line through C (Fig. 7). In fact, when this happens, the ni 6 Copyright \u00a9 2002 by ASME erms of Use: http://www.asme.org/about-asme/terms-of-use Dow vectors are all parallel to every single plane perpendicular to that intersection line. The H matrix is singular when its determinant vanishes. Since the H matrix is diagonal, its determinant is the product of its three diagonal entries and vanishes when at least one of them vanishes. Definition (23.2) inspection reveals that the i-th diagonal entry vanishes when the i-th leg is fully extended or folded, i.e., when the points Ai, Bi and Di (Fig. 5) lie on the same plane. Hence, the leg singularities occur when the 3-RRS wrist configuration has at least one leg fully extended or folded. In this paper a new three-equal-legged spherical parallel manipulator, named 3-RRS wrist, has been presented. The 3- RRS wrist is not overconstrained and exhibits a very simple architecture employing just three passive revolute pairs, three passive spherical pairs and three actuated revolute pairs adjacent to the frame. Moreover the kinematic analysis of the 3-RRS wrist has been addressed and fully solved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure6.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure6.1-1.png",
        "caption": "Figure 6.1 An object subjected to externally applied forces.",
        "texts": [
            " The second type of motion involves local changes of shape within a body, called deformations, which are the primary concern of the field of deformable body mechanics. If a body is subjected to externally applied forces and moments but remains in static equilibrium, then it is most likely that there is some local shape change within the body. The extent of the shape change may depend upon the magnitude, direction, and duration of the applied forces, material properties of the body, and environmen tal conditions such as heat and humidity. 6.3 Internal Forces and Moments Consider the arbitrarily shaped object illustrated in Figure 6.1, which is subjected to a number of externally applied forces. As sume that the resultant of these forces and the net moment acting on the object are equal to zero. That is, the object is in static equilibrium. Also assume that the object is fictitiously separated into two parts by passing an arbitrary plane ABCD through the object. If the object as a whole is in equilibrium, then its individual parts must be in equilibrium as well. If one of these two parts is considered, then the equilibrium condition requires that there is a force vector and/ or a moment vector acting on the cut section to counterbalance the effects of the external forces and moments applied on that part"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure11-1.png",
        "caption": "Fig. 11. Screw rotor for example 1.",
        "texts": [
            " For an easy comparison, the tooth profiles in examples 1 and 2 though are quite identical; the only difference between them is at the claw-shape. In example 3, the curve of shortened epicycloid is added to the tooth profile. In this paper, we mainly focus on the issue that different claw-shapes may affect its pump performance. Due to the same claw-shape design in example 1 and the patents, we will represent example 1 as the patent design. Figs. 8\u201310 represent the design results and locus of examples 1, 2 and 3, respectively. Figs. 11\u201313 illustrate the screw rotors in examples 1, 2 and 3, respectively. As shown in Fig. 11c, Fig. 12c and Fig. 13c, we can verify our drawings by calculating the equation of the line of action and then draw it out onto the screw rotor surface where it adheres. Our results then verify the accuracy of the rotor design. The performance and sealing properties will be discussed in the following sections. When area efficiency increases, the pump exhaust also increases. Therefore, one common method for estimating pump performance is to calculate the area efficiency by integration. That is to say, if the rotor tooth profile consists of multiple segment curves, each segment must be integrated and then summed to give the area of the rotor",
            " 18, which provides a lateral view of these three examples, indicates no blowhole phenomenon between the chamber and the tooth profile tip in example 1 but does show a blowhole phenomenon for examples 2 and 3, whose identical design in the claw-shape of the rotor may affect pump efficiency. The calculated results of these three examples are shown in Table 2, and the area efficiency in example 1 is lower than that in examples 2 and 3. The result shows the length of line of action in example 1 is the shortest because the sealing line between the mating rotors is not continuous as shown in Fig. 11d. Figs. 11\u201313 illustrate the inappropriateness of the design in example 1. In Fig. 11b, if we move the screw rotor to a certain angle, an obvious clearance may appear, indicating that the design of this example is inferior. However, in Fig. 12d and Fig. 13d, the lines of action are continuous; there is no clearance between the mating rotors in Fig. 12b and Fig. 13b. Thus, the designs in examples 2 and 3 are better than that in example 1. In contrast to the design in example 2, using a curve with shortened epicycloid for the tooth profile in example 3 can improve pump performance. By comparison of these two examples, it shows that their area efficiencies are approximate but the line of action in example 3 is shorter than that in example 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002525_00207170410001713033-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002525_00207170410001713033-Figure1-1.png",
        "caption": "Figure 1. The PVTOL aircraft (front view).",
        "texts": [
            " Section 3 gives the control of the vertical displacement while the pitch and horizontal displacement control are presented in } 4. Real-time experimental results are given in } 5. The conclusions are finally given in } 6. The PVTOL system equations are given by \u20acx \u00bc sin\u00f0 \u00deu1 \u00fe \" cos\u00f0 \u00deu2 \u20acy \u00bc cos\u00f0 \u00deu1 \u00fe \" sin\u00f0 \u00deu2 1 \u20ac \u00bc u2 9>= >; \u00f01\u00de where x is the horizontal displacement, y is the vertical displacement and is the angle the PVTOL makes with the horizontal line. u1 is the collective input and u2 is the couple as shown in figure 1. The parameter \" is a small coefficient which characterizes the coupling between the pitching moment and the lateral acceleration of the aircraft. The term 1 is the normalized gravitational acceleration. Let us use the following change of coordinates proposed in Olfati-Saber (1999) x \u00bc x \" sin\u00f0 \u00de y \u00bc y\u00fe \"\u00f0cos\u00f0 \u00de 1\u00de: ) \u00f02\u00de International Journal of Control ISSN 0020\u20137179 print/ISSN 1366\u20135820 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/00207170410001713033 Received 1 May 2003"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003225_j.euromechsol.2005.02.004-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003225_j.euromechsol.2005.02.004-Figure8-1.png",
        "caption": "Fig. 8. Kinematic structure of fully-isotropic translational parallel robot (a) and its associated graph (b).",
        "texts": [
            " We note that Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s mobility criterion largely used for mobility calculation of multi-loop mechanisms gives erroneous results when applied to these mechanisms. We emphasize on the simplicity of calculating mobility by using Eqs. (2) and (60) grouped together as MD = m\u2211 i=1 fi \u2212 rD = m\u2211 i=1 fi \u2212 k1\u2211 i=1 SAi \u2212 k2\u2211 j=1 SEj + SD n/1 \u2212 rl (61) or its particular form for the parallel mechanisms with elementary legs MC = m\u2211 i=1 fi \u2212 rC = m\u2211 i=1 fi \u2212 k\u2211 i=1 SAi + SC n/1. (62) Example 1. The translational robotic manipulator in Fig. 8 (Gogu, 2004) is a parallel mechanism C \u2190 A1\u2013A2\u2013A3 with three elementary legs A1 (1A \u2261 0\u20132A\u2013 \u00b7 \u00b7 \u00b7\u20135A), A2 (1B \u2261 0\u20132B\u2013 \u00b7 \u00b7 \u00b7\u20135B) and A3 (1C \u2261 0\u20132C\u2013 \u00b7 \u00b7 \u00b7\u20135C). To simplify the notation of the elements eAi (i = 1,2, . . . , k and e = 1,2, . . . , n) by avoiding the double index, we have denoted by eA the elements belonging to the leg A1 (eA \u2261 eA1), by eB the elements of the leg A2 (eB \u2261 eA2) and by eC the elements of A3 (eC \u2261 eA3). The reference platform is 1 \u2261 1A \u2261 1B \u2261 1C \u2261 0 and the mobile platform is 5 \u2261 5A \u2261 5B \u2261 5C ",
            " The dimensions of these three operational spaces give the spatiality of the elementary open chains associated with each leg Ai (SAi = 4, i = 1,2,3). The spatiality of the mobile platform in the parallel mechanism C given by Eq. (47) is SC 5/1 = dim(RA1 \u2229 RA2 \u2229 RA3 ) = 3. Three relative independent velocities (vx,vy,vz) exist between the mobile and reference platforms. The mechanism has 9 revolute and 3 prismatic joints ( \u2211m i=1 fi = 12). The number of joint parameters that have lost their independence in the closed loops of the parallel robotic manipulator in Fig. 8 given by Eq. (57) is r = rC = 4 + 4 + 4 \u2212 3 = 9. The mobility of the parallel robotic manipulator given by Eq. (62) is MC = 12 \u2212 9 = 3. Three independent joint parameters are necessary to describe the motion of any link of the mechanism. These parameters are the joint variables qi of the three prismatic joints connecting each leg to the reference element. The translational parallel manipulator presented in Fig. 8 is fully-isotropic (Carricato and Parenti-Castelli, 2002) and it was developed by the Department of Mechanical Engineering at the University of California (Kim and Tsai, 2002) under the name of PCM and by the Department of Mechanical Engineering at the University of Laval under the name of Orthogonal Tripteron (Gosselin et al., 2004). Kim and Tsai (2002) have shown that Chebychev\u2013Gr\u00fcbler\u2013Kutzbach\u2019s mobility criterion does not work for this parallel mechanism. Example 2. The parallel mechanism C \u2190 A1\u2013A2\u2013A3\u2013A4 in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure17-1.png",
        "caption": "Fig. 17. The line of action and the chamber.",
        "texts": [
            " 16, there is an intersection point z1 between the tip of the screw line of the active rotor and the chamber cusp line H\u2013H (see Fig. 16, point 2). Another intersection point z2 is between the tip of the screw line of the passive rotor and the chamber cusp line H\u2013H (see Fig. 16, point 3). This blowhole can be seen as a leakiness triangle which is composed of a chamber cusp, a sealing line tip and a height difference between the twin rotors on screw line H\u2013H. The existence of such a blowhole is observable from a 3-D picture. Fig. 17 shows the line of action and chamber for these three examples, in which the tip position of the chamber is X H \u00bc C 2 Y H \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 1 C 2 2 s \u00f034\u00de If the tip coordinate of the line of action (see Fig. 16, point 1) is X H 0 ; Y H 0\u00f0 \u00de, the distance between it and the chamber is LH 1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0X H X H 0 \u00de2 \u00fe \u00f0Y H Y H 0 \u00de2 q \u00f035\u00de and the height difference between the twin rotors on the screw line H\u2013H can be expressed as DZ \u00bc jZ1 Z2j \u00f036\u00de Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.31-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.31-1.png",
        "caption": "Figure 3.31 Problem 3.2.",
        "texts": [
            " Point A rep resents the center of gravity of the person's lower arm and 0 is a point along the center of rotation of the elbow joint. As sume that points 0, A, and B and force F all lie on a plane surface. If the horizontal distance between 0 and A is a = 15 cm, dis tance between 0 and B is b = 35 cm, total weight of the lower arm is W = 20 N, magnitude of the applied force is F = 50 N, and angle () = 30\u00b0, determine the net moment generated about Oby F and W. Answer: Mo = 5.75 N-m (ccw) Problem 3.2 Figure 3.31 illustrates a simplified version of a hamstring strength training system for rehabilitation and athlete training protocols. From a seated position, a patient or athlete flexes the lower leg against a set resistance provided through a cylindrical pad that is attached to a load. For the position illus trated, the lower leg makes an angle () with the horizontal. Point o represents the knee joint, A is the center of gravity of the lower leg, W is the total weight of the lower leg, F is the magnitude of the force applied by the pad on the lower leg in a direction perpendicular to the long axis of the lower leg, a is the distance between 0 and A, and b is the distance between 0 and the line of action of F measured along the long axis of the lower leg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003863_taes.2008.4560220-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003863_taes.2008.4560220-Figure1-1.png",
        "caption": "Fig. 1. Three-rotor aircraft.",
        "texts": [
            " This means that the control of the quadrotor direction (or yaw angle) will result in significant error which is not appropriate for cluttered and indoor environments. Moreover, the yawing torque is obtained by accelerating two motors and decelerating the two others. Over the past few years, we have worked on the above two mentioned configurations [20, 8, 21]. After many efforts to design an effective flying machine which combines the advantages of conventional helicopters and quadrotor vehicles, we have proposed the three-rotor aircraft as an alternative solution to small VTOL UAVs (Fig. 1). The mechanical structure of the proposed three-rotor aircraft is as simple as the conception of the quadrotor vehicle. Indeed, the absence of mechanical linkages and swashplate makes it more robust and easier to repair than classical helicopters, and increases its life duration. The originality of the configuration lies in its control mechanism for generating the required control forces and torques. The three-rotor aircraft consists of two body-fixed rotors and a tail tilting rotor with fixed-angle blades"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.28-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.28-1.png",
        "caption": "Figure 5.28 Resolution of the forces into their components.",
        "texts": [],
        "surrounding_texts": [
            "FMy = FM sine FJx = FJ coscp FJy = FJ sincp For the translational equilibrium in the x and y directions: L,:Fx=O: LFy=O: Simultaneous solutions of these equations will yield: F _ cosifJ W2 M - cos e sin ifJ - sin () cos ifJ F = cos() W2 J cos () sin ifJ - sin e cos ifJ (xi) (xii) For example, if () = 70\u00b0, ifJ = 74.8\u00b0, and W2 = 0.83W (W is the to tal weight of the person), then Eqs. (xi) and (xii) will yield FM=2.6Wand FJ =3.4W. Applications of Statics to Biomechanics 105 How would the muscle and hip joint reaction forces vary if the per son is carrying a load of Wo in each hand during single-leg stance (Figure 5.29)? The free-body diagram of the upper body while the person is carrying a load of Wo in each hand is shown in Figure 5.30. The system to be analyzed consists of the upper body of the per son (including the left leg) and the loads carried in each hand. To counterbalance both the rotational and translational (down ward) effects of the extra loads, the hip abductor muscles will ex ert additional forces, and there will be larger compressive forces generated at the hip joint. In this case, the number of forces is five. The gravitational pull on the upper body (W2) and on the masses carried in the hands (Wo) form a parallel force system. If these parallel forces can be replaced by a single resultant force, then the number of forces can be reduced to three, and the problem can be solved by ap plying the same technique explained above (Solution 2). For this purpose, consider the force system shown in Figure 5.31. M and N correspond to the right and left hands of the person where external forces of equal magnitude (Wo) are applied. G is the center of gravity of the upper body including the left leg. The vertical dashed line shows the symmetry axis (midline) of the person in the frontal plane, and G is located to the left of this axis. Note that the distance \u00a3} between M and G is greater than the distance \u00a32 between Nand G. If \u00a3}, \u00a32, W2, and Wo are given, then a new center of gravity (G') can be determined by applying the technique of finding the center of gravity of a sys tem composed of a number of parts whose centers of gravity are known (see Section 5.14). By intuition, G' is located somewhere between the symmetry axis and G. In other words, G' is closer to the right hip joint, and, therefore, the length of the moment arm of the total weight as measured from the right hip joint is shorter as compared to the case when there is no load carried in the hands. On the other hand, the magnitude of the resultant gravitational force is W3 = W2 + 2Wo, which overcompensates for the advantage gained by the reduction of the moment arm. Once the new center of gravity of the upper body is determined, including the left leg and the loads carried in each hand, Eqs. (xi) and (xi i) can be utilized to calculate the resultant force exerted by the hip abductor muscles and the reaction force generated at the hip joint: F _ cos</>' (W2+2WO) M - cos () sin </>' - sin () cos </>' I : I: M I' N + :1 ~ Wo I Wo 11 I W2 12 106 Fundamentals of Biomechanics and by replacing the angle 1> that the line of action of the joint reaction force makes with the horizontal with the new angle 1>' (Figure 5.32). 1>' is slightly larger than 1> because of the shift of the center of gravity from G to G' toward the right of the person. Also, it is assumed that the angle () between the line of action of the muscle force and the horizontal remains unchanged. What happens if the person is carrying a load of Wo in the left hand during a right-leg stance (Figure 5.33)? Assuming that the system we are analyzing consists of the upper body, left leg, and the load in hand, the extra load Wo carried in the left hand will shift the center of gravity of the system from G to G\" toward the left of the person. Consequently, the length of the lever arm of the total gravitational force W4 = W2 + Wo as measured from the right hip joint (Figure 5.34) will increase. This will require larger hip abductor muscle forces to counter balance the clockwise rotational effect of W4 and also increase the compressive forces at the right hip joint. It can be observed from the geometry of the system analyzed that a shift in the center of gravity from G to G\" toward the left of the person will decrease the angle between the line of action of the joint reaction force and the horizontal from 1> to 1>\". For the new configuration of the free-body shown in Fig ure 5.34, Eqs. (xi) and (xii) can again be utilized to calculate the required hip abductor muscle force and joint reaction force produced at the right hip (opposite to the side where the load is carried): F _ cos 1>\" (W2 + Wo) M - cos () sin 1>\" - sin () cos 1>\" cos () (W2 + Wo) cos () sin 1>\" - sin () cos 1>\""
        ]
    },
    {
        "image_filename": "designv10_8_0003067_tsmcb.2003.817029-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003067_tsmcb.2003.817029-Figure1-1.png",
        "caption": "Fig. 1. Nonlinear continuous function (u ) for the ith input u .",
        "texts": [
            " A general description of uncertain nonlinear systems with multiple inputs containing sector nonlinearities [17] and deadzones [18] is given in the form of (1) where is a vector of the state variables, is a vector of the control inputs of the system, is a vector of the uncertain parameters, is the state matrix of the normal part of the uncertain dynamic system, is the input matrix of the uncertain dynamic system, is a vector of the lumped uncertainties and external disturbances of the system, and is a vector of nonlinear input functions, and . To derive the control laws and to simplify the equation, the following assumptions are required. 1083-4419/04$20.00 \u00a9 2004 IEEE Assumption 1: In (1), the matrix pair (A,B) is controllable. Assumption 2: There exist known non-negative constants and , such that (2) Assumption 3: for . In addition, for the th input , the nonlinear input function shown in Fig. 1 is assumed to satisfy the following inequalities: for (3) and for (4) where is the lower bound of , and is the upper bound of . In Assumption 3, (3) and (4) describe the characteristics of sector nonlinearities and deadzones of input functions of the systems. If we release the upper bound limit, i.e., , (3) and (4) become for (5) and for (6) To design the control approach, we assume that , and is a design parameter. Then, (5) and (6) become for (7) and for (8) If the input functions for satisfy (7) and (8), then such nonlinear functions not only contain deadzones but also allow uncertainty outside of the deadzones with gain reduction tolerances "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002848_tia.2003.816480-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002848_tia.2003.816480-Figure1-1.png",
        "caption": "Fig. 1. Permeance I relative to branch I of the equivalent magnetic scheme.",
        "texts": [
            " The set of the flux equations is nonlinear and is solved by Newton\u2019s method. The magnetic field in each branch of the magnetic circuit is chosen as the variable. \u2022 Torque Determination\u2014Next, the torque developed by the motor is determined taking into account the saturation. \u2022 Inductance Determination\u2014The average inductances and the differential (incremental) inductances are calculated. \u2022 Eddy-Current Losses\u2014The eddy-current losses are determined using the equivalent magnetic scheme defined previously. To each permeance (Fig. 1) corresponding to a motor magnetic material part, the scheme is completed by an equivalent eddy current resistance, which is proportional to the dc resistance of the corresponding permeance and to the resistivity of the magnetic material. The equivalent eddy-current impedance for branch I is determined. Lam(I, I) is the equivalent permeance of the total magnetic scheme seen from the considered branch I. The eddy-current losses of the corresponding local permeance I is then proportional to the square of the resulting back EMF seen in the branch I and to the inverse of the equivalent local eddy-current impedance W (1) (2) (3) m (4) H (5) \u2022 Hysteresis Losses\u2014The method [6] considers the ferromagnetic material characterized by: the first magnetization characteristics; the external hysteresis loop corresponding to a totally saturated level and the internal loops"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002697_1350650011543529-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002697_1350650011543529-Figure2-1.png",
        "caption": "Fig. 2 Two-beam optical interferometry to measure EHD film thickness",
        "texts": [
            " This approach was first reported by Gustafsson et al. in 1994 [30] and has Proc Instn Mech Engrs Vol 215 Part J J03900 # IMechE 2001 at University of Liverpool on December 2, 2015pij.sagepub.comDownloaded from subsequently been further developed by a number of workers [31\u201334]. In 1996, this imaging method was combined with the use of a spacer layer to produce the spacer layer imaging technique (SLIM) [35]. The principle of classical two-beam optical interferometry, as applied by Gohar and Cameron to study EHL, is shown schematically in Fig. 2. A lubricated contact is formed between a reflective body (usually a steel or tungsten carbide ball or roller) and a transparent body (typically a glass, sapphire or diamond flat). Light is shone through the transparent body into the contact region. Here, \u2018division of amplitude\u2019 occurs and some of the light is reflected from the underside of the transparent disc while some passes through any oil film present, before being reflected back from the steel ball surface. Because they originate from the same source, the two reflected beams are coherent but, because one has travelled an extra distance, the two beams acquire a phase difference and undergo optical interference upon recombination"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure15.20-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure15.20-1.png",
        "caption": "Figure 15.20 Before collision.",
        "texts": [
            " The following example will illustrate some of the concepts in volved in two-dimensional collision problems. Example 15.8 Figure 15.19 illustrates an instant during a pool game. What the pool player wishes to do is to hit the stationary target ball (ball 2) by the cue ball (ball 1) so as to move the target ball toward and into the corner pocket. Consider that the cue ball is given a velocity of VIi = 5 m/ s toward the target ball, and that a line connecting the center of mass and the geometric center of the corner pocket make an angle () = 45\u00b0, as shown in Figure 15.20. The rectangular coordinates x and yare chosen in such a way that they respectively coincide with the line of impact (perpendicular to the contacting surfaces), and the plane of contact (tangential to the contacting surfaces). Assume that Impulse and Momentum 331 332 Fundamentals of Biomechanics the cue ball hits the target ball at a point along the line of impact, and that the balls have equal mass. Neglecting the effects of friction, rotation, and gravity, deter mine the velocities of the cue and target balls immediately after collision if the coefficient of restitution between them is e = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure2-1.png",
        "caption": "Fig. 2. Cross section of a commutator motor.",
        "texts": [
            ", for position control systems), acoustic noise, shape, volume, acceptability in hazardous e.nvironments, reliability, manufacturability, fail-safe features, initial cost, and present value of total lifetime cost including the cost of energy. 111. COMMUTATOR MOTORS Commutator motors (also known as direct-current motors) have been widely used for variable-speed drives. Because of their long history, it is convenient to begin with an examination of these to establish a basis of comparison for the variable-frequency machine types to be di:scussed later. Figure 2 shows a cross section of a typical machine. Around the outer structure, a number of iron poles project inward from a cylindrical iron yoke. Current in a field coil encircling each of the poles produces a magnetic flux in 1124 the air gap between the pole and the central 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 currentcarrying conductors. The coils of the armature winding are connected to a commutator or segmented mechanical switch mounted on the shaft",
            " For example, for a motor with a continuous rating of 50 kW at 2000 r/min (209 rad/s) with a cooling coefficient of 50 W/m2 . \"C, a temperature rise of 6OoC and an equivalent depth of armature conductor of 10 mm, the linear current density could be about 40 A/mm and the rotor dimensions might be chosen at about T = 95 mm and C = 190 mm. In addition to the loss in the armature winding, the commutator motor has losses in the iron laminations of the rotor core, conductor losses in the field coils, and in other compensating and commutating pole windings on the stator (not shown in Fig. 2), losses in the voltage drop of approximately 2 V in the commutator, loss due to friction at the bearings and commutator, and loss due to windage. Typical values for the efficiency of fully loaded 5 to 150 kW motors might be in the range 83 to 93% [2], [4]. Armature winding loss varies from 60% of the total loss for small motors to about 35% for large ones. C. Constant-Power Operation The number of turns in the armature winding and their series-parallel connections through the commutator to the brushes are chosen so that, at the base speed wb and with maximum field flux, the voltage generated by the armature is approximately equal to the maximum or base supply voltage V b "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003933_j.engfailanal.2010.11.009-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003933_j.engfailanal.2010.11.009-Figure7-1.png",
        "caption": "Fig. 7. Kinematic model of BWE working device [13].",
        "texts": [
            " The model represents the continuum discretized by the 4-node linear tetrahedron elements [11] in order to create the FEM model (1,917,704 nodes and 6,418,422 elements). The analysis of the external load is performed in accordance with the code [12]. It is worth mentioning that during the identification of the circumferential and lateral force, according to the above mentioned DIN code, the effects of the bucket wheel (BW) eccentricity are neglected in relation to the system lines of the boom and the boom inclination relative to the vertical and horizontal plane. Therefore, based on the model containing the above mentioned effects, Fig. 7, the in-house software RADBAG has been developed and validated [13,14], Figs. 8 and 9. This software enables the definition of the effect of resistance-to-excavation in any position of the bucket wheel boom (BWB). Functioning of the BWE is characterized by the phenomenon of an outstandingly dynamic character. The basic cause of this phenomenon is the fact that the buckets repeatedly get into contact with soil i.e., the changeability of the number of buckets to catch the soil. In this particular case, dynamic characteristics of the external load (f), shown below in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure9.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure9.5-1.png",
        "caption": "Figure 9.5 A linear dashpot and its force--displacement rate diagram.",
        "texts": [
            " The physical significance of this coefficient is similar to that of the coefficient of friction between the contact surfaces of solid bodies. The higher the coefficient of viscos ity, the \"thicker\" the fluid and the more difficult it is to deform. The coefficient of viscosity for water is about 1 centipoise at room temperature, while it is about 1.2 centipoise for blood plasma. The spring is one of the two basic mechanical elements used to simulate the mechanical behavior of materials. The second basic mechanical element is called the dashpot, which is used to simulate fluid behavior. As illustrated in Figure 9.5, a dashpot is a simple piston-cylinder or a syringe type of arrangement. A force applied on the piston will advance the piston in the direction of the applied force. The speed of the piston is de pendent upon the magnitude of the applied force and the fric tion occurring between the contact surfaces of the piston and cylinder. For a linear dashpot, the applied force and speed (rate of displacement) are linearly proportional, the coefficient of friction /-t (mu) being the constant of proportionality"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure11.29-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure11.29-1.png",
        "caption": "Figure 11.29 Problem 11.2.",
        "texts": [
            " Assume that at the instant when the ball is released, the person's hand is at a height ho = 1.5 m above the ground level. Neglecting the possible effects of air resistance, determine the maximum height hI that the ball reached, the total time t2 it took for the ball to ascend and descend, and the speed V2 of the ball just before it hit the ground. Note that this problem must be handled in two phases: ascend and descend. Also note that the speed of the ball at the peak was zero. Answers: hI = 6.6 m, t2 = 1.16 s, V2 = 11.4 m Problem 11.2 Consider the car shown in Figure 11.29. At posi tion 0, the car is stationary on a hill that makes an angle e with the horizontal. Assume that the gear of the car is at \"neutral\" and that at time to = 0 the brakes of the car are released. Under the effect of the gravitational acceleration g, the car will start moving down the hill. After some time, thecar will be at posi tion 1, which is at a distance d from position 0 measured parallel to the hill. Show that time tI to cover the distance between positions 0 and 1, and speed VI of the car at position 1 can be expressed as: tI = ~d g sine VI = J2gd sine Problem 11"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure4.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure4.5-1.png",
        "caption": "Fig. 4.5 Closed cross section",
        "texts": [],
        "surrounding_texts": [
            "The problem is solved (indirectly) by finding the stress function T which satisfies within the ellipse y2 z2 a2 + b2 = 1 the differential equation (4.14), and on the ellipse satisfies the boundary condition T = O. The function is { y2 z2 } T = m a2 + b2 - 1 , The stress components are (Eq. 4.13) 2z 2y IJxy = 2GrJm b2 ' IJxz = -2GrJm a2 The shear stress T is the resultant of IJ xy and IJ xz, and so y2 z2 T = 4GrJm a4 + b4 with the maximum value on the boundary at the ends of the minor axis, that is, at the points nearest the axis of the torsional rotations. 4.1 Solid Cross Sections 75 From Eq. (4.6), we determine by integration the function 7jJ(y, z) a 2 _ b2 7jJ = - Z--b2 yz. a + The lines of constant values of the warping are shown in Fig. 4.2. From these results, we can deduce the following relations MT Tmax = WT ' {} D Corresponding values of the polar moment of inertia J T and the section modulus W T may be determined for cross sections of different kinds: 1. Equilateral triangle Let the boundary of a torsion member be an equilateral triangle with h = V3a/2. Proceeding as for the elliptical cross section, we find MT Tmax = WT ' {} 1 3 WT = 20 a , V3 4 JT = -a . 80 (4.24) 76 4. Torsion of Prismatic Bars 2. Narrow rectangular cross section Consider a bar subjected to torsion. Let the cross section of the bar be a solid rect angle with width b and depth h, where b \u00ab h. From the different analogies (e.g. the soap-film analogy, originally proposed by L. Prandtl.),2 we may conclude that except for the region near z = \u00b1h/2 the stress components a xy and a xz are ap- f-b-j I y 1 Fig. 4.4 z Narrow rectangle proximately independent of z, and a xy ~ 0, a xz ~ T(Y) = 2G1'Jy. Thus, from Eq. (4.13), we determine T~T(y)= b; {l- (2:r}, and furthermore 1 3 Jr=3\"hb. (4.25) (4.26) (4.27) We note, however, that near the ends, of course, these results, which are valid only for narrow cross sections, do not apply. The exact theory for the rectangle is then required. The simple parabolic approximate form of T (Eq. 4.26) will give a good approx imation, since it differs from the true solution only in the small end zones. We may generalize Eq. (4.27) by introducing correction factors 0: and (3, as functions of the ratio h/b (see Table 4.1), to give 1 2 1 3 WT = 0: 3\" hb, Jr = (3 3\" hb . (4.28) 2 Analogies exist where physically different problems have similar mathematical descrip tions. In this case solutions - or experimental findings - from one problem may be trans ferred to the other - analogous - problem. The most known analogy to the torsion problem of prismatic bars is that of a membrane (soap film) fixed on a closed boundary, having the same shape as the cross section of the torsion bar, where pressure is applied to one side of the membrane. We therefore refer e.g. to the textbook of Boresi, Schmidt & Sidebottom, Advanced Mechanics of Materials, 5th. Edition, John Wiley & Sons, N.Y. etc., 1993. 4.2 Thin-Walled Closed Cross Sections 77 4.2 Thin-Walled Closed Cross Sections In the preceding section, we have discussed torsion of prismatic bars with solid cross sections. In the following sections, we now will examine this problem with thin-walled cross sections. We maintain the assumptions of St. Venant's theory about the displacement com ponents (Eqs. 4.1, 4.2), and furthermore - for the moment - assume unrestrained warping 'IjJ(y, z) in the x direction. In Section 3.2, we discussed beams of thin walled cross sections subject to shear forces. From this section, we take the modi fied description of thin-walled cross sections, with cross-sectional centerline (mid dle line), and additional rectangular coordinates (, along the centerline and 'f/, per pendicular to (. Thus, the thin-walled cross section is described by the coordinates y((), z(() of the centerline, and thickness J(() ofthe profile. for the shear stresses, and u=u(x,() (4.29) (4.30) for the displacements, constant in the 'f/ direction. We note that assumptions (4.29) coincide with the assumptions (3.37) for the shear stresses due to shear forces (Sec tion 3.2). Defining now the shear flow t( () as J 8/2 t(() = O\"xC, d'f/, (4.31) -8/2 we obtain with (4.29h t(() = T(()J((). (4.32) From the equilibrium (in axial direction) of a small element cut from the thin-walled tube (Fig. 4.6), we see that t = T( ()8( () = const. , (4.33) provided there are no axial stresses (J xx' Thus, the largest shear stress occurs where the thickness is smallest, and vice versa. Of course, if the thickness is uniform, then the shear stress T is constant around the tube. In order to relate the shear flow to the torque M T acting on the tube, consider an element of length d( in the cross section: The total shear force acting on the element is t de, and the moment of this force about any point 0 is dMT = a(()td(, (4.34) in which a( () is the distance from 0 to the tangent to the centerline. The total torque then is MT = t f a(()d( = 2Amt, (4.35) where the integral represents double the area Am enclosed by the centerline of the tube. From this equation, we find MT t = T(()8(() = 2Am ' (4.36) and finally, 4.3 Thin-Walled Open Sections 79 Tmax = (4.37) Bredt's first formula. To determine a relation between torque M T and twist {}, we start from assump tion (4.30), and (4.38) With these displacements, we find ) 1 { dux } ex((( =\"2 d( + {}a(() , (4.39) and thus from Hooke's law (4.40) Integrating this expression over the entire length of the centerline yields f T(() d( = c{ f dux + {} f a(() d(}. (4.41) The first integral of the right hand side vanishes (continuity of u x), and thus with Eq. (4.36), we finally arrive at 2 {f d( }-l Jr = 4Am 8(() , (4.42) Bredt's second formula. If in Eq. (4.41) the integrals are not taken over the entire length of the centerline, e.g. for the first integral of the right hand side J( dux = ux(() - ux(O) = {}{'l,b(() - 'l,b(O)} , (4.43) o Bredt's second formula is replaced by a slightly different relation (4.44) from which the distribution of the warping along the centerline may be calculated. 80 4. Torsion of Prismatic Bars Fig. 4.8 Thin-walled open section"
        ]
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.12-1.png",
        "caption": "Figure 6.12. Force sensors based on optical fibers. a. Contact force sensor; b. gripping force sensor.",
        "texts": [
            " The goal of the work described in [43] was the development of grippers with integrated sensors for gripping and contact force measurement. The gripper is actuated by piezoelectric bimorphs. A parallel movement of the gripper jaws is guaranteed by specially designed flexures. Force-sensitive elements and optical fibers have been integrated into the end-effectors. If a contact force acts on the gripped object, it is being transmitted through static friction forces (between object and end-effector) to the contact-force-sensitive elements (Figure 6.12a). Gripping forces are transmitted in a similar way to the gripping-force-sensitive elements (Figure 6.12b). Both elements transform the forces into deflections, causing the free end of the optical fiber to move relative to the fixed one. Thus, the intensity of the light interfacing with the receiving fiber is modulated by the force, and the force can be determined by measuring the change in intensity. Contact forces can only be measured correctly when the gripper\u2019s main axis is perpendicular to the working surface. Micromachined cantilevers with piezoresistors have been used at the Physikalisch-Technische Bundesanstalt, Germany, for two different applications: (i) as a sensor in a coordinate measurement machine [44], and (ii) as a portable gage, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003646_0005-1098(80)90082-5-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003646_0005-1098(80)90082-5-Figure1-1.png",
        "caption": "FIG. 1. Manipulator with three degrees of freedom.",
        "texts": [
            " This procedure is to ensure satisfaction of the condition (37). The condition (37) being satisfied, it should be checked whether )?~___){l(to). If this is satisfied, the imposed task is solved. If not, the 16 MIOMIR VUKOBRATOVIC a n d DRAGAN STOKIC control synthesis for system stabilization under large perturbations (Vukobratovi6, 1973; 1977a; 1978; 1976) is to be performed. 5. EXAMPLE OF A SYSTEM WITH ALL DEGREES OF FREEDOM POWERED: INDUSTRIAL MANIPULATOR In order to validate the proposed concept, a model of a three segment manipulator, shown in Fig. 1 (Vukobratovi6, 1977b), has been simulated. The manipulator mechanical model is given in the form (1) where n=3. The system has no degrees of freedom without actuators. Models of d.c. electromotors, S i are given in the form (2), where ni=3 for i= 1, 2, 3. All three degrees-of freedom are powered by d.c. electromotors, m = 3. The subsystems state vectors are-xi=(~ i, ~i i~), i~--the rotor current, so that k~ = 2 and N =9, ~ = (4,, 4, 0)L The complete system S model has been simulated on a digital computer, on the basis of the algorithm for setting the differential equations of active mechanisms dynamics (Vukobratovi6, 1976)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003271_978-3-642-83957-3_3-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003271_978-3-642-83957-3_3-Figure5-1.png",
        "caption": "Figure 5: Geometry of a 4R Elbow-Like Manipulator",
        "texts": [
            " Each Mi can be parametrized by a set of r independent parameters, If = {th,\u00b7\u00b7\u00b7,.pr}, which can be thought of as a natural coordinate system for the self-motions. For given x, the parametrization is typically unique (up to isomorphism), but the parametrization can vary as x varies in the workspace. The self-motion manifolds are best illustrated using two examples: a planar 3R manipulator (Figure 4) which is redundant with respect to the position of its end-effector, and a 4R regional manipulator which is similar to an \"elbow\" manipulator (Figure 5). The self-motion manifolds of the planar manipulator can be computed as follows. Let .p, which is the orientation of the third link relative to a fixed reference system, be the parameter describing the internal motion of the manipulator. There are two possible sets of joint angles, B. = {OI.,02.,03.} and Bb = {Olb,02b,03b}, which place the end-effector at (x\",Y .. ) with given .p. These solutions can be determined by evaluating the following equations: R2 = x~e +y~, +I~ - 213(xeecos.p +Yeesin.p) er = atan2(Yee -13 sin",
            " The two distinct self-motion manifolds in the preimage of point 1 physically corresponds to \"up elbow\" and \"down elbow\" self-motions which are an analogous generalization of the \"up elbow\" and \"down elbow\" configurations of a non-redundant two-link manipulator. Self-motions can be thought of as a natural generalization of the non-redundant manipulator concept of \"pose\" to redundant manipulators. In both cases, the self-motion manifolds are diffeomorphic 2 to a circle. However, the preimage of point 1 contains a 211' joint rotation while the other preimage does not. Now consider the 4R manipulator in Figure 5. The kinematic parameters of this arm (following the con ventions in [9]) are: 00 = 0; 01 = 02 = 11'/2; 03 = -11'/2; ao = al = a2 = 0; a3 = a4 = I; d l = d2 = d3 = d4 = O. Let the self-motion parameter, ,p, be the angle between the plane containing the third and fourth links and the vertical plane passing through joint axis 1. The following equations compute four inverse kinematic solutions, {Ola, 02a, 03a, 04a}, {Ou, 026 , 036 , 04a}, {Ol., O2., 03., 046}, {Old, OU, 03d, 046}, given x = (Zeo, Yeo, Zoe) and a value for the self-motion parameter, ,p",
            " All self motions in a C-bundle are homotopic, implying that the physical motion of the links in a self-motion are similar when the end-effector remains within one W-sheet. However, when crossing co-regular surfaces in C (or critical value manifolds in W), the homotopy class of the self-motion can change, and consequently, the physical motion of the links can change as well. This phenomenon can be demonstrated by considering a 7 R arm which is formed by adding a 3R wrist (with finite hand length) to the 4R manipulator of Figure 5 (additional kinematic parameters Q4 = 1r/2, Q5 = -1r/2, Q6 = 1r/2, as = as = a7 = 0, d5 = d6 = 0, d7 finite). In most parts of the workspace, the self-motion consists of a rotation of the plane containing links 3 and 4 about the line between the shoulder and the wrist. However, when axis 7 aligns with link 4, axes 1, 2, 3, and 4 are locked, and the self-motion manifests itself as a self-motion of wrist joint 5. This self-motion is physically very different from the nominal self-motion, and is separated in C from the nominal self-motions by a coregular surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003889_09544062jmes849-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003889_09544062jmes849-Figure4-1.png",
        "caption": "Fig. 4 Equivalent line of action and the plane of action for helical cylindrical gears",
        "texts": [
            " Hertz\u2019s theory is more accurate than FEbased contact analysis with a moderate or low number of elements, but the advantage of using FE method is that edge contacts can be taken into account. The Hertzian line contact formula is used in this study. The separately calculated structural and local contact stiffness values are combined using a theory of springs in series, the principle of which is shown in Fig. 3. The mesh stiffness variation of the cylindrical gear pair is modelled along an equivalent line of action in the middle of the facewidth (Fig. 4). This corresponds to actual meshing, which occurs at the plane of action [19, 20]. The meshing time period passing a transverse base pitch of the helical gear is tz [20] tz = 60 nrpmz1 (1) Thus, the total meshing time from start to finish is defined as tm = (\u03b5a + \u03b5\u03b2)tz (2) Examples of a single tooth pair\u2019s stiffness and a gear pair\u2019s mesh stiffness are presented in Fig. 5. Stiffness variation is studied along the equivalent line of action. Single tooth pair stiffness vector is copied with offset to show the other teeth in contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure15.21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure15.21-1.png",
        "caption": "Figure 15.21 After the collision.",
        "texts": [
            " (iii) and (iv), for two unknowns, (V2j)x and (vIjk Solving these equations simultaneously will yield: (e -1) (VIj)x = 2 (VIi)x (v) (e + 1) (V2j)x = 2 (VIih (vi) Substituting (VIi h = 3.54 ml sand e = 0.8 into these equations will yield: (VIj)x = -0.35 (V2j)x = 3.19 Hence, the velocities of the balls after the collision are: Y..Ij = -0.35 I + 3.541 (ml s) Y..2j = 3.19 I (m/s) Immediately after the collision, the target ball will move with a speed of 3.19 mls toward the comer pocket (i.e., along the positive x direction). As illustrated in Figure 15.21, the cue ball will move with a speed of VIj = )(0.35)2 + (3.54)2 = 3.56 mls along a direction that makes an angle arctan (3.54/0.35) = 84\u00b0 with the negative x direction, or at an angle f3 = 84\u00b0 - 45\u00b0 = 39\u00b0 with the horizontal. While utilizing the equations for the coefficient of restitution and conservation of momentum, we assumed that the velocity components of both balls would be in the positive x direction. As a result of our computations, we determined a negative value for (VIj)x, which means that it is acting along the negative x direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.41-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.41-1.png",
        "caption": "Figure 8.41 Fractured bone and its cross-sectional geometry.",
        "texts": [
            " The torque and angular displacement transducers measure the amount of torque applied on the specimen and the corresponding angular deformation of the specimen. The frac ture occurs when the torque applied is sufficiently high so that the stresses generated in the specimen are beyond the ultimate strength of the material. The data collected by the transducers of the torsion test ma chine can be plotted on a torque (M) versus angular deforma tion (angle of twist, e) graph. A typical M-e graph is shown in Example 8.4 A human femur is mounted in the grips of the torsion testing machine (Figure 8.41). The length of the bone at sections between the rotating (D) and stationary (E) grips is measured as L = 37 cm. The femur is subjected to a torsional loading until fracture, and the applied torque versus angular Multiaxial Deformations and Stress Analyses 177 displacement (deflection) graph shown in Figure 8.42 is ob tained. The femur is fractured at a section (section aa in Figure 8.41) that is e = 25 cm distance away from the stationary grip. The geometry of the bony tissue at the fractured section is ob served to be a circular ring with inner radius 'i = 7 mm and outer radius '0 = 13 mm (Figure 8.41). Calculate the maximum shear strain and shear stress at the frac tured section of the femur, and determine the shear modulus of elasticity of the femur. Solution: In Figure 8.41, () = 20\u00b0 is the maximum angle of deform ation (angle of twist) measured at the rotating grip at the instant when fracture occurred. The total length of the bone between the rotating and stationary grips is measured as L = 37 cm. There fore, the angular deformation is (200)/(37cm) = 0.54 degrees per unit centimeter of bone length as measured from the station ary grip. The fracture occurred at section aa which is e =25 cm away from the stationary grip. Therefore, the angular deflection ()aa at section aa just before fracture is (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure6.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure6.2-1.png",
        "caption": "Figure 6.2 Method of sections.",
        "texts": [
            " If one of these two parts is considered, then the equilibrium condition requires that there is a force vector and/ or a moment vector acting on the cut section to counterbalance the effects of the external forces and moments applied on that part. These are called the internal force and internal moment vectors. Of course, the same argument is true for the other part of the object. Furthermore, for the overall equilibrium of the object, the force vectors and moment vectors on either surface of the cut section must have equal magnitudes and opposite directions (Figure 6.2). For a three-dimensional object, the internal forces and moments can be resolved into their components along three mutually per pendicular directions, as illustrated in Figure 6.3. The force and moment vector components measured at the cut sections take special names reflecting their orientation and effects on the cut sections. Assuming that x is the direction normal (perpendicu lar) to the cut section, the force component Px in Figure 6.3 is called the axial or normal force, and it is a measure of the pulling or pushing action of the externally applied forces in a direction perpendicular to the cut section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003188_s10514-006-5204-6-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003188_s10514-006-5204-6-Figure3-1.png",
        "caption": "Figure 3. Model of link i.",
        "texts": [
            " When a snake-like robot creeps on a slope, it always slips in the normal direction, adding to the glide along the tangential direction. To analyze the creeping motion of the snake-like robot on a slope, the robot dynamics and its interaction with the environment must be considered. In this section, we formulate the dynamics of the snake-like robot that creeps on a slope and model the interaction of the robot with its environment, provided that the snake-like robot creeps on a plane and behaves as a rope with an infinitesimal diameter. Each link of the snake-like robot on a slope can be modeled as in Fig.3(a). On the basis of the Newton-Euler equation, we get the following equations for link i, f x i + f f x i \u2212 f x i+1 \u2212 mi g sin \u03c8 = mi i x\u0308G f y i + f f y i \u2212 f y i+1 = mi i y\u0308G \u03c4i \u2212 \u03c4i+1 \u2212 ( f f x i si \u2212 f f y i ci ) ( fi \u2212 Gi ) + ( f x i si \u2212 f y i ci ) Gi + ( f x i+1si \u2212 f y i+1ci ) ( i \u2212 Gi ) = Ii \u03c6\u0308i (5) wherein, \u03c4i is the torque at joint i, mi and Ii are the mass and the moment inertia of link i, f i ( f 0 = f n = 0) is the reaction force at joint i, f f i is the friction force at contact point of link i with the ground, and i = 0, 1, 2, \u00b7 \u00b7 \u00b7 , n \u2212 1",
            " (7) We have utilized the wheel on our robot to generate different friction between the tangential and normal directions. In this study, the interaction of the robot with the environment is expressed by the Coulomb friction. Since the robot almost always slips while climbing on a slope, the static friction does not greatly affect the result and is ignored, for the sake of simplicity. In addition, since we consider a robot moving only on a plane, the reaction force of each link perpendicular to the plane is affected only by its own gravity. As shown in Fig. 3(b), the friction force along the tangential direction, f f t i , and that along the normal direction, f f n i , are thus given by f f t i = \u2212\u00b5t mi g cos \u03c8 \u00d7 sign(\u03b4i r t ) (8) f f n i = \u2212\u00b5nmi g cos \u03c8 \u00d7 sign(\u03b4i r n) (9) where \u00b5t and \u00b5n express the friction coefficients in tangential and normal directions, while \u03b4i r t and \u03b4i r n express the displacement at the friction point. The friction forces along the x-axis and y-axis can be thus derived by f f x i = f f t i ci \u2212 f f n i si , f f y i = f f t i si + f f n i ci "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003795_978-3-540-85640-5_14-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003795_978-3-540-85640-5_14-Figure5-1.png",
        "caption": "Fig. 5. Saturation function and its gain characteristics.",
        "texts": [
            " Substituting q\u0307m into (15), |vdcos(\u03b1 \u2212 \u03b8 \u2212 \u03b4) + Lu3| \u2264 q\u0307m (16) |\u2212vdcos(\u03b1 \u2212 \u03b8 + \u03b4) + Lu3| \u2264 q\u0307m (17) |vdsin(\u03b8 \u2212 \u03b1) + Lu3| \u2264 q\u0307m, (18) the lower and upper boundary of u3 with respect to each wheel (lbi and ubi , i = 1, 2, 3) can be calculated as follows, lb1 = \u2212q\u0307m \u2212 vdcos(\u03b1 \u2212 \u03b8 \u2212 \u03b4) \u2264 Lu3 \u2264 q\u0307m \u2212 vdcos(\u03b1 \u2212 \u03b8 \u2212 \u03b4) = ub1 (19) lb2 = \u2212q\u0307m + vdcos(\u03b1 \u2212 \u03b8 + \u03b4) \u2264 Lu3 \u2264 q\u0307m + vdcos(\u03b1 \u2212 \u03b8 + \u03b4) = ub2 (20) lb3 = \u2212q\u0307m \u2212 vdsin(\u03b8 \u2212 \u03b1) \u2264 Lu3 \u2264 q\u0307m \u2212 vdsin(\u03b8 \u2212 \u03b1) = ub3 . (21) Then the dynamic boundary values of u3 are computed as lb = max(lb1 , lb2 , lb3)/L ub = min(ub1 , ub2 , ub3)/L, (22) where lb and ub are the low and up boundary. Considering the saturation function x2 = \u23a7\u23a8 \u23a9 ub, if x1 > ub x1, if lb \u2264 x1 \u2264 ub lb, if x1 < lb, (23) and its gain characteristics illustrated in Fig. 5, we can take the saturation function as a dynamic gain block ka, which has maximum value one and converges to zero when the input saturates. Then the closed-loop system of controlling the robot orientation is as shown in Fig. 6, in which a PD controller is used to control the robot orientation converging to the ideal \u03b8d, \u03c9 = k1(e\u03b8 + k2e\u0307\u03b8), (24) where e\u03b8 = \u03b8d \u2212 \u03b8, k1 and k2 are the proportional and derivative gains, respectively. It can be obtained that the closed-loop has only one pole \u2212kak1 1+kak1k2 and one zero \u22121/k2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure1-1.png",
        "caption": "Fig. 1. Face worm gear drive with a conical worm.",
        "texts": [],
        "surrounding_texts": [
            "Invention of face worm gear drives with conical and cylindrical worms by Saari [13,14] was a substantial contribution. One of the greatest advantages of such drives is the higher contact ratio as the result of simultaneous contact of several pairs of teeth during the cycle of meshing. Initially the design of the invented gear drives was based on application of worms provided by axial profiles as straight lines. The worms have been designed as helicoids of a constant lead angle. Investigation of the invented gear drives has been performed by Saari and his followers [13,14], Goldfarb and coworkers [3,4], Dudas [1] and other researchers [12]. Spiroid worm gear drives have been discussed as well in the Gear Handbook [16]. New modification of the face-gear drives have been proposed by Litvin and coworkers [8\u201311]. The bearing contact of the proposed drives is a localized and a favorable shape of transmission errors for reduction of noise and vibration is provided. This is achieved by double crowning of the worm. *Corresponding author. Tel.: +1-312-996-2866; fax: +1-312-413-0447. E-mail address: flitvin@uic.edu (F.L. Litvin). 0045-7825/02/$ - see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0045-7825 (02 )00235-9 The generation of face worm gear drives of all types of existing design is based on application of a hob for generation of the face-gear. The hob is similar to the worm of the drive. The disadvantage of such method of generation is the low precision of a hob used as a generating tool especially in the case of small dimensions of hob. The new geometry proposed in this article is based on application of head-cutters or head grinding tools that have higher precision and larger dimensions in comparison with a hob and enable to provide a higher productivity of the process of generation. The gear drives of new geometry may be generated similar to the generation of spiral bevel gears and hypoid gears [7,15]. The proposed new face worm gear drives (with conical and cylindrical worms) are provided with a localized bearing contact and predesigned parabolic function of transmission errors of low level. Such a function is able to absorb discontinuous linear functions of transmission errors caused by errors of alignment [8,9]. Therefore vibrations and noise of gear drives might be reduced. The localization of bearing contact is achieved by the mismatch of surfaces of generating head tools applied for generation of the face worm gear and the worm. Figs. 1 and 2 show in 3D space face worm gear drives with conical and cylindrical worms that have been investigated in this paper. The proposed new design of a face-gear drive is based on adaptation of the design parameters of a similar gear drive of existing design (based on generation of face-gear by a hob). This allows to build a bridge between both designs but affects as shown in Section 2 the dimensions of applied head cutters. The contents of the paper cover: (i) generation and analytical determination of tooth surfaces of the face-gear and the worm; (ii) simulation of meshing and contact; (iii) stress analysis. The developed theory is illustrated with numerical examples. The determination of conjugation of tooth surfaces of proposed gear drive required the application of theory of enveloping that is the subject of differential geometry and theory of gearing represented in the works by Zalgaller [17], Zalgaller and Litvin [18], Favard [2], Korn and Korn [6], Litvin [8,9], and other works."
        ]
    },
    {
        "image_filename": "designv10_8_0002969_a:1026100913269-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002969_a:1026100913269-Figure1-1.png",
        "caption": "Fig. 1. The computational domain in a channel: (a) top view and (b) side view. Fragments of the multiblock computational grid. Cylindrical grid with a patch: (c) top view and (d) side view; additional rectangular grid in the near wake with the dimple contour displayed: (e) top view and (f) side view; and (g) additional grid in the vicinity of the rounded sharp edge.",
        "texts": [
            " For the velocity transport equation, the corrections are not determined because, as a rule, only one iteration is made. For the majority of the remaining variables, the absence of this step somewhat delays convergence. And only for the pressure is it necessary to take into account corrections from other domains, because this is the only mechanism that enables one to automatically determine the constant specifying the accuracy in pressure. In order to describe the flow and heat transfer in the vicinity of dimples in a narrow channel, the following grids were introduced (Fig. 1): ai j k, , p HIGH TEMPERATURE Vol. 41 No. 5 2003 NUMERICAL SIMULATION OF VORTEX ENHANCEMENT OF HEAT TRANSFER 669 (i) an external rectangular grid for simulating the flow in a channel [if there are no dimples on the wall, this is the only grid for solving the problem (Figs. 1a and 1b)]; (ii) a cylindrical grid used to calculate the motion of the medium and heat transfer within a spherical dimple (Figs. 1c and 1d); (iii) a rectangular grid\u2014a patch on the axis of the cylindrical grid (Fig. 1c) is introduced to remove difficulties in calculating near-axis features; (iv) an additional rectangular grid (Figs. 1e and 1f) is internal with respect to the external grid and serves for a detailed calculation of flow and heat transfer in the vicinity of the dimple and in the wake behind it; (v) a curvilinear grid close to an orthogonal grid in the vicinity of the rounded sharp edge of the dimple (Fig. 1g) and intended for a more detailed description of a high-gradient flow in the zone where the curvature of the dimple contour subjected to flow changes sharply. For all grids, with the exception of the external one, two layers of peripheral cells are assigned to be coupled. These include side and upper layers and, for grid (ii), two more inner layers of the cylindrical grid. Further, the following procedure is performed in preparing input information. For each grid, we test the regions where it overlaps all other grids that are fully or partly within the tested grid",
            " The Prandtl number of the medium is set to 0.7, and the turbulence Prandtl number to 0.9. A series of calculations of convective turbulent heat transfer in the vicinity of spherical dimples with a rounded sharp edge (the radius of rounding was 0.05) and arranged on the wall of a narrow channel were performed at a fixed Reynolds number (Re = 104) for the dimple depth \u2206 varied from 0.04 to 0.24. The dimple diameter D and the maximum flow velocity at the channel inlet U were chosen as scales for going over to dimensionless variables. Figure 1 gives fragments of a multiblock computational grid that consists of about 450 000 cells. We consider a plane-parallel channel with a spherical dimple on the lower wall. A uniform flux with a characteristic velocity U and a boundary-layer thickness equal to 0.15 is preassigned at the inlet of the domain. Within the boundary layer, the longitudinal component of the velocity varies according to a 1/7 law, while the remaining components of the velocity and excess pressure are set to zero. The characteristics of turbulence at the inlet of the computational domain correspond to the conditions of the physical experiment in [8], the turbulence level of flow being 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.25-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.25-1.png",
        "caption": "Figure 5.25 Free-body diagram of the leg (a), and the geometric parameters (b).",
        "texts": [
            " 102 Fundamentals of Biomechanics muscles, F J is the magnitude of the joint reaction force applied by the pelvis on the femur, WI is the weight of the leg, W is the total weight of the body applied as a normal force by the ground on the leg. The angle between the line of action of the resultant muscle force and the horizontal is designated by O. A mechanical model of the leg, rectangular components of the forces acting on it, and the parameters necessary to define the geometry of the problem are shown in Figure 5.25. 0 is a point along the instantaneous axis of rotation of the hip joint, A is where the hip abductor muscles are attached to the femur, B is the center of gravity of the leg, and C is where the ground reaction force is applied on the foot. The distances between A and 0, B, and C are specified as a, b, and c, respectively. a is the angle of inclination of the femoral neck to the horizontal, and f3 is the angle that the long axis of the femoral shaft makes with the horizontal. Therefore, a + f3 is approximately equal to the total neck-to-shaft angle of the femur. Determine the force exerted by the hip abductor muscles and the joint reaction force at the hip to support the leg and the hip in the position shown. Solution 1: Utilizing the free-body diagram of the leg. For the solution of the problem, we can utilize the free-body diagram of the right leg supporting the entire weight of the person. In Figure 5.25a, the muscle and joint reaction forces are shown in terms of their components in the x and y directions. The resultant muscle force has a line of action that makes an angle 0 with the horizontal. Therefore: FMx = FM cosO FMy = FM sinO (i) (i i) Since angle 0 is specified (given as a measured quantity), the only unknown for the muscle force is its magnitude F M. For the joint reaction force, neither the magnitude nor the direction is known. With respect to the axis of the hip joint located at 0, ax in Figure 5.25b is the moment arm of the vertical component F My of the muscle force, and a y is the moment arm of F Mx. Similarly, (bx - ax) is the moment arm for WI and (cx - ax) is the moment arm for the force W applied by the ground on the leg. From the geometry of the problem: ax = a cosa ay = a sina bx = b cos f3 cx = c cos f3 (ii i) (i v) (v) (vi) N ow that the horizontal and vertical components of all forces in volved, and their moment arms with respect to 0 are established, Applications of Statics to Biomechanics 103 the condition for the rotational equilibrium of the leg about 0 can be utilized to determine the magnitude of the resultant mus cle force applied at A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002875_bf01686278-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002875_bf01686278-Figure2-1.png",
        "caption": "Fig. 2. The segment PP' of an orbit obtained by rotating the radius of curvature vector PQ into P'Q relative to the fixed center of curvature Q. The center of force is at C, and",
        "texts": [
            " For a body moving on a circular orbit with radius p with a uniform velocity v, NZWTON had shown in 1665 that the acceleration a is uniform and that it is directed towards the center of the orbit, with a magnitude [19] V 2 a = - - . (1) P This relation had been obtained also somewhat earlier by HUYGENS [20]. During this time NEWTON evidently had started already to think about the generalization of this result for an elliptical trajectory, as shown by a remark in his manuscript on circular motion [19, 21]: ness with that point of the Ellipsis. the dashed lines PC and P'C are the position vectors relative to C. Referring to Fig. 2, if the force is directed to a fixed center C then the appropriate generalization of Eq. (1) for the acceleration, assumed to be proportional to the force, at a point P on the orbit is [22] /)2 a, = - - (2) P where a, = a sin(~) is the component of the acceleration a normal to the velocity, p is the radius of curvature at P, and e is the angle between the radius vector C P and the tangent to the curve at P. During a small interval of time & the trajectory can then be approximated by rotating the radius of curvature vector through an angle 5q~ = v&/p "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure15.24-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure15.24-1.png",
        "caption": "Figure 15.24 The multi-force system can be reduced to a one-force and one-moment system.",
        "texts": [
            " Now that we have defined the basic concepts behind the rotational motion of rigid bodies, we can integrate our knowledge about translational and rotational motions to investigate their general motion characteristics. Consider the rigid body illustrated in Figure 15.23. Let m be the total mass of the body, and C be the location of its mass center. There are three coplanar forces acting on the body. Force F3 is not producing any torque about C because its line of action is passing through C (i.e., its moment arm is zero). Forces F 1 and F 2 are producing clockwise moments about C with magnitudes Ml =dlFl and M2 =d2F2, respectively. As illustrated in Figure 15.24, the three-force system can be reduced to a one-force and one-moment system such that L \u00a3 = F 1 + F 2 + F 3 is the net or the resultant force acting on the body and Me = Ml + M2 is the resultant of the couple-moments as measured about e. L F causes the body to translate and Me causes it to rotate about e. Recall that the translational motion of a body depends on its mass and the net force applied on it. Newton's second law of motion states that: (15.20) !I.e is the acceleration of the mass center of the body, and Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002457_s0094-114x(99)00036-1-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002457_s0094-114x(99)00036-1-Figure1-1.png",
        "caption": "Fig. 1. Illustration of the basic involute gear geometry. The actual location of the contact point between mating teeth varies with rotation, but must remain outside the base circle for no interference to occur. For additional details, see [6].",
        "texts": [
            " Similar analyses have undoubtedly been conducted over the years by experienced gear designers, perhaps involving signi\u00aecant trial and error, but to the authors' knowledge, the proposed methodology has not been expressed formally in the literature. As indicated in Section 1, the basic nomenclature for spur gear design adopted in [6] will be used in this paper. Important de\u00aenitions include the pitch diameter d, tooth number N, diametral pitch P (1/in. in English units), addendum diameter da, and face width b, as indicated in Fig. 1. For a mating gear and pinion, the corresponding variables will be denoted as dg, dp, Ng, Np, etc., when necessary. Note that N Pd and, for standard, full-depth involute teeth, the addendum diameter is given as da d 2=P: The base circle diameter is de\u00aened to be db dcos f where f represents the pressure angle. (The value of f 208 is used in this paper.) The maximum tooth bending stress s in the vicinity of the root \u00aellet is estimated as s FtP bJ KvKoKm 2:1 where Ft represents the tangential gear force, and J the Lewis spur gear geometry factor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure3.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure3.1-1.png",
        "caption": "Fig. 3.1 Solenoid actuator sketch",
        "texts": [
            " IEEE Transactions on Control Industrial Electronics 43(1):142\u2013152 18. Taylor E (1974) Dimensional analysis for engineers. Clarendon Press Oxford 19. Zienkiewics O, Taylor R, Nithiarasu P, Zhu J (2005) The Finite Element Method. Elsevier/Butterworth-Heinemann Part II Conventional Actuators Chapter 3 Design Analysis of Solenoid Actuators The solenoid actuators provide motion exciting a magnetic field where a plunger (movable part) tries to minimize the reluctance (i.e. the air gap ) moving to the less reluctance position. A typical geometry is shown in Figure 3.1. The geometric constants and aspect ratios can be defined as [4, 5, 3]: kri = ri r (3.1) kli = li l (3.2) \u03b7 = l r (3.3) 81 82 3 Design Analysis of Solenoid Actuators where the non-dimensional constants associated to the radial lengths correspond to kri, while the axial lengths constants correspond to kli. The filling factor can be computed as the ratio between the profitable copper section Suse and the overall actuator section Stotal as k f f = Suse Stotal = NAw Stotal (3.4) where Aw is the single copper wire section and N is the number of turns"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002321_jsvi.2000.2950-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002321_jsvi.2000.2950-Figure1-1.png",
        "caption": "Figure 1. Test linear bearing.",
        "texts": [
            " Second, we measure the vibration characteristics such as overall level of vibratory velocity and vibration spectra of the LGT recirculating linear ball bearing at a constant linear velocity. Third, to explain the main peaks which appeared in the vibration spectra, we examine the modes of the carriage and carry out the natural vibration analysis of the LGT recirculating linear ball bearing. Finally, we discuss the relationship between the main peak and the natural vibration of the carriage. The test linear bearings used in the vibration measurement are the LGT recirculating linear ball bearings shown in Figure 1. One test linear bearing consists of one pro\"le rail and one carriage with recirculating balls. Preloads of test linear bearings are light or medium. The preloading for the test linear bearings was made by inserting balls slightly larger than the ball groove space between the pro\"le rail and the carriage. Table 1 shows the test linear bearing speci\"cation. The test linear bearings in this study and those of a previous sound study [10] are identical. All test linear bearings were lubricated with mineral oil (ISO VG56)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure15-1.png",
        "caption": "Fig. 15. Cross section of inset PM motor.",
        "texts": [
            " If the saliency ratio is sufficient to produce a power factor equal to that of the induction motor, the stator winding loss will be the same. Also, the stator iron losses will be similar for the two motors. SLEMON: ELECTRICAL MACHINES FOR VARIABLE-FREQUENCY DRIVES 113s VIII. PM-RELUCTANCE MOTORS The surface PM motor considered earlier (Fig. 8) 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. Figure 15 shows a cross section of an inset PM motor. The magnets are inset into the rotor iron [33]. As a Ph4 motor, the direct axis is aligned with the magnets. Coiisidered as a reluctance machine, its direct-axis inductance will be small because of the near-unity relative permeabilily of the magnet material. The quadrature inductance 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 Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002965_tia.2005.855043-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002965_tia.2005.855043-Figure9-1.png",
        "caption": "Fig. 9. Description of different phasors.",
        "texts": [
            " The magnitude of is controlled at every instant by controlling the angle between components of and . To achieve this, a fictitious flux is defined. does not have any physical significance but its magnitude is used for control action of different Individual flux control algorithms. is the direct addition of and , without transforming them to a common axis (7) (7) If is the angle between the components of and , then the magnitude of is defined in (9) (8) (9) The magnitude of identifies (8)\u2013(14) (Fig. 9) (10) (11) (12) Automatically, a question arises: why is the magnitude of not used instead of to identify the phase angle sep- aration between the components of and ? (13) (14) Hence, whether is more or less from the reference value, cannot be judged by the magnitude of , because for both the cases it is less than the reference value. B. Individual Flux Control Algorithm #01 In this algorithm, both inverters are switched from their own hexagonal space-vector locations (Fig. 10). Magnitudes of individual fluxes are kept constant by a conventional two-level flux hysteresis controller [4]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.12-1.png",
        "caption": "Figure 7.12 Stress-strain diagram for axial loading.",
        "texts": [
            "l/l graph of a material is essentially the stress-strain diagram of that material. Different materials demonstrate different stress-strain relation ships, and the stress-strain diagrams of two or more materi als can be compared to determine which material is relatively stiffer, harder, tougher, more ductile, and/ or more brittle. Before explaining these concepts related to the strength of materials, it is appropriate to first analyze a typical stress-strain diagram in detail. Consider the stress-strain diagram shown in Figure 7.12. There are six distinct points on the curve that are labeled as 0, P, E, Y, V, and R. Point 0 is the origin of the a\u00b7\u00b7E diagram, which cor responds to the initial no load, no deformation stage. Point P represents the proportionality limit. Between 0 and P, stress and strain are linearly proportional, and the a-E curve is a straight line. Point E represents the elastic limit. The stress corresponding to the elastic limit is the greatest stress that can be applied to the material without causing any permanent deformation within the material",
            " The yield strength of such materials is determined by the offset method, illustrated in Figure 7.13. The offset method is applied by drawing a line parallel to the linear section of the stress-strain diagram and passing through a strain level of about 0.2 percent (0.002). The intersection of this line with the O'-E curve is taken to be the yield point, and the stress corresponding to this point is called the apparent yield strength of the material. Note that a given material may behave differently under differ ent load and environmental conditions. If the curve shown in Figure 7.12 represents the stress-strain relationship for a mate rial under tensile loading, there may be a similar but different curve representing the stress-strain relationship for the same material under compressive or shear loading. Also, tempera ture is known to alter the relationship between stress and strain. For a given material and fixed mode of loading, different stress strain diagrams may be obtained under different temperatures. Furthermore, the data collected in a particular tension test may depend on the rate at which the tension is applied on the spec imen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.2-1.png",
        "caption": "Figure 13.2 (J = (J2 - (Jl is the angular displacement in the time interval between tl and t2'",
        "texts": [
            " If one pair is known, then the other pair can be calculated because they are associated with a right-triangle: r is the hypotenuse, () is one of the two acute angles, and x and yare the lengths of the adjacent and opposite sides of the right-triangle with respect to angle (). Therefore: x = r cos(} y = r sin(} Expressing rand () in terms of x and y: r = Jx2 + y2 () = arctan (~) 13.2 Angular Position and Displacement (13.1) (13.2) Consider an object undergoing a rotational motion in the xy plane about a fixed axis. Let a be a point in the xy-plane along the axis of rotation of the object, and P be a fixed point on the object located at a distance r from a (Figure 13.2). Point P will move in a circular path of radius r and center located at O. Assume that at some time tll the point is located at PI which makes an angle (}I with the horizontal. At a later time t2, the point is at P2 which makes an angle (}2 with the horizontal. Angles (}I and (}2 define the angular positions of the point at times tl and t2, respectively. If () denotes the change in angular position of the point in the time interval between tl and t2, then () = (}2 -(}I is called the angular displacement of the point in the same time interval between"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.30-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.30-1.png",
        "caption": "Figure 13.30 Circular motion of B as observed from point A.",
        "texts": [
            " Angular Kinematics 291 292 Fundamentals of Biomechanics Since the angular velocity and acceleration of arm AB are given relative to point A, the motion characteristics of any point on arm AB can be determined with respect to the XY coordinate frame. Similarly, the motion of any point on arm BC can easily be analyzed relative to the xy coordinate frame. Motion of point B as observed from point A: Every point on arm AB undergoes a rotational motion about a fixed axis passing through point A with constant angular ve locity of WI = 2 rad/ s. Every point on arm AB experiences a uniform circular motion in the counterclockwise direction. As illustrated in Figure 13.30, point B moves in a circular path of radius \u00a31. Magnitudes of linear velocity in the tangential direc tion and linear acceleration in the normal direction of point B can be determined using: VB = \u00a31 WI aB=\u00a3l W12 The magnitude of the tangential component of the acceleration vector is zero since WI is constant or since ell = O. Therefore, VB and a B are essentially the magnitudes of the resultant linear velo city and acceleration vectors. To express these quantities in vec tor forms, let n1 and t1 represent the normal and tangential directions to the circular path of point B when arm AB makes an angle lh with the horizontal (Figure 13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002650_robot.2000.844824-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002650_robot.2000.844824-Figure6-1.png",
        "caption": "Figure 6: Data acquired during one measurement",
        "texts": [
            " The camera with close-up lenses can be easily attached to the body of the instrument, through a standard coupling mechanism. The pneumatic system is connected to the aspiration tube The profiles are extracted from the grabbed images in real time at a rate of 25 Hz and with a resolution of 30 pm , [31]. Real time extraction of the profiles avoids storage problems and can lead to on-line material parameter estimation in the future. The data acquired from an experiment performed ex-vivo on a pig kidney cortex, are shown in Figure 6. Applying the relative negative pressure P(t ) from Figure 6(a) resulted in the deformation illustrated in Figure 6(b), where the profiles of the created bulbs are given over time. These data are subsequently used to determine the numerical values of mechanical parameters goveming the continuum mechanics model chosen for the investigated tissue. The unknown material parameters C t 1 , z[sl, CI t N / m I and y[ 3 are determined via the inverse finite element method. A parameter identification algorithm performs a minimization of the squared differences between measured load-deformation data and data obtained through finite element simulation, using the Levenberg-Marquardt algorithm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002776_rob.20082-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002776_rob.20082-Figure3-1.png",
        "caption": "Figure 3. Projection of S\u201d a, S\u201d b onto a plane orthogonal to S\u201d u.",
        "texts": [],
        "surrounding_texts": [
            "This section is devoted to the determination of the rotation part of X. It will be shown that the rotation axis can be freely chosen with the restriction that it must lie in a given plane and, after choosing the axis, the rotation angle is uniquely determined. From Eq. 5 , we can deduce u a=Ruu bRu t , and so matrix Ru is the rotation which transforms the unit vector ub in ua ua=Ruub . There is an infinite number of possible rotations achieving this result Figure 1 . In fact, considering an arbitrary unit vector u which lies on the plane orthogonal to the difference between ua and ub, a rotation of an appropriate angle around u transforms ub into ua. To determine , it is convenient to represent vectors in an \u201cintrinsic\u201d frame whose axes u1, u2, and u3 are parallel to vectors v1, v2, and v3 v1 = ua ub, ua = 0 B C t, v2 = ua \u2212 ub, ub = 0 \u2212 B C t, v3 = ua + ub, u = cos 0 sin t, with B2+C2=1. The trivial case is u=u3, for which we obviously get = . As a second simple choice, we can select u=u1 getting cos =ua \u00b7ub. The value of for the general case is found by expanding ub=Ruua into its scalar terms see Eq. A1 in the Appendix ; we get = atan2 \u2212 2 cos CB cos 2C2 + B2 , cos 2C2 \u2212 B2 cos 2C2 + B2 , 6 where atan2 y ,x is the four-quadrant extension of arctan y/x . This term evaluates the angle of a vector whose components are y and x. The rotation matrix Ru can be evaluated by u and by means of Eq. A1 . The unit vector, u, represents the direction of the screw axis S\u201d u."
        ]
    },
    {
        "image_filename": "designv10_8_0002929_bf01257946-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002929_bf01257946-Figure2-1.png",
        "caption": "Fig. 2. Physical dimensions of base and top.",
        "texts": [
            " Fix an inertia frame (X, Y, Z) at the center of the lower platform with the Z-axis pointing vertically upward. Fix another moving coordinate system ( x , y , z ) at the center of gravity of the upper platform with the z-axis normal to the platform, pointing outward. In the sequel, these two coordinate systems are called the BASE frame and the TOP frame, respectively. The physical dimensions of the lower and upper platform and the coordinates of their vertices in terms of the BASE frame or the TOP frame are shown in Figure 2. To specify the configuration of the six-degree-of-freedom Stewart platform, six independent position-orientation variables are needed. Denote the location of the origin of the TOP frame with respect to the BASE frame by [px,pr , pz] T. Let (c~, 3, 7) represent rotation angles defined by serially rotating the TOP frame about three certain axes. Thus, the position and orientation of the upper platform is specified by Xp_ o = [Px, Pr, Pz, c~, 3, 7] x. A basic requirement for Xp_ o is that there is a one-to-one relationship between the system configuration and the value of Xp_o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002378_bf02481317-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002378_bf02481317-Figure2-1.png",
        "caption": "Fig. 2. Articulated robot arm with two degrees of freedom",
        "texts": [
            " Conceptual explanation of force-free control by an external force under gravity-free and friction-flee conditions. Dynamic equation of industrial articulated robot arms A dynamic equation of an articulated robot arm is given by 6 H(q)i) + D O + h(q, q) + g(q) = t\" (1) where H(q) is the inertia matrix, D is the friction matrix, h(q, dl) are the coupling nonlinear terms, g(q) is the gravity term, ~s is the input torque to the robot arm, q is the joint position, and e) is the derivative of q. In the case of an articulated robot arm with two degrees of freedom, as shown in Fig. 2, the parameters are derived as follows: A conceptual explanation of force-flee control is shown in Fig. 1. The left-hand side of Fig. 1 shows the ideal situation of force-free control where a virtual robot arm is connected to a friction-flee bearing in a gravity-flee space. The righthand side of Fig. 1 shows an actual robot arm which is driven by a motor in normal space under the influence of gravity. On the left-hand side, when an external force is added at the tip of the virtual robot arm, it rotates on the friction-free bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003366_tbme.2007.908069-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003366_tbme.2007.908069-Figure2-1.png",
        "caption": "Fig. 2. Calculating blade curve for a pair of Metzenbaum scissors. An analytical curve is fit to the edge of the upper blade.",
        "texts": [
            " ( is not zero because scissors\u2019 blades are slightly tapered as shown in Fig. 1.) The force felt by the user at the handle is calculated by (3) where is the distance between the pivot and the handle. The curve of the blade edge has a significant effect on the torque response of the scissors. Here, we define the curve of the edge of the upper blade in the Cartesian frame as (4) where is a point on the edge of the blade and is a nonlinear function. We obtain by fitting an analytical curve to the edge of the upper blade as shown in Fig. 2. We extract the blade edge from a real image of the blade. Considering (4), the displacement length caused by a blade with curve is obtained by (5) Fig. 1 shows two sequential time steps: and of a scissor cutting process. During , the opening angle of the scissors is changed from to , and the crack tip position is moved from to . The area of crack extension is . A fracture mechanics energy-based approach is used to estimate the torque and the crack tip position during cutting. Based on the principle of conservation of energy (6) where is the external work applied by the scissors, is the change in elastic potential energy stored in the plate, and is the irreversible work of fracture",
            " The pivot displacement and the opening angle were measured by encoders. An ATI Nano-17 force sensor attached to the rotational arm of the robot was used to measure the cutting forces. The force sensor was not connected to the upper blade, in order to prevent possible misalignments of the setup that would damage the force sensor. Two pairs of Metzenbaum scissors with different blade sizes were used. The function that represents the edge curve of a pair of Metzenbaum was obtained by geometrical calculations (considering a blade has a tapered, rectangular shape, Fig. 2) (19) where and were two constant coefficients. The coefficients for the small and large scissors were obtained based on measurements taken directly from the scissors. We took a picture of each pair of scissors and then set the coefficients fitting the curve to the edge of the upper blade of the scissors in the image (see Fig. 2). The coefficients were Small scissors Large scissors (20) The distance of the force sensor from the pivot of the scissors were Small scissors cm Large scissors cm. These lengths were used to calculate torques applied to scissors from the forces measured by the force sensor. We cut strips of four different materials: paper, plastic, cloth, and chicken skin. The width of all samples was approximately 2.3 cm. During each test, a sample was held along the straight edge of the upper blade of scissors by two clamps (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.23-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.23-1.png",
        "caption": "Figure 4.23 One-pulley traction.",
        "texts": [
            " If needed, these forces could be determined by considering the horizontal and vertical equilibrium of the pulley. Figures 4.23 and 4.24 illustrate examples of simple traction de vices. Such devices are designed to maintain parts of the human body in particular positions for healing purposes. For such de vices to be effective, they must be designed to transmit forces properly to the body part in terms of force direction and magni tude. Different arrangements of cables and pulleys can transmit different magnitudes of forces and in different directions. For example, the traction in Figure 4.23 applies a horizontal force to the leg with magnitude equal to the weight in the weight pan. On the other hand, the traction in Figure 4.24 applies a horizon tal force to the leg with magnitude twice as great as the weight in the weight pan. Example 4.4 Using three different cable-pulley arrangements shown in Figure 4.25, a block of weight W is elevated to a certain height. For each system, determine how much force is applied to the person holding the cable. Solutions: The necessary free-body diagrams to analyze each system in Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure17-1.png",
        "caption": "Fig. 17. Finite element model of the whole worm.",
        "texts": [
            " Step 6: The definition of the contact surfaces necessary for the finite element analysis is accomplished automatically, identifying all the elements of the model required for the formation of such surfaces. A symmetric master-slave method has been applied. This method causes the algorithm to treat each surface as a master surface. The finite element analysis has been performed for a face-worm gear drive with conical worm of common design parameters represented in Table 1. For the analysis the model of the whole worm (Fig. 17) and the whole face-gear (Fig. 18) have been substituted by a model of five-pair of teeth in meshing (Fig. 19) in order to save computational time. Elements C3D8I of first order have been used for the finite element mesh. The total number of elements is 55 672 with 68 671 nodes. The material used is steel with Young\u2019s modulus E \u00bc 206800 N/mm2 and Poisson\u2019s ratio 0.29. The torque applied to the face-gear is 50 Nm. Figs. 20\u201322 show how the bearing contact looks at the beginning, at the middle, and at the end of a cycle of meshing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003152_j.ijmachtools.2004.11.006-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003152_j.ijmachtools.2004.11.006-Figure2-1.png",
        "caption": "Fig. 2. Geometric definition of a generalized cutter. R1, Cutter major radius; R2, Cutter minor radius; h, Offset distance from NC programming point to the center of the toroidal surface; h0, Distance from the cutter tip point to the center of toroidal surface; f, Angle from a radial line through the cutter tip to the cutter bottom 0!f%p/2; b, Taper angle between the cutter side and the cutter axis, Kp/2!b!p/2; l, Cutter length measured from the cutter tip along the cutter axis.",
        "texts": [
            " Therefore, an arbitrary point P with respect to the moving frame {e} can be expressed in the reference frame as MP Z Cp\u00f0t\u00deC MRe\u00f0t\u00de, eP: (8) To compute the swept volume of the cutting tool during any trajectory, the tool configurations and the corresponding coordinate transformation from the moving frame to the reference coordinate frame have to be known. As for the geometry of the cutting tool, we focus on the geometric definition of a generalized cutting tool (also known as APTlike cutter) in this article. Then, the most commonly used tools, such as the ball-end and fillet-end cutter, will be derived based on the defined cutter geometry. Fig. 2 shows the geometric definition of a generalized cutter. Considering the envelope theory [5,6], to make the instantaneous tool velocity and surface normal valid, there are two limitations: (a) the boundary surfaces of the tool are C1-continuous (regular surfaces, non-degenerate case), (b) the cutter motion trajectory (NC-path) is C1-continuous or piecewise C1-continuous. In the following derivations the control point C(t) is considered to be located at an offset distance of h from the NC control point to the center of the toroidal surface along the axis A(t) (see Fig. 2). Allowing such an offset is necessary especially for the different NC programming definitions. For instance, the control point is sometimes located at the cutter tip, sometimes defined at the pivot point. Based on the description, the corresponding geometric definition of a cutter can be determined with respect to the moving frame. Given a generalized tool, the boundary surfaces of the tool can be decomposed into corner toroidal surface, upper and lower conical surfaces. These surfaces are represented with respect to the moving fame as eSL\u00f0u; vL; t\u00de Z vL tan 4 cos u vL tan 4 sin u h Kh0 CvL 0 B@ 1 CA; eST \u00f0u; vT ; t\u00de Z \u00f0R1 CR2 sin vT \u00decos u \u00f0R1 CR2 sin vT \u00desin u h KR2 cos vT 0 B@ 1 CA; eSU \u00f0u; vU ; t\u00de Z \u00f0RL u CvU tan b\u00decos u \u00f0RL u CvU tan b\u00desin u h KR2 sin b CvU 0 B@ 1 CA: (9) where eSL, eST and eSU are the representations of the lower conical, toroidal and upper conical surfaces with respect to the moving frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002528_978-3-662-04117-8-Figure7.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002528_978-3-662-04117-8-Figure7.1-1.png",
        "caption": "Figure 7.1: Experimental machine",
        "texts": [
            " Thomas Frenz In this chapter we are going to show an application example for the method of a systematic intelligent observer design presented in chapter 5. For a feed drive of a tool machine with unknown nonlinear friction a linear model is derived and a nonlinear observer is designed for the identification of the friction characteristic. The objective is to learn and compensate the sliding-friction of a feed drive of a lathe. Further information can be found in [1, 2, 3, 4, 5]. References on literat ure of the theoretical parts can be found in the chapters 3, 4 and 5 The examined tool machine is a Gildemeister GD 200 as shown in figure 7.1. The feed drive consists of a servo drive, a toothed belt gear, a screw spindle, a ball-and-screw spindle drive and a slide; here a hydrodynamic sliding bearing is used. The friction in feed drives originates mainly in the bearing assembly of the slide. It is advantageous for a well-damped mechanical system behaviour, but disadvan tageous for an exact positioning andjor contouring control. Thercfore we intend to leam the friction characteristic and compensate it using feedforward control. So we want to combine the advantage of a well damped mechanical system with a precise positioning andjor contouring control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003749_03052151003759125-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003749_03052151003759125-Figure2-1.png",
        "caption": "Figure 2. Set of rotor-bearing systems.",
        "texts": [
            " So, for each , the natural frequency \u03c9rad assumes a different value. Note that natural frequencies in radians per second, \u03c9rad, are differentiated from natural frequencies in hertz, \u03c9. The real part \u03c3 is related to the damping factor, and it must be negative for stable systems. A plot of the natural frequencies as a function of is called a Campbell diagram (Childs 1993, Genta 2005). The uncertainty related to the parameters of one rotor-bearing system is not high, but if a set of rotor-bearing systems is taken into account (see Figure 2), then the uncertainties are more important as each system may differ slightly from the others. The parametric probabilistic approach is used to model the uncertainties of the parameters, therefore the choice of the probability distribution function is crucial since all the stochastic simulations depend on this choice. The parameters modelled as random variables are the diameter of the shaft, d, the elasticity modulus, E, the mass of the rotor, mr, and the stiffness of the bearing, kb. The random variables related to these parameters are D, E , Mr and Kb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.57-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.57-1.png",
        "caption": "Figure 8.57 Both normal and shear stresses occur on a material element subjected to bending.",
        "texts": [
            " The shear stress is constant along lines Multiaxial Deformations and Stress Analyses 185 parallel to the neutral axis. The shear stress is maximum at the neutral axis, where Yl = 0 and Q is maximum. Maximum shear stresses for different cross-sections can be obtained by substi tuting the values of I and Q into Eq. (8.19), which are listed in Table 8.1. For example, for a rectangular cross-section: 3V Tmax = 2 b h Consider a cubical material element in a beam subjected to shear force and bending moment as illustrated in Figure 8.57. On this material element, the effect of bending moment M is represented by a normal (flexural) stress ax, and the effect of shear force V is represented by the shear stress Txy acting on the surfaces with normals in the positive and negative x (longitudinal) directions. As shown in Figure 8.57b, for the rotational equilibrium of this material element, there have to be additional shear stresses (Tyx) on the upper and lower surfaces of the cube (with normals in the positive and negative Y directions) such that numerically Tyx = Txy. The occurrence of Tyx can be understood by assuming that the beam is made of layers of material, and that these layers tend to slide over one another when the beam is subjected to bending (Figure 8.58). There are various experiments that may be conducted to analyze the behavior of specimens subjected to bending forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure1-1.png",
        "caption": "Fig. 1. Claw-type tooth profile.",
        "texts": [
            " Subsequently, Feng, Yueyuan, Ziwen and Pengcheng [15] presented a rotor geometry characteristics and mathematical models to predict the backflow within twin square-threaded screw pump. They also presented a discussion on the relationship between the slippage rate and the differential pressure, suction pressure, gas void fraction and the rotor rotational speed. From the comparison between the simulation result and experimental data, it shows that the model can simulate the working process of a twin square-threaded screw pump successfully. In the profile design shown in Fig. 1, the claw profile consists of an arc, an Archimedean and an epitrochoid that is generated by the tip point of the claw. Hence, its contact type is point to curve. Followings explains the existing disadvantages of the current design and propose our ideas on the improvement: (1) As shown in Fig. 1, there is a larger gas carryover at the claw-shape. This means a larger gas may be carried from high-pressure port back to low-pressure port. Thus, the pump performance may be reduced. In this paper, we propose a new claw-shape whose concept design is shown in Fig. 3. This new design of claw-shape is similar to Kashiyama patent [16] as shown in Fig. 4. Kashiyama developed twin-screw compressor with square-threaded rotor for the vacuum system and distinguished from the conventional one by the extra large wrap angle except the tooth profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure13-1.png",
        "caption": "Fig. 13. Screw rotor for example 3.",
        "texts": [
            " In example 3, the curve of shortened epicycloid is added to the tooth profile. In this paper, we mainly focus on the issue that different claw-shapes may affect its pump performance. Due to the same claw-shape design in example 1 and the patents, we will represent example 1 as the patent design. Figs. 8\u201310 represent the design results and locus of examples 1, 2 and 3, respectively. Figs. 11\u201313 illustrate the screw rotors in examples 1, 2 and 3, respectively. As shown in Fig. 11c, Fig. 12c and Fig. 13c, we can verify our drawings by calculating the equation of the line of action and then draw it out onto the screw rotor surface where it adheres. Our results then verify the accuracy of the rotor design. The performance and sealing properties will be discussed in the following sections. When area efficiency increases, the pump exhaust also increases. Therefore, one common method for estimating pump performance is to calculate the area efficiency by integration. That is to say, if the rotor tooth profile consists of multiple segment curves, each segment must be integrated and then summed to give the area of the rotor",
            " The calculated results of these three examples are shown in Table 2, and the area efficiency in example 1 is lower than that in examples 2 and 3. The result shows the length of line of action in example 1 is the shortest because the sealing line between the mating rotors is not continuous as shown in Fig. 11d. Figs. 11\u201313 illustrate the inappropriateness of the design in example 1. In Fig. 11b, if we move the screw rotor to a certain angle, an obvious clearance may appear, indicating that the design of this example is inferior. However, in Fig. 12d and Fig. 13d, the lines of action are continuous; there is no clearance between the mating rotors in Fig. 12b and Fig. 13b. Thus, the designs in examples 2 and 3 are better than that in example 1. In contrast to the design in example 2, using a curve with shortened epicycloid for the tooth profile in example 3 can improve pump performance. By comparison of these two examples, it shows that their area efficiencies are approximate but the line of action in example 3 is shorter than that in example 2. Therefore, example 3 could be thought better than example 2. According to the discussion above, we know the design of claw-shape in example 1 cannot form a well gas sealing between the twin-screw rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003124_j.ijar.2006.08.002-Figure16-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003124_j.ijar.2006.08.002-Figure16-1.png",
        "caption": "Fig. 16. The inverted wedge balancing mechanism.",
        "texts": [
            " 12\u201314, we observed that the settling time, overshoot performance and robustness of the proposed DSMFNNC control approach is better than fuzzy control [26] as Fig. 13 and SMC as Fig. 14. Consider a seesaw system as depicted in Fig. 15 and can be represented by the dynamical equation as u\u00fe mg sin h B _x \u00bc m\u20acx; \u00f0Mg sin h\u00der2 \u00fe mg sin\u00f0h\u00fe /\u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x2 \u00fe r2 1\u00de q \u00fe ur1 l _h \u00bc I\u20ach \u00f048\u00de where I is the wedge inertia, / is the angle that the cart makes with the wedge line and the system parameters (m,M, r1, r2, I) are (0.46, 1.41, 0.121,0.095). In a seesaw system as shown in Fig. 16, let x be the distance of the cart from the origin, h be the angle that the wedge makes with the vertical line, r1 be the height of the wedge and r2 be the center of mass of the center of mass of the wedge. The parameters of the dynamics equation can be defined as follows: x1 = h, _x2 \u00bc _h, x3 = x, _x4 \u00bc _x and s1 \u00bc c1\u00f0h z\u00de \u00fe _h \u00bc c1\u00f0x1 z\u00de \u00fe x2 \u00f049\u00de s2 \u00bc c2x\u00fe _x \u00bc c3x3 \u00fe x4 \u00f050\u00de with z \u00bc sat\u00f0s2=Uz\u00de Zu; 0 < Zu < 1 \u00f051\u00de In the experiment, the following specifications are used: c1 \u00bc 5; c2 \u00bc 0:5; Uz \u00bc 15; Zu \u00bc 0:9425; 11 \u00bc 0:1; 12 \u00bc 0:1 In this experiment, we turn out attention to the performance of the seesaw balance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002995_00022660510576028-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002995_00022660510576028-Figure6-1.png",
        "caption": "Figure 6 Reconstructed blades from polyworks reverse engineering software",
        "texts": [],
        "surrounding_texts": [
            "Based on the reconstructed blade polygonal model, tool paths for welding/cladding and machining can be generated For the blade tip repair, tool paths for welding/cladding process can be generated based on the blade top profile. It can be one path along the middle curve of the profile or multi-paths along the profile contour, mainly depending on the blade size, hollow/solid state blade and laser cladding parameter setting, such as feed rate, flow, speed, etc. Through the profile extraction programmed in the polyworks environment, blade tip profile and mid-curve for welding/cladding process can be generated automatically based on the polygonal model and can be output as IGES format. Figure 7 shows the repair profile for thin blade tip repair. Since the polygonal model is created on the worn part geometry, these extracted profiles fit to each worn part geometry and therefore can provide adaptive tool paths for a build-up process. Figure 5 An example of pre-repair section dimensional inspection Table I An example of pre-repair inspection report Report type 7 Blade section inspection Item Length Minimum length Deviation to min L Test Suggestion Chordal length 27.019 26.35 0.669 Pass Accept Width 1.679 1.55 0.129 Pass Note: The values shown above do not represent the real repair requirement D ow nl oa de d by U ni ve rs ity o f Pe nn sy lv an ia L ib ra ri es A t 0 4: 12 2 7 Fe br ua ry 2 01 6 (P T ) The deposited material can be controlled by intelligent input into the welding process. Parameters such as speed, power, and control of material feed rate can be adjusted to achieve the optimum height and weld geometry. Process controls can be implemented to ensure the process is maintained within acceptable limits. If lasers are used, feed back loops can be designed into the system to maintain aerospace quality and consistency. Once blades are built up through the laser cladding/welding technology, tool paths for material subtraction are generated based on the fitted nominal CAD model or the edited polygon model. An example of the created machining patch is shown in Figure 8. Since the model inherited the actual blade geometry and attitude, the tool paths created on this model are adaptive to each blade and realise adaptive welding/cladding and adaptive machining. Considering the blade airfoil curvature and complex geometry, a five-axis machining strategy is defined and being developed for the blade machining."
        ]
    },
    {
        "image_filename": "designv10_8_0003656_biorob.2008.4762859-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003656_biorob.2008.4762859-Figure1-1.png",
        "caption": "Fig. 1. Model for an actuator for the lower limbs",
        "texts": [
            " Over the past couple of years, several different control algorithms have been developed to control wearable robots for the lower limbs. In this section some of the existing controllers are shown and briefly analyzed. The control algorithms presented in the first three sections have a structure Manuscript received April 23, 2008. Matthew A. Holgate is with Arizona State University, Tempe Campus, matthew.holgate@asu.edu Alexander W. Bo\u0308hler is with Arizona State University, Tempe, Arizona 85287-6106 alexander.boehler@asu.edu Thomas G. Sugar is with Arizona State University, Polytechnic Campus, thomas.sugar@asu.edu shown in Fig. 1, where a DC motor is controlled in series with a transmission and linear spring that is attached to the ankle. One possibility to control a robot with the structure in Fig. 1 is to control the position y (which in this case is the position of the nut on the lead screw), which is the backside of the spring. The actual nut position ya can easily be measured with a motor encoder and then subtracted from a given reference command r. However, limitations are reached with a fixed nut pattern as soon as optimization of the controller for certain stages during gait is desired, or if one wants the reference command, which essentially is a gait pattern, to adjust itself for different walking speeds or different activities such as walking versus stair climbing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.8-1.png",
        "caption": "Figure 7.8 Shear stress.",
        "texts": [
            " To get a sense of shear stresses, hold a stack of paper with both hands such that one hand is under the stack while the other hand is above it. First, press the stack of papers together. Then, slowly slide one hand in the direction parallel to the surface of the papers while sliding the other hand in the opposite direction. This will slide individual papers relative to one another and generate frictional forces on the surfaces of individual papers. The shear stress is comparable to the intensity of the frictional force over the surface area upon which it is applied. Now, consider the cantilever beam illustrated in Figure 7.8a. A downward force with magnitude F is applied to its free end. To analyze internal forces and moments, the method of sections can be applied by fictitiously cutting the beam through a plane ABCD that is perpendicular to the centerline of the beam. Since the beam as a whole is in equilibrium, the two pieces thus obtained must individually be in equilibrium as well. The free body diagram of the right-hand piece of the beam is illustrated in Figure 7.8b along with the internal force and moment on the left-hand piece. For the equilibrium of the right-hand piece, there Stress and Strain 129 130 Fundamentals of Biomechanics F TA cT r C'i \u00a31 \u00a32 \u00a31+~\u00a31 \u00a32+~\u00a32 lB Dl L DJ F Figure 7.9 Normal strain. has to be an upward force resultant and an internal moment at the cut surface. Again for the equilibrium of this piece, the internal force must have a magnitude F. This is known as the internal shearing force and is the resultant of a distributed load over the cut surface (Figure 7.8c). The intensity of the shearing force over the cut surface is known as the shear stress, and is commonly denoted with the symbol r (tau). If the area of this surface (in this case, the cross-sectional area of the beam) is A, then: F r=- A (7.2) The underlying assumption in Eq. (7.2) is that the shear stress is distributed uniformly over the area. For some cases this assump tion may not be true. In such cases, the shear stress calculated by Eq. (7.2) will represent an average value. The dimension of stress can be determined by dividing the di mension of force [F] = [M][L]/[T2] with the dimension of area [L 2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure14-1.png",
        "caption": "Fig. 14 Some 3-DOF PPR-equivalent PMs of family 3: \u201ea\u2026 2-\u201eR RR\u2026NRa-R A\u201eRR\u2026BRARA, and \u201eb\u2026 2-\u201eRP R\u2026NRa-RA\u201eRP R\u2026BRA",
        "texts": [
            " 11 , with identical type of legs, the three P joints located on the base do not constitute a valid set of actuated joints. Thus, there are no 3-DOF PPR-equivalent PMs with identical types of legs. From these PPR-equivalent PMs obtained, a number of variations can be obtained using the techniques listed in the Appendix. For instance, Fig. 17 shows a 2-RP U-UP U PPR-equivalent PM. This PM is obtained from the 2- RP R NRa-RA RP R BRA PPR- NOVEMBER 2005, Vol. 127 / 1119 3 Terms of Use: http://asme.org/terms Downloaded F equivalent PM shown in Fig. 14 b by substituting a combination of two successive R joints with nonparallel axes with a U joint. As compared with the original PM, the variation has fewer links. It is also noted that PPR-equivalent PMs proposed in 15 are in fact the variations of the PPR-equivalent PMs shown in Fig. 16, which are obtained by a substituting a combination of two successive R joints with nonparallel axes with a U joint and b replacing the unactuated P joints each with a planar parallelogram. Virtual chains have been introduced to represent the motion patterns of 3-DOF motions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.6-1.png",
        "caption": "Figure 4.6 Moments due to coplanar forces.",
        "texts": [
            "7) are in scalar form and must be handled properly. For example, while applying the translational equilibrium condition in the x direc tion, the forces acting in the positive x direction must be added together and the forces acting in the negative x direction must be subtracted. As stated earlier, for a body to be in equilibrium, it has to be both in translational and rotational equilibrium. For a body to be in rotational equilibrium, the net moment about any point must be zero. Consider the coplanar system of forces illustrated in Figure 4.6. Assume that these forces are acting on an object in the xy-plane. Let dJ, d2, and d3 be the moment arms of forces FJ, F2, and F3 relative to point O. Therefore, the moments due to these forces about point a are: Ml = d1 Fl k. ~ = -d3 F3k. (4.8) In Eq. (4.8), k. is the unit vectorindicating the positive z direction. Moment Ml is acting in the positive z direction while M2 and ~ are in the negative z direction. Equation (4.8) can be substi tuted into the rotational equilibrium condition in Eq. (4",
            " The rotational equilibrium condition would also require us to have zero net moment in the x and y directions. For three-dimensional systems: LMz=O (4.10) Statics: Analyses of Systems in Equilibrium 53 Caution. The rotational equilibrium conditions given in Eq. (4.10) are also in scalar form and must be handled properly. For example, while applying the rotational equilibrium condition in the z direction, moments acting in the positive z direction must be added together and the moments acting in the negative z direction must be subtracted. Note that for the coplanar force system shown in Figure 4.6, the moments can alternatively be expressed as: MI = dl FI M2 = d2 F2 M3 = d3 F3 (ccw) (cw) (cw) (4.11) In other words, with respect to the xy-plane, moments are ei ther clockwise or counterclockwise. Depending on the choice of the positive direction as either clockwise or counterclockwise, some of the moments are positive and others are negative. If we consider the counterclockwise moments to be positive, then the rotational equilibrium about point 0 would again yield Eq. (4.9): dl FI - d2 F2 - d3 F3 = 0 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002697_1350650011543529-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002697_1350650011543529-Figure7-1.png",
        "caption": "Fig. 7 Set-up for ultrathin-film interferometry",
        "texts": [
            " It is possible, by obtaining optical path difference measurements at two angles of incidence, to eliminate the unknown refractive index of the oil film, and this has been applied in a stationary dropping-ball contact [35]. However, it does not yet appear to have been applied in moving contacts. In the late 1980s, the spacer layer method was extended, by combining it with a spectrometer and simple computer image analysis, to develop the ultrathin-film interferometric technique [25]. The overall method is shown schematically in Fig. 7. A contact is formed between a steel ball and a transparent disc coated successively with a thin semireflective chromium layer and a spacer layer of silica at least half a wavelength of light thick. White light is Proc Instn Mech Engrs Vol 215 Part J J03900 # IMechE 2001 at University of Liverpool on December 2, 2015pij.sagepub.comDownloaded from shone into the contact and the interfered reflected beam is directed to a spectrometer slit and dispersed by wavelength. The resulting spectral image is then detected by a blackand-white CCD camera and captured by a frame grabber. A typical image is shown in Fig. 7, where the edges of the contact can be seen as closely spaced bands, with a smoother variation across the centre of the contact. The lighter regions correspond to constructive interference at a particular wavelength and the darker regions to destructive interference. (This is quite similar to the fringes of equal chromatic order produced in the mica\u2013mica contact described earlier.) This image can then be processed in two ways. One is simply to determine the wavelength of maximum constructive interference in the central region of the contact, by determining an intensity versus wavelength curve across a central strip of the contact, as shown in Fig. 7, and hence finding the wavelength of maximum constructive interference. From this the mean thickness of the central oil film plus spacer layer film can then be determined using equation (2a). Alternatively, each row of pixels across the dispersed image can be analysed independently. This then yields a separation profile across the contact. There are a number of practical complications that have to be addressed in applying this technique. One is to determine accurately the spacer layer thickness in the contact at the prevailing pressure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003564_09544062jmes1082-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003564_09544062jmes1082-Figure2-1.png",
        "caption": "Fig. 2 The general 7-link 7R mechanism",
        "texts": [
            " This kinematics can be described in dual queternions like this Z\u0302 i\u22121X\u0302 i\u22121 (7) where Z\u0302 i\u22121 = Z i\u22121+ \u2208 Z 0 i\u22121 = Z i\u22121+ \u2208 Si\u22121Z i\u22121/2; Z i\u22121 = cos(\u03b8i/2) + sin(\u03b8i/2)(0 \u2217 i + 0 \u2217 j + 1 \u2217 k) = cos(\u03b8i/2) + sin(\u03b8i/2) \u2217 k Si\u22121 = 0 + 0 \u2217 i + 0 \u2217 j + si \u2217 k = si \u2217 k; X\u0302 i\u22121 = X i\u22121+ \u2208 X 0 i\u22121 + X i\u22121+ \u2208 Ai\u22121X i\u22121/2; X i\u22121 = cos(\u03b1i/2) + sin(\u03b1i/2)(1 \u2217 i + 0 \u2217 j + 0 \u2217 k) = cos(\u03b1i/2) + sin(\u03b1i/2) \u2217 i Ai\u22121 = 0 + (ai \u2217 i + 0 \u2217 j + 0 \u2217 k) = ai \u2217 i The general 7-link 7R mechanism has 7 links, so there are seven movements like that in Fig. 1. According to Fig. 2, the kinematics equation of the 7R serial mechanism can be given as Z\u0302 1X\u0302 1Z\u0302 2X\u0302 2Z\u0302 3X\u0302 3Z\u0302 4X\u0302 4Z\u0302 5X\u0302 5Z\u0302 6X\u0302 6Z\u0302 7X\u0302 7 = 1 (8) The inverse kinematics analysis of the 7R mechanism is that si, \u03b1i, ai, and \u03b87 are known parameters and Proc. IMechE Vol. 222 Part C: J. Mechanical Engineering Science JMES1082 \u00a9 IMechE 2008 at UNIV CALIFORNIA SAN DIEGO on April 13, 2015pic.sagepub.comDownloaded from other \u03b8 i (i = 1, 2, . . ., 6) need to be solved. According to the algorithm of dual quaternions, from equation (8) Z\u0302 1X\u0302 1Z\u0302 2X\u0302 2Z\u0302 3X\u0302 3Z\u0302 4X\u0302 4 = X\u0302 \u2217 7Z\u0302 \u2217 7X\u0302 \u2217 6Z\u0302 \u2217 6X\u0302 \u2217 5Z\u0302 \u2217 5 (9) Setting left and right sides of equation (9) as U\u0302 and V\u0302 U\u0302 = V\u0302 (10) where U\u0302 = U 1+ \u2208 U 2 = u11 + u12i + u13j + u14k + \u2208 (u21 + u22i + u23j + u24k); V\u0302 = V1+ \u2208 V 2 = v11 + v12i + v13j + v14k + \u2208 (v21 + v22i + v23j + v24k) From equation (10), as u1i = v1i and u2i = v2i (i = 1, 2, 3, 4) Dj \u23a1 \u23a2\u23a2\u23a3 c\u03b85c\u03b86 c\u03b85s\u03b86 s\u03b85c\u03b86 s\u03b85s\u03b86 \u23a4 \u23a5\u23a5\u23a6 EjC 1234 ( j = 1, 2) (11) where c\u03b8k =cos(\u03b8k/2), s\u03b8k = sin(\u03b8k/2), (k = 1, 2, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003827_j.engstruct.2008.05.011-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003827_j.engstruct.2008.05.011-Figure5-1.png",
        "caption": "Fig. 5. Semi-circular balcony loaded normal to its plane.",
        "texts": [
            " It can be appreciated that when the arch factor is smaller, then the bigger internal forces and the smaller the deflections are (Fig. 4). That happens because the arch factor and its slenderness are inversely proportional. 4. Circular balcony in global coordinates In this example, the parametric equations that represent the circular arch geometry are: x = r cos(s/r); y = r sin(s/r); z = 0 considering the radius r , centre in the origin of coordinates and contained in the plane xy as shown in the Fig. 5. Known these equations, versors of the curved line expressed in the Frenet frame can be projected in the global coordinate system Pxyz as follows: t = (\u2212 sin(s/r), cos(s/r), 0) ; n = (\u2212 cos(s/r),\u2212 sin(s/r), 0) ; b = j = (0, 0, 1) . Neglecting the shearing deformation and assuming that the section inertia product is null, the resulting differential system (from general equation (7)) for a circular balcony loaded normal to its plane is given by DVz + qz = 0 \u03b22Vz + DMx + mx = 0 \u03b21Vz + DMy + my = 0 \u2212 [ \u03b221 GIt + \u03b222 EIn ] Mx + [ \u03b21\u03b22 GIt \u2212 \u03b21\u03b22 EIn ] My + D\u03b8x \u2212 \u0398x = 0[ \u03b21\u03b22 GIt \u2212 \u03b21\u03b22 EIn ] Mx \u2212 [ \u03b221 GIt + \u03b222 EIn ] My + D\u03b8y \u2212 \u0398y = 0 \u2212 \u03b22\u03b8x \u2212 \u03b21\u03b8y + D\u03b4z \u2212 \u039bz = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003498_j.snb.2006.05.010-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003498_j.snb.2006.05.010-Figure2-1.png",
        "caption": "Fig. 2. Design of (A) glucose optode and (B) oxygen reference optode.",
        "texts": [
            " The exclusive goal of these tests was to investigate the capability of this technique for the safe placement of the hybrid sensor into the tissue. Monitoring of glucose and oxygen over a longer period was not performed, due to a short time of A. Pasic et al. / Sensors and he other. The measuring period for each glucose solution was etween 5 and 6 min. . Results and discussion .1. Development of hybrid sensor The hybrid sensor consists of two pO2 optodes (fiber-optic xygen microsensors), which are based on the luminescence uenching of fluorescence molecules by oxygen [19]. The gluose sensitive optode (Fig. 2A) is obtained by the coating of ommercially available pO2 optode with the layer containing mmobilized enzyme GOX and an outer membrane. The oxyen indicator serves in that case as transducer for the rate at hich oxygen is consumed during the enzymatic oxidation. An uter layer acts as diffusion barrier for the glucose molecules. It akes sure that the sensor response is mass transfer rather than nzyme kinetically limited. The reference oxygen optode, shown in Fig. 2B, is the same ommercially available pO2 optode which is used as transducer or the glucose sensor. However, it is coated with an additional embrane which has a protective function but serves also as an ptical isolation due to carbon black particles inside the memrane. In the hybrid sensor the both optodes are in the close proximty which enables the crosstalk between them. Optical isolation f at least one optode (in our case the oxygen reference optode) is herefore required to circumvent this interference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.9-1.png",
        "caption": "Figure 14.9 Force F applied on the wrench produces a clockwise torque about the centerline of the bolt.",
        "texts": [
            "0) = 1246 N Therefore, at the very end of the ski jump track, air resistance is applying a horizontal force of Rl = 105 N to retard the motion of the skier and the track is applying a vertical force of R2 = 1246 N on the skis. Note that R2 includes the effects of the weight Wand rotational inertia man of the ski jumper. 14.2 Torque and Angular Acceleration Torque is the quantitative measure of the ability of a force to rotate an object. The mathematical definition of torque is the same as that of moment, studied in detail in Chapter 3. Consider the bolt and wrench arrangement illustrated in Figure 14.9. Force F applied on the wrench rotates the wrench, which advances the bolt into the wall by rotating it in the clockwise direction. The magnitude of torque M due to force F about 0 is: M = r Ft = r F sin<jJ (14.7) The line of action of M is perpendicular to the plane of rotation and its direction can be determined by using the right-hand rule (in this case, clockwise). An object would rotate about an axis if the rotational motion of the object is not constrained and if there is a net torque acting on the object about that axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure13-1.png",
        "caption": "Fig. 13 Actuation wrenches of some legs for PPR-equivalent parallel kinematic chains",
        "texts": [
            " Considering that the order of a screw system is coordinate system free, the Z-axis is placed along the virtual axis of a PPRequivalent PM for simplicity reason. The validity condition of actuated joints can be expressed as 01 2 3 1 1 1 2 1 3 0 4 For example, the possible 3-legged PPR-equivalent PM corresponding to the 2- RRR NRa- RR B RRR A PPR-equivalent parallel kinematic chain Fig. 10 is the 2- R RR NRa- R R B RRR A PPR-equivalent PM Fig. 12 a . The actuation wrenches of all the actuated joints are shown in Figs. 13 b and 13 c . In the R R B RRR A leg Fig. 13 b , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axis of the unactuated R joint within RR B and is parallel to the axes of the R joints within RRR A. In the R RR NRa leg Fig. 13 c , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 parallel to the axes of the R joints within RRR N. It can be found that the sixth scalar components of 01, 2, 3, 1 1 and 1 2 and 1 3 are all equal to 0. Thus, the validity condition of the actuated joints Eq. 4 is not satisfied. The possible 2- R RR NRa - R R B RRR A PPR-equivalent PM is thus discarded. The possible 3-legged PPR-equivalent PM corresponding to the 2- RRR NRa-RA RRR BRA PPR-equivalent parallel kinematic chain Fig. 9 b is the 2- R RR NRa-R A RRR BRA PPRequivalent PM Fig. 12 b . The actuation wrenches of all the actuated joints are shown in Figs. 13 a and 13 c . In the R A RRR BRA leg Fig. 13 a , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axis of the unactuated RA joint and is parallel to the axes of the R joints within RRR B. In the R RR NRa leg Fig. 13 c , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not parallel to the axes of the R joints within RRR N. It can be proved that the set of actuated joints is valid since the validity condition Eq. 4 of the actuated joints is satisfied. Based on the above validity condition of actuated joints, a number of PPR-equivalent PMs have been identified. Due to the large amount of PPR-equivalent PMs and space limitation, only several PPR-equivalent PMs are presented Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002882_313-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002882_313-Figure8-1.png",
        "caption": "Figure 8. Photograph of a capacitive pressure sensor built in PCB technology.",
        "texts": [
            " The moveable electrode is formed by a membrane made of a polyimide foil of 8 \u00b5m in thickness coated with a 20 nm thin film of aluminium by sputtering. A via in the third PCB layer allows the thin film electrode to be contacted. Besides that the board contains the pressure chamber and carries the fluidic and electric connectors. The metal layer on the membrane surface and the fixed electrode in the sensor chamber form a capacitance. A pressure difference between the pressure and sensor chambers leads to a deformation of the membrane changing the electrode spacing and as a result of this the sensor capacitance. Figure 8 shows a laboratory sample of the sensor described. The sensor has a nominal capacitance of 22 pF and a nearly linear behaviour in the pressure range of \u22125 to +15 hPa with an average sensitivity of 1 pF hPa\u22121. By simply scaling the dimensions the pressure range of the sensor can be changed. In this paper, the first results of fluidic microsystem components based on printed circuit board technology are presented. The capabilities of this technology have been demonstrated by several examples. A capacitance bubble detector able to give a warning if gas bubbles are detected and two components for a pH-regulation system keeping the physiological environment of cell cultures stable have been described"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003870_1.4001003-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003870_1.4001003-Figure9-1.png",
        "caption": "Fig. 9 Gear alignment curves prior to and after rotating",
        "texts": [
            " All these accord with he thought of equal intensity, as shown in Fig. 6. Thus the folowing is mainly focused in the expression of the curves. In the plane iCOCjC of the coordinate system SC iC , jC ,kC in ig. 9, we establish the gear common symmetry alignment curve iven as x = cos = e cot cos y = sin = e cot sin 28 o facilitate the establishment of the tooth equation of the spiral evel gears, a small rotating angle C is introduced and decribed as C= s\u2212 /2 by shifting the starting point of the curve ligned along axis jC, as shown in Fig. 9. Thus, the Eq. 28 ecomes x = e cot cos \u2212 C y = e cot sin \u2212 C 29 his gives the common symmetric gear alignment curve; considring the loxodrome angle j, two actual boundaries of the tooth an be obtained, as demonstrated in Fig. 10. This angle can then e used to modify the above curve function by introducing a new otating angle as j = C j. Both + and signs are sed for expressing the right and left tooth profiles. This modified unction of the gear alignment curve is given as follows: 21008-6 / Vol. 132, FEBRUARY 2010 om: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.37-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.37-1.png",
        "caption": "Figure 4.37 Including the weights of the arms.",
        "texts": [
            " The scalar method could still be applied in a step by-step manner by considering one component of the applied force at a time, solving the problem for that component alone, repeating this for all three components, and then superimpos ing the three solutions to obtain the final solution. Obviously, this would be quite time consuming. On the other hand, the extension of the vector method to analyze such problems is very straightforward. All one needs to do is to redefine the applied force vector as P = Pxi + Pyj + Pzlf, and carry out exactly the same procedure outlined above. \u2022 In this example, it is stated that the weight of the beam was negligibly small as compared to the force applied at C What would happen if the weight of the beam was not negligible? As illustrated in Figure 4.37, assume that we know the weights WI and W2 of the arms AB and BC of the beam along with their centers of gravity (points D and E). Also, assume that D is located in the middle of arm AB and E is located in the middle of arm BC We have already discussed the vector representation of RA and P. The vector representations of WI and W2 are: The positions vectors of points D and E relative to A are: a r1 = - k - 2- b . k r2 = --l +a - 2- - Therefore, the moments due to WI and W2 relative to A are: M W aWl"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.18-1.png",
        "caption": "Figure 6.18. Force-controlled pushing using an AFM cantilever. a. Side view of the experimental setup with AFM cantilever, workpiece, and reference object; b. top view of the configuration at the start (left) and end of the alignment process (right) (from [75], courtesy of SPIE).",
        "texts": [
            " Within the last few years, several nanohandling systems either based on commercial AFMs or on custom-made AFM instruments, have been developed [68\u201373]. At the Korea Institute of Science and Technology, an AFM has been built especially for nanohandling [74]. It is made up of a nanomanipulator with three degrees of freedom and piezoresistive AFM cantilevers. Zesch et al. used a piezoresistive AFM cantilever for force-controlled pushing of sub-millimeter-sized silicon parts on a silicon substrate [75]. The substrate can be positioned using a precision table. The cantilever is mounted on a piezoelectric 196 Stephan Fahlbusch positioning stage (Figure 6.18a). With this setup, microobjects can be aligned laterally relative to each other (Figure 6.18b). By measuring the contact forces between object and AFM cantilever it is possible to draw conclusions as to whether the object is moved, if it got lost, or if it hit an obstacle. The measured forces are typically between of 0.8 \u03bcN and 3.5 \u03bcN during pushing and twice as high when static friction has to be overcome. The biggest problems of this method are instabilities during pushing, as well as non-predictable movements or jumping of the microobject. The basic element of the nanohandling system developed at the University of Minnesota, USA, is an IC probing station into which a three-axes nanopositioning unit was integrated [76, 77]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure3.18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure3.18-1.png",
        "caption": "Figure 3.18. Different possible cases and possible result of self-organization (dashed arrows). a. System behavior 1 2 0 0 1 0d dg g . Local disorder leads to locally high approximation error. b. System behavior 1 2",
        "texts": [
            "38 and depends on the degree of disorder of the three nodes rn , mw n and cn , and on the approximation error c of the candidate node cn : , , , , , , , ,max , , , , , , , , ,p l h p l p h l h p l p h c c cr t r r t r r (3.40) where ( , , , , )l h l hy t x x y y x describes a linear transition from ly to hy between lx and hx . Figure 3.17 shows the characteristic curve of pr with typical values of 0 1l c , 1 0h c , 0p lr , 0 7p hr , 30l \u00b0 , 120h \u00b0 , 0,p lr and 1 0p hr . The idea behind Equation 3.40 is to decrease the self-organization learning rate smoothly from a high value for disordered SOLIM maps that approximate badly, to a low value for ordered SOLIM maps that approximate well (Figure 3.18). Learning Controller for Microrobots 81 m a ag p p . Low approximation error but not well- ordered output support vectors. c. System behavior 1 2 0 5 1 5d dg g . Ordered output support vectors but locally high approximation error. d. In all cases, self-organization helps by decreasing the degree of disorder and the approximation error. 82 Helge H\u00fclsen SOLIM self-organization minimizes the angle between mc w p p and m rw p p , which is consequently chosen as a measure for the degree of disorder "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002813_02783640022066996-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002813_02783640022066996-Figure3-1.png",
        "caption": "Fig. 3. 3-link manipulator.",
        "texts": [
            " It is needless to assign values to the other link physical parameters because of the same reason in ii). In case link n has one base parameter JUDGMENT We have only to check that mn = MRn \u2212 MR(n + 1) > 0. (54) ASSIGNMENT mn is obtained uniquely above. We have only to assign arbitrary values to rx n and r y n since rz n is not needed in the latter judgment. at Virginia Tech on August 21, 2014ijr.sagepub.comDownloaded from 6. Example In this section, we apply the given results on a 3-degree-offreedom manipulator. The manipulator is shown in Figure 3 and the kinematic parameters are as follows: 1L1 = 0, 2L2 = [1 0 0]t , \u03b11 = 0, \u03b12 = \u2212\u03c0 2 , \u03b13 = 0. (55) The base parameters of the manipulator are as follows: ZZR3 = I zz g3 + m3[(rx 3 )2 + (r y 3 )2], XXR3 = I xx g3 \u2212 I yy g3 + m3[(ry 3 )2 \u2212 (rx 3 )2], XYR3 = I xy g3 \u2212 m3(r x 3 )(r y 3 ), XZR3 = I xz g3 \u2212 m3(r x 3 )(rz 3), YZR3 = I yz g3 \u2212 m3(r y 3 )(rz 3), MXR3 = m3r x 3 , MYR3 = m3r y 3 , (56) ZZR2 = I zz g2 + m2[(rx 2 )2 + (r y 2 )2] +m3([L2]x)2, XXR2 = I xx g2 \u2212 I yy g2 + m2[(ry 2 )2 \u2212 (rx 2 )2] \u2212m3([L2]x)2, XYR2 = I xy g2 \u2212 m2(r x 2 )(r y 2 ), XZR2 = I xz g2 \u2212 m2(r x 2 )(rz 2) \u2212 m3(r z 3)([L2]x), YZR2 = I yz g2 \u2212 m2(r y 2 )(rz 2), (57) The values of link physical parameters are calculated under the assumption that each link of the manipulator is made with a uniform rod and a lumped mass, as shown in Figure 3. The set of base-parameter values calculated using the link-physicalparameter values is given in Table 1. Figure 4 shows the feasible region for link 3. x31 and x33 are independent variables for link 3. The feasible region has been reduced according to the method shown in the Reducing the feasible region section of i) in Section 5. For this particular manipulator, we can reduce the feasible region more by considering the expression of ZZR1. In fact, we see from (59) that we must have at least ZZR1 \u2212 I yy g3 \u2212 m3[(rx 3 )2 + (rz 3)2] \u2212 m3([L2]x)2 > 0, (59) Base Parameter Value ZZR3 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002528_978-3-662-04117-8-Figure8.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002528_978-3-662-04117-8-Figure8.2-1.png",
        "caption": "Figure 8.2: Elastic two-mass system with backlash and jriction",
        "texts": [
            " In the control concepts in [1, 2, 4, 5] it must be known in advance, if a system contains backlash and if so, its magnitude. Here we propose an observer structure which is able to determine if a system con tains backlash, and, if it does, to karn the backlash width. The performance and stability of the approach can be proven mathematically. To identify the backlash characteristic, we use a neural network that is able to rebuild any continuous mathematical function. 8.2.1 Model of an Elastic Two-Mass System We consider the following electro-mechanical drive train shown in figure 8.2. is modeled as aspring with coefficient c and a parallel damping element with coefficient d. The motion of the load can be subdued to nonlinear friction. This elastic two-mass system is a common model for many mechanical systems (i.e. mechatronic systems). The signal fiow graph of the above system is shown in figure 8.3. The blocks marked with \u00df(.) and :F(.) describe the nonlinearities of the plant, backlash and friction, respectively. The parameter TN is the normalizing time constant, mw is an additional disturbance torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002528_978-3-662-04117-8-Figure9.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002528_978-3-662-04117-8-Figure9.3-1.png",
        "caption": "Figure 9.3: Possible form of eccentricity",
        "texts": [
            " In opposite to the indirect control method presented here, aglobai (direct) method is presented in the chapters 10 and 11. In real plants the non-circularity of the winders can lead to undesired oscillations of the tension force, which lead to problems in controlling the output thickness of the material behind the roll bite. Such eccentricities can be caused for example by clamping the steel. This fact leads to an elevation at the clamping point which can also be seen, when furt her material is wound up (figure 9.3). The aim in this context is to identify the radius with respect to the angle position online. Based on this knowledge, a compensation algorithm can be implemented to damp the oscillations. Figure 9.3 shows a possible form of the eccentricity for one rotation in case of the rewinder where an additional increase of the mean value of the radius can be seen. This means, that there is a time-variant disturbance which has to be identified. It must be noted that this is only a possible form of eccentricity which is used for simulation in this case. Figure 9.4 shows the plant-observer structure of the whole system based on the method of identification of isolated nonlinearities. The drive system is assumed to be a two-mass system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.13-1.png",
        "caption": "Figure 14.13 Some of the forces acting on the lower leg.",
        "texts": [
            " The arms of the goniometer are aligned with the estimated long axes of the thigh and shank, and the axis of rotation of the goniometer is aligned with the estimated axis of rotation of the knee joint. The subject is then asked to extend the lower leg as rapidly as possible. The signals received from the electrogoniometer's potentiometer are stored in a computer, and are used to calculate the angular displacement () of the lower leg as measured from its initial vertical position. Using a finite difference (numerical differentiation) technique, the angular ve locity wand angular acceleration a of the lower leg are also computed. Some of the forces acting on the lower leg are shown in Figure 14.13, along with the geometric parameters of the model under consideration. This model is based on the assumption that the quadriceps muscle is the primary muscle group responsible for knee extension. Point 0 represents the instantaneous center of rotation of the knee joint. The patellar tendon is attached to the tibia at A. For the position of the lower leg relative to the upper leg shown in Figure 14.13, it is estimated that the line of pull of the patellar tendon force F m makes an angle f3 with the long axis of the tibia. The lever arm of F m relative to 0 can be represented by a distance a that changes as the lower leg moves up through the range of motion. The total weight of the lower leg is Wand its center of gravity is located at B, which is at a distance b from 0 measured along the long axis of the tibia. The intended direction of motion is counterclockwise (extension). At an instant when () = 60\u00b0, w = 5 rad/s, and a = 200 rad/s2, and assuming that W = 50 N, a = 4 cm, b = 22 cm, f3 = 24\u00b0, and the mass moment of inertia of the lower leg about the knee joint is 10 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003933_j.engfailanal.2010.11.009-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003933_j.engfailanal.2010.11.009-Figure12-1.png",
        "caption": "Fig. 12. Some locations for measuring welding residual stress.",
        "texts": [
            " The existence of cold cracks was also not detected by Tekken tests [21] on 6 test specimens and CTS tests on 4 test specimens. All test specimens that were used to test cracking susceptibility were obtained from test samples which are formed in strict compliance with the prescribed welding technology. Given the fact that omissions in the welding technology are being made during BW manufacturing, measurements of the welding residual stresses are carried out using the centre hole drilling method. Rosettes (HBM RY61) are placed at 23 measuring points located on undeformed and undamaged parts of the construction, Fig. 12. The measurement results, Table 7, indicate a high level (above yield strength) of welding residual stresses. Identification of the stress\u2013strain state of the BW body is performed after its repair. All measurement points, Fig. 13, are located on the part of BW which is not affected by the occurrence of cracks and deformations. Measurement results related to stress values and stress distribution in respective domains of the structure, Table 8, and acquired during excavation of compact gray clay, confirm the results obtained by FEA",
            " one bucket wheel speed, are defined by the following expression: ri \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 \u00bd\u00f0rx;tot ry;tot\u00de2 \u00fe \u00f0ry;tot rz\u00de2 \u00fe \u00f0rz rx;tot\u00de2 \u00fe 3\u00f0s2 xy \u00fe s2 yz \u00fe s2 zx\u00de r ; where by the coordinates of stress tensor rx,tot and ry,tot are included effects of external load (index el, Table 2) and welding residual stresses (index res, Table 7): rx,tot = rx,el + rx,res and ry,tot = ry,el + ry,res. Such calculated extreme values are used as a basis to determine the corresponding mean values (rmean) and amplitudes of overall stresses (ra) at critical points (measuring points from 4 to 9, Fig. 12), Table 9. In accordance with the recommendations [24,25], it is adopted that the fatigue limit of considered critical butt welds (V joint) is Se,t = 63 MPa, if performed NDT of the root, otherwise Se,nt = 45 MPa. Based on these values of fatigue limits, the minimum values of the experimentally determined value rUTS,min = 545 MPa (Table 3), as well as minimum value rUTS,min = 490 MPa determined by standard [19], are defined limit lines in the modified Goodman diagrams, Fig. 17. All combinations of the mean stress and the alternating stress in BW body critical zones, Table 9, are lying below the limit line A\u2013B connecting the fatigue limit Se,t and rUTS,min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.27-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.27-1.png",
        "caption": "Figure 13.27 Double pendulum.",
        "texts": [
            "p = 2f + 5 i That is, according to person A or relative to the XY coordi nate frame, the ball is moving to the right with a speed of 2 m/ s and upward with a speed of 5 m/ s (Figure 13.26). At this instant, the magnitude of the net velocity of the ball is Vp = .)(2)2 + (5)2 =5.4 m/s. 13.12 Linkage Systems A linkage system is composed of several parts connected to each other and/ or to the ground by means of hinges or joints, such that each part constituting the system can undergo motion rel ative to the other segments. An example of such a system is the double pendulum shown in Figure 13.27. A double pendulum consists of two bars hinged together and to the ground. Linkage systems are also known as multilink systems. If the angular velocity and acceleration of individual parts are known, then the principles of relative motion can be applied to analyze the motion characteristics of each part constituting the multilink system. The following example will illustrate the procedure of analyzing the motion of a double pendulum. How ever, the procedure to be introduced can be generalized to ana lyze any multilink system",
            " An important concept associated with linkage systems is the number of independent coordinates necessary to describe the motion characteristics of the parts constituting the system. The number of independent parameters required defines the degrees of freedom of the system. For example, the two-dimensional motion characteristics of the simple pendulum shown in Figure 13.28 can be fully described by 0 that defines the loca tion of the pendulum uniquely. Therefore, a simple pendulum has one degree of freedom. On the other hand, parameters 01 and O2 are necessary to analyze the coplanar motion of bar BC of the double pendulum shown in Figure 13.27, and therefore, a double pendulum has two degrees of freedom. Example 13.4 Double pendulum. Assume that arms AB and BC of the double pendulum shown in Figure 13.29 are undergoing coplanar motion. Let il = 0.3 m and \u00a32 = 0.3 m be the lengths of arms AB and Be, and (h and 02 be the angles arms AB and BC make with the vertical. The angular velocity and acceleration of arm AB are measured as WI =2 rad/s (counterclockwise) and al =0 relative to point A. The angular velocity and acceleration of arm BC is measu red as W2 =4 rad/s (counterclockwise) and a2 =0 relative to point B"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003036_jctb.280440202-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003036_jctb.280440202-Figure1-1.png",
        "caption": "Fig. 1. Chemical species formed in substrate conversion by microbes.",
        "texts": [
            "1 Microbiological basis Although microbial sensors have been intensively studied, little knowledge is available about the biochemical mechanisms. The physiology of microorganisms used in the microbial sensor is characterized by conditions of extreme nutrient limitation. The metabolism is in a \u2018stand-by\u2019 state so as to guarantee the survival of the cell. These physiological limitation conditions determine both the stability and sensitivity of biosensors. In general, the microbial cell has been simply considered as a black box (Fig. 1) . The substrate of interest is degraded by the microbial cell, metabolic products are formed and oxygen is consumed under aerobic conditions. The microbial cell envelope forms a diffusion barrier. Solutes can pass only via specific translocation systems, either with an active transport system or by facilitated diffusion; passive transport by diffusion is of minor importance. Active Process control of microbiul sensors 87 transport, which allows accumulation of substrates against a concentration gradient, requires highly specific carrier proteins and consumes metabolic energy",
            " The expression of most transport systems is regulated at the level of transcription of the genes encoding the systems. Induction or derepression is observed when the presence or absence of given substances demands a new transport activity. In contrast, facilitated diffusion does not need metabolic energy. After the uptake the substrate is degraded specifically by the metabolic sequences of the enzyme networks of the microbial cell. In general, the microbial species chosen for biosensor development must fulfil at least one of the two criteria (see Fig. 1): (i) aerobic uptake of oxygen in the respiratory process for assimilation of the substrates (in this case the microbial sensor is constructed by coupling the microorganisms with an amperometric oxygen electrode); or (ii) electrode-active products liberated derived from reactions of the microbial metabolism, e.g. protons, ammonium ions, H2S, CO, and H,Oz, which can be detected by potentiometric or amperometric electrodes. Almost all microorganisms used for the construction of microbial sensors, e.g. bacteria, fungi (including yeasts and actinomycetes) and algae (see Table 1) have been assessed according to these criteria. 2.2 Physical basis of the transducer The optimal choice of transducer will depend on the products and substrates involved in the biocatalytic process (Fig. 1). It should be highly specific for the indicated species and respond rapidly within the chosen concentration range. 2.2.1 Poteritiometric electrodes These operate under equilibrium conditions. Ions in solutions are quantified as a result of changes in electrode potential brought about by association with a sensing membrane. Ion-selective electrodes (ISE) have been successfully developed for H +, Na\u2019, K+, Li t , Ca\u201d, NH: and a number of anions, a few drugs and other substances. In potentiometric gas-sensing probes, a gas-permeable membrane is placed on the ion-selective membrane separated by a thin layer of the appropriate filling solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003665_j.snb.2006.12.051-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003665_j.snb.2006.12.051-Figure2-1.png",
        "caption": "Fig. 2. Chemical structure of: (a) Nafion\u00ae; (",
        "texts": [
            " Ten CFME ere tested and six were sufficiently sensitive to permit a comlete study. Electrochemical experiments were carried out in a 0-mL glass voltammetric cell at room temperature (20 \u25e6C). .2. Reagents ig. 1. 2D optical image of the commercialized carbon fiber microelectrode CFME) (magnification 400\u00d7). 370 M. Sba\u0131\u0308 et al. / Sensors and Actuators B 124 (2007) 368\u2013375 b) nic t ( t f E 2 a t f o o c s v n d c C a w F d r t i fi t fi u m a w F a o d p e a e a m ration range was prepared between 0.01 and 50 mg L\u22121. NiTSPc batch 20526KA) and Nafion\u00ae (see Fig. 2) were purchased from he Aldrich and used as received. Deionized water was obtained rom a Elga Labwater ultrapure-water system (Purelab-UVF, lga, France). .3. Procedure A carbon fiber microelectrode was immerged into a stirring cetate buffer containing the desired concentration of MPT in he 10 ml electrochemical cell. SWV scanning was performed rom \u22121.1 to +0.3 V with a step potential of 10 mV, amplitude f 60 mV and a frequency of 60 Hz, the optimized conditions btained (see Section 3). The carbon microfiber electrodes were first electrochemially pre-treated in a mixture of H2SO4 (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.32-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.32-1.png",
        "caption": "Figure 8.32 A plane perpendicular to the centerline cuts the shaft into two.",
        "texts": [
            " The analyses of structures with noncircular cross-sections subjected to torsional loading are complex and beyond the scope of this text. Consider the solid circular shaft shown in Figure 8.30. The shaft has a length f and a radius r o. AB represents a straight line on the outer surface of the shaft that is parallel to its centerline. Note that a plane passing through the centerline and cutting the shaft into two semicylinders is called a longitudinal plane, and a plane perpendicular to the longitudinal planes is called a transverse plane (plane abcd in Figure 8.32). In this case, line AB lies along one of the longitudinal planes. The shaft is mounted to the wall at one end, and a twisting torque with magnitude M is applied at the other end (shown in Figure 8.30 with a double-headed ar row). Owing to the externally applied torque, the shaft deforms in such a way that the straight line AB is twisted into a helix AB'. The deformation at A is zero because the shaft is fixed at that end. The extent of deformation increases in the direction from the fixed end toward the free end",
            " This variation is such that the deformation is zero at the center, increases toward the rim, and reaches a maximum on the outer surface. Angle () in Figure 8.31 is called the angle of twist and it is a measure of the extent of the twisting action that the shaft suffers. From the ge ometry of the problem: () = _ar_c_l_en.....;g::;..t_h_B_B_' (8.24) Equations (8.23) and (8.24) can be combined by eliminating the arc length BB'. Solving the resulting equation for the angle of twist will yield: (8.25) Now consider a plane perpendicular to the centerline of the shaft (plane abcd in Figure 8.32) that cuts the shaft into two segments. 174 Fundamentals of Biomechanics Since the shaft as a whole is in static equilibrium, its individual parts have to be in static equilibrium as well. This condition re quires the presence of internal shearing forces distributed over the cross-sectional area of the shaft (Figure 8.33). The intensity of these internal forces (force per unit area) is the shear stress r. The magnitude of the shear stress is related to the magnitude M of the applied torque, the cross-sectional area of the shaft, and the ra dial distance r between the centerline and the point at which the shear stress is to be determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002587_s0924-0136(04)00220-1-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002587_s0924-0136(04)00220-1-Figure5-1.png",
        "caption": "Fig. 5. (a) Wetting of a liquid on a solid substrate and equation of Young with \u03c3SV, \u03c3SL and \u03c3LV the surface free energies of the system, (b) transition from half cylinder to sphere depending on the dimensions of the molten laser pool.",
        "texts": [
            " Another disadvantageous phenomenon arising during SLM is balling. It occurs when the molten material does not wet the underlying substrate due to the surface tension, which tends to spheroidise the liquid. This results in a rough and bead-shaped surface, obstructing a smooth layer deposition and decreasing the density of the produced part. Consider a flat, undeformable, perfectly smooth and chemically homogeneous solid surface (S) in contact with a non-reactive liquid (L) in the presence of a vapor (V) phase. This metastable equilibrium is depicted in Fig. 5a. If the liquid does not completely cover the solid, the liquid surface will intersect the solid surface at a contact angle \u03b8 that corresponds to a minimum of the total free energy of the system. The value of \u03b8 obeys the classical equation of Young (1804) (see Fig. 5a) [20]. Since the interaction time during laser melting is very short, order of magnitude of milliseconds, the equation of Young holds. In reality the molten pool created by the moving laser spot can be approximated by a half cylinder. Therefore an additional reduction of the surface free energy appears: when the total surface of the molten pool becomes larger than that of a sphere with the same volume, the balling effect takes places (see Fig. 5b). Thus, the laser parameters should be selected in such a way that the length to diameter ratio of the molten pool is as small as possible [21]. A process window for continuous wave as well as for pulsed laser operation mode is experimentally determined. Similar process windows are also presented by [21]. In Fig. 6a, laser power P and scan speed v are varied for a single powder layer scanned on top of a base plate. The layer thickness is 0.25 mm and the applied scan spacing is 0.1 mm. The spot of the laser beam has a diameter of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.21-1.png",
        "caption": "Figure 4.21 A cable-pulley arrangement.",
        "texts": [
            "20b, if we slide the forces to point P and express them in terms of their components, we can observe equilibrium in the x and y directions such that: In the x direction: In the y direction: RAx = Tx RAy+Ty = W \u2022 The fact that R A and T have an equal magnitude and they both make a 53\u00b0 angle with the horizontal is due to the symmetry of the problem with respect to a plane perpendicular to the xy plane that passes through the center of gravity of the beam. 4.9 Cable-Pulley Systems and Traction Devices Cable-pulley arrangements are commonly used to elevate wei ghts and have applications in the design of traction devices used in patient rehabilitation. For example, consider the simple ar rangement in Figure 4.21 where a person is trying to lift a load through the use of a cable-pulley system. Assume that the per son lifted the load from the floor and is holding it in equilibrium. The cable is wrapped around the pulley, which is housed in a case that is attached to the ceiling. Figure 4.22 shows free-body diagrams of the pulley and the load. r is the radius of the pulley and 0 represents a point along the centerline (axle or shaft) of the pulley. When the person pulls the cable to lift the load, a force is applied on the pulley that is transmitted to the ceiling via the case housing the pulley"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003281_1.1848523-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003281_1.1848523-Figure1-1.png",
        "caption": "FIG. 1. Schematic view of laser repair process.",
        "texts": [
            " Temperature distribution and gradient in the first deposited layer and sequential layer are compared. The predicted melt pool dimension and melt pool peak temperature have been verified by experimental calibration using the complementary metal\u2013oxide\u2013semiconductor sCMOSd camera and dual-wavelength temperature sensor. Laser material deposition and repair are complicated interactions which involve laser and base metal interaction, laser and powder interaction, and powder and melt pool interaction. Figure 1 illustrates the schematic process view of the laser repair process. The nozzle initially is positioned at a certain location, which aligns with the edge of the hole. When the repair process starts, the laser beam goes through the powder cloud and irradiates on the surface of the base part to form the melt pool. The powders are injected from the coaxial nozzle along the same path of the laser beam and are heated during the flight. After the powders are injected into the melt pool, they are captured by the melt pool and solidified to create the clad layer after the laser or substrate moves forward",
            " Before their temperatures cool down to room temperature, the second heating process starts; as expected, peak temperatures of these four points are much lower in the second thermal cycle due to the lift of the melt pool location in the z direction. In such a case, the solid/liquid interface reaches an average cooling rate of more than 3000 \u00b0C/s. Moreover, the deposition pattern has essential influences on the thermal experiences of the part. Figure 9 illustrates the temperature histories at points A, B, and C marked in Fig. 1. For the zigzag deposition pattern shown in Fig. 1, the thermal cycle of points A, B, and C are about 1260, 630, and 1260 ms, respectively. It can be noted that the peak temperatures of points B and C are higher than A, which explains the differences of the remelt layer thickness between the left and right corners. Unlike points A and C located on the edge of the hole, point B is exposed a longer time to the laser beam when the laser beam passed through; correspondingly, higher peak temperature is reached at point B. The experiments were carried out on the laser deposition system sRofin-Sinar 025d and a five-axis CNC milling machine system sFadal VMC-3016Ld"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure11.13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure11.13-1.png",
        "caption": "Figure 11.13 Free fall.",
        "texts": [
            "4 One of the most common examples of uniformly accelerated motion is that of an object allowed to fall vertically downward, which is called free fall. Free fall is a consequence of the effect of gravitational acceleration on the mass of the object. If the possible effects of air resistance are ignored (assuming that the motion occurs under vacuum), then the object released from a height would move downward with a constant acceleration equal to the magnitude of the gravitational acceleration, which is about 9.8 m/s2. As illustrated in Figure 11.13, consider a person holding a ball at a height h = 1.5 m above the ground level. If the ball is released to descend, how much time would it take for the ball to hit the ground and what would be its impact velocity? Solution: This is another example of uniaxial motion with con stant acceleration. Once the ball is released, it moves downward with constant acceleration ao = 9.8 m/ s2, which is the magnitude of the gravitational acceleration. In Figure 11.14, the direction of motion of the ball is identified with the y axis such that positive y direction is downward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure8.7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure8.7-1.png",
        "caption": "Fig. 8.7 Stresses (J\" {){) and (J\" 'P'P in a spherical shell",
        "texts": [],
        "surrounding_texts": [
            "A conical shell is considered filled with water, and subjected to the fluid pressure ('\"Y is the specific weight of water). The z weight of the shell itself is assumed to be negligible. For a conical shell, we have iJ = const. We therefore introduce a new coordinate s, and with the following transformations R{} diJ = ds, (R{) ---+ 00, diJ ---+ 0) the foregoing formulas retain their validity: 7r iJ = 2\" - 0: , 1'( s) = s sin 0: , 1'(s) R<p ( s) = = stan 0: . coso: The loading is given as s Pn ( s) = '\"Y H (1 - H cos 0:), p{} ( s) = 0 . We thus get from Eqs. (8.37) 1 s n{}{} ( s) = hO\" {}{} = \"6 '\"Y H stan 0: (3 - 2 H cos 0: ) s n<p<p (s) = hO\" <p<p = '\"Y H stan 0: (1 - H cos 0:) . 8.5 Exercises to Chapter 8 Problem 8.1: A circular plate with radius R is simply supported at the edge and is subjected to a constant pressure Po as shown in the di agram. Using the Kirchhoff plate theory, compute 1. the deflection of the middle surface, 2. the stresses in the plate. Problem 8.2: 8.5 Exercises to Chapter 8 147 Itt t t t t ttl po ~R -L r =-t: The simply supported circular plate of Problem 8.1 is subjected to a singular verti cal force F at the center of the plate. Using Kirchhoff's plate theory, compute the deflection of the middle surface and the moments. Problem 8.3: A clamped circular plate of thickness h and radius R is heated such that after some time a stationary temperature (difference) field e (z) = {} 0 + {}l Z is observed across the plate, where {}o is the temperature (difference) in the middle plane, and {} 1 is the gradient of the field in z direction. Compute the stresses that are induced by this heating. Problem 8.4: The clamped annular plate of Example 8.4 is subjected to a vertical shear force q 0 at its outer edge. Compute the deflection w, the shear force qr. and the moments mrr and m'P'P. Problem 8.5: A strip of a plate with the dimensions given in the diagram below is built in at one end and subjected to constant load (per unit length) q R and a moment (per unit length) mR at the other end. 1. Calculate the maximum displacement of the plate using the Kirchhoff plate theory. 2. Determine the point, value, and sign of maximum stress. 3. Give the equation of the deflection curve of the plate. 4. Consider an assemblage of n beams each of width b lying next to each other as shown in the second diagram. Compute the deflection curve of this model and compare the solution with that of a plate with the width nb. 148 8. Plates and Shells Problem 8.6: A spherical shell is simply supported at an angle of 79 0 as shown in the figure. The shell is filled with water. Compute the membrane forces for this shell. Problem 8.7: The system shown in the figure is sup posed to be a model of a soccer stadium to be constructed for the Indomitable Li ons of Cameroon. If the thickness of the shell is h(79), and it is loaded by its own weight only, compute the stress resultants n<p<p and n1')1') using the membrane theory of shells of revolution. Assume the thick ness of the shell to be a linear function of 79. Beam: z 9. Stability of Equilibrium"
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.5-1.png",
        "caption": "Figure 5.5 Forces acting on the lower arm.",
        "texts": [
            " Common injuries of the elbow include fractures and disloca tions. Fractures usually occur at the epicondyles of the humerus and the olecranon process of the ulna. Another elbow injury is known as \"tennis elbow,\" which occurs as a result of re peated and forceful pronation and supination movements of the elbow. Example 5.1 Consider the arm shown in Figure 5.4. The elbow is flexed to a right angle and an object is held in the hand. The 88 Fundamentals of Biomechanics forces acting on the forearm are shown in Figure 5.5a, and the free-body diagram of the forearm is shown on a mechanical model in Figure 5.5b. This model assumes that the biceps is the major flexor and that the line of action of the tension (line of pull) in the biceps is vertical. Point 0 designates the axis of rotation of the elbow joint, which is assumed to be fixed for practica~ purposes. Point A is the attachment of the biceps muscle on the radius, B is the center of gravity of the forearm, and C is a point on the forearm that lies along a vertical line passing through the center of gravity of the weight in the hand. The distances between 0 and A, B, and Care measured as a, b, and c, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure12-1.png",
        "caption": "Fig. 12. Phasor diagrams for PM motor: (a) for maximum torque per ampere, (b) for unity power factor, (c) for leading power factor.",
        "texts": [
            " SLEMON: ELECTRICAL MACHINES FOR VARIABLE-FREQUENCY DRIVES 1131 The stator voltages or currents are then constructed by switching action of the inverter to have the desired relative instantaneous angle. For the current-source drive, using the equivalent circuit of Fig. 10, the torque can be derived as the air-gap power divided by the mechanical angular velocity and expressed as Figure 11 shows the torque as a function of the angle p. For a given value of stator current, maximum driving torque can be obtained with a rotor angle of ,8 = 90\". For this condition, the electrical variables are displayed in the phasor diagram of Fig. 12(a) which shows that the supply power factor is less than unity. Operation in this condition is practical up to the speed at which the voltage limit of the inverter is reached. Above this speed, a more appropriate operating condition is one which provides for unity power factor by increase of the lead angle p a:s shown in the phasor diagram of Fig. 12(b), thus maximizing the utilization of the inverter volt-ampere rating. As shown in the operating region of Fig. 11, this causes only a small reduction in torque. For regeneration, the rotor angle P 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. The motor can be operated with a leading or capacitive stator current by increase of the angle 6 by which the voltage leads the field axis as shown in Fig. 12(c). This condition is desired for some large drives since it allows use of a load-commutated inverter, i.e., one where the switches are tumed off by their currents going to zero rather than requiring auxiliary tum off means (21. D. Magnet Protection Demagnetization of a part of the magnet can occur if the flux density in that part ir reduced to less than the kneepoint flux density BD of Fig. 9. This can result in permanent reduction in torque capability since it is usually not feasible to remagnetize the magnets without disass,embly of the motor. As seen in the phasor diagrams of Fig. 12, the stator current is normally controlled to lead the effective magnet current by 90\" 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 effective airgap flux is unchanged. The limiting value of permissible stator current is that which brings the flux density down to BD at the lagging edge. Most PM motors are designed to withstand considerable overload currents without danger to the magnets"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure17-1.png",
        "caption": "Fig. 17 2-RP U-UP U PPR-equivalent PMs",
        "texts": [
            " Due to the large amount of PPR-equivalent PMs and space limitation, only several PPR-equivalent PMs are presented Figs. 12 b and 14\u201316 . It is noted that for the PMs corresponding with the sole PPRequivalent parallel kinematic chain, 3- PP NRa Fig. 11 , with identical type of legs, the three P joints located on the base do not constitute a valid set of actuated joints. Thus, there are no 3-DOF PPR-equivalent PMs with identical types of legs. From these PPR-equivalent PMs obtained, a number of variations can be obtained using the techniques listed in the Appendix. For instance, Fig. 17 shows a 2-RP U-UP U PPR-equivalent PM. This PM is obtained from the 2- RP R NRa-RA RP R BRA PPR- NOVEMBER 2005, Vol. 127 / 1119 3 Terms of Use: http://asme.org/terms Downloaded F equivalent PM shown in Fig. 14 b by substituting a combination of two successive R joints with nonparallel axes with a U joint. As compared with the original PM, the variation has fewer links. It is also noted that PPR-equivalent PMs proposed in 15 are in fact the variations of the PPR-equivalent PMs shown in Fig. 16, which are obtained by a substituting a combination of two successive R joints with nonparallel axes with a U joint and b replacing the unactuated P joints each with a planar parallelogram"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003649_j.actaastro.2008.12.004-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003649_j.actaastro.2008.12.004-Figure1-1.png",
        "caption": "Fig. 1. Coordinate definition of spacecraft with one VSCMG.",
        "texts": [
            " This paper is organized in five sections. First, the equations of motion of a rigid spacecraft with multiple CMGs are introduced. Then, the NINN is introduced. An adaptive control law with a new update law for spacecraft with uncertainty is followed. In the next section, the stability analysis is presented. Finally, the proposed method is demonstrated using numerical simulation study. Consider a spacecraft installed with one variable speed control moment gyro which has been widely studied in the past couple of decades (see Fig. 1). The gimbal inertia matrix and flying wheel inertia matrix based on the gimbal frame orientation are denoted as Ig and Id , respectively. The angular velocity vectors of the gimbal frame and the flying wheel are defined as c\u0307g,-g with respect to the gimbal frame orientation, respectively. The angular velocity vector of the spacecraft with respect to the body frame can be derived from the gimbal frame coordinate system such that x= Cxg (1) where xg is the angular vector based on the gimbal frame coordinate, andC denotes the associated direction cosine matrix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.16-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.16-1.png",
        "caption": "Figure 12.16 hI = l sin () and h2 = O.",
        "texts": [
            " (ii) for the takeoff speed V2 of the ski jumper will yield: V2 = J2ge sine (i i i) Solution (b): Conservation of energy method Since the effects of nonconservative forces due to friction and air resistance are assumed to be negligible, this problem can also be analyzed by utilizing the principle of conservation of energy. Between positions 1 and 2 of the ski jumper: [Kl + [PI = [K2 + [P2 1 2 1 2 2mv1 +mghl = 2mv2 +mgh2 (iv) In Eq. (i v), the first term on the left-hand side is zero since VI = O. If we measure heights relative to the bottom of the track (or se lecting 2 to be the datum as shown in Figure 12.16), then height h 2 = 0 and the height of the top of the track is hI = e sin e. There fore, the second term on the right-hand side of Eq. (i v) is zero as well. Substituting hI =(sine into Eq. (iv), eliminating the re peated parameter m, and solving Eq. (i v) for V2 will again yield Eq. (iii). Solution (c): Using the equation of motion The equation of motion in the direction of motion (x) is: (V) Substituting Wx = mg sine into Eq. (v), eliminating m, and solv ing Eq. (v) for the acceleration of the ski jumper in the x direction will yield: ax = g sine (vi) Linear Kinetics 269 270 Fundamentals of Biomechanics Since the acceleration of the ski jumper is due to gravity only, what we have is a one-dimensional motion with constant accel eration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002570_physrevlett.86.4044-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002570_physrevlett.86.4044-Figure1-1.png",
        "caption": "FIG. 1. The geometry of simple shear experiment: Small strains \u00b4xz 1 2 \u00b4eivt are applied with three principal orientations of the nematic director n, labeled G (for n along the shear gradient), D (displacement), and V (vorticity). The director changes by jdnj u.",
        "texts": [
            " In more complex, nonideal elastomers this parameter may be less clearly defined. Nevertheless, it has to be a function of nematic order parameter Q T , satisfying a linear limit r 1 1 aQ at small Q. In the isotropic phase, at Q 0 and r 1, the elastic constants become, as expected: C1 2C4 2C5 m, D1 D2 0 and the elastic energy (1) reduces to a classical Lam\u00e9 expression. In an incompressible material, all deformations are essentially shears. We shall examine two relevant simple shear geometries, D and V , as shown in Fig. 1. These are the geometries that one achieves in a typical dynamicmechanical experiment since in all known cases the director is confined to the sample plane. The geometry of uniaxial extension, more commonly found in studies of \u00a9 2001 The American Physical Society equilibrium stress-strain, is less appropriate for an oscillating regime because of possible slow relaxation [5] and incomplete sample recovery. The simple oscillating shear \u00b4 t , externally applied to the sample, is the single xz component of the full Cauchy strain, the same for each director orientation in Fig. 1. It also automatically satisfies the necessary incompressibility constraint. The issue of possible director gradients and corresponding Frank elasticity in nematic elastomers has been discussed in the literature [1,6]. It is known that, unless there are special reasons for a director singularity (such as in disclinations or narrow domain walls), the Frank elastic effects play a minor role in the free energy balance and can be neglected. Perhaps this approximation needs to be reconsidered if a sheared sample is very thin in the z direction. However, in a practical situation with a sample thickness d 100 mm and more, ignoring the effect of nematic director gradients is a reasonable first approximation. The elastic free energy density, Eq. (1), takes the form, in the cases D and V of Fig. 1: FD C5 1 1 8 D1 1 2D2 \u00b42 2 1 2 D1 1 D2 \u00b4u 1 1 2D1u2, (3) FV C4\u00b42, where the small change in director orientation dn is taken equal to the angle u. Clearly, one does not expect director rotation to occur in the \u201clog-rolling\u201d geometry V . Signs of unusual elastic response arise immediately. If the director is allowed to rotate, u adopts its optimal value, minimizing F for a given deformation \u00b4. Returning the resulting u \u00b4 to Eqs. (3), the free energy at a given strain is also optimal: uD D1 1 D2 2D1 \u00b4, FD "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.59-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.59-1.png",
        "caption": "Figure 8.59 Three-point bending apparatus.",
        "texts": [
            "57b, for the rotational equilibrium of this material element, there have to be additional shear stresses (Tyx) on the upper and lower surfaces of the cube (with normals in the positive and negative Y directions) such that numerically Tyx = Txy. The occurrence of Tyx can be understood by assuming that the beam is made of layers of material, and that these layers tend to slide over one another when the beam is subjected to bending (Figure 8.58). There are various experiments that may be conducted to analyze the behavior of specimens subjected to bending forces. Some of these experiments will be introduced within the context of the following examples. Example 8.6 Figure 8.59 illustrates an apparatus that may be used to conduct three-point bending experiments. This appara tus consists of a stationary head (A) to which the specimen (B) is attached, two rings (C and D), and a mass (E) with weight W applied to the specimen through the rings. For a weight W = 1000 N applied to the middle of the specimen and for a support length of e = 16 cm (the distance between the left and the right supports), determine the maximum flexural and shear stresses generated at section bb of a specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003803_05698197808982859-Figure19-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003803_05698197808982859-Figure19-1.png",
        "caption": "Figures 19 and 20 compare, respectively, the dry contact and undefbrmed dent profiles with the dent profile under much larger film thickness conditions (/to = 0.78 pm). Under these larger film thickness conditions, the deformation around the dent is far less than the dry contact case shown in Fig. 19 and approaches very closely the undeformed profile as shown in Fig. 20.",
        "texts": [],
        "surrounding_texts": [
            "i l i I . , \\I I !4% 11, !\\#F PI te!-\\\n1.6 r c l n t l i ~ v l ~ i ' i wv l ) t l l ( l 1w o t i r t i ( . orrlrr nl' r r l r r r r r r I i r i x t . l i t l i t - r r l l r . 1.2 l l r t r 7 i n l > c o n t a t r ~ I . I ~ ~ C I I ~ P .\nFsavn~ t l i r ~ : ~ t ~ r l p c , l n r of f ; ~ ~ i p ~ r . . i m p ~ r t : i n t r r l n c i < l r r . n - .% f i r m i s i f i t - i l r l 1 t r r n t . r nl Klllf ~ ) I i r n r r m r n ; ~ t r r l rhc- p ~ - r - c \\ l r r r . . 4 illl<l st1 P S \u20ac <lllt i r l ~ l l l l l ~ ~ r l 1 ;It t11r ( I (* ! l l ~ l 1 0 1 1 l ( l 1 ~ ~ . \\ l ' l l ! ~ ~ * p v t n \\ -\n0 \\ i~ i r a ~ i t l \\TIT<< <,I!~.~I~:I~~oII\\ h,ii<* 111~1 IWPII ~ ~ i : ~ t l ( + , ~t I\\ p b \\ h i - -240 -200 -160 -120 -80 -a0 hlr ~n t l x * i l i ~ [ - c 1 1 t r 17ic*dtS\\ I I I ~ 1 1 r n r ! \\ t .~IIw[I I # \\ lo( .I! t 111.1\nX, IJm c-I frt t%. ! ' h i s r .III 1 ) ~ ,~i-< ~ t ~ ~ i j l l i ~ l t i - c l In 1 <111111;1t1iiq IIM+ (a) h w l pmflls of Flg. l4(a) i ! v n . ~ t ! l k film lhii k i i c < ~ II~~~.I\\III,P~II(=II~< o f l h t * d t . r ~ r *, i11t I ) I ~ *\nSIt!ll( c l r i ( on t ' l i - t i I t V l t 111 flfilt. 3 t l d t It1- l ~ l l ~ l ~ ~ l ) ! lil(.(! (!t*l11\n~ m ~ f i l t . ( s t? lu\\ ir.ti t-).\n7-111- \\1:1ti( r i ~ t - : ~ \\ i ~ r t ~ r i ~ t ~ t i t \\ 01 111r l ~ t = ~ ~ ~ i l ~ l mrlrrl r ! i \\ crb11-\nIJ[! q h c * t m in 1- i~ . 7 r:111. foi <-il~~ip,~rv\\o~j ~ I R ! ln)qtn\\. i ~ c , 61~11-\nm 4 INLCT ~idrtxvl a \\ t - v ~ r t > ~ ~ r r w o ~ i d i1to11 1 ' 1 ~ [I~:H II\\ I[~:I~IVII 0\nl::: -X)(I -160 -120 -80 -40 0 ~ ~ ~ i r l i t i o t i ~ 1 ~ 1 . r ~ ~ ~ ~ o i 1 d ~ ~ o 1 1 ~ ~ ~ : 1 1 i 1 ~ ~ ~ 1 ~ ; i ~ t t i ~ ~ ~ ~ l 1 ~ 1 i 1 t ~ ~ ~ 1 ~ 1 1 : 1 1 1 l 1 ~\nX, urn c u p w i ~ n c n t q r c l ~ r + r c + t h r ~ ~ b : i u i n x r ~ m I l t i r t / t : t r~ ~ ~ l c > c . i ~ ~ r < - . ;I<-\n<t1111irig \\ ~ R O [ I ~ ~ I < I I ~ ~ ~ I ( (,\\. I\\ I .2 X i (!'' Y/ITI' I ! 7.\\,Olln l t \\ i ) .\n(b) Dmt pmflle of Plg. 1qb) 'I 11t. i i i r c t . f i ~ r . c - r ~ r r n 1.7 i n S t - < m{h;lstlr.ch t l l v wpnr G ~ t i r r r i t x . r ~ t t - r . ~ ~\n111i' \\Ill fL14 th'4 i11l i l 1101 11bt' c l t > ~ t ~ ~ ~ l ~ t * f ~ ~ f ~ ~ ~ l i ~ ~ ~ l I i # l ~ . ' i ' l l t h K.31) I ) < * - c - a\n~ t \\ ~ t - ( ~ i i 111r \\I I~ i a l t vk tt irI1i11 I I I ~ i l t - l i t i\\ :I rt-xt111 of 111th (lvl6>rIII,II~<III I > o t l ~ 11tr \\ ! t ~ l t ~ ; + l l #I~ICI tit* ~; ippt i~i t a ( l i \\L. Sin, c\n4\"\nf l i ( + q1~r .1 l j a l l II;IS .ti1 r l z \\ t i ~ - ~M,cIIIII~\\ , i p p i o ~ ~ t i ~ ~ ~ ~ ~ l ~ o r ~ r l1.1Ii INLET\n0 l : L f l 7 = -80 -49 .- - 0 1.-I-- t h n r of \\ n p p t ~ t ~ r . . rt r v i l l c. l :~*~ic .dl! rlc*form to ;t $i.c;alcr rivr10 RD 120 I69 200 gr.rhrb rli;~n t Z ~ c . ~ : ~ p p l i t r c .\nX, ~ t m I I 1hcr.r tr.cl-t, IO !:I 11) c l l l l i t (ITI tf11. p t . t - t ~ ~ ~ t r ~ l i \\ t ~ i l r ~ r i o t ~\n(el 0en1 pmflle of Flg. 14(c) : t r . r ) t ~ ~ ~ r l IIIC ~ l r ' n f t ~ ~ i e l r ~ ~ I ~ I ~ I l a ,~ t r . r l r . c * r ~ t l ~ l i r r ~ i c , OIIC \\ * , r ) ~ l l ~ l\nrxpt*~ I1 1 a t . rI(-III ~ILIIW 10 IoftL I i L r t II,II I ~ I ~ I IV Ii(*:~vih lo,i(lt.il FIR. 15--bnt pmfllw ~ F F P ~ , 14 tb).ndtcJ;h - 0.30 rlm,u - 0.0d32ml- pt~IiI,. ,,r F I ~ . 7 , 1111 ,l~l~li~i,lll,ll I ~ ~ , I ~ ~ I ~ , = ,f III,. l,r,.'iYll( ,,\n4 a f . I i11iii11~ 11 fj11n t l ~ i c Lst t -%\\ t/1~,1 \\~),~F.I~II IC 111t- k t ~ t i ; t [ <*\\. 1 Iyt, 111 r 3 w ~ i t v d i ~ t i it~1111{)r1 . 10111~1! r l i t - 1Ir i11 t \\ o ~ t I i l ~ t , ~~!C.IIITC-:I! 11 , f h . t l of 111(' r l ~ t ( r r l l t n t I r nqr. I !I;II i\\. IIIC p ~ - t - < \\ ~ ~ l - r . 11 if11111 1111. t a1.1t~ 4 TV:IT<-~I In f t ~ r ({VIII 1, ill !n* 7 ~ ~ 4 ) a ~ ~ ~ c l t l i ~ ~ r v ~ 1 1 1 I w :q p~ I ~ \\ \\ ~ I I C I 1.r ( 1 1 11ti) o r 1\\11 1 1 i ~ i t ~ IIW 1 I t - I II~.VII I)TI-\\\\II~I* . t~~~ l l111(1 ll!r \\ll(>ixlIlt=r 111 1YlV cIcr1t\n' I l t i c 1tt*;1\\ i l t * l ~> ,~~ l r i l ( 1 1 I 4 6111t.ir I 1) ro l i I tb i'i 4 r ~ ~ t ~ ~ ~ , ~ ~ - t * i l st ~ t h\n111r l r ~ I w ( ;II(-c! p r < d i ! t > t i1 1 . i ~ . i 7 n !I~-IC* 111r 4 VII~T:I! 171111\n1lti(k.11(*\\< i\\ 11.1 I p i 1 1 . TIN, I{+O 11~(1f i I t - \\ t ~ i ~ x t . 1 ~ r r 1 \\II- - * + * IWI ~ n i i n > w r I \\rt r I i : ~ t r l i t - r l l - ~ , p t - s t t ~ l l l t l r j l 111th c l t ~ n r r , i ~ rh. tc 1 1 8 88\nI p r o l i l t - t r1111i ~r l r . \\ . ( ' r r n ~ l ) : ~ ~ htr11 'I! 111t. 1it.r) ~ w r l f i l e k + l l r r ~ r \\ lf1.11\n-4 t h v r1 r .n~ i\\ ricrt :I< w.I<.I~~\\ r l t . l r> l -mr.11 11nrlr.r I1111t-II : t ~ c r I r r ~ i l -\nt I i t i r l ~ 1 5 :I< i t i s i ~ n i l t - i r r ~ t i ( l l t ~ < r ~ ~ \\ 11) J ~ ! ~ I ~ J * I I I . T Y ~ I ( - i, It.<\\ ::[ 1 / / 6 k ~ kJ ~nr: r i l ~ c . d c l ~ ~ r i ~ i ~ r i ~ l n #I[ r tic 1 ~ ~ 1 i l i 1 1 ~ r t l ~ c of i l t r ( l r r ~ f t1:111 III~, rt,111-\nEL 0 R1- -2' '-A~ l NL FT 111 ! iq, IS, f ! ~ t ~ 11nt1r! (11 r?~ tb t l r h - ~ i t p t ~ ~ f i l t - 1)1)?:4i11tvj f r f ~ t t ?\n0 4 17 - - - a-3 i t l t * < i f III\\ t~ a t ih as ( I ~ B I I ~ , I ~ C ~ ! 1, i t ] ! t l t n ~ ~ ! l ) r ~ r f i l t ~ 1~11t!t-i r t ~ c I I I I 1 I I d t i ~ : ~ i r ~ i c t ~ * t i ( i i ~ ~ r t ~ i \\ I)[ I IK. 17. r l i IOIII~ ;!\\I $+ IT!! t l i v l i t - \\ 4 n l i -\n-no +d0 n on I?r) \\HI 200 ?,lr r l i r ~ l i l t ~ . r tit. ~ ~ t ~ r l c - f i ~ l - r ~ u . r l s l t Z i I t - ( ;11t IIV ~ l r r ~ t a c l b i oI .I%\nw I t . p r r . \\ r . r ~ ~ i ~ ~ r : ~ h t . t l r a r ~ t <lr,~l,r. r\\ h r . 8 ~ 1 1 1 ~ i ~ i l l ~ l r n r r - t r l FIf 11)\nFlg, l&Photomlcragraph snd prenls of dent lor large film thickness; h - 0.78 pm. - - - - - - 0 LUBRICdnD\nDRY CONTdCT ;PROFILE UNDER LOAD (37. R Nl I'III I 4lrc \\!IIIIIIII~I < ; t r i l l I h;ti ~IE~II r ! ~ i + , ~ t * ~ i . ( ~ x \\ r ~ I(-I,I~ i v d v '\"r -- a< l( l\\t, ( 4 ~ 1 l l ~ < I l l [:I( t, ll( i 111 t l t44>\\t I ll(, \\ ~ l i > 1 1 ~ ~ ! < ~ 1 \\. ' n l ~ l)Vtn\\- .a,1111 1' 1 I \\ < ' i\\ \\ h o ~ \\ [I 111 I l t - :I 111111 ~11111 01 IIIC~ III.IY~IIIII~II f I c r ~ t - N* .4% -4,- *M - r1.111 I )V I~ \\F { I I v , 111r I~I~II~~~IIC'I! t=I :~\\ t ic ITIII<IIIIII\\ :111r! t IIV 111- 0 INLET-I t i ~ t ~ ~ i * ~ i r n \\ I>( f l i t , 1111 i {m, \\II ~ t i ~ / ~ o i ~ ! ; i i ~ ~ I ut r o w t ! ~ t i > r * t ~ \\ i ~ ~ ~ i 1% -1M -120 -SO -40 , <\\-*.&+-, 0 do 80 tilt, l * ! < I i l l \\ of i ! I t * ~ l l r ~ l l l ~ ~ t ~ l . t I I1 I< ~ 1 \\ ~ 1 1 1 ~ ~ t ~ ( I tI1,lf l h t , p i , ! l l P X, urn i ~ ~ ~ ~ i , ~ l l l ~ ~ ~ l : ~ l i i ~ l ~ l ~ i ~ t l ~ g , ~ ~ ~ ~ m p B l ~ ~ n o ~ ~ w c t r n t a c t ~ m p r o f l i e w r + k p r a f l l a u n d s r l \\ t * l t?, !11t- TII C.~\\III iq i i%th 11itb ih.111 \\ t l { > ~ l ! r ! ( ~ i IOT ( 1 1 \\ ~#TII~I( I dynnrnlc eondltlons of Flg. 10(cJ: h - 0.14 pm.\nD ow\nnl oa\nde d\nby [\nE C\nU L\nib ra\nri es\n] at\n2 2:\n43 2\n3 A\npr il\n20 15",
            "Influence of Debris Dent on EHD Lubrication 47\n------ 0 LUBRICATED DRY CONTACT PROFllE\n. . UNDER LOAD (37.8 NJ\nFlg. 19-Comparison of heavily loaded dry contact dent profiie with profile under dynamic conditions of Fig. 15; h , = 0.78 pm.\n---- -0 LUBRICATED UNDEFORMED PROFILE (STYLUS TRACE)\nhas created a pressure environment around the dent which allows the dent to pass through the Hertzian region in an \"undeformed\" state; i.e., the pressure around the dent is everywhere equal to the Hertzian pressure for smooth surfaces. Comparing the profiles of Fig. 18 shows that, under dynamic conditions where the film thickness is 0.14 pm, the local deformation around the dent is significantly greater than its undeforn~ed condition.\nsuch as the debris dent considered here. Under pure rolling conditions, the local EHD film thickness in and around the dent are developed during its passage through the inlet region. The dominating influence that the inlet region has on film thickness is well established (17), (20). The additional feature illustrated here is that EHD effects are very local in nature. The local film thickness that is associated with a given element in the Hertzian region is the result of the integrated hydrodynamic pressure that element has encountered while passing through the inlet region. If a surface defect substantially modifies the shape of the inlet region, as shown in Fig. I l(a), it will also modify the local hydrodynamic pressure generation and local film thickness within that region. Because the surface modification at the leading edge of the dent is less favorable for pressure generation than the trailing edge, the local film thickness is observed to be slightly lower at the leading edge than it is at the trailing edge.\nBecause of the importance of the inlet region, it is instructive to compare the characteristic inlet dimensions with the dimensions of the debris dent. The inlet region can be defined as the region upstream of the Hertzian region where significant hydrodynamic film forming pressure is generated. The inlet region has a finite size which varies with the thickness of the central film thickness (h,). In the work on starvation (1 7), two inlet dimensions (Sf and hb), as shown in Fig. 21, were used to describe the boundaries of the inlet region. The dimension of hb can be thought of as the thickness of the inlet region gap where significant hydrodynamic pressure commences, and the dimension of Sr can be thought of as the distance over which the inlet pressure is generated. As shown in (1 7), these inlet dimensions are related to ho in the following way\nValues of hb and Sf for the three central film thicknesses used in the experiments are shown in Table 3. For the film thickness range considered here, Sf is between one and two orders of magnitude larger than h,, indicating that the convergent inlet region is a great deal longer than it is thick. This feature is characteristic of many debris dents. The one\nPRESSURE f -\nvide a reasonably clear understanding of the EHD phenomena associated with the presence of a surface defect Fig. 21--Schematic drawing showing characteristic inlet dimenslono\nD ow\nnl oa\nde d\nby [\nE C\nU L\nib ra\nri es\n] at\n2 2:\n43 2\n3 A\npr il\n20 15",
            "conrirlr.rr-d hrrc iu rnr~cll Inn~rr (81) pm) titan i t iq derp (0.X prn ).\nI T :I r hnrartrri*;til- inlct cnnvrrRcnrc anglr (F i s rlefint+rl ;IF\ni t I ~ ~ < ~ r ; ~ r r * r l in F I ~ . 21, i t can tw <Ii~wn ~h >I\n( t ~ t l # , l ~ ~ ~ rp = arr tan 2.27 - /{ 3 3\nffg. 224mfls (a) end Ib) md o ~ e s ~ a l t ~racklnp (c) md (d) st rurlscr dents. (Arrows indicate spall formallon at trnlltng edge of dents )\nD ow\nnl oa\nde d\nby [\nE C\nU L\nib ra\nri es\n] at\n2 2:\n43 2\n3 A\npr il\n20 15"
        ]
    },
    {
        "image_filename": "designv10_8_0003002_bf01258296-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003002_bf01258296-Figure4-1.png",
        "caption": "Fig. 4. A robot arm of two revolute joints.",
        "texts": [
            " Using specific PRicker coordinates, A v p is then represented by the 3 x 3 minors of al,1 al,2 al,3 0 ) a2,1 a2, 2 a2, 3 0 . Pl P2 P3 1 Then the first three components of A v p, P2,3,0, P3A,o, P1,2,0, are independent of pl, P2, p3, giving us a translation vector. Similarly, in d-dimensional space, we can represent a rotation by a center which is a d - 1-extensor, and a translation by a d - 1-extensor at infinity. Now, suppose that we have a robot arm, which for the moment we will take to.have only two revolute joints, serially connected (Figure 4). Let us impart an instantaneous rotation at both joints simultaneously, given by the centers Col(S1, r! \u00d7 Sl) and co2($2, r2 x S2). Then the net instantaneous motion of the end effector has center co(S, T) = Col(S1, rl x S1) + 032(82, r2 x S2). This 6-tuple does not necessarily have its first three components S orthogonal to its last three components T, as is the case with a 2-extensor, so (if the two axes are skew) it is an indecomposable 2-tensor, representing a screw motion. A great deal of the instantaneous kinematic theory of robot arms can be thought of in terms of antisymmetric 2-tensors, that is, in terms of the vector space V (2), see Hunt (1978) and Lipkin and Duffy (1982), for example"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.19-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.19-1.png",
        "caption": "Figure 8.19 Analyses of the material element in Figure 8.18.",
        "texts": [
            " Using Mohr's circle, determine the maximum shear stress in duced and the plane of maximum shear stress. Multiaxial Deformations and Stress Analyses 165 Solution: For the given magnitude of the externally applied force and the cross-sectional area of the bar, the normal stress induced in the bar in the x direction can be determined as ax = F/A. As illustrated in Figure 8.18 b, ax is the only component of the stress tensor on a material element with sides parallel to the x and y directions. Based on the plane stress element of Figure 8.18b, Mohr's circle is drawn in Figure 8.19a. Note that there is only a tensile stress of magnitude ax on surface A, and there is no stress on surface B. Therefore, on the i-a diagram, point A is located along the a-axis at a distance ax from the origin, and point B is essentially the origin of the i-a diagram. The center C of the Mohr's circle lies along the a-axis between B and A, at a distance ax /2 from both A and B. Therefore, the radius of the Mohr's circle is ax /2. Point F on the Mohr's circle represents the orientation of the material element for which the shear stress is maximum. The magnitude of the maximum shear stress is equal to the radius of the Mohr's circle: ax F i max = - =- 2 2A On the Mohr's circle, point F is located 900 counterclockwise from A. Therefore, as illustrated in Figure 8.19b, the material element for which the shear stress is maximum can be obtained by rotating the material element given in Figure 8.18b in the clockwise direction through an angle (h = 450 \u2022 Note that ax is the maximum normal stress on the Mohr's circle. Therefore, point A on the Mohr's circle represents the orienta tion of the material element for which the normal stresses are max imum and minimum, and the material element in Figure 8.18b represents the state of principal stresses. Example 8.3 Consider the material element shown in Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.50-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.50-1.png",
        "caption": "Figure 4.50 Problem 4.2.",
        "texts": [
            " The distance between A and B is e = 6 m and the dis tance between A and.D is d = 2 m. (Note that one-third of the board is located on the left of the roller support and two-thirds is on the right. Therefore, for the sake of force analyses, one can assume that the board consists of two boards with two different weights connected at D.) If the diving board has a total weight of 1500 N, determine the reactions on the beam at A and D. Answers: RA = 2318 N U) RD = 4602 N (t) Problem 4.2 The uniform, horizontal beam shown in Figure 4.50 is hinged to the ground at A and supported by a frictionless roller at D. The distance between A and B is e = 4 m and the distance between A and D is d = 3 m. A force that makes an angle f3 = 60\u00b0 with the horizontal is applied at B. The magnitude of the applied force is P = 1000 N. The total weight of the beam is W=400N. By noting that three-quarters of the beam is on the left of the roller support and one-quarter is on the right, calculate the x and y components of reaction forces on the beam at A and D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure7-1.png",
        "caption": "Fig. 7. Coordinate systems of the screw surfaces.",
        "texts": [
            " (17), we obtain the following equation of undercutting: r1 \u00bc 4b2n\u00f01\u00fe 2n\u00de b\u00f01\u00fe 2n\u00de\u00bdcos\u00f0# /\u00de k cos\u00f0#\u00fe 2n# /\u00de \u00bd sin#\u00fe k sin\u00f0#\u00fe 2n#\u00de \u00fe2b\u00bd2nk cos 2n#\u00fe cos\u00f0# /\u00de k\u00f01\u00fe 2n\u00de cos\u00f0#\u00fe 2n# /\u00de \u00bdsin#\u00fe 2n sin# k sin\u00f0#\u00fe 2n#\u00de 2n sin / 8>< >: 9>= >; \u00f025\u00de r2 \u00bc 4b2n\u00f01\u00fe 2n\u00de b\u00f01\u00fe 2n\u00de\u00bd cos\u00f0# /\u00de \u00fe k cos\u00f0#\u00fe 2n# /\u00de \u00bd cos#\u00fe k cos\u00f0#\u00fe 2n#\u00de 2b\u00bd2nk cos 2n#\u00fe cos\u00f0# /\u00de k\u00f01\u00fe 2n\u00de cos\u00f0#\u00fe 2n# /\u00de \u00bdcos#\u00fe 2n cos# k cos\u00f0#\u00fe 2n#\u00de 2n cos / 8>< >: 9>= >; \u00f026\u00de To obtain the equations of the screw surface and line of action for the twin rotors on the space, we create a 3-D coordinate system as shown in Fig. 7, where S1a and S2b are rigidly attached to the rotational axes of screw rotors 1 and 2, respectively. Because the twin rotor profiles are the same, they rotate in opposite directions at a constant rotational angle w. The operations of their coordinate transformation are as follows: M1a;1 \u00bc cos w sin w 0 0 sin w cos w 0 0 0 0 1 pw 0 0 0 1 2 66664 3 77775 M2b;2 \u00bc cos w sin w 0 0 sin w cos w 0 0 0 0 1 pw 0 0 0 1 2 66664 3 77775 where p is the pitch and w is the rotational angle. Therefore, the equation of the screw surface for rotor 1 is R1a \u00bcM1a;1rsur1 \u00f027\u00de and for rotor 2 is R2b \u00bcM2b;2rsur2 \u00f028\u00de where rsur1 and rsur2 are the plane profiles of rotor 1 and 2, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002576_s0094-114x(97)00101-8-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002576_s0094-114x(97)00101-8-Figure1-1.png",
        "caption": "Fig. 1. Coordinate system S1 and geometry of the cup-shaped grinding wheel.",
        "texts": [
            " The generating train of Gleason No 463 hypoid grinder is designed to perform the Modi\u00aeed Roll Motion by means of a special cam reciprocator mechanism. The mechanism of Gleason No. 463 hypoid grinder can be divided into four major parts: (a) cup-shaped grinding wheel, (b) special Modi\u00aeed Roll generating train, (c) feeding and driving mechanisms, and (d) work head assembly. The detailed description of the mechanism investigated by Lin, et al. [20] and the Gleason Works [21] is omitted here. The axial cross-section of the cup-shaped grinding wheel is straight edges in the a-a cross section as shown in Fig. 1, and it can be expressed in coordinate system S1(x1, y1, z1) as follows: R1 uj; bj x1 y1 z1 8<: 9=; rm2 W 2 uj sincj \u00ff sinbj rm2 W 2 uj sincj \u00ff cosbj \u00ffuj coscj 8><>: 9>=>;; 1 where j= i and o, and parameters ui, bi, uo and bo are the head cutter surface coordinates of inside and outside blades, respectively. Subscript ``i'' indicates the inside blade, and ``o'' represents the outside blade; the ``2 '' sign should be regarded as `` + '' sign for the outside blade (j = o), and ``\u00ff '' sign for the inside blade (j= i)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.24-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.24-1.png",
        "caption": "Figure 4.24 3-pulley traction.",
        "texts": [
            " Such devices are designed to maintain parts of the human body in particular positions for healing purposes. For such de vices to be effective, they must be designed to transmit forces properly to the body part in terms of force direction and magni tude. Different arrangements of cables and pulleys can transmit different magnitudes of forces and in different directions. For example, the traction in Figure 4.23 applies a horizontal force to the leg with magnitude equal to the weight in the weight pan. On the other hand, the traction in Figure 4.24 applies a horizon tal force to the leg with magnitude twice as great as the weight in the weight pan. Example 4.4 Using three different cable-pulley arrangements shown in Figure 4.25, a block of weight W is elevated to a certain height. For each system, determine how much force is applied to the person holding the cable. Solutions: The necessary free-body diagrams to analyze each system in Figure 4.25 are shown in Figure 4.26. For the analysis Statics: Analyses of Systems in Equilibrium 65 of the system in Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003747_05698197908982899-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003747_05698197908982899-Figure1-1.png",
        "caption": "Fig. 1--Geometry of the problem",
        "texts": [
            " In this approach, the heat input from the meshing zone must be averaged o u t over o n e revolution, so that there will be a steady heat input o n each tooth through a revolution of D ow nl oa de d by [ N or th C ar ol in a St at e U ni ve rs ity ] at 2 0: 13 2 8 Ju ly 2 01 2 Pretliction o f the Bulk Tempera ture in Spur Gears Based o n Finite Element T e m p e r a t i ~ r e Analysis 2 7 the gear. Similarly convective heat transfer coefficients o n tooth faces has to be averaged over a revolution. - fhe geometry of a gear tooth is shown i l l Fig. 1. T h e governing equation ant1 the bo~undary conditions are: a7' k - = I ( 7 - 7') - q o n Regionm (meshing tooth face) a t 1 a7' - k - = I t , (7' - T,,) o n Region I (nonrneshing tooth face, an to11 land, I~ot tom land) a7' - k - = I t , (7' - T,,) on Region s (gear surface) az I t , = con\\,ecti\\le heat transfer coefficient o n gear surface I t l = convecti\\re heat transfer coefficient 011 tooth faces, top 1;und and I~ot tom land 7' = I~ulk temperature T,, = zumbient temperature It = thermal concluctivity of gear material tr = normal coorclinate per l~enc l ic~~la r to z direction q = steady heat f l u s along the meshing tooth i'r~cc, fiunction of positio~l on tooth Face T h e last t\\vo I>oundary conditions arises from the a s s t ~ n ~ p - tion of equaliry of temperatut"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003190_ja0569196-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003190_ja0569196-Figure4-1.png",
        "caption": "Figure 4. Two procedures for monolayer assemblage of DI on the electrode",
        "texts": [
            " Analysis of the immobilized enzyme responses thus requires determining the homogeneous kinetic characteristics of the biotinylated diaphorase (b-DI), and seeing whether biotinylation has degraded the enzyme activity. The same experiments as described above for DI were carried out with b-DI, leading to: indicating that approximately half of the enzyme has been deactivated by the biotinylation reaction. Immobilization. Two procedures, based on avidin-biotin affinity, were used to immobilize the enzyme on the electrode surface (Figure 4). In procedure A, a saturated monolayer of neutravidin is first adsorbed on the surface of a carbon electrode, (35) The value we find for this limit is ca. 10 times larger than previous literature data.26 The reason is the unwarranted use, in the latter analysis, of the firstorder approximation (eq 12) for cosubstrate concentrations that are not small enough for this approximation to be valid, as clearly appears in Figure 1c. ipl FSCP 0 ) 2x2 \u03b3xkcatCE 0DP CP 0 [1 - ln(1 + k2CP 0 kcat ) k2CP 0 kcat ] (12) ipl FSCP 0 ) 2x2 \u03b3xkcatCE 0DP CP 0 (13) ipl FSCP 0 ) x2 \u03b3xk2CE 0DP (14) k1 ) 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003014_1.2895905-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003014_1.2895905-Figure2-1.png",
        "caption": "Fig. 2 A sliding nates",
        "texts": [
            " With C specified, we can now focus on the coefficient matrix for generalized velocity component derivatives from Eq. (44) by grouping all other terms into the function h. This gives TrCTACTfi = h(q, u). (48) The matrix A is the same as defined in Eq. (17). To obtain first-order decoupled equations for the constrained system we simply choose T to be the proper congruency transformation, this time for cTAc, using the procedure outlined earlier. Example: Unreduced Configuration Coordinates. We will now repeat the example carried out above, but now using the dependent configuration coordinates shown in Fig. 2. The constraint imposed by the rigid rod is temporarily removed. The position Jacobians for the two masses now appear as and 0 00] 49, The resulting A matrix is [. m 0 : 1 A = 0 - m 2 . ( 5 1 ) - m 2 0 -me] Now we must find the orthogonal complement to reimpose the constraint. Therefore, the constraint representation should be put in the form of Eq. (35). For the simple pendulum this constraint is written as Bq = [0 q2 q3]~l = 0. (52) To find an orthogonal complement the zero eigenvectors of BTB must be found"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure2-1.png",
        "caption": "Fig. 2. Carryover phenomenon between two mating rotor.",
        "texts": [
            " In this paper, we propose a new claw-shape whose concept design is shown in Fig. 3. This new design of claw-shape is similar to Kashiyama patent [16] as shown in Fig. 4. Kashiyama developed twin-screw compressor with square-threaded rotor for the vacuum system and distinguished from the conventional one by the extra large wrap angle except the tooth profile. The transverse sections of Kashiyama\u2019s profiles are formed by cycloid and involute curves and may not be conjugate at all. However, our design on claw-shape is completely conjugate. (2) As shown in Fig. 2, there is a gas carryover phenomenon between two mating rotors. This carryover phenomenon will affect the size of clearance as they mesh closely. If the clearance could not maintain a tiny size during operation, it may lead to larger leakage and reduce the pump performance. Besides, Fig. 2 indicates the patent design is unable to conjugate at all. Thus, we use the theory of gearing to design the rotor profile for reducing the design problem (shown in Fig. 2). Here, we analyze and improve the aspect of the patent design [11\u201313]. After improving the rotor profile, we compare pump performance in terms of carryover, area efficiency and length of line of action. The coordinate systems of the plane conjugate tooth are created as shown in Fig. 5, where point g is an important location (related to parameters R and a) for the claw-shape, R is the distance from point g to Of, and a is the angle measured from the xf axial to point g. Point g can be represented in the coordinate system S1 as r \u00f0g\u00de 1 \u00bc R cos a R sin a 1 2 64 3 75 \u00f01\u00de As shown in Fig",
            " (16) yields q3 and allows us to check whether or not they are satisfied by Eq. (14). If not, the value of q2 must be modified. The trigonometry method can also be used to obtain a1, a2, a3 and subsequently yields all the center coordinates of the circular arc. Eq. (15) can verify whether the center of the circular arc is inside the pitch circle or not. If it is, there is no carryover. However, the center of the circular arc is outside the pitch circle then the carryover occurs. This phenomenon can be illustrated as shown in Fig. 2. For joining multiple curves, the parameter values can be determined by the method above to produce a complete profile. From the theory of gearing [17], we know the undercutting equations would be as follows: r1 \u00bc ox1 oh V \u00f012\u00de x1 fh f/ d/ dt \u00bc 0; r2 \u00bc oy1 oh V \u00f012\u00de y1 fh f/ d/ dt \u00bc 0 \u00f017\u00de Operating Eq. (17) yields the following: r1 \u00bc rqi cos\u00f0h /\u00de sin h 2\u00bdcxi cos h r cos\u00f0h /\u00de \u00fe cyi sin h \u00f0cyi \u00fe qi sin h r sin /\u00de \u00f018\u00de r2 \u00bc rqi cos\u00f0h /\u00de cos h\u00fe 2\u00bdcxi cos h r cos\u00f0h /\u00de \u00fe cyi sin h \u00f0cxi \u00fe qi cos h r cos /\u00de \u00f019\u00de where or1 oh \u00bc qi sin hi\u00fe qi cos hj fh \u00bc cxi cos h cyi sin h\u00fe r cos\u00f0h /\u00de f/ \u00bc r cos\u00f0h /\u00de V \u00f012\u00de 1 \u00bc \u00bd2\u00f0cyi \u00fe qi sin h\u00de 2r sin / i\u00fe \u00bd 2\u00f0cxi \u00fe qi cos h\u00de \u00fe 2r cos / j We can verify whether the tooth profile has undercutting or not by Eq",
            " No matter which application is used, the design of claw-type rotor in examples 2 and 3 could perform better than that in example 1. In this paper, we use the conjugate theory to design a claw-type rotor from which we derive the mathematical model of the tooth profile and its design constraints. The following are our conclusions: (1) We use example 1 to illustrate the lack of the patents [11\u201313]. In these patents, the shapes of rotors (not claw-shape segment) cannot conjugate at all because of the gas carryover phenomenon (shown in Fig. 2). However, we have overcome this problem by new shape design using the conjugate theory. (2) Besides, example 1 verifies the drawbacks of gas sealing on the claw-shape design that is as same as these patents. Because of the obvious interstices between the two mating screw rotors, the result performance of a vacuum pump may be inferior. (3) We propose a new claw-shape which is connected by a cycloid curve and its envelope curve. From example 2, we improve the patent design of the space between the two mating screw rotors, not only to eliminate clearance but also to reduce gas carryover and improve sealing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.20-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.20-1.png",
        "caption": "Figure 3.20 Example 3.4.",
        "texts": [
            "18 An exercise to strengthen the shoulder muscles, and a simple model of the arm. b 38 Fundamentals of Biomechanics Example 3.4 Consider the total hip joint prosthesis shown in Figure 3.19. The geometric parameters of the prosthesis are such that \u00a31 = 50 mm, \u00a32 = 100 mm, (h = 45\u00b0, and fh = 90\u00b0. Assume that, when standing symmetrically on both feet, a joint reaction force of F = 400 N is acting at the femoral head due to the body weight of the patient. For the sake of illustration, consider three different lines of action for the applied force, which are shown in Figure 3.20. Determine the moments generated about points Band C on the prosthesis for all cases shown. Solution: For each case shown in Figure 3.20, the line of action of the joint reaction force is different, and therefore the lengths of the moment arms are different. From the geometry of the problem in Figure 3.20a, we can see that the moment arm of force F about points Band C are the same: d1 = \u00a31 cos(h = (50)(cos45\u00b0) = 35 mm Therefore, the moments generated about points Band Care: MB = Me = d1 F = (0.035)(400) = 14 N-m (cw) For the case shown in Figure 3.20b, point B lies on the line of action of the joint reaction force. Therefore, the length of the moment arm for point B is zero, and: MB =0 For the same case, the length of the moment arm and the moment about point Care: d2 = \u00a32 costh = (100)(cos45\u00b0) = 71 mm Me = d2 F = (0.071)(400) = 28 N-m (ccw) For the case shown in Figure 3.20c, the moment arms relative to Band Care: d3 = \u00a31 sin(h = (50)(sin45\u00b0) = 35 mm d4 = d3 + \u00a32 = (35) + (100) = 135 mm Therefore, the moments generated about points Band Care: MB = d3 F = (0.035)(400) = 14 N-m Me = d4 F = (0.135)(400) = 54 N-m (ccw) (ccw) 3.7 The Couple and Couple-Moment A special arrangement of forces that is of importance is called couple, which is formed by two parallel forces with equal mag nitude and opposite directions. On a rigid body, the couple has a pure rotational effect. The rotational effect of a couple is quan tified with couple-moment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002990_s0022112006009153-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002990_s0022112006009153-Figure7-1.png",
        "caption": "Figure 7. Geometry of liquid rope coiling in the inertio-gravitational regime. ei (i = 1, 2, 3) are Cartesian unit vectors fixed in a frame rotating with the rope, and di are orthogonal material unit vectors defined at each point on its axis, d3 being the tangent vector. The parameters Q, a0, H , R and \u2126 are defined as in figure 1. (a) Geometry of the tail, modelled as an extensible string with negligible resistance to bending and twisting. This string lies in the plane normal to e2, and d1 \u00b7 e2 = 0. The lateral displacement of the axis from the vertical is y(s), where s is the arclength measured from the injection point. (b) Geometry of the rope near the contact point. Bending and twisting are important in a boundary layer of arcwise extent \u03b4 near this point. Right at the contact, d1 is horizontal and points towards the center of the circle (of radius R) along which the rope is laid down.",
        "texts": [
            " The character of the new regime is revealed most clearly by the shape of the coiling rope. Figure 6(b) shows the lateral displacement x1(s) of the rope in the plane containing the injection point and the contact point, for four numerical solutions with \u03a01 = 106, \u03a02 = 0.316, and different values of H (g/\u03bd2)1/3. These four solutions are denoted by the points S1\u2013S4 on the corresponding curve of frequency vs. height (figure 6a). Figure 6(c) shows, for the same solutions, the moment M1(s) associated with bending about a local basis vector d1 that is normal to the axis of the rope (figure 7b). Solution S1 corresponds to pure gravitational coiling with negligible inertia. Here the rope is nearly vertical except in a thin boundary layer near the contact point s = where viscous forces associated with bending are significant. As H increases (solutions S2 and S3), however, the displacement of the rope becomes significant along its whole length, even though bending is still confined to a thin boundary layer near s = (figure 6c). A further important indication is obtained by comparing the structures of the numerical solutions at the first two turning points S3 and S4 (figure 6a)",
            " The balance of gravity and the centrifugal force normal to the tail requires \u03c1gA sin \u03b8 \u223c \u03c1A\u21262y, (3.1) where A is the area of the cross-section of the tail, \u03b8 is its inclination from the vertical, and y is the lateral displacement of its axis. Because y \u223c R and sin \u03b8 \u223c R/H , (3.1) implies that \u2126 is proportional to the scale \u2126IG = ( g H )1/2 , (3.2) which is just the angular frequency of a simple pendulum. Further insight can be obtained by examining in more detail the dynamics of a whirling liquid string, a simple model of which is sketched in figure 7(a). In the Appendix, we show that the lateral displacement y of the axis of the string satisfies the boundary-value problem k\u22121 sin k(1 \u2212 s\u0303)y \u2032\u2032 \u2212 y \u2032 + \u2126\u03032y = 0, y(0) = 0, y(1) finite, (3.3) where primes denote differentiation with respect to the dimensionless arclength s\u0303 = s/H and \u2126\u0303 = \u2126(H/g)1/2. The three terms in (3.3) represent the axis-normal components of the viscous, gravitational and centrifugal forces, respectively, per unit length of the string. The dimensionless parameter k measures the degree of gravityinduced stretching of the string, and satisfies the transcendental equation 0 = 2B cos2 1 2 k \u2212 3k2, (3",
            "5) to eliminate H from the inertio-gravitational scaling law \u2126 \u223c (g/H )1/2 and using the definitions of \u2126G, \u2126I and \u03a01, we obtain \u2126 \u2126G \u223c \u03a0 \u22125/32 1 ( \u2126I \u2126G )\u221215/8 , (3.6) in agreement with figure 5(d). While the whirling string model explains well the frequencies of the multiple solution branches, it cannot explain why these branches fold back on themselves at turning points. We now demonstrate that this behaviour is due to the influence of inertia in the bending boundary layer near the contact point. The geometry of this region is sketched in figure 7(b). Despite our previous usage, it is not quite accurate in this case to call the bending boundary layer a \u2018coil\u2019, because its arcwise extent \u03b4 is independent of the radius R of the contact point. This is clear from figure 6, which shows that the numerical solutions at the first two turning points S3 and S4 have different values of R \u2261 x1(H ), but identical distributions of the bending moment M1(s). To estimate \u03b4, consider the balance of forces acting within the boundary layer in the d1-direction",
            " Decroocq of BP kindly provided data on the surface tension coefficient of HYVIS 30. Careful and constructive reviews by three anonymous referees helped greatly to improve the manuscript, and we are grateful to one of them for suggesting the \u2018resonance\u2019 interpretation of the multiple frequencies. Consider a liquid string with density \u03c1 and dynamic viscosity \u00b5, injected at volumetric rate Q from a circular hole of area A0 \u2261 \u03c0a2 0 and rotating with a steady angular velocity \u2126 about a vertical axis (figure 7a). Because the string can stretch, its cross-sectional area A(s) and the fluid velocity U (s) \u2261 Q/A(s) along it are functions of the arclength s measured from the injection point s = 0. The string is assumed to be nearly vertical, and its total length \u2248 H is maintained constant by continual removal of the fluid that passes the cross-section s = H . We assume that the string has negligible resistance to bending and twisting, so that its motion is governed by a balance among gravity, inertia and the axial tension associated with stretching"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002965_tia.2005.855043-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002965_tia.2005.855043-Figure1-1.png",
        "caption": "Fig. 1. Machine winding.",
        "texts": [
            " 3 ) There are more control options for the SPIM compared to a three-phase induction machine. In this paper, control options for the SPIM are used properly to establish the direct torque control (DTC) technique. It was found that torque ripple can be reduced significantly in the SPIM. When the phase belt of a three-phase induction machine with an even number of slots per pole per phase is split into two equal halves, an SPIM results with two sets of stator coils with their axes separated by 30 electrical degrees (Fig. 1) [1]\u2013[3]. Configuring the SPIM in this fashion, sixth harmonic torque pulsations are avoided. The supply to the A2B2C2 winding group is 30 phase advanced from that of the A1B1C1 winding group. When an SPIM is operated in this fashion, individual MMFs generated from each set of windings will algebraically add up to generate resultant MMF. If any fifth and seventh harmonic components are present in the voltage, they will not generate any fifth and seventh harmonic rotor currents due to the split winding pattern",
            " Thus, the torque of the SPIM can also be expressed as the vector cross product of and , where is the rotor flux of the SPIM. To control the torque and the flux directly, the main goal of DTC, is rotated along a circular trajectory, selecting appropriate voltage vectors from both the inverters, similar to the three-phase DTC algorithm (Fig. 4). DTC is stator side control of ac machines. Estimations of machine torque and stator fluxes are to be calculated from the available state variables and parameters of the machine. is measured from the resultant three-phase axis (Fig. 1). and are measured from their own individual axes (Fig. 1). Resultant electromagnetic torque ( ) can be expressed as the algebraic addition of individual torques ( and ) contributed by both the inverters [3]. (1) (2) (3) (4) (5) (6) A total of 49 different space phasor locations are possible in the SPIM drive. The outermost locations form a 12-sided polygon. In this method is rotated in a circular trajectory, switching the vectors from the outermost 12-sided polygon (Fig. 5). As is rotated in a circular trajectory, it induces sinusoidal voltages and currents in the rotor and the output torque is free from sixth harmonic torque pulsations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002791_s0957-4158(99)00052-5-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002791_s0957-4158(99)00052-5-Figure8-1.png",
        "caption": "Fig. 8. Trajectory (\u00ff58).",
        "texts": [],
        "surrounding_texts": [
            "Figs. 8, 11 and 14 show one step motion of biped locomotion robot on the slope obtained by the energy minimizing evaluation function Eq. (8). Figs. 9, 12 and 15 show the positions of ZMP. The large circles and small circle display the positions of ZMP during single support period and double support period respectively. During single support period, ZMP must exist in the rectangular domain drawn by a solid line, and during double support period, ZMP must exist in the hexagonal domain drawn by a dashed line. These \u00aegures show that all the positions of ZMP are in the domain of support surface and then the biped locomotion robot is stable. Furthermore, Figs. 10, 13 and 16 show the total powers of actuators. The \u00aegures show that desired powers of actuators are very low. By giving the large number of penalty value, the trajectory which satis\u00aees constraints is generated easily, and the energy-optimized trajectory has successfully been found (Figs. 11\u00b116)."
        ]
    },
    {
        "image_filename": "designv10_8_0003878_j.neunet.2008.03.010-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003878_j.neunet.2008.03.010-Figure8-1.png",
        "caption": "Fig. 8. Simulation model, made of two legs, a spine and supported at the front by a wheeled structure that translates forwards, the wheels being guided the rails. The joint connecting the structure to the spine prevents it from rotating around the roll axis. The spine can thus rotate only around the pitch axis but the body could still collapse in the worst case. Two touch sensors were added at the tip of the legs to detect contact of the feet with the ground.",
        "texts": [
            " The parameters of the interneurons are given in Table 7 while the synaptic weights of their connections to the IMm and VGs_m neurons in the MOSS are given in Table 8. Using this implementation, we can change the walking speed by adjusting the value of the single control input \u03a8 while driving the LC. All the simulationswere carried out usingWebots (http://www. cyberbotics.com), a commercial mobile robot simulation software developed by Cyberbotics Ltd. In order to validate our Leg Controller (LC) architecture, we tested it on the hind leg model represented in Fig. 8. Each leg is actuated by one independent LC. Two touch sensors are attached to the feet in order to detect the contact with the ground. Themass of the pelvis and the spine are respectively 1.4 kg and 0.8 kg and the spine is 25 cm long. The front part of the spine is supported by a large tetrapod wheeled structure guided by two pairs of rails so that the spine has only two degrees of freedom: translation backwards/forwards and rotation around the pitch axis. The mass of the wheeled structure is around 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003421_0167-6911(89)90036-4-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003421_0167-6911(89)90036-4-Figure2-1.png",
        "caption": "Fig. 2. Total distributed sliding mode of v, + uv x = 0, on v = exp( - x 2 ).",
        "texts": [],
        "surrounding_texts": [
            "Consider a dynamical system described by a feedback-controlled FOQPDE: ~v~__~ ~ ~v \"~- ' ~ - S i ( v , x , t, u) = b(v , x, t, u) , i = 1 (2.1a) y = h ( v , x, t) (2.1b) 0167-6911/89/$3.50 \u00a9 1989, Elsevier Science Publishers B.V. (North-Holland) where y is the sca lar -valued ou tpu t funct ion, x represents the vector of local spat ia l coord ina te funct ions x i def in ing po in ts on an open set in R\", t denotes time, while u = u(v, x, t) is a d is t r ibu ted feedback cont ro l law taking values in R. The funct ion v is the unknown scalar funct ion, regarded as the d i s t r ibu ted ' s t a te ' of the cont ro l led system. F o r each smooth solut ion v of (2.1), the X, 's are the smooth componen t s of a t ime-varying con t ro l -pa ramet r i zed vector field X, which is assumed to be local ly nonzero and def ined on an open set of R\". The funct ion b : R n + 3 - + R and the funct ion h : R\" \u00f7 3 __, R are local ly smooth funct ions of their arguments . Cond i t ion y = 0 is assumed to local ly def ine an isola ted smooth man i fo ld solut ion v = ~ ( x , t), i.e., h(q>(x, t) , x, t)=-O. The graph of v is assumed to be a smooth t ime-varying surface with local ly nonzero grad ien t except poss ib ly on a set of measure zero. This surface is addressed as the sliding manifold, or the sliding surface, and is local ly def ined as S = {(v , x, t ) ~ R \" + 2 : v=dp(x, t ) } . Al l our cons idera t ions and results are of a local charac te r on a given open set N of R \"+2 descr ibed by the local coord ina te funct ions (v, x, t). The pro jec t ion of such an open set N on to R \"+1 is labe led as M and such a set is equ ipped with local coord ina tes (x , t). Fo r a given smooth feedback funct ion u = u(v, x, t), and a cor respond ing solut ion v of (2.1), the vector field c o l [ S i r , x , t , u ) , 11 is a smooth vector field local ly def ined on M. Definition 1 [1]. G iven an n-d imens iona l surface y in M and a (not necessar i ly smooth) funct ion ~p : y ~ R, the Cauchy data, or the initial condition, of the F O Q P D E (2.1) is cons t i tu ted by the pa i r (~p, y). The n-d imens iona l submani fo ld F in N, represented by the graph of q, on ~,, is called the initial submanifold. Given a smooth feedback funct ion u, an init ial subman i fo ld F is noncharacteristic at the po in t ( x 0, to) in 4', if the vector c o l [ X ( v 0 , Xo, to, U(Vo, x0, to ) ) , 1] in R \"+1 is not tangent to ), at the po in t ( x o, to), with v 0 = \u00a2k(x 0, to). It will be assumed th roughout that for a given smooth d is t r ibu ted feedback cont ro l u(v, x, t) and a given Cauchy da t a ( represented by the noncharacteristic ini t ial cond i t ion subman i fo ld F in R\"+2), the g raph of the solut ion v of (2.1) is local ly smooth, with nonzero g rad ien t everywhere on the open set N where we car ry our cons idera - tions, except, possibly, on a set of measure zero. This a ssumpt ion is sat isf ied in several classical physical examples . (See, for instance, A r n o l d [1], p. 62.) Ava i l ab le to the cont ro l le r is a distributed variable structure feedback switching law: (u+(v , x, t) for y > 0, (2.2) u = ( [ u _ ( v , x, t) f o r y < 0 , with u+(v, x, t) > u-(v , x, t), locally. Defini t ion 2. A d i s t r ibu ted s l iding regime is said to local ly exist on an open set -/ff of the man i fo ld S if and only if the total derivative of the ou tpu t funct ion of the con t ro l led system (2.1)-(2.2) satisfies (see [10]): d y l im d y < 0 and l im - ~ - > 0. (2.3) y ~ +0 d t y ~ - 0 TO simpl i fy no ta t ion we in t roduce the vector z = col(v, x, t) of local coord ina te funct ions and the con t ro l -pa ramet r i zed vector field = c o l [ b ( z , u), X ( z , u), 1] referred to as the characteristic direction field of (2.1). The Lie derivative of a scalar funct ion h(z) with respect to the vector field ~, for a given feedback cont ro l inpu t u = u(z), is de no t e d by L~z.u(z))h or s imply by L~h. In local coord ina tes : L~h = ( S h / S v ) b ( z , u) + ( S h / S x ) X ( z , u) + ah/at. Theorem 1. For a given Cauchy data (~p, \"t) defining an initial submanifold 1\" with nonempty intersection with N, a distributed sliding regime locally exists for system (2.1)-(2.2) on an open set .Ap (-'= N ~ S) of S, if and only if the phase flows corresponding to the controlled characteristic direction field of (2.1), which arise from the initial submanifold q~, exhibit such a local sliding regime on JV\" under the influence of the switching law (2.2). Proof. Suppose a distributed sliding mode locally exists for (2.1)-(2.2) on an open set JV\" of S. Then, the total time derivatives of y, at any point z in N, belonging to the graph of the solution of the controlled equation, can be computed in terms of the directional derivatives along the controlled characteristic direction field ~. These derivatives are given by: f o r y > O: d y = [ S h / b v ] d v / d t + [ Sh /Sx ] d x / d t + [ Sh/Ot ] dt = [Sh /Sv ]b (v , x, t, u +) + [ S h / 3 x ] X ( v , x, t, u +) + [Sh/St] = L ~ ( , . , + ( , ) ) h < O; f o r y < O: d y = [ S h / S v ] d v / d t + [ a h / O x ] d x / d t + [ ah /a t l dt = [Sh /Sv]b (v , x, t, u - ) + [ S h / S x ] X ( v , x, t, u - ) + [Sh/St] = L~(..u-(.))h > O. In other words, the controlled dynamical system described by the following set of ordinary differential equations: dz d-7 = ~ ( ' ' u), (2.4a) y = h ( z ) , (2.4b) (also known as the controlled characteristic equation (2.1)), with initial conditions taking values in F, exhibits a local sliding regime on the open set .,4 r of the sliding manifold S, determined by y = 0, when u is governed by the switching law (2.2). Sufficiency follows easily by assuming that a sliding mode exists for the controlled characteristic system and hypothesizing, at the same time, that a distributed sliding mode does not exist. By reversing the arguments presented above, a contradiction is easily established. [] Local sliding regimes, on subsets of S, of the distributed controlled system (2.1), (2.2) are, hence, completely characterized in terms of the local sliding motions - on the same manifold S - of the finite dimensional time-varying system (2.4) controlled by a switching law of the form (2.2). Theorem 2. A distributed sliding regime exists on an open set ~ of S for system (2.1), (2.2) if and only if there is an open neighborhood N of S in R n+ 2 where ~uL~h * O. (2.5) Proof. If L,h does not depend locally on u then, changing the control u from u+(z) to u - ( z ) at points z of LAP does not have any effect on the sign of L,h. Therefore, there exists an open set N in R n+2, containing ~,r, where the existence conditions (2.3) are violated and a sliding regime can not locally exist on sV'. To proof sufficiency, suppose L~h(z) explicitly depends on u, locally around sV in N. Let e - ( z ) be a smooth, locally strictly positive function of z. Then, by virtue of the implicit function theorem, the equation L , h ( z , u ) = e - ( z ) locally has a unique smooth solution u = u-*(z ) such that = t - ( z ) > O. Similarly, by the same arguments, given a smooth locally strictly negative function e+(z), a smooth control law u = u ~ ( z ) locally exists such that = < 0 . Hence, conditions (2.3) are locally valid around N and a sliding regime exists on the open set dV\" of S for the found distributed variable structure feedback control law: u + ( z l = u + ' ( z ) for h ( z ) > 0, u = u - ( z ) u -~(z ) for h ( z ) < O. [] Definition 3. For all initial states z located on the open set X of S, the unique distributed control function, uEQ(z), locally constraining the distributed trajectories to the sliding manifold S, in the region of existence ~V of the sliding motion, is known as the distributed equivalent control. (i.e., the equivalent control turns the open set ~4 r of S into a ocal integral manifold of the characteristic controlled direction field defined on ~ for some given initial Cauchy data defined on JV'). The resulting characteristic dynamics, ideally con- 180 H. Sira-Ramirez / Distributed sliding mode control strained to S, will be addressed as the characteristic ideal sliding dynamics. (See the original concept in Utkin [10] for ODE's . ) A coordinate-free description of such dynamics in S is: dz d-7 = ~ ( z ' uEQ(z)) , h(z ) = 0 . (2.6) The direction field ~(z, uEQ(z)) will be referred to as the equivalent direction field. Given an arbitrary smooth, noncharacteristic initial n-dimensional submanifold F of the zero output manifold v = ~(x , t), every integral manifold of the equivalent direction field, ~(z, uEQ(z)), is evidently a local solution, specified by v = q~(x, t), of the PDE representing the distributed ideal sliding dynamics: i~v ~ ~v ~ + ~-- -X, (v , x , t, uEQ(v, x, t)) i= 1 iSx~ A necessary and sufficient condit ion for an open set ~V\" of S to qualify as a local ( n + l ) - dimensional integral manifold of the controlled trajectories (2.6) is that the gradient of h be locally poin twise o r thogona l to the s m o o t h equivalent direction field ~(z, uEQ(z)), i.e., L,<:,uEo~z>)h(z ) = 0 for z ~ ,A r. (2.8) For an exposition of the results available for the assessment of the existence of sliding regimes in systems of the general form (2.4), the reader is refered to Sira-Ramirez [7] and to [8,9] for other classes of systems. 3. Example Consider the controlled system described by - v + e x p ( - x ) for-a<x<a, (3.1b) Y = 0 elsewhere. Let w be a given positive constant. The distributed variable structure control law u = w s i g n [ - v + e x p ( - x 2 ) ] , excercised along each possible characteristic, creates a distributed sliding regime on the manifold y = 0 when the controlled motions start from, say, the initial submanifold defined by: r = ((v, x ) :v where (exp[- 2 ] ~(x)= I for --a+~<x<a+~, 0 elsewhere with ~ a given positive constant satisfying ~ > 2a. Figures 1 and 2 depict the nature of the sliding regime creation process on y = 0 by means of the distributed controlled motions of (3.1)."
        ]
    },
    {
        "image_filename": "designv10_8_0002582_202-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002582_202-Figure1-1.png",
        "caption": "Figure 1. The double pendulum model of the golf swing; (a) at the beginning of the downswing; (b) at the release point; (c) after releasing the club and (d) at impact.",
        "texts": [
            " The first part of this section on the physics of the golf swing will focus on the double pendulum swing model, and its variations, along with its use in determining ways to increase the clubhead speed. The use of three-link swing models in the analysis of golf swings will then be discussed. Following this, some of the kinematic, kinetic and force measurements that have been taken on golfers, both skilled and unskilled, and their relationship to the swing models, will be presented. 2.1.1. Double pendulum model. Figure 1 shows the motion of the arms and golf club during a typical downswing. The primary model that golf researchers have used to analyse this motion is based on a double pendulum or double link system. The two links that are used in this model are included in figure 1. The upper link represents the golfer\u2019s shoulders and arms, which rotate about a central hub corresponding roughly to a point between the golfer\u2019s shoulders. The lower link represents the golf club, which rotates about a point or hinge located at the centre of the hands and wrists of the golfer. The basis for the double pendulum model stems from the modern practice of keeping the left arm (for a right-handed golfer) straight during the downswing. In the model the backswing is normally ignored and the two links begin in the stationary position that is shown in figure 1(a). The angular position of the lower link, \u03b8 , at the top of the backswing is referred to as the backswing angle while the angular position of the upper link, with respect to the lower link, is referred to as the wrist-cock angle, \u03b1. During the downswing the two links are taken to rotate in a single plane that is inclined to the vertical. In the basic version of the model the hub is taken to be fixed in position and all the golfer\u2019s efforts in rotating his or her hips, trunk and arms are equated to a single couple, \u03c40, applied at this central pivot",
            " The downswing in the double pendulum model has, therefore, typically been divided into two distinct stages. During the first stage of the downswing the wrist-cock angle is fixed and the double pendulum system rotates as one. The value of the wrist-cock angle during this first stage is primarily determined by the ability, or inability, of a golfer to cock his or her wrists. The couple exerted by the hands and wrists, \u03c4h, on the club or lower link, which is required to maintain this wrist-cock angle, will initially be positive for the orientation shown in figure 1(a). During this time the hands and wrists are basically behaving as a stop in preventing the club from falling back towards the golfer. As the downswing proceeds the centrifugal force acting on the lower link will increase and the couple required by the hands and wrists to maintain the wrist-cock angle will subsequently decrease. When the required couple drops to zero the lower link will, unless prevented, begin to swing outwards. This is referred to as a natural release. Jorgensen (1970) showed that for the basic double pendulum swing model the required hand couple drops to zero when the upper link has swung through an angle, given by \u03b2 in figure 1(b), of IL/2LUSL, where SL and IL are the first and second moments of the club about the centre of the golfers hands and LU is the length of the upper link. For a typical golf swing and driver this corresponds to an angle of approximately 47\u02da. The angular position of the upper link at the point where the club swings out, \u03b8 in figure 1(b), is referred to as the release angle. An expert golfer normally swings the club in such a manner that the wrist-cock angle stays fixed beyond the natural release point. If the hands and wrists continue to hold the club at a constant wrist-cock angle after the natural release point, the couple they exert must become increasingly negative. A typical downswing lasts on the order of 200 ms and the first stage is normally modelled as lasting from 100 to 150 ms. The second stage of the downswing begins when the club swings outwards, either naturally or with a delayed release, and ends when contact with the ball is made. The hands and wrists are normally modelled as exerting no couple during this stage. In the case of a delayed release, the club will swing out much more rapidly than is the case for a natural release due to the larger centrifugal force that is acting on it. As is shown in figure 1(d), the golf ball is typically positioned ahead of the hub so that at impact the final wrist-cock angle, \u03b1, is not equal to zero. Daish (1972), Lampsa (1975) and Jorgensen (1970, 1994) derive the equations of motion for the basic double pendulum model using the Langrangian approach. Expressions for the kinetic energies of the two links are determined and the potential energy of the system is equated to the work done by the couples, which are exerted at the hub and at the hands. In the simplest case, where the effects of gravity are neglected, Daish (1972) derives the following equations of motion: A\u03b8\u0308 + B\u03c6\u0308 cos(\u03c6 \u2212 \u03b8) \u2212 B\u03c6\u03072 sin(\u03c6 \u2212 \u03b8) = \u2212\u03c40 + \u03c4h (1a) and B\u03b8\u0308 cos(\u03c6 \u2212 \u03b8) + B\u03b8\u03072 sin(\u03c6 \u2212 \u03b8) + C\u03c6\u0308 = \u2212\u03c4h, (1b) where the generalized coordinates, \u03c6 and \u03b8 , are the angular positions of the two links with respect to the vertical. The angular position of the upper link, \u03b8 , is as shown in figure 1(a), while \u03c6, the angular position of the lower link, is given by \u03b8 + \u03b1. The constants A, B and C, are functions of the mass, the length and the first and second moments of the two links. During the first stage of the downswing the wrist-cock angle, \u03c6 \u2212 \u03b8 , is held fixed and the general equations reduce to \u03b8\u0308 = \u03c6\u0308 = \u2212\u03c40 I , (2) where I is the moment of inertia of the whole system about the hub. The orientation of the club at impact, in the two-stage double pendulum model, will depend on the magnitude of the couple applied at the hub, as well as the backswing, initial wrist-cock, and release angles. In figure 1(d) the club is in the vertical position at impact, which, in general, is what would be wanted. Figure 2 shows an example where the values for the hub couple, release angle and wrist-cock angle, are the same as were used for figure 1, but the backswing angle is greatly reduced. In this case the hands will be ahead of the clubhead at impact and the ball would be missed or at best miss-hit. In the case of an increased backswing angle, with the other parameters fixed, the model shows that the clubhead will lead the hands at impact. Timing is, therefore, crucial in the model, as it is with a real golf swing, and changing one parameter in the model will normally require another parameter to be changed if the clubhead is to make solid contact with the golf ball",
            " Delaying the release of the club results in greater clubhead speed at impact by keeping the club closer to the hub during the downswing so that the first and second moments of the double pendulum system about the hub will be reduced. Delaying the release will, however, also have an effect on the orientation of the club at impact, with the hands, in general, leading the clubhead at impact. Pickering and Vickers (1999) also investigated the effect of positioning the golf ball forward of the hub point. This is normally the practice of golfers and is included in figure 1(a). One benefit of doing this is that for a properly timed swing the clubhead speed will be increasing throughout the downswing. Positioning the ball forward and thereby delaying the impact will, therefore, result in a greater clubhead speed at impact. Pickering and Vickers specifically determined the ball position that would result in the maximum horizontal component of clubhead velocity at impact in their swing model. They found that in the case of a drive and with a natural release, the optimal ball position was 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.14-1.png",
        "caption": "Figure 6.14. Piezoresistive micro force sensor. a. Detail with glass needle as endeffector; b. integrated into a two-fingered robot hand (from [51], \u00a9 2001 IEEE).",
        "texts": [
            " Two different types of this gripper were developed. One version had four piezoresistors connected into a full Wheatstone bridge and one smaller version had only two piezoresistors. An analog PI controller was implemented to allow for force-controlled gripping of microparts. A similar force sensor was developed at the Mechanical Engineering Laboratory, Japan, in co-operation with Olympus [51]. By using semiconductor technologies and micromachining, two strain gages were integrated into a silicon cantilever (Figure 6.14a). Additionally, the cantilever was etched down to a thin membrane to amplify the mechanical stress. The strain gages have an opposite gage factor to increase the resolution of the sensor. Due to the lack of a suitable calibration, the resolution could only be calculated theoretically to be 2 nN. A thin glass needle was glued to the end of the force sensor as an end-effector. Two sensor/end-effector devices were integrated into a two-fingered micromanipulator (Figure 6.14b). By using two sensors and mounting them rotated by 90\u00b0, a force feedback in two axes could be realized. Force Feedback for Nanohandling 191 Piezoelectric micro force sensors. The use of piezoelectric force sensors based on films of polyvinylidene fluoride (PVDF) is a new approach in microrobotics research. PVDF is a semi-crystalline polymer consisting of monomer chains of (\u2013CH2\u2013CF2\u2013)n. It has strong piezoelectric properties due to a large electronegativity of the fluorine atoms in comparison to the carbon atoms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003429_tia.2006.887234-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003429_tia.2006.887234-Figure1-1.png",
        "caption": "Fig. 1. Rotor structure of the tested flux-barrier-type SynRM.",
        "texts": [
            " Since electrical parameter variations are expressed by continuous even functions, which are differentiable for the entire current and speed ranges, this state equation can be used in simulating the correct transient characteristics of various operating conditions. As an example, steady-state characteristics of a conventional vector-controlled SynRM with constant d-axis current and transient characteristics of a maximum efficiency vector-controlled SynRM are calculated from the state equation and are verified with experimental results measured by on-load test. A. Measurement of d- and q-Axes Inductances Fig. 1 shows the rotor structure of the tested flux-barriertype SynRM with a distributed stator winding. Table I shows the ratings and mechanical constants. Fig. 2 shows the test circuit used in measuring the d- and q-axes inductances, Ld and Lq , taking cross-magnetic saturation into account. First, by applying a low dc voltage to the a\u2013b winding, the rotor is aligned to the d-axis position for a\u2013b winding. Afterward, the rotor must be locked in this position during this test. Second, the voltage \u03bd(t) and current i(t), shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002400_s0167-6911(98)00039-5-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002400_s0167-6911(98)00039-5-Figure4-1.png",
        "caption": "Fig. 4. Path of a cart with two trailers corresponding to a ve-dimensional system in power form.",
        "texts": [
            " Notice that the control laws drives the states to the origin at di erent time scales. This is more evident in Fig. 2 where it is shown the logarithm of the norm of the states. The linear slope indicates exponential rate of convergence. Moreover, notice that the slopes of the states x3; x4 and x5 are steeper than those of x1 and x2 which decay with the same rate (k = k1 = 1). The time history of the control e ort is shown in Fig. 3. It is a well-known fact that a system in power (or chained) form can be used to describe the kinematics of a cart with trailers. Fig. 4 shows the path of a cart with two trailers corresponding to a ve-dimensional system in power form and the results in Fig. 1. Fig. 4 makes it clear how the control prefers to move the cart to a better position instead of trying to perform a sharp left turn with subsequent corrections of the nal cart=trailer posture. We use the method of invariant manifolds to construct exponentially convergent feedback control laws for n-dimensional nonholonomic systems in power form. The construction of the proposed control laws is based on a recursive algorithm which uses the invariant manifolds as new coordinates in order to construct a series of generated systems in power form of reduced dimension"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.22-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.22-1.png",
        "caption": "Figure 12.22 Problem 12.5.",
        "texts": [
            " It is ob served that between x = a and x = 9 m, the force is proportional to the square root of displacement: 10 15 272 Fundamentals of Biomechanics CD------Oi Determine the work done by Fx on the object to move the object from: (a) x=Otox=4mand (b) x = 0 to x = 9 m. Answers: (a) 32 J and (b) 108 J. Problem 12.4 As illustrated in Figure 12.21, a ball is dropped from a height h measured from the ground level. If the air resis tance is neglected, show that the speed of the ball as a function of height y measured from the ground level can be expressed as: v = \"f2g (h - y) Here, g is the magnitude of the gravitational acceleration. Problem 12.5 As illustrated in Figure 12.22, consider a ski jum per moving down a track to acquire sufficient speed to accom plish the ski jumping task. The length of the track is f, the track makes an angle () with the horizontal, and the coefficient of fric tion between the track and the skis is j.L. If the ski jumper starts at the top of the track with zero initial speed, determine expressions for: (a) the takeoff speed V2 of the ski jumper at the bottom of the track using the work-energy theorem, and (b) the acceleration ax of the ski jumper using the equation of motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.22-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.22-1.png",
        "caption": "Figure 8.22 Explaining the maximum shear stress theory.",
        "texts": [
            " This theory assumes that yielding occurs when the maximum shear stress in a material element reaches the value of the maximum shear stress that would be observed at the instant when yielding occurred if the material were subjected to uniaxial tension. Assume that a material is subjected to a simple (uniaxial) tension test until yielding. The stress level at yielding is recorded as O'yp. The maximum shear stress to which this ma terial is subjected can be determined by constructing a Mohr's circle (see Example 8.17) which is illustrated in Figure 8.22. It is clear that the maximum shear stress in simple tension is equal to half of the normal stress. In this case, the normal stress is also the yield strength of the material in tension, and therefore: 0' x O'yp Tmax = - =- 2 2 (8.18) The maximum stress theory states that if the same material is subjected to any combination of normal and shear stresses and the maximum shear stress is calculated, the yielding will start when the maximum shear stress is equal to Tmax. For example, consider that the material is subjected to a combination of nor mal and shear stresses in the xy plane as illustrated in Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.40-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.40-1.png",
        "caption": "Figure 5.40 Rotational and translatory components of F M'",
        "texts": [],
        "surrounding_texts": [
            "\u2022 The force F M exerted by the quadriceps muscle on the tibia through the patellar tendon can be expressed in terms of two co mponents normal and tangential to the long axis of the tibia (Fig ure 5.40). The primary function of the normal component F Mn of the muscle force is to rotate the tibia about the knee joint, while its tangential component F Mt tends to translate the lower leg in a direction collinear with the long axis of the tibia and applies a compressive force on the articulating surfaces of the tibiofemoral joint. Since the normal component of F M is a sine function of 110 Fundamentals of Biomechanics angle (), a larger angle between the patellar tendon and the long axis of the tibia indicates a larger rotational effect of the muscle exertion. This implies that for large () ,less muscle force is wasted to compress the knee joint, and a larger portion of the muscle tension is utilized to rotate the lower leg about the knee joint. \u2022 One of the most important biomechanical functions of the patella is to provide anterior displacement of the quadriceps and patellar tendons, thus lengthening the lever arm of the knee extensor muscle forces with respect to the center of rotation of the knee by increasing angle () (Figure 5.41a). Surgical removal of the patella brings the patellar tendon closer to the center of rotation of the knee joint (Figure 5.41b), which causes the length of the lever arm of the muscle force to decrease (d2 < d1). Losing the advantage of having a relatively long lever arm, the quadri ceps muscle has to exert more force than normal to rotate the lower leg about the knee joint. \u2022 The human knee has a two-joint structure composed of the tibiofemoral and patellofemoral joints. Note that the quadriceps muscle goes over the patella, and the patella and the muscle form a pulley-rope arrangement. The higher the tension in the mus cle, the larger the compressive force (pressure) the patella exerts on the patellofemoral joint. We have analyzed the forces involved around the tibiofemoral joint by considering the free-body diagram of the lower leg. Having determined the tension in the patellar tendon, and as suming that the tension is uniform throughout the quadriceps, we can calculate the compressive force applied on the patello femoral joint by considering the free-body diagram of the patella (Figure 5.42a). Let F M be the uniform magnitude of the tensile force in the patellar and quadriceps tendons, Fp be the magni tude of the force exerted on the patellofemoral joint, a be the angle between the patellar tendon and the horizontal, y be the angle between the quadriceps tendon and the horizontal, and \u00a2 be the unknown angle between the line of action of the com pressive reaction force at the joint (Figure 5.42b). We have a three-force system and for the equilibrium of the patella it has to be concurrent. We can first determine the common point of intersection Q by extending the lines of action of patellar and quadriceps tendon forces. A line connecting point Q and the point of application of F p will correspond to the line of action of F p. The forces can then be translated to Q (Figure 5.42c), and the equilibrium equations can be applied. For the equilibrium of the patella in the x and y directions: LFx=O: LFy=O: F p cos \u00a2 = F M (cos Y - cos a) Fp sin\u00a2 = FM (sin a - sin y) These equations can be solved simultaneously for angle \u00a2 and the magnitude F p of the compressive force applied by the femur Applications of Statics to Biomechanics 111 on the patella at the patellofemoral joint: Fp = (COS y - cosa) FM cos\u00a2 -1 ( sin a - sin y ) \u00a2 = tan cosy - cosa 5.10 Mechanics of the Ankle The ankle is the union of three bones: the tibia, the fibula, and the talus of the foot (Figure 5.43). Like other major joints in the lower extremity, the ankle is responsible for load-bearing and kinematic functions. The anatomical configuration of the ankle joints is similar to that of the hip. The ankle joint is inherently more stable than the knee joint, which requires ligamentous and muscular restraints for its stability. The ankle joint complex consists of the tibiotalar, fibulotalar, and distal tibiofibular articulations. The ankle (tibiotalar) joint is a hinge or ginglymus-type articulation between the spool-like convex surface of the trochlea of the talus and the concave distal end of the tibia. Being a hinge joint, the ankle permits only flexion-extension (dorsiflexion-plantar flexion) movement of the foot in the sagittal plane. Other foot movements include in version and eversion, inward and outward rotation, and prona tion and supination. These movements occur about the foot joints such as the subtalar and transverse tarsal joints between the talus and calcaneus. The ankle mortise is maintained by the shape of the three artic ulations, and the ligaments and muscles crossing the joint. The integrity of the ankle joint is improved by the medial (deltoid) and lateral collateral ligament systems, and the interosseous lig aments. There are numerous muscle groups crossing the ankle. The most important ankle plantar flexors are the gastrocnemius and soleus muscles (Figure 5.44). Both the gastrocnemius and soleus muscles have attachments to the posterior surface of the calcaneus via the Achilles tendon. The gastrocnemius muscle is more effective as a knee flexor if the foot is elevated, and more effective as a plantar flexor of the foot if the knee is held in exten sion. The plantar extensors are posterior muscles. There are also anterior (tibialis anterior, extensor digitorum longus, extensor halluc is longus, peroneus tertius) and lateral (peroneus longus, peroneus brevis) muscles whose primary function is to provide pronation and supination, and inward and outward rotation of the foot. The ankle joint responds poorly to small changes in its anatom ical configuration. Loss of kinematic and structural restraints 1 2 3 ___ \"\",T- 4 '-'\"'~- 5 POSTERIOR (BACK) 6 SUPERIOR (Top) 112 Fundamentals of Biomechanics , , w FM%' .... r--..:.....;~~ .... -- x 'FJ% , Figure 5.46 Components of the forces acting on the foot. due to severe sprains can seriously affect ankle stability and can produce malalignment of the ankle joint surfaces. The most common ankle injury, inversion sprain, occurs when the body weight is forcefully transmitted to the ankle while the foot is inverted (the sole of the foot facing inward). Example 5.7 Consider a person standing on tiptoe on one foot (a strenuous position illustrated). The forces acting on the foot during this instant are shown in Figure 5.45. W is the person's weight applied on the foot as the ground reaction force, F M is the magnitude of the tensile force exerted by the gastrocnemius and soleus muscles on the calcaneus through the Achilles tendon, and F J is the magnitude of the ankle joint reaction force applied by the tibia on the dome of the talus. The weight of the foot is small compared to the weight of the body and is therefore ignored. The Achilles tendon is attached to the calcaneus at A, the ankle joint center is located at B, and the ground reaction force is applied on the foot at C. For this position of the foot, it is estimated that the line of action of the tensile force in the Achilles tendon makes an angle () with the horizontal, and the line of action of the ankle joint reaction force makes an angle f3 with the horizontal. Assuming that the relative positions of A, B, and C are known, determine expressions for the tension in the Achilles tendon and the magnitude of the reaction force at the ankle joint. Solution: We have a three-force system composed of musc:e force F M' joint reaction force F J ' and the ground reaction force W. From the geometry of the problem, it is obvious that for the position of the foot shown, the forces acting on the foot do not form a parallel force system. Therefore, the force system must be a concurrent one. The common point of intersection (0 in Figure 5.45) of these forces can be determined by extending the lines of action of Wand F M' A straight line passing through both points a and B represents the line of action of the joint re action force. Assuming that the relative positions of points A, B, and C are known (as stated in the problem), the angle (say f3) of the line of action of the joint reaction force can be measured. Once the line of action of the joint reaction force is determined by graphical means, the magnitudes of the joint reaction and muscle forces can be calculated by translating all three forces involved to the common point of intersection at a (Figure 5.46). The two unknowns F M and F J can now be determined by apply ing the translational equilibrium conditions in the horizontal (x) and vertical (y) directions. For this purpose, the joint reaction and muscle forces must be decomposed into their rectangular components first: FMx = FM cos() FMy = FM sin() F I x = F I cos f3 Fly = FI sinf3 Applications of Statics to Biomechanics 113 For the translational equilibrium of the foot in the horizontal and vertical directions: LFx=O: LFy=O: Flx=FMx FlY= FMy + W Simultaneous solutions of these equations will yield: F _ W> cosf3 M - cos () sin f3 - sin () cos f3 F = W> cos() I cos () sin f3 - sin () cos f3 For example, assume that () = 45\u00b0 and f3 = 60\u00b0. Then: FI =2.73 W 5.11 Discussion Analyses of posture and movement are based on an understand ing of the leverage afforded gravitational force by the body po sition. Lifting while the arms are flexed requires less effort than lifting with arms extended. This knowledge enables us not only to grade exercises effectively but also to minimize gravitational effects in our daily activities. Low back injuries usually result from ignorance of safe lifting techniques that minimize gravi tational effects. Arm and shoulder strain may result from pro longed use of hands away from the midline of the body where the center of gravity is located. It should be noted here that there are other factors that influence the level of difficulty of performing certain tasks. For example, we must consider the length of the antagonist muscles and relative size of the various body segments. The point of insertion of a muscle or tendon varies from person to person. A slight variation in the point of insertion of a ten don can change the force distribution between the muscle and related joint considerably, as in the case of the biceps muscle and elbow joint. The farther a tendon lies from the axis of the joint, the better its ability to handle the turning effect of the segment 114 Fundamentals of Biomechanics about the joint, which can be a considerable advantage for lifting and throwing. While analyzing the gravitational forces in body movement, consider the fact that the downward gravitational pull of the body is opposed by an equal upward push of the supporting surface regardless of whether the person is reclining, sitting, or standing. Sufficient floor reactions in terms of frictional forces are necessary for the stabilization of the body. Frictional forces are also important for walking and running. The joints of the body sustain compressive forces. Both the superincumbent and the supporting segment of the joint resist equal and opposite forces applied to their respective articular surfaces. The shape of the joints and the arrangement of reinforcing ligaments and tendons are such that the upright posture is maintained with an economy of muscular effort. Researchers in the field of biomechanics have suggested various mathematical models to evaluate the forces involved in different muscles, bones, and joints of the human body during its vari ous activities and static postures. Some of these models attempt to take into consideration the contributions of more than one muscle group. Different researchers utilize different formula tion techniques and different criteria for the prediction of mus cle forces. Some classic papers have been written describing these new approaches to the study of skeletal muscle, and many researchers have presented the application and refinement of these methods in more recent publications. Seireg and Arvikar (1973) developed a mathematical model for evaluating the muscle forces necessary to maintain the human body equilibrium in standing, leaning, and stooping. These researchers utilized linear optimization techniques in the pre diction of muscle forces. Penrod et al. (1974) investigated the problem of distribution of forces among muscles at a joint. In order to arrive at a unique solution for the redundant (statically indeterminate) system, they suggested that the solution must be based on optimizing the total muscle effort. They applied the resulting mathematical formulation to a two tendon model. Crowninshield and Brand (1981) developed a nonlinear model for predicting the muscle activity during locomotion. These investigators utilized the criterion of maximum endurance of musculoskeletal function to develop a model based on the in versely nonlinear relationship of muscle force and contraction endurance. More recently, Yamaguchi et al. (1995) refined the mathematical modeling for this problem. In a review paper, Dul et al. (1984a) compared the characteris tics and performance of several linear and nonlinear criteria for load sharing between synergistic muscles reported in the litera ture. Based on the assumption that during a physical activity the muscular fatigue is minimized, the same group of researchers Applications of Statics to Biomechanics 115 (Dul et al., 1984b) developed a model for predicting the load sharing mechanisms between muscles. In 1995, Cholewicki et al. proposed a new approach to this model. 5.12 Suggested Reading Chaffin, D.B., and Andersson, G.B.J. 1991. Occupational Biomechanics. 2nd ed. New York: John Wiley & Sons. Cholewicki, J., McGill, S.M., and Norman, RW. 1995. Comparison of muscle force and joint load form an optimization and EMG-assisted lumbar spine model: Towards development of a hybrid approach. J. Biomechanics 28:321-31. Crowninshield, RD., and Brand, RA 1981. A physiologically based criterion on muscle force prediction in locomotion. J. Biomechanics 14:793-801. Dul, J., Townsend, M.A, Shiavi, R, and Johnson, G.E. 1984a. Muscu lar synergism-I. On the criteria for load sharing between synergistic muscles. J. Biomechanics 17:663-673. Dul, J., Johnson, G.E., Shiavi, R, and Townsend, M.A 1984b. Muscular synergism-II. A minimum-fatigue criterion for load sharing between synergistic muscles. J. Biomechanics 17:663-673. Goel, v.K., Weinstein, J.N. 1990. Biomechanics of the Spine: Clinical and Surgical Perspective. Boston: CRC Press, Inc. Kroemer, K.H.E., Marras, W.S., McGlothlin, J.D., McIntyre, D.R, and Nordin, M. 1990. On the measurement of human strength. Int. J. Indus trial Ergonomics 6:199-210. LeVeau, B.F. 1992. Williams & Lissner's Biomechanics of Human Motion. 2nd ed. Philadelphia: w.B. Saunders Company. McMinn, RM.H., Hutchings, R.T. 1988. Color Atlas of Human Anatomy. 2nd ed. Chicago: Year Book Medical Publishers Inc. Nordin, M., Andersson, G.B.J., Pope, M.H. (Eds.) 1997. Musculoskeletal Disorders in the Workplace: Principles & Practice. Philadelphia: Mosby Year Book, Inc. Nordin, M., and Frankel, V.H. 1989. Basic Biomechanics of the Muscu loskeletal System. 2nd ed. Philadelphia: Lea & Febiger. Penrod, 0.0, Davy, D.T., and Singh, D.P. 1974. An optimization ap proach to tendon force analysis. J. Biomechanics 7:123-129. Roebuck, J.A 1995. Anthropometric Methods: Designing to Fit the Hu man Body. Monographs in Human Factors and Ergonomics: Alphonse Chapanis, Series Editor. Santa Monica: Human Factors & Ergonomics Society. Seireg, A, and Arvikar, RJ. 1973. A mathematical model for eval uation of force in lower extremities of the musculoskeletal system. J. Biomechanics 6:313-326. 116 Fundamentals of Biomechanics Simon, S.R. (Ed.) 1994. Orthopaedic Basic Science. Rosemont, IL: American Academy of Orthopaedic Surgeons. Thompson, C.W. 1989. Manual of Structural Kinesiology. 11th ed. St. Louis, MO: Times Mirror/Mosby. Wilson, J.R., Corlett, E. N. (Eds.) 1995. Evaluation of Human Work: A Practical Ergonomics Methodology. 2nd ed. Bristol, UK: Taylor & Francis. Winter, D.A. 1990. Biomechanics and Motor Control of Human Behavior. 2nd ed. New York: John Wiley & Sons. Yamaguchi, G.T., Moran, D.W., and Si, J. 1995. A computationally ef ficient method for solving the redundant problem in biomechanics. J. Biomechanics 28:999-1005. Chapter 6 Introduction to Deformable Body Mechanics 6.1 Overview / 119 6.2 Applied Forces and Deformations / 119"
        ]
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.4-1.png",
        "caption": "Fig. 6.4 Drawings of the mechanical systems of Figure 6.3, in the same order, (a) a serial arrangement of an ideal stroke generator and a spring between two rigid walls and (b) a parallel arrangement of the same two components, with one end fixed",
        "texts": [
            " The small triangle near the top of each symbol allows distinguishing positive and negative forces in the graph: a compression (positive) force is represented by a current flowing toward the triangle, whereas a tension (negative) force \u201cflows\u201d in the opposite direction (from the triangle towards the other terminal). A positive stroke (elongation) is represented by a positive voltage measured from the terminal with the triangle to the other one, while a negative voltage represents a negative stroke (shortening). According to this convention, the circuits of Figure 6.3, which look similar, represent two different mechanical systems (see Figure 6.4). Further, we will introduce symbols for ideal stroke and force sensors, to provide the graphs with the corresponding indications (see Figure 6.5(a)). The attribute \u201cideal\u201d refers to the fact that the force in the stroke sensor as well as the stroke of 162 6 Design Principles for Linear, Axial Solid-State Actuators the force sensor is assumed to be zero. The sensors work like a voltmeter and an ammeter, respectively and are provided with a plus mark to relate the sign of the measured quantity to the displayed value (if, for instance, the force \u201cflows\u201d towards the plus sign, the sensor outputs a positive value"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002327_s0094-114x(97)00056-6-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002327_s0094-114x(97)00056-6-Figure3-1.png",
        "caption": "Fig. 3. Gear mesh model.",
        "texts": [
            " Following Zorzi and Nelson [13], the total virtual work of the axial torque on the bending curvatures is dW Z l 0 TGdB0 \u00ff TBdG0 ds Z l 0 T dB0dG0 0 1 \u00ff1 0 B G ds 6 In the above Equation (6), the axial torque is time dependent and varies from element to element. For ith element it is given as T t GJ l ai 1 \u00ff ai Equation (6) can now be rewritten as dW dfqgT Z l 0 T C0 T 0 1 \u00ff1 0 C dsfqg 7 where the shape function matrix is given by C 0 \u00ffN1 N2 0 0 0 \u00ffN3 N4 0 0 N1 0 0 N2 0 N3 0 0 N4 0 with N1 1 l3 2s3 \u00ff 3s2l l3 N2 1 l3 s3l\u00ff 2s2l2 sl3 N3 1 l3 \u00ff2s3 3s2l N4 1 l3 s3l\u00ff s2l2 The incremental sti ness matrix [ Ks Ti] due to the axial torque is then obtained from Equation (7) as Ks Ti Z l 0 T C0 T 0 1 \u00ff1 0 C ds 8 which is de\u00aened in the Appendix. Figure 3 shows a gear pair, in which the teeth are replaced by equivalent sti ness and damping along the pressure line. In the present model, damping is not taken into account. The gear mesh force is Fh kh Vg 2 \u00ff Vg 1 sinfp Wg 2 \u00ffWg 1 cosfp \u00ff r1ag1 r2a g 2 9 On gear 1, the components of the gear mesh force can be expressed as FhV1 Fh sinfp kh \u00ffS2 \u00ff SC 0 0\u00ff r1S S2 SC 0 0\u00ff r2S fqgg FhW1 Fh cosfp kh \u00ffSC\u00ff C2 0 0\u00ff r1C SC C2 0 0\u00ff r2C fqgg Th1 r1Fh kh \u00ffr1S\u00ff r1C 0 0\u00ff r21 r1S r1C 0 0\u00ff r1r2 fqgg 10 Similarly, on gear 2, FhV2 \u00ffFh sinfp kh S2 SC 0 0 r1S\u00ff S2 \u00ff SC 0 0 r2S fqgg FhW2 \u00ffFh cosfp kh SC C2 0 0 r1C\u00ff SC\u00ff C2 0 0 r2C fqgg Th2 r2Fh kh \u00ffr2S\u00ff r2C 0 0\u00ff r1r2 r2S r2C 0 0\u00ff r22 fqgg 11 For the gear pair, we can obtain Mg 1 Mg 2 f qgg O1 Gg 1 O2 O1 Gg 2 f _qgg kh S1 S2 fqgg fFg s g 12 where Mg 1 Md 1 Gg 1 Gg 1 S1 S2 SC 0 0 r1S \u00ffS2 \u00ffSC 0 0 r2S SC C2 0 0 r1C \u00ffSC \u00ffC2 0 0 r2C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 r1S r1C 0 0 r21 \u00ffr1S \u00ffr1C 0 0 r1r2 26666664 37777775 S2 \u00ffS2 \u00ffSC 0 0 \u00ffr1S S2 SC 0 0 \u00ffr2S \u00ffSC \u00ffC2 0 0 \u00ffr1C SC C2 0 0 \u00ffr2C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 r2S r2C 0 0 r1r2 \u00ffr2S \u00ffr2C 0 0 r22 26666664 37777775 and fqggT fVg 1W g 1B g 1G g 1a g 1V g 2W g 2B g 2G g 2a g 2g The strain energy and the dissipation function of an eight coe cient bearing can be written as cyy cyz czy czz _Vb _Wb kyy kyz kzy kzz Vb Wb fFb s g 13 Equations (2), (5), (8), (12) and (13) can be combined for the system to give M f qg O1 G C f _qg K \u00ff KT fqg 0 14 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002864_1.2829170-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002864_1.2829170-Figure2-1.png",
        "caption": "Fig. 2 IMeshing tooth pair",
        "texts": [
            " The obtained surface equation is a function of three variables Uc, a^ and S, respectively the cutter blade edge angular position, the work roll angle and the position of a point along the cutter blade edge: S = f(ac, a ,) (10) The position of any point P on the generated tooth surface is defined by a combination (a^, a^). The solution of Eq. (10) is a series of contact points between the cutter blade edge and the work describing a line along the path of the cutter edge defined by its position angle a .\u0302. The bounded envelope, along the work roll angle 0:3, of a series of such lines in the work reference frame X gives the generated pinion tooth, Fig. 2, shown in mesh with a nongenerated gear tooth. A Newton-Raphson iterative algorithm is used to numerically solve Eq. (10) [2, 3] . Journal of Mechanical Design The above presented simulation includes adjustments and movements found in most existing spiral-bevel and hypoid cut ting machines. Tooth Surface Measurement and Error Surface Tooth surface measurement is usually performed by a Coordi nate Measurement Machine (CMM) using a high precision probing head which, when displaced in different directions, detects where contact is made with an obstacle such as a tooth flank (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002350_(sici)1521-4109(199809)10:12<808::aid-elan808>3.0.co;2-k-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002350_(sici)1521-4109(199809)10:12<808::aid-elan808>3.0.co;2-k-Figure4-1.png",
        "caption": "Fig. 4. Oxidative electropolymerization of 0.5 mM 1 and 0.5 mM 2 in CH2Cl2 \u00fe 0.1 M TBAP, by repeated potential scans between \u00b90.5 and 1.5 V at a platinum electrode. Scan rate: 100 mV s\u00b91.",
        "texts": [
            " In order to improve the electropolymerization properties of 1 as well as the conductivity of the poly1 film, we attempted to electropolymerize 1 in the presence of a tris bipyridyl ruthenium(II) complex containing three pyrrole groups as the polymerizable moiety (2). The ruthenium complex exhibits a reversible metalcentered redox couple (RuII/III) at a potential (1.2 V) corresponding to the oxidation of pyrrole groups [23]. Consequently the latter can act as a relay for the electropolymerization of pyrrole derivatives. In addition, the presence of the electroactive compound 2 in the polymeric film could be useful to estimate the thickness of the copolymer. Figure 4 shows the oxidative electropolymerization of 0.5 mM 1 and 0.5 mM 2 by cycling the potential from \u00b90.5 to 1.5 V. The continuous increase in the amplitude of the Ru(II)/Ru(III) Electroanalysis 1998, 10, No. 12 redox process indicates the formation of an electropolymerizable film on the electrode surface. In contrast to the poly1 formation, 2 confers a redox conductivity to the resulting copolymer. This allows a sustained growth of the polymeric film. Figure 5 depicts the cyclic voltammogram exhibited by the resulting modified electrode upon transfer into an electrolyte free of monomers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003899_s10472-009-9125-x-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003899_s10472-009-9125-x-Figure5-1.png",
        "caption": "Fig. 5 Two control parameters in local interaction (a, b)",
        "texts": [
            " ri attempts to maintain du with its two neighbors, forming an isosceles triangle at each time instant. By repeatedly doing this, three robots will configure themselves into an equilateral triangle with side length du. 3.2 Convergence of local interactions Let\u2019s consider the circumscribed circle of an equilateral triangle whose center is pct of pi ps1 ps2 configured from the positions of three robots and radius is du/ \u221a 3. The motion planning of the robots is performed by controlling the distance from pct and the internal angle (See Fig. 5a). First, the distance is controlled by the following equation d\u0307i(t) = \u2212a(di(t) \u2212 dr) (10) where a is a positive constant and dr represents the length du/ \u221a 3. Indeed, the solution of (10) is di(t) = |di(0)|e\u2212at + dr that converges exponentially to dr as t approaches infinity. Secondly, the internal angle is controlled by the following equation \u03b1\u0307i(t) = k ( \u03b2i(t) + \u03b3i(t) \u2212 2\u03b1i(t) ) (11) where k is a positive number. Because the total internal angle of a triangle is 180\u25e6, (11) can be rewritten as \u03b1\u0307i(t) = k\u2032(60\u25e6 \u2212 \u03b1i(t)), (12) where k\u2032 is 3k. Likewise, the solution of (12) is \u03b1i(t) = |\u03b1i(0)|e\u2212k\u2032t + 60\u25e6 that converges exponentially to 60\u25e6 as t approaches infinity. Note that (10) and (12) imply that the trajectory of ri converges to dr and 60\u25e6, an equilibrium state shown in Fig. 5b. This also implies that three robots eventually form an equilateral triangle with du. In order to prove the correctness, we will take advantage of stability based on Lyapunov\u2019s theory [35]. The stability theorem states if there exists a scalar function fl,i of the state x = [di(t) \u03b1i(t)]T with continuous first order derivatives such that fl,i is positive definite, f\u0307l,i is negative definite, and fl,i \u2192 \u221e as \u2016 x \u2016\u2192 \u221e, then the equilibrium at the desired state [dr 60\u25e6]T is asymptotically stable. Thus, at the desired configuration Ei, the energy level of the scalar function is minimized",
            ") The derivative of the scalar function is given by f\u0307sc,i = f\u0307l,i = \u2212(di \u2212 dr) 2 \u2212 (60\u25e6 \u2212 \u03b1i) 2. (16) Equation 16 is negative definite. Finally, fsc,i is radially unbounded since it tends to infinity as \u2016 x \u2016\u2192 \u221e. Therefore, the equilibrium state is asymptotically stable, implying that ri reaches a vertex of Ei from an arbitrary Ti. Next, the collective scalar function Fsc of a swarm of robots is a nonzero function with the property that any solution of the set of algebraic constraints on range and bearing (see Fig. 5b) is closely related to a set of equilibria for {ri|1 \u2264 i \u2264 n} and vice versa. Without loss of generality, Fsc is a diminished energy function with a scalar potential. Now we prove the convergence of the algorithm for a swarm of n robots. Lemma 3 Under Algorithm 2, ||pi \u2212 ps1|| and ||pi \u2212 ps2|| converge into du for all robots. Proof The n-order scalar function Fsc is defined as Fsc = n\u2211 i=1 fsc,i = n\u2211 i=1 \u2211 Ti (dk \u2212 du) 2 + n\u2211 i=1 fl,i. (17) From Lemma 2, it is straightforward to verify that Fsc is positive definite and F\u0307sc is negative definite"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003878_j.neunet.2008.03.010-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003878_j.neunet.2008.03.010-Figure2-1.png",
        "caption": "Fig. 2. Left: joint angles. Right: musculoskeletal model: Iliopsoas (IP: hip flexion), Anterior Biceps (AB: hip extension), Posterior Biceps and Semitendinosus (PB: hip extension and knee flexion), Vastus Lateralis (VL: knee extension), Gastrocnemius (Gas: knee flexion and ankle extension), Tibialis Anterior (TA: ankle flexion) and Soleus (Sol: ankle extension).",
        "texts": [
            " As it is broadly admitted that the control system for locomotion in vertebrates is distributed and modular (Burrows, 1996; Rossignol, 1996), we considered first the implementation of the neural controller responsible for the stepping movement of a single leg. This neural controller is referred to in this article as the Leg Controller (LC) and is represented in Fig. 1. An overview of the LC structure is given in Section 3.2, while the details of its implementation are presented in Section 4. The symbols and abbreviations used throughout this paper are given in Table 1. The model is made of three links (thigh, shank and foot), connected by three articulations (hip, knee and ankle) and actuated by a set of seven muscles as represented in Fig. 2. The mass and dimensions of each link are given in Table 2. Most of the muscles are acting over a single joint (IP, AB, VL, TA and Sol) but two of them are biarticular muscles (PB and Gas). We used the muscle model of Brown, Scott, and Loeb (1996), with parameters from Ekeberg and Pearson (2005) (only an overview of this model is given in this article, readers interested in the details should refer to these papers). The muscle fascicles are modeled as active contractile elements (CE) in parallelwith passive elastic elements (PE)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003879_14763141.2010.492430-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003879_14763141.2010.492430-Figure2-1.png",
        "caption": "Figure 2. Hand location and components of hand forces at TO1 with (a) a steel or bamboo pole and (b) a flexible pole.",
        "texts": [
            " Finally, with regard to the energy processes observed in mechanical and simulation studies, the vaulter has to (i) produce a high amount of kinetic energy just prior to the take-off phase in order to compensate for its inevitable decrease and (ii) be able to develop high muscular strength in the shoulders, arms, and trunk to limit energy dissipation in the body and store more strain energy in the pole. The elastic capacities of the flexible poles (fibreglass or carbon) allow the vaulter to store strain energy in the pole. With this type of pole, it is possible to keep a greater distance between the two hands than with rigid poles (steel), which allows for easier control of pole bending by the application of force perpendicular to the longitudinal axis of the pole and D ow nl oa de d by [ U ni ve rs ity o f W in ds or ] at 0 5: 10 2 1 Se pt em be r 20 13 in opposite directions (Figure 2). Indeed, the upper hand exerts forward and downward resultant force, whereas the lower hand applies forward and upward resultant force (Hay, 1980; Dapena and Braff, 1983; Angulo-Kinzler et al., 1994; Morlier, 1999; Morlier and Mesnard, 2007). Hubbard modelled the flexible pole as a large slender rod and used large deflection theory to calculate pole deformation as a function of the force and moment applied by the vaulter (Hubbard, 1980a, 1980b). His model determined that the reaction force of the pole (Fp, in N), was linearly related to its shortening chord, when there was no applied moment and in considering the stiffness of the pole (the Euler buckling load) and its chord shortening"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002864_1.2829170-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002864_1.2829170-Figure3-1.png",
        "caption": "Fig. 3 Principle of tooth flanl< measurement",
        "texts": [
            " A Newton-Raphson iterative algorithm is used to numerically solve Eq. (10) [2, 3] . Journal of Mechanical Design The above presented simulation includes adjustments and movements found in most existing spiral-bevel and hypoid cut ting machines. Tooth Surface Measurement and Error Surface Tooth surface measurement is usually performed by a Coordi nate Measurement Machine (CMM) using a high precision probing head which, when displaced in different directions, detects where contact is made with an obstacle such as a tooth flank (Fig. 3). The probe is a small sphere of known radius, and the CMM knows at each instant the exact position of the center of the probe [5, 6, 7 ] . The comparison between the measured and simulated surfaces is based on the theoretical and measured coordinates. To obtain the error surface, e.g., the difference between the theoretical and measured coordinates in the direction of the SEPTEMBER 1998, Vol. 120 / 431 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002915_978-4-431-66942-5_8-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002915_978-4-431-66942-5_8-Figure7-1.png",
        "caption": "Fig. 7 Full Section",
        "texts": [
            " if the angle between bottom and top plate equals 90 degrees as in fig. 6 the edge points foim a quarter of a regular polygon having 20 edges. The maximum angle between the two border plates is 140 degrees. Although the bending of the rubber cannot be controlled very exactly, the model proved to be suffi cient to develop control sequences for the robots' locomotion. P(r,<p,z) \u00a5 l z I <p X Two joints are used to build one section which consists of four drives (8 motors), two rubber kernels and one controller see fig 7. The drives and the controller are of rigid shape and cannot bend. When two sections are mounted to form the snake, two drives of neighbour sections cling together. So between two kernel joints we have either two drives and a controller (inside the section) or two drives belonging to different sections. Therefore within the snake there is always a rigid part of 70 or 60 mm between two bendable kernel joints of length 90 mm. Hence one obvious difference to real snake is the fact that our robot has some stiff parts",
            " For each of the four drives of a section the controller has to set the direction of rotation and to switch the drives on and off. We cannot control the motors' speed which we think is not important. Besides controlling the drives the SLIO reports the sensor information to the PC. There are four tactile sen sors, four sensors for rotation control (one for each drive), and two position sensors (one for each joint). The position sensors signal when the maximum bending for a joint is reached. The tactile sen sors (4 microswitches) shall detect obstacles which the robot touches. A picture of one section is given in fig. 7. When building the whole snake the sections are just plugged together using banana pins which are not only used for conducting the analogue power supply but are also sufficient as holding device. An extra connector is used for the CAN-Bus and digital power supply. This makes it very easy to exchange a section e.g. for maintenance purposes. 2.3 The Software The software is organized in three levels: \u2022 sensor and actuator level \u2022 functional level and \u2022 application level At the sensor and actuator level the sensor data are read and the drives are switched on and off"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure9.13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure9.13-1.png",
        "caption": "Figure 9.13. Control system",
        "texts": [
            "12a, the principal components of the setup are shown: a piezoresistive cantilever is used for measuring the indentation force; the piezoresistive cantilever also plays the role of an indenter, as the indentation has been performed with the help of the cantilever tip; the cantilever is mounted in a special holder which assures the necessary electrical connections; the holder with the cantilever is carried by means of a linear table driven by a Nanomotor\u00ae which is also known as an NMTmotorized table; it also plays the role of a sensor measuring the indentation depth. The piezoresistive cantilever and the NMT-motorized table are described below (Sections 9.2.1.3 and 9.2.1.4). It should be noted that the test is performed in the horizontal direction (x-direction). Figure 9.12b indicates how a specimen is held and how the cantilever is pressed onto the specimen surface. 284 Iulian Mircea and Albert Sill Material Nanotesting 285 A control system is required for performing the tests (Figure 9.13). The entire set-up is controlled by a computer, which evaluates and processes the measurement data and the input signals. This PC is connected to the controller of the NMTmotorized table. The PC sends data to the controller and reads the encoder signal from the NMT table. The output voltage of the Wheatstone bridge of the piezoresistive cantilever is AD-converted and measured by a bridge amplifier. The SEM also is equipped with a PC. Nanoindentation tests require very sensitive force sensors. One of the recent technical solutions is to use piezoresistive cantilevers, which are most commonly used for performing atomic force microscopy, e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.4-1.png",
        "caption": "Figure 6.4. Piezoresistive three-axes micro force sensor. a. Schematic view of the sensor (from [25], \u00a9 Springer-Verlag 2001, with kind permission of Springer Science and Business Media); b. working principle (from [33], courtesy of Shaker Verlag).",
        "texts": [
            " All sensors have been manufactured using silicon micromachining and are based on integrated, piezoresistive elements, so-called piezoresistors. The sensitive element is either a crosswise structure or a so-called boss membrane. Details such as resolution, sensitivity or linearity are often not available from the literature. The lateral dimensions of the sensors range from 2.4 \u00d7 2.4 mm2 to 5 \u00d7 5 mm2 and their maximum measurement range is between 0.01 N and 10 N. The three-axes force sensor described in [25] is used for mechanical investigations of micromechanical structures (Figure 6.4a). The basic element is a boss membrane made out of silicon onto which a stylus has been glued. If a force acts on the pin, the membrane gets deformed and mechanical stress occurs in the 180 Stephan Fahlbusch membrane. The areas of maximum stress are at the border of the membrane and at the intersection between membrane and boss (Figure 6.4b). Into these areas, 24 piezoresistors have been implanted and connected to three Wheatstone bridges. Mechanical stress causes a change of the resistances and thus a change of the three bridge voltages. If the resistors are connected in a suitable way, the bridge voltages are proportional to the three components of the force acting on the pin. The dimensions of this sensor are 5 \u00d7 5 \u00d7 0.36 mm3. A piezoelectric micro force sensor for microhandling was described for the first time in [26]. The dimensions of the sensor were 16 \u00d7 2 \u00d7 1 mm3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002813_02783640022066996-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002813_02783640022066996-Figure1-1.png",
        "caption": "Fig. 1. N DoF manipulator.",
        "texts": [
            " In Section 4, making use of \u201cvirtual parameters\u201d (Osuka and Mayeda 1988), we give the condition for which a set of base parameters can determine a positive definite inertial matrix. Then we show a scheme to judge if a set of baseparameter values is physically impossible or not in Section 5. Section 6 presents these results on a 3-DoF manipulator. We give the conclusions in Section 7. 2. Description of Manipulator In this paper, we consider the manipulator having a general open-loop kinematic chain with N rigid links as shown in Figure 1. We number the links successively from 0 to N; link 0 is a stationary pillar. We then apply the method in (Mayeda, Yoshida, and Osuka 1990) to attach a coordinate system (oi; xi , yi , zi ) to link i. oi denotes the origin of the coordinate system. Let \u03b1i denote the twist angle between zi\u22121-axis and zi-axis about xi\u22121-axis. Let \u03b8i denote the joint variable for rotational link and qi for translational link, which is the distance from reference point pi to oi as shown in Figure 1. Then, 3 \u00d7 3 rotation matrices are defined. Li denotes the vector from oi to pi+1 if link i + 1 is translational and the vector from oi to oi+1 if link i + 1 is rotational. Let r(i) denote the link number of the rotational link, which is nearest and base side to a translational link i, e.g., if link i\u22121 is translational and i \u2212 2 is rotational, r(i) = i \u2212 2. Furthermore, let K be the maximum link number such that the z-axes of all the rotational links between link number 1 and K are parallel. However, twist angle of any translational link i (1 \u2264 i \u2264 K) is arbitrary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003306_j.bioeng.2006.06.003-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003306_j.bioeng.2006.06.003-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of sensor: a, platinum wire; b, glass; c, Teflon cap; d, PVA membrane. \u2018\u2018Reprinted Doretti et al. (1999), with permission from Portland Press.\u2019\u2019",
        "texts": [
            " An aqueous solution of HEMA and VCA was exposed to g-radiation and cross-linked with methylolpropane trimethacrylate forming a sponge-like Scheme 5. Coupling reaction of cholinesterase with HEMA\u2013VCA copolymer material, which was sliced to obtain a membrane (see Scheme 5). Enzyme immobilization was performed by dropping a buffered enzymatic solution, first on one side of the membrane and, then, on the other side. The system was incubated overnight with the aim of blocking the unreacted carbonate groups until membrane formation. The membrane was placed on the platinum electrode surface as is illustrated in Fig. 2. The amperometric transducer consisted of a platinum wire sealed in a glass tube. The biosensor was used in a batch system and the determination of acylcholine derivatives (acetylthiocholine, butyrylcholine and butyrylthiocholine) was performed electrochemically at +0.6 V by measuring the H2O2 generated in the oxidation of choline produced by the hydrolysis of the substrate. The butyrylthiocholine sensor yielded a linear response range between 5 and 100 mM, a detection limit of 2 mM, and a response time smaller than 2 min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003809_acc.2010.5530520-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003809_acc.2010.5530520-Figure13-1.png",
        "caption": "Fig. 13. Situations of the verification of the racket.",
        "texts": [
            " From the relationships u = f \u03b1u xc zc and v = f \u03b1v yc zc , the errors in (u, v) are calculated as ev uv = 0.81 and e\u03c9 uv = 0.64 [pixel]. Since ev uv and e\u03c9 uv are smaller than 1 [pixel], the errors of 0.5 [m/s] and 20 [rad/s] may be caused by the quantization errors. Because all the errors in Figs. 11 and 12 are smaller than these errors, the experimental data shows the validation of the rebound model on the table. The rebound model on the racket is verified by the 4 cases of (a) Top spin, (b) Back spin, (c) Side-top spin (vby > 0) and (d) Side-back spin (vby < 0) as illustrated in Fig. 13. The parameters in the rebound model are indentified as er = 0.81, kp = 1.9 \u00d7 10\u22123 [1/kg]. Figures 14 and 15 show the case of the pure top and back spins and the case of the sidetop spin of vby > 0 and vby < 0. The red data is used for the identification of the parameters and the blue data is used for the verification. The circles and squares represent the top and back spin in Fig. 14 and the side-top spin of vby > 0 and the one of vby < 0 in Fig. 15. It is confirmed that the red and blue data are close to the solid lines with the errors due to the quantization errors of the image data"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure9.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure9.2-1.png",
        "caption": "Figure 9.2. Sharp indenters: a. Rockwell indenter; b. Vickers indenter; c. Berkovich indenter (from [4], courtesy of Synton-MDP AG, Switzerland)",
        "texts": [
            " This procedure will be explained later in Section 9.1.1.5. The method can also be applied for coating systems, but there are some difficulties especially with regard to very thin coatings. In this case, in order to avoid the influence of the substrate material, special testing conditions should be considered. This will also be discussed in Section 9.1.1.5. The method is called sharp instrumented indentation because of the shape of the indenter, which can be conical for Rockwell indenters or pyramidal for Vickers and Berkovich indenters [4] (Figure 9.2). This test method has some advantages: in principle, it can be applied on specimens and components of any geometry, requiring only a small quantity of material. There are also several disadvantages in evaluating the test results from sharp indentation experiments. The extent to which these techniques can be used to quantify material properties is limited by the current understanding of the complicated material response during indentation experiments. For example, obtaining constitutive equations from indentation techniques has traditionally been limited to stress-free, perfectly elastic plastic material, not, therefore, giving critical information regarding residual stress and strain hardening"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003863_taes.2008.4560220-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003863_taes.2008.4560220-Figure2-1.png",
        "caption": "Fig. 2. Three-rotor rigid body and associated reference frames.",
        "texts": [
            " The originality of the configuration lies in its control mechanism for generating the required control forces and torques. The three-rotor aircraft consists of two body-fixed rotors and a tail tilting rotor with fixed-angle blades. The two front rotors rotate in opposite directions, thereby eliminating reactive anti-torques. Since the two front rotors are powered by two independent motors, their angular velocities can be controlled to produce the main thrust as well as the roll torque. The tail rotor can be tilted laterally (see Fig. 2) using a servo-motor in order to provide the yawing torque. Finally, the pitch torque is obtained by varying the angular speed of the tail rotor. 784 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 44, NO. 2 APRIL 2008 Contrary to the quadrotor aircraft, the yawing torque generated by the three-rotor helicopter is well understood and well modeled since it is expressed as the product of the lateral component of f3 and the distance l3. During manual flight tests the three-rotor aircraft performs the translational flight better than the quadrotor aircraft",
            " The full model of a helicopter involving the flexibility of rotors, fuselage aerodynamics and actuators dynamics is very complex [22]. For control practical purposes, the aerial robot can be considered as a rigid body evolving in a 3D space [23] with a mechanism for generating the control force and torque vectors. The body forces and moments acting on the airframe are the rotation speed of each motor wi, (i= 1,2,3) and the tilt angle (\u00ae) of the tail rotor. The force vector generated by propellers is expressed in the rigid body frame B = (eb1,eb2,eb3) (see Fig. 2) as Fb = (0,f3 sin\u00ae,f1 +f2 +f3 cos\u00ae) T: (1) Let us denote by (O1,O2,O3) the application points of the forces (f1,f2,f3), respectively. Then, the torque vector MB F induced by these forces with respect to the mass center G can be expressed in B as follows, (see Fig. 2): MB F = \u00a1! GO1\u00a3 (0,0,f1)+ \u00a1! GO2\u00a3 (0,0,f2) + \u00a1! GO3\u00a3 (0,f3 sin\u00ae,f3 cos\u00ae): (2) The components of MB F in the body frame are MB F = 0B@ l2(f1\u00a1f2) \u00a1l1(f1 +f2)+ l3f3 cos\u00ae \u00a1l3f3 sin\u00ae 1CA : (3) The distances li (i= 1,2,3) are defined in Fig. 2. The drag force for each of the blades is given as Qi = (0,0, (\u00a11)i\u00b7!2i )T, i= 1,2 Q3 = (0,\u00b7! 2 3 sin\u00ae,\u00b7! 2 3 cos\u00ae) T (4) where \u00b7 is a positive constant characterizing the propeller aerodynamics [22] and !i is the angular velocity of rotor i. Furthermore, there exists other parasitic moments specific to the three-rotor helicopter. Indeed, tilting the tail rotor laterally results in additional small moment. An adverse reaction moment appears when precessing the tail rotor laterally. It depends essentially on the tail rotor inertia Ip and on the tilt angle acceleration \u00ae\u0308",
            " Fb = (0,0,u) T+N\u00bfb (10) with N = 0B@0 0 0 0 0 \u00a11=l3 0 0 0 1CA (11) and u= f1 +f2 +f3 cos\u00ae (12) is the body-vertical component of the force vector which is considered as the nominal control force. REMARK 1 Note that the change of input variables in (12) and (8) defines a diffeomorphism, i.e., the original control inputs (f1,f2,f3,\u00ae) can be recovered from (u,\u00bfTb ) which are computed from the control law. The equations of motion for a rigid body subject to a body force FB 2R3 and a torque \u00bfb 2R3 applied to the center of mass G and specified with respect to the body coordinate frame B (see Fig. 2) are given by the following Newton-Euler equations in B, [2, 8, 24] m _\u00c0B +\u2212\u00a3m\u00c0B = FB J _\u2212+\u2212\u00a3 J\u2212 = \u00bfb (13) where \u00c0B 2 R3 and \u2212 2 R3 are, respectively, the body velocity vector and the body angular velocity vector expressed in the body frame B. m 2 R is the mass, and J 2R3\u00a33 is an inertial matrix expressed in B. FB is the gravity force mg and the body-lift vector Fb generated by propellers. The position \u00bb = (x,y,z)T 2 R3 and the velocity of the helicopter center of gravity \u00c0I 2R3 can be also expressed in the inertial frame I = (e1,e2,e3)",
            " Substituting (27) and (37) into (20), and considering that after a large finite time Tz, u\u0303\u00bc 0 and sh(\u00b4,z)\u00bc 1, then the horizontal movement dynamics can be represented as follows mx\u0308=\u00a1mg tan\u03bc cos\u00c1 \u00a1 tan\u03bc tan\u00c1f( _\u0301,\u00b4, \u00bf\u0303\u00c1) my\u0308 =mg tan\u00c1+ 1 cos\u00c1 f( _\u0301,\u00b4, \u00bf\u0303\u00c1) \u03bc\u0308 =\u00a12 _\u03bc\u00a1 \u03bc+ \u00bf\u0303\u03bctrans \u00c1\u0308=\u00a12 _\u00c1\u00a1\u00c1+ \u00bf\u0303\u00c1trans : (29) PROPOSITION 2 There exists positive real constants (c\u03bc,d\u03bc,c\u00c1,d\u00c1) satisfying c\u03bc > d\u03bc and c\u00c1 > d\u00c1, such that the system (29) is asymptotically stable considering the control law \u00bf\u0303\u03bctrans =\u00a1\u00bec\u03bc ( _\u03bc+2\u03bc\u00a1 _x=g) \u00a1\u00bed\u03bc ( _\u03bc+3\u03bc\u00a1 3_x=g\u00a1 x=g) \u00bf\u0303\u00c1trans =\u00a1\u00bec\u00c1( _\u00c1+2\u00c1+ _y=g) \u00a1\u00bed\u00c1( _\u00c1+3\u00c1+3_y=g+ y=g): (30) The proof of Proposition 2 is developed in Appendix B. In this section, we describe the experimental setup platform of the three-rotor helicopter including sensors and real-time architecture. The experimental results obtained using the proposed controller applied to the designed three-rotor aircraft are presented. We have built a three-rotor aircraft as shown in Fig. 2. The parameters of the three-rotor craft are m= 0:5 kg, l1 = 0:07 m, l2 = 0:24 m, l3 = 0:33 m. For simplicity we have developed a Simulink-based platform using MATLAB Simulink xPC target (see Fig. 4). We have used the commercial radio Futaba to transmit the signals to the three-rotor aircraft. The radio joystick potentiometers have been connected through the data acquisitions cards, Advantech PCL-818HG (16 channels A/D) and Advantech PCL-726 (6 channels D/A) to the PC (xPC target module). In order to measure the position (x,y,z) of the rotorcraft, we have used the 3D tracker system POLHEMUS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002831_robot.1993.292248-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002831_robot.1993.292248-Figure4-1.png",
        "caption": "Fig. 4 Some m o b i l e y e l l s carry t h e same object coordinatedly",
        "texts": [
            " 8. If it is assumed that the goal of the unit-&) is constant, Eq. 9 can be derived. Ek(t+dt)=Ek(t)( 1 -Kj (t)Cj(t)2) Eq. 9. To satisfy Eq. 4, the gain expressed by Kj(t) has to satisfy the following conditions, Therefore, if the gain of each unit is satisfied the Eq. 10, the total system is expected to be stable. 4. Simulations of a Control of The Multi Mobile Cells 4.1. A Modeling and Assumptions We applied the proposed decision making method to a distributed coordinated control of the CEBOT. Figure 4 shows a conceptual picture of conveyance by the multi mobile cells. The given task of the system is \" Carry the object to a goal point!\". It is assumed that the object is conveyed by some mobile cells shown in Fig. 4. Figure 5 shows a mobile cell which we have developed[5]. The mobile cell has two wheels controlled independently, so that the cell can move straight, turn, and rotate freely. The cell has its own CPU, the docking devices, the ultra-sonic sensors for coilision avoidance, the photo-sensors for position detection, and the communication devices. The autonomous docking, the communication Drotocol. and the exoerimental results Eq. 10. Fig. 5 A photo of a mobi le ce l l on communication among cells in both docked state and undocked state have already been studied and presented [1,2,51"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003809_acc.2010.5530520-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003809_acc.2010.5530520-Figure10-1.png",
        "caption": "Fig. 10. Situations of the verification of the table.",
        "texts": [
            " The coefficient of restitution of the table et can be calculated as et = \u221a h2 h1 , (21) where h1 and h2 are the first and second heights of the dropped ball. et is identified as et = 0.93 by averaging 25 data points. The dynamical friction coefficient \u00b5 is estimated as \u00b5 = 0.25 by measuring the drastic change in the value of the spring balance instrument at the sliding where the weighted ball on the table with the weight 2.0[kg] was pulled. The rebound model on the table is verified by the 4 cases of (a) Top spin, (b) Back spin, (c) Side-top spin and (d) Side-back spin as illustrated in Fig. 10. Figure 11 shows the verifications of the cases of the top and back spins, where the circles and squares represent the top and back spins. Since the experimental data of (a) and (b) is the cases of the pure top spin (\u03c9by < 0) and pure back spin (\u03c9by > 0) with vby, \u03c9bx, \u03c9bz \u2243 0, (vbx, vbz) [m/s] and \u03c9by [rad/s] are only shown. The horizontal and vertical axes are the experimental values and the calculated values from the model of the translational and rotational velocities after the rebound. The solid lines represent the cases where these values are the same"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003502_0020-7403(86)90016-0-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003502_0020-7403(86)90016-0-Figure2-1.png",
        "caption": "FIG. 2. (a) Displacements at the end of a spring; (b) the same as (a) but turned upside down. (Circles with crosses are shown at both ends in both views. These represent vectors directed into the paper for ul and u2.)",
        "texts": [
            " Moreover, since a linearly elastic system is being dealt with, k must also be symmetrical. Thus, although the matrices X and Y contain complex elements in general and are both unsymmetrical the product YX- t must be real and symmetricaL This is by no means easy to prove algebraically, but our computing confirms that it is so, apart from extremely small round off errors. Not only must k be real and symmetrical, but also the geometrical symmetry of the spring itself has considerable implications for the form of k. Figure 2(a) shows a spring with the directions of u, v, and w at each of the two ends. For simplicity the spring is shown as having exactly one turn, but the following argument remains valid, however many turns there are. If Fig. 2(a) is turned upside down Fig. 2(b) is obtained. However, because of the geometrical symmetry the bottom end can still be regarded as end 1 and the top end as end 2. Thus there has been a transformation of the end displacements as follows: Ut ~U2 , 121 ~ --V2, W l ~--- --W 2. Similar results obtain for the rotation, force and moment components at the two ends, and the whole operation can be described by the following transformations: dl ---, - H d 2 , d2--, - H d x Pl --* - H p 2 , P2 --* - H p l , (65) where H is the diagonal matrix defined by equation (50)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003847_icsma.2008.4505621-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003847_icsma.2008.4505621-Figure3-1.png",
        "caption": "Fig 3. Roll, pitch and yaw angles.",
        "texts": [
            " * Drag torque td is proportional to propeller In order to model quadrotor dynamics a frame of reference should be defined. Let E be an earth fixed frame with mutually orthogonal axes x, y, z with unit vector li, 7j, Ak. The center point of this frame is 0. Quadrotor is placed in this frame of reference with its center of mass at 0. If / is the length of arms then each motor M1 to M4 can be located by position vectors as shown in Figure 2, and given as: The free body diagrams of quadrotor with reference to E are shown in Figure 3. Figure The free body diagrams of quadrotor with reference to E are shown in Figure 3. Figure 3(a) shows the yaw angular displacement which is represented by 1, and it is due to rotation about positive z-axis. to the rotation about positive x-axis, and is represented by 0. Figure 3(c) represents the pitch angular displacement, which is about positive y-axis and is represented by (D. Lifting forces generated by the spinning propeller and the weight, are responsible for all the motion of body, as the external effects such as air friction, wind pressure etc. have been neglected. Consider a detailed free body diagram of quadrotor with reference to E, as shown in Figure 4. All the forces shown in the figure by Fi are located from the origin of E by position vectors Li as mention in the previous section",
            " Propellers mounted on motors M1 and M3 spin in the clockwise direction at speeds Q1 andQ3 respectively and those mounted on motors M2 and M4 spin in counter- clockwise direction at speeds Q 2 and 03 respectively. The imbalance of the forces F] , where i = 1, 3 or 2, 4 results in moment, along a direction perpendicular to the plane formed by the force s and the vector Li. This torque is responsible for the rotation of machine along x-axis and y-axis. The rotation about z-axis is due to imbalance of clockwise and counter-clockwise torques. Figure 3(b) shows the front view of quadrotor along with an axis that is perpendicular to the plane formed by the frame of machine. This angular displacement is due QUADROTOR BODY Determination of moment of inertia can be divided into two parts, firstly about x and y-axis and secondly about z-axis. It is assumed that if the machine is rolling, pitching and spinning etc. then that does not change the moment of inertia about a specific axis. 6.1 Moments of inertia along x and y-axis In derivation of moment of inertia along x (and y) axis following assumptions are made: * Motors M1 and M3 are cylindrical in shape with radius p, height h and mass m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002721_a:1019687400225-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002721_a:1019687400225-Figure1-1.png",
        "caption": "Figure 1. Geometric parameters of a serial robot.",
        "texts": [
            " , qn}, is obtained by a direct geometric DGM, which is computed as follows: \u22121Tn+1 = Z0T1(q1) \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 n\u22121Tn(qn)E, (1) where Z = \u22121T0 is the transformation matrix defining the location (position and orientation) of frame R0 with respect to frame R\u22121, E = nTn+1 is the transformation matrix defining the location of the end effector frame Rn+1 with respect to frame Rn, and jTi is the 4 \u00d7 4 homogenous transformation matrix defining the location of frame Ri with respect to frame Rj , whose general form is given as jTi = [ jAi jPi 0 0 0 1 ] (2) where jAi represents the (3 \u00d7 3) orientation matrix, and jPi is the (3 \u00d7 1) vector giving the position of the origin of frame Ri referred to frame Rj . The link frames R1, . . . , Rn are defined using the Khalil and Kleinfinger notation [9, 12] (Figure 1). Frame Ri is defined so that zi is along the axis of joint i, and xi is along the common normal between zi and zi+1. Frame Ri is defined with respect to frame Ri\u22121 by the matrix i\u22121Ti , which is a function of the parameters (\u03b1i, di , \u03b8i , and ri): i\u22121Ti = Rot(x, \u03b1i)Trans(x, di )Rot(z, \u03b8i)Trans(z, ri) =   cos(\u03b8i) \u2212 sin(\u03b8i) 0 di cos(\u03b1i) sin(\u03b8i) cos(\u03b1i) cos(\u03b8i) \u2212 sin(\u03b1i) \u2212ri sin(\u03b1i) sin(\u03b1i) sin(\u03b8i) sin(\u03b1i) cos(\u03b8i) cos(\u03b1i) ri cos(\u03b1i) 0 0 0 1   , (3) where Rot(k, \u03d5) is the transformation matrix of a rotation of an angle \u03d5 about the axis k, and Trans(k, a) represents a translation matrix of a distance a along the axis k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002321_jsvi.2000.2950-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002321_jsvi.2000.2950-Figure8-1.png",
        "caption": "Figure 8. Supporting condition and coordinate of carriage.",
        "texts": [
            " For this reason, the occurrence of the main peaks in the vibration spectra changes with the measurement points. OF CARRIAGE 4.2.1. Frequency expressions for rigid-body natural vibration of carriage From section 4.1, it can be presumed that the main peaks appearing in the vibration spectra are caused by the natural vibrations of the carriage. Recently, to explain the peaks that appear in the sound spectra of the LGT recirculating linear ball bearing itself, one [10] of the authors considered the vibratory system as shown in Figure 8 and derived the frequency expressions for the rigid-body natural vibration of the carriage. In Figure 8, the origin o of the coordinates oxyz coincides with the position of the center of gravity of the carriage while it does not vibrate. Although the x-axis is not seen in Figure 8, it is parallel to the longitudinal direction of the pro\"le rail. Since the x-axis is also parallel to the driven direction of the carriage, the displacement of the carriage along the x-axis is not considered. Moreover, a is the contact angel, a is the distance from the origin o to the contact point of the upper circuits of the recirculating balls of the carriage and the distributed normal spring in the direction parallel to the z-axis. b is the distance from the origin o to the contact point of the lower circuits of the recirculating balls of the carriage and the distributed normal spring in the direction parallel to the z-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure7.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure7.1-1.png",
        "caption": "Fig. 7.1 Thin plate",
        "texts": [
            " the principal stresses and planes for the centroid of the cross section I-I. Take the flexural rigidity of the beam to be EJ. Assume that all deformations due to normal forces are negligible. Problem 6.11: Compute the forces in each member of the given truss. All members of the truss, save member 7, have the same cross-sectional aI area A, and Young's modulus E. (AEh = (2\u00b7 AE)/ [(2 + 3V2)] 6.7 Exercises to Chapter 6 119 ~F I\u00b7 a \u00b71- a .1 .. a \u00b71 120 6. Simple Beams II: Ellergy Prillciples Consider a thin plate of uniform thickness, made of an elastic material (see Fig. 7.1). Assume that all forces applied to its boundary or in its interior are distributed uniformly across the thickness h. Evidently, the stresses 0-zz, 0-zx, 0-zy vanish on both faces of the plate, and it is unlikely that they assume substantial values in the interior. Therefore their presence may be neglected entirely. Additionally, it is plausible to assume that the other three components 0-xx, o-yy, o-yx do not depend on z. The stress system described by these assumptions is called a plane stress"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.15-1.png",
        "caption": "Figure 14.15 Rotational motion of a body about a fixed axis.",
        "texts": [
            " The conditions of the equilibrium of the system can be represented by the following equations valid along the directions normal and tangential to the path of motion: LFn =0: LFt =0: Fjn - Fmn + Fin + Wn = 0 Fjt - Fmt + Fit + Wi = 0 Solving these equations for the components of the joint reaction force will yield: Substituting the known parameters by their mathematical ex pressions will yield: F jt = F m sin fJ - mba - W sin B Now, substituting the numerical values and carrying out the calculations will yield: Fjn = (1488)(cos24) - (5.1)(0.22)(5)2 - (50) (cos 60) = 1306N Fjt = (1488)(sin24) - (5.1)(0.22)(200) - (50)(sin60) = 338N Therefore, the magnitude of the resultant force applied by the femur on the tibia is Fj = J(Fjn? + (Fjt)2 = 1349 N. 14.7 Rotational Kinetic Energy Assume that the rigid body shown in Figure 14.15 is composed of many small particles and that the body rotates about a fixed axis with an angular velocity w. If mi and Vi are the mass and the speed of the ith particle in the body, respectively, then the kinetic energy of the particle is: At any instant, every particle in the body has the same angular velocity w, but the linear velocity of each particle depends on its distance measured from the axis of rotation. If ri is the perpen dicular distance between the i th particle and the axis of rotation (Le"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002751_0094-114x(95)00121-e-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002751_0094-114x(95)00121-e-Figure2-1.png",
        "caption": "Fig. 2. Generat ing mechani sm and geometry o f rack cutter.",
        "texts": [
            " The arc length on the pitch ellipse, measured from initial point N to point M, can be calculated by applying the equation r7 (dr) SMX = r2+ ~ d~bl dO *~\" a(1 - E-)x/E + 2Ecosq~, + 1 = (1 + Ecosq51) 2 d4), (7) M A T H E M A T I C A L M O D E L O F T H E R A C K C U T T E R For simplicity, the generation of elliptical gears can be considered a two-dimensional problem. All methods for manufacturing of elliptical gears can be kinematically considered to consist of a rack cutter that performs pure rolling on the pitch ellipse in the generating process, as shown in Fig. 2(a). In this paper, a standard rack cutter [9] with a complete cutter surface, as shown in Fig. 2(b), is chosen. The shape of the rack cutter consists of two straight lines that form a pressure angle ~, with respect to the )(,-axis. The circular arcs of radius r with centers at C and D generate the fillet surfaces of elliptical gears, while the straight line M~oi)M~( ) ( i = 3, 4 indicates regions 3 and 4 o f the rack cutter, respectively) generates the working tooth surfaces of the elliptical gears. Backlash is also considered in the mathematical model, when a negative value of Ab is chosen. In the process of tooth surface generation, axis Y, must coincide with the tangent direction of the pitch 882 Shinn-Liang Chang et al. ellipse, as shown in Fig. 2(a). The contact point of the pitch ellipse and rack cutter pitch line is located at the Y,-axis of coordinate system S,(X<,Y<), and the rack cutter translates along the X, and Y, axes. Because each tooth of an elliptical gear may have a different shape, both sides of the rack cutter must be considered. Therefore, the rack cutter may be divided into six regions, as shown in Fig. 2(b). Regions 1 and 6 of the rack cutter surface can be considered to generate the bottom land of elliptical gears, regions 2 and 5 the fillet surface, and regions 3 and 4 the working tooth surface. The addendum curve, which may be considered to be the shape of the gear blank, is a curve equidistant from the pitch ellipse [4]. The equations of the rack cutter, represented in the coordinate system S,(X,,Y,), can be obtained as described in Sections 3.1-3.3. Undercut t ing analysis of elliptical gears 883 Regions 1 and 6 o f rack cutter surfaces Recall that regions 1 and 6 (the top land) of the rack cutter surface are used to generate the bottom land of elliptical gears. As shown in Fig. 2, d\"' is the design parameter of the rack cutter surface that determines the location of points on the rack cutter surface. From the rack cutter geometry, equations for regions 1 and 6 of the rack cutter surface can be expressed as follows: and ,, = yxl\"] = { - a, + rsin\u00a2, - I [ ~m _ ~,,, R, _ + r (8) 7~m 0 <_ {o~< ---2- _ b , - a, t a n q / , - rcostp,, i = 1,6. where {\"~= IM~o'~Ml~l (i = 1, 6) represents the distance measured from the initial point Ml;k along the straight line M~o'~M[ '~ to any point MI ') on the top land of rack cutter surface. Parameter m is the module, r is the radius of the circular arc, 0, is the pressure angle, and a, and b, are design parameters shown in Fig. 2. The upper sign of equation (8) indicates region 1 of the rack cutter surface while the lower sign indicates region 6. The unit normals and normals to regions 1 and 6 of the rack cutter surface are represented by the equation and \"~(i) ,,,I \" , i = 1,6 (9) \"\" I h r l ' ' = --- ' x k,, - ' , ~?fl0 where R-~ ~ indicates the position vector of the rack cutter surface represented in coordinate system S,, as expressed in equation (8). Equations (8) and (9) yield the following for the unit normals to regions 1 and 6 of the rack cutter surface: Regions 2 and 5 o f rack cutter surfaces Regions 2 and 5 of the rack cutter surface are used to generate different sides of the fillet surface of elliptical gears. O is the design parameter of the rack cutter surface which determines the location of points on the fillet. Here we have d\"~ = O (Fig. 2(b)) in this case. The position vectors for regions 2 and 5 of the rack cutter surface can be expressed as follows: R:!' J \"xli~'~ { - a , + r s i n ~ b , - r c o s O = ~-\"h'\"qJ = _+ b, + a, tamk, +_ rcos~,-T- r s in0J ' (11) and 0 < 0 < 90 \u00b0 - ~,., i = 2,5 The upper sign of equation (11) indicates region 2 of the rack cutter surface, while the lower sign represents region 5. The unit normals to regions 2 and 5 of the rack cutter surfaces can be obtained by applying equation (9), which results in the following expression: -T- cosO'( n~'i' = - s i n 0 J ( 1 2 ) Regions 3 and 4 o f rack cutter surfaces Regions 3 and 4 of the rack cutter surface are used to generate different sides of the working tooth surface of elliptical gears",
            "I, i= 3,4 The upper sign of equation (13) indicates region 3 of the rack cutter surface, while the lower sign indicates region 4 of the rack cutter surface. The unit normals to regions 3 and 4 of the rack cutter surfaces can be obtained as follows: n . , = )\" -T- sinO,'~ \" [ - c o s O , J (14) To derive the mathematical model for the complete tooth profile of elliptical gears, coordinate systems S , (X , , IT,), SI(XI, Y0, and Ss(X s, Yt) must be set up. The coordinate systems S,, S~, and 5'i are attached to the rack cutter, elliptical gear, and gear housing, respectively, as shown in Fig. 2(a). The contact lines of the gear blank and rack cutter, represented in coordinate system S,, can be obtained by simultaneously considering the following equations [5]: and R ( / ' = R(,f'({\"'), i = 1 . . . . . 6 (15) and f sin7 cos7 rlcos(~l + S'cos'~ 1 [M~,] = - cos), sin7 - r l s i n q S l + S'sin7 , 0 0 1 where ~t) = 0 and E') = - S; S is the translation distance of the rack cutter and can be obtained from the equation of meshing (equation (18)); and r~ is the distance measured from the rotation axis Z1 to the instantaneous center of rotation I",
            " Equation (19) may be simplified as follows: )'~fJ = - r~sin\u00a2,J + ( - a, + r s i n ~ , - where matrix {n,,n,} r represents the unit normal at any point on the pitch ellipse, as expressed by equation (6). Equation (20) shows that the bottom land of an elliptical gear is a curve equidistant from the pitch ellipse, and this equidistance is ( a , - rsin$, + r) in the negative direction of the unit normal. Fillets o f the elliptical gear tooth surfaces Fillets of the elliptical gear tooth surfaces are generated by regions 2 and 5 of the rack cutter surface, as shown in Fig. 2. According to equations (11), (12), (17) and (18), the fillet of elliptical gear tooth surfaces can be represented by xl ~= ( - a, + r s i n $ , - rcos0)sin)' + ( + b, ++_ a, tan~, + rcos\u00a2,.-T- rsin0)cos7 + r~cos\u00a2l + Scos7 yt,~) = _ ( _ a, + rsin~, - rcos0)cos7 + ( + h, + a, t a n $ , + rcosqJ, T- rsin0)sin7 - r,sin\u00a2, + Ssin7 S = + ( - a, + rsinqL)tanO T- (b, + a,.tan$, + rcos@,), (21) where 0 < 0 _< 90 c - $, and i = 2, 5. The upper sign indicates the fillet of elliptical gears generated by region 2 of the rack cutter, while the lower sign represents the fillet of elliptical gears generated by region 5 of the rack cutter. Work ing surfaces o f the elliptical gear Working surfaces of the elliptical gear are generated by regions 3 and 4 of the rack cutter surface, as shown in Fig. 2. According to Equations (13), (14), (17) and (18), the working surface of an elliptical gear can be represented by .'d, ~>= ( - a, + F\"~cos~p,)sin7 + ( _+ b, +_ a, tan$, T- ((i~sin@,)cos7 + rlcos\u00a2l + Scos]J yl i' = - ( - a, + #\"'cos\u00a2,)cos7 + ( + b,. + a,.tan~k,-T- {\")sin\u00a2,)sin7 - r,sin\u00a2, + Ssin 7 F(i) _ a, + b,sinff,. + Ssinff , . , (22) COSI//, where {\"' = ]M~)MI~]. The upper sign indicates the working surface of the elliptical gear generated by region 3 of the rack cutter, and the lower sign represents the working surface of the elliptical gear generated by region 4 of the rack cutter",
            " In the design of elliptical gears, one constraint that must be satisfied is that the circumference of the pitch ellipse must equal the product of the number of teeth n and the circular pitch p. Otherwise, the generated elliptical gear will have an incomplete tooth [7]. An example is given below that illustrates how to determine the tooth profile of an elliptical gear. The tooth profile of an elliptical gears obtained by applying the proposed method is compared with that obtained by applying the evolute method. Example 1. The standard rack cutter shown in Fig. 2(b) is chosen to generate an elliptical gear with module m = 5.0 mm, number of teeth n = 45, pressure angle ~b, = 20 \u00b0, radius of circular arc r = 0.3 module, Ab = 0 mm for non-backlash, and major semi-axis a = 125 mm. The short semi-axis b is calculated by solving for the pitch ellipse circumference S = rtmn and equation (7). It is found that b = 99.261 mm and E = 0.608. The computer program developed here and computer graphics were applied to obtain the complete tooth profile of the elliptical gear shown in Fig",
            " It is clear that the proposed mathematical model and generation method can be used to generate the tooth profile not only for working surfaces but also for fillets and bottom lands, whereas the evolute method can only generate the working surfaces. The addendum and dedendum curves are generated so that they are equidistant from the pitch ellipse. The results also show that the profiles of the working surfaces generated by these two methods are exactly the same. Example 2. The standard rack cutter shown in Fig. 2(b) is also chosen to generate an elliptical gear with major axis 2a = 41.465 mm, short axis 2b = 38.103 mm, number of teeth n = 21, pressure angle ~b, = 20 , radius of circular arc r = 0.3 module and Ab = - 0.03 mm for backlash consideration. The module m is then calculated by solving for the pitch ellipse circumference S = rtmn and equation (7). It is found that m = 1.895 mm and e = 0.394. By substituting the above design and calculated parameters into the developed mathematical model and computer program, the profile of the elliptical gear can be obtained",
            " When undercutting occurs, the thickness near the gear fillets will be decreased. Therefore, both the load capacity of the tooth and the length of the line of action are also reduced. Mathematically, the problem of preventing undercutting is the problem of avoiding the appearance of singular points on the generated tooth shape. A method proposed by Litvin [5], which considers the relative velocity and equation of meshing between the gear blank and rack cutter, is applied here to determine the limit of the rack cutter parameters, Figure 2 shows the relative motion between the gear blank and rack cutter. We shall consider under what circumstances a singular point appears on the working surface of elliptical gears generated by region 3 of the rack cutter. The relative velocity between the gear blank and rack cutter, represented in coordinate system S,, can be obtained as follows: V~, ~2' = co~(b, + a, tan~, - {'3'sin~b, + S) i, + og~(a, - {~3~cos~b,) j, (23) Recall that the equation of meshing for the working surface and rack cutter surface is expressed by the third part of equation (22)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003694_jst.65-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003694_jst.65-Figure1-1.png",
        "caption": "Figure 1. Cave setup for the rowing simulator.",
        "texts": [
            " Consequently, four DOF of the oar (three rotational DOF and one translational DOF along the longitudinal oar axis), as well as the user\u2019s body movement, have to be measured. Furthermore, the mechanical properties of the oar and the oar lock should be based on those of a competitive rowing boat. The acoustic and visual feedback should be synchronized with the movements in all DOF. Optical flow should provide feedback on the boat movement. The rowing simulator was integrated in an already existing Cave setup (Figure 1). This Cave comprises three large projection screens (4 3m, projectors; Projectiondesign, Fredrikstad, Norway) which surround the user. Furthermore, a closed ring of loudspeakers (112 speakers and four subwoofers; Iosono GmbH, Erfurt, Germany) surrounds the Cave. In the plane of this ring, virtual sound sources can be generated at arbitrary positions by applying the method of wave field synthesis. The measurement setup of the rowing simulator consists of a shortened, instrumented single scull boat mounted on a podium inside the cave"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003549_j.jsv.2006.11.008-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003549_j.jsv.2006.11.008-Figure2-1.png",
        "caption": "Fig. 2. The components of internal forces and moments.",
        "texts": [
            " w \u00bc cos2a/R, t \u00bc cosa sina/R and r are the curvature, the tortuosity of the helix and the density, respectively. Tt, Tn and Tb are the components of the internal forces in the t, n and b directions, and Mt, Mn and Mb are the components of the internal moments in the t, n and b directions, respectively, which are defined as [4,5] Tt \u00bc EA dUt ds wUn , (6a) Tn \u00bc GA bn dUn ds \u00fe wUt tUb Ob , (6b) Tb \u00bc GA bb dUb ds \u00fe tUn \u00fe On , (6c) Mt \u00bc GJ dOt ds wOn , (6d) Mn \u00bc EIn dOn ds \u00fe wOt tOb , (6e) Mb \u00bc EIb dOb ds \u00fe tOn . (6f) Fig. 2 shows the components of internal forces and moments. E and G are Young\u2019s modulus and the shear modulus. bn and bb are the Timoshenko coefficients. The substitution of (6a)\u2013(6f) into (5a)\u2013(5f) yields the following set of governing equations: EA d2Ut ds2 w2 GA bn Ut w EA\u00fe GA bn dUn ds \u00fe wt GA bn Ub \u00fe w GA bn Ob \u00bc o2rAUt, (7a) ARTICLE IN PRESS J. Lee / Journal of Sound and Vibration 302 (2007) 185\u2013196 189 w EA\u00fe GA bn dUt ds \u00fe GA bn d2Un ds2 w2EA\u00fe t2 GA bb Un t GA bn \u00fe GA bb dUb ds t GA bb On GA bn dOb ds \u00bc o2rAUn, \u00f07b\u00de wt GA bn Ut \u00fe t GA bn \u00fe GA bb dUn ds \u00fe GA bb d2Ub ds2 t2 GA bn Ub \u00fe GA bb dOn ds t GA bn Ob \u00bc o2rAUb, (7c) GJ d2Ot ds2 w2EInOt w EIn \u00fe GJ\u00f0 \u00de dOn ds \u00fe wtEInOb \u00bc o2rJOt, (7d) t GA bb Un GA bb dUb ds \u00fe w EIn \u00fe GJ\u00f0 \u00de dOt ds \u00fe EIn d2On ds2 GA bb \u00fe w2GJ \u00fe t2EIb On t EIn \u00fe EIb\u00f0 \u00de dOb ds \u00bc o2rInOn, \u00f07e\u00de w GA bn Ut \u00fe GA bn dUn ds t GA bn Ub \u00fe wtEInOt \u00fe t EIn \u00fe EIb\u00f0 \u00de dOn ds \u00fe EIb d2Ob ds2 GA bn \u00fe t2EIn Ob \u00bc o2rIbOb"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002848_tia.2003.816480-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002848_tia.2003.816480-Figure5-1.png",
        "caption": "Fig. 5. FLUX2D equiflux lines of the tested motor.",
        "texts": [
            " Then, the iron losses are deduced by computing the total copper losses in each part. C. Application to a BLDC Torque Motor The considered BLDC torque motor has a mechanical power of 6.4 kW, at a rated speed of 149 r/min and a synchronous frequency of 82 Hz. Fig. 4 shows the testing bench. Knowing the dc motor losses, the no-load BLDC machine losses can be deduced. As it is difficult to separate the mechanical and the iron losses, a constant friction torque of 2 N m is set based on measurements. Fig. 5 shows FLUX2D equiflux lines. FEM results are presented in Figs. 6\u20138, which present the evolutions of rotor yoke, stator yoke, and teeth flux densities versus the angular position of the rotor. Figs. 9\u201311 compare both methods computations of iron losses in the motor. Corresponding comparisons with measurements are presented in Fig. 12. The two methods present a relative difference with the measurements. The estimated iron losses are always greater than the measured one. Possible explanations of the discrepancies, currently under evaluation, are as follows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002458_0956-7151(93)90021-j-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002458_0956-7151(93)90021-j-Figure6-1.png",
        "caption": "Fig. 6. The configuration of annuli used for numerical analysis, with E r > E m.",
        "texts": [
            " Emphasis is given to the \u00a2r=(x) stress on the crack plane, z = 0. However, arz is also calculated at the interface of nearest neighbor fibers and compared with ~. This comparison addresses the incidence of sliding at those interfaces. In some cases, a~,(z) is calculated at nearest neighbor fiber locations. For elastically homogeneous systems, the calculations explicitly refer to the hexagonal fiber arrangement shown in Fig. 1. These results are presented first. However, when Ef=/=Em, the annular configuration depicted in Fig. 6 is used. The nearest and next-nearest neighbor fibers are considered to be located within annuli having the fiber modulus for that location. Outside the second annulus, the material is considered to be homogeneous and have the actual composite modulus. tPoisson's ratio is assumed to be the same for both. The salient trends in or= for the elastically homogeneous system are summarized in Figs 7-11. The Act= stress concentration on the crack plane diminishes as z/a r decreases (Fig. 7), such that the largest HE et al",
            " (ii) The radius of the radial zone that experiences a significant stress concentration, designated 3R. The hypothesis used here is that, at the small levels of r/~rf relevant to the mechanism transition, since 3~ ~> s, stress gradients in z are small t (Fig. 10). Consequently, the stress on the crack plane (z = 0) is used for analysis of the tHence, the mechanism transition is not explicitly affected by 3 c . relative survival probabilities of fiber rows within t5 R . The definition of 3 R is critical. The following rationalization is used; with reference to Fig. 6. I f the outer \"annulus\" of next-nearest neighbor fibers, width 3e, exhibits a higher failure probability than the inner annulus of nearest neighbor fibers, width 2s, then a well-defined crack-like criticality cannot develop. 878 HE et al.: THE ULTIMATE TENSILE STRENGTH OF COMPOSITES Instead, fiber failures are more likely to occur in other regions of the composite in which long lengths of fiber are subject to a uniform stress, of. For this case, composite failure is likely to proceed by global load sharing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003214_cdc.2005.1583480-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003214_cdc.2005.1583480-Figure2-1.png",
        "caption": "Fig. 2. Opposed lateral tilting and the associated moments",
        "texts": [
            " But this modification results in complex dynamical model of the vehicle. This issue is resolved by synthesizing an appropriate controller which takes into account these complications. For more details on system design and technical analysis, refer to ([4], [8]). Differential propeller speeds: Since it is possible to modify independently the speed of each propeller, then the rolling moment can be given by \u03c4\u03c6 = l(P1 \u2212 P2) (1) where l is the distance from the motors to the aerodynamic center O (see Figure 2). P1 and P2 are the lifts generated by each propeller. Longitudinal Tilting (LT): The longitudinal tilting of the propellers is controlled by two inboard servos. The yaw moment is obtained by differential longitudinal tilting of the rotors. Indeed, the difference of lift longitudinal components creates a yawing moment with respect to G as follows \u03c4\u03c8 = l(P1 sin \u03b11 \u2212 P2 sin \u03b12) (2) where \u03b11 and \u03b12 are the longitudinal tilt angles. Since the center of gravity G is located below the tilt axes, thus, the sum of longitudinal components of P1 and P2 generates a pitching moment with respect to G",
            " This moment acts on the airframe, causing loss of control authority and resulting in instability. Moreover, when the propellers have an angle of attack in longitudinal flight, they have a severe tendency to pitch up. They create substantial positive pitching moments. We conclude that the method by itself offers no practical means for countering these effects, and stability can not be obtained using only longitudinal tilting of the propellers. These issues may be resolved by combining this LT with an opposed lateral tilting. Opposed Lateral Tilting (OLT): Referring to Figure 2, forcing propellers to precess laterally in opposite directions will create gyroscopic moments (M1\u03b2 ,M2\u03b2) which are perpendicular to their respective spin and tilt axes [8], and directed as shown in Figure 2. Their total magnitude, calculated in Section III, is given by M\u03b2 = M1\u03b2 + M2\u03b2 = Ir\u03b2\u0307(\u03c91 + \u03c92) cos \u03b2 (4) with Ir is the fan inertia moment about spin axis. Also, a non-zero tilt angle \u03b2 will generate a component of the propeller torque vector along the lateral axis E2, creating a pitching moment on the aircraft in the same direction as M\u03b2 . Then, the pitching moment created by OLT is the sum of the components of the gyroscopic moments and fan torques (Q1,Q2) resolved along the E2 axis: \u03c4\u03b8\u03b2 = Ir\u03b2\u0307(\u03c91 + \u03c92) cos \u03b2 + (Q1 + Q2) sin \u03b2 (5) The experimental tests showed that the moment \u03c4\u03b8\u03b2 caused by OLT is weak and not sufficient for controlling the pitch movement and establishing forward motion of the aircraft",
            " The OLT and the LT have to be programmed (assigned by the controller) in such manner to optimize the aircraft behavior at all operating points in the flight envelope. The complete dynamics of a helicopter is quite complex and somewhat unmanageable for the purpose of control. Therefore, we consider a helicopter model as a rigid body incorporating a force and moment generation process [5]. The equations of motion for a rigid body subject to body force F0 \u2208 R 3 and torque \u03c4 \u2208 R 3 applied at the center of mass and specified with respect to the body coordinate frame A = (E1, E2, E3) (see Figure 2) are given by the Newton-Euler equations in A, which can be written as{ m\u03c5\u0307A + \u2126 \u00d7 m\u03c5A = F0 J\u2126\u0307 + \u2126 \u00d7 J\u2126 = \u03c4 (6) where \u03c5A \u2208 R 3 is the body velocity vector, \u2126 \u2208 R 3 is the body angular velocity vector, m \u2208 R specifies the mass, and J \u2208 R 3\u00d73 is an inertial matrix. F0 combines the force of gravity and the lift vector F generated by the propellers. The first equation in (6) can be also expressed in the inertial frame I = (Ex, Ey, Ez). By defining \u03be = (x, y, z) and \u03c5I as the position and the velocity of the helicopter relative to I, we can write{ \u03be\u0307 = \u03c5I , m\u03c5\u0307I = RF \u2212 mgEz J\u2126\u0307 + \u2126 \u00d7 J\u2126 = \u03c4 (7) where R \u2208 SO(3) is the rotation matrix of the body axes relative to I, satisfying R\u22121 = RT and det(R) = 1. It can be obtained based on Euler angles \u03b7 = (\u03c8, \u03b8, \u03c6) which are (yaw, pitch and roll) (cf. [5] and [9] for its expression). In the following, we express the force/moment pair (F, \u03c4 ), exerted on the helicopter. To develop our analysis, we use two additional coordinate frames: A1 = (A1x, A1y, A1z) and A2 = (A2x, A2y, A2z) which are associated to the rotor n\u25e61 and rotor n\u25e62, respectively (see Figure 2). The tilt movement of the rotors is obtained by a rotation \u03b2 around the axes Aix and then a rotation \u03b1i around the lateral axis E2, i = 1, 2. Therefore, the orientation of the rotors n\u25e61, n\u25e62 with respect to A can be defined by the rotational matrices T1, T2 whose expressions are given, respectively, by\u23a1 \u23a3 c\u03b11 s\u03b11s\u03b2 s\u03b11c\u03b2 0 c\u03b2 \u2212s\u03b2 \u2212s\u03b11 c\u03b11s\u03b2 c\u03b11c\u03b2 \u23a4 \u23a6 , \u23a1 \u23a3 c\u03b12 \u2212s\u03b12s\u03b2 s\u03b12c\u03b2 0 c\u03b2 s\u03b2 \u2212s\u03b12 \u2212c\u03b12s\u03b2 c\u03b12c\u03b2 \u23a4 \u23a6 (8) Force vector: The force F generated by the rotorcraft is the resultant force of the thrusts generated by the two propellers",
            " We therefore find M\u03b1 = 2\u2211 i=1 TiM Ai \u03b1i = Ir \u239b \u239d\u2212\u03c91\u03b1\u03071c\u03b11 + \u03c92\u03b1\u03072c\u03b12 0 \u03c91\u03b1\u03071s\u03b11 \u2212 \u03c92\u03b1\u03072s\u03b12 \u239e \u23a0 (13) M\u03b2 = 2\u2211 i=1 TiM Ai i\u03b2 = Ir\u03b2\u0307 \u239b \u239d(\u03c91s\u03b11 \u2212 \u03c92s\u03b12)s\u03b2 (\u03c91 + \u03c92)c\u03b2 (\u03c91c\u03b11 \u2212 \u03c92c\u03b12)s\u03b2 \u239e \u23a0 (14) Fan torques: As the blades rotate, they are subject to drag forces which produce torques around the aerodynamic center O. These moments act in opposite direction relative to \u03c9. QA1 1 = (0, 0,\u2212Q1)T , QA2 2 = (0, 0, Q2)T (15) The positive quantities Qi can be written as a function of propeller speeds: Qi = Ct\u03c9 2 i , Ct > 0. Similarly, these torques can be written in A as Q = 2\u2211 i=1 TiQ Ai i = \u239b \u239d\u2212(Q1s\u03b11 \u2212 Q2s\u03b12)c\u03b2 (Q1 + Q2)s\u03b2 \u2212(Q1c\u03b11 \u2212 Q2c\u03b12)c\u03b2 \u239e \u23a0 (16) Thrust vectoring moment: Denote O1 (O2) the application point of the thrust P1 (P2). From Figure 2, we can define O1G = (0,\u2212l,\u2212h)T and O2G = (0, l,\u2212h)T as positional vectors expressed in A. Then, the moment exerted by the force F on the airframe is MF = (T1P1) \u00d7 O1G + (T2P2) \u00d7 O2G (17) After some computations/development, we obtain MF = \u239b \u239dl(P1c\u03b11 \u2212 P2c\u03b12)c\u03b2 + h(P1 \u2212 P2)s\u03b2 h(P1s\u03b11 + P2s\u03b12)c\u03b2 \u2212l(P1s\u03b11 \u2212 P2s\u03b12)c\u03b2 \u239e \u23a0 (18) Adverse reactionary moment: As described in Section II, this moment appears when forcing the rotors to tilt longitudinally. It depends especially on the propeller inertia It and on tilt accelerations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002882_313-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002882_313-Figure6-1.png",
        "caption": "Figure 6. Photograph of a micropump with integrated electronics built in PCB technology.",
        "texts": [
            " A typical measured flow versus back pressure curve of a PCB micropump delivering water is depicted in figure 5. The pump shows a linear dependence of the flow on the applied back pressure. The maximum flow rate of approximately 470 \u00b5l min\u22121 is achieved without back pressure. The flow stops at a back pressure of approximately 135 hPa. The driving frequency and the mean power consumption of the pump averages 0.9 Hz and 900 mW, respectively. The outer dimensions of the PCB pump without electronics measures 14 \u00d7 17.5 \u00d7 3.2 mm3. A photograph of a delivering pump with integrated electronics is shown in figure 6. The pumps reach a compression ratio of up to 30% and thus are tolerant of gas bubbles in the liquid and capable of self-filling. The structure of a capacitive membrane sensor for pressure measurement is schematically shown in figure 7. It consists of three PCB layers with an intermediate flexible foil layer forming the membrane. The first board contains a horizontal fluid channel for connecting the reference pressure port to the sensor chamber located in the second PCB layer. A height difference between the static electrode and the other wires is produced either by milling or by selective electroplating and defines the spacing between the electrodes of the measuring capacitance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.1-1.png",
        "caption": "Figure 6.1. Sensors for gripping and contact force measurement integrated into the gripper and the manipulator, respectively",
        "texts": [
            " In robotics, force sensors are used to measure the interaction forces between gripper/end-effector, the part to be handled, and the environment. Typically, forces are divided into two classes: When gripping a part, the gripping forces which occur between gripper and part are of special interest. When manipulating a part, e.g., during assembly, moving on a surface, or mechanical characterization, the contact forces have to be known. Sensors to measure the gripping forces are integrated into the gripper \u2013 ideally into the gripper jaws. Contact force sensors can be mounted between gripper/end-effector and manipulator (Figure 6.1). A gripper has to ensure a fixed position and orientation, i.e., pose of the part with respect to the robot\u2019s last joint. In this manner, the gripper has to exert and withstand forces and torques. The main disturbing factors are forces of inertia due to the robot\u2019s acceleration as well as contact forces between the part and other objects within the working space. In micro- and nanohandling, forces of inertia play only a minor role, due to much smaller weights of the parts with respect to their gripping area, whereas adhesion forces prevail"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002589_robot.1999.770363-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002589_robot.1999.770363-Figure2-1.png",
        "caption": "Figure 2. Kinematic description of the ith leg",
        "texts": [
            " Such sensors are commercially available with good precision and moderate price. Furthermore, they are easy to use. After a brief description in section 2 of the .class of parallel robots which are considered, we will give the kinematic calibration method in section 3, simulation results will be given in section 4. [41 PI. 2. Description and modeling of the robot The parallel robot studied here is composed of a fixed base and a movable platform connected with six legs (Figure 1). The kinematic description of each leg is illustrated in Figure 2, only the prismatic joint is motorized. The base connections are composed of Universal joints (U-joints) and the platform connections are composed of Spherical joints (S-joints). The centers of the U-joints and S-joints are respectively denoted by Ai and Bi (i = 1 to 6). The leg lengths vector representing the variables of the prismatic joints gives the configuration of the parallel robot: q = I 91 92 q 3 q4 q5 q6 IT (1) 2.1. The geometric parameters We define the frame Fo fvted with respect to the base and F, fixed with respect to the movable platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002721_a:1019687400225-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002721_a:1019687400225-Figure3-1.png",
        "caption": "Figure 3. Gravity effect on link i.",
        "texts": [
            " The transformation of wrenches from one frame Ri to another frame Rj , is carried out using the following relation:{ jFOj jMOj } = i T j { iFOi iMOi } , (8) where i j is the (6 \u00d7 6) transformation matrix between screws, it is computed in terms of the elements of the transformation matrix between frames as follows i T j = [ jAi 03\u00d73 j P\u0302i jAi jAi ] , (9) where j P\u0302i is the skew-symmetric matrix associated with the vector jPi = {Px Py Pz}T such that j P\u0302i = [ 0 \u2212Pz Py Pz 0 \u2212Px \u2212Py Px 0 ] . (10) The computation of the forces and moments on the links is carried out using a simplified recursive Newton\u2013Euler algorithm which is deduced from that used for computing the inverse dynamic model computation [10, 13, 16]. The algorithm makes use of masses and the first moments of the links, which are denoted for link i by mi and MSi , respectively. The first moment vector is fixed when referred to frame Ri (Figure 3), it is given by: MSi = {MXi MYi MZi}T. In our case, where joint velocities and accelerations are zero, the forwind recursive equations provide gravity acceleration \u22121g referred to the frames Ri and Rai . They are given by: ig = iAi\u22121 i\u22121g for i = 1, . . . , n + 1, (11) aig = aiAi ig for i = 1, . . . , n. (12) We assume the load as a lumped mass mp located at the endpoint of the robot (origin of frame Rn+1). Thus, the wrench at point Bn+1 is given by{ a(n+1)FBn+1 a(n+1)MBn+1 } = { mp a(n+1)An+1 n+1g 03\u00d71 } "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.16-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.16-1.png",
        "caption": "Figure 14.16 A particle located at PI is displaced by an angle () or arc length s to position P2\u2022",
        "texts": [
            "15) defines the rotational kinetic energy of a body in terms of the mass moment of inertia and angular velocity of the body, and it is analogous to the kinetic energy t'K = !mv2 associated with linear motion. 14.8 Angular Work and Power By definition, the work done by a force is equal to the magnitude of the force times the corresponding displacement. The angular work done by a force applied on a rotating body is related to the angular displacement of the body. Consider a body rotating about a fixed axis at 0 due to an applied force F. As illustrated in Figure 14.16, let PI and P2 represent the positions of a point in the body at times tl and t2, respectively. In the time interval between tl and t2, the body rotates through an arc of length s Angular Kinetics 311 312 Fundamentals of Biomechanics or angle (). The work done by F on the body is equal to the magnitude of the component of the force vector in the direction of motion (tangential component, Ft ), times the displacement s: The arc length is related to the angular displacement through the radius of the circular path of motion as s = r()"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003124_j.ijar.2006.08.002-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003124_j.ijar.2006.08.002-Figure7-1.png",
        "caption": "Fig. 7. Structure of a ball-beam system.",
        "texts": [
            " However, the duration of the action- as the cart passes through the origin may not be long enough to reduce the speed of the cart to zero. The value c2 of must not be too large, otherwise the cart will be always oscillating around the origin. Figs. 4\u20136 shows the simulation results. It is found that the pole and the cart can be stabilized to the equilibrium point. Further, the proposed control cannot only settling time and overshoot to decrease but also performance and robustness better than DSMC and DFSMC [9]. Consider a ball-beam system as depicted in Fig. 7 and its dynamic is described below: _x1 \u00bc x2 _x2 \u00bc u\u00fe d _x3 \u00bc x4 _x4 \u00bc B\u00f0x3x2 2 G sin x1\u00de \u00f040\u00de where x1 = h, the angle of the pole with respect to the vertical axis; x2 \u00bc _h, the angle velocity of the pole with respect to the vertical axis; x3 = r, the position of the cart; x4 \u00bc _r, the velocity of the cart; B \u00bc MR2 Jb\u00feMR2 where Jb, moment of inertia of the ball; M, mass of the ball; R, radius of the ball; g, acceleration of gravity. The center of rotation is assumed to be frictionless and ball is free to roll along the beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003371_1.2768079-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003371_1.2768079-Figure1-1.png",
        "caption": "Fig. 1 Arched ball bearing radially loaded",
        "texts": [
            " The present paper proposes an extension of this work to decribe the ball equilibrium of bearing up to four-contact points ith a five DOF inner ring. Some subroutines developed in a revious work 6 have been reused. For simplification purposes, he procedure described in this article supposes that the raceways re rigid and only assumes elastic deformations of the contacts etween rolling elements and raceways Hertz contacts . A way to onsider the structural deformation of the rings and housing is resented elsewhere 7 . eometry Consideration The model has been developed imposing the outer ring fixed in pace. Figure 1 shows the arched bearing in a radial contact position. 1Product of the shaft speed in rpm by the pitch diameter of the bearing in illimeters. Contributed by the Tribology Division of ASME for publication in the JOURNAL OF RIBOLOGY. Manuscript received November 16, 2006; final manuscript received arch 26, 2007. Review conducted by Michael Lovell. Paper presented at the SME/STLE 2007 International Joint Tribology Conference TRIB2007 , San Digo, CA, October 22\u201324, 2007. ournal of Tribology Copyright \u00a9 20 om: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms The ball contacts at two points at the bottom of the outer raceway. The radial contact angle for outer raceway r o can be written as r o = sin\u22121 go 2ro \u2212 D 1 A distance, which needs to be formulated, is the distance from the tip of arch to the bottom of the ball in radial contact position, as shown in Fig. 1. From this figure and using the Pythagorean theorem for h, hm = \u2212 D 2 \u2212 2rm \u2212 D 2 cos r m + 1 2 D 4rm \u2212 D + 2rm \u2212 D 2 cos2 r m 1/2 2 where m= i or m=o for inner or outer raceway, respectively. With h known, conventional bearing parameters can be formulated as Pd = Sd + 2 ho + hi 3 with Sd = do \u2212 d\u0304i \u2212 2 D + ho + hi 4 where d\u0304i is the inner raceway diameter after centrifugal growth has been considered 8 . The pitch diameter dm can be expressed as dm = d\u0304i + Sd 2 + D 5 Figure 2 shows the arched bearing while in the axial position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003892_1.3020444-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003892_1.3020444-Figure1-1.png",
        "caption": "FIG. 1. Schematic of Newton\u2019s cradle experiments.",
        "texts": [
            " With regard to contact duration, the softsphere models correctly predict that the striker particle separates from the three-body contact prior to the separation of the two initially motionless particles. Quantitative modeldata comparisons are also made, although the emphasis of this work is targeted at the differences between three-body collisions and two-body collisions rather than providing a critical analysis between existing soft-sphere models. To investigate the postcollisional behavior of a normal head-on collision between three solid spheres, a pendulumbased apparatus inspired by Newton\u2019s cradle is used. As illustrated in Fig. 1, each particle is hung from two lines to make a V shape. The pivot points in each V-shaped pendulum are approximately 33 cm apart and the length of each line is 1 m. The three pendulums are spaced one-particle diameter 2.54 cm apart, so that when not in motion, the particles are touching, but no force occurs between them. The pendulum line is made of an ice fishing line manufactured by Berkley with a spring constant of 1.2 N/m. The stiff line balances the centripetal force experienced by the striker particle as it travels down the arc, effectively eliminating any vertical motion upon collision with the stationary particles at the bottom of the arc",
            "03 1011 N /m2, Poisson\u2019s ratio =0.28, yield strength Y =2.03 109 N /m2, density =7830 kg /m3, and radius R =1.27 cm. The properties of the stainless steel particles are Young\u2019s modulus E=1.93 1011 N /m2, Poisson\u2019s ratio =0.35, yield strength Y =3.10 108 N /m2, density =8030 kg /m3, and radius R=1.27 cm. The normal three-body collision is achieved by pulling back along the arc the striker particle, which is then released and allowed to collide with the two motionless touching particles at the bottom of the arc. As labeled in Fig. 1, particle 1 refers to the striker particle, particle 2 refers to the middle particle, and particle 3 is the end particle opposite to the striker particle. The striker particle is held by a door attached to a track along the arc. The position of the door can be moved along the track in order to achieve different impacting velocities when released. The door is spring loaded and is released by a solenoid. Once released, particle 1 collides with particle 2, and particles 2 and 3 travel up the arc. Due to gravity g, the particles will eventually come back down the arc and collide a second time; however, data are only taken before and after the first three-body collision",
            "11 take the same form as that of Kuwabara and Kono5 and thus are not listed separately. Note that all of these models are quasistatic in nature. For the particles examined here, collision durations are larger than estimates of the wave propagation time,22 thereby lending support to the quasistatic treatment. Table I contains the force law for each of the soft-sphere collision models and the associated input parameters. The notation introduced in the table includes the following: subscripts a and b refer to properties associated with particles a and b, respectively Fig. 1 , m refers to particle mass if no subscript is included, the equation is valid only for identical spheres with mass m , Fn refers to the repulsive normal force experienced by a particle during contact, and refers to particle \u201coverlap.\u201d The particle overlap is defined as = max 0,Ra + Rb \u2212 rb \u2212 ra , 1 where r refers to the position of a given particle center. Also listed in Table I is the regime for which each of the force laws was developed. For further details, the reader is referred to Ref. 19",
            " Similarly, the inputs to the T model10 are based on material properties, although Thornton and co-workers recognized the sensitivity of the predictions to the value used for the \u201ccutoff pressure\u201d py input23,24 and fitted this value to match measurements of other quantities.25,26 Accordingly, the fitted value of py obtained by Stevens and Hrenya19 is used in the current effort. To obtain model predictions for the postcollisional velocities of all particles using the various soft-sphere models, three identical particles are initially positioned in a line and touching but not overlapping separated by two-particle radii . In order to mimic the Newton\u2019s cradle setup Fig. 1 , particles 2 and 3 are initially motionless, while particle 1 is given a nonzero impact velocity Vimp in the direction of particle 2. The position and velocity of each particle are then tracked throughout the collisional process using the force laws given in Table I. Specifically, the repulsive force Fn is determined at any point in time as a function of overlap , and this force is used in conjunction with Newton\u2019s law of motion no other forces are considered to move forward in time. An explicit integration scheme is used to solve the initial-value problem",
            " Although e is a function of impact velocity, the values used in the hard-sphere model are assumed constant for purposes of simplicity, as this assumption does not impact the conclusions. In particular, e=0.88 and 0.99 are used for the stainless and chrome steel systems, respectively, based on the measurements of Stevens and Hrenya19 in the midrange of the velocities examined. To apply the two-particle hard-sphere collision model to the three-body collision, a series of two-body collisions is carried out by assuming an infinitesimal spacing between the initially motionless particles particles 2 and 3 in Fig. 1 . Accordingly, the postcollisional velocities of particles 1 and 2 V1 and V2 are first found using Eqs. 2 and 3 where V1o=Vimp and V2o=0. The postcollisional velocity of particle 2 V2 is then used as the precollisional velocity when resolving the subsequent collision between particles 2 and 3 V2o =V2 and V3o=0 . Once the outcomes of this first series of collisions are performed, a check is then made as to whether V1 V2 and V2 V3. Otherwise, a faster particle will catch up to the slower particle and a secondary collision will occur",
            " Namely, the first collision between particles 1 and 2 leads to a perfect exchange of velocity, as does the second collision between particles 2 and 3. Correspondingly, V3=Vimp while particles 1 and 2 remain motionless at the bottom of the pendulum arc V1=V2=0 . In the first phase of the work, experiments are performed to characterize the outcome of the normal, three-body collision. Based on experience with the Newton\u2019s cradle desktop toy i.e., without the aid of a high-speed camera , the pulling away and subsequent release of the impacting particle particle 1 in Fig. 1 is expected to lead to a velocity exchange with the other end particle particle 3 , while particles 1 and 2 remain touching at the bottom of the arc. The experimental results obtained via high-speed imaging, however, indicate that the expected Newton\u2019s cradle outcome is not observed. Instead, particles 1 and 2 separate slowly after colliding, as shown in the snapshots and corresponding velocity data of Fig. 3. The velocities and separation of particles 1 and 2 are quite small relative to that of particle 3, which explains why the desktop toy gives the appearance of the traditional Newton\u2019s cradle outcome",
            " In fact, high-speed images were also taken of a commercially available Newton\u2019s cradle toy composed of five spheres, and the four spheres remaining at the bottom of the arc after collision were also observed to separate slightly. For purposes of notation, the Newton\u2019s cradle outcome particles 1 and 2 in contact after collision will hereafter be referred to as NC, while the fully separated outcome no particles in contact after collision will be referred to as FS. Perhaps even more surprising than the FS outcome though is that the striker particle particle 1 reverses its direction negative velocity after the collision Fig. 1 . This behavior is representative of the entire parameter space investigated, as displayed in Fig. 4. Specifically, Fig. 4 contains plots of postcollisional velocities of each sphere V1, V2, and V3 over a range of impact velocities Vimp for the case of chrome steel subplot a and stainless steel subplot b particles. For each system, particles 1 and 2 display a slow separation after the collision FS , with particle 1 reversing its direction and particle 2 continuing in the same direction as the impacting particle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.3-1.png",
        "caption": "Figure 3.3 Moment of a force about a point.",
        "texts": [
            " However, the mathematical definition of moment and torque is the same. Therefore, it is sufficient to use moment to discuss the common properties of moment and torque vectors. 3.2 Magnitude of Moment The magnitude of the moment of a force about a point is equal to the magnitude of the force times the length of the shortest dis tance between the point and the line of action of the force, which is known as the lever or moment arm. Consider a person on an exercise apparatus who is holding a handle that is attached to a cable (Figure 3.3). The cable is wrapped around a pulley and attached to a weight pan. The weight in the weight pan stretches the cable and produces a tensile force F in the cable. This force is transmitted to the person's hand through the handle. Assume that the magnitude of the moment of force F about point 0 at the elbow joint is to be determined. To determine the shortest distance between 0 and the line of action of the force, extend the line of action of F and drop a line from 0 that cuts the line of action of F at right angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002518_s0263574797000027-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002518_s0263574797000027-Figure10-1.png",
        "caption": "Fig . 10 . PUMA 560 Robot with A Long Tool .",
        "texts": [
            " The convergence of the kinematic error is faster for a smaller m , however collision between robot and obstacles may occur even though kinematic error threshold has been met . Thus the appropriate choice of m depends on the problem at hand . The PUMA 560 robot arm has six joints . When both the Cartesian position and orientation are taken into account , the PUMA 560 arm is a non-redundant robot . However , if we only consider the position of the end point of an attached tool , the PUMA 560 arm as shown in Figure 10 will become a redundant robot since the tool tip in the three-dimensional Cartesian space is related to five joint angles (a two degree redundancy) . With the joint angle and link parameters defined in Table III , the positional forward kinematics is expressed as follows : X 5 C 1 [ d 6 ( C 2 3 C 4 S 5 1 S 2 3 C 5 ) 1 S 2 3 d 4 1 a 3 C 2 3 1 a 2 C 2 ] 2 S 1 [ d 6 S 4 S 5 1 d 2 ) (15) Y 5 S 1 [ d 6 ( C 2 3 C 4 S 5 1 S 2 3 C 5 ) 1 S 2 3 d 4 1 a 3 C 2 3 1 a 2 C 2 ] 1 C 1 ( d 6 S 4 S 5 1 d 2 ) (16) Z 5 d 6 ( C 2 3 C 5 2 S 2 3 C 4 S 5 ) 1 C 2 3 d 4 2 a 3 S 2 3 1 a 2 S 2 (17) A set of 15 points on a straight line , as shown in Figure 11(a) and listed in Table IV , is used for training "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002761_robot.1989.100120-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002761_robot.1989.100120-Figure5-1.png",
        "caption": "Fig. 5. Graphic Display of the simulated motion of a Space Vehicle/Manipulator System",
        "texts": [
            " This scheme can be used not only for real-time control, but for planning of a feasible motions of vehicle and manipulator. This approach deals with the total nonlinearity of the space vehicle/manipulator systems without neglecting nonlinearity of higher order, and enables any allowable change of vehicle orientation. A general graphic simulator that can simulate any open link manipulators on a vehicle has been developed on SUN3 a t the Center for Robotic Systems in Microelectronics, University of California, Santa Barbara. A sample of graphic display of motion is shown in Fig. 5. To verify the effectiveness of the proposed approach, numerical simulation is currently being undertaken using this simulator. This material is supported by the National Science Foundation under Contract number 8421415. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the Foundation. REFERENCES [l] Alexander, H.L., and Cannon, R.H.,\u201cExperiments on the Control of a Satellite Manipulator.\u201d Proceedings of 1987 American Control Conference, Seattle, WA, June 1987"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003334_s11071-007-9306-2-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003334_s11071-007-9306-2-Figure1-1.png",
        "caption": "Fig. 1 Bearing coordinate systems",
        "texts": [
            " In this paper, a five-degree-of-freedom model will be improved to study the effect of axial preload on the nonlinear dynamic characteristics of a flexible rotor system supported by angular contact ball bearings. Floquet theory, numerical integration technique, Poincar\u00e8 maps, and power spectra will be employed to analyze the nonlinear behaviors, bifurcation and dynamic stability of the rotor bearing system with or without unbalanced force. Based on the previous work in [8], a five-degree-offreedom model of angular contact ball bearing is improved to determine the nonlinear bearing forces. 2.1 Coordinate systems and transformations Two sets of coordinate systems, as shown in Fig. 1, are defined for the purpose of bearing modeling. The inertial coordinate system (x, y, z), which is fixed in space, is a convenient orthogonal set of coordinates with the origin at the bearing (inner race) center. The z-axis is along the bearing rotational axis. The local rolling element coordinate system (r,Z,\u03c6), with the same z-axis and origin at the nominal position of the inner race center of curvature, is fixed in the rolling element. The general motion and load of the bearings can be completely described in five degrees of freedom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003870_1.4001003-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003870_1.4001003-Figure11-1.png",
        "caption": "Fig. 11 Actual center-gear alignment curves",
        "texts": [
            " But the unit normal vector of the boundaries should be obtained at first. np = iC jC dxp d dyp d dxp d 2 + dyp d 2 = sin \u2212 j + iC \u2212 cos \u2212 j + jC 31 Thus the equation of the two actual center-gear alignment curves is obtained as xp = xp \u2212 j \u2212 lj sin \u2212 j + yp = yp + j \u2212 lj cos \u2212 j + 32 Substituting Eq. 30 into Eq. 32 , it yields xp = e cot cos \u2212 j \u2212 j \u2212 lj sin \u2212 j + yp = e cot sin \u2212 j + j \u2212 lj cos \u2212 j + 33 where j \u2212 lj is the distance of half width of the tooth thickness or space width shown in Fig. 11 . Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use 5 n T v a t B b a g i b t t t m l T b S N P F N P F r F b J Downloaded Fr Simulation and Verification of the Nutation Drive To verify the mathematical model, 3D models of all parts of a utation drive reducer are created using the parameters given in able 1. The virtual assembling for the reducer is carried out in a irtual environment by the steps when the prototype was being ssembled. Figure 12 indicates the exploded virtual assembly of he nutation drive reducer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002858_0191-8141(92)90061-z-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002858_0191-8141(92)90061-z-Figure5-1.png",
        "caption": "Fig. 5. Developable surface. At all points on a generator thc surface has the same dip and strike.",
        "texts": [
            " the configuration of contours that could be swept out by the spikes of a rake or comb (Fig. 4c). Some of the above features, such as the elliptical closure of contours, occur only at specific positions on the map; the exact position depending on the orientation of the surface relative to the horizontal. To analyse the curvatures at all points on a map involves drawing isotrend lines. The proposed method utilizes the property that developable surfaces are made up of straight lines or generators along which the strike and dip of the tangent planes to the surface are constant (Fig. 5). On the map, points are sought on successive contour lines where the trends of the contours are equal (Fig. 6). These points are located using the method for constructing dip isogons on fold profiles (Ramsay 1967, p. 363, Ragan 1985, p. 207). These points are then joined to form lines of constant contour trend or isotrend lines. Conclusions can be drawn regarding the morphology of the folded surface on the basis of the pattern shown by the isotrend lines on a map. If the surface developed by isometric bending, the isotrend lines will be straight lines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.18-1.png",
        "caption": "Figure 13.18 nand t are the normal (radial) and tangential directions at point P.",
        "texts": [
            " For example, e =Owhen t =Oand t = r =2s, and e =n/6=0.52 rad or 30\u00b0 when t = tM = 0.232 s. These are consistent with the initial data presented in Figure 13.14. Also note that angular velocity is a cosine function of time. The amplitude of the w versus t curve shown in Figure 13.17 is equal to the coefficient n 2 /4 = 2.47 rad/ s in front of the cosine function in Eq. (viii). Similarly, the amplitude of the angular acceleration is n 3/4 = 7.75 rad/s2\u2022 13.7 Rotational Motion About a Fixed Axis Consider the arbitrarily shaped object in Figure 13.18. Assume that the object is undergoing a rotational motion in the xy-plane about a fixed axis that is perpendicular to the xy-plane. Let 0 and P be two points in the xy-plane, such that 0 is along the axis of rotation of the object and P is a fixed point on the rotating object located at a distance r from O. Owing to the rotation of the object, point P will experience a circular motion with r being the radius of its circular path. To describe circular motions, it is usually convenient to define velocity and acceleration vectors with respect to two mutually perpendicular directions normal (radial) and tangential to the circular path of motion. These directions are indicated as nand t in Figure 13.18, and are also known as local coordinates. By 286 Fundamentals of Biomechanics definition, the velocity vector.!!. is always tangent to the path of motion. Therefore, for a circular motion, the velocity vector can have only one component tangent to the circular path of motion (Figure 13.19) . .!!. is called the tangential or linear velocity. The magnitude v of the velocity vector can be determined by considering the time rate of change of relative position of point P along the circular path: ds v=- dt (13"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002910_9.273337-FigureI-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002910_9.273337-FigureI-1.png",
        "caption": "Fig. I . Fig. 2",
        "texts": [],
        "surrounding_texts": [
            "34 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 39, NO. 1, JANUARY 1994\nAn appropriate way to find an optimal solution for all x in the region of interest is the method of dynamic programming. Its numerical properties have been investigated earlier, e.g., in [18]-[211. Bounds on the errors, which are caused by implementation details of the dynamic programming iteration, have been obtained for finite time interval cost criteria [18], for discounted cost criteria [19], or based on the assumption that the iteration defines a contraction mapping [20], [21]. These results use assumptions that are much different from what would be needed for the stable feedback design problem considered here. It turns out that the numerical computation of J ( z ) is likely to fail as a generally applicable design tool because fundamental problems arise, as discussed in detail in Section 11.\nTo avoid these difficulties, the present paper uses the concept of practical asymptotical stability, a cost criterion with terminal cost and free end time, and a piecewise constant parameterization of the feedback. Based on this, a wellfounded theory is established for the numerical design of nonlinear state regulators, which solves the design problem as posed. A numerical stability test of the computed result is also given.\n11. PROBLEM FORMULATION\nA. The Plant\nConsider a nonlinear plant P\nZt+l = f (x t ,u t ) (1)\nwith state xt E R\", control ut E R\", and discrete time t E Z:. It is assumed that f : R\" x R\" --t R\" is continuous.\nFurther let G C R\" be any prespeciJied bounded region in the state space, which contains a neighborhood of the origin.\nGiven P and G, it is typically unknown whether or not a feedback controller exists, such that the resulting feedback system is asymptotically stable for all initial conditions z E G. The objective here is to set up a numerical design method, that can handle this situation and which computes a stabilizing feedback controller, if one exists.\nB. Asymptotic Controllability and Stability\nA solution of (1) starting with initial state x and control sequence g = {uo, u1, u2, . . .} will be denoted by xt =\nDe3nition 1 (Asymptotic Controllability of P): The plant (P) is said to be asymptotically controllable from G to the origin, if there is a cr(r, t) E K,' such that for every x E G there exists a control sequence g = g(z) such that\nMx,zL).\nl l4t(~,zL(~))lI + l.t(.)I 5 4l l~ l l> t )>\ntEZ$. (2)\n0 For state feedback laws ut = k ( x t ) , where IC : R\" + Rm is\nDejinition 2 (Asymptotic Stability): A feedback loop xt+l = f ( x t , k ( x t ) ) , with trajectories denoted by &(z), is said to be asymptotically stable from G to the origin, if there is a a(r,t) E KO such that for every z E G\nl l 43~ ) l l + ll~(&(4)11 5 4l l~ l l> t )>\ntEZo+. (3)\nU The inclusion of an asymptotic requirement on the input in the above two definitions is made for simplicity; it can be dropped if desired.\nC. Background Theory\nWe are interested in a feedback controller that generates asymptotic control in the sense of Definition 2. For the existence of such a controller, asymptotic controllability is obviously necessary. But if the plant is asymptotically controllable, then such a controller exists and, in addition, exists in the form of state feedback. This is summarized by Theorem 1, which we consider as essentially known. The proof of the theorem is constructive, and this construction serves as a starting point for developing our numerical feedback design method.\nTheorem I: A feedback k such that the closed-loop system xt+l = f(xt,lc(zt)) is asymptotically stable from G to the origin exists, if and only if the plant is asymptotically controllable from G to the origin.\nProofi Asymptotic controllability is obviously necessary for asymptotic stabilizability. Sufficiency can be shown constructively, where the essential steps are as follows.\nIf the plant is asymptotically controllable from G to the origin, then a continuous, positive definite function [(z, U ) exists2 such that for all z E G the right-hand side of\nis well defined and assumes values below some finite constant\nLet M denote the set of points in R\" such that the right-hand 70 := S U P , ~ G J (x ) . side of (4) exists, and define\nWe note that G c ro. Moreover, in r0 we have J ( x ) is positive definite and decrescent, the latter as a consequence of the asymptotic controllability.\nFor all z E ro the function J ( x ) satisfies the equation\nSince !( . ) is positive definite, the existence of k(z) follows, such that for all z E r0\n(7)\nany feedback function, the stability of the resulting feedback system is defined as follows. 2~~ see this, let T' := supzEG 11x11 and let U ( . ) characterize the asymptotic controllability according to (2). Then one may take, for example, e(z ,u ) = p'(JJzlJ + 1Ju11), where p' E Kv is such that p ' (U(r ' , t ) ) is summable over t . 'For a definition of function classes K v , Km see Appendix A.l.",
            "KREISSELMEIER AND BIRKHOLZER NUMERICAL NONLINEAR REGULATOR DESIGN\nHence, J ( z ) is a Lyapunov function in ro and k ( z ) is an asymptotically stabilizing feedback control from G to the\nJ ( z ) , as defined by (4) or (6), is called a control Lyapunov function [l2I3 because a controller k ( z ) exists such that J ( z ) is a Lyapunov function for the controlled plant. Setting up the iteration\nJ T + ~ ( x ) = i$ [e(z, U ) + J~(f(z, 7 ~ ) ) 1 ,\norigin. 0\nJo(x) E 0. T E 2: (8)\nwhich is of the dynamic programming type, it follows that J T ( z ) converges to J ( z ) in I'o as T + 03. This gives rise to a mathematical feedback construction, where J ( z ) is specified as the limit of (8) first, and then k ( z ) is chosen so as to satisfy (7). From this construction an algorithm for numerical computations may be derived. A numerical design method which is general, computer implementable, and reliable, however, would not be obtained in this way for a number of reasons to be discussed below.\nExample: Consider the computation of J ( z ) at two discrete points z1,z2. Suppose that f ( zz ,u ) for i = 1 , 2 lie on certain segments of a straight line between z1 and 22, as indicated in Fig. 1. For computation purposes, let J ( z ) at intermediate points on this line be approximated by linear interpolation. Then, with l ( z , u ) 2 [(z), (8) results in\nJT+l(zz) 2 ((ZZ) + ( J T ( X 3 ) ) .\nJ O ( 2 , ) = 0\nfor i = 1,2, and thereby\ni.e., the iteration diverges if e(zi) # 0, (i = 1 , Z ) . Such a divergence may occur even when the discretization density is arbitrarily high. To see this, consider a continuous time plant with a flow of trajectories as shown in Fig. 2 and a path length from zt to zt+l of (?(ut) . IIxtJI, where a(.) E [0,1/10] is continuous. (Note that the discrete time mapping ( z t ,u t ) -+ zt+l is continuous, although the under0 lying continuous time system is not.) 3Different from [12], a control Lyapunov function is not assumed differentiable nor continuous here.\n35\nD. The Problem of a Reliable Numerical Feedback Design\nLet us assume that an analytic solution to the feedback design problem is not available and, therefore, a pointwise numerically computed solution is wanted. Assume further that any cost of computation in terms of storage and computation time would be acceptable, provided two things: First, it must be guaranteed that, no matter what the plant is, if there exists a solution to the problem, then the implemented design algorithm will find one. And second, the associated cost of computation must be finite. These are the main requirements being pursued here for a reliable numerical feedback design method.\nIt is evident that the feedback construction (7), (8) cannot be used for numerical computations unless modifications such as approximations, interpolations, and parameterizations are made. For a reliable design method, all such modifications must be included in an extended theoretical background and, in particular, the stability of the feedback loop must be established theoretically for a controller, which is defined and can be computed by a finite implementable algorithm.\nIn this sense, this paper seeks to extend the above background theory toward a reliable numerical feedback design. There are at least three basic subproblems involved:\nThe bounded computing region problem: The computations must involve G, the desired stability region. They must also involve ro, the region of closed-loop system trajectories (3, which is typically unknown and larger than G. So one has to set up a sufficiently large computing region to include T'O. But then the computing region may contain points or subsets where J(n:) is undefined, which is numerically intractable.\nMoreover, when computing J ( x ) , the term J ( f (n : , U ) ) in (6) or (8) can be evaluated only at points f ( z , u ) within the computing region. But in most cases, the possible trajectories of the plant cannot but leave the computing region from certain points or subsets. Ways of handling this problem will introduce systematic errors, which may propagate far into the computing region through the need of interpolation. The finite parameterization problem: Since only finite computer storage is available, J ( z ) as well as k ( z ) must be parameterized by a finite number of parameters.",
            "36 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 39, NO. 1, JANUARY 1994\nThe parameterization should be of a standardized type, B. Practical Control Lyapunov Function applicable to all plants P, which are asymptotically controllable. It is well known [22] that certain plants cannot be stabilized by a continuous k(x) (see also Section V for an example). Hence, at least for the feedback, the parameterization must also be capable of representing discontinuous functions.\nWith a finite, standardized type of parameterization, both J ( x ) and k ( x ) can only be represented within limited accuracy. But a parameterized feedback, which is in this way constrained and nevertheless asymptotically stabilizes the plant, may not exist. iii) The systematic error propagation problem: If J T ( x ) is represented in parameterized form with limited accuracy, then systematic errors are introduced in (8), and the iteration may diverge. As the above example shows, this can occur even when the parameterization density is good enough for representing the true functions within an arbitrarily small, nonzero error bound. As a consequence, even with highest parameterization accuracy, an accumulation of systematic errors to substantial amounts may occur, and, therefore, the computed JT(z) is not guaranteed to be a control Lyapunov function. Accordingly, a feedback k(x), which is computed from J T ( z ) , is not ensured to be stabilizing from G to the origin.\nTo account for the above and related problems, the present paper uses three modifications: First, practical asymptotical stability is used, which can be made arbitrarily close to asymptotical stability. Second, a cost criterion with terminal cost and free terminal time is used. And third, a parameterized controller which is piecewise constant in the state space is used, where the parameterization density remains as a free design parameter. These ingredients are properly combined to a theoretically founded, reliable numerical feedback design method, which also includes a numerical stability test.\n111. PRACTICAL STABILITY AND FEEDBACK CONTROL\nA. Practical Asymptotical Stability\nIn an asymptotically stable system, all trajectories will go to the origin asymptotically. We say that a system is practically asymptotically stable if its trajectories go to a neighborhood of the origin\n(9)\nasymptotically in a way as specified by the following definition.\nDejinition 3 (Practical Asymptotical Stability): A feedback system xt+l = f(zt, k(xt)) is said to be practically asymptotically stable from G to N(ro) , if there exists a ~ ( r , t ) E K,, such that for all x E G\nN ( r ) := { x E R n ~ ~ ~ x ~ ~ 5 r }\nll&(x)II + llk(4:(x))ll I max{ro, 4l l4 l>t)}7\n. _\nAs a candidate of a practical control Lyapunov function, i.e., a control Lyapunov function for practical asymptotical stability, we define the extended cost criterion\nrt'-i 1\nIt differs from the infinite time horizon criterion J ( x ) through the fact that it considers the cost over all possible finite time horizons with terminal cost V and takes the infinium of these.\nThroughout the paper, unless otherwise stated, let !(x,u) and V ( x ) be continuous and positive definite, with estimates %, pe, gp -% E Kp such that for all x E R\", U E R\"\n~ e ( l l ~ l l ) + (Pe(llxll) I '(x, U ) 5 (Pe(Ilx11) + (Pe(llull) (12) (13) g~(l l~ l l ) 5 V ( 4 5 (PV(11~11)\nand with a bounded region c R\" such that\ne(., U ) > v ( x ) V x 61 r, U E R\" . (14)\nWe start the investigation of V ( x ) by writing the term for t' = 0 separately in (1 l), which gives the equivalent representation of V ( z ) as\nf r t ' - i\nFour properties of V ( x ) , which are fundamental for the subsequent theoretical results and the numerical computation of V ( x ) and k ( z ) by a finite algorithm, follow as immediate consequences of the above definitions.\ni) V ( x ) satisfies the inequality\nV ( x ) 5 V ( x ) V x E R\" (16)\ni.e., V ( x ) is well-defined everywhere, no matter whether the plant is asymptotically controllable or e(x ,u) is summable along appropriate trajectories.\nii) By inequality (14) we further obtain\nV ( x ) = V(.) v z 61 i? (17)\ni.e., outside F the function V is known a priori, and so a computation of V reduces to the bounded, known region F. iii) For the computation of V ( x ) in r, only the bounded set of controls\nwhere i: := sup,,^ 11x11 needs to be considered. This is because it follows from (16) that the summation term in (15) can be relevant only if !(&,ut) 5 v ( x ) for all t E [O, t']. Using (10) this gives ye((lutll) 5 V(x) and, thus, ut E v. t E Z o + . (10) 0 Note that practical asymptotical stability specializes to asymptotical stability in the limit, when TO = 0."
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.35-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.35-1.png",
        "caption": "Figure 8.35 Shear stress varies linearly with radial distance.",
        "texts": [
            " \u2022 For a given shaft and applied torque, the torsional shear stress T is a linear function of the radial distance r measured from the center of the shaft. The shear stress is distributed non uniformly over the cross-sectional area of the shaft. At the center of the shaft, r = 0 and T = O. The stress-free centerline of the solid circu lar shaft is called the neutral axis. The magnitude of the torsional shear stress increases in the direction from the center toward the rim, and reaches a maximum on the circumference of the shaft where r = ro and T = Mrol J (Figure 8.35). \u2022 Torsion formula takes a special form, T = 2M/rrr 0 3, at the rim of a solid circular shaft for which J = rrr 0 4/2. This equation in dicates that the larger the radius of the shaft, the harder it is to deform it in torsion. \u2022 Since y = T 1 G = Mr 1 G J , the greater the magnitude of the ap plied torque, the larger the shear stress and shear deformation. The greater the shear modulus of the shaft material, the stiffer the material and the more difficult to deform it in torsion. \u2022 The shear stress discussed herein is that induced in the trans verse planes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003537_annals.1389.024-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003537_annals.1389.024-Figure4-1.png",
        "caption": "FIGURE 4. Distribution of t-force and axonemal distortion. When the dyneins on one side of the axoneme engage and generate tension to bend the flagellum, as shown in (A), most or all of the tension ends up accumulated on doublet 1 and doublets 5 and 6. As a consequence most, or all, of the global t-force (see text for description of global t-force) will be exerted across the axoneme from doublet 1 to doublets 5 and 6. This positions the t-force to put stress on the cp and spoke linkages as well as the attached dyneins. Which of these two pathways experiences the greater share of the t-force tension will depend in great measure on the mechanical properties of the spoke\u2013cp axis. After the dynein bridges release, as shown in (B), all of the t-force must be held by the spoke\u2013cp axis and the nexin links. This will produce a distortion of the axoneme as illustrated in (B). The extent of the distortion will depend on the mechanical properties of the spoke\u2013cp axis. Adapted from Lindemann27; reproduced with permission.",
        "texts": [
            " Applying the same quick-freeze deep-etch technique to rapidly frozen beating flagella might confirm that such a transition to the undocked state is present in the strongly bent regions of actively beating flagella. If, in fact, the axoneme is using t-force to switch the dyneins, then the t-force will be acting to distort the axoneme during the beat cycle. When the dyneins release from their cross-bridged active configuration the doublets should recoil away from each other in response to the unsupported t-force acting on the nexin links and spokes as illustrated in FIGURE 4. This raises the second issue for experimental verification: 2. Does the axoneme distort during the beat cycle? Recently, Sakakibara et al. used AFM to demonstrate that the action of the dynein motors results in an oscillation of the axoneme diameter in immobilized sea urchin flagella.34 This would indicate that engagement of the dynein motors alters the inter-doublet spacing, which is consistent with the Geometric Clutch hypothesis. Additionally, the transmission electron microscope (TEM) images presented by Mitchell using a fixation technique that successfully preserved the waveform of the Chlamydomonas beat, appear to show that the axoneme becomes wider in the bent regions.35 This is exactly what would be expected if the t-force were distorting the axoneme, as in FIGURE 4. While these observations are suggestive, more definitive evidence is needed to confirm that the inter-doublet distances change during the normal beat cycle. The changes in spatial relationships within the axoneme of active flagellar or cilia should be visible in freeze fracture replicas of fast frozen flagella or cilia, such as those so elegantly presented by Goodenough and Heuser.30,36 The new technique of Cryo-EM tomography should also be capable of seeing the change in doublet separations if vitrified specimens of active flagella are examined",
            "41 The Geometric Clutch mechanism suggests that anchoring the doublets at the tip rather than the base should also be able to restore beating, and in that case the direction of bend propagation should be reversed, as illustrated in FIGURE 5. This prediction remains to be tested. When a flagellum or a cilium beats, the dyneins on the doublets of one hemicircle of the axoneme must work together to generate the tension that bends the flagellum. This means that in most cilia or flagella the dyneins on doublets 1, 2, 3, and 4 work together to bend the axoneme in one direction and the dyneins on doublets 6, 7, 8, and 9 work together to bend the axoneme in the opposite direction (see FIG. 4). The force that is contributed by the concerted action of each of these two dynein groups ends up as tension and compression on doublets 1 and 5\u20136. In the flagella and cilia of metazoans, the 5\u20136 doublets are permanently bridged and act as a unit. Consequently, all (or most) of the tension contributed by the dyneins ends up directed across the center of the axoneme. This also means that most, or all, of the t-force that develops acts across the central axis as well. Since the radial spokes from doublets 1 and 5\u20136 appear to interact with the cp projections this raises the question of the role of the spoke\u2013cp axis in the distribution of the t-force, as illustrated in FIGURE 4. There are many unanswered questions regarding the role of the spoke\u2013cp axis in managing the t-force. In the context of the Geometric Clutch mechanism this is a crucial issue; the points of major interest are illustrated in FIGURE 6. The flexibility of the cp projections could play a role in governing the distribution of t-force between the dyneins and the spokes. The more the t-force that is carried by the spoke\u2013cp axis, the less t-force the dynein motors will experience; thus, a greater curvature will develop before dynein disengagement occurs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure16-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure16-1.png",
        "caption": "Fig. 16 Some 3-DOF PPR-equivalent PMs of family 2: \u201ea\u2026 2-\u201eR RR\u2026NRa-\u201eR RPR\u2026A, and \u201eb\u2026 2-\u201eP RR\u2026NRa-\u201eP RPR\u2026A",
        "texts": [
            " For instance, Fig. 17 shows a 2-RP U-UP U PPR-equivalent PM. This PM is obtained from the 2- RP R NRa-RA RP R BRA PPR- NOVEMBER 2005, Vol. 127 / 1119 3 Terms of Use: http://asme.org/terms Downloaded F equivalent PM shown in Fig. 14 b by substituting a combination of two successive R joints with nonparallel axes with a U joint. As compared with the original PM, the variation has fewer links. It is also noted that PPR-equivalent PMs proposed in 15 are in fact the variations of the PPR-equivalent PMs shown in Fig. 16, which are obtained by a substituting a combination of two successive R joints with nonparallel axes with a U joint and b replacing the unactuated P joints each with a planar parallelogram. Virtual chains have been introduced to represent the motion patterns of 3-DOF motions. A procedure for the type synthesis of 3-DOF PPR-equivalent PMs has also been proposed. Using the 1120 / Vol. 127, NOVEMBER 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 proposed procedure, 3-DOF PPR-equivalent PMs are synthesized in three steps: a type synthesis of legs, b type synthesis of 3-DOF parallel kinematic chains, and c selection of actuated joints"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure15.22-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure15.22-1.png",
        "caption": "Figure 15.22 Perfectly elastic collision of two pool balls.",
        "texts": [
            " If the collision were a perfectly elastic one (i.e., e = 1), then Eqs. (v) and (vi) would yield (vIjh = 0 and (VIj)y = (vlih. Therefore, Impulse and Momentum 333 334 Fundamentals of Biomechanics the velocity vectors for the balls after the collision would be: JLlj = 3.54 i (m/s) JL2j = 3.541 (m/s) Immediately after the collision, the target ball would move with a speed of 3.54 ml s along the positive x direction (toward the comer pocket) and the cue ball would move with the same speed along the positive y direction, as illustrated in Figure 15.22. The balls would move at right angles to each other after the collision. 15.8 Angular Impulse and Momentum The rotational analog of linear momentum is called angular mo mentum. Angular momentum is defined as the product of the mass moment of inertia and the angular velocity of the body un dergoing rotational motion and is commonly denoted with L: L = I w (15.17) The impulse-momentum theorem for rotational motion relates ap plied torque and change in angular momentum. If a torque with magnitude M is applied to a rotating body in the time interval between tl and t2 so that the angular momentum of the body is changed from Ll to L2, then the impulse-momentum theorem for rotational motion states that: (15"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003134_56.808-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003134_56.808-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic top view of a hexapod showing leg numbering, boundary lines for foot placing. and reachable areas of legs. (b) The reachable area o f each leg.",
        "texts": [
            " Based on the above observations, the tripod gaits for straight-line walking over flat terrain can be generalized to cover the case of tripod gaits on constant slope terrain. Thus we have the following theorem: Theorem 5 Assume a hexapod is to walk on a constant slope plane with slope angle 0. The tripod gait for straight-line walking with stability margin S is as follows: 1 ) The foothold positions are as shown on Fig. 3(a). 2) The sequence of movement for body and legs is as given by Similarly, for crab walk on a slope plane, the forbidden areas for the triangular support pattern could be redefined as shown in Fig. 1 1, and we have the following hexapod tripod gait as given by Theorem 6. Theorem 6 Assume a hexapod is to walk on a constant slope plane with slope angle 8. The crab-walk tripod gait of a hexapod, at crab angle a and with stability margin S, is as follows: 1) The foothold positions are as shown on Fig. 8. 2) The sequence of movement for body and legs is as given in 4) The duty factor (23) A (0, a , 0) + 2A(O) + 26(a) 2A(0, a , 0)+2A(0)-2S+26(a) \u2018 P(S, a , e ) = Remark 5: Theorem 6 is a very general result that quantitatively characterizes the foothold positions, the stability margin, and the sequence of movement of body and legs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure9-1.png",
        "caption": "Fig. 9 \u201ea\u2026 2-\u201eRRR\u2026NRa-RA\u201eRRR\u2026BRA PPR-equivalent parallel kinematic chain with a PPR virtual chain added; \u201eb\u2026 2-\u201eRRR\u2026N Ra-RA\u201eRRR\u2026BRA PPR-equivalent parallel kinematic chain",
        "texts": [
            " 8 e and the RR B RRR A leg Fig. 8 f are both a 1- -system. The axis of the basis wrench is perpendicular to the axes of all the R joints within a same leg. All the legs for PPR-equivalent PMs obtained are listed in Table 1. For legs with ci=0, one is interested in legs with simple structures: RUS, PUS, and UPS legs. 1 By assembling two or more legs for PPR-equivalent parallel kinematic chains shown in Table 1, we obtain parallel kinematic chains in which the moving platform can undergo a PPRequivalent motion Fig. 9 . The geometric relation between different legs has also been shown in the notation of legs we proposed in Sec. 7. To guarantee that the DOF of the moving platform is three, the wrench system of the parallel kinematic chain must be a 1- 0-2- -system Fig. 4 . NOVEMBER 2005, Vol. 127 / 1117 3 Terms of Use: http://asme.org/terms Downloaded F It is found that not arbitrary set of m, where m 2, legs can be used to construct an m-legged PPR-equivalent parallel kinematic chain since the union of their leg-wrench systems may be not a 1- 0-2- -system",
            " A PPR-equivalent parallel kinematic chain of family 3 has two legs with a 1- 0-1- -system and one leg with a 1- -system. The required legs can be selected from Table 1. By assembling these legs, we obtain PPR-equivalent parallel kinematic chains of family 3. For example, a set of two RRR NRa legs with a 1- 0-1 - -system and one RA RRR BRA leg with a 1- -system can be 1118 / Vol. 127, NOVEMBER 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 used to construct a 2- RRR NRa-RA RRR BRA PPR-equivalent parallel kinematic chain Fig. 9 b . A set of two RRR NRa legs with 1- 0-1- -system and one RR B RRR A legs with a 1- -system can be used to construct a 2- RRR NRa - RR B RRR A PPR-equivalent parallel kinematic chain Fig. 10 . It is learned from Table 2 that among the combinations of sets of leg-wrench systems, there is only one combination, the combination of three 1- 0-2- , in which all the leg-wrench system are of the same type. From Table 1, there is one type of leg, PP NRa, with a 1- 0-2- wrench system. Thus there is only one 3-legged PPR-equivalent parallel kinematic chain, 3- PP NRa Fig",
            " 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 parallel to the axes of the R joints within RRR N. It can be found that the sixth scalar components of 01, 2, 3, 1 1 and 1 2 and 1 3 are all equal to 0. Thus, the validity condition of the actuated joints Eq. 4 is not satisfied. The possible 2- R RR NRa - R R B RRR A PPR-equivalent PM is thus discarded. The possible 3-legged PPR-equivalent PM corresponding to the 2- RRR NRa-RA RRR BRA PPR-equivalent parallel kinematic chain Fig. 9 b is the 2- R RR NRa-R A RRR BRA PPRequivalent PM Fig. 12 b . The actuation wrenches of all the actuated joints are shown in Figs. 13 a and 13 c . In the R A RRR BRA leg Fig. 13 a , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axis of the unactuated RA joint and is parallel to the axes of the R joints within RRR B. In the R RR NRa leg Fig. 13 c , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not parallel to the axes of the R joints within RRR N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003684_j.matdes.2008.06.037-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003684_j.matdes.2008.06.037-Figure6-1.png",
        "caption": "Fig. 6. Measurement of a tooth temperature.",
        "texts": [
            " A Klingernberg PFS-600 Gear Lead/Profile tester apparatus was used to check the contact errors for all the experimental samples. The experimental setup was not stopped unless there was a tooth breakage or sudden thermal damage, as when the gears were stopped, the tooth flash temperature decreased immediately. Therefore, to observe the thermal damage on the surface of the gears, the gears were digitally photographed 20 times for every 10 min. The temperature of the tooth surface was measured and investigated using a non-contact temperature sensor that was installed in the experimental setup, as shown in Fig. 6. The non-contact infrared temperature sensors were mounted at a distance of about 6 mm from the contact surface of the test gear. The net surface temperature of the test gears was monitored continuously using a computer-based data acquisition system. Temperature of the tooth surface and the service life of the plastic gears were evaluated. After each experiment, the associated AISI 8620 gears were replaced with substitute gears and cleaned with a solvent. For each experimental condition, five gears were used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.29-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.29-1.png",
        "caption": "Figure 5.29 Carrying a load in each hand.",
        "texts": [
            "28, the unknown magnitudes F M and F J of the muscle and joint reaction forces can now be determined simply by trans lating W2, F M' and F J to point Q, and decomposing them into their components along the horizontal (x) and vertical (y) directions: FMy = FM sine FJx = FJ coscp FJy = FJ sincp For the translational equilibrium in the x and y directions: L,:Fx=O: LFy=O: Simultaneous solutions of these equations will yield: F _ cosifJ W2 M - cos e sin ifJ - sin () cos ifJ F = cos() W2 J cos () sin ifJ - sin e cos ifJ (xi) (xii) For example, if () = 70\u00b0, ifJ = 74.8\u00b0, and W2 = 0.83W (W is the to tal weight of the person), then Eqs. (xi) and (xii) will yield FM=2.6Wand FJ =3.4W. Applications of Statics to Biomechanics 105 How would the muscle and hip joint reaction forces vary if the per son is carrying a load of Wo in each hand during single-leg stance (Figure 5.29)? The free-body diagram of the upper body while the person is carrying a load of Wo in each hand is shown in Figure 5.30. The system to be analyzed consists of the upper body of the per son (including the left leg) and the loads carried in each hand. To counterbalance both the rotational and translational (down ward) effects of the extra loads, the hip abductor muscles will ex ert additional forces, and there will be larger compressive forces generated at the hip joint. In this case, the number of forces is five"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003371_1.2768079-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003371_1.2768079-Figure2-1.png",
        "caption": "Fig. 2 Arched ball bearing axially loaded",
        "texts": [
            " The radial contact angle for outer raceway r o can be written as r o = sin\u22121 go 2ro \u2212 D 1 A distance, which needs to be formulated, is the distance from the tip of arch to the bottom of the ball in radial contact position, as shown in Fig. 1. From this figure and using the Pythagorean theorem for h, hm = \u2212 D 2 \u2212 2rm \u2212 D 2 cos r m + 1 2 D 4rm \u2212 D + 2rm \u2212 D 2 cos2 r m 1/2 2 where m= i or m=o for inner or outer raceway, respectively. With h known, conventional bearing parameters can be formulated as Pd = Sd + 2 ho + hi 3 with Sd = do \u2212 d\u0304i \u2212 2 D + ho + hi 4 where d\u0304i is the inner raceway diameter after centrifugal growth has been considered 8 . The pitch diameter dm can be expressed as dm = d\u0304i + Sd 2 + D 5 Figure 2 shows the arched bearing while in the axial position. From this figure, the distance between the center of curvature of the inner and left-outer race can be written as A = ro + ri \u2212 D = BD 6 where B= fo+ f i\u22121. From the right hand side of Fig. 2, = ro \u2212 ro 2 \u2212 go 2 2 7 thus, the contact angle can be expressed as OCTOBER 2007, Vol. 129 / 80107 by ASME of Use: http://www.asme.org/about-asme/terms-of-use U o p r C r F s 8 Downloaded Fr f = arccos A \u2212 Pd/2 \u2212 A 8 nder external applied loads or imposed rotations and translations f the inner ring Fig. 3 , the raceway curvature centers reach final ositions, as schematically presented in Fig. 4. In this figure, the ight- and left-outer raceway groove curvature centers Cor and ol are fixed in space, whereas inner centers Cir and Cil moves elative to these fixed points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.12-1.png",
        "caption": "Figure 3.12 The net moment.",
        "texts": [
            " Therefore, the moment of force F y about point 0 is: M = r F y = r F sin 0 (cw) Note that this is also the moment dF generated by the resultant force vector F about point 0, because d = r sinO. Moment and Torque 33 34 Fundamentals of Biomechanics 3.6 The Net or Resultant Moment When there is more than one force applied on a body, the net or resultant moment can be calculated by considering the vector sum of the moments of all forces. For example, consider the coplanar three-force system shown in Figure 3.12. Let d1, d2, and d3 be the moment arms of F l' F 2' and L relative to point O. These forces produce moments M1, M2, and M:3 about point 0, which can be calculated as follows: M1 = d1 F1 M2 = d2 F2 M3 = d3 F3 (cw) (cw) (ccw) The net moment Mnet generated on the body due to forces F l' F 2' and L about point 0 is equal to the vector sum of the mo ments of all forces about the same point: (3.2) A practical way of determining the magnitude and direction of the net moment for coplanar force systems will be discussed next. Note that for the case illustrated in Figure 3.12, the individual moments are either clockwise or counterclockwise. Therefore, the resultant moment must be either clockwise or counterclock wise. Choose or guess the direction of the resultant moment. For example, if we assume that the resultant moment vector is clock wise, then the clockwise moments M1 and M2 are positive and the counterclockwise moment M:3 is negative. The magnitude of the net moment can now be determined by simply adding the magnitudes of the positive moments and subtracting the negatives: (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure24-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure24-1.png",
        "caption": "Fig. 24. Cylindrical worm thread surfaces in 3D space.",
        "texts": [
            " The stresses are represented as unitless parameters in function of the worm rotation rm1 \u00bc r1 rmax1 ; \u00f013\u00de rm2 \u00bc r2 rmax2 \u00f014\u00de where r1 and r2 are the bending and contact stresses of Mises and rmax1 and rmax2 are the maximum bending and contact stresses of Mises on the face-gear. In the example developed, rmax1 \u00bc 168 N/mm2 and rmax2 \u00bc 1090 N/mm2. The load is always shared by three pairs of teeth, therefore the contact ratio is 3. The discussed geometry of the drive is considered as a particular case of the geometry of the drive with a conical worm. The generation of the face-gear and the worm are based on the same principles as described in Sections 2\u20134. It requires application of tilted head-cutters, but generally of a larger tilt of the tool. Fig. 24 shows the cylindrical worm that is generated by a tilted head-cutter. The TCA has been performed for a gear drive of design parameters represented in Table 2. A predesigned parabolic function of transmission errors absorbs indeed the discontinuous functions of transmission errors caused by errors of alignments (Fig. 25(a)). Fig. 25(b) and (c) shows that the bearing contact of a misaligned gear drive is localized and directed longitudinally as designed. The bearing contact is localized, and the path of contact is directed longitudinally"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002609_027836402760475379-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002609_027836402760475379-Figure3-1.png",
        "caption": "Fig. 3. KUKA 361 IR robot.",
        "texts": [
            " A comparison between the WLS method and the ML method is also carried out in an experimental way. Direct comparison of the estimated robot parameters with the correct values is not possible because they are not available. Instead, the accuracy of the actuator torque prediction of the different models is compared. This is a valuable criterion, especially for applications that involve advanced robot control such as the computed torque control method. The methods are applied to estimate the parameters of the three first axes of the industrial KUKA 361 robot (see Figure 3) already mentioned in Section 4. Therefore, the same dynamic robot model and comparable excitation trajectories based on five-term Fourier series are used. Again the fundamental frequency of the trajectories is 0.1 Hz, the sampling rate is 150 Hz and the number of periods used for the estimations are 16, with 1500 samples in each period. Data is collected after the transient response of the robot has died out. Joint angles are measured by means of encoders mounted on the motor shafts, and actuator torques are measured indirectly by means of motor current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure8-1.png",
        "caption": "Fig. 8. Cross section of permanent magnet motor.",
        "texts": [
            " These motors use magnets to produce the air-gap magnetic field rather than using field coils as in the commutator motor or requiring a magnetizing component of sp <itor current as in the induction motor. Significant advantages arise from the reduction in losses and improvement in efficiency. The two most common types of PM motors are classified as 1) synchronous (i.e., with a uniformly rotating staltor field as in an induction motor) and 2) switched trapezoidal (i.e., with a stator field which is switched in discrete steps). The latter type is discussed in Section VI. PM motors are made in a number of configurations. One of the simplest is shown in cross section in Fig. 8. The rotor has an iron core which may be soliid or may be made of punched laminations for simplicity in manufacture. Thin permanent magnets are mounted on ihe surface of this core using epoxy adhesives. Alternating ma,gnets of opposite magnetization direction produce radially directed flux density across the air gap. This flux density then reacts with currents in windings placed in slots on the inner surface of the stator to produce torque. PM motors are normally constructed with totally enclosed rotors",
            " The magnets on PA4 rotors are normally magnetized before assembly. Special holding fixtures are required to prevent damage (due to forces encountered during assembly and disassembly. In Section IV, it was noted that the maximum airgap flux density in induction motors is usually in the range 0.7-0.9 T because magnetic saturation limits the flux density in the stator teeth to the range 1.4-1.8 T and because optimum design usually results in nearly equal slot and tooth widths [28]. Thus an ideal magnet material for use in the synchronous PM motor of Fig. 8 would be capable of producing an air-gap flux density with peak value similar to that in an induction motor. A . Permanent Magnets A review of the characteristics of the major PM materials provides a basis for appreciating the potential and limitations of PM motors. Magnetization characteristics of the most common magnetic materials currently used in motors are shown in Fig. 9. All of these PM materials have their magnetic domains well aligned resulting in an essentially straight-line relationship in much if not all of the second quadrant of the B-H loop",
            " Experience with other materials would however lead to an expectation of lower cost in the future as volume of use is increased since two of the basic materials iron (77%) and boron (8%) cost relatively little and neodymium is one of the more prevalent of the rareearth elements. Bonded NdFeB magnets can be produced at a considerably lower cost but the residual flux density is lower, i.e., about O . H . 7 T. B . Equivalent Circuit For the synchronous type of PM motor with surface magnets as shown in Fig. 8, the stator is essentially identical to that of an induction motor. The three-phase windings are each distributed to provide a near-sinusoidal distribution of linear current density around the air-gap periphery so that a set of phase currents, sinusoidally varying in time, will set up a field which is sinusoidally distributed peripherally and is rotating at an electrical angular velocity w,, i.e., a mechanical angular velocity of (2/p)w,. Each magnet may be viewed as a circumferential loop with a current of about 800B, amperes for each millimeter of magnet thickness",
            " These PM SI FUON: ELECTRICAL MACHINES FOR VARIABLE-FREQUENCY DRIVES I133 motors have the additional advantage that their mass and volume can be made considerably less than either induction or commutator motors of similar maximum torqut: rating [401. VI. SWITCHED OR TRAPEZOIDAL PM MOTORS The other major class of PM motor drives is alternatively known as trapezoidally excited motors, or brushless dc motors, or simply as switched motors [41 I. They have stator windings that are supplied in sequence with nearrectangular pulses of current. A cross section of one type of motor is shown in Fig. 13. In most respects, this switched motor is identical in form with the synchronous PM motor of Fig. 8. For this two-pole motor, the rotor magnets extend around approximately 180\" peripherally. The stator windings are generally similar to those of an induction or synchronous motor except that the conductors of each phase winding are distributed uniformly in slots over two arcs of 60' (or somewhat less in some designs). The windings of this type of motor are connected in a star comfiguriAon. The electrical supply system is designed to provide a current which can be switched sequentially to pairs of the three stator terminals",
            " Losses and EfSlciency Synchronous reluctance motors can have an advantage in efficiency over induction motors of similar rating. The rotor loss which accounts for about 20--30% of the induction motor losses is small or negligible. If the saliency ratio is sufficient to produce a power factor equal to that of the induction motor, the stator winding loss will be the same. Also, the stator iron losses will be similar for the two motors. SLEMON: ELECTRICAL MACHINES FOR VARIABLE-FREQUENCY DRIVES 113s VIII. PM-RELUCTANCE MOTORS The surface PM motor considered earlier (Fig. 8) 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. Figure 15 shows a cross section of an inset PM motor. The magnets are inset into the rotor iron [33]. As a Ph4 motor, the direct axis is aligned with the magnets. Coiisidered as a reluctance machine, its direct-axis inductance will be small because of the near-unity relative permeabilily of the magnet material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.15-1.png",
        "caption": "Figure 13.15 Inverted pendulum.",
        "texts": [
            " In this range, the angular displacement of the trunk assumes negative values. The purpose of this example is to illustrate the means of ana lyzing experimentally collected data. The specific task is to find a function that can express the angular displacement of the sub ject's trunk as a function of time, from which we can derive ex pressions for the angular velocity and acceleration of the trunk. Solution: The problem may be easier to visualize if we form an analogy between the upper body and a mechanical system called the inverted pendulum, shown in Figure 13.15. An inverted pendulum consists of a concentrated mass m attached to a very light rod of length e that is hinged to the ground through an axis about which it is allowed to rotate. In this case, the concentrated mass represents the total mass of the upper body. The hinge corresponds to the disk between the fifth lumbar vertebra and the sacrum, about which the upper body rotation occurs in the sagittal plane. Length e is the distance between the fifth lumbar vertebra and the center of gravity of the upper body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002466_s004220050558-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002466_s004220050558-Figure2-1.png",
        "caption": "Fig. 2. a The stance leg is modeled by a linear variable sti ness CLEG and damping jLEG. b The resulting force-elongation (F - dL) relationship is realized by two muscles",
        "texts": [
            " Although the force length relationship is assumed to be linear, the sti ness can be varied with the level of activation. Since a muscle can be loaded by a tension force only at least two muscles are needed to work as an agonist-antagonist couple under a pre-tension U0 . Increasing the sti ness of both the muscles by an equal amount results in an increase in joint sti ness, similar to co-contraction in biological organisms (Winters et al. 1988). The stance leg elongation is modeled by a linear spring-damper combination with sti ness CLEG and damping jLEG (Fig. 2a), here realized by two muscles (Fig. 2b). This simpli\u00aecation is often made in biomechanical models of running (Alexander 1984; McMahon 1984). The hip joint is modeled by a rotational springdamper combination with sti ness CHIP and damping jHIP (Fig. 3a), here realized by two \u00afexor-extensor muscle pairs (Fig. 3b). With the sti ness and damping terms added to (1), the complete equations of motion can be written in the following general form: M x x N x; _x _x G x C x D _x 2 where C x 3 1 sti ness matrix, D _x 3 1 dissipation matrix. The matrices M;N;G;C, and D are derived and given as a function of system parameters in Appendix A",
            " Muscle activation dynamics is neglected, so the sti ness change is instantaneous. For the bipedal model, the trigger events are chosen intuitively as follows. The push-o trigger signal is chosen to be the stance leg angle reaching a critical value uPO (Fig. 4) on tPO. In orbit the trailing leg angle at the beginning of the step n Un TL equals the trailing leg angle at the beginning of the step n 1 Un 1 TL . Therefore, uPO cannot be chosen larger than UTL. During the push-o phase the stance leg plantar \u00afexor sti ness (Fig. 2b) will be increased by dCLEG. The push-o phase ends when the swing leg hits the ground. The hip activation is triggered at the beginning of the swing phase. During the activation period the swing leg hip extensor, and the stance leg hip extensor (Fig. 3b) are increased in sti ness by dCHIP. In the model, the inertia of the hip mass is assumed to be zero, so if the orientation of the body is to remain near vertical, a swing leg extensor and contralateral extensor are equally activated. The hip activation phase ends after a time DtHIP has elapsed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003728_j.cnsns.2009.01.001-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003728_j.cnsns.2009.01.001-Figure2-1.png",
        "caption": "Fig. 2. Position of the centre of mass of the cylinder i.",
        "texts": [
            " (24) it can be concluded that two matrices playing the roles of the inertia matrix and the Coriolis and centripetal terms matrix are: IP jB T \u00f027\u00de d dt IP jB T \u00f028\u00de It must be emphasized that these matrices do not have the properties of inertia or Coriolis and centripetal terms matrices and therefore should not, strictly, be named as such. Nevertheless, throughout the paper the names \u2018\u2018inertia matrix\u201d and \u2018\u2018Coriolis and centripetal terms matrix\u201d may be used if there is no risk of misunderstanding. If the centre of mass of each cylinder is located at a constant distance, bC, from the cylinder to base platform connecting point, Bi, (Fig. 2), then its position relative to frame {B} is: BpCi jB \u00bc bC l\u0302i \u00fe bi \u00f029\u00de where, l\u0302i \u00bc li klik \u00bc li li \u00f030\u00de li \u00bc BxP\u00f0pos\u00de jB \u00fe Ppi jB bi \u00f031\u00de The linear velocity of the cylinder centre of mass, B _pCi jB , relative to {B} and expressed in the same frame, may be computed as: B _pCi jB \u00bc Bxli jB bC l\u0302i \u00f032\u00de where Bxli jB represents the leg angular velocity, which can be found from: Bxli jB li \u00bc BvP jB \u00fe BxP jB Ppi jB \u00f033\u00de As the leg (both the cylinder and piston) cannot rotate along its own axis, the angular velocity along l\u0302i is always zero, and vectors li and Bxli jB are always perpendicular"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003429_tia.2006.887234-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003429_tia.2006.887234-Figure5-1.png",
        "caption": "Fig. 5. Circuit model of SynRM with equivalent stator iron loss resistance.",
        "texts": [
            " In addition, extremely small currents are rarely used for the commanded id to stabilize the main flux level. Thus, we did not use the measured Ld values for id = 1 A for the identifications. Similarly, we attached greater importance to normal operation current than to large current unused in normal operation. As a result, although we did not employ an assumption such that both d- and q-axes fluxlinkages converge to the same level at large current [1], the total identification error of Ld from id = 3 A to id = 10 A was practicably minimized. Fig. 5 shows a circuit model of SynRMs with an equivalent stator iron loss resistanceRm [6]. In Fig. 5, the relation between currents and flux linkages is written as   iaib ic   =   ima imb imc   + 1 Rm P    \u03bba \u03bbb \u03bbc     (5) where  \u03bba \u03bbb \u03bbc   =   La Mab Mca Mab Lb Mbc Mca Mbc Lc     ima imb imc   La = ls + Lg0 \u2212 Lg2 cos(2\u03b8re) Lb = ls + Lg0 \u2212 Lg2 cos(2\u03b8re + 2\u03c0/3) Lc = ls + Lg0 \u2212 Lg2 cos(2\u03b8re \u2212 2\u03c0/3) Mab = \u2212Lg0/2 \u2212 Lg2 cos(2\u03b8re \u2212 2\u03c0/3) Mbc = \u2212Lg0/2 \u2212 Lg2 cos(2\u03b8re) Mca = \u2212Lg0/2 \u2212 Lg2 cos(2\u03b8re + 2\u03c0/3). Here, P is the differential operator (= d/dt), Rm is the equivalent iron loss resistance (in ohms), and ls is the armature leakage inductance (in henry)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002491_027836499401300404-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002491_027836499401300404-Figure4-1.png",
        "caption": "Fig. 4. The forbidden parts of the trajectory are drawn in dashed lines. The gray zones are forbidden zones of the workspace. On the left the constraints are only the link lengths, and on the right there is a constraint on one of",
        "texts": [],
        "surrounding_texts": [
            "329\n2.3.1. Distance Betrveen the Lines\nThe distance l12 between the lines associated with links 1\nand 2 can be written as:\nBecause\nthe inequality l12 2 < d leads to a second-order inequality P~ (a) > 0. The intervals .~d on A included in [0,1] such that PI (A) is positive define the parts of the trajectory for which the distance between the lines is less than or equal to d.\nLet Q~, Q2 be the points on lines 1,2 belonging to their common perpendicular. If these points belong to the links for some values of A in Id, then there is link interference. We define al, a2 by:\nConsequently, point Qi belongs to link i if ai is in [0,1]. Using equation (10), o;],o;2 can easily be obtained as:\nwhere the r, s, t are constants. Let 7~ be the intervals included in [0,1] such that 7~ is positive or equal to 0 (i.e., ai > 0) and IFi be the intervals in [0,1 ] where P~~ - Pd(A) is negative or equal to 0 (i.e., az < 1). We may remark that all these intervals can be easily obtained from the above equations. The set ID of intervals of A in [0,1] where the distance between the links is the distance between the lines and is less than d is therefore:\n- - - -\nIf Id is an empty set, the distance between the lines (which is a lower bound of the distance between the links) is always greater than d, and therefore link interference cannot occur. If Id is not empty and ID is empty, we cannot state whether the distance between the links is less than d, as this distance is always greater or equal to the distance between the lines. The distance between the links is therefore different from the distance between the lines.\n2.3.2. Distance Between the Points Bi and Their Projections\nThe distance l from point Bj to line 2 can be written as:\nThe inequality l < d leads to a second-order inequality n2 _ Pl \u2019 (.-B) 2: 0, and interference will occur if the projection Q of Bl on line 2 belongs to link 2. We define 01 such that A2Qi = ,QtA2B2, and the above condition will be fulfilled if (3\u00a1 belongs to [0,1]. Equations (2) and (1) lead to:\nLet Tgj be the intervals included in [0,1 such that\nThe set of intervals\nI~j , i, j E [ 1, b], i ~ j defines the components of the :\ntrajectory for which interference occurs between links i and j.\n2.3.3. Distance Between the Points A2 and Their Projections\nThe distance lA~ from point A1 to line 2 is:\nThe components of the trajectory for which link interference occurs are defined by the intervals such that 1 A2 - d < 0, which is equivalent to a second-order\nI\n~2 inequality PA\u2019 (A) > 0 under the condition that the projection ~1 of ~4i on line 2 belongs to link 2. We define /-l1 such that A2Qi = pIA2B2 and ~1 belongs to link 2 if ~C1 is in [0,1 ]. Equations (2) and (1) lead to:\nwhere the a, b, f are constants. Let IAi denote the in-\ntervals included in [0,1 such that Pi A2 > 0 (IA12 < c0,\nP2 2 > 0 (W >_ 0), ~ - Q(A) :::; 0 (~1 :::; 1). The set of intervals IA; , i, j E [ 1, 6], I # j defines the components\ni , _\nof the trajectory on which interference between links i and j occurs.\n2.3.4. Distance Between Points Ai and Bj The distance between points A2 and B} can be written as:\nat UQ Library on March 13, 2015ijr.sagepub.comDownloaded from",
            "330\nwhich is a second-order polynomial in A. We denote by IAi B~ the intervals of A included in [0,1] such that PAiB/\u00c0) - d2 S; 0. These intervals define the parts of the trajectory for which the distance from Bj to Ai is less than d. An analysis of this inequality (Merlet 1993b) enables us to establish the following rule:\nRule 7: Let a be the angle between the vectors Aimi + CBj, MiM2. If the distance between the points A2 and Bj is greater than d when the endeffector location is M1 and M2, then the distance between these points will be less than d for some C on the line joining M] and M2 if and only if:\nThe union had of all the forbidden intervals for A for each constraint describes the parts of the trajectory that are outside the workspace. We get:\n2.4. Computation Time\nThe above algorithms have been implemented in a workspace computation program. This program is written in C on a Sun Sparc2 workstation. The computation time for verifying the link lengths constraints is approximately 1.6 ms if the trajectory is correct and 2 ms if some points are outside the workspace. A computation time of 1.34 to 1.72 ms is necessary for checking link interference between a pair of links. As for the mechanical limits on the passive joints, the computation time for one face of one pyramid is approximately 0.3 ms.\nIf we check all the constraints, the computation time for a trajectory is approximately 29 ms. Such a time seems to be adequate with a real-time computation.\n2.5. Examples\nWe have performed trajectory verification for a prototype of a parallel manipulator developed by Arai et al. (1990) at the Mechanical Engineering Laboratory in Tsukuba (Figs. 4 and 5).\n3. Trajectory With a Varying Orientation In the case of a constant orientation we have seen that the constraints can be expressed under the form of algebraic equations in the variable A. If we now introduce a varying orientation, we have no more algebraic constraints,\nthe base joints (computation time: 1. 99 ms and 3.16b ms j.\nas A will appear in the sines and cosines of the rotation matrix.\nTo get algebraic constraints equations, we split the trajectory in elementary parts such that the change in the orientation will be small. As the orientation will affect\nonly the vector CB, we will use a first- or secondorder approximation for this vector. Let Mi, M2 denote the extremities of one elementary part of the trajectory; \u2019ljJ1, 01, CPI the angles describing the orientation of the end effector at point M1; and ~2~2. CP2 the angles of the end effector at point M2. Between points M, and M2 (Fig. 6)\nat UQ Library on March 13, 2015ijr.sagepub.comDownloaded from",
            "331\nthe position of point C is defined by equation (1), and the orientation angles can be written as:\nUsing a first- or second-order approximation of CB leads to:\nwhere the vectors Ul, U2 are only dependent on the relative position of B and the angles V)1,01,01 and ~2~2.~2- Under this assumption we may now analyze the various constraints on an elementary part T of the trajectory.\n3.1. Link Length Constraints\nBy using equation (1) and a second-order approximation (23), we obtain the square of the link length p2 as a third-order polynomial Pp(A). As for the constant orientation case, the analysis of the polynomial PP(~) - Pmax2, ~PP(~) - Prrun enables us to compute the intervals of A in [0,1 such that the link length is greater than its maximum value or lower than its minimal value.\n3.2. Constraints on the Passive Joints\nUsing a second-order approximation of CB (23) together with equation ( 1 ), the constraint equation (7) leads to a second-order inequality. Analysis of this inequality yields the intervals on A such that some point of the link lies outside the pyramid. By considering all the set of faces of every pyramid, we get those parts of the trajectory that do not satisfy the joints constraints. A similar analysis can be done for the passive joints of the mobile plate. The following simplification rules can be established (Merlet 1993b):\nRule 8: Let ni be the external normal to the face i of the pyramid describing the constraints on the base joint. Let U1, U2 be the vectors of the second-order approximation of CB. If, at the extreme points of T, the vector AB lies inside the pyramid with respect to face and if U2.n;T > 0, then the constraint on the joint is satisfied on the whole T. Rule 9: If, at the extreme points of T, the vector AB lies inside the pyramid with respect to face i, this constraint will not be satisfied at some points of T if and only if:\n3.3. Link Interference\n3.3.1. Distance Between the Lines\nLet ll~ denote the distance between lines 1 and 2. By using equation (1) and a first-order approximation (22), the inequality ll~ < d can be written as a fourth-order polynomial in A P(A) > 0.\nIf the common perpendicular points Ql, Q2 of lines 1\nand 2 belong to the links, we get link interference. We define a], a2 such that A1Q1 = 0: 1 Al HI, A2Q2 = a2A2B2 and we get:\nwhere r, s, t are constants. We compute the intervals of [0,1] where P(A) > 0 (i.e., lt2 < c~, P(az) > 0 {i.e., ai > 0), P(c~z) - Pd :::; 0 (i.e., aj < 1). All these intervals can be easily derived from the analysis of the various polynomials. The intersection ID of all these intervals defines the components of T for which link interference occurs. If Id is empty, the distance between the lines (which is a lower bound of the distance between the links) is always greater than d. Consequently, the distance between the links is also always greater than d. If Id is not empty and ID is empty, we cannot conclude that the distance between the lines is less than d, but the distance between the links is greater than the distance between the lines.\n3.3.2. Distance Between the Points Bi and Their\nProjections\nThe distance l from point Bl to line 2 is given by equation (14). Using equations (1) and (23), the inequality\nr)2\n1 <_ d leads to a fourth-order inequality PB\u2019 (a) > 0. Link interference will occur if this inequality is satisfied and if the projected point Q, of B1 on line 2 belongs to link 2. We get\nQi will belong to link 2 if 01 is in [0,1]. Let Tgj be the\nintervals included in [0,1] such that PB~ > 0 (1 < dj,\nat UQ Library on March 13, 2015ijr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_8_0002856_0378-4371(92)90056-v-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002856_0378-4371(92)90056-v-Figure1-1.png",
        "caption": "Fig. 1. Coordinates for calculating the matrix D(lmm l'rn'tT') by reflection of a sphere in a plane. The image sphere lies in z < 0.",
        "texts": [
            "1) to show that the matrix elements of the resistance operator Z, and of the operator ~ /wh ich gives the mobilities, could be constructed from the matrix elements of A T, which are defined in the following manner: aT( r , r') ~ D(Imcr, l'm'o\") Vlmo.(r R1) ** ' = + - - V l ' m ' a ' ( r - R 1 ) , (3 .1 ) lmo' , l 'm'o\" D(lmo', l'm' o\") = ( w,+,~8~ IArlw,+~,~,a.) f 1 f = d r - a(lr- R~I - a ) d r ' 1 a(lr' - e l i - - O) Og a +* Wrm, ,(r - - e l ) (3.2) X w l m ~ ( r _ R l ) . A / ' ( r , r , ) . + , . Here the v t ~ ( r - R1) are a complete set of solutions to (2.1), regular for all r, defined in ref. [6] and in I in terms of spherical polar coordinates about the sphere centre at R 1 (see fig. 1). The mode labels l, m, o- are integers taking values l = 1, 2, 3 . . . . ]rn I ~< l, ~r = 0, 1, 2 as explained in ref. [6] and I. The + + w~m~(r-R1) are an adjoint set of functions orthonormal to the vt,,~ on a spherical surface of radius a about R1. The mathematical problem reduces to evaluating the integrals (3.2) using the expression (2.16) for AT. As explained in I, the general strategy for evaluating (3.2) reduces to first expanding the Oseen tensor T O (or the scalar function X) about the image sphere centre at - R 1 (see fig. 1) and then using a shift theorem for appropriate solutions to the Navier-Stokes equations [10] together with a reflection theorem to finally evaluate (3.2) by simple orthonormality relations. We will indicate the detailed procedures in the briefest possible manner here, putting most detailed results in the appendix. We first examine the contribution of A/'1 by using the expansion of / 'o (r - rR) about the image point -R~ derived in I, G.S. Perkins, R.B. Jones / Spherical-particle-phonon-boundary interaction H 453 To(r rR ) 1 E 1 ",
            "1) regular everywhere but at r = R, and the normalization factors ntm are 4w (l + m ) ! ) 1/2 n,m = ( Z - m ) ! \" (3.4) We use a shift theorem [10] to express the v~m~(r + R1) in terms of Vl+,m,a,(r - Ri) , 454 G.S. Perkins, R.B. Jones / Spherical-particle-phonon-boundary interaction H v~mo-(r+R,)= ~ S+-(2R1;Izmzcr2, t lm,6r1)V[mz~z(r-Rx) . (3.5) 12m2~r2 + t Finally, a reflection theorem derived in I enables us to express Vlm~(r R + R 1) in + t terms of Vl,m,c~,(r - R 1 ) , V/+mlo-1 (~, (~) : E e(l lm,o' l , 12m,0-2 ) Vl+mlcr2 (0, ~O), 12 o-2 (3.6) where 0 = -rr - 0 (see fig. 1). The contribution of AT\"~ to D, denoted by D~, can then be written as Da(lm~r, l'm'~r') = --~mm' 1 ~ 1 - --5-- S+-(2R1; lmo', 11mo-1) 77 /lO. 1 nllm \u00d7 e(lmmo'l, l 'm~r'). (3.7) The coefficients S +-(2R1; lmo', llmo\" ~) are defined by the shift theorem for the VTm ~ and are given explicitly in ref. [10] while the coefficients e(lm~r, l'mo~') are given in I. Since ]Rll = h, D~ depends on the normal distance to the wall h through the coefficients S +-. Next consider the contribution of AT 2. From (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002442_02783640122068218-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002442_02783640122068218-Figure2-1.png",
        "caption": "Fig. 2. Analytical model of two-degree-of-freedom swing leg.",
        "texts": [
            " In contrast, by means of the negative feedback from the shank joint angle \u03b83 to the input torque T at the thigh joint, the system\u2019s stiffness matrix becomes asymmetrical. Thus, the swing motion would change so that the shank motion delays at about 90 degrees from the thigh motion. Through this feedback, it is also expected that the kinetic energy of the swing leg increases and that the reaction torque (\u2212T ) will make the support leg rotate in the forward direction in a region where \u03b83 > 0. The self-excitation of the swing leg based on the asymmetrical matrix is explained in detail below. Figure 2 depicts the two-DOF swing leg model whose first joint is stationary. To make Figure 2 compatible with Figure 5b, the upper and lower links are termed the second and third links, respectively. To generate a swing motion like a swing leg, only the second joint is driven by the torque T2, which is given by the negative position feedback of the form T2 = \u2212k\u03b83. (1) From the fundamental study of the asymmetrical stiffness matrix-type self-excitation (Ono and Okada 1994a), it is known that damping plays an important role in inducing the at RUTGERS UNIV on August 11, 2015ijr.sagepub.comDownloaded from self-excited motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.68-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.68-1.png",
        "caption": "Figure 8.68 A bench test.",
        "texts": [
            " A structure may be subjected to two or more of these loads simul taneously. To analyze the overall effects of such combined load ing configurations, first the stresses generated at a given section of the structure due to each load are determined individually. Next, the normal stresses are combined (added or subtracted) together, and the shear stresses are combined together. The fol lowing example is aimed to illustrate how combined stresses can be handled. 190 Fundamentals of Biomechanics Example 8.9 Figure 8.68 illustrates a bench test performed on an intertrochanteric nail. The nail is firmly clamped to the bench and a downward force with magnitude F = 1000 N is applied. Determine the stresses generated at section bb of the nail which is located at a horizontal distance d = 6 em measured from the point of application of the force on the nail. The geometry of the nail at section bb is a square with sides a = 15 mm. Solution: The nail is hypothetically cut into two parts by a plane passing through section bb, and the free-body diagram of the proximal part of the nail is shown in Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.35-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.35-1.png",
        "caption": "Figure 4.35 Vector method.",
        "texts": [
            " Now, consider the rotational equilibrium of the beam in the x direction: MAx = M2 = 24N-m (-x) For the rotational equilibrium of the beam in the y direction: MAy =0 Finally, the rotational equilibrium of the beam in the z direction requires that: LMz=O: MAz = Ml = 36 N-m (-2) Therefore, the reactive moment at A has two non-zero compo nents in the x and y directions. Now that we determined the components of the reactive force and moment at A, we can also Statics: Analyses of Systems in Equilibrium 69 calculate the magnitudes of the resultant force and moment at A: RA = J RAx2 + RAy2 + RAz2 = RAy = 120 N MA = J MAx2 + MAl + MAz2 = 43.3 N-m The second method of analyzing the same problem utilizes the vector properties of the parameters involved. For example, the force applied at C and the position vector of point C relative to A can be expressed as (Figure 4.35): P = - P i = -120 i r.. = -b \u00a3 + a If = -0.30 \u00a3 + 0.20 If Here, f, j, and If are unit vectors indicating positive x, y, and z directions, respectively. The free-body diagram of the beam is shown in Figure 4.36 where the reactive forces and moments are represented by their scalar components such that: First, consider the translational equilibrium of the beam: RA + P = 0 (RAx \u00a3 + RAy i + RAz If) + (-120 D = 0 RAx \u00a3 + (RAy -120) j + RAz If = 0 For this equilibrium to hold: RAx = 0 RAy = 120 N (+y) RAz = 0 As discussed in the previous chapter, by definition, moment is the cross (vector) product of the position and force vectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003371_1.2768079-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003371_1.2768079-Figure7-1.png",
        "caption": "Fig. 7 Left-inner-race contact",
        "texts": [
            " he equations for the inertia forces and moments on the ball j can e written as Fxj = 0 17 Fyj = 0 18 Fzj = mb 1 2 d\u0304m mj 2 19 M\u0304xj = 0 20 M\u0304yj = J Rj mj sin j 21 M\u0304zj = \u2212 J Rj mj cos j sin j 22 ith d\u0304m the pitch diameter when dynamic effects have acted on he ball defined by d\u0304m = dm + 2 fo \u2212 0.5 D + ol cos ol \u2212 2 fo \u2212 0.5 D cos f 23 ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms From Fig. 6, x = R cos cos 24 y = R cos sin 25 z = R sin 26 Internal Kinematics. Figure 7 shows the contact of the ball with the left-inner race. Assume that the ball is fixed in the plane of the paper. Let the inner race rotate with angular velocity i. According to Hertz, the radius of the elastically deformed surface in the plane of the major axis of the pressure ellipse is Ril = 2f iD 2f i + 1 27 From Fig. 7, a point Xil ,Yil on this race has the linear velocity due to the term i cos il: V1il = \u2212 i cos il d\u0304m 2 cos il \u2212 r\u0304il 28 where OCTOBER 2007, Vol. 129 / 803 of Use: http://www.asme.org/about-asme/terms-of-use B h T d D V B d r c A T w I l V m l 8 Downloaded Fr r\u0304il = Ri 2 \u2212 Xil 2 \u2212 Ri 2 \u2212 ail 2 + D 2 2 \u2212 ail 2 29 ecause of x cos il and z sin il, a point Xil ,Yil on the ball as the linear velocity V2il = r\u0304il x cos il \u2212 y sin il 30 he velocity with which the inner race slips on the ball in the Y irection is VYil = V1il \u2212 V2il 31 VYil = \u2212 d\u0304m i 2 + r\u0304il \u2212 x cos il + z sin il + i cos il 32 ue to y, all points within the pressure area have a slip velocity Xil along the X axis at the ball/inner ring left contact, VXil = \u2212 Y r\u0304il 33 ecause of the components of velocity, which lie along the line efined by il, there is a spin of the left-inner race Sil with espect to the ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003795_978-3-540-85640-5_14-Figure13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003795_978-3-540-85640-5_14-Figure13-1.png",
        "caption": "Fig. 13. The real omnidirectional robot.",
        "texts": [
            " 12 shows the root locus of an open-loop system in the critical situation with k2 = 0.0515, where all the poles of the closed-loop system locate in the left-half plane whatever positive value kak1 is. Otherwise, when k2 is less than 0.0515, the root locus may cross the imaginary axis, and the poles of closes-loop system may move to the right-half plane when ka goes to zero. The control algorithm discussed above has been tested in our robot laboratory having a half-field of the RoboCup middle size league. The omnidirectional robot is shown in Fig. 13. An AVT Marlin F-046C color camera with a resolution of 780 \u00d7 580 is assembled pointing up towards a hyperbolic mirror, which is mounted on the top of the omnidirectional robot, such that a complete surrounding map of the robot can be captured. A self-localization algorithm described in [13] based on the 50 Hz output signal of the camera gets the robot\u2019s position in the play field in real time. The wheels are driven by three 60W Maxon DC motors and the maximum wheel velocity is 1.9m/s. Three wheel encoders measure the real wheel velocities, which are steered by three PID controllers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002528_978-3-662-04117-8-Figure7.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002528_978-3-662-04117-8-Figure7.2-1.png",
        "caption": "Figure 7.2: Two-mass model",
        "texts": [
            " Thercfore we intend to leam the friction characteristic and compensate it using feedforward control. So we want to combine the advantage of a well damped mechanical system with a precise positioning andjor contouring control. For the observer design first a linear model has to be derived. In this case, the feed drive is modeled as a linear two-mass system according to the theory of Lagrange. This results, including the differential equation of the servo drive, in a linear model of fifth order. The signal fiow chart of the model is shown in figure 7.2. Validations have shown, that with respect to its natural mechanical modes, the feed drive can be described by only two natural frequencies. Figure 7.3 shows measured signals compared to simulated data of the linear model while exciting the speed controller of the system with sinusoidal excitation signal in the right column and a rectangular excitation signal in the left colunm. For the curves of the measured signals solid lines are used, the simulated data has dotted lines. It can easily be noticed, that significant errors remain between the simulated and the measured signals"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003134_56.808-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003134_56.808-Figure11-1.png",
        "caption": "Fig. 11. The forbidden area of crab walk tripod gait on a constant slope plane, where S(a) = AB and A(0) = E.",
        "texts": [],
        "surrounding_texts": [
            "IEEE JOURNAL OF ROBOTICS AND AUTOMATION, VOL. 4, NO. 4, AUGUST 1988 43 1\nf o r b l d d e n reg ions o f s u p p o r l pattern A H J G\ns u p p o r t p o t t e r n A H J C - ~ ~\nt o r b i d d e n r e g i o n f o r b i d d e n r e q i o n r p a t t e r n ADEF p o l l e r n AGHI O f s u p p o r t __\nTheorem 3 Assume a hexapod i s walking on a flat terrain (0 = 0). The crab walk tripod gait of the hexapod, at crab angle a and with zero stability margin, is as follows:\n1) The sequence of the movement of the body (center of gravity) and the transfer legs are as shown in Table 11, in which\nBl = B3 = 6(a) and B2 = B4 = A (0, a)\nwhere A (0, a) + 26(a) = n(a) , and the foothold positions denoted by 0, 1 , 2, and 3 are as shown on Fig. 7.\n2) The stride length\nX(0, a)=2A(O, a)+26(a). (1 1)\n3) The duty factor\nA (0, a ) + 26(a) p(O, a ) = 2 A ( 0 , a)+26(a) .\nProof: The proof is similar to that of Theorem 2, expect for the foothold positions as shown on Fig. 7 and Bl = B3 = 6(a), B2 = Bd = A ( 0 , a). Hence, the proof is omitted.\nQ.E.D. Note that Theorem 3 can be further extended to generate the tripod\ngait of the hexapod for crab walking with stability margin S. In fact, if the foothold positions denoted by 0, I , 2, 3, are as given by Fig. 8, and if the body (center of gravity) moves a distance Bl = B3 = S t6(a) during phase 1 and phase 3, and a distance B2 = B4 = A ( S , a) during phase 2 and phase 4 (where A (s, a) = n(a) - 2S - 26(a)) then we have the crab-walk tripod gait with stability margin S. Hence, we have the following result.\nTheorem 4\nAssume a hexapod is to walk on a flat terrain (0 = 0). The crab walk tripod gait of a hexapod, at crab angle a and with stability margin S > 0, is as follows:\n1) The sequence of movement of the body and legs is as shown on Table 11, in which\nB l = B j = S + 6 ( a ) and B 2 = B 4 = A ( S , a)\nand the foothold positions are as shown on Fig. 8. 2) The stride length\nX(S, a ) = 2 A ( S , a)+2S+26(CY).\n3) The duty factor\nA (0, a) + 26(CY) 2 A (0, a ) + 26(a) - 2s p(S9",
            "432 IEEE JOURNAL OF ROBOTICS AND AUTOMATION, VOL. 4. NO. 4. AUGUST 1988\nv. THE TRIPOD GAITS ON A CONSTANT-SLOPE TERRAIN\nConsider a hexapod walking with a crab angle a on a constantslope terrain, as shown in Fig. 9. Now it is easy to see that the center of gravity of the hexapod will shift a distance h tan 0, where 0 is the slope angle and h is the height between q( t ) and the sloped plane, away from the horizontal plane. As a result, the critical support patterns of the tripod gait for crab walking on the sloped plane will also shift a distance A(0) = h tan 0 compared to that on the perfectly flat terrain, as illustrated by Fig. 9. Furthermore, the forbidden areas for the triangular support pattern are redefined as shown on Fig. 10.\nBased on the above observations, the tripod gaits for straight-line walking over flat terrain can be generalized to cover the case of tripod gaits on constant slope terrain. Thus we have the following theorem:\nTheorem 5 Assume a hexapod is to walk on a constant slope plane with slope angle 0. The tripod gait for straight-line walking with stability margin S is as follows:\n1 ) The foothold positions are as shown on Fig. 3(a). 2) The sequence of movement for body and legs is as given by\nSimilarly, for crab walk on a slope plane, the forbidden areas for the triangular support pattern could be redefined as shown in Fig. 1 1, and we have the following hexapod tripod gait as given by Theorem 6.\nTheorem 6 Assume a hexapod is to walk on a constant slope plane with slope angle 8. The crab-walk tripod gait of a hexapod, at crab angle a and with stability margin S, is as follows:\n1) The foothold positions are as shown on Fig. 8. 2) The sequence of movement for body and legs is as given in\n4) The duty factor\n(23) A (0, a , 0) + 2A(O) + 26(a)\n2A(0, a , 0)+2A(0)-2S+26(a) \u2018 P(S, a , e ) =\nRemark 5: Theorem 6 is a very general result that quantitatively characterizes the foothold positions, the stability margin, and the sequence of movement of body and legs. In fact, Theorems 1-5 are all special cases of Theorem 6. Any of Theorems 1-5 can be derived from Theorem 6 by substituting suitable values of 0 and a.\nSince the slope angle 0 affects the stability margin of the support pattern of the hexapod, there must be some specific value of 0 that causes zero stability margin. In the following, we will investigate the maximal slope angle, Omax, so that the hexapod can walk without causing instability. The following theorem shows the result.\nTheorem 7 The maximal slope angle, Omax, that the crab-walking tripod gait of",
            "IEEE JOURNAL OF ROBOTICS AND\nc 0 E\n0, J\n0, U .- L c ln\nAUTOMATION. VOL. 4, NO. 4, AUGUST 1988\n( e m ) I 5000 f\nI d l\nI30 00\n110 00\n90.00\n70.00\ne = o .\n8 . 5 '\n8.10'\n8.15.\ne . 2 0 .\n50.00 1 I I I I 0 . 0 0 3.00 6.00 9.00 12.00 15.00 ( e m )\nS t a b i l i t y Marg in\n(a)\n8 - 1 5 O\n8 . 2 0 0\n433\nS Y M O L S\n0 0'0' 0 a = 5 \" A a = 10.\n+ a = 1 5 ' x a = 2 0 0\nI .oo\n0 0 c\n0 8 0\nm 0.60\n0 . 4 0 I I I I I 0.00 300 6 00 900 12 00 I 5 0 0 ( e m )\nS l a b i l i t y Margin\n(b) Fig. 12. (a) The relation between stride length and stability margin as a function of slope angle and crab angle. (b) The relation\nbetween duty factor and stability margin as a function of slope angle and crab angle.\na hexapod can walk stably at is VI. CONCLUSIONS\nProof: Since the maximal slope angle for a crab-walking tripod gait occurs at S,,, = 0, therefore\nA (0, a , ~ n l a , ) = 0\nor\n?(a) - 2 A(@,,, = h tan Om,, =\nThus\nRemark 7: In the case of walking straighforward (i.e., a = O), then 6(a) = 0, and ~ ( a ) = P . Therefore\nP e,,,=tan-' -\n2 h\nResults have been generated which quantitatively characterize the stability margins of the hexapod tripod gaits. In particular, the mathematical expression representing the relations between the stability margin, the stride length, and the duty factor are formulated.\nThe tripod gait of the hexapod for crab walking over perfectly flat terrain and over constant slope terrain are derived, respectively. We reiterate that these results are obtained based on the assumptions that 1 ) the hexapod has a symmetrical structure, 2) the reachable area of each leg is a rectangular region, 3) the initial foothold positions should be specified before the locomotion starts, and 4) the sequence for liftoff and placing the feet are as specified. It should be noted that by simply combining derived tripod gaits for moving straightforward and crab walking, one can achieve obstacle avoidence path planning and, possibly, the suitable gaits for a hexapod walking over irregular surface which can be approximated by the piecewise segments of perfect flat terrain and the constant slope terrain. Thus far, some preliminary results have been obtained. The complete solutions to this problem are still under investigation.\nREFERENCES\n[ I ] R . B. McGhee and A . A . Frank, \"On the stability properties of quadruped creeping gait,\" Math. Biosci., vol. 3 . pp. 331-351, 1968."
        ]
    },
    {
        "image_filename": "designv10_8_0003891_s12283-009-0028-1-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003891_s12283-009-0028-1-Figure1-1.png",
        "caption": "Fig. 1 The modeled shafts were capable of deflecting about two axes. a Deflection along the Y axis represents lead/lag motion. b Deflection along the X axis represents toe-up/toe-down motion",
        "texts": [
            " The first involves the shaft\u2019s ability to store and subsequently release strain energy which could result in an increase in clubhead speed. The second is by altering the orientation of the clubhead relative to the ball at impact. The orientation of the clubhead will affect the distance the ball travels by changing the launch angle relative to the horizontal, the direction of ball flight, and the spin rate of the ball. Prior to impact with the ball, the shaft can be measured bending about three orthogonal axes fixed to the grip end of the club. Deflection along the Y axis represents lead/lag motion (Fig. 1a), while deflection along the X axis represents toe-up/toe-down motion (Fig. 1b). Twisting about the longitudinal, Z, axis of the shaft can also occur. Compared to the magnitude of deflection about the other axes, twisting about the longitudinal axis has a negligible influence on both the orientation of the clubhead and its velocity at impact, and therefore, will not be considered in this paper [2]. Butler and Winfield [2] measured peak deflection values in the lag direction as large as 7 cm, and peak deflections in the toe-up direction greater than 15 cm. In their study, three golfers swinging the same club at 46 m/s, produced toe-down deflections at impact that S",
            " The model was capable of torso rotation, horizontal abduction at the shoulder, external rotation at the shoulder, and ulnar deviation at the wrist. Four muscular torque generators, which adhered to the force\u2013velocity and activation rate properties of human muscle, were incorporated to add energy to the system. The four segments of the modeled club were connected in series by rotational spring-damper elements (Fig. 3). The hand and most proximal club segment were combined to represent a single segment, Club_Proximal [5]. The shafts were capable of deflecting about two axes (Fig. 1). Further details on model development and parameters have previously been presented [9]. Three versions of the same base model were used in this study. They differed only with regards to the constraint parameters governing the maximum torque output from the four torque generators. This allowed the role of shaft flexibility to be evaluated for golfers that generate three different levels of clubhead speed (i.e. Golfer-Slow *35 m/s, Golfer-Medium *43 m/s, and Golfer-Fast *50 m/s). These clubhead speed values represent the minimum, average, and maximum clubhead speeds measured by Brown et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002352_1.2830138-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002352_1.2830138-Figure2-1.png",
        "caption": "Fig. 2 Displacement o f ball center and nner ring",
        "texts": [
            " The displacement vector {S} describes the three linear and two rotational motions, [Sx 8y 6Z yx yy] T, while the loading is represented by {F} = [Fx F, Fz Mx My] T. In order to find ball load equilibrium, displacements and loads of the inner ring must be transformed to the ball coordinate system at the inner ring groove center. The groove center displacement is {u} = [ur uz 6}T, and the loading is {Q} = [QrQzM]T. {S} = [Jty] r{\u00ab} {\u00a5\u201e\\ = [R<nT{Q} W>] = COS (j) 0 0 sin (/> 0 0 0 \u2014zp sin (f> 1 rp sin 4> 0 - s i n 4> zp cos (j> \u2014rpcos 4> cos 4> (1) (2) For the ball load equilibrium, the geometry and loading of the ball and the raceways are analyzed (Fig. 2) . The inner ring groove center and ball center motion are defined by the contact angle a and the center lengths /. These are found geometrically, given the initial center length l0, the unknown ball displacement v, and the unknown inner ring displacement u. The contact deformation is then the change in the center length. O'I li l0i Og le l0i (3) Contact loads are calculated with Hertzian theory for spherical contact where K is the load-deflection parameter and is found using the method described by Harris (1990)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002957_s0263574703005216-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002957_s0263574703005216-Figure3-1.png",
        "caption": "Fig. 3. Limit positions of the mechanism for links 1 and 4 connected to the ground link.",
        "texts": [
            " Therefore, the full rotatability constraint for the mechanism in Figure 2(a) requires L0 +L1 <L2 +L3 +L4 and L4 +L4 < L1 +L2 +L3. However, for a parallel five-bar manipulator, these two conditions reduce to L0 <2L2. When L0 +L1 =L2 +L3 +L4 and L0 +L4 = L1 +L2 +L3, the centerlines of all links are collinear, the mechanism is a change-point mechanism. On the other hand, when L0 +L1 >L2 +L3 +L4 and L0 +L4 >L1 +L2 +L3, the mechanism is a double-rocker mechanism; the active joints cannot make a full rotation.35 Each of the active joints can move between two limit positions shown in Figure 3. Such a five bar mechanism can be called quadruple-rocker mechanism \u2013 drawing the same analogy from a double-rocker-four-bar mechanism known as triple-rocker mechanism.37 Hence, the problem is formulated as a constrained nonlinear optimisation problem. A computer program based on a sequential quadratic programming method is prepared in MATLAB to accomplish the constrained minimization of the OF as a function of the synthesis parameters, starting with an initial value for each parameter. For 300 \u2264 1 \u22643900 and 4 = 1, many optimisation trials with different initial values for the synthesis parameters were conducted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.7-1.png",
        "caption": "Figure 7.7 Normal stress.",
        "texts": [
            "5 is unique for a particular material, in dependent of the geometries of the specimens used during the experiments. This type of representation eliminates geometry as one of the variables, and makes it possible to focus attention on the mechanical properties of different materials. For example, consider the curves in Figure 7.6, representing the mechanical behavior of materials A and B in simple tension. It is clear that material B can be deformed more easily than material A in a uniaxial tension test, or material A is \"stiffer\" than material B. 7.4 Simple Stress Consider the cantilever beam shown in Figure 7.7a. The beam has a circular cross-section, cross-sectional area A, welded to the wall at one end, and is subjected to a tensile force with magnitude F at the other end. The bar does not move, so it is in equilib rium. To analyze the forces induced within the beam, the method of sections can be applied by hypothelically cutting the beam into two pieces through a plane ABCD perpendicular to the centerline of the beam. Since the beam as a whole is in equilib rium, the two pieces must individually be in equilibrium as well. This requires the presence of an internal force collinear with the externally applied force at the cut section of each piece. To sat isfy the condition of equilibrium, the internal forces must have the same magnitude as the external force (Figure 7.7b). The in ternal force at the cut section represents the resultant of a force system distributed over the cross-sectional area of the beam (Fig ure 7.7c). The intensity of the internal force over the cut section (force per unit area) is known as the stress. For the case shown in Figure 7.7, since the force resultant at the cut section is per pendicular (normal) to the plane of the cut, the corresponding stress is called a normal stress. It is customary to use the symbol a (sigma) to refer to normal stresses. The intensity of this dis tributed force mayor may not be uniform (constant) throughout the cut section. Assuming that the intensity of the distributed force at the cut section is uniform over the cross-sectional area A, the normal stress can be calculated using: F a == A (7.1) If the intensity of the stress distribution over the area is not uniform, then Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002898_0890-6955(95)00091-7-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002898_0890-6955(95)00091-7-Figure1-1.png",
        "caption": "Fig. 1. LLLRR type machine (rotational head type).",
        "texts": [
            " A five-axis machine tool has 5 d.f. to position the tool exactly perpendicular to the workpiece in the working space. One of the rotational axes is for rotation and another one is for tilting. (The tilt angle is defined by the surface normal and the tool axis at the point of contact with the workpiece surface.) (1) LLLRR(1): The cutting tool is supported by a double pan head, i.e. the tool has two rotational axes: one for rotation, another for tilting. The feed motion may be located either at the tool or at the table (see Fig. 1). (2) RLLLR: The workpiece is supported by a turn table and the tool is supported by a single pan head, i.e. the tool has one rotational degree of freedom. The other rotational axis is located at the rotational table. (3) RRLLL: The workpiece is supported by a double turn table, i.e. the work table has two rotational axes: Positioning accuracy improvement in five-axis milling by post processing 225 (a) having a rotational table on the tilting one; (b) having a tilting table on the rotational one",
            " The machine produces different types of error trace patterns depending on the structure and set-up of the machine. Different kinds of theoretical error trace patterns are developed based on Table 2, Table 3, Equation (13), Equation (17) and Equation (18). The individual error is diagnosed to find the actual geometry of the machine. Details of measurement system of LLLRR type machines are described in [9]. 3.2. Machine specification The experimental part of the work was performed with the LLLRR type machine of VALMET Aviation Industries located at Halli, Finland. The diagram of the machine is shown in Fig. 1 (see also Table 4). 3.3. Results of the experiment C-axis: (1) offset along X-axis with magnitude of 15 ~tm; (2) offset along Y-axis 4 I.tm; (3) misalignment is negligible. Positioning accuracy improvement in five-axis milling by post processing 231 (I) offset is - 1 0 lxm for the X-axis and - 1 5 pin for the Z-axis; (2) misalignment was unseparable or negligible. Spindle axis: according to the analysis, the spindle axis produces an angle with the 7__~,~-axis of 0.0318 \u00b0 and 89.99841 \u00b0 with the Yb~-axis when the machine is in zero position (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002650_robot.2000.844824-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002650_robot.2000.844824-Figure4-1.png",
        "caption": "Figure 4: Design of the instrument",
        "texts": [
            " The measurement of more than just one-dimensional force-displacement information leads to more realistic parameter determination, whereas measuring the deformation over time permits estimation of constants describing time dependent behavior (C [ ] and z [SI). We developed a vision-based device to perform the measurements. The device permits controlled application of negative relative pressure and tracks the profiles of small deformations caused during the measurement process. With a periscope geometry, obtained by placing a small mirror beside the aspiration hole, as indicated in Figure 4, it is possible to observe the profile of the deformed tissue with a camera placed at the other end of the tube. The method allows to measure the desired profile very accurately, rapidly and without contact with the tissue. An optical fiber fixed in the tube, illuminates the scene. The aspiration tube is integrated together with the instrument handle, the pressure sensor and the light fiber, forming the body of the instrument. This body is very ergonomic and sterilizable with standard sterilizing procedures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002414_20.996020-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002414_20.996020-Figure8-1.png",
        "caption": "Fig. 8. Experimental setup.",
        "texts": [
            " All the physical parameters are listed in Table I, except setting 40 mm in order to magnify the effect that the eddy currents tend to concentrate toward the edge of the direction in the rectangular pole projection area. It is also observed that the greatest braking torque is occurred at the ends of the rectangular pole projection area. This information of the eddy current distribution will help us calculate more accurate braking torque. To validate the accuracy of the proposed model, the braking torque is measured by experiment. The experimental setup com- posed of the rotating disk and electric motor is shown in Fig. 8 [6]. The electric motor is used to rotate the disk with the constant angular velocity. The mechanical dynamic equation of the system is (46) , and are the moment of inertia, the viscous-friction coefficient, the torque constant, and armature-winding current of the motor. First, to obtain the viscous-friction torque , the experiment is conducted without applying the current to the electromagnet. Then, (46) yields in the steady state condition to (47) Since is known from the electric motor specification, we can measure the viscous-friction torque indirectly by measuring "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.5-1.png",
        "caption": "Figure 3.5 The right-hand-rule.",
        "texts": [
            "3 Direction of Moment The moment of a force about a point acts in a direction perpen dicular to the plane upon which the point and the force lie. For example, in Figure 3.4, point 0 and the line of action of force F lie on plane A. The line of action of moment M of force F about point o is perpendicular to plane A. The direction and sense of the mo ment vector along its line of action can be determined using the Moment and Torque 31 32 Fundamentals of Biomechanics right-hand-rule. As illustrated in Figure 3.5, when the fingers of the right hand curl in the direction that the applied force tends to rotate the body about point 0, the right hand thumb points in the direction of the moment vector. More specifically, extend the right hand with the thumb at a right angle to the rest of the fingers, position the finger tips in the direction of the applied force, and position the hand so that the point about which the moment is to be determined faces toward the palm. The tip of the thumb points in the direction of the moment vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure9.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure9.4-1.png",
        "caption": "Figure 9.4 Stress-strain rate diagram for a linearly viscous fluid.",
        "texts": [
            " For fluids, stresses are not depen dent upon the strains but on the strain rates. If the stresses and strain rates in a fluid are linearly proportional, then the fluid is called a linearly viscous fluid or a Newtonian fluid. Examples of linearly viscous fluids include water and blood plasma. For a linearly viscous fluid: (9.4) In Eq. (9.4), rJ (eta) is the constant of proportionality between the stress a and the strain ratei: , and is called the coefficient of viscosity of the fluid. As illustrated in Figure 9.4, the co efficient of viscosity is the slope of the a-i: graph of a New tonian fluid. The physical significance of this coefficient is similar to that of the coefficient of friction between the contact surfaces of solid bodies. The higher the coefficient of viscos ity, the \"thicker\" the fluid and the more difficult it is to deform. The coefficient of viscosity for water is about 1 centipoise at room temperature, while it is about 1.2 centipoise for blood plasma. The spring is one of the two basic mechanical elements used to simulate the mechanical behavior of materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003870_1.4001003-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003870_1.4001003-Figure3-1.png",
        "caption": "Fig. 3 Sketch of tooth generation of the bevel gear",
        "texts": [
            " This leads to the 3D modeling that is then used to facilitate manufacturing of the tooth profile, in which the gear alignment curve with the constant helical angle is used for tracking the end-milling cutter. The mathematical models enable the use of numerical generation of the tooth profile data and improvement of the performance of a conventional gear cutting machine. Further, the new method avoids cutter interference especially with the internal bevel gear. 2 Coordinate Transformation of the Spiral Bevel Gear Meshing in the Nutation Drive The meshing between the external and internal spiral bevel gears in the nutation drive is illustrated in Fig. 3 and can be considered as external and internal bevel gear meshings with an imaginary crown gear which has a pitch cone angle of 90 deg, and therefore, a pitch cone surface is at right angles to its axis . Consequently, the tooth profiles of a double circular-arc spiral bevel gear can be seen as an enveloping process generated by the imaginary rotating crown gear with respect to the bevel gear. The motion between the crown gear and that of the external or internal bevel gear can be considered as the pure rolling of two pitch cones"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003450_ac00164a007-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003450_ac00164a007-Figure1-1.png",
        "caption": "Figure 1. Coordinate system of the two-dimenslonal glucose sensor.",
        "texts": [
            " The response to a step change of glucose concentration is monotonic and rapid when the membrane is thin and the immobilized enzyme activity is high. When the concentrations of glucose and oxygen are changed simultaneously, however, the transient current may undergo an inflection before reaching steady state due to differences in substrate mass transfer. Analogous effects are expected for the two-dimensional design. THEORETICAL SECTION The Coordinate System. The two-dimensional sensor and coordinate system are shown in Figure 1. The core is a cylindrical oxygen sensor or electrode, active on its curved surface, of radius re and length L. The oxygen sensor is covered by a hydrophobic membrane with inner radius re and outer radius rl. The next layer is the enzyme gel with inner radius q and outer radius r,. The gel layer is, in turn, surrounded by an outer hydrophobic membrane or tube that extends from an inner radius r. to an outer radius r,, the total radius of the sensor. The inner and outer hydrophobic membranes are impermeable to glucose and are therefore characterized only by their thicknesses and transport parameters for oxygen, the respective diffusion coefficients, Do, and DOH, and partition coefficients, mol and aoH"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure9.11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure9.11-1.png",
        "caption": "Figure 9.11. Schematic representation of the variable contact curvature radius",
        "texts": [
            " They also determined the mechanical properties of teeth after about 15 minutes; in this time, the containing water was expected to evaporate. It was found that the mechanical properties of teeth depend on the water content. The name spherical indentation refers to the shape of the indenter, which is a sphere (Figure 9.10). Spherical indentation began with Hertz\u2019s theory in 1880. Spherical indentation has some advantages over sharp indentation. First of all, it has a variable contact pressure, which is suitable for studying pure elastic contact. Moreover, it has a variable contact curvature radius (Figure 9.11). Therefore, this method shows the ability to simulate real contact conditions. However, it is difficult to measure the contact radius experimentally, especially in the elastic regime that is characteristic for nanoindentation. While sharp indentation depends on the indentation depth, spherical indentation depends on the sphere radius [21], the hardness increasing with a decreasing indenter radius. In the case of spherical indentation, the roughness of the surface of the tested material is important; an asperity can lead to a false evaluation of the contact area at the maximum load [22]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003864_s0094837300003286-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003864_s0094837300003286-Figure4-1.png",
        "caption": "FIGURE 4. Tail of shark showing the relationship of the angle of elevation (el) to the thrust angle (th) and heterocercal angle (het), and the relationship between the forward thrust F and the upward thrust B.",
        "texts": [
            " Grove and Newell (1936) credit a personal com munication from Watson for the view that the net result of epibatic thrusts at the front and back of the body is to offset the weight of the fish in water. Grove and Newell attacked the problem by means of models of tails rotated in a tank and confirmed an epibatic effect of a heterocercal tail. In addition to the epibatic effect, they also proposed a simple mechanism by which the tail could deliver a horizontal thrust if the actions of the epicaudal and hypochordal lobes were offsetting around the notochordal axis (1936, figure 4 ) . Harris (1936, 1938) extended these experiments by use of wind tunnel tests of a model of Mustelus. Experiments on the lines of those of Grove and Newell were developed by Affleck (1950) who showed that in fact a whole range of effects could be produced by variation in the shape and orientation of heterocercal, hypocercal and homocercal models. Alexander (1956) continued the experiments further by the use of whole amputated tails instead of models and, in producing the first quantitative data, again confirmed an epibatic effect from a heterocercal tail",
            " In fishes with a heterocercal tail, such an orientation of the thrust is produced as the result of a balance between opposing tendencies in the tail and the mechanism will be termed the \"balanced thrust\" mechanism. The correct balance of forces for such an orientation, in the simple model we have considered so far, can be calculated as follows. The correct line of action departs from the horizontal by an angle depending on the horizontal distance between the center of gravity and the center of effort of the fin, and on the vertical elevation of the center of effort above the longitudinal axis containing the center of gravity. This defines the angle of elevation of the tail (Figure 4, el). The angle between the line of thrust and the long axis of the tail itself may be termed the (dorsal) thrust angle (Figure 4, th) and it will be seen that the thrust angle plus the angle of elevation are equal to the heterocercal angle. Balance will occur (Figure 5) when the hypobatic thrust F, is balanced by a per pendicular epibatic thrust B, the resolution of the two forces giving a net thrust through the center of gravity. The relative dimensions of F and B are given as follows. At balance, B = at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0094837300003286 Downloaded from https://www.cambridge",
            " Changes may also be effected by modification of the change in transverse speed of the tail during the beat, although Gray (1933) and most other authors believe that it is always symmetrical. Referring back to our simple model, we can calculate a series of \"balanced\" values of the (dorsal) thrust angle and angle of rotation for different hypothetical ratios of F/T (Table 1). Because it seems reasonable that the upper limit on the angle of rotation would be 45\u00b0, we can also place upper limits on the angles of thrust and therefore, given the relationship between the angle of thrust and the heterocercal angle (Figure 4 ) , upon the latter also. The relation ship F/T changes during the stroke. The maxi mum value, in the curves developed from the Squalus acanthias data, is approximately 2.10 for the dorsal lobe. Therefore, if this curve is generally applicable, from Table 1 we can see that for all values of the thrust angles that are less than 26\u00b0 (heterocercal angle of 33\u00b0) a available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0094837300003286 Downloaded from https://www.cambridge.org/core"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002751_0094-114x(95)00121-e-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002751_0094-114x(95)00121-e-Figure1-1.png",
        "caption": "Fig. 1. Basic properties of pitch ellipse for elliptical gears.",
        "texts": [
            " Therefore, the relative velocity and equation of meshing [5] between the rack cutter and elliptical gear must be considered. The mathematical model and undercutting analysis proposed here are very helpful in the design and production of high-precision elliptical gears. G E O M E T R I C P R O P E R T I E S OF T H E E L L I P S E The geometric equations and properties of ellipses have been described in detail in the literature [4, 8]. Several important equations will be derived here for convenience and to pro\u00a2ide a more complete characterization of elliptical gears. Figure 1 shows a pitch curve of the elliptical gear; the pitch curve can be represented in polar coordinates by a(1 -- ~2) r~ - 1 + Ecos~b~ b 2 - a(l + EcosqS,) ' (1) where E = e/a = x ~ - b 2 / a is the eccentricity, a is the major semi-axis, and b is the minor Undercutting analysis of elliptical gears 881 semi-axis. The position vector of the pitch ellipse may also be represented in the Cartesian coordinate system as follows: b2cosq~, x~ - a(1 + Ecosq~I) b2sinq~l (2) Y~ = a(1 + Ecostpt) The unit tangent vector at any point M on the pitch ellipse can be obtained by differentiating and znormalizing equation (2). Therefore, z t = r , i t + r y J , - sin~b, x/E: + 2ECOS~b, + 1 i, + E + cos~b, j, (3) x/E 2 + 2EcosqS~ + 1 From the geometry of the pitch ellipse shown in Fig. 1, it can be found that the tangent vector at any point on the pitch ellipse is z~ = cos7 i~ + sing, j, (4) From equations (3) and (4), the relationship between ~, and 7 can be expressed as follows: - sin~b, COS~f = x / d + 2EcosqL + 1 o r sin), = E + cos4~, (5) x/E 2 + 2ECOS~Pl + 1 The unit normal vector n~ may also be obtained by nl = T~ \u00d7 k~ = sin 7 i~ - cos7 j~ = n , i, + n,. j , , (6) where k~ is the unit vector along the Z,-axis of the Cartesian coordinate system. The arc length on the pitch ellipse, measured from initial point N to point M, can be calculated by applying the equation r7 (dr) SMX = r2+ ~ d~bl dO *~\" a(1 - E-)x/E + 2Ecosq~, + 1 = (1 + Ecosq51) 2 d4), (7) M A T H E M A T I C A L M O D E L O F T H E R A C K C U T T E R For simplicity, the generation of elliptical gears can be considered a two-dimensional problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure6.5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure6.5-1.png",
        "caption": "Figure 6.5. Capacitive micro force sensor for biological cell handling. a. Schematic representation of the sensor; b. detail of the comb drives (from [27], \u00a9 2002 IOP Publishing, with kind permission of IOP Publishing).",
        "texts": [
            " The dimensions of this sensor are 5 \u00d7 5 \u00d7 0.36 mm3. A piezoelectric micro force sensor for microhandling was described for the first time in [26]. The dimensions of the sensor were 16 \u00d7 2 \u00d7 1 mm3. A prototype was built but was neither characterized nor integrated into a microgripper. Information about the performance of this sensor, such as resolution or accuracy, is not available. A two-axes capacitive force sensor for the handling and characterization of biological cells was presented in [27], Figure 6.5a. Force Feedback for Nanohandling 181 The outer fixed frame and the inner moveable plate are connected by four springs. A force acting on the tip causes a movement of the inner plate and thus a change of the distance between each pair of the comb-like capacitors. The force can be calculated from the total capacity. The stiffness of the sensor, and thus its measurement range, can be adjusted by changing the dimensions of the springs. To be able to measure forces in the x- and y-directions, several comb drives were arranged perpendicularly (Figure 6.5b). Two capacitors in the middle of the inner plate were designed as reference capacitors for the signal-processing circuit. Strain and force measurement can also be realized using optical methods. For instance, either passive micro strain gages which are mechanically amplified can be used [28] (Figure 6.6), or strain in the nanometer range is measured using a light-optical microscope and image-processing tools [29]. By using this method, it is possible to measure forces with a resolution in the micronewton range"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002816_j.mechmachtheory.2004.06.003-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002816_j.mechmachtheory.2004.06.003-Figure1-1.png",
        "caption": "Fig. 1. A wrench acting on a body while it is undergoing an instantaneous motion.",
        "texts": [
            " A wrench of zero pitch represents a pure force whereas a wrench of infinite pitch denotes a pure couple. If a wrench, $r \u00bc q$\u0302r, acts on a rigid body such that it produces no work while the body is undergoing an infinitesimal twist, $ \u00bc dq$\u0302, the two screws are said to be reciprocal screws. The virtual work performed by the wrench is given by [17,24] dW \u00bc qdq\u00bds \u00f0rr sr \u00fe hrsr\u00de \u00fe sr \u00f0r s\u00fe hs\u00de \u00bc qdq\u00bd\u00f0h\u00fe hr\u00de\u00f0s sr\u00de \u00fe sr \u00f0r s\u00de \u00fe s \u00f0rr sr\u00de : \u00f08\u00de From the geometry of the lines associated with the two screws shown in Fig. 1, the following relationship are obtained s sr \u00bc cos a; \u00f09\u00de sr \u00f0r s\u00de \u00fe s \u00f0rr sr\u00de \u00bc a \u00f0s sr\u00de \u00bc a sin a; \u00f010\u00de where a is a vector along the common perpendicular leading from the axis of $ to $r, and a is the twist angle between the axes of $ and $r, measured from $ to $r about the common perpendicular according to the right-hand rule. Substituting Eqs. (9) and (10) into (8), we obtain dW \u00bc qdq\u00bd\u00f0h\u00fe hr\u00de cos a a sin a : \u00f011\u00de By definition, the virtual work produced by the two reciprocal screws is equal to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003152_j.ijmachtools.2004.11.006-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003152_j.ijmachtools.2004.11.006-Figure3-1.png",
        "caption": "Fig. 3. Illustration of a five-axis tool motion in the reference coordinate frame. E, NC control point; P, An arbitrary point on the toroidal surface; M, An arbitrary point on the lower conical surface.",
        "texts": [
            " Hence, a full swept profile of the tool can be generated by connecting these partial swept profiles, which are described on the individual boundary surface patches. Let V(P) be the velocity of an arbitrary point on the toroidal surface, let VE be the velocity of the origin of the moving frame. In the reference coordinate frame (the machine coordinate system), the velocity of P is given by MVT \u00f0P\u00de Z VE Cu! EP Z VE C \u00f0h KR2 cos vT \u00de\u00f0u!e1\u00de C \u00f0R1 CR2 sin vT \u00decos u\u00f0u!e2\u00de C \u00f0R1 CR2 sin vT \u00desin u\u00f0u!e3\u00de (14) where EP is vector from control point E to point P (see Fig. 3). Applying MNT(P)$MVT(P)Z0, in consideration of the vector operation relationships [3] yields the swept profile of the toroidal surface fT: fT \u00f0u; vT ; t\u00de Z sin vT \u00bd\u00f0e2,VE\u00decos u C \u00f0e3,VE\u00desin u C \u00f0e3,u\u00deh cos u Ccos vT \u00bd\u00f0Ke1,VE\u00de C \u00f0e3,u\u00deR1 cos u Z 0: (15) Therefore vT \u00f0u; t\u00de Z tanK1 \u00f0e1,VE\u00deK \u00f0e3,u\u00deR1 cos u \u00f0e2,VE\u00decos u C \u00f0e3,VE\u00desin u C \u00f0e3,u\u00deh cos u \u00f016\u00de or u\u00f0vT ; t\u00de Z sinK1 FTffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 T CD2 T p \" # KxT p KsinK1 FTffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 T CD2 T p \" # KxT ; 8>>< >>>: (17) where BT Z \u00f0e3,VE\u00desin vT DT Z \u00f0e2,VE\u00desin vT C \u00f0e3,u\u00de\u00f0h sin vT CR1 cos vT \u00de FT Z \u00f0e1,VE\u00decos vT cos xT Z BTffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 T CD2 T p ; sin xT Z DTffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2 T CD2 T p : 8>>>>< >>>>: Let V(M) be the velocity of an arbitrary point on the lower conical surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure2.7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure2.7-1.png",
        "caption": "Figure 2.7 Concurrent forces.",
        "texts": [
            " Therefore, with respect to the Cartesian (rectangular) coordinate frame, it is sufficient to analyze coplanar force systems by considering the x and y components of the forces involved. 2.9 Collinear Forces A system of forces is collinear if all the forces have a common line of action. For example, the forces applied on a rope in a rope-pulling contest form a collinear force system (Figure 2.6). 2.10 Concurrent Forces A system of forces is concurrent if the lines of action of the forces have a common point of intersection. Examples of con current force systems can be seen in various traction devices, as Force Vector 21 22 Fundamentals of Biomechanics illustrated in Figure 2.7. Owing to the weight in the weight pan, the cables stretch and forces are applied on the pulleys and the leg. The force applied on the leg holds the leg in place. 2.11 Parallel Forces A set of forces form a parallel force system if the lines of action of the forces are parallel to each other. An example of a parallel force system is illustrated in Figure 2.8 by a human arm flexed at a right angle and holding an object. The forces on the forearm are the weight of the object, the weight of the arm itself, the tension in the biceps muscle, and the joint reaction force at the elbow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.15-1.png",
        "caption": "Figure 8.15 Maximum shear stress.",
        "texts": [
            " Remember that the response of a material to different modes of loading are different, and different physical properties of a given material must be considered while analyzing its behavior under shear, tension, and compression. Note that Eqs. (8.14) and (8.15) are useful for calculating the maximum and minimum normal stresses. For a given structure and loading conditions, the maxi mum normal stress computed usingEq. (8.14) maybe well within the limits of operational safety. However, the structure must also be checked for a critical shearing stress, called the maximum shear stress. The maximum shear stress, i max, occurs on a material element for which the normal stresses are equal (Figure 8.15). Therefore, Eqs. (8.10) and (8.11) can be set equal, and the result ing equation can be solved for the angle of orientation, ()2, of the element on which the shear stress is maximum. This will yield: ()2 = - tan 1 _l(ay - ax) 2 2 i xy (8.16) Multiaxial Deformations and Stress Analyses 163 An expression for the maximum shear stress, Tmax, can then be derived by replacing () in Eq. (8.12) with (}z: ( ax - a y )2 2 Tmax = 2 + Txy (8.17) A graphical method of finding principal stresses will be dis cussed next"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002327_s0094-114x(97)00056-6-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002327_s0094-114x(97)00056-6-Figure2-1.png",
        "caption": "Fig. 2. 10 DOF shaft beam element.",
        "texts": [
            " The displacements V, W and the corresponding slopes B, G for lateral motion and the spin speed O with torsional velocity a\u00c7 are as denoted. The kinetic energy of the disk for lateral motion is given by [8] Td 1 2 md _Vd 2 _Wd 2 1 2 IdD _Bd 2 _Gd 2 \u00ff 1 2 IdP O _ad Bd _Gd \u00ff Gd _Bd 1 2 IdP O _ad 2 1 Following Lagrangian approach, we can obtain Md f qdg O Gd f _qdg fFd s g 2 where Md md 0 md 0 0 IdD 0 0 0 IdD 0 0 0 0 Idp 26666664 37777775 sym Gd 0 0 0 0 0 0 0 0 \u00ffIdp 0 0 0 0 0 0 26666664 37777775 skew sym and fqdgT fVdWdBdGdadg Figure 2 shows a 2 noded shaft element with 10 degrees of freedom. The modi\u00aeed kinetic energy including the torsional motion is [8] Ts 1 2 Z l 0 frA _V 2 _W 2 ID _B 2 _G 2 g ds \u00ff 1 2 Z l 0 fIP O _a B _G\u00ff G _B \u00ff IP O _a 2g ds 3 The modi\u00aeed potential energy including shear deformation [15] and torsional de\u00afection is given by [8] Us 1 2 Z l 0 EI B0 2 G0 2 ds 1 2 Z l 0 K0GA V0 \u00ff G 2 W0 B 2 ds 1 2 Z l 0 GJ a0 2 ds 4 Following Lagrangian approach, we can obtain Ms f qsg O Gs f _qsg Ks fqsg fFs sg 5 where fqgT fq1q2q3q4q5q6q7q8q9q10g Ms Ms T Ms R Ms y Ms T Ms T 0 F Ms T 1 F2 Ms T 2 Ms R Ms R 0 F Ms R 1 F2 Ms R 2 Gs Gs 0 F Gs 1 F2 Gs 2 Ks Ks 0 F Ks 1 Ks y and F 12EI K0GAl2 The elements of the above matrices are given in the Appendix"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002918_robot.1999.774027-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002918_robot.1999.774027-Figure1-1.png",
        "caption": "Figure 1: Manipulator with hyper degrees of freedom",
        "texts": [
            " In this paper, we show some important properties of the Shape Jacobian. In Section 2, we give descriptions of a kinematics of an HDOF manipulator and a parameterized spatial curve. In Section 3, we review the definition of the Shape Jacobian proposed by the authors in order to control the shape of a manipulator. In Section 4, we show significant properties of the Shape Jacobian in geometric flavor. In Section 5, we summarize the results in this paper. 2 Preliminaries Suppose that an HDOF manipulator satisfies the following assumption (Figure 1): Assumption 1 (HDOF Manipulators) An HDOF manipulator has 1. a serial rigid chain structure, and 2. 2-degree-of-freedom(2DOF) revolute joints. 0 The above assumption is satisfied by manipulators developed in [S] and [7], [8]. Under Assumption 1, by the coordinate setting method shown in [4], the kinematics of the manipulator can be expressed as @ i = @ i - l R w , i , (1) R w , i = R(as,i ,Oa,i)R(am,i, Om+), (2) pi = pi-l + l@ie=, , i = l , - - . , n (3) where @ , E SO(3) is the frame attached to the i - th link, Rw,i E SO(3) is the rotation matrix of the i -th 2DOF revolute joint, R(a, 0 ) E SO(3) the rotaion matrix about a unit-length ax is a E 913 through an angle 8 E [ -T n ) , a8,i, a,,+ E 913 are the unit-length and constant rotational axes of the joint, O a , i , e,,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.61-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.61-1.png",
        "caption": "Figure 8.61 Stress distribution at a section of the specimen in",
        "texts": [
            "01)3 = 0 125 X 10-6 m3 88' Therefore, the maximum shear stress occurring at section bb along the neutral axis is: (500)(0.125 x 10-6) 6 <max = (8.33 x 10-10)(0.01) = 7.5 x 10 Pa = 7.5 MPa Remarks: Note that magnitudes and directions of internal shear force and bending moment are different at different sections of the specimen. At a given section, the internal shear force and bending moment are functions of the horizontal distance be tween the left support (or the right support) and the section. This is illustrated in Figure 8.61a for a section that lies some where between the left support and where the load W is applied Multiaxial Deformations and Stress Analyses 187 on the specimen. If the distance between the left support and the section is x, then the magnitude of the internal bending moment at the section is: In other words, M is a function of x. The stress distribution at the same section is shown in Figure 8.61b. The upper layers of the specimen are under compression (negative CTx ), while the lower layers are in tension (positive CTx ). Also, a downward shear stress (rxy) acts throughout the section. Also indicated in Figure 8.61b are two material elements, A and B. The nonzero stress tensor components acting on the surfaces of these material elements are shown in Figure 8.62. It is clear that the state of stress at the upper layers of the specimen is different than the state of stress at the lower layers. Example 8.7 Consider the beam shown in Figure 8.63a. The ex ternally applied force and the reactions at the supports bend the beam (three-force bending), subjecting it to shear stresses. In addition to shear, the upper layers of the beam are subjected to compression and the lower layers to tension"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003916_b978-0-12-220105-9.50011-4-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003916_b978-0-12-220105-9.50011-4-Figure3-1.png",
        "caption": "Fig. 3. Typical cell for cyclic voltammetry.",
        "texts": [
            " After the peak, the current decreases because the electroactive species near the electrode has been reduced, and the species can get to the electrode surface only by diffusion. At some appropriate potential, the direction of potential scan is reversed, and an anodic peak is found due to the oxidation of the product formed during the first half of the scan. The process can be repeated a number of times, if desirable, for the purpose of building up the concentration of some unstable intermediates. The theory of cyclic voltammetry for a number of situations has been worked out in some detail.17 The type of cell generally used is shown in Fig. 3. The S.C.E. reference electrode is isolated in a salt bridge that terminates with a tip containing fibers sealed in asbestos or a crack between soft glass and Pyrex. This prevents any of the solution inside the bridge from getting into the main cell but allows electrical contact. The bridge is usually filled with some of the sample solution. The salt bridge is placed in a tube ending in a fine glass Luggin capillary, the tip of which is placed about 1 mm from the working electrode surface.18 The purpose of the capillary is to reduce the iR drop between the reference and the working electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003194_0278364904038366-Figure33-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003194_0278364904038366-Figure33-1.png",
        "caption": "Fig. 33. Top view of the AV.",
        "texts": [
            " Energy Method The complex potential \u03c9(z) is given by \u03c9(z) = U(t)\u03c91(\u03b6 )+ V (t)\u03c92(\u03b6 )+ (t)\u03c93(\u03b6 ) +\u03b3c(t)\u03c94(\u03b6 )+ \u2211 k \u03b3k\u03c95(\u03b6 ; \u03b6k(t)) (34) where \u03b6 = F\u22121(z) with F : \u03b6 \u2192 z being the Joukowski transformation (1) \u03c91(\u03b6 ) = \u2212 r 2 c \u03b6 + \u03b6c + a2 \u03b6 + \u03b6c (35) \u03c92(\u03b6 ) = \u2212i r2 c \u03b6 \u2212 i\u03b6c \u2212 i a2 \u03b6 + \u03b6c (36) \u03c93(\u03b6 ) = \u2212i ( \u03b6cr 2 c \u03b6 + a2 r 2 c /\u03b6 + \u03b6\u0304c \u03b6 + \u03b6c + a4\u03b6c (\u03b6 + \u03b6c)(r2 c + \u03b42) +a 4 + r2 c \u2212 \u03b44 2(r2 c \u2212 \u03b42) ) (37) \u03c94(\u03b6 ) = i log \u03b6 rc (38) \u03c95(\u03b6 ; \u03b6k) = i log ( \u2212 rc \u03b6k \u03b6 \u2212 \u03b6k \u03b6 \u2212 r2 c /\u03b6\u0304k ) . (39) The sum of the kinetic energies of the AV and of the surrounding water is given by T = L 2 \u03c1 \u222b Sv d\u03c9 dz ( d\u03c9 dz ) dA+ 1 2 q\u0307TM(q)q\u0307 where \u03c1 is the density of the water, and L is the out-of-plane dimension of the foil. The integral in the first term is taken over the area outside the foil and outside any free vortices. Let Qs(z) = [\u03c91(z), \u03c92(z), \u03c93(z)] \u2208 C1\u00d73, and ignoring central and free vortices, we have d\u03c9 dz (z) = dQs(z) dz  U(t)V (t) (t)   . The kinematic relationship (Figure 33) + Lf (\u03b8\u0307 + \u03b1\u0307) = \u03b1\u0307 + \u03b8\u0307 , (40) where Ld, Lh and Lf are the AV parameters which are shown in Figure 33, implies that  UV   = Q2(q)q\u0307 for some Q2(q\u0304) \u2208 3\u00d74. Thus, we define the combined inertia matrix of the system to be Mm(q) :=M(q) + L\u03c1QT 2 (q)RS  \u222b Sv dQs dz T dQs dz dA   QT 2 (q) (41) whereRS[\u00b7] denotes the real symmetric part of the argument. The second term of eq. (41) is the hydrodynamic added mass whereas the first term is the inertia of the AV itself. The total kinetic energy (4) can then be written as T = 1 2 q\u0307TMm(q)q\u0307. The added mass component in eq. (41) can be evaluated using the Area Theorem (Milne-Thomson 1968), which states that, given f (z, z\u0304) which is a continuous and differentiable function in the area A enclosed by the contour C, an area at PENNSYLVANIA STATE UNIV on May 23, 2015ijr"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003752_j.triboint.2008.07.008-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003752_j.triboint.2008.07.008-Figure9-1.png",
        "caption": "Fig. 9. Gear frame assembly.",
        "texts": [
            " The authors have also simultaneously monitored the operating conditions such as temperature, viscosity, film thickness and specific film thickness in order to integrate and assess fault severity and operating conditions of the gearbox. Severity of defect can be assessed by the information of stiffness reduction in gear teeth. In the modal test setup, the test pinion was clamped with a specially designed frame in which a pair of diametrically opposing teeth was machined to accommodate the test pinion. Fig. 9 shows the photograph of pinion and frame assembly used in the modal test assembly. The steel rectangular section was fabricated as a frame in which two tapered slots were machined at the mid span of the inner faces of the two vertical sides, which enabled the pinion to be held firmly by its two opposite teeth. The gear teeth were supported across their entire face width, so that the measured vibration responses were due to stiffness of both the teeth. The suspended teeth in the frame were excited by an impact hammer, causing the frame assembly to vibrate in a direction perpendicular to a plane passing through the pinion body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003684_j.matdes.2008.06.037-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003684_j.matdes.2008.06.037-Figure10-1.png",
        "caption": "Fig. 10. The thermal damage in unmodified gears with 8 mm of tooth width: (a) 8.5 Nm 1500 rpm and (d) 13 Nm tooth load and 1500 rpm.",
        "texts": [
            " The wear depths of the modified gear along the profile were less than the wear depths of the unmodified gear. This was especially true for the case where the unmodified spur gears were thermally deformed suddenly and wore out quickly; however, there was no thermal deformation in the modified gears at the same conditions and the wear was less than the wear on the unmodified gear. Although the accumulated heat that came about during the operation of the unmodified gears was partially expelled, the heat in the region, shown with hidden lines in the ellipsoid in Fig. 10 was not expelled as much as the heat in the other parts of the gears. With the increasing temperature in this region, the mechanical properties of the plastic materials were degraded and reduced. Therefore, especially under high loads and torque transmissions, he experiment after 1000 rpm. he experiment after 1500 rpm. the service life of the plastic gears was shortened. As shown in Fig. 11a and b, the damage to the tooth varied under various tooth loads and velocities. There was only wear at 1000 rpm under both tooth loads",
            " 11a, the tooth temperature of unmodified gears under a 8.5 Nm tooth load at a velocity of 1000 rpm was shown to quickly increase at the beginning of the experiment (Fig. 12a) and then stay constant at a temperature of about 67 C. Under a 13 Nm tooth load, the tooth temperature increased faster compared to the first loading and reached a temperature of 78 C in a short period of time. In the first phase of the experiment, the tooth temperature was higher especially in the ellipsoid region shown in Fig. 10a\u2013d, and this led to the earlier thermal damage of the tooth. In the first phase of the experiment, this sudden change in the gears happened faster at 1500 rpm (Fig. 12b), and after a period of time, gear tooth breakages occurred . As shown in Fig. 12a and b, a sudden rise in the gear temperature was spread out in the unmodified spur gear tooth surface from near the pitch region to the entire tooth surface. In the beginning of the experiment, the plastic pinion had the highest tooth temperature at the center area of the tooth width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure8-1.png",
        "caption": "Figure 8, Schematic of generation by grinding worm.",
        "texts": [
            " (b) The concept of direct derivation of Ez by E~ is based on the two-parameter enveloping process. The process of such enveloping is based on application of two independent sets of parameters of motion. Topology of Modified Surfaces 1069 (i) One set of parameters relates the angles of rotat ion of the worm and the pinion as Cw N1 - - z ~1 Nw ' ( 5 ) wherein N~ is the number of worm threads and N1 is the number of the pinion teeth. Usually, N~ - 1. (ii) The second set of parameters relates the displacement s~ of the worm (Figure 8), that is collinear to the axis of the pinion, and a small rotat ional angle ~1 of the pinion about the pinion axis as S w - p , ( 6 ) 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 [6]. The schematic of generation of E1 by E~ is shown in Figure 8. In the process of meshing of E,, and El , the worm surface Ew and the involute pinion surface perform rotat ion about crossed axes. The shortest distance is executed as E~I = %1 + r ,~ . (7) 1070 F.L. LITVIN e t al. Surfaces E~, and E1 are in point tangency. Feed motion of the worm is provided as a screw motion with the screw parameter of the pinion. GENERATION OF MODIFIED TOOTH SURFACE BY A GRINDING WORM. The worm thread surface Ew is an involute surface that generates an involute pinion tooth surface E1 when the double enveloping process is governed by the linear relations given in (5),(6)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003870_1.4001003-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003870_1.4001003-Figure2-1.png",
        "caption": "Fig. 2 Kinematic diagrams of the two-stage nutation drive",
        "texts": [
            " The input shaft is also an xis of the internal gear 2. The external gear 3 is fixed to the xternal gear and located inside the external gear 1. The external ear 3 engages with the internal gear 4 that is attached to the utput shaft and coaxial with it. The external gear 1 meshing with he internal gear 2 creates the first stage nutation drive. The exernal gear 3 meshing with the internal gear 4 creates the second tage nutation drive. The kinematic diagram of this two-stage nuation drive is illustrated in Fig. 2, where gears 1 and 3 are the xternal ones and gears 2 and 4 the are internal ones, as shown in ig. 1, and shaft 5 is the input shaft. The transmission ratio of this wo-stage nutation drive can be obtained as i14 = z1z4 z1z4 \u2212 z2z3 = sin 1 sin 4 sin \u00b7 sin 1 \u2212 3 1 here zi i=1, . . . ,4 is the tooth numbers of gear i i=1, \u00af ,4 , i i=1, \u00af ,4 represents the pitch cone angle of the spiral bevel 1Corresponding author. Contributed by the Power Transmission and Gearing Committee of ASME for ublication in the JOURNAL OF MECHANICAL DESIGN"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002307_a:1026567812984-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002307_a:1026567812984-Figure6-1.png",
        "caption": "Figure 6. Abstraction of the hand-eye system.",
        "texts": [
            " By computing the intrinsic and extrinsic parameters through the camera movements we can gain the geometrical relationship between the camera positions relative to the world coordinates. The position of the robot arm or vehicle, on the other hand, is always known due to the angular position of the step motors of the device which are permanently controlled by the computer. The problem of hand-eye calibration arises when we try to find out the group transformation between the reference coordinates of the mechanical device and the coordinate frame of the camera. An abstraction of the geometry of a camera mounted on an robot arm is depicted in Fig. 6. The classical way to describe the hand-eye problem in mathematical terms is by using transformation matrices. This problem was firstly formulated as a matrix equation of an Euclidean transformation by Shiu and Ahmad [36] and Tsai and Lenz [39], respectively AX = XB (61) where the matrices A = A1A\u22121 2 and B = B1B\u22121 2 express the elimination of the transformation between hand\u2013base and world. From the expression (61) the following matrix equation and a vector equation can be derived by splitting the Euclidean transformation into rotation and translation components RARX = RX RB (62) (RA \u2212 I)tX = RX tB \u2212 tA"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003191_tia.1986.4504785-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003191_tia.1986.4504785-Figure1-1.png",
        "caption": "Fig. 1. Coil placement of one phase of double-layer lap winding having 7/9 slot pitch.",
        "texts": [
            " This paper describes a new method which permits the measurement of air-gap flux in a low-cost reliable manner. The implementation of this flux sensing scheme does not involve placing additional search coils in the motor slots or inserting hall probes but uses the coils of the motor themselves as the sensing medium. Hence negligible additional cost is incurred by the introduction of flux sensing. Components used external to the motor involve only low-cost operational amplifiers and transconductance-type multipliers. To describe the flux sensing scheme being proposed, Fig. 1 shows a typical placement of coils around the stator of a typical 36-slot four-pole machine. The windings shown are associated with one of the three motor phases (windings of the other two phases are not shown). This type of winding is called a double-layer lap winding and is the most popular pattern for winding ac induction or synchronous machine armatures. Note that the winding which makes up a phase actually consists of a number of individual coils which are connected in series and/or parallel to form a given phase winding. The coils which are located in the same part of consecutive slots are called a phase belt and are always connected in series in order to result in phasor addition of the induced voltages. 0093-9994/86/0700-0731$01.00 \u00a9 1986 IEEE IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-22, NO. 4, JULY/AUGUST 1986 vas It is useful to consider the voltage induced, specifically in coils n1 and n3 in Fig. 1. Note that these two coils are, in general, displaced spatially by an electrical angle, say 2c. The voltages induced in these two coils are therefore out of phase by the same angle 2e. The voltage induced in the two coils can be diagrammed with respect to the three normal phase voltages as shown in Fig. 2. In general, the voltage induced in these two coils are normally summed together with the \"middle\" coil of the phase belt in Fig. 1 to produce a voltage which is in phase with the voltage of phase a on Fig. 2, as shown in Fig. 3. It is useful to consider, however, the result obtained when the voltages induced in these two coils are subtracted rather than added. In this case a voltage is measured which is displaced 900 with respect to phase a. This component is sometimes called the d component in electrical machine analysis. The process of subtracting the voltages enables the measurement of the flux in a particular direction which can be integrated in much the same manner as with search coils to measure the instantaneous air-gap flux in a particular direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003864_s0094837300003286-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003864_s0094837300003286-Figure12-1.png",
        "caption": "FIGURE 12. Possible balance of forces in a fish in which the hypochordal angle is too great to allow a \"balanced thrust\" from the ventral hypochordal lobe. The line of thrust from the ventral hypochordal lobe (V) lies behind the center of gravity, but this offsets a corresponding orientation of the line of thrust from the dorsal lobe ( D ) , resulting in a line of net thrust (D') again passing through the center of gravity.",
        "texts": [
            " Assuming again that the relationship of F/T estimated for Squalus acanthias is of general application, we can see that in forms in which the dorsal and ventral thrust angles do not exceed 26 and 21\u00b0, respectively, a continuous \"balanced\" orientation of the lines of thrust from the tail is possible. They will combine so that the net line of thrust lies somewhere between them, depending on the relative areas of the dorsal lobe and ventral hypochordal lobe and the forces generated within them. If the dorsal and ventral thrust angles exceed these values, balance is potentially lost but is regained if the imbalances are offsetting. As Figure 12 shows, the imbalances must largely be offsetting, because they are of opposite sign. The dorsal lobe, at the peak develop ment of thrust, will develop a hypobatic mo ment as the line of thrust falls behind the center of gravity. The ventral hypochordal lobe will develop a corresponding epibatic moment. If the magnitudes of these can be matched there will be balance. From this we can make the prediction that all sharks in which the dorsal thrust angle exceeds 26\u00b0 a ventral hypochordal lobe is essential"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002820_s0003-2670(01)01608-7-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002820_s0003-2670(01)01608-7-Figure4-1.png",
        "caption": "Fig. 4. Proposed mechanism for the CuPc:His enzymeless biosensor response.",
        "texts": [
            " Cleavage of the O\u2013O bond and hydrogen extraction from the substrate forms water, copper-oxo and substrate radical, which consequently combine to form hydroxylated product. In our case, the hydrogen peroxide addition in the working solution could increases or generates the formation of CuII\u2013O\u2013O\u2013H and consequently, the rate of the substrate oxidation. On the other hand, the regeneration of the oxidized catecholamines by applying an adequate potential is feasible. On this basis, the mechanism presented in Fig. 4 was proposed for this enzymeless biosensor. Initially, Cu2+ in presence of H2O2 forms the CuII\u2013O\u2013O\u2013H species. This species will oxidize catechol to form 1,2-quinone. In this stage, that represents the most important step for phenol quantification, occurs the electrochemical reduction of the quinone species on the electrode surface, through the application of a suitable potential. This mechanism also explains the high sensitivity of the sensor by the signal amplification due to the cycle reaction [5,27]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.27-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.27-1.png",
        "caption": "Figure 5.27 Forces involved form a concurrent system.",
        "texts": [
            " F J is the magnitude of the reaction force applied by the head of the femur on the hip joint at E. W2 = W - WI (total body weight 104 Fundamentals of Biomechanics minus the weight of the right leg) is the weight of the upper body and the left leg acting as a concentrated force at G. Note that G is not the center of gravity of the entire body. Since the right leg is not included in the free-body, the left-hand side of the body is \"heavier\" than the right-hand side, and G is located to the left of the original center of gravity (a point along the vertical dashed line in Figure 5.27) of the person. The loca tion of G can be determined utilizing the method provided in Section 4.12. By combining the individual weights of the segments constitut ing the body under consideration, the problem is reduced to a three-force system. It is clear from the geometry of the problem that the forces involved do not form a parallel system. Therefore, for the equilibrium of the body, they have to form a concurrent system of forces. This implies that the lines of action of the forces must have a common point of intersection (Q in Figure 5.27), which can be obtained by extending the lines of action of W2 and F M' A line passing through points Q and E designates the line of action of the joint reaction force F J' The angle ifJ that F J makes with the horizontal can now be measured from the geometry of the problem. Since the direction of F J is de termined through certain geometric considerations, the num ber of unknowns is reduced by one. As illustrated in Fig ure 5.28, the unknown magnitudes F M and F J of the muscle and joint reaction forces can now be determined simply by trans lating W2, F M' and F J to point Q, and decomposing them into their components along the horizontal (x) and vertical (y) directions: FMy = FM sine FJx = FJ coscp FJy = FJ sincp For the translational equilibrium in the x and y directions: L,:Fx=O: LFy=O: Simultaneous solutions of these equations will yield: F _ cosifJ W2 M - cos e sin ifJ - sin () cos ifJ F = cos() W2 J cos () sin ifJ - sin e cos ifJ (xi) (xii) For example, if () = 70\u00b0, ifJ = 74"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002957_s0263574703005216-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002957_s0263574703005216-Figure1-1.png",
        "caption": "Fig. 1. Planar manipulator with all synthesis parameters. Note that the angle is from the longitudinal axis of the ith link.",
        "texts": [
            "29 Sets of optimisation trials were accomplished to prove that the proposed optimisation methodology was an efficient, versatile and systematic procedure, and could be employed to determine the best possible link lengths and mass distribution parameters of a * Force balancing, gravity balancing and static balancing are used interchangeably in the mechanism literature. five-bar parallel manipulator, without going through a great deal of analysis. However, it must be kept in mind that the optimum solutions depend on the initial values assigned to the synthesis parameters and they do not necessarily represent a global minimum. The five-bar planar manipulator considered in this study is shown in Figure 1, where its two joints (A and E) connected to the ground are active and the others are passive joints. The input motions of the active joints can be independent from each other or be provided via a set of gears maintaining a specified phase angle between the two active joints in order to generate an infinite number of different motions from the output point C.5 Analytical expressions for the coordinates of the output point C, where the end effector is mounted, are obtained for the provided joint inputs 1 and 4, and the specified link lengths L0, L1, L2, L3, L4 and the angle 0",
            " The equations describing the forces acting on links 1, 2, 3, and 4 are put in a matrix-vector form; [M][F]=[Fg] (11) where M, F, and Fg denote the matrix of known mechanism dimensional parameters and joint angles, the vector of unknown forces, and the gravitational force vector, respectively. As seen from the determinant of M given below, it is singular when 4 = 2 + 3 2 + 2 (2k+1) for k=0, 1 . . . or 1 = 2 or 2 = 3. | M |= 2L2 2L 2 4 cos 4 2 + 3 2 sin( 1 2)sin 2 3 2 (12) Assuming that the matrix M is non-singular throughout the operation range of the manipulator. Equation (11) is solved for the unknown forces, FAx, FAy, FBx, FBy, FCx, FCy, FDx, FDy, for which mathematical expressions are given in Appendix A. The parameters defining the geometry of the manipulator depicted in Figure 1 are the link lengths L0, L1, L2, L3, L4. It must be recalled that the configuration dependent Jacobian matrix of a robot manipulator is involved in the force and motion transfer between the actuators and the end effector. Depending on the Jacobian matrix either relating the end effector velocity to the actuator velocity vector and vice versa, the motion and force errors propagated from the actuators to the end effector is bounded by the condition number of the Jacobian matrix.30,31 The condition number of the Jacobian matrix is not only a measure of how accurate the force and motion transfer between the actuators and the end effector is accomplished, but also the measure of the ease with which the manipulator can arbitrarily change its pose (position and orientation) and apply forces in arbitrary directions",
            " (iii) The mechanism must obey the assemblability condition,5,34 which requires that L0 <Lm +Lm 1 + \u00b7 \u00b7 \u00b7 L1, provided that L0 and Lm are the longest and shortest links of the mechanism, respectively. It must be noted that when L0 =Lm +Lm 1 + \u00b7 \u00b7 \u00b7 L1, all the links are collinear and the mechanism is a change-point mechanism. This is known as zero mobility condition.35 The mechanism will not move unless a special precaution is taken to pass through the change-position configuration. (iv) The transmission angle , which is the angle between L2 and L3 of Figure 1, must be 50\u00b0\u2264 \u2264130\u00b0, ideally be 90\u00b0, for effective force transmission from two coupler links to the output point C. Especially when its deviation from 90\u00b0 is greater than 500, it causes unacceptable higher acceleration and jerk, and objectionable noise at high speeds. It must also be continuous between the desirable ranges.1,5 Referring to Figure 2(a), it is mathematically expressed as; cos =1 q2 2L2 2 (15) (v) For the sake of generality, it is required that the links connected to the active joints make unlimited rotations",
            " A force-balanced mechanism requires that its potential energy consisting of gravitational and elastic potential energies is constant for all configurations of the mechanism.17 The total potential energy is formulated as V=MTgRg +Ve (16) where MT is the total mass of the moving links, Rg is the vertical component of the position vector R , given by Equation (20), describing the mass center of the mechanism, and Ve is the elastic potential energy of the system, which is not applicable for the balancing approach adopted in this paper. Using the notation given in Figure 1, the position vector R describing the mass center of the mechanism is38 R = 1 MT 4 i=0 mir i (17) where r i is the position vector describing the mass center Gi of the ith moving link with a mass of mi with respect to the reference point A. The individual position vectors are expressed in complex numbers as r 1 =R1e j( 1 + 1), r 2 =L1e j 1 +R2e j( 2 + 2), r 3 =L0e j 0 +L4e J 4 +R3e j( 3 + 3), r 4 =L0e j 0 +R4e j( 4 + 4), (18) The exponential terms are related to each other by the loop closure equation L1e j 1 +L2e j 2 =L0e j 0 +L3e j 3 +L4e j 4 (19) The exponential term ej 3 (or ej 2) is extracted from Equation (19), and then substituted into Equation (18)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003911_j.jtbi.2008.06.034-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003911_j.jtbi.2008.06.034-Figure2-1.png",
        "caption": "Fig. 2. Two spring-mass gaits with a double stance and no flight phase, one qualitatively similar to a cockroach run (a), the other similar to a human walk (b). In a running cockroach, the CoM reaches maximum height when all six legs are on the ground (Full and Tu, 1990, 1991). In human walking, the CoM height is maximal at the middle of each single stance phase (Geyer et al., 2006).",
        "texts": [
            " For the running gaits of interest, the CoM trajectory within a stance phase is mirror-symmetric about mid-stance (a vertical line through the foot contact point) and the CoM velocity vector is horizontal at mid-stance. The two parameters characterizing the space of such one-step periodic solutions can then be taken as the spring compression or CoM height at mid-stance and the horizontal velocity at mid-stance. The spring-mass model is also capable of gaits with a double stance phase but no flight phase, as discovered by Holmes et al. (2006b) and Geyer et al. (2006). Two qualitatively different examples are shown in Fig. 2, one resembling running gaits of cockroaches (Fig. 2a; Holmes et al., 2006b) and another resembling the walking gaits of humans (Fig. 2b; Geyer et al., 2006). Here M1 denotes mid-stance of leg-1, which continues in ground contact until lift-off at LO1. Leg-2 begins ground contact at TD2, before leg-1 loses contact, leading to a double stance phase. The lengths of leg-1 at LO1 and leg-2 at TD2 are both equal to l0. MDB denotes the middle of a symmetric double stance phase. Note the difference in where double stance occurs relative to CoM height in the two gaits. The following counting arguments show that the set of such one-step periodic gaits is also characterized by two parameters (again given mass m, leg length l0, and stiffness k)",
            " Assuming symmetry about mid-stance as above, each singlestance phase now requires specification of three parameters: horizontal velocity and vertical compression at mid-stance, and additionally, the duration of the single stance phase (because this phase does not end when one leg leaves the ground). Since the length of leg-2 at touch-down is l0, the touch-down angle follows from the state at TD2, and therefore is not an free parameter. The equations of motion for the double stance phase can be integrated forward in time until the vertical velocity of the CoM falls to zero (e.g., at the point MDB in Fig. 2). All that is required for a symmetric periodic gait is that the horizontal distance from the foot C1 to MDB be exactly half the distance between the stance feet C1 and C2 (the step length). This ensures that integrating Eqs. (1) and (2) forward in time from MDB will be identical to integrating the same equations backward in time, with a mirror-reflection about the vertical line through MDB. This one constraint on the three parameters implies that the space of such periodic solutions is a two-parameter family",
            " 4c compares GRFs of a spring-mass model with speed, step period, duty factor, mass, and average body height approximately matched to those of a running cockroach, Blaberus discoidalis (Full and Tu, 1990; Ting et al., 1994). As noted above, single stance corresponds to support by one tripod of the insect\u2019s double tripod gait, and double stance to both tripods (all six legs) being on the ground. While there is good qualitative agreement in shape and the net force directions are similar (compare Fig. 4c with 3c), quantitative comparisons of force magnitudes (dotted and solid curves in panel (b)) are less encouraging. As noted in Section 2.2 and Fig. 2b, human walking also has double-stance phases, but they are qualitatively different from those of cockroach running. In human walking, the midpoint of single stance is when the CoM is at its highest point. This is almost exactly out of phase with the cockroach gait, in which the highest CoM position occurs during the double-stance phase. Geyer et al. (2006) first showed that the qualitative aspects of human walking can be achieved by a spring-mass model with bipedal support. arison with the best-fit spring-mass model",
            " We illustrate by computing branches of gaits over representative speed ranges for the three animals considered in Section 3.3. Fig. 5 shows graphs of non-dimensional step length versus nondimensional speed for a range of duty factors encompassing flight and double stance phases. The non-dimensional quantities are defined as follows: non-dimensional speed \u00bc uffiffiffiffiffiffi gl0 p , (8) non-dimensional step length \u00bc Ls l0 , (9) where u denotes the average forward speed and Ls the physical step length. We only show branches with double-stance gaits (dark solid curves) qualitatively similar to that in Fig. 2a. The running gaits with flight phases (light solid curves) are all qualitatively similar to Fig. 4a, and there is a smooth continuation of these types of gaits from duty factors less than 0.5 to duty factors greater than 0.5. We investigated the stability of these gaits under the constant touch-down angle protocol by finding eigenvalues of the Jacobian obtained by computing how perturbations of mid-stance conditions change the state at the next mid-stance. The regions of stability are qualitatively similar in all three cases: in particular, none of the double stance gaits we considered were stable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003795_978-3-540-85640-5_14-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003795_978-3-540-85640-5_14-Figure1-1.png",
        "caption": "Fig. 1. Kinematics diagram of the base of an omnidirectional robot.",
        "texts": [
            " The remainder of this paper introduces the kinematic model of an omnidirectional middle-size Robocup robot in section 2; Path following and orientation tracking problems are solved based on the inverse input-output linearized kinematic model in section 3, where the actuator saturation is also analyzed; section 4 presents the identification of actuator dynamics and their influence on the control performance. Finally, the experiment results and conclusions are discussed in sections 5 and 6, respectively. The mobile robot used in our case is an omnidirectional robot, whose base is shown in Fig. 1. It has three Swedish wheels mounted symmetrically with 120 degrees from each other. Each wheel is driven by a DC motor and has a same distance L from its center to the robot\u2019s center of mass R. Besides the fixed world coordinate system [Xw, Yw], a mobile robot fixed frame [Xm, Ym] is defined, which is parallel to the floor and whose origin locates at R. \u03b8 denotes the robot orientation, which is the direction angle of the axis Xm in the world coordinate system. \u03b1 and \u03d5 denote the direction of the robot translation velocity vR observed in the world and robot coordinate system, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003334_s11071-007-9306-2-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003334_s11071-007-9306-2-Figure3-1.png",
        "caption": "Fig. 3 Positions and displacements of race-curvature centers and ball center",
        "texts": [
            " With the small motion assumption, the relationship between {uj } and {U} is as follows: {uj } = [Tj ]{U}, (3) where [Tj ] is the transformation matrix [8, 9] [Tj ] = [ cos\u03d5j sin\u03d5j 0 \u2212zp sin\u03d5j zp cos\u03d5j 0 0 1 rp sin\u03d5j \u2212rp cos\u03d5j 0 0 0 \u2212 sin\u03d5j cos\u03d5j ] . (4) The angular location of the j th rolling element, \u03d5j , can be obtained from \u03d5j = 2\u03c0(j \u2212 1) N + \u03c9ct + \u03d50. (5) The varying compliance frequency or the ball passage frequency can be described as the cage speed times the number of balls. \u03c9vc = \u03c9c \u00b7 N. (6) 2.2 Ball equilibrium It is assumed that the effects of centrifugal force and gyroscopic moment of ball may be ignored. When the outer race is stationary and the inner race is displaced under the bearing loading, as shown in Fig. 3, the distances between the j th ball center and the inner, outer race centers of curvature, respectively, can be given by Li = ri \u2212 Db/2 \u2212 ci, Lo = ro \u2212 Db/2 \u2212 co, (7) tan\u03b1j = (Li + Lo) sin\u03b10 + uzj (Li + Lo) cos\u03b10 + urj = aj bj , (8) lij + loj = \u221a a2 j + b2 j . (9) The overall contact deformation between the j th ball and races is \u03b4j = lij + loj \u2212 Li \u2212 Lo \u2212 ci \u2212 co, (10) where the negative values means loss of contact. If the contact deformation is positive, the contact force could be determined using the Hertzian contact theory [20]; otherwise, no load is transmitted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.10-1.png",
        "caption": "Fig. 6.10 Characteristic curves of (a) an actuator and (b) of a linear spring in the respective Fuplanes. (c) Interaction of both curves in the same Fu-plane (F=actuator force)",
        "texts": [
            " 4 Since a pre-strain state can be represented by an equivalent pre-stress state (see also 6.3.6) we will not distinguish, in the following, between the two conditions. For the sake of brevity, the term pre-stress will mostly be used to denote any of the two states. 6.3 Theory of Single-Stroke Linear Solid-State Actuators 165 The graph of Figure 6.9 represents the case of an actuator interfaced with a linear elastic structure. The actuator\u2019s characteristic (4) is represented, in the Fu-plane, by a straight line as shown in Figure 6.10(a). Figure 6.10(b) shows the graph of Equation 6.7, which provides the characteristic of the linear spring. Since, however, the forces in the two elements have different signs (according to the node rule the sum of the actuator force and of the spring force must be zero), one of the curves has to be mirrored with respect to the u-axis in order to be plotted on the same plane of the other one. If the plane of the actuator force and stroke is chosen (actuator force: F; spring force: -F), both curves are represented as in Figure 6.10(c). The intersection point supplies the values of the actual actuator force and stroke and lies somewhere between the free-stroke and the blocking condition. The slopes of the curves correspond to the respective values of the stiffness. The higher the stiffness ratio is (structure\u2019s stiffness ks over actuator\u2019s stiffness ka), the closer the point of intersection will be to the blocking condition; the lower the ratio, the closer it will come to the free-stroke condition (see Figure 6.11). The actual values for force and stroke are computed by simultaneously solving the equations F + ka (u\u2212ui) = 0 (6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002967_iros.2004.1389445-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002967_iros.2004.1389445-Figure4-1.png",
        "caption": "Fig. 4. Force and \" m i U link 1,",
        "texts": [
            " While we assume that link units are point-contacted with ground through wheel, we can have the postion of contact point ,PI; E R3, its velocity PJi E R3, and its acceleration PJ; E R3 as same as (lO),(llj.(lZ), They are given by P G i = P i + W ; X I C ; (11) P G ; = P; +3; x lo; + w , x (U< x 1c;) PJi = P; + l J i P,, = P< + wi x I , ; (i = 0 -72 - 1) (13) (14) ~ J ~ = ~ + ~ ; x I ~ ~ + w ~ x ( w ~ x I J ; ) 15) where 1 J ; E R3 is a vector from joint i to the contact point of link i. 111. DYNAMICS OF SNAKE ROBOTS To make possible dynamic analysis of the motion of 3-dimensional snake-like robots, we derive the robot dynamics by Newton-Euler method. From Fig.4, we have basic Newton-Euler equation of (16) link i. They are described by f; - f i+ l + f e i + mig = miPci ni - ni+~ - loi x f i + (li - I C ; ) x (-f;+l) + ( 1 J ; - Ici) X f e i = I;&; +U; x (1;~;) (17) where f; E R3 describes the moment acted at joint i. f o , fn , no, n, E R3 show the force and moment at the head and tail of robot, f e ; E R3 is the force from ground at contact point of link i, mi E R is mass of Link i. I; E PX3 is inertia tensor of link i , g = g[O,O, -1' E R3 is gravity acceleration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003414_ma00197a027-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003414_ma00197a027-Figure3-1.png",
        "caption": "Figure 3. Polyethylene single crystal with curved 200-type edge (schematic). Dashed lines symbolize folds.",
        "texts": [
            " The curved 200-type face of polyethylene single crystals exhibits precisely this behavior when g, and G2, are extracted from the growth rate and crystal shape data of Organ and Keller by using the method of analysis devised by Mansfield4 to obtain g2m In the following, we outline the treatment of certain of the data of Organ and Keller to illustrate how curved edges arise. IV. Reduced Substrate Completion Rates and Curved Edges: The Mansfield Equations for Growth of a Crystal with Two Types of Sectors It is useful to show how a substrate completion rate that has been reduced by the effect of lattice strain can lead directly to a curved edge. The system we have in mind is depicted in Figure 3, which shows a somewhat idealized version of a polyethylene single crystal with both 110- and 3050 Hoffman and Miller 200-type sectors. This sketch draws heavily on the findings of Wittmann and L o ~ z . ~ ' Khoury and have shown that the chains in the 200-type sectors exhibit tilt and that this tilt is variable; we take this to be consistent with the presence of lattice strain. The edgewise rate of advance of the 200-type sector is the velocity h, which is controlled in part by Gllo, the growth rate of the 110 face",
            " The velocity h is determined by both the growth of the adjoining 110 sector and the advance of the 200 sector according to h = (Gllo/cos A) - Gm tan A[l - (h/g200)2]1/2, where the angle A is set by the unit cell dimensions, a and b: A = tan-l ( a / b ) = 32.9'. The functions B ( x , t ) and L(x,t) are the concentrations of right and left moving steps on the 200 growth front. The quantity i = i2 , is the nucleation rate, and g = g,, is the substrate completion rate on the 200-type face. When carried out in the context of the geometry given in Figure 3, the solutions of the above equations have been shown by Mansfield to lead to4 K2 G2oo curvature C = - = -11 - [ l - (h/g200)2]1/2] 2ht 2h Two useful expressions for the aspect ratio A, also arise from the treatment: tan 0 + tan A 1 + 2C tan 0 A , = To the above may be added the general definition The reason for mentioning these alternative forms for A, will become apparent when we discuss the data of Organ and Keller on polyethylene single crystals. The meaning of the quantities in the above expressions is given in Figure 3. From eq 32b it is evident that curvature appears only when g,, is slightly greater than h. It is for this reason that we earlier sought expressions based on nucleation theory for a substrate completion rate that was comparable in magnitude to the growth rate of a normal facet (in this case Gllo). It is only when os > 0 is invoked in this system for the 200-type face that this occurs. In the normal strain-free case, g,, >> h, which gives no curvature. The curved edge actually possesses numerous nucleation and growth sites, but nucleation and substrate completion are Macromolecules, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003780_j.msea.2008.07.021-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003780_j.msea.2008.07.021-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic illustration of the DMD process (b) Photograph",
        "texts": [
            " Deposition procedures and materials DMD was performed with a 2 kW Rofin diode laser providing pproximately equal amounts of 808 and 940 nm radiation. The eam was focussed to give a rectangular profile approximately mm \u00d7 2 mm with a nominally Gaussian distribution in the short xis direction and top hat distribution in the long axis direction. arrangement for deposition experiments used in the present study. he beam was focussed approximately at the deposition point for he feedstock wire which was \u201cfront fed\u201d into the beam at an ngle of approximately 45\u25e6, as shown schematically in Fig. 1(a). he DMD process was performed under a controlled atmosphere y surrounding the workpiece and laser head with a flexible transarent enclosure which was evacuated and then back-filled with igh purity argon gas. The experimental arrangement is shown n Fig. 1(b). Waspaloy walls were deposited onto 10 mm thick aspaloy base plate using commercially available 1.2 mm diamter welding wire as feedstock. The base plate was obtained from ommercially available hot worked and solution treated Waspaloy illet. The chemical compositions of wire and base plate are given n Table 1. Wall deposits, approximately 6 mm wide by 100 mm ong, were produced by making successive laser tracks one on top f the other, with the traverse direction of the substrate perpendiclar to the long axis of the laser beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002457_s0094-114x(99)00036-1-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002457_s0094-114x(99)00036-1-Figure3-1.png",
        "caption": "Fig. 3. Schematic illustration of a three-stage spur gear reduction unit with the associated design variables indicated including gear and pinion diameters, face width, diametral pitch, and core hardness values. The driving torque Tin and overall speed ratio e are prescribed.",
        "texts": [
            " In this section, the design variables and constraint set for a three-stage spur gear reduction unit is developed in the standard form described in Eqs. (3.1) and (3.2). Similar formulations for a two-stage unit, as well as for a greater number of stages, would follow in an obvious fashion. A completely general formulation for an arbitrary number N of stages appears straightforward, but would be considerably more awkward for presentation here. A schematic illustration of the three-stage unit is shown in Fig. 3. The unit is driven by an input torque Tin and an overall speed ratio e for the gear train is prescribed. For each stage the following constraints, as outlined in Section 2, must be enforced: Tooth bending fatigue failure (2.1) and (2.2): FtP bJ KvKoKmRS 0nCskrkms 4:1 Tooth surface fatigue failure (2.3)\u00b1(2.5): Cp Ft bdI KvKoKm r RSfeCLiCR 4:2 Gear face width (2.6): 9 P RbR14 P 4:3 Interference (2.7): dagR2 \u00ff dbg=2 2 c2sin2 f q 4:4 Minimum pinion tooth number: Npr16 4:5 As indicated in the preceding discussion (4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002391_mssp.1999.1237-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002391_mssp.1999.1237-Figure1-1.png",
        "caption": "Figure 1. Schematic representation of a ball bearing: (a) ball bearing, (b) load distribution.",
        "texts": [
            " The whole mechanism is assembled in the casing which contains lubricants. The output shaft drives the output gear which transmits the motion to the di!erential. The gearbox vibration signals are recorded with piezoelectric accelerometers located on the casing. The vibration signals are low-pass \"ltered at 11.2 kHz and then sampled at 22.5 kHz. The angular position of the driving shaft is given by a pulse generator. The vibration signals correspond to a single-point defect on the inner race of the ball bearing of the driven shaft. A ball bearing (cf. Fig. 1(a)) is composed of the inner race, the outer race, the elements (the balls) and the cage guiding the elements (the cage does not appear on Fig. 1(a)). The important geometrical quantities of the bearing [5] are the number of rolling elements N, the element diameter d b , the average diameter d m and the contact angle a. The bearing load may be decomposed into two components, one in the x}z-plane which transmits the rotation, and one in the y-axis direction caused by the helical wheels. As shown in Fig. 1(b), the load distributes itself unequally on the rolling element. The force in the y-direction slightly translates the shaft. The contact axis of the rolling elements is tilted with the so-called contact angle a from the vertical plane x}z. The contact angle increases with the load. It is not known a priori but is upper bounded. In this section, we are interested in the modelling of the vibration signal in the fault-free case. For this, each element of the gearbox is considered in terms of the excitation and in terms of the vibration transmission",
            "f or ) (5) where f ir is the rotation frequency of the inner race (\"shaft) and f or the rotation frequency of the outer race. If the outer race is \"xed to the casing, f or \"0. The exact determination of the fault frequency supposes that the contact angle is perfectly known. In practice, it is only known approximately. In addition, this modelling cannot account for possible sliding e!ects and instantaneous contact angle variations. The radial load applied to the bearing is not isotropic and this results in the so-called load distribution [see Fig. 1(b)] which is a function of the angular position. If the defect is on the outer race, the impulse train has a constant amplitude because the fault location does not change with respect to the load distribution. Considering now an inner race fault, the amplitude of the defect will change with respect to its angular position. McFadden and Smith [5] consider that the impulse train is modulated (in amplitude) by the function q(h)\"Gq 0A1! 1 2e (1!cos h)B n for DhD)h .!9 0 elsewhere (6) where q 0 is the maximum load intensity, e the load distribution factor, h "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003899_s10472-009-9125-x-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003899_s10472-009-9125-x-Figure6-1.png",
        "caption": "Fig. 6 Dynamically changing neighbors by the minimum perimeter test (a ri moves toward pti, b ri selects new neighbors according to the minimum perimeter)",
        "texts": [
            " When three neighboring robots are all aligned, the centroid pct is set to the center point of the line segment between ps1 and ps2. If ri is located on the line segment, pti is set to the point \u221a 3du 2 away from pct. Otherwise, pti is set to the point du\u221a 3 away from pct. Now, Algorithm 2 is proposed to enable a swarm of robots to be arranged in \u2211n i=1 Ei. 4.2 Convergence of self-configuration Let\u2019s assume that when ri arrives at pti, a new robot D is found in close vicinity as illustrated in Fig. 6. Then, under Algorithm 2, ri selects D as s1, since it is located the shortest distance, and C as s2, since the distance from ps1 to pi via ps2 can be minimized. Thus, ri shuffles its neighbors within SB at each time instant, enabling the robots to configure themselves without having adjacent triangles partly overlapping each other. We now introduce a modified scalar function of (13) in order to consider the effect of changing neighbors. Lemma 2 Under Algorithm 2, ||pi \u2212 ps1|| and ||pi \u2212 ps2|| converge into du for ri after a finite number of activation steps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002898_0890-6955(95)00091-7-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002898_0890-6955(95)00091-7-Figure4-1.png",
        "caption": "Fig. 4. Kinematics diagram of five-axis machine (extracted from Fig. 1).",
        "texts": [
            " m 0 1 (14) 0 0 Now the final transformation is given by Ttot = Am'A t'A2\"A3\"Aa'As'To (15) To is the transformation at the zero position and Ai is the transformation based on the Rodrigues equation. 2.2.2. Error model offive-axis machine tools. Joint axes orientations are varied with the degree of misalignment. If we find the value of l and n in the reference coordinate system then m is given by m = l ~ 1 2 - n 2 (16) The location of the actual joint varies with the location of the plane. In the modeling of the zero position, the machine zero position and the coordinate system are defined before defining the unit vector of each axis. The unit vector from Fig. 4. is defined as follows (Table 2): [l,m,n] are the direction cosines of individual axis in the reference coordinate system. The rows 0-4 are for the five axes of the machine. The above model is for the ideal case. According to Table 2, the X-axis should pass through the point Po [Po~, Poy, Poz] with a direction cosine [1,0,0]. If Pot is the real point [Po#:Por] through which the X-axis passes then aPo = Oi + (Pyor-eyo) j + (Pzor-Pzo)k (17) where APoy=(Py:Poy) and APo~--(Po=--Poz) are small deviations in the position of the origin in the base Y- and Z-directions, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002896_bf02672531-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002896_bf02672531-Figure1-1.png",
        "caption": "Fig. 1 - Schematic of the heat-affected region showing the shape of the melt pool and the resulting trace during continuous laser remelting.",
        "texts": [
            " By assuming that phase equilibrium applies throughout, conditions within the processed material are given directly by the temperature or enthalpy of the material, thus avoiding any necessity to locate phase boundaries. The relationship between temperature, T, and enthalpy, H, is given by H(T) = c(T') dT' + (1 - f s (T) )L [11 where c(T) and L are the volumetric specific heat and latent heat, respectively. The solid fraction fs is deduced from a Scheil or Brody-Flemings model in the case of dendritic solidification or may be a step function if solidification is planar, as occurs with pure or eutectic material. Figure 1 shows schematically the region modeled. It considers only the heat-affected zone around the laser beam, implicitly assuming that the workpiece is significantly larger than this volume. In an Eulerian coordinate system, the equation of energy of the material moving with velocity, -vb, relative to the laser beam is given by OH OH - - - vb = div (K(T) grad (T)) [2] at O~ where K is the temperature-dependent conductivity and is the traverse direction (shown parallel to the x-axis). Note that any convection due to fluid flow in the molten region is not considered here. Equations [1] and [2] are solved within the region f~ with the internal boundaries I'1 (Figure 1) chosen so that the temperature at the edge of the calculation domain is close to the initial temperature Ta of the base material. More precisely, the boundary condition at F1 is specified by the Rosenthal point source model: 02] T(, ,r ) = T. + f~P exp ~ -vb(~ + r)} 2rrffr I. 2ff (~, r) E F l [3] where r is the radial distance from the point heat source, P is the power of the heat source, and 8, /3, and t~ are the average thermal diffusivity, surface absorption, and thermal conductivity, respectively. The surface of the material F2 is assumed to remain flat during laser remelting, thus neglecting the effects of surface tension and gas pressure on the liquid region. The laser energy is distributed (Figure 1) depending on the configuration of the specific laser and the optical characteristics of its focusing mirrors. To simulate accurately the conditions in the immediate vicinity of the beam, the model utilizes a normalized one-dimensional radial function F(p)* given by a polynomial or sum- *A normalized radial function means that 27r f0 ~ F ( p ) . p dp = 1. mation of Gaussian functions which best fit the particular laser energy distribution. This function is then numerically integrated in order to find the local energy, qi, impinging on each mesh: q,=Pfd, fa dy "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.33-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.33-1.png",
        "caption": "Figure 4.33 Scalar method.",
        "texts": [
            " The lengths of arms AB and BC are a = 20 cm and b = 30 cm, respectively, and the magnitude of the applied force is P = 120N. Assuming that the weight of the beam is negligibly small as compared to the magnitude of the applied force, determine the reactions at the fixed end of the beam. This is a three-dimensional problem and we shall employ two methods to analyze it. The first method will utilize the concepts of couple and couple-moment introduced in the previous chap ter, and the second method will utilize the vector properties of forces and moments. The scalar method of analyzing the problem is described in Figure 4.33 and it involves the translation of the force applied on the beam from C to A. First, to translate P from C to B, place a pair of forces at B that are equal in magnitude (P) and acting in opposite directions such that the common line of action of the new forces is parallel to the line of action of the original force at C (Figure 4.33a). The downward force at C and the upward force at B form a couple. Therefore, they can be replaced by a couple moment illustrated by a double-headed arrow in Figure 4.33b. The magnitude of the couple-moment is Ml = b P. Applying the right-hand-rule, we can see that the couple-moment acts in y Lx P ~Mc d R~==~f~==~B~- W f Figure 4.31 Forces acting on the beam. y x c v ____ -+~_______ Z p Figure 4.32 Example 4.6. 68 Fundamentals of Biomechanics the positive 2 direction. Therefore: Ml = b P = (0.30)(120) = 36 N-m (+2) As illustrated in Figure 4.33c, to translate the force from B to A, place another pair of forces at A with equal magnitude and opposite directions. This time, the downward force at Band the upward force at A form a couple, and again, they can be replaced by a couple-moment (Figure 4.33d). The magnitude of this couple-moment is M2 = a P and it acts in the positive x direction. Therefore: M2 = a P = (0.20)(120) = 24 N-m (+x) Figure 4.34 shows the free-body diagram of the beam. P is the magnitude of the force applied at C which is translated to A, and Ml and M2 are the magnitudes of the couple-moments. RAx, RAy, and RAz are the scalar components of the reactive force at A, and MAx, MAy, and MAz are the scalar components of the reactive moment at A. Consider the translational equilibrium of the beam in the x direction: The translational equilibrium of the beam in the y direction re quires that: LFy=O: RAy = P = 120N (+y) For the translational equilibrium of the beam in the 2 direction: Therefore, there is only one non-zero component of the reactive force on the beam at A and it acts in the positive y direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002708_60.937201-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002708_60.937201-Figure4-1.png",
        "caption": "Fig. 4. Magnetic main path of a half pole section in circumferential size of the machine.",
        "texts": [
            " Subsequent assumptions are made: \u2014 the investigated machine is a low voltage three-phase induction motor with a squirrel cage rotor \u2014 only the fundamental air-gap field-waves are considered for both fundamental and harmonic voltages \u2014 the saturable permeability of the core material used is related to the fundamental air gap induction \u2014 hysteresis effects of the core material are neglected. Additionally, it was requested that separate loss calculations should be possible for the various sections of the core. In the following an harmonic of the order will be indicated by the index . The loss calculation model derived was based on Maxwell\u2019s equations applied to Fig. 4 resulting the equivalent circuit shown in Fig. 5. It comprises also lumped impedances for simulating the eddy current paths in the stator and rotor circuits. As described in [12] it was learned that the eddy currents and their feedback on the field in the core sections must be taken into account particularly in case of higher voltage harmonics. The following expressions for correlating the magnetic fluxes to the magnetomotive forces in Fig. 4 were gained for the various core sections of the: \u2014 stator yoke section: (1) \u2014 stator tooth section: (2) \u2014 rotor yoke section: (3) \u2014 rotor tooth section: (4) with: height of the stator yoke section penetration depth of a harmonic in a stator yoke sheet core length sheet thickness reduced length for the magnetomotive force in the stator yoke section height of the rotor yoke section penetration depth of a harmonic in a rotor yoke sheet reduced length for the magnetomotive force in the rotor yoke section height of a stator tooth width of a stator tooth penetration depth of a harmonic in a stator tooth sheet height of a rotor tooth width of a rotor tooth penetration depth of a harmonic in a rotor tooth sheet",
            " Introducing the voltage representing the voltage induced in the stator winding less the voltage induced by the coil-end stray flux (6) results in: (7) An similar equation will be obtained for the rotor: (8) The voltages and can be derived from the \u2013 - relationships given by equations (1)\u2013(4). It is suitable to correlate the fluxes of the core sections with the main harmonic flux . Thus the air-gap voltages can be described by the following expressions: (9) (10) (11) (12) Ampere\u2019s law applied to the magnetic main path shown in Fig. 4 delivers: (13) where represents the ampere-turn resulting from stator and rotor ampere-turns at the same circumferential position. At the position the following expression is valid: (14) All included in the above equation are the magnetization currents of the appropriate sections. Thus the magnetomotive forces depicted in Fig. 4 are obtained as: (15) (16) (17) (18) (19) Inserting equations (15)\u2013(19) into the equations (9)\u2013(12) \u2013 -relations are received. This permits to define the so-called iron-impedances : (20) (21) (22) (23) Finally, equations (6)\u2013(23) lead to the equivalent circuit shown in Fig. 5. The calculation of the circuit elements , and bases on commonly known equations [8], [9]. Introducing the iron impedances now it is possible to consider the eddy-current feedback upon the exciting field and to give a prediction about the expected harmonic iron losses represented by the real part of these iron impedances for each voltage harmonic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure3.16-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure3.16-1.png",
        "caption": "Fig. 3.16 Small element of a beam with distribution of stresses",
        "texts": [],
        "surrounding_texts": [
            "L 'P which can also be used to control our calculations. The horizontal components cancel each other. Obviously, however, this shear flow has a resultant twisting moment about the x-axis, which must be equivalent to the moment produced by the transverse shear force Q"
        ]
    },
    {
        "image_filename": "designv10_8_0003966_b911365g-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003966_b911365g-Figure1-1.png",
        "caption": "Fig. 1 Sketch of the swimmer in ring-like confinement. Indicated are the rod center-of-mass position in polar coordinates r \u00bc (r, q), the rod orientation f, and the relative orientation with respect to the wall, w \u00bc f q. The swimmer is confined to a ring of dimensions R1 < r < R2. The propelling force F and the torque M are also indicated.",
        "texts": [
            " D ow nl oa de d by U ni ve rs ity o f V ic to ri a on 2 7/ 10 /2 01 4 11 :4 7: 35 . of length L and width d. Neglecting hydrodynamic interactions with the confining walls, its overdamped motion in two dimensions is governed by the Langevin equations for the rod centerof-mass position _r \u00bc bD$[Fu\u0302 VV(r,f) + f] (1) and for the rod orientation _f \u00bc bDr[M vfV(r,f) + s] , (2) respectively, where dots denote time derivatives and b 1 \u00bc kBT is the thermal energy. The angle f denotes the swimmer\u2019s orientation with respect to the x-axis, as sketched in Fig. 1. The rod\u2019s short time diffusion tensor D \u00bc Dk(u\u0302 5 u\u0302) + Dt(I u\u0302 5 u\u0302) (3) is given in terms of the short time longitudinal (D||) and transverse (Dt) translational diffusion constants, with the orientation vector u\u0302\u00bc (cosf, sinf), I the unit tensor and 5 a dyadic product. Dr is the short time rotational diffusion constant. Fu\u0302 is a constant effective force that represents the internal propulsion mechanism responsible for the deterministic motion in the rod orientation, and M is a constant effective torque, originating from the internal propulsion mechanism or from an external field, which yields the deterministic circular motion (see the sketch in Fig. 1). V(r, f) is an external confining potential. f and s are the zero mean Gaussian white noise random force and random torque originating from the solvent, respectively. Their variances are given by fk\u00f0t\u00de fk\u00f0t 0 \u00de \u00bc 2d\u00f0t t 0\u00de= b2Dk ; ft\u00f0t\u00de ft\u00f0t 0 \u00de \u00bc 2d\u00f0t t 0\u00de= b2Dt ; s\u00f0t\u00des\u00f0t 0 \u00de \u00bc 2d\u00f0t t 0\u00de= b2Dr ; (4) where f||, ft are the components of f parallel and perpendicular to u\u0302, respectively. The bars over the quantities denote a noise average. Henceforth, we consider a very thin rod of length L [ d, for which the short-time diffusion constants in the threedimensional bulk are given by Dr/D|| \u00bc 3/(2L2), Dt \u00bc D||/2",
            "31 Next, we introduce a circular, ring-like potential of purely repulsive walls, which confines the swimmer\u2019s motion to a ring of dimensions R1 < r < R2, where r \u00bc |r| is the radial coordinate of the swimmer\u2019s center-of-mass position. For simplicity, we model the confinement by an integrated segment-wall power-law potential in the radial direction, V\u00f0r;w\u00de \u00bc \u00f0 L 2 L 2 v\u00f0r; l;w\u00dedl ; (5) where w \u00bc f q is the difference between the angular coordinate of the swimmer\u2019s center-of-mass position q and its orientation f, i.e., w is the relative angle of the swimmer\u2019s center of mass with respect to the closest point on either of the two confining walls (see Fig. 1). The segment-wall potential of the rod segment at the position l along the contour is given by v\u00f0r; l;w\u00de \u00bc \u00f0bL\u00de 1 ( L R1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 \u00fe l2 \u00fe 2rl cosw p n \u00fe L R2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 \u00fe l2 \u00fe 2rl cos w p n) ; (6) if the rod segment is situated between the two walls, i.e., if R1 2 < r2 + l2 + 2rl cos w < R2 2, and infinite otherwise",
            " The lap frequency and the angular diffusion constant, DU \u00bc lim t/N \u00f0q\u00f0t\u00de Ut\u00de2 2t ; (26) are plotted as a function of the torque-to-force ratio M/(LF) for the same constant force bFL \u00bc 60 and the same confining radius R2 \u00bc 30L, as already considered before, in Fig. 6. U(M/(LF)) is compared to the lap frequency obtained in the absence of thermal noise, which we discuss at first as a reference case. In this situation\u2013under appropriate initial conditions\u2013the swimmer orientation adopts the value of the stable sliding mode w2;s for torque-to-force ratios smaller than the critical value x2(R2). The latter critical value is given by eqn (16) for hard walls and is slightly smaller for soft walls, as seen in Fig. 1. According to eqn (17) the velocity along the channel is an increasing function of the angle w2;s in the case of hard walls; this behaviour is preserved in the case of soft walls and reflected in the decreasing absolute value of U as a function of torque-to-force ratio in Fig. 6. Apart from the lap frequency we also measured the mean angular velocity of the swimmer orientation, Fig. 6 The lap frequency U as a function of M/(LF) in dish- and ring-like confinements for the same parameters as in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003574_1.3142883-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003574_1.3142883-Figure2-1.png",
        "caption": "Fig. 2 Schematic of the ball bearing",
        "texts": [
            " In the rotor-ball bearing system, usually, the outer ace of the ball bearing is fixed to the bearing housing and the nner race is rigidly fixed to the rotating shaft. When ball bearing orks, with the contact position between balls and races periodially varying, the total stiffness and compliance of bearing vary eriodically, and the varying compliance of bearing is a parametic excitation of the rotor-balling bearing coupling system; hence, he so-called varying compliance VC vibration is generated. VC ibration is an inherent vibration, and it always exists even if the earing is newly installed and is fault-free. Figure 2 is a schematic of a ball bearing model, which makes eference to the literature 13 . The excitations of ball bearing ome from two aspects: one is the rotor imbalance, and the other s the continuous periodic change in the total stiffness of the bearng, which is a parametric excitation. In the ball bearing model, it is supposed that the balls are eqispaced between the surfaces of the inner and the outer races, and he contact angles are not considered. Vin is the tangent velocity of he contact point between the ball and the inner race; inner is the otating angular velocity of the bearing inner race; R is the radius f the outer race; and r is the radius of the inner race"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.17-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.17-1.png",
        "caption": "Figure 7.17 Load-elongation diagram for a linear spring.",
        "texts": [],
        "surrounding_texts": [
            "7.18 Exercise Problems / 147 7.1 Basic Loading Configurations An object subjected to an external force will move in the direc tion of the applied force. The object will deform if its motion is constrained in the direction of the applied force. Deformation implies relative displacement of any two points within the ob ject. The extent of deformation will be dependent upon many factors including the magnitude, direction, and duration of the applied force, the material properties of the object, the geom etry of the object, and environmental factors such as heat and humidity. In general, materials respond differently to different loading configurations. For a given material, there may be different me chanical properties that must be considered while analyzing its response to, for example, tensile loading as compared to loading that may cause bending or torsion. Figure 7.1 is drawn to illus trate different loading conditions, in which an L-shaped beam is subjected to forces F l' F 2' and L. The force F 1 subjects the arm AB of the beam to tensile loading. The force F 2 tends to bend the arm AB. The force L has a bending effect on arm BC and a twisting (torsional) effect on arm AB. Furthermore, all of these forces are subjecting different sections of the beam to shear loading. 7.2 Uniaxial Tension Test The mechanical properties of materials are established by subjec ting them to various experiments. The mechanical response of materials under tensile loading is analyzed by the uniaxial or simple tension test that will be discussed next. The response of materials to forces that cause bending and torsion will be re viewed in the following chapter. The experimental setup for the uniaxial tension test is illustrated in Figure 7.2. It consists of one fixed and one moving head with attachments to grip the test specimen. A specimen is placed and firmly fixed in the equipment, a tensile force of known magni tude is applied through the moving head, and the corresponding elongation of the specimen is measured. A general understand ing of the response of the material to tensile loading is obtained by repeating this test for a number of specimens made of the same material, but with different lengths, cross-sectional areas, and under tensile forces with different magnitudes. 7.3 Load-Elongation Diagrams Consider the three bars shown in Figure 7.3. Assume that these bars are made of the same material. The first and the second bars have the same length but different cross-sectional areas, and the second and third bars have the same cross-sectional area but Stress and Strain 127 128 Fundamentals of Biomechanics different lengths. Each of these bars can be subjected to a se ries of uniaxial tension tests by gradually increasing the applied forces and measuring corresponding increases in their lengths. If F is the magnitude of the applied force and ~l is the in crease in length, then the data collected can be plotted to obtain a load versus elongation diagram for each specimen. Effects of geometric parameters (cross-sectional area and length) on the load-bearing ability of the material can be judged by drawing the curves obtained for each specimen on a single graph (Fig ure 7.4) and comparing them. At a given force magnitude, the comparison of curves 1 and 2 indicate that the larger the cross sectional area, the more difficult it is to deform the specimen in a simple tension test, and the comparison of curves 2 and 3 in dicate that the longer the specimen, the larger the deformation in tension. Note that instead of applying a series of tensile forces to a single specimen, it is preferable to have a number of specimens with almost identical geometries and apply one force to one specimen only once. As will be discussed later, a force applied on an object may alter its mechanical properties. Another method of representing the results obtained in a uniax ial tension test is by first dividing the magnitude of the applied force F with the cross-sectional area A of the specimen, nor malizing the amount of deformation by dividing the measured elongation with the original length of the specimen, and then plotting the data on a F / A versus ~l / l graph as shown in Figure 7.5. The three curves in Figure 7.4, representing three specimens made of the same material, are represented by a single curve in Figure 7.5. It is obvious that some of the information provided in Figure 7.4 is lost in Figure 7.5. That is why the representation in Figure 7.5 is more advantageous than that in Figure 7.4. The single curve in Figure 7.5 is unique for a particular material, in dependent of the geometries of the specimens used during the experiments. This type of representation eliminates geometry as one of the variables, and makes it possible to focus attention on the mechanical properties of different materials. For example, consider the curves in Figure 7.6, representing the mechanical behavior of materials A and B in simple tension. It is clear that material B can be deformed more easily than material A in a uniaxial tension test, or material A is \"stiffer\" than material B. 7.4 Simple Stress Consider the cantilever beam shown in Figure 7.7a. The beam has a circular cross-section, cross-sectional area A, welded to the wall at one end, and is subjected to a tensile force with magnitude F at the other end. The bar does not move, so it is in equilib rium. To analyze the forces induced within the beam, the method of sections can be applied by hypothelically cutting the beam into two pieces through a plane ABCD perpendicular to the centerline of the beam. Since the beam as a whole is in equilib rium, the two pieces must individually be in equilibrium as well. This requires the presence of an internal force collinear with the externally applied force at the cut section of each piece. To sat isfy the condition of equilibrium, the internal forces must have the same magnitude as the external force (Figure 7.7b). The in ternal force at the cut section represents the resultant of a force system distributed over the cross-sectional area of the beam (Fig ure 7.7c). The intensity of the internal force over the cut section (force per unit area) is known as the stress. For the case shown in Figure 7.7, since the force resultant at the cut section is per pendicular (normal) to the plane of the cut, the corresponding stress is called a normal stress. It is customary to use the symbol a (sigma) to refer to normal stresses. The intensity of this dis tributed force mayor may not be uniform (constant) throughout the cut section. Assuming that the intensity of the distributed force at the cut section is uniform over the cross-sectional area A, the normal stress can be calculated using: F a == A (7.1) If the intensity of the stress distribution over the area is not uniform, then Eq. (7.1) will yield an average normal stress. It is customary to refer to normal stresses that are associated with tensile loading as tensile stresses. On the other hand, compressive stresses are those associated with compressive loading. It is also customary to treat tensile stresses as positive and compressive stresses as negative. The other form of stress is called shear stress, which is a measure of the intensity of internal forces acting parallel or tangent to a plane of cut. To get a sense of shear stresses, hold a stack of paper with both hands such that one hand is under the stack while the other hand is above it. First, press the stack of papers together. Then, slowly slide one hand in the direction parallel to the surface of the papers while sliding the other hand in the opposite direction. This will slide individual papers relative to one another and generate frictional forces on the surfaces of individual papers. The shear stress is comparable to the intensity of the frictional force over the surface area upon which it is applied. Now, consider the cantilever beam illustrated in Figure 7.8a. A downward force with magnitude F is applied to its free end. To analyze internal forces and moments, the method of sections can be applied by fictitiously cutting the beam through a plane ABCD that is perpendicular to the centerline of the beam. Since the beam as a whole is in equilibrium, the two pieces thus obtained must individually be in equilibrium as well. The free body diagram of the right-hand piece of the beam is illustrated in Figure 7.8b along with the internal force and moment on the left-hand piece. For the equilibrium of the right-hand piece, there Stress and Strain 129 130 Fundamentals of Biomechanics F TA cT r C'i \u00a31 \u00a32 \u00a31+~\u00a31 \u00a32+~\u00a32 lB Dl L DJ F Figure 7.9 Normal strain. has to be an upward force resultant and an internal moment at the cut surface. Again for the equilibrium of this piece, the internal force must have a magnitude F. This is known as the internal shearing force and is the resultant of a distributed load over the cut surface (Figure 7.8c). The intensity of the shearing force over the cut surface is known as the shear stress, and is commonly denoted with the symbol r (tau). If the area of this surface (in this case, the cross-sectional area of the beam) is A, then: F r=- A (7.2) The underlying assumption in Eq. (7.2) is that the shear stress is distributed uniformly over the area. For some cases this assump tion may not be true. In such cases, the shear stress calculated by Eq. (7.2) will represent an average value. The dimension of stress can be determined by dividing the di mension of force [F] = [M][L]/[T2] with the dimension of area [L 2]. Therefore, stress has the dimension of [M]/[L][T2]. The units of stress in different unit systems are listed in Table 7.1. Note that stress has the same dimension and units as pressure. 7.5 Simple Strain Strain, which is also known as unit deformation, is a measure of the degree or intensity of deformation. Consider the bar in Figure 7.9. Let A and B be two points on the bar located at a distance iI, and C and D be two other points located at a distance 12 from one another, such that 11 > 12. 11 and 12 are called gage lengths. The bar will elongate when it is subjected to tensile loading. Let ~ll be the amount of elongation measured between A and B, and ~l2 be the increase in length between C and D. ~ll and ~.e2 are certainly some measures of deformation. However, they depend on the respective gage lengths, such that ~.el > ~.e2. On the other hand, if the ratio of the amount of elongation to the gage length is calculated for each case and compared, it would be observed that (~.eI!.el) ~ (~.e2/.e2). Elongation per unit gage length is known as strain and is a more fundamental means of measuring deformation. As in the case of stress, two types of strains can be distinguished. The normal or axial strain is associated with axial forces and de fined as the ratio of the change (increase or decrease) in length, b.l, to the original gage length,l, and is denoted with the symbol E (epsilon): b.l E=- l (7.3) When a body is subjected to tension, its length increases, and both b.l and E are positive. The length of a specimen under compression decreases, and both b.l and E become negative. The second form of strain is related to distortions caused by shearing forces. Consider the rectangle (ABCD) shown in Figure 7.10, which is acted upon by a pair of shearing forces. Shear forces deform the rectangle into a parallelogram (AB'C'D). If the relative horizontal displacement of the top and the bottom of the rectangle is d and the height of the rectangle is l, then the average shear strain is defined as the ratio of d and l, which is equal to the tangent of angle y (gamma). This angle is usually very small. For small angles, the tangent of the angle is approxi mately equal to the angle itself. Hence, the average shear strain is equal to angle y (measured in radians), which can be calculated using: d y= l (7.4) Strains are calculated by dividing two quantities having the di mension of length. Therefore, they are dimensionless quantities and there is no unit associated with them. For most applica tions, the deformations and, consequently, the strains involved are very small, and the precision of the measurements taken is very important. To indicate the type of measurements taken, it is not unusual to attach units such as cm/ cm or mm/ mm next to a strain value. Strains can also be given in percent. In engineering applications, the strains involved are of the order of magnitude 0.1 percent or O.OOL Figure 7.11 is drawn to compare the effects of tensile, compres sive, and shear loading. Figure 7.11a shows a square object (in a two-dimensional sense) under no load. The square object is ruled into 16 smaller squares to illustrate different modes of deforma tion. In Figure 7.11b, the object is subjected to a pair of tensile forces. Tensile forces distort squares into rectangles such that the dimension of each square in the direction of applied force (axial dimension) increases while its dimension perpendicular to the direction of the applied force (transverse dimension) decreases. In Figure 7.11c, the object is subjected to a pair of compressive forces that distort squares into rectangles such that the axial di mension of each square decreases while its transverse dimension 132 Fundamentals of Biomechanics increases. In Figure 7.11d, the object is subjected to a pair of shear forces that distort the squares into diamonds. 7.6 Stress-Strain Diagrams It was demonstrated in Section 7.3 that the results of uniaxial tension tests can be used to obtain a unique curve represent ing the relationship between the applied load and correspond ing deformation for a material. This can be achieved by divid ing the applied load with the cross-sectional area (F/A) of the specimen, dividing the amount of elongation measured with the gage length (D.l/l), and plotting a F / A versus D.l/l graph. Note, however, that for a specimen under tension, F / A is the average tensile stress (1 and D.l / l is the average tensile strain E. There fore, the F / A versus D.l/l graph of a material is essentially the stress-strain diagram of that material. Different materials demonstrate different stress-strain relation ships, and the stress-strain diagrams of two or more materi als can be compared to determine which material is relatively stiffer, harder, tougher, more ductile, and/ or more brittle. Before explaining these concepts related to the strength of materials, it is appropriate to first analyze a typical stress-strain diagram in detail. Consider the stress-strain diagram shown in Figure 7.12. There are six distinct points on the curve that are labeled as 0, P, E, Y, V, and R. Point 0 is the origin of the a\u00b7\u00b7E diagram, which cor responds to the initial no load, no deformation stage. Point P represents the proportionality limit. Between 0 and P, stress and strain are linearly proportional, and the a-E curve is a straight line. Point E represents the elastic limit. The stress corresponding to the elastic limit is the greatest stress that can be applied to the material without causing any permanent deformation within the material. The material will not resume its original size and shape upon unloading if it is subjected to stress levels beyond the elastic limit. Point Y is the yield point, and the stress ay cor responding to the yield point is called the yield strength of the material. At this stress level, considerable elongation (yielding) can occur without a corresponding increase of load. V is the highest stress point on the a-E curve. The stress au is the ultimate strength of the material. For some materials, once the ultimate strength is reached, the applied load can be decreased and con tinued yielding may be observed. This is due to the phenomena called necking that will be discussed later. The last point on the a-E curve is R, which represents the rupture or failure point. The stress at which the rupture occurs is called the rupture strength of the material. For some materials, it may not be easy to determine or dis tinguish the elastic limit and the yield point. The yield strength of such materials is determined by the offset method, illustrated in Figure 7.13. The offset method is applied by drawing a line parallel to the linear section of the stress-strain diagram and passing through a strain level of about 0.2 percent (0.002). The intersection of this line with the O'-E curve is taken to be the yield point, and the stress corresponding to this point is called the apparent yield strength of the material. Note that a given material may behave differently under differ ent load and environmental conditions. If the curve shown in Figure 7.12 represents the stress-strain relationship for a mate rial under tensile loading, there may be a similar but different curve representing the stress-strain relationship for the same material under compressive or shear loading. Also, tempera ture is known to alter the relationship between stress and strain. For a given material and fixed mode of loading, different stress strain diagrams may be obtained under different temperatures. Furthermore, the data collected in a particular tension test may depend on the rate at which the tension is applied on the spec imen. Some of these factors affecting the relationship between stress and strain will be discussed later. 7.7 Elastic Deformations Consider the partial stress-strain diagram shown in Figure 7.14. Y is the yield point, and in this case, it also represents the propor tionality and elastic limits. O'y is the yield strength and Ey is the corresponding strain. (The O'-E curve beyond the elastic limit is not shown.) The straight line in Figure 7.14 represents the stress strain relationship in the elastic region. Elasticity is defined as the ability of a material to resume its original (stress-free) size and shape upon removal of applied loads. In other words, if a load is applied on a material such that the stress generated in the material is equal to or less than O'y, then the deformations that took place in the material will be completely recovered once the applied loads are removed (the material is unloaded). An elastic material whose O'-E diagram is a straight line is called a linearly elastic material. For such a material, the stress is linearly proportional to strain, and the constant of proportionality is called the elastic or Young's modulus of the material. Denoting the elastic modulus with E: (7.5) The elastic modulus, E, is equal to the slope of the O'-E diagram in the elastic region, which is constant for a linearly elastic material. E represents the stiffness of a material, such that the higher the elastic modulus, the stiffer the material. The distinguishing factor in linearly elastic materials is their elastic moduli. That is, different linearly elastic materials have different elastic moduli. If the elastic modulus of a material is known, then the mathematical definitions of stress and strain (0' = F j A and E = l:!.ljl) can be substituted into Eq. (7.5) to de rive a relationship between the applied load and corresponding 134 Fundamentals of Biomechanics O'y Y ------ P $ 0 \u20acy \u20ac Figure 7.15 Stress-strain diagram for a nonlinearly elastic material. T o -- 11/ G oL----------------~ Figure 7.16 Shear stress versus shear strain diagram for a linearly elastic material. deformation: Ff b..f= EA (7.6) In Eq. (7.6), F is the magnitude of the tensile or compressive force applied to the material, E is the elastic modulus of the material, A is the area of the surface that cuts the line of action of the applied force at right angles, f is the length of the material measured along the line of action of the applied force, and b..f is the amount of elongation or shortening in f due to the applied force. For a given linearly elastic material (or any material for which the deformations are within the linearly elastic region of the O'-E diagram) and applied load, Eq. (7.6) can be used to calculate the corresponding deformation. This equation can be used when the object is under a tensile or compressive force. Not all elastic materials demonstrate linear behavior. As illus trated in Figure 7.15, the stress-strain diagram of a material in the elastic region may be a straight line up to the proportion ality limit followed by a curve. A curve implies varying slope and nonlinear behavior. Materials for which the O'-E curve in the elastic region is not a straight line are known as nonlinear elastic materials. For a nonlinear elastic material, there is not a single elastic modulus because the slope of the O'-E curve is not con stant throughout the elastic region. Therefore, the stress-strain relationships for nonlinear materials take more complex forms. Note, however, that even nonlinear materials may have a linear elastic region in their O'-E diagrams at low stress levels (region between 0 and P in Figure 7.15). Some materials may exhibit linearly elastic behavior when they are subjected to shear loading (Figure 7.16). For such materials, the shear stress, r, is linearly proportional to the shear strain, y, and the constant of proportionality is called the shear modulus or the modulus of rigidity, which is commonly denoted with the symbol G: r=Gy (7.7) The shear modulus of a given linear material is equal to the slope of the r-y curve in the elastic region. The higher the shear modulus, the more rigid the material. Note that Eqs. (7.5) and (7.6) relate stresses to strains for linearly elastic materials, and are called material functions. Obviously, for a given material, there may exist different material functions for different modes of deformation. There are also constitutive equations that incorporate all material functions. 7.8 Hooke's Law The load-bearing characteristics of elastic materials are similar to those of springs, which was first noted by Robert Hooke. Like springs, elastic materials have the ability to store poten tial energy when they are subjected to externally applied loads. During unloading, it is the release of this energy that causes the material to resume its undeformed configuration. A linear spring subjected to a tensile load will elongate, the amount of elongation being linearly proportional to the applied load (Fig ure 7.17). The constant of proportionality between the load and the deformation is usually denoted with the symbol k, which is called the spring constant or stiffness of the spring. For a linear spring with a spring constant k, the relationship between the applied load F and the amount of elongation dis: F =kd (7.8) By comparing Eqs. (7.5) and (7.8), it can be observed that stress in an elastic material is analogous to the force applied to a spring, strain in an elastic material is analogous to the amount of defor mation of a spring, and the elastic modulus of an elastic material is analogous to the spring constant of a spring. This analogy be tween elastic materials and springs is known as Hooke's Law. 7.9 Plastic Deformations We have defined elasticity as the ability of a material to regain completely its original dimensions upon removal of the app lied forces. Elastic behavior implies the absence of permanent deformation. On the other hand, plasticity implies permanent deformation. In general, materials undergo plastic deformations following elastic deformations when they are loaded beyond their elastic limits or yield points. Consider the stress-strain diagram of a material shown in Fig ure 7.18. Assume that a specimen made of the same material is subjected to a tensile load and the stress, a, in the specimen is brought to such a level that a> ay\u2022 The corresponding strain in the specimen is measured as E. Upon removal of the applied load, the material will recover the elastic deformation that had taken place by following an unloading path parallel to the initial linearly elastic region (straight line between 0 and P). The point where this path cuts the strain axis is called the plastic strain, Ep' that signifies the extent of permanent (unrecoverable) shape change that has taken place in the specimen. The difference in strains between when the specimen is loaded and unloaded (E - E p) is equal to the amount of elastic strain, Ee, that had taken place in the specimen and that was recovered upon unloading. Therefore, for a material loaded to a stress level beyond its elastic limit, the total strain is equal to the sum of the elastic and plastic strains: E = Ee + Ep (7.9) 136 Fundamentals of Biomechanics -+-i'--__ ------'~ (a) ---c=::=:::=::J (b) Figure 7.19 Necking. R L-_______________ \u20ac Figure 7.20 Conventional (solid curve) and actual (dotted curve) stress-strain diagrams. The elastic strain, Ee, is completely recoverable upon unloading, whereas the plastic strain, Ep, is a permanent residue of the de formations. 7.10 Necking As defined in Section 7.6, the largest stress a material can endure is called the ultimate strength of that material. Once a material is subjected to a stress level equal to its ultimate strength, an increased rate of deformation can be observed, and in most cases, continued yielding can occur even by reducing the applied load. The material will eventually fail to hold any load, and rupture. The stress at failure is called the rupture strength of the material, which may be lower than its ultimate strength. Although this may seem to be unrealistic, the reason is due to a phenomenon called necking and because of the manner in which stresses are calculated. Stresses are usually calculated on the basis of the original cross sectional area of the material. Such stresses are called conven tional stresses. Calculating a stress by dividing the applied force with the original cross-sectional area is convenient but not neces sarily accurate. The true or actual stress calculations must be made by taking the cross-sectional area of the deformed material into consideration. As illustrated in Figure 7.19, under a tensile load a material may elongate in the direction of the applied load but contract in the transverse directions. At stress levels close to the breaking point, the elongation may occur very rapidly and the material may narrow simultaneously. The cross-sectional area at the narrowed section decreases, and although the force required to further deform the material may decrease, the force per unit area (stress) may increase. As illustrated with the dotted curve in Figure 7.20, the actual stress-strain curve may continue having a positive slope, which indicates increasing strain with increasing stress rather than a negative slope, which implies increasing strain with decreasing stress. Also the rupture point and the point corresponding to the ultimate strength of the material may be the same. 7.11 Work and Strain Energy In dynamics, work done is defined as the product of force and the distance traveled in the direction of applied force, and energy is the capacity of a system to do work. Stress and strain in de formable body mechanics are respectively related to force and displacement. Stress multiplied by area is equal to force, and strain multiplied by length is displacement. Therefore, the prod uct of stress and strain is equal to the work done on a body per unit volume of that body, or the internal work done on the body by the externally applied forces. For an elastic body, this work is stored as an internal elastic strain energy, and it is the release of this energy that brings the body back to its original shape upon unloading. The maximum elastic strain energy (per unit vol ume) that can be stored in a body is equal to the total area under the a-E diagram in the elastic region (Figure 7.21). There is also a plastic strain energy that is dissipated as heat while deforming the body. 7.12 Strain Hardening Consider the a-E diagram shown in Figure 7.23. Between 0 and A a tensile force is applied on the material and the material is deformed beyond its elastic limit. At A, the tensile force is removed, and the line AB represents the unloading path. At B the material is reloaded, this time with a compressive force. At C, the compressive force applied on the material is removed. Between C and 0, a second unloading occurs, and finally the material resumes its original shape. The loop OABCO is called the hysteresis loop, and the area enclosed by this loop is equal to the total strain energy dissipated as heat to deform the body in tension and compression. 7.14 Properties Based on Stress-Strain Diagrams As defined earlier, the elastic modulus of a material is equal to the slope of its stress-strain diagram in the elastic region. The elastic modulus is a relative measure of the stiffness of one material with respect to another. The higher the elastic modulus, the stiffer the material and the higher the resistance to deformation. For example, material 1 in Figure 7.24 is stiffer than material 2. Stress and Strain 137 138 Fundamentals of Biomechanics A ductile material is one that exhibits a large plastic deforma tion prior to failure. For example, material 1 in Figure 7.25 is more ductile than material 2. A brittle material, on the other hand, shows a sudden failure (rupture) without undergoing a considerable plastic deformation. Glass is a typical example of a brittle material. Toughness is a measure of the capacity of a material to sustain per manent deformation. The toughness of a material is measured by considering the total area under its stress-strain diagram. The larger this area, the tougher the material. For example, material 1 in Figure 7.26 is tougher than material 2. The ability of a material to store or absorb energy without per manent deformation is called the resilience of the material. The resilience of a material is measured by its modulus of resilience, which is equal to the area under the stress-strain curve in the elastic region. The modulus of resilience is equal to ayEy/2 or a;/2E for linearly elastic materials. Although they are not directly related to the stress-strain dia grams, there are other important concepts used to describe ma terial properties. A material is called homogeneous if its proper ties do not vary from location to location within the material. A material is called isotropic if its properties are independent of direction or orientation. A material is called incompressible if it has a constant density. 7.15 Idealized Models of Material Behavior Stress-strain diagrams are most useful when they are repre sented by mathematical functions. The stress-strain diagrams of materials may come in various forms, and it may not be pos sible to find a single mathematical function to represent them. For the sake of mathematical modeling and the analytical treat ment of material behavior, these diagrams can be simplified. Some of these diagrams representing certain idealized material behavior are illustrated in Figure 7.27. A rigid material is one that cannot be deformed even under very large loads (Figure 7.27a). A linearly elastic material is one for which the stress and strain are linearly proportional, with the modulus of elasticity being the constant of proportionality (Fig ure 7.27b). A rigid-perfectly plastic material does not exhibit any elastic behavior, and once a critical stress level is reached, it will deform continuously and permanently until failure (Figure 7.27c). After a linearly elastic response, a linearly elastic-perfectly plastic material is one that deforms continuously at a constant stress level (Figure 7.27d). Figure 7.27e represents the stress strain diagram for rigid-linearly plastic behavior. The stress-strain diagram of a linearly elastic-linearly plastic material has two distinct regions with two different slopes (bilinear), in which stresses and strains are linearly proportional (Figure 7.27f). 7.16 Mechanical Properties of Materials Table 7.2 lists properties of selected materials in terms of their tensile yield strengths (ay), tensile ultimate strengths (au), elas tic moduli (E), shear moduli (G), and Poisson's ratios (v). The significance of the Poisson's ratio will be discussed in the follow ing chapter. Note that mechanical properties of a material can vary depending on many factors including its content (for ex ample, in the case of steel, its carbon content) and the processes used to manufacture the material (for example, hard rolled, strain hardened, or heat treated). As will be discussed in later chapters, biological materials exhibit time-dependent proper ties. That is, their response to external forces depends on the rate at which the forces are applied. Bone, for example, is an anisotropic material. Its response to tensile loading in different directions is different, and different elastic moduli are estab lished to account for its response in different directions. There fore, the values listed in Table 7.2 are some averages and ranges, and are aimed to provide a sense of the orders of magnitude of numbers involved. Table 7.2 Average mechanical properties of selected materials. (1 MPa = 1,000,000 Pa, 1 GPa = 1,000,000,000 Pa) YIELD umMATE ELASTIC SHEAR POISSON'S MAI'ERIAL STRENGTH STRENGTH MODULUS MODULUS RATIO ay(MPa) au (MPa) E (GPa) G (MPa) v Muscle - 0.2 - - 0.49 Tendon - 70 0.4 - 0.40 Skin - 8 0.5 - 0.49 Cortical Bone 80 130 17 3.3 0.40 Glass 35-70 - 70-80 - - Cast Iron 40-260 140-380 100-190 42-90 0.29 Aluminum 60-220 90-390 70 28 0.33 Steel 200-700 400-850 200 80 0.30 Titanium 400-800 500-900 100 45 0.34 Figure 7.28 illustrates the tensile stress-strain diagrams of a few materials. Steel and aluminum are relatively stiff and have high ultimate strengths. Glass and dry bone are brittle. Wet bone has the lowest ultimate strength and elastic modulus. Stress and Strain 139 STRESS Steel &------- STRAIN Figure 7.28 Gross comparison of stress-strain diagrams of selected materials. 140 Fundamentals of Biomechanics F A- B- @ 7.17 Example Problems The following examples will demonstrate some of the uses of the concepts introduced in this chapter. Example 7.1 A circular cylindrical rod with radius r = 1.26 cm is tested in a uniaxial tension test (Figure 7.29). Before applying a tensile force of F = 1000 N, two points A and B that are at a distance lo = 30 cm (gage length) are marked on the rod. After the force is applied, the distance between A and B is measured as 11 = 31.5 cm. Determine the tensile strain and average tensile stress generated in the rod. Solution: By definition, the tensile strain is equal to the ratio of the amount of elongation to the original length. The amount of elongation, I:!:.l, is the difference between the gage lengths before and after deformation: I:!:.l = 11 -lo = 31.5 - 30.0 = 1.5 cm Therefore, the tensile strain E generated in the rod is: I:!:.l 1.5 E = - = - = 0.05cm/cm lo 30 The bar has a circular cross-section with radius r = 1.26 cm or r = 0.0126 m. The cross-sectional area A of the bar is: A = 7r r2 = (3.1416)(0.0126)2 = 5 X 10-4 m2 The average tensile stress is equal to the applied force per unit area of the surface that cuts the line of action of the force at right angles. In this case, it is the cross-sectional area of the rod. Therefore: F 1000 6 (1 = - = = 2,000,000 = 2 x 10 Pa = 2 MPa A 0.0005 Example 7.2 Two specimens made of two different materials are tested in a uniaxial tension test by applying a force of F = 20 kN (20 x leY N) on each specimen (Figure 7.30). Specimen 1 is an aluminum bar with elastic modulus El = 70 GPa (70 x 109 Pa) and a rectangular cross-section (1 cm by 2 cm). Specimen 2 is a steel rod with elastic modulus E2 = 200 GPa (200 x 109 Pa) and a circular cross-section (radius 1 cm). Calculate tensile stresses developed in each specimen. Assum ing that the tensile stress in each specimen is below the propor tionality limit of the material, calculate the tensile strain for each specimen. Also, if the original length of each specimen was 30 cm, what are their lengths after deformation? Solution: The tensile stress is equal to the ratio of the applied force and the cross-sectional area of the specimen. The cross sectional areas of the specimens are: Al = (1 cm)(2 cm) = 2 cm2 = 2 x 10-4 m2 A2 = rr(l cm)2 = 3.14 cm2 = 3.14 x 10-4 m2 Therefore, the tensile stresses developed in each specimen are: F 20 X 103 6 0\"1 = - = 4 = 100 x 10 Pa = 100 MPa Al 2 x 10- F 20 X 103 6 0\"2 = - = 4 = 63.7 x 10 Pa = 63.7 MPa A2 3.14 x 10- That is, the aluminum bar (specimen 1) is stressed more than the steel rod (specimen 2). To calculate the tensile strains corresponding to tensile stresses 0\"1 and 0\"2, we can assume that the deformations are elastic and that the stresses 0\"1 and 0\"2 are below the proportionality limits for aluminum and steel. In other words, the stresses are linearly proportional to strains and the elastic moduli E1 and E2 are the constants of proportionality. Hence: E1 = 0\"1 = 100 X 106 = 1.43 X 10-3 E1 70 X 109 _ 0\"2 _ 63.7 X 106 _ 0 2 X 0-3 E2 - E2 - 200 X 109 -.3 1 These results suggest that the aluminum bar is stretched more than the steel rod. The original length of each specimen was lo = 30 cm. After deformation, assume that the aluminum bar is elongated by .:lll to length iI, and the steel rod is elongated by .:ll2 to length 12. By definition, tensile strain is E = .:lillo, or the amount of elongation is .:ll = Elo. On the other hand, the length of the specimen after deformation is equal to the original length plus the amount of elongation. For example, for the aluminum bar, 11 = lo + .:ll, or 11 = lo(1 + E1)' Therefore: 11 = lo (1 + E1) = 30(1 + 0.00143) = 30.0429 cm 12 = lo (1 + E2) = 30(1 + 0.00320) = 30.0960 cm In other words, the increase in length of the aluminum bar and the steel rod is less than 1 mm. Stress and Strain 141 142 Fundamentals of Biomechanics R=7l ~ Example 7.3 An experiment was designed to determine the elastic modulus of the human bone (cortical) tissue. Three al most identical bone specimens were prepared. The specimen size and shape used is shown in Figure 7.31, which has a square (2 x 2 mm) cross-section. Two sections, A and B, are marked on each specimen at a fixed distance apart. Each specimen was then subjected to tensile loading of varying magnitudes, and the lengths between the marked sections were again measured electronically. The following data were obtained: Applied Force, F (N) Measured Gage Length, i (mm) 5.000 o 240 480 720 5.017 5.033 5.050 Determine the tensile stresses and strains developed in each specimen, plot a stress-strain diagram for the bone, and deter mine the elastic modulus (E) for the bone. Solution: The cross-sectional area of each specimen is A = 4 mm2 or 4 x 10-6 m2. When the applied load is zero, the gage length is 5 mm, which is the original (undeformed) gage length, lo. Therefore, the stress and strain developed in each specimen can be calculated using: F l -lo a=- A \u20ac=-- lo The following table lists stresses and strains calculated using the above formulas: F (N) a x 106 (Pa) i(mm) \u20ac(mm/mm) 0 0 5.000 0.0 240 60 5.017 0.0034 480 120 5.033 0.0066 720 180 5.050 0.0100 In Figure 7.32, the stress and strain values computed are plotted to obtain a a-\u20ac graph for the bone. Notice that the relationship between the stress and strain is almost linear, which is indicated in Figure 7.32 by a straight line. Recall that the elastic modulus of a linearly elastic material is equal to the slope of the straight line representing the a-\u20ac rela tionship for that material. Therefore: a 180 x 106 9 E = - = = 18 x 10 Pa = 18 GPa \u20ac 0.0100 Example 7.4 Figure 7.33 illustrates a fixation device consist ing of a plate and two screws, which can be used to stabilize fractured bones. During a single leg stance, a person can apply his/her entire weight to the ground via a single foot. In such situations, the total weight of the person is applied back on the person through the same foot, which has a compressive effect on the leg, its bones, and joints. In the case of a patient with a frac tured leg bone (in this case, the femur), this force is transferred from below to above (distal to proximal) the fracture through the screws of the fixation device. If the diameter of the screws is D = 5 mm and the weight of the patient is W = 700 N, determine the shear stress exerted on the screws of a two-screw fixation device during a single leg stance on the leg with a fractured bone. Solution: Free-body diagrams of the fixation device and the screws are shown in Figure 7.34. Note that the screw above the fracture is pushing the plate downward, whereas the screw be low the fracture is pushing the plate upward. Each screw is ap plying a force on the plate equal to the weight of the person. The same magnitude force is also acting on the screws but in the opposite directions. For example, for the screw above the fracture, the plate is exerting an upward force on the head of the screw and the bone is applying a downward force. The effects of the forces applied on the screws are such that they are trying to shear the screws in a plane perpendicular to the centerline of the screws. With respect to the cross-sectional areas of the screws, these are shearing forces. The shear stress T generated in the screws can be calculated by using the following relationship between the shear force F and area A over which the shear stress is to be determined: F T=- A In this case, F is equal to the weight (W = 700 N) of the patient. Since the diameters of the screws are given, the cross-sectional area of each screw can be calculated as A = rr D2/4 = 19.6 mm2 or A = 19.6 x 10-6 m2. Substituting the numerical value of A and F = W = 700 N into the above formula and carrying out the computation will yield T = 35.7 x 106 Pa. Note that if we had a four-screw rather than a two-screw fixa tion device as shown in Figure 7.35, then each screw would be subjected to a shearing force equal to half of the total weight of the patient. Stress and Strain 143 144 Fundamentals of Biomechanics Example 7.5 Specimens of human cortical bone tissue were sub jected to a simple tension test until fracture. The test results revealed a stress-strain diagram shown in Figure 7.36, which has three distinct regions. These regions are an initial linearly elastic region (between 0 and A), an intermediate nonlinear elasto plastic region (between A and B), and a final linearly plastic region (between B and C). The average stresses and correspond ing strains at points 0, A, B, and C are measured as: Point Stress O\"(MPa) Strain E(mm/mm) o A B C o 85 114 128 0.0 0.005 0.010 0.026 Using this information, determine the elastic and strain hard ening moduli of the bone tissue in the linear regions of its O\"-E diagram. Note that the strain hardening modulus is the slope of the O\"-E curve in the plastic region. Also, find mathematical ex pressions relating stresses to strains in the linearly elastic and linearly plastic regions. Solution: The elastic modulus E is the slope of the O\"-E curve in the elastic region. Between 0 and A, the bone exhibits linearly elastic material behavior, and the O\"-E curve is a straight line. The slope of this line is: O\"A-O\"a 85x106-0 9 E = = = 17 x 10 Pa = 17 GPa EA - EO 0.005 - 0.0 The strain hardening modulus E' is equal to the slope of the O\"-E curve in the plastic region. Between Band C, the bone exhibits a linearly plastic material behavior, and its O\"-E curve is a straight line. Therefore: E' _ o\"c - O\"B _ 128 X 106 - 114 X 106 _ 9 - EC - EB - 0.026 _ 0.010 - 0.875 x 10 Pa The stress-strain relationship between 0 and A is: 0\" 0\" = E E or E = - E The relationship between 0\" and E in the linearly plastic region between Band C can be expressed as: ') 1 0\" = O\"B + E (E - E B or E = E B + E' (0\" - O\"B) For example, the strain corresponding to a tensile stress of 0\" = 120 MPa can be calculated as: _ 0 010 120 x 106 - 114 x 106 _ E -. + 0.875 x 109 - 0.017 Example 7.6 Consider the structure shown in Figure 7.37. The horizontal beam AB has a length l = 4 m, weight W = 500 N, and is hinged to the wall at A. The beam is supported by two identical steel bars of length h = 3 m, cross-sectional area A = 2 cm2, and elastic modulus E = 200 GPa. The steel bars are attached to the beam at Band C, where C is equidistant from both ends of the beam. Determine the forces applied by the beam on the steel bars, the reaction force at A, the amount of elongation in each steel bar, and the stresses generated in each bar. Assume that the beam material is much stiffer than the steel bars. Solution: This problem will be analyzed in three stages. Static analysis. The free-body diagram of the beam is shown in Figure 7.38. The total weight, W, of the beam is assumed to act at its geometric center located at C. RA is the magnitude of the ground reaction force applied on the beam through the hinge joint at A, and T1 and T2 are the forces applied by the steel bars on the beam. Note that only a vertical reaction force is considered at A since there is no horizontal force acting on the beam. We have a coplanar force system with three unknowns: RA, T}, and T2. There are three equations of equilibrium available from statics. Since there is no horizontal force, the horizontal equilib rium of the beam is automatically satisfied. Therefore, we have two equations but three unknowns. In other words, we have a statically indeterminate system and the equations of equilibrium are not sufficient to fully analyze this problem. We need an addi tional equation that will be derived by taking into consideration the deformability of the parts constituting the system. The vertical equilibrium of the beam requires that: L Fy = 0 : T1 + T2 + RA = W (i) For the rotational equilibrium of the beam about pOint A: 1 1 LMA=O: :2T1+T2=:2W (ii) Geometric compatibility. The horizontal beam is hinged to the wall at A, and the weight of the beam tends to rotate the beam about A in the clockwise direction. Because of the weight of the beam, which is applied as tensile forces T1 and T2 on the bars, the steel bars will deflect (elongate) and the beam will slightly swing about A (Figure 7.39). Because of the forces acting on the beam, the beam may bend a little as well. Since it is stated that the beam material is much stiffer than the steel bars, we can ignore the deformability of the beam and assume that it main tains its straight configuration. If 81 and 82 refer to the amount Stress and Strain 145 146 Fundamentals of Biomechanics \u00a3/2 Figure 7.39 Deflection of the beam. of deflections in the steel bars, then from Figure 7.39: 61 62 (I\u00b7 I\u00b7 I\u00b7) tana~-~l/2 l Note that this relationship is correct when deflections (61 and 62) are small for which angle a is small. Next we need take into consideration the relationship between applied forces and corresponding deformations. Stress-strain (force-deformation) analyses. The steel bars with length h elongate by 61 and 62. Therefore, the tensile strains in the bars are: 82 1:2 =- h (i v) The bars are subjected to tensile forces Tl and T2. The cross sectional area of each bar is given as A. Therefore, the tensile stresses exerted by the beam on the steel rods are: Tl T2 al = A a2 = A (v) Assuming that the stresses involved are within the proportional ity limit for steel, we can apply the Hooke's law to relate stresses to strains: al = E 1:1 (vi) Now, we can subtitute Eqs. (iv) and (v) into Eqs. (vi) so as to eliminate stresses and strains. This will yield: Tl h T2 h 61 = E A 82 = E A (vii) Note that from Eq. (iii): (vii i) Substituting Eqs. (vii) into Eq. (viii) will yield: T2 = 2 Tl (ix) Now, we have a total of three equations, Eqs. (i), (ii), and (ix), with three unknowns, RA, Tl, and R2. Solving these equations simultaneously will yield: 1 Tl = SW= lOON 2 T2 = SW=200N 2 RA= SW=200N Once tensile forces Tl and T2 are determined, Eqs. (vii) can be used to calculate the amount of elongations, Eqs. (v) can be used to calculate the tensile stresses, and Eqs. (iv) can be used to calculate the tensile strains developed in the steel bars: Tl 6 al = A = 0.5 x 10 Pa = 0.5 MPa T2 6 a2 = A = 1.0 x 10 Pa = 1.0 MPa al 6 El = E = 2.5 x 10- a2 -6 E2 = E = 5.0 x 10 Note that the calculated strains are very small. Correspondingly, the deformations are very small as predicted earlier while de riving the relationship in Eq. (iii). Also note that the stresses developed in the steel bars are much lower than the proportion ality limit for steel. Therefore, the assumption made to relate stresses and strains in Eqs. (vi) was correct as well. 7.18 Exercise Problems Problem 7.1 Complete the following definitions with appropri ate expressions. (a) Unit deformation of a material as a result of an applied load is called ------ (b) The internal resistance of a material to deformation due to externally applied forces is called _____ _ (c) is a measure of the intensity of internal forces acting parallel or tangent to a plane of cut, while ______ are associated with the intensity of internal forces that are perpendicular to the plane of cut. (d) On the stress-strain diagram, the stress corresponding to the is the highest stress that can be applied to the material without causing permanent deformation. (e) On the stress-strain diagram, the highest stress level corresponds to the of the material. (f) For some materials, it may not be easy to distinguish the yield point. The yield strength of such materials may be determined by the ____ _ (g) is defined as the ability of a material to resume its original (stress-free) size and shape upon removal of applied loads. (h) For linearly elastic materials, stress is linearly proportional to strain and the constant of proportionality is called the ____ of the material. Stress and Strain 147 148 Fundamentals of Biomechanics (i) The distinguishing factor in linearly elastic materials is their ------ G) Materials for which the stress-strain curve in the elastic region is not a straight line are known as _____ _ materials. (k) is the constant of proportionality between shear stress and shear strain for linearly elastic materials. (1) A mathematical equation that relates stresses to strains is called a ------ (m) The analogy between elastic materials and springs is known as _____ _ (n) ______ implies permanent (unrecoverable) deformations. (0) The area under the stress-strain diagram in the elastic region corresponds to the energy stored in the material while deforming the material. (p) energy is dissipated as heat while deforming the material. (q) The area enclosed by the signifies the total strain energy dissipated as heat while loading and unload ing a material. (r) The technique of changing the yield point of a material by loading the material beyond its yield point is called (s) The elastic modulus of a material is a relative measure of the of one material with respect to another. (t) A material is one that exhibits a large plastic deformation prior to failure. (u) A material is one that shows a sudden failure (rupture) without undergoing a considerable plastic deformation. (v) is a measure of the capacity of a material to sustain permanent deformation. The toughness of a ma terial is measured by considering the total area under its stress-strain diagram. (w) The ability of a material to store or absorb energy without permanent deformation is called the of the material. (x) If the mechanical properties of a material do not vary from location to location within the material, then the material is called _____ _ (y) If a material has constant density, then the material is called (z) If the mechanical properties of a material are indepen dent of direction or orientation, then the material is called Answers: Given at the end of the chapter. Problem 7.2 Curves in Figure 7.40 represent the relationship between tensile stress and tensile strain for five different ma terials. The // dot// on each curve indicates the yield point and the // cross\" represents the rupture point. Fill in the blank spaces below with the correct number referring to a material. Material __ has the highest elastic modulus. Material Material is the most ductile. is the most brittle. Material __ has the lowest yield strength. Material __ has the highest strength. Material __ is the toughest. Material Material is the most resilient. is the most stiff. Answers: Given at the end of the chapter. Problem 7.3 Consider two bars, 1 and 2, made of two differ ent materials. Assume that these bars were tested in a uniaxial tension test. Let Fl and F2 be the magnitudes of tensile forces applied on bars 1 and 2, respectively. El and E2 are the elastic moduli and Al and A2 are the cross-sectional areas perpendic ular to the applied forces for bar 1 and 2, respectively. For the conditions indicated below, determine the correct symbol relat ing tensile stresses 0\"1 and 0\"2 and tensile strains El and E2. Note that //>// indicates greater than, // <\" indicates less than, //=\" in dicates equal to, and //?\" indicates that the information provided is not sufficient to make a judgement. (a) If Al > A2 and Fl = F2, then 0\"1 >=? < 0\"2 and E1 >=? < E2 (b) If El > E2, Al = A z, and Fl = Fz, then 0\"1 >=? < o\"z and El >=? < E2 Answers: Given at the end of the chapter. Problem 7.4 Figure 7.41 illustrates a bone specimen with a cir cular cross-section. Two sections, A and B, that are fo = 6 mm distance apart are marked on the specimen. The radius of the specimen in the region between A and B is ro = 1 mm. This specimen was subjected to a series of uniaxial tension tests until fracture by gradually increasing the magnitude of the ap plied force and measuring corresponding deformations. As a Stress and Strain 149 150 Fundamentals of Biomechanics (J (MPa) 300 -rn-rn-rnrrrrrrrrrrrr-rn-rn 200 +H+H-++If-H-H\"D+\"I+++t+H+H 100+H+H~f-H-H+H+++t+H+H O~~~~~~LU+W~ o 0.5 1.0 1.5 2.0 2.5 1':(%) result of these tests, the following data were recorded: Record # Force, F (N) Deformation, !:il (mm) 1 94 0.009 2 190 0.018 3 284 0.027 4 376 0.050 5 440 0.094 If record 3 corresponds to the end of the linearly elastic region and record 5 corresponds to fracture point, carry out the follow ing: (a) Calculate average tensile stresses and strains for each record. (b) Draw the tensile stress-strain diagram for the bone speci- men. (c) Calculate the elastic modulus, E, of the bone specimen. (d) What is the ultimate strength of the bone specimen? (e) What is the yield strength of the bone specimen? (Use the offset method.) Answers (approximately): (c) E = 20 GPa (d) au = 140 MPa (e) a y = 118 MPa Problem 7.5 Human femur bone was subjected to a uniaxial tension test. As a result of a series of experiments, the stress strain curve shown in Figure 7.42 was obtained. Based on the graph in Figure 7.42, determine the following parameters: (a) Elastic modulus, E. (b) Apparent yield strength, ay (use the offset method). (c) Ultimate strength, au. (d) Strain, El, corresponding to yield stress. (e) Strain, E2, corresponding to ultimate stress. (f) Strain energy when stress is at the proportionality limit. (a) E = 14.6 GPa (b) ay = 235 MPa (c) au = 240 MPa (d) El = 0.018 (e) E2 = 0.020 (f) 1.235 MPa Problem 7.6 Consider the uniform, horizontal beam shown in Figure 7.43a. The beam is hinged to a wall at A and a weight W2 is attached on the beam at B. Point C represents the center of gravity of the beam, which is equidistant from A and B. The beam has a weight WI = 100 N and length.e = 4 m. The beam is supported by two vertical rods, 1 and 2, attached to the beam at D and E. Rod 1 is made of steel with elastic modulus El = 200 GPa and a cross-sectional area Al = 500 mm2, and rod 2 is bronze with elastic modulus E2 = 80 GPa and A2 = 400 mm2. The original (undeformed) lengths of both rods is h = 2 m. The distance between A and D is dl = 1 m and the distance between AandEisd2 =3m. The free-body diagram of the beam and its deflected orientation is shown in Figure 7.43b, where Tl and T2 represent the forces exerted by the rods on the beam. Symbols 81 and 82 represent the amount of deflection the steel and bronze rods undergo, respectively. Note that the beam material is assumed to be very stiff (almost rigid) as compared to the rods so that it maintains its straight shape. (a) Calculate tensions Tl and T2, and the reactive force RA on the beam at A. (b) Calculate the average tensile stresses 0'1 and 0'2 generated in the rods."
        ]
    },
    {
        "image_filename": "designv10_8_0002650_robot.2000.844824-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002650_robot.2000.844824-Figure3-1.png",
        "caption": "Figure 3: The tissue aspiration method",
        "texts": [
            " Assuming axisymmetry and homogeneous tissue in the portion covered by the aspiration tube (diameter of 1 cm in our system), a complete description of the deformation is given by the profile of the aspirated tissue. The implemented measurement process consists in varying the relative negative pressure in the tube and determining the functions z( r, 1 ) and P ( r ) , where t is the time from the start of the measurement, P ( t ) , the negative relative pressure in the tube at time t and z( r, r ) the profile of the deformation, as illustrated in Figure 3. Thus, we track over time the applied negative pressure and the resulting deformation. The measurement of more than just one-dimensional force-displacement information leads to more realistic parameter determination, whereas measuring the deformation over time permits estimation of constants describing time dependent behavior (C [ ] and z [SI). We developed a vision-based device to perform the measurements. The device permits controlled application of negative relative pressure and tracks the profiles of small deformations caused during the measurement process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure4.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure4.12-1.png",
        "caption": "Fig. 4.12 Element of a thin-walled profile",
        "texts": [
            "29) 1, i.e. rr X7) = O. From Eq. (4.50), it immediately follows that (4.54) and rrXX = rr(x,() = EExx = E{}'7jJ(() (4.55) for the axial stresses due to restrained warping. This axial stress must, since the loading is purely torsional, form a zero-force resultant on the cross section N = L rr(x, () dA = E{}' L 7jJ(() dA = 0, (4.56) which is fulfilled if Eq. (4.51) has been used to determine 7jJ(0). The equilibrium equation in axial direction for a small element cut out from the thin-walled section (see Fig. 4.12) is at = -O(i) orr o( ., ax' (4.57) 4.4 Influence of Restrained Warping 87 and, with (4.55) ~ = -Eo(()7jJ((){}\"(x). The resulting torque is (4.34) MT = f a(()t(x, () de (4.58) (4.59) where now t(x, () is no longer constant. Differentiating function 7jJ(() (Eq. 4.44) with respect to ( yields d7jJ 2Am {f d( }-l a(() = -d(\" + o(() o(() (4.60) Introducing this result into (4.59) leads to f d7jJ MT = - d(\" t(x, () d( + GJr{}(x) , (4.61) where use has been made of Eqs. (4.35), (4.41), and (4.42) 2. Integration by parts of the first integral then allows the introduction of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002397_095440603762554668-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002397_095440603762554668-Figure6-1.png",
        "caption": "Fig. 6 Specimen for measuring density and mechanical properties: (a) density; (b) tensile strength; (c) fatigue strength",
        "texts": [
            " Although the model dimension is not controlled strictly in the laser scan process, the titanium model has an almost identical dimension to the original one. The surface roughness of C01502 # IMechE 2003 Proc. Instn Mech. Engrs Vol. 217 Part C: J. Mechanical Engineering Science at Erciyes Universitesi on January 14, 2015pic.sagepub.comDownloaded from the model could not be measured with a conventional instrument using a stylus. The specimens for measuring density and mechanical properties of the titanium model are shown in Fig. 6. The cubic samples were used for density measurement and were examined by optical and scanning electron microscopy (SEM). Density was measured using the Archimedes principle. Evaluation of the tensile strength was carried out on a universal tensile testing machine at a speed of 0.5 mm/s. Torsional fatigue tests were carried out at up to 107 cycles in order to investigate the fatigue limit. The process parameters of the laser scanning are shown in Table 2 [11]. The in uence of the peak power and the scan speed on the density and mechanical properties are examined in the experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002864_1.2829170-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002864_1.2829170-Figure1-1.png",
        "caption": "Fig. 1 Simulation reference frames for cutting processes",
        "texts": [
            "asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use which states that the relative speed vector Vr between contacting surfaces must be in a plane tangent to the meshing surfaces at any contact point. During cutting, at any contact point common to both the generating surface described by the rotating cutter blade edge and the generated surface attached to the work, the expression for the relative speed vector V\u0302 z in a common general reference frame Z (Fig. 1) is stated as: V = V - V \" rz \u00bb cz ~ \\ (2) where Vrz is the relative speed vector between cutter and work, Vcz is the speed vector of a point belonging to the cutter attached to a cradle rotating about axis Wi, and Vwz is the speed vector of a corresponding point belonging to the work rotating about axis Xi. The work speed vector V\u201ex in reference frame X, rigidly connected to the work, is; X X , (3) where X \u201e, is the position of a common point between cutter and work, given in the work reference frame X, and <w\u201ex is the work rotation vector given by: 0 0 -Ra (4) where Ra is the ratio of roll between the work and the cradle, such that: Ra = \u2014 (5) where Uj is the work roll angle and L[ is the cradle angle of rotation",
            "33 Journal of Mechanical Design SEPTEMBER 1998, Vol. 120 / 433 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use The following machine settings are modified separately to show how the error surface is changed: machine root angle, spiral angle, cutter tilt, cutter point diameter, work offset, ma chine center to back and decimal ratio. For each machine setting change, the error surface is recalculated and its changes are described. Figure 1 should be consulted hereinafter to link the stated machine setting changes to the simulation model. Figures 5 to 8 show what are called 1st order changes [6] , e.g., with minimal curvature or surface twist changes. \u2022 In Fig. 5, the machine root angle is changed by 5 ' , as would be the case when cutting by the Spread Blade, Formate, Helixform or Duplex Helical cutting processes; the resulting error surface is a combination of spiral angle error on both tooth flanks, tooth taper error which is a difference in spiral angle error between the tooth flanks, spiral and pressure angle errors and slight surface twist or bias"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002939_j.mechmachtheory.2005.11.005-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002939_j.mechmachtheory.2005.11.005-Figure10-1.png",
        "caption": "Fig. 10. PUMA robot ( 2.79 6 q1 (in rad) 6 2.79, 3.93 6 q2 (in rad) 6 0.79, 0.79 6 q3 (in rad) 6 3.93).",
        "texts": [
            " The results converge towards the exact analytical expression for one joint and approximate the second joint solution with a small average error. This regression would have to be repeated for each multiple inverse kinematics solution. The current work evaluates the multiple inverse kinematics solutions of the SCARA robot simultaneously by using the forward kinematic equations of the robot and solving Eq. (20) as a multimodal optimization problem using a real-coded GA. Simulation experiments were also performed on a PUMA robot shown in Fig. 10. The inverse kinematics problem for the PUMA robot can be stated as: Table Result S. No. 1 2 3 4 5 Min C1\u00f0a2C2 \u00fe a3C23 \u00fe d4S23\u00de d2S1 S1\u00f0a2C2 \u00fe a3C23 \u00fe d4S23\u00de \u00fe d2C1 d4C23 a3S23 a2S2 8>>< >: 9>>= >; X Y Z 8>>< >: 9>>= >; subject to qL k 6 qk 6 qU k k \u00bc 1; 2; 3 \u00f021\u00de where the DH parameters a2, a3, d2 and d4 are 431.8 mm, 20.32 mm, 149.09 mm and 433.07 mm, respectively. The following control parameters were used for the GA: Population size = 150, Crossover probability = 0.9, SBX distribution index g = 50, tmax (for purpose of calculation of mutation probability) = 800",
            " The values of the joint variables evaluated may thus seemingly lie outside the actual joint variable limits as can be seen for the values of q2 in the fourth configuration of simulation experiment no. 1, the value of q3 in the first configuration of simulation experi- ment nos. 2, 3 and 4 and the values of q2 and q3 in the fourth configuration of simulation experiment nos. 2, 3 and 4. However, these values lie within the joint variable limits based on the link coordinate frame assignment given in Fu et al. [2] (shown in Fig. 10) considering the fact that a joint variable value +b and (2p b) are equivalent. The real-coded GA evaluates the joint variable values within the joint variable limits correctly in these instances. The fitness values of the feasible multiple solutions obtained using niching strategy 2, Dq, for the simulation experiments are given in Table 2 and can be used for multiplicity resolution. Fig. 13(a)\u2013(d) show the distribution of individuals in the population at the initial, two intermediate and generation number 260 of the realcoded GA for the simulation experiment no"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003623_elan.200904648-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003623_elan.200904648-Figure7-1.png",
        "caption": "Fig. 7. Magnetically controlled biofuel cell with the biocatalytic anode based on the reconstituted NAD\u00fe-dependent LDH and biocatalytic cathode based on the reconstituted COx/Cyt c system. (Adapted from ref. 113, with permission; Copyright American Chemical Society, 2005).",
        "texts": [
            "electroanalysis.wiley-vch.de 747 A biofuel cell composed of bioelectrocatalytic electrodes based on reconstituted enzymes was applied to demonstrate the phenomenon of the current enhancement in the presence of a constant magnetic field [113]. The biofuel cell included a lactate-oxidizing anode based on reconstituted lactate dehydrogenase (LDH; EC 1.1.1.27, from rabbit muscle, type II) [114, 115], while the oxygen-reducing cathode was based on cytochrome oxidase integrated with cytochrome c (COx-Cyt c) [99] (Fig. 7). Both bioelectrocatalytic electrodes included redox enzymes interacting with the corresponding cofactors/natural mediators NAD\u00fe and Cyt c for LDH and COx, respectively, immobilized in an aligned monolayer configuration. An additional mediator - pyrroloquinoline quinone (PQQ) facilitated the electron transfer from the enzymatically reduced NADH to the electrode conducting support. The biofuel cell produced an open circuitry voltage, Voc, of ca. 120 mV and a short circuitry current density, isc, of ca"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002649_oceans.2000.881362-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002649_oceans.2000.881362-Figure1-1.png",
        "caption": "Fig. 1 A nonlinear switching curve.",
        "texts": [
            " A variation of the above controller structures is to use a hyperbolic tangent function instead of a saturation function [41[61: S U = k tanh(-) + ueq 4 (3) It is proven that if k is large enough, the sliding model controllers of (l), (2) and (3) are guaranteed to be asymptotically stable [4]. Sliding Mode Fuzzy Control (SMFC) Pontryagin\u2019s maximum principle states that for 2 dimensional time optimal controller design, there exists a nonlinear switch curve such that the control can have maximal value on one side of the switching curve and minimal value on the other side of the curve. The nonlinear switching curve often has the form depicted in Fig. 1. It also shows there can be a switching band around the switching line to alleviate chattering. There are two problems associated with nonlinear time optimal controller design. First, how to get the true switching curve. For nonlinear systems, this switching curve is very difficult to get analytically. Secondly, how to approximate the nonlinear curve. To solve the first problem, we proposed to use system open loop experimental data. Under the maximal control command, the system output should be saturated after a period of time",
            " The ith rule for a Sliding Mode Fuzzy Controller is expressed as follows: 1 e+ Aje + cj IF e is and e is B, , THEN U; = ba t ( 4i Notice that the rule output function is not necessarily a saturation function, it could be a sign function or hyperbolic tangential function too. The fuzzification of e and e are illustrated in Fig. 3. The constant coefficients of Ai and ci are determined by the open loop experimental data. They are determined in such a way that the slop of the nonlinear switching curve is followed. Usually, the at-sea data has oscillation that reflects the environment disturbance and measurement noise. The magnitude of the oscillation can be use to determine the coefficient 4;. Notice that in Fig. 1 the switching curve can be either a function of e , or a function of e . Much less number of rules are needed to approximate this 1-dimensional function. This is how a Sliding Mode Fuzzy Controller reduces the rule base size. A typical rule for the simplified rule base is as the foIIowing. Antecedents Heading emor e PB PM ZERO NM NB ) e+ Aje + cj IF e is A;, THEN U; = hat( 4; Output Functions Thickness 4; Slope 2; Offset C; 1.5 0.01 13.5 3.0 2.0 1.5 3.0 3.0 0.0 3.0 2.0 -1.5 1.5 0.01 -13.5 A Sliding Mode Fuzzy Pitch Controller and a Sliding Mode Fwzy Heading Controller A sliding mode fuzzy pitch controller and a sliding mode fuzzy heading controller have been designed for the OEX series A W s that are developed in Ocean Engineering Department of Florida Atlantic University"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003134_56.808-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003134_56.808-Figure9-1.png",
        "caption": "Fig. 9. The hexapod walks on the constant slope plane",
        "texts": [
            " The crab walk tripod gait of a hexapod, at crab angle a and with stability margin S > 0, is as follows: 1) The sequence of movement of the body and legs is as shown on Table 11, in which B l = B j = S + 6 ( a ) and B 2 = B 4 = A ( S , a) and the foothold positions are as shown on Fig. 8. 2) The stride length X(S, a ) = 2 A ( S , a)+2S+26(CY). 3) The duty factor A (0, a) + 26(CY) 2 A (0, a ) + 26(a) - 2s p(S9 432 IEEE JOURNAL OF ROBOTICS AND AUTOMATION, VOL. 4. NO. 4. AUGUST 1988 v. THE TRIPOD GAITS ON A CONSTANT-SLOPE TERRAIN Consider a hexapod walking with a crab angle a on a constantslope terrain, as shown in Fig. 9. Now it is easy to see that the center of gravity of the hexapod will shift a distance h tan 0, where 0 is the slope angle and h is the height between q( t ) and the sloped plane, away from the horizontal plane. As a result, the critical support patterns of the tripod gait for crab walking on the sloped plane will also shift a distance A(0) = h tan 0 compared to that on the perfectly flat terrain, as illustrated by Fig. 9. Furthermore, the forbidden areas for the triangular support pattern are redefined as shown on Fig. 10. Based on the above observations, the tripod gaits for straight-line walking over flat terrain can be generalized to cover the case of tripod gaits on constant slope terrain. Thus we have the following theorem: Theorem 5 Assume a hexapod is to walk on a constant slope plane with slope angle 0. The tripod gait for straight-line walking with stability margin S is as follows: 1 ) The foothold positions are as shown on Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003365_diacare.5.3.190-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003365_diacare.5.3.190-Figure4-1.png",
        "caption": "FIG. 4. A schematic of the membrane-covered, rotated disc electrode sys~",
        "texts": [
            " The hydrogen-peroxide-based sensor has certain potential disadvantages for longterm implantation, but may be effective in other applications. Thus, modeling can provide directions and useful insights for sensor development. The practical problems are, first, to experimentally determine the parameters called for by the model, and, second, to devise methods for fabrication of membranes with desirable properties. MEMBRANE CHARACTERIZATION To complement our modeling approach, we have developed a membrane-covered rotated disc electrode apparatus for membrane characterization.12 As shown in Figure 4, the system is composed of a rotated shaft that contains both a disc working electrode and a high-impedance reference electrode. The rotation rate is precisely determined by a stepper motor control system. With the hydrophilic gel membrane mounted directly against the disc electrode surface, the mass transfer properties of the two substrates are first determined individually in the absence of the enzymatic reaction. The reaction is prevented by alternately not supplying one of the substrates while determining the transport properties of the other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003818_10426910902809776-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003818_10426910902809776-Figure2-1.png",
        "caption": "Figure 2.\u2014(a) Improved conventional IM nail with sieve-like head; (b) Preliminary design of IM nail with attendance instruments.",
        "texts": [
            " For the fixation of the radius bone head (caput radii) fractures in the elbow joint a special Intramedullary (IM) D ow nl oa de d by [ U O V U ni ve rs ity o f O vi ed o] a t 0 9: 36 0 3 N ov em be r 20 14 nail had been developed. The nail prototypes were manufactured with conventional and LENS technology. Material used for machining of the IM nail is titanium alloy Ti6Al4V in classical form (bars) for conventional processing technologies and in powder form (45 m grain size) for LENS technology. With conventional machining technologies (turning and drilling) we get a full nail form with two lines of fixation screw holes on the head of the nail and two stabilizing screw holes in the lower part of the nail [Fig. 2(a)]. For this design attendance instruments had to be developed [Fig. 2(b)]. Due to incapability of fulfilling predicted biofunctionality requirements, the conventional preliminary design had to be changed and improved. The sievelike nail head form had been developed, and cadaver biofunctionality test results fulfilled required demands. The nail produced with LENS technology is hollow, thin-walled, and with two stabilizing screw holes in the lower part. Fixation of the fragments of the caput radii is done with drilling screw holes during the surgical operation to the head of the nail coincidentally in the best possible way to gain primary stabilization of the fracture"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure2-1.png",
        "caption": "Figure 2. Illustration of hob profiles for generation of a pinion with chamfers.",
        "texts": [
            " Heat t reatment of gear tooth surfaces (performed after rough cutting) is required in many applications of gear drives. Then, a finishing process becomes necessary for elimination of distortions of tooth surfaces. Among the existing finishing processes, grinding is the preferable one due to its high accuracy [2]. Grinding by a worm-shape tool (see below) is an extension of the finishing of process of gears. There is a tendency at present in application of hobs with a modified shape, for instance, of hobs that may produce a chamfer, cutting out the tip of the gear tooth (Figure 2). For this reason, the hob tooth is designed with a ramp. It is expected that the tool designer is familiar with the tooth element proportions and the applied design parameters such as the module, helix angle, shape of the chamfer, etc. Chamfers on the top, front, and back sides of gear teeth are provided to avoid edge contact that may occur on the respective tooth part due to gear misalignment. Existence of chamfers complicates the finishing process, but this inconvenience has to be accepted. Providing of chamfers should not be considered as the indulgence of ignoring of possible existence of singularities in the zone between the chamfers and involute part of tooth surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure15-1.png",
        "caption": "Fig. 15. Carryover positions for example 2 or 3.",
        "texts": [
            " Therefore, one common method for estimating pump performance is to calculate the area efficiency by integration. That is to say, if the rotor tooth profile consists of multiple segment curves, each segment must be integrated and then summed to give the area of the rotor. As shown in Fig. 14, where A is the area of the rotor and Ac is the area of carryover, the formula for the area efficiency g is g \u00bc 2\u00f0pq2 1 A Ac\u00de pq2 1 \u00fe 4rq1 \u00f032\u00de The area of carryover in example 1 is shown in Fig. 14 and those of examples 2 and 3 are in Fig. 15. When we calculate the area efficiency, we must subtract the area of carryover. 1 parameter values for these three examples le 1 Pitch radius: r = 50 First segment is circular arc: q1 = 70, C1 = (0,0), a1 = 90 Second segment is circular arc: q2 = 30, C2 = (0,40), a2 = 36.87 Third segment is circular arc: q3 = 80, C3 = (30,0), a3 = 53.13 le 2 Pitch radius: r = 50, a = 12.87 First segment is circular arc: q1 = 70, C1 = (0,0), a1 = 77.13 Second segment is circular arc: q2 = 30, C2 = (0,40), a2 = 36"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002882_313-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002882_313-Figure1-1.png",
        "caption": "Figure 1. Principle of fluidic microsystems based on PCB technology.",
        "texts": [
            " Furthermore, all the electronics necessary for sensing, analysing or controlling the fluidic properties can be placed onto the same PCB. The basic idea of PCB-based fluidic systems is to modify the well known multilayer technology utilizing conventional double-sided copper-plated rigid base material (FR4). To create fluidic channels the copper of the PCBs is structured (by chemical wet etching) forming the lateral borders of the channel. By stacking one structured PCB upon the other the vertical borders of the channel are created. Figure 1 schematically shows the principle. The thickness of the copper and the total thickness of one PCB are selectable (18\u2013105 \u00b5m copper 100\u20131500 \u00b5m total, respectively). For connecting the single PCBs, a special 0960-1317/01/050528+04$30.00 \u00a9 2001 IOP Publishing Ltd Printed in the UK 528 adhesive technique has been used. The single boards are dipped into an adhesive liquid of certain viscosity (epoxy resin solved in ethanol, the viscosity approximately equals 3\u20136 mPa s) and coated with a thin uniform adhesive film (2\u20136 \u00b5m) by pulling them out of the solution with a constant velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure5-1.png",
        "caption": "Figure 5. Installment of grinding worm.",
        "texts": [
            " (ii) A special grinding worm is not required for the finishing process since the geometry of the applied grinding worm is based on the involute profiles of the crossed section of the pinion. (iii) No additional finishing processes are necessary since the obtained pinion tooth surface is provided with profile and longitudinal crowned areas that have been designed in advance. Topology of Modified Surfaces 1067 2. G E N E R A T I O N B Y A GRINDING WORM WORM INSTALLMENT. The installment of the grinding worm with respect to the pinion is based on schematic representation of meshing of two helicoids (Figure 5). The drawing of Figure 5 yields that the crossing angle is determined as ~/wl = A1 q- Aw, (1) where A1 and Aw are the lead angles on the pitch cylinders of the pinion and the worm. Figure 5 shows tha t the pitch cylinders of the worm and the pinion are in tangency at point M tha t belongs to the shortest distance between the crossed axes. The velocity polygon at M satisfies the relation v ( ~ ) - v (1) = # i t . ( 2 ) Here, v (~) and v (1) are the velocities of the worm and the pinion at M; it is the unit vector directed along the common tangent to the helices; # is the scalar factor. Equation (2) indicates tha t the relative velocity at point M is collinear to the unit vector it. Grinding w o r m ~ ~ M "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002437_1.555409-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002437_1.555409-Figure3-1.png",
        "caption": "Fig. 3 Interaction of a rolling element with the waviness on race surfaces",
        "texts": [
            " The force exerted by the kth rolling element on the inner and outer races are equal and opposite. Therefore, the total excitation force applied by all the rolling elements in the direction of radial load, can be expressed as F1d52F2d5( K51 Z Fek . (22) In order to obtain the solutions for a distributed defect, an appropriate function representing the type of defect, has to be substituted for w(f) in the expression for excitation force ~Eq. ~21!!. The interaction of a rolling element with the waviness on inner and outer races, is shown in Fig. 3. Since the race surfaces are closed, the waviness on the races can be expressed as periodic functions. However, in the following discussion, a single order of waviness of frequency m and amplitude b has been considered. Expressions have been derived for amplitudes of spectral components caused by this order of waviness on the outer and inner races. The amplitude of a particular spectral component can be determined by substituting the appropriate values of m and corresponding values of b in the expression"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003271_978-3-642-83957-3_3-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003271_978-3-642-83957-3_3-Figure7-1.png",
        "caption": "Figure 7: Determining the Number of SeH-Motioua Figure 8: 3R Manipulator Null Spaces 4 at each point of C4 with as many as two distinct self-motioua, yielding as many as two 2-dimeuaional preimages. These preimages may coalesce at a subchain singularity to form a single connected preimage, or the 3R subchain may only have one self-motion on C4, leading to one 2-dimensional self-motion. By induction, this analysis can be extended to planar manipulators with 5 or more joints to show that there are at most two self-motion manifolds for all redundant planar manipulators. Furthermore, this physical reasoning can be extended to spherical, regional, and spatial manipulators [2) to show that:",
        "texts": [
            " The inverse kinematic solution in (8) was found by a reassembly approach. That is, the end-effector is fixed to (x \u2022\u2022 , y.,) by a virtual revolute joint and the structure is broken into two subcomponents (at joint 3), a non-redundant 2R manipulator and a 1R link. Let C3 denote the circle of joint 3 locations formed by rotating link 3 about (x,., y \u2022\u2022 ). In C, the self-motion manifolci of this manipulator will be the product of 2R subchain inverse kinematic pre image of C 3 and the motion of joint 3. If C3 lies entirely within the workspace of the 2R subchain (Figure 7(a)), the 2R sub chain can position joint 3 on C3 (to insure consistent reassembly of the manipulator) in two distinct ways, and consequently the inverse image of (x \u2022\u2022 , y \u2022\u2022 ) consists of two disjoint self-motion manifolds, each containing a complete 2\". rotation of joint 3. In Figure 7(b) only one continuous arc segment of C3 is within the workspace of the 2R subchain. The 2R subchain can reach points on this arc in two configurations. However, the 2R subchain is in a singular configuration at the two points where C3 intersects the 2R workspace boundary. Both inverse preimages of the arc join at the subchain singularities (since 112 = 0 in both cases) to form one self-motion manifold, diffeomorphic to a circle. In Figure 7(c) C3 intersects the workspace of the 2R subchain in two disjoint arcs. Because the 2R sub chain is singular when the arcs intersect the 2R workspace boundaries, there is only one solution on each arc, resulting in a total of two solutions, each diffeomorphic to a circle, but not containing a 2\". joint rotation. [Note, the manipulators in Figure 7 are not all drawn to scale.] The preimage manifolds of an nR planar manipulator (n ~ 4) can be analyzed by induction. Divide a 4R manipulator at the origin of link frame 4 into a 3R redundant subchain (links 1, 2, and 3) and a single link (link 4). Let C4 be the circle formed by rotating link 4 about (x.\" y,.). The 3R subchain can position joint Theorem 1: For any regular x e W, an n-revolute-jointed redundant manipulator can have no more self-motions than the ma:r:imum number of inverse kinematic solutions of a non-redun dant manipulator of the same class"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003365_diacare.5.3.190-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003365_diacare.5.3.190-Figure2-1.png",
        "caption": "FIG. 2. Details of the glucose electrode.",
        "texts": [
            " In the presence of oxygen and glucose, this electrode produces a glucose-modulated, oxygen-dependent current, igmo-* The other major component is an oxygen electrode without an enzyme membrane, which registers the oxygen-dependent current of the ambience, i0. Both oxygen electrodes operate at a characteristic applied electrochemical potential Vapp with respect to a high-impedance reference electrode, and require an indifferent counter electrode to which the current passes. With the circuit configuration depicted here, the glucose electrode current is subtracted from the oxygen electrode current to give a glucose-dependent difference current ig, which is ultimately the signal of interest. More details of the glucose electrode are shown in Figure 2. Facing the body will be a biocompatible membrane of se- *Symbols: Throughout this article, the following symbols are used: A, electrode area (cm); Big, Bi0, Biot numbers, dimensionless mass transport parameters; ce, immobilized enzyme concentration (mol/cm3); c', dimensionless glucose concentration at the membranesolution interface; c* , effective substrate concentration ratio, a dimensionless design parameter defined in Eq. (9); Dg,D0, solute diffusion coefficients in the membrane (cm2/s); DgB, DoB, solute diffusion coefficients in the bulk (cm2/s); F, Faraday constant (A s/mol eq);i, subscript corresponding to either glucose, g or oxygen, o; id, diffusion current (A) defined in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003667_med.2008.4602064-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003667_med.2008.4602064-Figure2-1.png",
        "caption": "Fig. 2. The quadrotor benchtest.",
        "texts": [
            " The Inertial Measurement Unit (IMU) model and the corresponding assumptions are given too. Section III presents the bank of observers/estimators that is implemented to provide the N + 1 attitude estimates. The fault tolerant switching strategy is proposed in section IV. Section V is devoted to the presentation of the results obtained for various fault scenarios when the switching strategy is applied to the quadrotor. Conclusions and future directions are presented at the end of the paper. 978-1-4244-2505-1/08/$20.00 \u00a92008 IEEE 1094 Figure 2 depicts the quadrotor benchtest. A quadrotor is regarded as a composition of two PVTOL (Planar Take-Off and Landing vehicle) whose axes are orthogonal allowing a movement of six degrees of freedom. Two frames are considered (see Figure 3): the inertial frame R(ex,ey,ez) and the body frame B(e1,e2,e3) attached to the structure with its origin at the center of mass of the quadrotor. The quadrotor is mechanically simpler than classical helicopters: it has constant pitch blades. Each one of the four electric motors drives one blade: it provides the thrust forces f j, ( j = 1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.31-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.31-1.png",
        "caption": "Figure 8.31 () is the angle of twist.",
        "texts": [
            " The extent of deformation increases in the direction from the fixed end toward the free end. Angle y in Figure 8.30 is a measure of the deformation of the shaft, and it represents the shear strain due to the shear stresses induced in the transverse planes. The tangent of angle y is approximately equal to the ra tio of the arc length BB' and the length f of the shaft. For small deformations, the tangent of this angle is approximately equal to the angle itself measured in radians. Therefore: arc length BB' y = (8.23) f As illustrated in Figure 8.31, the amount of deformation within the shaft also varies with respect to the radial distance r mea sured from the centerline of the shaft. This variation is such that the deformation is zero at the center, increases toward the rim, and reaches a maximum on the outer surface. Angle () in Figure 8.31 is called the angle of twist and it is a measure of the extent of the twisting action that the shaft suffers. From the ge ometry of the problem: () = _ar_c_l_en.....;g::;..t_h_B_B_' (8.24) Equations (8.23) and (8.24) can be combined by eliminating the arc length BB'. Solving the resulting equation for the angle of twist will yield: (8.25) Now consider a plane perpendicular to the centerline of the shaft (plane abcd in Figure 8.32) that cuts the shaft into two segments. 174 Fundamentals of Biomechanics Since the shaft as a whole is in static equilibrium, its individual parts have to be in static equilibrium as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002321_jsvi.2000.2950-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002321_jsvi.2000.2950-Figure9-1.png",
        "caption": "Figure 9. Overall view of \"nite element model.",
        "texts": [],
        "surrounding_texts": [
            "4.3.1. Finite element model From section 4.1, it can be presumed that the main peaks with the #exural mode are caused by the #exural natural vibrations of the carriage. Then, to explain the main peaks with the #exural mode, the analysis of the natural vibration of test linear bearings was carried out by the \"nite element method (FEM). In the analysis, we used the FEM software COSMOS/M. The overall view and the details of the \"nite element model of the test linear bearing are shown in Figures 9 and 10, respectively. To model the carriage block and the end caps, an eight-node solid element was chosen in COSMOS/M. In the model, the mass m b of each ball in the load zone. l L , the spring constant K C caused by the elastic contact between the carriage and each ball, the spring constant K R caused by the elastic contact between the pro\"le rail and each ball were considered. To simplify the analysis, we assumed that the ball interval is equal and one ball is located in the center of the load zone as shown in Figure 10. In addition, we assumed that K C is equal to K R because the raceway groove radii of the carriage and those of the pro\"le rail in the test linear bearing are identical. Based on these assumptions, K C and K R can be expressed as K C \"K R \"2 l L k Z L , (8) where Z@ L is the number of balls in the load zone in one circulation when one ball is located in the center of the load zone. In the analysis using FEM, we used the material constants, Z@ L , m b , K C and K R for test linear bearings as shown in Table 3. 4.3.2. Results of analysis using the ,nite element method The results of the analysis using FEM on the natural vibration of the carriage are shown in Figure 11(a) and (b). Figure 11(a) and (b) indicates the results of the analysis using FEM of the light preloaded bearing and those of the medium preloaded bearing, respectively. These results are for the 17 652 elements model. In the process of the analysis, we con\"rmed that each natural frequency calculated by using the number of elements of about 10 000 or more tends to converge to constant values. Moreover, we con\"rmed that the mode shape is not a!ected by the number of elements. It is clear from Figure 11 that the #exural natural vibrations of the carriage exist theoretically, in addition to the rigid-body natural vibrations of the carriage. By comparing Figures 7(a), (b) and 11(a), (b), it is clear that the modes of the rigid-natural vibrations and the #exural vibrations of the carriage are almost the same as the measured vibration modes. To compare the frequency of the main peaks and the natural frequency of the carriage, the results of the analysis using FEM are listed in the right-hand column of Table 2. Although the #exural natural frequencies of the carriage obtained by FEM are lower than those of the main peaks with the #exural mode of the carriage, these are numerically roughly equal. Thus, it is veri\"ed that the main peaks with the \"rst, second and third #exural modes of the carriage are caused by the \"rst, second and third #exural natural vibrations of the carriage respectively. Moreover, the rigid-body natural frequencies of the carriage obtained by FEM almost agree with those of the main peaks with the rigid-body mode of the carriage. In addition, the natural frequencies obtained by FEM for the medium preloaded bearing are larger than those for the light preloaded bearing in the same way as are the frequencies of the corresponding peaks. The reason for this is that the spring constants K C and K R of the medium preloaded bearing are larger than those of the light preloaded bearing."
        ]
    },
    {
        "image_filename": "designv10_8_0003187_j.mechmachtheory.2005.12.006-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003187_j.mechmachtheory.2005.12.006-Figure1-1.png",
        "caption": "Fig. 1. Geometry of the Stewart platform manipulator: (a) the manipulator and (b) bottom platform.",
        "texts": [
            " We derive the singularity condition of the Stewart platform in terms of the task-space coordinates, i.e., using a parameterization of SE(3). We denote the position of the centre of the top platform, the point p, by the vector (x,y,z)T, and the orientation of the top platform by R 2 SO(3). The loop-closure equations can be written as p\u00fe Rai bi lisi \u00bc 0 i \u00bc 1; . . . ; 6 \u00f01\u00de where li denotes the length of the ith leg and ai,bi locate the leg connection points with respect to the platform centers in respective frames (see Fig. 1(a)), and si denotes the ith screw axis along the respective leg. The screw axis can be written in terms of the Cartesian, and actuated variables as si \u00bc 1 li \u00f0p\u00fe Rai bi\u00de \u00f02\u00de Denoting the actuation force along the ith leg as fi, the wrench imparted on the top platform may be expressed in the base reference frame as W i \u00bc \u00f0fisi; \u00f0Rai\u00de fisi\u00de \u00f03\u00de Using the expression for si from Eq. (2), Wi may be written as W i \u00bc fi li \u00f0p\u00fe Rai bi\u00de; fi li \u00f0\u00f0Rai\u00de \u00f0p bi\u00de\u00de \u00f04\u00de Denoting the force and moment parts of the resultant wrench applied on the top platform due to all the leg forces as W \u00bc P6 i\u00bc1W i \u00bc \u00f0F; M\u00de, the equation for statics of the top platform may be written as 1 l1 \u00f0p\u00fe Ra1 b1\u00de1 ",
            " However, we choose the X axis to pass through the connection point of the first leg in each platform, such that the spacings are given by ct = (0,2ct, 2p/3,2p/3 + 2ct, 4p/3,4p/3 + 2ct), cb = (0, 2cb, 2p/3,2p/3 + 2cb, 4p/3,4p/3 + 2cb) respectively in the top and bottom platform. In this way, three of the leg connection points lie on the axes of symmetry, and the arrangement results in a significant reduction of complexity in all subsequent computations. The manipulator along with the frames of reference used is shown in Fig. 1(a), and the bottom platform, in Fig. 1(b). With the above choice of the coordinate system, the SRSPM is described by 9 parameters: (rt,cb,ct) defining the architecture, and 6 local coordinates of SE(3)\u2014as seen later an algebraic representation of the rotation matrix is chosen using the Rodrigue\u2019s parameters c = (c1,c2,c3) (see Appendix A for details) as this helps in symbolic computations. Therefore, the singularity manifold, M, can be described by a hyper-surface in R9, each point of which defines one singular configuration.4 In kinematic computations and in attempts to obtain closed-form analytic expressions, we frequently come across large and complex mathematical expressions involving algebraic and trigonometric terms",
            " We use the same architecture as in Section 4.4. The orientation of the top platform is also chosen as in the examples of Sp, and the position is set to x = y = 0. The z component of position is obtained from Eq. (20), which yields three solutions for each set of x,y and other parameters. We use only the positive values of z in the following. Example 1. We choose x = y = 0, c1 = 0.4, c2 = 0.2, c3 = 0.6 and evaluate a singularity corresponding to Sp. For these numerical values, Eq. (20) reduces to Fig. 1 (c) c1 = 0:1115z3 \u00fe 0:0533xz2 \u00fe 0:3502yz2 \u00fe 0:0478z2 \u00fe 0:1046x2z 0:1431y2z 0:3778xz\u00fe 0:1582xyz 0:2817yz\u00fe 0:2994z\u00fe 0:0266x2 \u00fe 0:0854y2 \u00fe 0:0988x 0:1512xy \u00fe 0:0046y 0:1550 \u00bc 0 2. Singular configurations of the SRSPM at x = y = 0, z = 0.2091, c2 = 0.1, c3 = 0.1: (a) c1 = 0.0889, (b) c1 = 0.0000, 0.4139, (d) c1 = 1.5384 and (e) c1 = 21.1170. Substituting x = y = 0 in the above polynomial, we get 0:1115z3 \u00fe 0:0478z2 \u00fe 0:2994z 0:1550 \u00bc 0 and the solution of the above cubic gives z = 0.5282,1.5735, 1.6732"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002969_a:1026100913269-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002969_a:1026100913269-Figure6-1.png",
        "caption": "Fig. 6. The patterns of spreading over the surface of a dimple of depth \u2206 = 0.22 with (a) symmetric and (b) asymmetric vortex structures, along with comparison of the distributions of the ratio of the local coefficient of heat transfer from a dimpled surface to the local coefficient of heat transfer from a smooth wall in the (c) longitudinal and (d) transverse midsections of the dimple. Curves 1 and 2 correspond to (a) two-cell and (b) single-cell patterns of spreading, respectively.",
        "texts": [
            " In the case of a two-cell vortex structure in a dimple, swirling jets interacting in the symmetry plane are formed owing to the income of mass from the upper and lower halves of the dimple (Fig. 7a). An asymmetric vortex structure with a predominant transverse transfer of a liquid medium is generated owing to the input of mass only from the upper half of the dimple. For the deep dimples under consideration, the deformation of the laminar temperature wall boundary layer in a dimple associated with structural rearrangement becomes pronounced. This deformation leads to the enhancement of heat transfer in its vicinity (Fig. 4). As follows from Fig. 6, the transition from a two-cell structure to a one-vortex one is accompanied by a significant increase in local heat fluxes in two characteristic midsections of the dimple with a depth of 0.22. One can see from Fig. 8a that, as a result, the coefficient of relative heat transfer from a spherical dimple increases by jumps to almost 1.6, and that for the region in the wake behind the dimple increases to 1.44. The last circumstance confirms the conclusions drawn in [24]. x, y, and z, Cartesian coordinates; U, velocity of incident flow; D, diameter of dimple; \u2206, depth of dimple; \u03b4, increment of dependent variable; u, v, and w, longitudinal, vertical, and transverse components of velocity; k, energy of turbulent pulsations; \u03b5, rate of dissipation of turbulent energy; \u03c9, specific rate of dissipation of turbulent energy; p, excess pressure referred to double velocity head; T, temperature; a, coefficients of difference equations; S, source terms; c and Q, sweep coefficients; Re and Pr, Reynolds number and Prandtl number; Nu, Nusselt number; and Nu/Nupl, coefficient of relative heat transfer of assigned element of surface subjected to flow"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure5.19-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure5.19-1.png",
        "caption": "Figure 5.19 Forces acting on the lower body of the athlete.",
        "texts": [
            " FJn is the magnitude of the normal component of F J compressing the articulating joint surface, and F J t is the magnitude of its tangential compo nent having a shearing effect on the joint surfaces. Forces in the muscles and ligaments of the neck operate in a manner to counterbalance this shearing effect. Example 5.4 Consider the weight lifter illustrated in Figure 5.18, who is bent forward and lifting a weight Woo At the position Applications of Statics to Biomechanics 99 shown, the athlete's trunk is flexed by an angle e as measured from the upright (vertical) position. The forces acting on the lower portion of the athlete's body are shown in Figure 5.19 by considering a section passing through the fifth lumbar vertebra. A mechanical model of the athlete's lower body (the pelvis and legs) is illustrated in Figure 5.20 along with the geometric parameters of the problem under consider ation. W is the total weight of the athlete, WI is the weight of the legs including the pelvis, W + Wo is the total ground reac tion force applied to the athlete through the feet (at C), F M is the magnitude of the resultant force exerted by the erector spinae muscles supporting the trunk, and F I is the magnitude of the compressive force generated at the union (0) of the sacrum and the fifth lumbar vertebra"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002965_tia.2005.855043-Figure21-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002965_tia.2005.855043-Figure21-1.png",
        "caption": "Fig. 21. Phasor diagram.",
        "texts": [
            " Ch1: m , Ch2: m . During the and states, the switching logic remains the same as in Algorithm #02. During and states, both inverters are not switched to zero vectors. One of them is kept at active state to reduce the resultant torque ripple and to correct the phase angle between the components of individual fluxes. Output of the torque ripple controller ( ) decides which inverter is to be switched at active state. For example, when and , only is rotated. Similarly, when and , only is rotated (Fig. 21). The switching table for this method is given in Table IV (a) and (b). Advantages: 1) Torque ripple is considerably reduced. The ripple is lesser in magnitude compared to three-phase DTC scheme. In three-phase DTC scheme, during the state, stator flux is stopped. Rotor flux moves quickly and the rate of decrease in the angle between them is also fast. Therefore, the torque ripple is high. However, in this method during the state, resultant stator flux is also rotated but at a slower rate compared to the rotor flux"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002780_robot.1999.770457-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002780_robot.1999.770457-Figure6-1.png",
        "caption": "Figure 6: Modelling of the intralimb coordination by two neuro-oscillators per joint angle, switched by the interlimb coordination network.",
        "texts": [
            " Currently we mainly investigate statically stable motion1. In figures 2 and 3 gait diagrams and joint angle trajectories for a typical statically stable gait with We currently work on a biologically inspired leg for dynamically stable locomotion [4], which includes biological research results of small mammal locomotion [5 ] . Main aspects of this Figure 3: Joint angle trajectories of the right fore leg for the statically stable gait (left) and for the dynamically stable gait (right). Angles in radians are plotted against time. (see fig. 6 for a closer look of the leg construction.) The analysis of the joint angle trajectories and the gait diagram shows the periodic character of the movement on different control levels. Further important aspects can be seen in the joint angles trajectories, which consist of two different parts describing stance and swing phase of the corresponding leg. So the joint angle trajectories can be interpreted as being generated by superimposing two oscillations. 3 Adaptive Control Architecture The used strategy for representing the locomotion of BISAM is to build up a coupled neuro-oscillator architecture with a rather basic neuron model as elementary oscillator",
            " example for this will be given by the learning of ankle joint reflexes. Third, higher behavior levels add actions to the output of the oscillator or even dominate them. Higher behaviors must run with higher priority to ensure the security of the robot. If, for example, an inclinometer or an angle velocity sensor of the body detects an overturning to one side, the posture control has to adjust the corresponding legs exclusively. 3.2 Intralimb Coordination The architecture of the coupled neuro-oscillators for modelling intralimb coordination is shown in figure 6. Caused by the analysis of the joint angle trajectories in figure 3 the movements of single joints are modelled with two elementary oscillators of which one is respon- sible for the swing phase and the other one for the stance phase. Networks with three neurons are used as elementary oscillators in order to generate smoother trajectories. The use of two oscillators per joint angle rises the question, how appropriate this partition is (figure 7). Beside the fact that the single periodic movements in stance and swing phase are much easier to model in comparison to the whole joint angle movement, another important aspect of this concept can be seen when observing the robustness of the controller in uneven terrain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003118_ip-a-1:19880074-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003118_ip-a-1:19880074-Figure2-1.png",
        "caption": "Fig. 2 Simulation of closed magnetic core",
        "texts": [
            " 5 Closed cores In many electrical devices, for example transformers, the core will form a closed magnetic circuit. In practice, the shape of the core is usually toroidal or rectangular. However, with some justification, we shall conveniently side-step the issue of shape by imagining the core to have been cut open and straightened out to its length /. A return flux path of zero reluctance is then provided by placing the straightened-out core between two infinite plates of perfect magnetic material (/1 = 00, a \u2014 0) as shown in Fig. 2. This effectively closes the magnetic circuit as required. This simulation is designed, of course, to facilitate analysis. Nevertheless, it is soundly based, and may be expected to give good accuracy for turns reasonably close to the core, provided that / > b (assuming a realistic core shape). It is thought that this latter condition will apply in many practical cases of interest. 5.1 Derivation of closed-core formula Let the energising turn be located halfway along the straightened core. Note that this can always be arranged 472 IEE PROCEEDINGS, Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003809_acc.2010.5530520-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003809_acc.2010.5530520-Figure5-1.png",
        "caption": "Fig. 5. Ball velocities just before and after the rebound.",
        "texts": [
            " For the jthe feature point, the following rotational relationship holds [9]: pblj [i + 1] = eb\u03c9\u2206tpblj [i], eb\u03c9\u2206t \u2248 I3 + \u03c9\u0302\u2206t, (2) where \u03c9\u0302 \u2208 R 3\u00d73 is the skew-symmetric matrix which corresponds to the cross product of \u03c9. Note that the terms of the higher order with respect to \u2206t are approximated to 0 because of the small \u2206t. Substituting the 2nd eq. into the 1st eq. of (2) leads to pblj [i + 1] = pblj [i] + \u2206t\u03c9\u0302pblj [i], where \u03c9\u0302pblj [i] is calculated as \u03c9\u0302pblj [i] = \u03c9 \u00d7 pblj [i] = \u2212pblj [i] \u00d7 \u03c9 = \u2212p\u0302blj [i] \u00d7 \u03c9. Then, we get p\u0302blj [i]\u03c9 = \u2212vblj [i], vblj [i] := pblj [i + 1] \u2212 pblj [i] \u2206t . (3) Figure 5 shows the rebound of the ball from the table, where (vb,\u03c9b) and (v\u2032 b, \u03c9 \u2032 b) are the translational and rotational velocities of the ball just before and after the rebound and \u03a3B is the reference frame with the z-axis normal to the table. The simplest model of the rebound phenomenon is described by the equations of v\u2032 bz = \u2212etvbz , v\u2032 bx = vbx and v\u2032by = vby , where et is the coefficient of restitution of the table in the z direction. In this model, it is assumed that there is no friction on the table"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003891_s12283-009-0028-1-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003891_s12283-009-0028-1-Figure3-1.png",
        "caption": "Fig. 3 The initial configuration for the 3D, six-segment model used to simulate the downswing. Note that the most proximal club segment was comprised of both the golfer\u2019s hand and grip of the club",
        "texts": [
            " Although not explicitly reported by any of the previously mentioned researchers, bending in the toe-up/ toe-down direction may also alter ball flight. The purpose of this paper was to gain an understanding of the role that shaft stiffness plays during the golf swing. This was accomplished through the use of mathematical modeling and optimized computer simulation techniques. 2 Methods 2.1 Model description A representative mathematical model of a golfer was constructed using a six-segment (torso, arm, and four club segments), 3D, linked system (Fig. 3). The golfer portion of the model had four degrees of freedom. The model was capable of torso rotation, horizontal abduction at the shoulder, external rotation at the shoulder, and ulnar deviation at the wrist. Four muscular torque generators, which adhered to the force\u2013velocity and activation rate properties of human muscle, were incorporated to add energy to the system. The four segments of the modeled club were connected in series by rotational spring-damper elements (Fig. 3). The hand and most proximal club segment were combined to represent a single segment, Club_Proximal [5]. The shafts were capable of deflecting about two axes (Fig. 1). Further details on model development and parameters have previously been presented [9]. Three versions of the same base model were used in this study. They differed only with regards to the constraint parameters governing the maximum torque output from the four torque generators. This allowed the role of shaft flexibility to be evaluated for golfers that generate three different levels of clubhead speed (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure22-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure22-1.png",
        "caption": "Fig. 22. Face-gear drive with conical worm: bearing contact at the end of the cycle of meshing.",
        "texts": [],
        "surrounding_texts": [
            "The finite element analysis has been performed for a face-worm gear drive with conical worm of common design parameters represented in Table 1. For the analysis the model of the whole worm (Fig. 17) and the whole face-gear (Fig. 18) have been substituted by a model of five-pair of teeth in meshing (Fig. 19) in order to save computational time. Elements C3D8I of first order have been used for the finite element mesh. The total number of elements is 55 672 with 68 671 nodes. The material used is steel with Young\u2019s modulus E \u00bc 206800 N/mm2 and Poisson\u2019s ratio 0.29. The torque applied to the face-gear is 50 Nm. Figs. 20\u201322 show how the bearing contact looks at the beginning, at the middle, and at the end of a cycle of meshing. The results obtained by finite element analysis confirm the longitudinal path of contact and the avoidance of edge contact. Fig. 23 shows the variation of bending and contact stresses on the face-gear from the beginning of the contact to the end of contact on one tooth of the face-gear. The stresses are represented as unitless parameters in function of the worm rotation rm1 \u00bc r1 rmax1 ; \u00f013\u00de rm2 \u00bc r2 rmax2 \u00f014\u00de where r1 and r2 are the bending and contact stresses of Mises and rmax1 and rmax2 are the maximum bending and contact stresses of Mises on the face-gear. In the example developed, rmax1 \u00bc 168 N/mm2 and rmax2 \u00bc 1090 N/mm2. The load is always shared by three pairs of teeth, therefore the contact ratio is 3."
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure11.20-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure11.20-1.png",
        "caption": "Figure 11.20 h is the maximum elevation and l is the horizontal range of motion.",
        "texts": [
            " In some cases, the objective of the projectile motion may be to increase the horizontal range of motion to a maximum. This is particularly true for a ski jumper, for example. Other situations may require a control over the height, which is the case for a high jumper. Therefore, it may be useful to derive some expressions for the horizontal range and maximum height of the projectile motion. Such derivations will be performed within the context of the following example problem. Example 11.5 Consider Figure 11.20, which shows the trajec tory of a projectile motion along with some of the parameters involved. Xo = 0 and yo = 0 because the origin of the xy coordi nate frame is chosen to coincide with the initial position of the object. Let tl be the time it takes to reach the peak, and t2 be the total time of flight. At the peak, Yl = h, Vyl = 0, and Xl = t;2 from the symmetry of the motion. At the location where the ob ject lands, X2 = f. and Y2 = o. The maximum height h reached by the object can be determined by noting that Vyl = 0 at the peak"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.14-1.png",
        "caption": "Fig. 6.14 (a) Mechanical work performed by the actuator while interfaced with a passive structure without pre-stress. (b) Work produced against linear structures of different stiffness; stiffness matching condition (thick line, dark shaded area)",
        "texts": [
            "3 Theory of Single-Stroke Linear Solid-State Actuators 169 that the strength boundaries are passive, i.e. external to such triangular domain and therefore do not affect the actuator\u2019s operation domain. While the induced stroke is increased from zero to ui, the point on the plane which is identified by the actuator force and stroke will move on the characteristic curve of the host structure. The mechanical work performed by the actuator (effective stroke work) will then be given by the portion of the actuator\u2019s operation domain which is below the structure\u2019s characteristic curve (see Figure 6.14(a)). It is evident that the area of the activation domain 1 2 Wn = Fbui = kau2 i (6.14) represents the maximum possible amount of work which can be performed by the actuator (in a single activation process from zero to the given value of induced strain) under the given conditions. If the host structure has a linear characteristic (see Figure 6.14(b)), the effective stroke work will be given by the area of a triangular region: W = 1 2 Fu (6.15) with F and u as the actual values of the actuator force and stroke when the induced stroke reaches the value ui. For a given solid-state actuator and a given value of the induced strain, the effective stroke work depends on the stiffness of the host structure. In particular, if the stiffness of the host structure vanishes, the effective stroke work vanishes as well (the actuator works under free stroke condition, which implies F = 0)",
            " The condition (6.18) (stiffness matching condition) is of basilar importance for the design of solid state actuators. We summarize it: The maximum effective stroke work of a linear solid-state actuator: \u2022 which works against the stiffness of a linear passive structure \u2022 without pre-stress \u2022 and with passive strength boundaries amounts to one eighth of the nominal stroke work. This result can also be applied in presence of active strength boundaries, if they do not intersect the stiffness matching path (see Figure 6.14(b)). If strength boundary and stiffness matching path intersect, the maximum effective stroke work is lower. For the case represented in Figure 6.14(c), in which the strength boundary is a simple force limit (independent of the actuator stroke): F \u2264 Flim (6.22) the maximum effective stroke work amounts in this case to Wmax = 1 2 Flimui ( 1\u2212 Flim Fb ) (6.23) In the case in which the strength limit force is very low with respect to the block- ing force: Flim Fb (6.24) it holds Wmax 1 2 Flimui (6.25) The condition (6.24) is typical for active materials with high active strain, like Shape Memory Alloys (SMA). The considered case of an actuator working against a linear stiffness without pre-stress covers only a part of the conceivable application scenarios",
            " In this case, and for the above examined case of an actuator working against a linear stiffness without pre-stress and with passive strength boundaries (or strength boundaries which do not intersect the stiffness matching path) the maximum effective stroke work reads Wmax = 1 8 Wn = 1 8 wnV (6.50) with Wmax = 1 8 wn = 1 8 E\u03b52 i (6.51) as the effective energy density of the active material. A special case of practical relevance is the already examined case of a strengthrelated force boundary (see Figure 6.14(c)) in which the boundary results from the allowable axial stress of the material. In this case Equations 6.23 and 6.25 read respectively Wmax = 1 2 \u03c3lim\u03b5i ( 1\u2212 \u03c3lim E\u03b5i ) V (6.52) Wmax 1 2 \u03c3lim\u03b5iV (6.53) so that the maximum effective stroke work can be, again, expressed as the product of a material constant and the actuator\u2019s volume. The design relevance of the results (6.50) and (6.52)\u2013(6.53) is given by the fact that if the mechanical work to be produced by the actuator is known, the minimum amount (volume) of active material needed for actuation is definite independently of the actuator geometry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.7-1.png",
        "caption": "Figure 14.7 Circular end region of a ski jump track.",
        "texts": [
            "80m/s m m At position 4, Wt4 = W cos(45) is the only tangential force: Wt4 m g cos( 45) 2 at4 = - = = g cos(45) = 6.93 m/ s m m There is no tangential force at position 5, and therefore, atS = O. 302 Fundamentals of Biomechanics t (f) Now that we calculated the tangential components of the ac celeration vector, we can also calculate the angular acceleration of the gymnast using: at a= r Notethatr = 1m. Therefore,a} = 0,a2 = 6.93rad/s2,a3 = 9.80 rad/s2, a4 = 6.93 rad/s2, and as = O. Example 14.2 Figure 14.7 illustrates the circular end region of a ski jump track. The radius of curvature of the track at this region is r = 50 m. At the end of the track, the direction normal to the track coincides with the vertical and the direction tangential to the track coincides with the horizontal. Consider a 70 kg ski jumper who is decelerating at a rate of 1.5 m/ S2 due to air resistance. If the friction on the track is neg ligible and the ski jumper reaches the end of the track with a horizontal velocity of v = 20 m/ s, determine the forces applied on the skier by the air resistance and the track"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.22-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.22-1.png",
        "caption": "Figure 3.22 Translation of a force from point PI to P2\u2022",
        "texts": [
            " If F is the magni tude of the forces forming the couple and d is the perpendicular distance between the lines of actions of the forces, then the mag nitude of the couple-moment is: (3.4) The direction of the couple-moment can be determined by the right-hand-rule. 3.8 Translation of Forces The overall effect of a pair of forces applied on a rigid body is zero if the forces have an equal magnitude and the same line of action, but are acting in opposite directions. Keeping this in mind, consider the force with magnitude F applied at point PI in Figure 3.22a. As illustrated in Figure 3.22b, this force may be translated to point P2 by placing a pair of forces at P2 with equal magnitude (F), having the same line of action, but acting in op posite directions. Note that the original force at PI and the force at P2 that is acting in a direction opposite to that of the original force form a couple. This couple produces a counterclockwise moment with magnitude M = d F , where d is the shortest dis tance between the lines of action of forces at PI and P2. Therefore, as illustrated in Figure 3.22c, the couple can be replaced by the couple-moment. Provided that the original force was applied to a rigid body, the one-force system in Figure 3.22a, the three-force system in Figure 3.22b, and the one-force and one couple-moment system in Figure 3.22c are mechanically equivalent. 40 Fundamentals of Biomechanics y Ty 1. o ~~-------+------x Figure 3.24 The moment about 0 isM=r.. xF . 3.9 Moment as a Vector Product We have been applying the scalar method of determining the moment of a force about a point. The scalar method is satis factory to analyze relatively simple coplanar force systems and systems in which the perpendicular distance between the point and the line of action of the applied force are easy to calculate. The analysis of more complex problems can be simplified by utilizing additional mathematical tools"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003911_j.jtbi.2008.06.034-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003911_j.jtbi.2008.06.034-Figure1-1.png",
        "caption": "Fig. 1. The bipedal spring\u2013mass model has a point-mass upper body and two massless legs that behave like passive linear springs. Leg forces act along the line joining foot contact point and center of mass.",
        "texts": [
            " Several variants have been used, including the telescoping leg as a general force-actuator (Alexander, 1980; Srinivasan and Ruina, 2006), a simple passive linear or non-linear spring (McGeer, 1990; McMahon and Cheng, 1990; Blickhan and Full, 1993; Farley and Gonzalez, 1996; Seyfarth et al., 2002; Ghigliazza et al., 2003; Geyer et al., 2005), and a spring in series with a general force-actuator (Alexander, 1992). These models serve as analogs that simplify the problem of understanding the mechanics of legged locomotion of real animals. They have been used both to describe what is observed, and to predict what might happen in nature. Most significantly for the purposes of this paper, it has been found that center-of-mass (CoM) motions of the spring-mass model (Fig. 1) are qualitatively similar to those of running animals over a wide range of body mass, and with differing numbers of legs (Blickhan and Full, 1993; Farley and Gonzalez, 1996). Here we examine in greater depth the approximation of bipedal, quadrupedal, and hexapedal animal gaits by the springmass model, and discuss the sagittal-plane stability of the most ll rights reserved. vasan). common instantiation of this model over the parameter regimes appropriate for three representative animals. The spring-mass model is typically restricted to the sagittal plane, a practice that we follow in the present paper",
            " In Section 3, we describe how the model is fitted to data by estimating apparent leg stiffness, we introduce a simple test of a key assumption, and we compare CoM motions and ground reaction forces (GRFs) predicted by the model with data from running humans and cockroaches, and a trotting horse. Stability of these three families of gaits, corresponding to the three different apparent leg stiffnesses derived from data, is considered in Section 4, and we conclude in Section 5. The spring-mass model or spring-loaded inverted pendulum (SLIP, Fig. 1) is generally used to describe bipedal running, although it has been applied to animals as diverse as cockroaches, centipedes and oxen, over a wide range of speed and body mass (Blickhan and Full, 1993). Single leg stance is typically assumed, but here we allow double stance phases, as in Geyer et al. (2006). We describe the model in Section 2.1, and characterize its solutions in Section 2.2. The spring-mass model (Fig. 1) has a point-mass upper body G with mass m. The position of G in the sagittal plane at time t is \u00f0xG\u00f0t\u00de; yG\u00f0t\u00de\u00de with respect to the inertial frame as shown. Locomotion proceeds in the positive x direction. The two massless legs with point-feet are denoted leg-1 and leg-2 when convenient, with foot positions xc1 and xc2, respectively, when in ground contact. The ground is assumed level and horizontal, so that yc1 \u00bc yc2 \u00bc 0, and legs exert forces F1\u00f0t\u00de and F2\u00f0t\u00de on the body only when in ground contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003646_0005-1098(80)90082-5-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003646_0005-1098(80)90082-5-Figure6-1.png",
        "caption": "FIG. 6. Biped model in frontal plane.",
        "texts": [
            " Thus there is no need for nominal control synthesis, but rather the system has to be stabilized around the given point in state space. In this case the control task reduces to maintaining the position of the system (posture) under perturbed initial conditions. 18 MIOMIR VUKOBRATOVIC and DRAGAN STOKIC We shall here examine one simplified biped model in order to show the efficiency of forcefeedback for postural stabilization. A biped system with two d.o.f, should be stabilized around the vertical position shown in Fig. 6. The model parameters (lengths, masses and moments of inertia of its members) are chosen in such a way that the model represents an anthropomorphic biped system in the frontal plane, the parameters are denoted in Fig. 6. The model is assumed to have two degrees of freedom; between the foot and support (~b), and the motion of the trunk relative to the vertical axis (plane motion 0). The degree of freedom of the trunk is assumed to be powered by the actuator S ~, the model of which is given in the form (2) with n~=3, n=2, m = l and N=5 . The state vector for subsystem is x ~ =(0, 0, JR), where i g is the rotor current of the d.c. motor, used as an actuator. The state vector of the complete system is thus x=(0, 0, JR, qS, ~)x. However, it should be noted that for qS=0, the system structure is changed, because of the contact of the second leg with the ground, but the presence of this contact increases the stability margin of the system. The level of nominal dynamics is trivial in this task: 0\u00b0=0, qS\u00b0=0, u\u00b0 =Ustat~ It is obvious, however, that the point ~b=0, q~=0, 0=0, 19=0, iR =ist,,c cannot be an equilibrium point for the model of Fig. 6, since arbitrarily small deviations in q5 cause a change in system structure. Thus, practical stability round the nominal position will be discussed. The system will be considered practical stable if for VX(to)e,X I it is guaranteed that-x(t)~X', for Vt~Tand x(t)~X r for Vt~T~, where X '={x , 10[=<0.05rad, [0]__<0.5 rads -1, l i , [ < l a , 14,1__<o.a5 rad, +<0}, X '={x, 101__<0.6 rad, ]0[<1 raOs -x, li,,l_-__5z, 1~1_-<0.15 14,1=<1 rads-~}, X ~ ={x, 101_-__0.08 tad, 101_---0.1 rads 1, Ii~I_<_IA, 14,1 <0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002691_1.1357163-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002691_1.1357163-Figure6-1.png",
        "caption": "Fig. 6 Moment and load distribution of the pitch circle in a ball bearing under a combined radial and axial load",
        "texts": [
            "a) and for the contact of a ball with the outer race is rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/07/20 In Eq. ~28.a! and Eq. ~28.b!, the parameter d i* and do* can be attained from Table 1 if the values of F(r) i and F(r)o are available. Then, the effective elastic modulus K for the bearing system is written as: K5~Ko 21.51Ki 21.5!21.5 (29) The normal load Q applied to the ball is given as: Q5Kd1.5 (30) The normal load components in the axial and radial directions, as shown in Fig. 6, are expressed as: ~1! axial direction Qa j5Q sin a j (31.a) JUNE 2001, Vol. 123 \u00d5 307 13 Terms of Use: http://asme.org/terms Downloaded F ~2! radial direction Qr j5Q cos a j (31.b) where a j is the contact angle of the jth ball in a bearing. Summation of the load components for a bearing with Z balls gives the total load ~see Fig. 6! in the axial direction as: Fa5( j51 Z Qa j (32.a) and for the total load in the radial direction as: Fr5( j51 Z Qr j cos c (32.b) A moment is induced in the y-direction because the force component Qa in the axial direction in not uniformly distributed around the bearing ~see Fig. 6!. The moment is M5( j51 Z Qa jS dm 2 cos c D (33) where dm5~do1di!/2 and eccentricity of axial load is e5 M Fa (34) 3.1 Confirmation of Validity of the Present Method. In this study, two tori for the inner and outer races were created for use in the calculations of the bearing. Parameters such as the bearing axial and radial loads, the contact angle of each ball, the total elastic deformation of a ball at two contact points, the moment created due to the nonsymmetrical axial forces, and the distance of the moment from the center line of the shaft are readily obtained if the deformations in the axial and radial direction, da and dr , are available"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure9-1.png",
        "caption": "Fig. 9. Face-gear and head-cutter in 3D space: avoidance of interference.",
        "texts": [
            " The gear tooth surface is generated as a copy of the tool surfaces and is represented in S2 by the matrix equation r2 ug; hg \u00bc M2grg ug; hg : \u00f07\u00de Here ug; hg are the surface coordinates of the head-cutter represented by vector function rg ug; hg . Matrix M2g describes the coordinate transformation from the tilted head-cutter to coordinate system S2. Elements of matrixM2g are determined by position vector 020g and direction cosines of coordinate axes of Sg (Fig. 8). The investigation of avoidance of interference may be accomplished analytically but it requires derivation of equations of tooth surfaces of many teeth and equations of their intersection with the head-cutter. The authors have used computer graphics as shown in Fig. 9. Avoidance of interference may require in some case the increase of the tilt of the head-cutter. Coordinate systems applied for derivation are shown in Fig. 10. Fixed coordinate systems Sn and Sm are rigidly connected to the frame of the generating machine. Movable coordinate systems Sd and S1 are rigidly connected to the cradle d of the generating machine and the worm, respectively. Schematics of worm generation are shown in Figs. 6 and 7. The worm is generated by a tilted head-cutter (Figs. 6 and 7)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002700_70.563652-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002700_70.563652-Figure2-1.png",
        "caption": "Fig. 2. A system of coupled links.",
        "texts": [
            " Finally, the conclusions are given in Section V. The n n generalized inertia matrix (GIM), I, associated with the dynamic equations of motion of an n-link n-DOF serial manipulator, as shown in Fig. 1, is derived in [7], which is given as I T T MT; where M diag(M1; ;Mn) (1) and T is the 6n n natural orthogonal complement (NOC) matrix [7], whereas the 6 6 matrix elements, Mi, for i = 1; ; n, of the 6n 6n generalized mass matrix, M of (1), are the extended mass of the ith link with respect to its mass center Ci, Fig. 2, i.e., Mi Ii O O mi1 (2) in which Ii and mi are the 3 3 inertia tensor about Ci and the mass of the ith link, respectively. Alternatively, the GIM, I, is derived in [8] as I T T d ~MTd; where ~M T T l MTl (3) and Td diag(p1; ;pn). Note from the comparison of (1) and (3), T = TlTd [8], which actually allows one to write the analytical expressions for the elements of the GIM, (8). Moreover, the symmetric 6n 6n matrix, ~M, is derived as ~M ~M1 BT 21 ~M2 BT n1 ~Mn ~M2B21 ~M2 BT n2 ~Mn ... ... . . . ... ~MnBn1 ~MnBn2 ~Mn (4) where the 6 6 matrices, Bij , along with the 6-D vectors, pi, for i; j = 1; ; n, are associated with the relation between the twist of the ith link, ti [ T i ; _c T i ] T \u2014 i and _ci being the 3-D vectors of angular velocity and linear velocity of the mass center of the ith link, Ci, respectively,\u2014and that of the jth link, tj , i.e., ti = Bijtj + pi _ i (5) where _ i is the joint rate of the ith revolute joint, as shown in Fig. 2, and the 6 6 matrix, Bij , and the 6-D vector, pi, are defined by Bij 1 O Cij 1 and pi ei ei di (6) 1 and O being the 3 3 identity and zero matrices, respectively, which, henceforth, should be understood as of being dimensions compatible with the size of the matrix in which they appear. Also, Cij is the 3 3 cross-product tensor associated with the vector, cij cj ci of Fig. 2, which is defined as, Cijx cij x, for any arbitrary 3-D vector, x, whereas the 3-D vectors, ei and di, are the unit vector parallel to the axis of the ith revolute joint and a position vector, respectively. For other type of joints, e.g., prismatic, vector pi should be derived accordingly. Furtheromre, the 6 6 matrices, ~Mi, for i = 1; ; n, as in (4), are the mass matrix of the ith composite body that consists of rigidly connected links, #i; ;#n, with respect to Ci. Matrix ~Mi can be obtained recursively as ~Mi Mi + ~Mi;i+1 where ~Mi;i+1 B T i+1;i ~Mi+1Bi+1;i (7) and ~Mn+1 O since no (n+ 1)st link exists, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.23-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.23-1.png",
        "caption": "Figure 8.23 Combined state of stress and its Mohr's circle.",
        "texts": [
            " In this case, the normal stress is also the yield strength of the material in tension, and therefore: 0' x O'yp Tmax = - =- 2 2 (8.18) The maximum stress theory states that if the same material is subjected to any combination of normal and shear stresses and the maximum shear stress is calculated, the yielding will start when the maximum shear stress is equal to Tmax. For example, consider that the material is subjected to a combination of nor mal and shear stresses in the xy plane as illustrated in Figure 8.23a. For this state of stress, the maximum shear stress Tmax can be determined by constructing a Mohr's circle (Figure 8.23b) or using Eq. (8.17). Yielding will occur if Tmax is equal to or greater than O'yp/2. The maximum distortion energy theory is a widely accepted crite rion that states the conditions for yielding of ductile materials. It is also known as the von Mises yield theory or the Mises-Hencky theory. This theory assumes that yielding can occur when the root mean square of the differences between the principal stresses is equal to the yield strength of the material established in a simple tension test. Let 0'1 and 0'2 be the principal stresses in a plane state of stress, and O'yp be the yield strength of the material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.30-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.30-1.png",
        "caption": "Figure 3.30 Problem 3.1.",
        "texts": [
            "30)(200) i =50k-60i - - The negative sign in front of 60 i indicates that the x component of the moment vector is acting in the negative x direction. Fur thermore, there is no component associated with the unit vector j, which implies that the y component of the moment vector is zero. Therefore, the moment about point A has the following components: Mx = 60N-m My = 0 Mz = 50N-m ( - x direction) (+z direction) These results are consistent with those obtained using the scalar method. 3.10 Exercise Problems Problem 3.1 Consider a person using an exercise apparatus who is holding a handle that is attached to a cable (Figure 3.30). The cable is wrapped around a pulley and attached to a weight pan. The weight in the weight pan stretches the cable and produces a tensile force F in the cable. This force is transmitted to the person's hand through the handle. The force makes an angle () with the horizontal and applied to the hand at B. Point A rep resents the center of gravity of the person's lower arm and 0 is a point along the center of rotation of the elbow joint. As sume that points 0, A, and B and force F all lie on a plane surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003265_s0022112088001077-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003265_s0022112088001077-Figure1-1.png",
        "caption": "FIGURE 1. Definition sketch.",
        "texts": [
            " In the above-mentioned hypotheses, both the flow fields defined on the domains gi = ( ( r , 8 ) : 0 < r < R, 0 < 0 < x ) and 9' EE ( ( r , 8): R < r < o 0 , O < 8 < x ) may be described by the set of linearized Navier-Stokes equations v * v = 0, ( 5 ) p y o = p V x V x o , (6a ) O = V X V associated with the following set of boundary conditions 400 0 < 8 < 7 t (i) continuity of normal and tangential velocity on the whole drop surface 17) (8) vi(R,8) = v; (R,8) = - yz (8 ) , vb(R, 8) = v w , O), where z ( 8 ) is the surface displacement with respect to the unperturbed, spherical shape ; (ii) Continuity of tangential stresses and balance of the normal momentum on the free portion of the drop surface 0 < 8 < 8, S:,(R, 8 ) = f$'O(R, 8), (9) Sf,(R,O)-S;,(R,8) = CT , (10) where (iii) no-slip condition drop surface 8, d 8 d x Moreover the following volume s,, = -p+2pvr, ,; and no radial deformation on the supported portion of the vs(R, 6) = 0, (11) z(e) = 0. (12) integral condition expresses the conservation of the drop z sinOd8 = 0. In the above equations p and p are the density and the coefficient of viscosity of the fluids, CT is the surface tension, R the unperturbed drop radius and 8, = 7t - ko where k0 is the support angle (see figure 1). Boundedness of velocity and pressure a t the origin and at infinity is also required. Equations (5)-(13) determine an eigenvalue problem which is reduced, in the following, to a simpler form in order to allow for the use of an efficient approximate numerical method of solution. 2.2 . The solution for inner and outer flow Jields Use is made here of the standard (Morse & Beshbach 1953) decomposition of a solenoidal vector w , w = V x ( B + V x C ) with B=Bn,, C=Cn,, (14) previously used by Miller & Scriven (1968) and Propseretti (1980) for the case of a free drop"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003134_56.808-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003134_56.808-Figure10-1.png",
        "caption": "Fig. 10. The support patterns of crab walk tripod gait on constant slope plane and flat terrain with stability matgin S.",
        "texts": [
            " Now it is easy to see that the center of gravity of the hexapod will shift a distance h tan 0, where 0 is the slope angle and h is the height between q( t ) and the sloped plane, away from the horizontal plane. As a result, the critical support patterns of the tripod gait for crab walking on the sloped plane will also shift a distance A(0) = h tan 0 compared to that on the perfectly flat terrain, as illustrated by Fig. 9. Furthermore, the forbidden areas for the triangular support pattern are redefined as shown on Fig. 10. Based on the above observations, the tripod gaits for straight-line walking over flat terrain can be generalized to cover the case of tripod gaits on constant slope terrain. Thus we have the following theorem: Theorem 5 Assume a hexapod is to walk on a constant slope plane with slope angle 0. The tripod gait for straight-line walking with stability margin S is as follows: 1 ) The foothold positions are as shown on Fig. 3(a). 2) The sequence of movement for body and legs is as given by Similarly, for crab walk on a slope plane, the forbidden areas for the triangular support pattern could be redefined as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003376_54852.378508-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003376_54852.378508-Figure1-1.png",
        "caption": "Figure 1. Point-plane constraint intersection.",
        "texts": [
            " (Unfortunately a head of such hair would be extremely expensive to compute). The edge and diagonal springs together control the Young's modulus of the strand, whilst the diagonal springs affect the shear and twisting moduli. The method of integration appropriate to compute the position of each point mass depends in part on how external constraints are implemented. Impulse-based collisions detect whether the motion of a point intersects a surface. If it does, the new position and velocity are computed analytically (see Figure 1). For a point mass travelling from Pj to Pj+i, the intersection position (xl, yD will be given by: yi = ys x~ = xj+t + (3,, - Yj*O ~ . ~ For an inelastic collision, the new position (xi+t ,Yj~t ) is given by: ' y j+t = Yi + rn (y l --yj+l) xf+l = Xi + r t (x l - -Xj+I) where r, is the coefficient of normal reflection, and r, is the coefficient of tangent reflection. The advantage of such a scheme is that the collision detection calculation is simple to compute. It is equivalent to intersecting a ray with a surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003634_ip-d:19820005-Figure7-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003634_ip-d:19820005-Figure7-1.png",
        "caption": "Fig. 7 Example 3: nonlinearity (also example 4)",
        "texts": [
            "2 fl\"1 k = 1 The convergence point of their regulator corresponds to the choice A = 1 - 1 . 6 ? - 1 B = 1.6 They used the model P = \\~pq-1 with p = 0 giving a unity feedback control. Fig. 6 gives the corresponding Nyquist diagrams for p = 0, 0.5 and 0.9. The locus for p = 0 passes through - 1, and thus the corresponding closed-loop system is unstable. Withp = 0.5 and p = 0.9, the locus does not encircle \u2014 1, and thus the corresponding closed-loop systems are stable. Example 3 Consider a symmetrical memoryless nonlinearity defined by the relation of Fig. 7. The gain, in the input/output sense, of the operator (TV\"1 \u2014 1) is thus \\/m \u2014 1. For this nonlinearity, incremental gain is identical to gain. Let the linear system be defined by A = l-aq'1 \\>a>0 B = 1.0 C = 1.0 k = 1 and choose P = 1 \u2014pq~l such that 0<p<a (i.e. the desired closed-loop system is faster than the open-loop system). If TV is at the output of the linear system, then from theorem 2 we require, with the model-reference design method (Q = 0), that sup | 1 \u2014 aq~ - l \\-pq which implies that 1 \u2022(1/m-l) 2 + a + p ,1+a a-p If the nonlinearity TV is at the input, theorem 4 gives an identical condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.65-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.65-1.png",
        "caption": "Figure 8.65 Analyses of the element in Figure B.63c.",
        "texts": [
            " y Lx - ~ A ~a\" -- Tyx - __ Tyx 188 Fundamentals of Biomechanics Once the radius of the Mohr's circle is established, principal stresses and maximum shear stress can be determined as 0\"1 = r O\"x/2 (tensile), 0\"2 =r + O\"x/2 (compressive),and rmax =r. To deter mine the angle of rotation, (h, of the plane for which the stresses are maximum and minimum, we need to read the angle between lines CA and CD (in this case, it is 21h counterclockwise), divide it by two, and rotate the stress element in Figure 8.63b in the clockwise direction through an angle {h. This is illustrated in Figure 8.64b. Analyses of the material element in Figure 8.63c are illustrated graphically in Figure 8.65 . Example 8.8 Figure 8.66 illustrates a bench test that may be used to subject bones to bending. In the case shown, the distal end of a human femur is firmly clamped to the bench and a horizontal force with magnitude F = 500 N is applied to the head of the femur at point P. Determine the maximum normal and shear stresses generated at section aa of the femur that is located at a vertical distance h = 16 cm measured from point P. Assume that the geometry of the femur at section aa is circular with inner radius ri = 6 mm and outer radius r 0 = 13 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003329_j.mechmachtheory.2007.06.011-Figure5-1.png",
        "caption": "Fig. 5. Coordinate systems of the plane conjugate tooth.",
        "texts": [
            " If the clearance could not maintain a tiny size during operation, it may lead to larger leakage and reduce the pump performance. Besides, Fig. 2 indicates the patent design is unable to conjugate at all. Thus, we use the theory of gearing to design the rotor profile for reducing the design problem (shown in Fig. 2). Here, we analyze and improve the aspect of the patent design [11\u201313]. After improving the rotor profile, we compare pump performance in terms of carryover, area efficiency and length of line of action. The coordinate systems of the plane conjugate tooth are created as shown in Fig. 5, where point g is an important location (related to parameters R and a) for the claw-shape, R is the distance from point g to Of, and a is the angle measured from the xf axial to point g. Point g can be represented in the coordinate system S1 as r \u00f0g\u00de 1 \u00bc R cos a R sin a 1 2 64 3 75 \u00f01\u00de As shown in Fig. 5, two rotors rotate with a constant gear ratio in opposite directions about parallel axes so that point g can generate a locus. The locus of the tooth profile r \u00f01\u00de 2 in coordinate system S2 is then obtained by coordinate transformation: r \u00f01\u00de 2 \u00bcM21r \u00f0g\u00de 1 \u00bcM2f Mf 1r \u00f0g\u00de 1 \u00f02\u00de where the superscript of r \u00f01\u00de 2 indicates the segment 1 of the claw-shape in Fig. 3 and M2f \u00bc cos / sin / 2r cos / sin / cos / 2r sin / 0 0 1 2 64 3 75 Mf 1 \u00bc cos / sin / 0 sin / cos / 0 0 0 1 2 64 3 75 In order to derive the conjugate profile of segment 1, we can copy the same profile as r \u00f01\u00de 2 on the rotor 1 and use u instead of /, which is written as: r \u00f01\u00de 2 \u00bc r \u00f01\u00de 2x r \u00f01\u00de 2y 1 2 64 3 75 \u00bc R cos\u00f0a 2u\u00de 2r cos u R sin\u00f0a 2u\u00de \u00fe 2r sin u 1 2 64 3 75 \u00f03\u00de In order to avoid the tooth interference during the meshing of claw-shape, we should find out the angle a and u first"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure3.13-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure3.13-1.png",
        "caption": "Figure 3.13. Approximation: a. Preliminary estimate \u02c6 mwp by inversion of mapping. b. Better estimate ,e ap by scaling down support vector change \u02c6 m mw w",
        "texts": [
            " The approximation step updates the output support vector of the node mw n that has the highest influence on the pair of system input ap and measured system output mg . The self-organization in output space then locally arranges the output support vectors of the nodes around mw n according to the topology and thus ensures that the inverse of the mapping is continuous as well. The self-organization in input space, if activated at all, arranges the input support vectors of the nodes according to the topology. The idea behind SOLIM approximation (Figure 3.13a) is to change an output support vector mw p in the mapping m mp m g , such that a mp p , i.e., the SOLIM map passes through the point a mp g of the system behavior. There are several output support vectors that have an influence on mp but since only one point of the system behavior is given, the output support vector mw p with the highest influence is used for updating. First, the synthesis equation for mp is rearranged to identify the influences of different output support vectors on the output: a mp p , (3",
            "31 for mw p yields an expression for a preliminary estimate \u02c6 mwp of mw p , and calculating the difference between the estimate \u02c6 mwp and the old value of mw p , yields a relatively simple expression: 1\u02c6 m m m m a m w w w wf p p p p (3.32) The substitution mw is given by the simpler notation m m m w i w . The interpolation and extrapolation influences of the winning node mw n follow the same rule with m m m w i wf f and m m m w i w x x , respectively. If mw p were to be updated to \u02c6 mwp , mg would be mapped to ap . But, assuming that the gradient of the SOLIM map is similar to the gradient of the system behav- 78 Helge H\u00fclsen ior (Figure 3.13b), scaling down the change \u02c6 m mw w pp of mw p by mwf yields a better estimate ,e ap for mw p . The interpolation weight mwf is chosen to scale down because it describes the ratio of , m e a w p p to \u02c6 :m mw w pp , \u02c6mm m m e a ww w wfp p p p , (3.33) , 1 .m m e a a m w w p p p p (3.34) Finally, mw p is moved towards ,e ap with a constant approximation learning rate p a : ( ) ( ) , ( ) , m m m new old e a old p a w w w p p p p . (3.35) During SOLIM self-organization, all neighbor pairs r cn n R of the winning node mw n , whose topology vectors are in-line with respect to mw c in topology space, are changed in the output space to be in-line with mw p "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002540_proc-758-ll1.9-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002540_proc-758-ll1.9-Figure3-1.png",
        "caption": "Figure 3. Schematic of the rippling phenomenon encountered in the SOM mechanism.",
        "texts": [
            " The thermo-physical model presented in this paper describes the amplitude behavior of the observed surface micro-relief and estimates the resulting surface roughness Ra. It is assumed that the surface relief formed acquires the shape of a sinusoid of fixed propagation vector, k and spatial phase \u03c6. Ra values were measured from laser polished tracks that showed an increment in roughness with reducing scan speed above the as-received value, as well as the characteristic surface wavelength of each track \u03bb. These measurements provided data to validate the model. Figure 3 illustrates a schematic diagram of the different variables that are involved in the formation of a surface relief \u2206h whenever a laser beam traverses the surface of the material causing a depth of melt h. Anthony and Cline [8] modeled analytically this surface-rippling phenomenon observed during laser surface melting of metals. The steady-state form of the Navier-Stokes equation (i.e., Newton\u2019s Second law) for an incompressible fluid in two dimensions (x, z) over a horizontal surface was solved analytically together with the continuity equation, Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure3-1.png",
        "caption": "Fig. 3. Generation of face worm gear.",
        "texts": [
            " The contents of the paper cover: (i) generation and analytical determination of tooth surfaces of the face-gear and the worm; (ii) simulation of meshing and contact; (iii) stress analysis. The developed theory is illustrated with numerical examples. The determination of conjugation of tooth surfaces of proposed gear drive required the application of theory of enveloping that is the subject of differential geometry and theory of gearing represented in the works by Zalgaller [17], Zalgaller and Litvin [18], Favard [2], Korn and Korn [6], Litvin [8,9], and other works. The generation is performed by a tilted head-cutter with straight line profiles of blades (Fig. 3). The tilt of the head-cutter allows to avoid interference of the head-cutter with teeth that neighbor to the space being generated. Fig. 4 illustrates schematically the generation of the face-gear. The tool is mounted at the cradle c of the generating machine (Fig. 4) and performs rotation about the tool axis. The face-gear R2 and the cradle c are held at rest and the tooth surface of the face-gear is generated as the copy of the tool surface. Indexing of face-gear has to be provided for generation of each space of the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003830_1.3309728-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003830_1.3309728-Figure1-1.png",
        "caption": "Figure 1. Color online Description of the compression cell with the anode and cathode reactions, ion conduction, and catalyst layers.",
        "texts": [
            " Alkaline cells were tested in a compression cell configuration where the membrane electrode assembly MEA was simply pressed together under a mechanical force, holding the test fixture together. Acidic conditions were tested with hot-pressed MEAs where the ionomer was postcoated onto each electrode, and then the assembly was hot-pressed onto each side of a membrane. address. Redistribution subject to ECS terms129.108.9.184aded on 2014-08-14 to IP Compression Cell Compression cells were made by painting platinum\u2013ruthenium on a carbon catalyst onto nickel foam for the anode and by painting laccase on carbon support onto a GDL BASF LT2500W , as shown in Fig. 1. The electrodes were then placed into the mechanically compressed test fixture and tested with a water\u2013methanol\u2013potassium hydroxide mix for fuel, with the cathode using ambient air at ambient temperature 23\u00b0C . The compression cell consisted of a reservoir that contains 8 mL of static fuel/electrolyte solution. The two electrodes were separated by a polysulfone membrane doped with zirconium IV oxide and soaked in 50% potassium hydroxide anion exchange membrane AEM , which was prepared as needed in the laboratory by the following procedure that was a modification of the procedure described in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003698_1.40060-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003698_1.40060-Figure1-1.png",
        "caption": "Fig. 1 Axisymmetric rigid body with two controls.",
        "texts": [
            ", domain of validity) on which the synthesized nonlinearH1 control is valid. D ow nl oa de d by U N IV E R SI T Y O F IL L IN O IS o n Ja nu ar y 29 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .4 00 60 A. Modeling of Axisymmetric Spacecraft In this section, we will present an axisymmetric rigid body spacecraft model [18] with two control torques acting perpendicular to each other and its symmetry axis. To describe spacecraft dynamics, two reference frames will be introduced (see Fig. 1 and [18,28]). The first one is the body-fixed reference frame b b\u03021; b\u03022; b\u03023 , which is located at the center of mass and aligned along the principal axes of axisymmetric spacecraft. In the body-fixed reference frame, denote the angular velocity vector andmoment of inertia with respect to three body axes as !1, !2, !3 and I1, I2, I3. We assume that b\u03023 is pointing along the symmetry axis and I1 I2. Furthermore, two control torques T1 and T2 are generated along b\u03021 and b\u03022 axes and span a two-dimensional plane orthogonal to the axis of symmetry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003265_s0022112088001077-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003265_s0022112088001077-Figure8-1.png",
        "caption": "FIGURE 8. Qualitative plot of the dependence on E of the eigenvalues h = b + io. The plot the way the bifurcation points A, B, C... in (a ) evolve and disappear with increasing w * 0; ---, o = 0).",
        "texts": [
            " It is however possible to gain a better insight into the origin and the successive disappearance of the wiggles as $, is increased, through a comparison between the cases $o = 0 and $, = (figure 7). For $, = 0 and, say, the second eigenvalue the complex solution bifurcates a t point A into two purely real branches. The intersection of these branches with the decreasing purely real branches corresponding to higher modes gives rise to other bifurcation points like B, C, D in figure 7. , indicates 11'0 (-> The corresponding plot for $,, = lop6, even if very close to the one for $, = 0, appears to be quite different and more complicated. The three-dimensional plot of figure 8 qualitatively illustrates the way by which the transition occurs between $o = 0 (figure 8 a ) and $,, = (figure 8 d ) . As soon as k0 > 0, the bifurcation point B disappears in the simple way shown in figure 8 ( b ) , while the point C splits up into two bifurcation points C' and C\", which are connected by a complex branch. Further increases in 9, cause the pointsA and C' first to coalesce (figure 8 c ) and then to disappear (figure 8 d ) , giving rise to a 'wiggle'. As is increased further, the wiggle becomes gradually smoother and finally vanishes. Oscillations of a supported drop in an immiscible Jluid 41 1 In the same way we may observe the coalescence and then disappearance of points C\"-D', D\"-E' and so on for all the other bifurcation points. The wiggles are thus seen to be intimately connected with the fact that all bifurcation points in the plot for $o = 0 must disappear when $o is increased and indicate a singular behaviour of the eigenvalue problem as the perturbation (a+ 1) tends to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure2-1.png",
        "caption": "Fig. 2. Face worm gear drive with a cylindrical worm.",
        "texts": [],
        "surrounding_texts": [
            "The generation of face worm gear drives of all types of existing design is based on application of a hob for generation of the face-gear. The hob is similar to the worm of the drive. The disadvantage of such method of generation is the low precision of a hob used as a generating tool especially in the case of small dimensions of hob.\nThe new geometry proposed in this article is based on application of head-cutters or head grinding tools that have higher precision and larger dimensions in comparison with a hob and enable to provide a higher productivity of the process of generation. The gear drives of new geometry may be generated similar to the generation of spiral bevel gears and hypoid gears [7,15].\nThe proposed new face worm gear drives (with conical and cylindrical worms) are provided with a localized bearing contact and predesigned parabolic function of transmission errors of low level. Such a function is able to absorb discontinuous linear functions of transmission errors caused by errors of alignment [8,9]. Therefore vibrations and noise of gear drives might be reduced.\nThe localization of bearing contact is achieved by the mismatch of surfaces of generating head tools applied for generation of the face worm gear and the worm. Figs. 1 and 2 show in 3D space face worm gear drives with conical and cylindrical worms that have been investigated in this paper. The proposed new design of a face-gear drive is based on adaptation of the design parameters of a similar gear drive of existing design (based on generation of face-gear by a hob). This allows to build a bridge between both designs but affects as shown in Section 2 the dimensions of applied head cutters.\nThe contents of the paper cover:\n(i) generation and analytical determination of tooth surfaces of the face-gear and the worm; (ii) simulation of meshing and contact; (iii) stress analysis.\nThe developed theory is illustrated with numerical examples. The determination of conjugation of tooth surfaces of proposed gear drive required the application of theory of enveloping that is the subject of differential geometry and theory of gearing represented in the works by Zalgaller [17], Zalgaller and Litvin [18], Favard [2], Korn and Korn [6], Litvin [8,9], and other works.",
            "The generation is performed by a tilted head-cutter with straight line profiles of blades (Fig. 3). The tilt of the head-cutter allows to avoid interference of the head-cutter with teeth that neighbor to the space being generated.\nFig. 4 illustrates schematically the generation of the face-gear. The tool is mounted at the cradle c of the generating machine (Fig. 4) and performs rotation about the tool axis. The face-gear R2 and the cradle c are held at rest and the tooth surface of the face-gear is generated as the copy of the tool surface. Indexing of face-gear has to be provided for generation of each space of the gear.\nBlades of the gear head-cutter are shown in Fig. 5(a). The angles ag of blade profile are of different magnitude for the convex and concave sides of the space of the face worm gear. Circular arc profiles of the blade fillet are provided for the generation of the fillet of the gear.\nThe generation of the worm is performed by a tilted head-cutter mounted on the cradle d of the generating machine (Fig. 6). The worm and the cradle d perform related rotations determined as\nx\u00f0w\u00de\nx\u00f0d\u00de \u00bc N2\nN1\n\u00f01\u00de\nwhere N2 and N1 are the number of teeth and threads of the face-gear and the worm. The rotation of the head-cutter is provided for obtaining the desired velocity of cutting (grinding) and is not related with the meshing of cradle d and the worm.\nFig. 7 illustrates the installment of the worm with respect to the cradle d. The process of generation of the worm simulates its meshing with the face-gear. The face-gear is represented in Fig. 7 as cradle d that carries the head-cutter. The worm head-cutter and cradle d may be considered as rigidly connected each to other in the process of meshing of cradle d with the worm. The surface of the head-cutter simulates the tooth surface of the face worm gear.\nThe process of worm generation provides for the gear drive: (i) localization of bearing contact, and (ii) a parabolic function of transmission error. Localization of contact is achieved by deviation of profiles of blades of worm head-cutter with respect to the blades of gear head-cutter (see Section 3). Parabolic function of transmission errors is provided by variation of distance Em\u00f0w1\u00de (Fig. 7) during the worm generation where w1 is the angle of worm rotation performed during the process of worm generation."
        ]
    },
    {
        "image_filename": "designv10_8_0003594_j.snb.2009.11.068-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003594_j.snb.2009.11.068-Figure2-1.png",
        "caption": "Fig. 2. The schematic diagram for the procedure of in-channel modification of biosensor electrodes. (a) The gold-electrode bases (light grey colored) to be modified to enzyme working electrode (W), Ag/AgCl reference electrode (R), and platinum counter electrode (C). (b) Modification of the gold base W with MPA self-assembled monolayer. During the modification, electrode bases R and C were partially contaminated by the MPA solution. The hatched areas represent the MPA SAM formed on gold base surfaces. (c) Electrochemical desorption of the MPA SAM from gold bases R and C. (d) Modification of gold base R to Ag/AgCl reference electrode by silver and chloride electroplating. A NaAgSO3 or KCl plating solution was added into the detection cell as the electroplating bath. A phosphate buffer solution was pumped to flush the microchannel during the plating process to protect the MPA-modified working electrode from being contaminated by the plating species. The medium grey area represents the Ag/AgCl film deposited on gold base R. (e) Modification of gold base C to platinum counter electrode by platinum electroplating. The dark grey area represents the platinum film deposited o e afte t a min c",
        "texts": [
            " irstly, the gold base for working electrode (abbreviated as gold orking electrode) was modified with a layer of MPA self- et with integrated three-electrode system; 9. assembled microchip integrated with PTFE tubing; 12. carrier solution vial; 13. sample solution vials; 14. electrochemical assembled monolayer (SAM) that was later used to immobilize glucose oxidase. Thus, a stream of 5 mmol L\u22121 MPA solution in ethanol was driven by a syringe pump to pass the gold working electrode from the sampling probe through the microchannel at the flow rate of 6 L min\u22121 for 12 h (referred to Fig. 2b). The spent MPA solution out of the channel was entered into the detection cell where it was periodically removed by filter-paper wicks. Therefore, the second and third gold-electrode bases located in the cell might be contaminated by the MPA solution. The MPA-modified working electrode was sequentially flushed with absolute ethanol and DDW, each for 20 min. Before silver electroplating of the second gold base (for reference electrode) and platinum electroplating of the third gold base (for counter electrode), both gold bases were electrochemically cleaned in a 0.1 mol L\u22121 phosphate solution by application of \u22121.1 V (vs. a separate, miniaturized Ag/AgCl reference electrode, saturated KCl) for 10 min to remove the non-purposively formed MPA SAM layer (Fig. 2c). After the detection cell was rinsed with DDW, a stream of 0.1 mol L\u22121 phosphate buffer solution at a flow rate of 1 L min\u22121 was driven to flush the microchannel in the direction from the sampling probe to the detection cell, meanwhile a 0.2 mL of silver plating solution was added into the detection cell. Then, silver electroplating of the second gold base was performed 556 Y. Wang et al. / Sensors and Actuators B 145 (2010) 553\u2013560 b s r 1 0 r s t w i b b t o n p c t 2 ( a 2 i b r G t r n gold base C",
            " (f) Immobilization of GOx onto the MPA-modified working electrod he GOx-modified electrode. A: the off-chip micro Ag/AgCl reference electrode with ounter electrode. y scanning from \u22120.4 to \u22120.2 V and finally back to \u22120.4 V (vs. a eparate, miniaturized Ag/AgCl reference electrode with a satuated KCl bridge) at the rate of 5 mV s\u22121, followed by scanning in mol L\u22121 KCl solution containing 1 mmol L\u22121 K3Fe(CN)6 between and 0.5 V for 2 cycles and finally back to 0 V at the scanning ate of 50 mV s\u22121 (Fig. 2d). During the electroplating process, the tream of 0.1 mol L\u22121 phosphate buffer solution was kept running hrough the channel so as to prevent the in-channel MPA-modified orking electrode from being contaminated by the electroplatng solution. To electrically deposit platinum onto the third gold ase, the detection cell was filled with 0.2 mL platinum plating ath, and the electrode was electroplated by scanning from \u22120.5 o 0.5 V for 20 cycles and finally back to \u22120.5 V at the scanning rate f 50 mV s\u22121 (Fig. 2e). During the platinum electroplating, the chanel was also flushed with the buffer solution the same as for silver lating. After the silver and platinum electroplating, the detection ell and microchannel were flushed with DDW. To immobilize GOx onto the MPA-modified working electrode, he MPA assembled on the working electrode was activated with mmol L\u22121 EDC and 5 mmol L\u22121 NHS in 0.1 mol L\u22121 MES solution pH 5.0) that was filled inside the channel. After 30 min for the ctivation reaction, a 0.1 mol L\u22121 MES buffer (pH 5.0) containing mg mL\u22121 GOx, 2 mmol L\u22121 EDC and 5 mmol L\u22121 NHS was filled nto the channel, making the GOx coupled with the activated caroxyl groups of the MPA assembled on the electrode. The coupling eaction was conducted for 4 h at 4 \u25e6C with periodically renewed Ox solution inside the channel (Fig. 2f). Finally, the enzyme elecrode, and the channel network including the detection cell were insed with 25 mmol L\u22121 phosphate buffer (pH 7.0) and ready to r activating the carboxyl group of MPA by EDC and NHS. The black area represents iaturized salt bridge filled with saturated KCl solution; B: the off-chip micro Pt wire be used. When not in use, the enzyme electrode was stored at 4 \u25e6C with the channel being filled with 25 mmol L\u22121 phosphate buffer. 2.4. Micro flow-injection system The -FI-AD system, as illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003612_00124278-200708000-00023-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003612_00124278-200708000-00023-Figure2-1.png",
        "caption": "FIGURE 2. Experimental schematic of the measurement of the maximal voluntary contraction.",
        "texts": [
            " In the control (no stretching) condition, subjects maintained both legs at rest for 2 minutes on the chair. All subjects performed the control, and 30 and 60 seconds of the stretching conditions with balanced order to rule out an order effect. Maximal Voluntary Contraction The MVC test was conducted immediately after the second assessment of hamstring flexibility. This test was performed using the subject\u2019s dominant leg, and all subjects used the right leg. The experimental schematic of the measurement of the isometric strength of knee flexion is depicted in Figure 2. Subjects were restrained on the chair using nylon bands. The knee of the dominant leg was connected to a load cell (RTB-100; Syowasokki, Japan) with a leg band and steel wire through a fixed pulley to change the wire direction. Subjects crossed their arms in front of their chest and the knee angle of the dominant leg was set at 90 . When the investigators signaled to start, subjects flexed the dominant leg with maximal effort for 4 seconds, followed by a 4-second rest interval. They repeated this maximal effort 3 times"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003634_ip-d:19820005-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003634_ip-d:19820005-Figure6-1.png",
        "caption": "Fig. 6 Nyquist plots for example 2: p = 0,0.5,0.9",
        "texts": [
            "9 Example 2 {Goodwin andRamadge [9]) Goodwin and Ramadge [9] analysed a reduced-order minimum-variance-type regulator operating on a particular system and showed it to be unstable. This example considers the same system but includes a (nonunit) reference model which gives stability. The system they considered is described by Ao = 1 - 0.Sq Bo = 1.6 +0.2 fl\"1 k = 1 The convergence point of their regulator corresponds to the choice A = 1 - 1 . 6 ? - 1 B = 1.6 They used the model P = \\~pq-1 with p = 0 giving a unity feedback control. Fig. 6 gives the corresponding Nyquist diagrams for p = 0, 0.5 and 0.9. The locus for p = 0 passes through - 1, and thus the corresponding closed-loop system is unstable. Withp = 0.5 and p = 0.9, the locus does not encircle \u2014 1, and thus the corresponding closed-loop systems are stable. Example 3 Consider a symmetrical memoryless nonlinearity defined by the relation of Fig. 7. The gain, in the input/output sense, of the operator (TV\"1 \u2014 1) is thus \\/m \u2014 1. For this nonlinearity, incremental gain is identical to gain"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002929_bf01257946-Figure5-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002929_bf01257946-Figure5-1.png",
        "caption": "Fig. 5. Singularity, Case 2.",
        "texts": [
            "OXT2 OZT2 x/3 LOXr2 o~r2 x/3a [ OLI OL2 OL10L2 ] I OL3 2 LO-2~rl OZrl OZT10XT1 j LOX\u2022 2 sinfl + OL3 q cos fl| (48) J The first term in (48) is always nonzero which can be shown by OL l OL 2 OL 1 OL 2 _ 1 x/3b O)(T10ZT1 OZT10XT1 LIL2 ~ - ZT1 \u2022 0. Thus, the Jacobian is singular if the last term in (48) is equal to zero. Before examining that term, we need to first express sin fl and cos fl in terms of the coordinates of the vertices of the upper platform. From the definition of the rotation angles, it can be seen that in this configuration (c~ = 3' = 0\u00b0)fl is nothing but the angle between the upper platform and the base. Since the side T 1 T3 is parallel to the Y-axis, referring to the side-view of this configuration shown in Figure 5, sin/3 and cos/3 are easily expressed as sin/3 = 2(ZT2 - - Zri) cos/3 - - 2 ( X r l - - X T 2 ) ( 4 9 ) x/3a ' x/3a Substituting OL3/OXT2 , OL3/OZT2 and (49) into the second term of (48) yields OL3 OL3 cos/3] O~-~r2 sin~ + ~ XT2 %- d/V~L3 %- b/2v~ (ZTI _ ZT2) _ _ ~ (XT1 XT2) {I 1 j [ , J ) 1 XT1+ (2d+b) Z T 2 - XT2+ (2d+b) ZT1 \u2022 Evidently, if (50) 1 XT1 + ~ (b + 2d) Zrl = ~v~l ' (51) ZT2 XT2 %- ~ (b + 2d) then (50) is zero and consequently det {A} = det {J(Xp_o)} = 0. Now let's focus our attention on condition (51). Suppose XTI(Xr3) and ZTI(ZT3) are fixed. If the lengths of L3 and L4 are varied (recall that any time L3 = L4 in this configuration), then the upper platform is going to rotate about T 1T 3 as shown in Figure 5. Note that at any time the distance from Xrl to side B3B 4 is (XT~ + (b +2d ) /2v~) and from XT2 to B3B 4 is (XT2 %-(b%-Zd)/Zv/3). When, and only when, the upper platform is rotated to a certain position where the middle point of T 1T3, the middle point of B3B4, and the vertix T2 are on one line, then condition (51) holds, which gives the Fact 2. If the side T 1 T 3 of the upper platform is parallel with the Y-axis and the plane formed by L3, B3B4, L4 is coplanar with the upper platform, then this configuration corresponds to a singularity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002556_j.bios.2003.11.010-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002556_j.bios.2003.11.010-Figure2-1.png",
        "caption": "Fig. 2. Production of steps for screen-printed electrode.",
        "texts": [
            " Twenty milliters of the prepared HP 5020-chitopeal, 4% sodium alginate, 4 and 5% -carrageenan and free cells were placed in 500 ml shaking flasks containing 100/200 ml of the pyocyanin production medium and stirred on a rotary shaker for 10 days at a constant temperature of 27 \u25e6C. Thin layer chromatography was performed on a silica gel F254 plate with methanol\u2013chloroform (1:1) as solvent. UV-Vis absorption spectra were measured using a Shimadzu UV-2400PC recording spectrophotometer. The electrode was composed of Ag lead, carbon working and counter electrodes and an Ag/AgCl reference electrode on the polyethylene telephtarate film prepared using the screen-printed technique (Fig. 2). The conditions of construction of electrode were as follows: Ag lead used Ag ink (Asahi Chemical Research Laboratory Co., Ltd.) and dried at 150 \u25e6C for 30 min. Carbon working and counter electrodes used carbon ink (Asahi Chemical Research Laboratory Co., Ltd.) and dried at 150 \u25e6C for 20 min. Ag/AgCl reference electrode used Ag/AgCl ink (Acheson (Japan) Limited) and dried at 120 \u25e6C for 15 min. Insulation resist used Insulation resist ink (Asahi Chemical Research Laboratory Co., Ltd.) and dried at 130 \u25e6C for 10 min"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure10-1.png",
        "caption": "Fig. 10 2-\u201eRRR\u2026NRa-\u201eRR\u2026B\u201eRRR\u2026A PPR-equivalent parallel kinematic chain",
        "texts": [
            " By assembling these legs, we obtain PPR-equivalent parallel kinematic chains of family 3. For example, a set of two RRR NRa legs with a 1- 0-1 - -system and one RA RRR BRA leg with a 1- -system can be 1118 / Vol. 127, NOVEMBER 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 used to construct a 2- RRR NRa-RA RRR BRA PPR-equivalent parallel kinematic chain Fig. 9 b . A set of two RRR NRa legs with 1- 0-1- -system and one RR B RRR A legs with a 1- -system can be used to construct a 2- RRR NRa - RR B RRR A PPR-equivalent parallel kinematic chain Fig. 10 . It is learned from Table 2 that among the combinations of sets of leg-wrench systems, there is only one combination, the combination of three 1- 0-2- , in which all the leg-wrench system are of the same type. From Table 1, there is one type of leg, PP NRa, with a 1- 0-2- wrench system. Thus there is only one 3-legged PPR-equivalent parallel kinematic chain, 3- PP NRa Fig. 11 , with identical type of legs. For an m-legged PPR-equivalent parallel kinematic chain, if the total of the orders, i=1 m ci, of all of its leg-wrench systems is greater than 3, it is an overconstrained hyperstatic kinematic chain",
            " Here, the actuation wrench j i of joint j in leg i is any one wrench which is not reciprocal to the twist of joint j and reciprocal to all the twists of the other joints within leg i. Considering that the order of a screw system is coordinate system free, the Z-axis is placed along the virtual axis of a PPRequivalent PM for simplicity reason. The validity condition of actuated joints can be expressed as 01 2 3 1 1 1 2 1 3 0 4 For example, the possible 3-legged PPR-equivalent PM corresponding to the 2- RRR NRa- RR B RRR A PPR-equivalent parallel kinematic chain Fig. 10 is the 2- R RR NRa- R R B RRR A PPR-equivalent PM Fig. 12 a . The actuation wrenches of all the actuated joints are shown in Figs. 13 b and 13 c . In the R R B RRR A leg Fig. 13 b , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axis of the unactuated R joint within RR B and is parallel to the axes of the R joints within RRR A. In the R RR NRa leg Fig. 13 c , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not rom: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003728_j.cnsns.2009.01.001-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003728_j.cnsns.2009.01.001-Figure3-1.png",
        "caption": "Fig. 3. Position of the centre of mass of the piston i.",
        "texts": [
            " (55) is pre-multiplied by JT Di the kinetic component of the generalized force applied to {P} due to each cylinder rotation is obtained in frame {B}: PfCi\u00f0kin\u00de\u00f0rot\u00de jB \u00bc JT Di Ci fCi\u00f0kin\u00de\u00f0rot\u00de jB \u00bc JT Di d dt \u00f0ICi\u00f0rot\u00de jB JDi T\u00de B _xP jBjE \u00fe JT Di ICi\u00f0rot\u00de jB JDi T B\u20acxP jBjE \u00f056\u00de The inertia matrix and the Coriolis and centripetal terms matrix of the rotating cylinder may be written as: JT Di ICi\u00f0rot\u00de jB JDi T \u00f057\u00de JT Di d dt ICi\u00f0rot\u00de jB JDi T \u00f058\u00de These matrices represent the inertia matrix and the Coriolis and centripetal terms matrix of a virtual moving platform that is equivalent to each rotating cylinder. If the centre of mass of each piston is located at a constant distance, bS, from the piston to moving platform connecting point, Pi, (Fig. 3), then its position relative to frame {B} is: BpSi jB \u00bc bS l\u0302i \u00fe Bpi jB \u00fe BxP\u00f0pos\u00de jB \u00f059\u00de The linear velocity of the piston centre of mass, B _pSi jB , relative to {B} and expressed in the same frame, may be computed as: B _pSi jB \u00bc _li \u00fe Bxli jB \u00f0 bS l\u0302i\u00de \u00f060\u00de B _pSi jB \u00bc JGi BvP jB BxP jB \" # \u00f061\u00de where the jacobian JGi is given by: JGi \u00bc I bS ~\u0302lT i ~ li \u00f0I bS ~\u0302lT i ~ li\u00de P ~pT i jB h i \u00f062\u00de The linear momentum of each piston, Q Si jB , can be represented in frame {B} as: Q Si jB \u00bc mS B _pSi jB \u00f063\u00de where mS is the piston mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003466_027836498300200302-Figure6-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003466_027836498300200302-Figure6-1.png",
        "caption": "Fig. 6. Approach length L versus approach angle A in the indicated planes for the Cincinnati-Milacron T3 3",
        "texts": [
            " The maximum approach length L from the hand point P to Q can be given by where Ro,i is either Ra or Ri, depending on which sphere is intersected. R is the radial distance from the origin to Q, and h is the hand length. Only positive values of L are true in (Eq. 6), and these lengths must also lie entirely in the region bounded by the R, and Ro spheres. Figure 3A shows the approach lengths to a point at different angles. The approach lengths of general robots can be . investigated by using the numerical technique described in Section 4 to move the hand out from a given point at a specified orientation until a limit is reached. Figure 6 shows a typical summary of approach lengths versus approach angles in two planes. 4. Arm Movement The problem of determining the joint angles or variables for a given manipulator to produce some required hand position or motion is the first step in manipulator motion control (Pieper and Roth 1969). The simple structure of current industrial manipulators allows us to derive the explicit equations for determining joint parameters (Pieper and Roth 1969; Duffy 1980; Paul 1981 ). Development of an explicit (in a joint variable) equation for a general manipulator is difficult and it leads to the problem of finding the roots of a very-high-order polynominal (Duffy and Crane 1980)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.51-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.51-1.png",
        "caption": "Figure 4.51 Problem 4.3.",
        "texts": [
            " The distance between A and B is e = 4 m and the distance between A and D is d = 3 m. A force that makes an angle f3 = 60\u00b0 with the horizontal is applied at B. The magnitude of the applied force is P = 1000 N. The total weight of the beam is W=400N. By noting that three-quarters of the beam is on the left of the roller support and one-quarter is on the right, calculate the x and y components of reaction forces on the beam at A and D. Answers: RD = 1421 N (t) RAx =500 N (~) RAy = 155 N (,I.) Pro b lem 4.3 The uniform, horizontal beam shown in Figure 4.51 is hinged to the wall at A and supported by a cable attached to the beam ate. C also represents the center of gravity of the beam. At the other end, the cable is attached to the wall so that it makes an angle () = 68\u00b0 with the horizontaL If the length of the beam is e = 4 m and the weight of the beam is W = 400 N, calculate the tension T in the cable and components of the reaction force on the beam at A. Answers: T = 431 N RAx = 162 N (-+) RAy = 0 Problem 4.4 Using two different cable-pulley arrangements shown in Figure 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003510_icorr.2007.4428522-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003510_icorr.2007.4428522-Figure2-1.png",
        "caption": "Fig 2 Schematic representation of the VMC and the exoskeleton. Ky is the virtual spring stiffness, the vertical distance between the hip and ankle, y_ref the reference trajectory height, lU the upperleg length, lL the lower leg length and Theta k and Theta h respectively the knee and hip angles.",
        "texts": [
            " The robot will most likely function somewhere between these extremes, guiding the patient much like a physical therapist would do. In order to implement this type of support we have decided to use virtual model control (VMC) [8]. This control method has been used in biped robots but is new for the use in exoskeletons. In this study we want to assess if we can selectively control the subject's step height. We have implemented a VMC to make sure the test subject achieves a required level of foot clearance during the swing phase. (see Fig 2) The VMC model consists of a spring damper system connected to the ankle with a stiffness Ky. The required force Fy is calculated from the virtual spring Ky and the deviation of the reference vertical distance (y_ref) from the vertical distance (y): Fy = Ky (YrefY)(The current position of the ankle is calculated from the hip and knee angles and the segment lengths (see (1.3)). The reference vertical position of the ankle with respect to the hip is calculated from a reference trial (see description of experimental protocol)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure13.34-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure13.34-1.png",
        "caption": "Figure 13.34 Expressing unit vectors lli and h in terms of Cartesian unit vectors f and 1:",
        "texts": [
            " Therefore, the deriva tion of velocity and acceleration vectors for point C relative to the xy coordinate frame follows the same procedure outlined for the derivation of velocity and acceleration vectors for point B relative to the XY coordinate frame. The magnitudes of the tangential velocity and normal acceleration vectors of point C relative to Bare: VC/B = \u00a32 W2 aC/B = \u00a32 W22 If !12 and h are unit vectors in the normal and tangential direc tions to the circular path of C when arm BC makes an angle 02 with the vertical, then: ll.C/B = VC/B h = \u00a32 W2 h !le/B = -aC/B !12 = -\u00a32 W22 !12 From Figure 13.34, unit vectors !12 and h can be expressed in terms of Cartesian unit vectors \u00a3 and 1 as: !1z = sin 02 \u00a3 - cos021 h = COS02\u00a3 + sin 021 Therefore, the velocity and acceleration vectors of point C rela tive to the xy coordinate frame can be written as: Qc/B = \u00a32 WZ (cos 02\u00a3 + sin 02 D !lC/B = -\u00a32 wl (sinOzi - cos02D Substituting the numerical values of \u00a32 = 0.3 m, 02 = 45\u00b0, and W2 = 4 rad / s, and carrying out the necessary calculations we obtain: ll.C/B = 0.85\u00a3 +0.851 !lC/B = -3.39 \u00a3 + 3.39 1 (iii) (iv) Angular Kinematics 293 294 Fundamentals of Biomechanics Motion of point C as observed from point A: We determined the velocity and acceleration of point C relative to B, and velocity and acceleration of point B with respect to A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003124_j.ijar.2006.08.002-Figure11-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003124_j.ijar.2006.08.002-Figure11-1.png",
        "caption": "Fig. 11. Structure of the TORA system.",
        "texts": [
            " The simulated state responses and combined control efforts of a cart\u2013pole system and a ballbeam system by the DSMFNNC system are depicted in Figs. 8\u201310. It is found that the ball-beam system can be stabilized to the equilibrium point, and shown that h and r converge to zero, respectively. Further, the proposed control cannot only settling time and overshoot to decrease but also performance and robustness better than DSMC and DFSMC [9]. The translational oscillations with a rotational actuator (TORA) problem is depicted in Fig. 11. The TORA features both the challenges of an inherent nonlinearity and the benefits of a physically meaningful concept of energy storage. A horizontal rotational proof mass (no gravity effect) is attached to a translating cart by means of a dc motor. The cart is inertially fixed by a spring with no damping and the sole actuation is through the dc motor torque. The objective of the problem is to use the torque input to attenuate disturbances to the base translational mass using the proof mass. The motion of oscillations as follows: \u00f0M \u00fe m\u00de\u20acxc \u00fe mr\u00f0\u20ach cos h _h2 sin h\u00de \u00fe kxc \u00bc d \u00f0I \u00fe mr2\u00de _h2 \u00fe m\u20acxcr cos h \u00bc N \u00f041\u00de where M represents the total mass of the rotor and car, m is the rotor mass, xc is translational position, d is the disturbance force acting on the cart, h is the rotational angle, k is the stiffness of the linear spring, I is the moment of inertia of the eccentric mass, N represents the control torque applied to proof mass, and r is the radius of rotation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002669_s0967-0661(02)00013-8-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002669_s0967-0661(02)00013-8-Figure1-1.png",
        "caption": "Fig. 1. Adopted system of coordinates: the inertial frame \u00f0E; x; y; z\u00de and the body-fixed frames \u00f0B; xb; yb; zb\u00de:",
        "texts": [
            " In Section 3, the adopted depth controllers are presented, while simulation results are reported and discussed in Section 4. Section 5 contains concluding remarks and describes future system developments. To derive a general non-linear model that describes the dynamics of an underwater vehicle either a Newtonian or a Lagrangian formalism can be adopted. Considering the vehicle as a rigid body with six degrees of freedom, let m1 \u00bc \u00bd u v w T denote the translational velocity vector and let v2 \u00bc \u00bd p q r T denote the angular velocity vector in a body frame \u00f0B;xb; yb; zb\u00de; see Fig. 1, attached to the vehicle. The relative position of the origin of the body frame with respect to the origin of the inertial frame \u00f0E; x; y; z\u00de; see Fig. 1, is expressed by its inertial frame coordinates g1 \u00bc \u00bd x y z T while the orientation parameters of the body frame with respect to the inertial frame are expressed by g2 \u00bc \u00bdf y c T: Denoting by g \u00bc gT1 gT2 T and v \u00bc vT1 vT2 T ; respectively, the generalized coordinates and the generalized velocities of the vehicle, the kinematic equations are written as \u2019g \u00bc J\u00f0g\u00den; J\u00f0g\u00de \u00bc J1\u00f0g2\u00de 06 6 06 6 J2\u00f0g2\u00de \" # : The generalized fluid velocity and the relative velocity between the vehicle and the fluid are denoted by vc \u00bc uTc 01 3 T and vr\u00bc v vc; respectively, where uc is the linear velocity of the fluid in the body-frame coordinates which is assumed irrotational"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003638_1.2900714-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003638_1.2900714-Figure12-1.png",
        "caption": "Fig. 12 Geometrical parameters for the influence of flanges",
        "texts": [
            " At low-medium rotational speeds Rec 6000 , since viscous orces are influential on the drag torque, the lubricant was heated o impose an identical temperature for all the tests and, in this ay, the same oil viscosity. It has been found that the dimensioness ratio P / Pref does not depend on parameters related to speed r gear tooth geometry Fig. 11 while the gear diameter appears s a prominent factor since churning power loss reductions are ore significant for larger gears. By using dimensional analysis whose parameters are defined in Fig. 12 , the experimental reults lead to the following relationship: P Pref = 2.17 Dp Df 3/4 ja Rp 0.383 Dp/Df 4 here Pref is determined using Eqs. 1 and 2a . It should be emphasized that 4 is valid only when flange di- meters are larger than gear diameters; otherwise, the suction of he lubricant by the teeth is not affected and no loss reduction is bserved. The fact that power reductions are expected, i.e., / Pref 1, implies that the axial clearance is limited by the conition ig. 11 Influence of axial clearances at low rotational speeds n experimental churning losses ournal of Mechanical Design om: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.27-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.27-1.png",
        "caption": "Figure 8.27 Comparing ductile (1) and brittle (2) fractures.",
        "texts": [
            " The stress at which the fa tigue curve levels off is called the endurance limit of the material, which is denoted by ae in Figure 8.26. Below the endurance limit, the material has a high probability of not failing in fatigue no matter how many cycles of stress are imposed upon the material. A brittle material such as glass or ceramic will undergo elas tic deformation when it is subjected to a gradually increasing load. Brittle fracture occurs suddenly without exhibiting consid erable plastic deformation (Figure 8.27). Ductile fracture, on the other hand, is characterized by failure accompanied by consider able elastic and plastic deformations. When a ductile material is subjected to fatigue loading, the failure occurs suddenly with out showing considerable plastic deformation (yielding). The fatigue failure of a ductile material occurs in a manner similar to the static failure of a brittle material. Multiaxial Deformations and Stress Analyses 171 The fatigue behavior of a material depends upon several factors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure12-1.png",
        "caption": "Fig. 12 Some possible PPR-equivalent parallel manipulators: \u201ea\u2026 2-\u201eR RR\u2026NRa-\u201eR R\u2026B\u201eRRR\u2026A, \u201eb\u2026 2-\u201eR RR\u2026NRa-R A\u201eRRR\u2026BRA",
        "texts": [
            " Here, the actuation wrench j i of joint j in leg i is any one wrench which is not reciprocal to the twist of joint j and reciprocal to all the twists of the other joints within leg i. Considering that the order of a screw system is coordinate system free, the Z-axis is placed along the virtual axis of a PPRequivalent PM for simplicity reason. The validity condition of actuated joints can be expressed as 01 2 3 1 1 1 2 1 3 0 4 For example, the possible 3-legged PPR-equivalent PM corresponding to the 2- RRR NRa- RR B RRR A PPR-equivalent parallel kinematic chain Fig. 10 is the 2- R RR NRa- R R B RRR A PPR-equivalent PM Fig. 12 a . The actuation wrenches of all the actuated joints are shown in Figs. 13 b and 13 c . In the R R B RRR A leg Fig. 13 b , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axis of the unactuated R joint within RR B and is parallel to the axes of the R joints within RRR A. In the R RR NRa leg Fig. 13 c , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not rom: http://mechanicaldesign",
            "org/ on 05/06/201 parallel to the axes of the R joints within RRR N. It can be found that the sixth scalar components of 01, 2, 3, 1 1 and 1 2 and 1 3 are all equal to 0. Thus, the validity condition of the actuated joints Eq. 4 is not satisfied. The possible 2- R RR NRa - R R B RRR A PPR-equivalent PM is thus discarded. The possible 3-legged PPR-equivalent PM corresponding to the 2- RRR NRa-RA RRR BRA PPR-equivalent parallel kinematic chain Fig. 9 b is the 2- R RR NRa-R A RRR BRA PPRequivalent PM Fig. 12 b . The actuation wrenches of all the actuated joints are shown in Figs. 13 a and 13 c . In the R A RRR BRA leg Fig. 13 a , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axis of the unactuated RA joint and is parallel to the axes of the R joints within RRR B. In the R RR NRa leg Fig. 13 c , the first R joint is actuated. 1 i can be chosen as any 0 whose axis intersects the axes of the three unactuated R joints and is not parallel to the axes of the R joints within RRR N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002591_978-94-017-0657-5_3-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002591_978-94-017-0657-5_3-Figure1-1.png",
        "caption": "Figure 1. Geometry of a spatial 3-PRRR parallel manipulator.",
        "texts": [
            " Carricato and Parenti-Castelli (2001) presented a family of 3-DOF parallel manipulators with pure translational motion. In this paper, a parallel manipulator that employs only revolute and prismatic joints to achieve translational motion of the moving platform is presented. In what follows, the kinematic structure of the manipulator is described. The kinematics and stiffness of the manipulator are studied. Some design considerations are discussed. Finally, a prototype CPM is demonstrated to show its feasibility. 2. Kinematic Structure z The kinematic structure of the Cartesian parallel manipulator is shown in Fig. 1, where a moving platform is connected to a fixed base by three PRRR (prismatic-revolute-revolute-revolute) limbs. The moving platform is symbolically represented by a circle defined by points BI ' B2 , and B3 and the fixed base is defined by three guide rods passing through AI' A2 , and A3 , respectively. The three revolute joint axes in each limb are located at points Ai' Mi' and Bi' respectively, and are parallel to the ground-connected prismatic joint axis. Furthermore, the three prismatic joint axes, passing through point Ai for i = 1,2, and 3, are parallel to the X, Y, and Z axes, respectively",
            " In the linear actuation method, one actuator drives the prismatic joint in each limb whereas in the rotary actuation method, an actuator drives the first revolute joint of each limb. However, the rotary actuation method is shown to be impractical because of the existence of singularities within the workspace (Kim and Tsai 2002). In what follows, the machine with three linear actuators is presented. The forward and inverse kinematic analyses are trivial since there exists a one-to-one correspondence between the end-effector position and the input joint displacements. Referring to Fig. 1, each limb constrains point P to lie on a plane which passes through point Ai and is perpendicular to the axis of the linear actuator. Consequently, the location of P is determined by the intersection of three planes and a simple kinematic relation can be written as (2) where p = [Px,py,Pzf denotes the position vector of the end-effector. Similarly, the velocities and output forces of the end-effector also have a one-to-one relationship with those of prismatic actuators. Taking the time derivative of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure7.25-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure7.25-1.png",
        "caption": "Figure 7.25 Material 1 is more ductile and less brittle than 2.",
        "texts": [
            "14 Properties Based on Stress-Strain Diagrams As defined earlier, the elastic modulus of a material is equal to the slope of its stress-strain diagram in the elastic region. The elastic modulus is a relative measure of the stiffness of one material with respect to another. The higher the elastic modulus, the stiffer the material and the higher the resistance to deformation. For example, material 1 in Figure 7.24 is stiffer than material 2. Stress and Strain 137 138 Fundamentals of Biomechanics A ductile material is one that exhibits a large plastic deforma tion prior to failure. For example, material 1 in Figure 7.25 is more ductile than material 2. A brittle material, on the other hand, shows a sudden failure (rupture) without undergoing a considerable plastic deformation. Glass is a typical example of a brittle material. Toughness is a measure of the capacity of a material to sustain per manent deformation. The toughness of a material is measured by considering the total area under its stress-strain diagram. The larger this area, the tougher the material. For example, material 1 in Figure 7.26 is tougher than material 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure18-1.png",
        "caption": "Fig. 18. Finite element model of the whole face-gear.",
        "texts": [
            " Step 6: The definition of the contact surfaces necessary for the finite element analysis is accomplished automatically, identifying all the elements of the model required for the formation of such surfaces. A symmetric master-slave method has been applied. This method causes the algorithm to treat each surface as a master surface. The finite element analysis has been performed for a face-worm gear drive with conical worm of common design parameters represented in Table 1. For the analysis the model of the whole worm (Fig. 17) and the whole face-gear (Fig. 18) have been substituted by a model of five-pair of teeth in meshing (Fig. 19) in order to save computational time. Elements C3D8I of first order have been used for the finite element mesh. The total number of elements is 55 672 with 68 671 nodes. The material used is steel with Young\u2019s modulus E \u00bc 206800 N/mm2 and Poisson\u2019s ratio 0.29. The torque applied to the face-gear is 50 Nm. Figs. 20\u201322 show how the bearing contact looks at the beginning, at the middle, and at the end of a cycle of meshing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.4-1.png",
        "caption": "Figure 12.4 A block is being pulled on a horizonal surface.",
        "texts": [
            " For two-dimensional motion analysis there are two governing equations, and therefore, the number of unknowns to be determined cannot be more than two. In linear kinetics, the unknowns are either forces or accel erations. \u2022 Include the correct directions of forces and accelerations in the solution, along with their units. \u2022 The kinematic relations between position, velocity, and accel eration can also be utilized if the information about the velocity and/ or position of the object analyzed is given or required. Linear Kinetics 259 260 Fundamentals of Biomechanics Example 12.1 As illustrated in Figure 12.4, consider a block of mass m = 50 kg, which is being pulled on a rough, horizontal surface by a person using a rope. Assume that the person is applying a constant force of T = 150 N on the block, the rope makes an angle 0 = 30\u00b0 with the horizontal, and the coefficient of kinetic friction between the block and the horizontal surface is J.L = 0.2. Determine the acceleration of the block if the bottom surface of the block remains in full contact with the floor throughout the motion. Solution: The free-body diagram of the block is shown in Figure 12"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.74-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.74-1.png",
        "caption": "Figure 8.74 Problem 8.5.",
        "texts": [
            " Assuming that the weight of the beam is negligible, calculate: (a) the reactive forces on the beam at A and B; (b) the internal shearing force, Vaa, and bending moment, Maa , at section aa of the beam which is 2 meters from A; (c) the internal shearing force, Vbb, and bending moment, Mbb, at section bb of the beam which is 3 meters from A; (d) the first moment, Q, of the cross-sectional area of the beam; and (e) the maximum shear stress, raa, generated in the beam at section aa. (a) RA=300 N (t), RB = 100 N (t) (b) Vaa = 100 N, Maa =200 N-m (c) Ybb = 100 N, Mbb = 100 N-m (d) Q = 0.0005 m 3 (e) raa = 7500 Pa Problem 8.5 Consider the plane stress element shown in Figure 8.74 representing the state of stress at a material point. If the magnitudes of the stresses are such that ax = 200 Pa, ay = 100 Pa, and rxy = 50 Pa, calculate the magnitudes of principal stresses 194 Fundamentals of Biomechanics 0\"1 and 0\"2, and the maximum shear stress, \"max, generated at this material point. 0\"1 = 208 Pa (tensile), 0\"2 = 108 Pa (compressive), \"max =158 Pa Answers to Problem 8.1: (a) Poisson's ratio (b) second-order tensor (c) principal stresses (d) principal planes (e) maximum shear stress (f) Mohr's circle (g) failure (h) fatigue (i) endurance limit (j) Brittle (k) Ductile (1) stress concentration effects (m) torsion (n) neutral axis (0) 45 (p) static (q) method of sections (r) flexure Chapter 9 Mechanical Properties of Biological Tissues 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002657_70.345948-Figure8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002657_70.345948-Figure8-1.png",
        "caption": "Fig. 8. Nine DOF cyclic Cartesian path",
        "texts": [
            " 6 shows the output sequence for joint path end-point planning to a specified task space positiodorientation in the presence of an obstacle. Fig. 7 shows the path sequence generated for a path following task incorporating a straight line translation coupled with a rotation of 180\u201d about the tip I- axis. Because of the manipulator joint limits, this can only be accomplished by switching the PUMA\u2019S pose from elbow-up to elbow-down at some intermediate point. As in the planar examples, the present algorithm accomplishes a smooth transition between these arm configurations. The final example (Fig. 8) illustrates a cyclic joint path sequence computed for the arm to follow a circular task space path while maintaining a fixed tool orientation (perpendicular to the plane of the circle). For the cases shown, the planar examples required from seven to ten iterations to reduce the task error and meet all the constraints, while the spatial examples ranged from 10 to 25 iterations. Discretization levels ranged from S = 10 to 40 in size. For the 9 DOF redundant arm planning scenario, this represents a small computational load for the Sun SPARC-station used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003912_s0022112073001849-Figure2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003912_s0022112073001849-Figure2-1.png",
        "caption": "FIGURE 2. The co-ordinate system.",
        "texts": [
            " Bakker (1928) refers only to Neumann and Wangerin and since that time no further work appears to have been done to clarify the situation. In this paper the problem will be examined by the methods of the calculus of variations, which permit a unified approach to the determination of the equilibrium and its stability. The vanishing of the first variation of the total energy gives rise to the equations for equilibrium, and the criteria for stability are derived from the second variation. In order to carry out the variational treatment we need an expression for the total energy of the drop. Figure 2 shows the vertical cross-section of half of the 48-2 756 E. Pitts drop hanging from the horizontal support ABC, and introduces a convenient co-ordinate system. If we calculate the energy per unit length of surface in the z direction in figure 2, then for half of the drop an element of length ds (in the x, y plane) a t P contributes y ds, where y is the surface tension. The horizontal element of liquid a t P contributes potential energy, which we shall reckon relative to the level ABC; thus the contribution is - (h - y) xgpdy, where h is the height OB of the drop, g is the acceleration due to gravity and p is the liquid density. The interface between the liquid and the support also contributes to the energy an amount proportional to the length BC which we may write as bx,, where b is a constant",
            " Thus if the total energy of the whole drop per unit length in the z direction is 2E, we have If 2A is the total area of the cross-section of the drop, then For a given value of A, the value of E will depend on the shape x(y) of the drop. The equilibrium profile will be that which minimizes E, subject to the condition that A is constant. Applying the standard methods of the calculus of variations, we obtain the well-known equations relating hydrostatic pressure, surface tension and the curvature of the surface, and find that the profile of the drop must cut the y axis at right angles at 0, and that we also must have b = - 7 ~ 0 ~ 8 , where 8 is the angle of contact shown in figure 2. In addition, it follows that there cannot be corners in the profile and that the Weierstrass condition for a strong minimum is satisfied by the integrand in the definition of E. This formal approach of course merely reproduces the results usually derived directly by simple physical arguments. It will be convenient to use dimensionless variables, choosing (y/pg)* as the unit of length and defining K as the height of the drop and 2h as the length of the drop in contact with the support, i.e. K = h(Y/Pd-+, A = Xo(y/Pg)-*",
            " Also, when y is equal to p, the profile has an inflexion point. Equation (3) may be integrated immediately with the result (4) 1 2 2y -py + 1 = xu( 1 + x;)-*, u = py - *y2, (5) so that x; = ( l -U)2/U(2-U) . (6 ) This shows that o < u < 2 . (7) 0 < p . (8) If we put u = 2 sin2 4 (9) xy = cot 24) (10) where we have used the condition that when y is zero xy is infinite. We now put Since y is necessarily positive, it follows from ( 5 ) that equation (7) is automatically satisfied and we find and thus tan 2 4 is the gradient of the curve at P (see figure 2). At C, xu is equal tolcot 0, so that there 4 is equal to $9. From ( 5 ) y =pG-(,u2-4sin24)t, (11) so that, when 4 is zero y is zero. From (10) and (1 1) we obtain which may be expressed in terms of elliptic integrals of the first and second kinds : (13) Provided p is greater than 2, the value of 4 varies between zero and $0, which corresponds to its value at the point C. From (1 1) we see that y is never equal to p, and hence the profile does not have a point of inflexion. However, if p is less than 2, equation (13) is transformed by standard methods into x = p-l( 2 - p2) F (2p-1, 4) + puE( 2p-1, 4) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure3-1.png",
        "caption": "Figure 3. Schematic illustration of generation by a grinding worm and three axes grinding machine.",
        "texts": [
            " Chamfers on the top, front, and back sides of gear teeth are provided to avoid edge contact that may occur on the respective tooth part due to gear misalignment. Existence of chamfers complicates the finishing process, but this inconvenience has to be accepted. Providing of chamfers should not be considered as the indulgence of ignoring of possible existence of singularities in the zone between the chamfers and involute part of tooth surfaces. The authors propose application for the finishing process of a worm-shape tool (Figure 3) that enables to obtain a modified regular tooth surface, avoid areas of severe contact stresses, and Topology of Modified Surfaces 1065 absorb t r ansmiss ion errors, if they occur. I t is sufficient to modify the geometry of only one member of the ma t ing gears, usually, of the pinion. The basic idea of the proposed finishing process by the gr inding worm is appl ica t ion of modified roll for the too th generat ion. The mot ions applied for genera t ion are, 1066 F . L . LITVIN et al. (i) the feed motion of the grinding worm along the face width of the pinion, and (ii) the rolling motions of the grinding worm and pinion blank. Modified roll means substitution of linear relations of motions by parabolic ones obtained by application of three axes grinding machine. The motions are represented schematically in Figure 3, (i) axis one corresponds to the displacement of the grinding worm across the face width of the pinion blank, (ii) along axis two is performed the rotation of the grinding worm, (iii) along axis three is performed rotation of the pinion blank. Combination of the motions above provide profile and longitudinal crowning in the desired zones of pinion tooth surface. Figure 4 shows an example of nine desired zones of crowned pinion tooth surface, where (i) Zone 0 is the involute area wherein linear relations of parameters of motions are applied and no modifications are provided"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure3-1.png",
        "caption": "Fig. 3. Cross section of an induction motor.",
        "texts": [
            " difficulty in producing a totally enclosed motor for some hazardous applications, a limit on the constant power speed range due to increased difficulty in commutation at low values of flux, a relatively low maximum rotor speed limited by mechanical stress on the commutator, relatively high cost. INDUCTION MOTORS Most induction motors are designed to operate from a three-phase source of alternating voltage [l], [ 5 ] , [6]. For variable-speed drives, the source is normally an inverter which 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 Fig. 3. Slots in the inner periphery of the stator accommodate three phase windings a,b , and c. The tums in each winding are distributed so that a current in the winding produces an approximately sinusoidally distributed flux density around the periphery of the air gap. When three currents which are sinusoidally varying in time flow through the three symmetrically placed windings, an air-gap flux density is produced which is sinusoidally distributed around the gap and is rotating at an angular velocity equal to the angular frequency w, of the stator currents",
            " The continuous values of the rtrts linear current density K , in the rotor and K , 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 T b of the motor. The force per unit of rotor surface area is roughly comparable for induction and commutator motors. The base angular velocity w6 of the motor will be fixed by the needs of the mechanical load to be driven. For the two-pole motor shown in Fig. 3, the required base value of angular frequency of stator currents w, will differ from w6 by the angular frequency W R of the rotor currents. For small values of W R , the torque will be proportional to W R as shown in Fig. 4. For motoring action, W R will be positive. 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 W R negative, i.e., the sequence of the rotor currents is reversed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003199_ip-epa:20050507-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003199_ip-epa:20050507-Figure9-1.png",
        "caption": "Fig. 9 Prototype 22-pole, 24-slot modular PM machine mounted on dynamometer test rig",
        "texts": [
            " As can be seen, the frequencies of the harmonics are integer multiples of the fundamental radial force frequency 733.33Hz. It should also be noted that although the amplitudes of the high-order time harmonics are relatively low, they may still induce significant vibrations. IEE Proc.-Electr. Power Appl., Vol. 153, No. 6, November 2006 The foregoing analysis of the radial force characteristics of a three-phase modular PM machine has been validated by vibration measurements on the prototype 22-pole, 24-slot machine, which is shown in Fig. 9 mounted on a dynamometer test rig. The machine is connected to a four-quadrant DC power supply via a three-phase diode bridge rectifier and was operated as a generator. Figure 10 shows a typical phase current waveform. An accelerometer was mounted on the machine housing to measure vibrations under various operating conditions. Figure 11a shows the vibration spectrum that was measured on no load at a rotor speed of 2000 rpm, which is around the middle of the operating speed range for the particular modular machine under consideration"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure5.1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure5.1-1.png",
        "caption": "Fig. 5.1 Beam element",
        "texts": [
            " If the beam is initially straight, this assumption is true, and it can serve as a good approximation if the curvature of the beam is small. However, for beams with con siderable initial curvature, this curvature has to be taken into account. From the statics of curved beams, we know the differential equations for the resultants N(s), Q(s) and M(s) (5.1) where a new coordinate s has been introduced in the direction of the curved beam axis, such that x=x(s), z=z(s), (5.2) and n( s), q( s) and m( s) are the distributed forces and moments, respectively, acting on the curved beam axis. As shown in Fig. 5.1, R( s) denotes the radius of curvature at any point s of the beam axis. Moreover, with the transformation ds = R(s)dcp, (5.3) 96 5. Curved Beams we may introduce an alternative description of Eqs. (5.1) as functions of angle cp, which sometimes is of advantage. We note that in the limit for vanishing curvature 1/ R these differential equations take the same form as Eqs. (3.43), where then s is replaced by x. It will be assumed here that the axis of the beam is a plane curve, and that the beam has a plane of symmetry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure1.10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure1.10-1.png",
        "caption": "Fig. 1.10 Sample piezoelectric actuators. Courtesy of Cedrat",
        "texts": [],
        "surrounding_texts": [
            "The deformation directions are shown in Figure 1.11. It is important to note that all the parameters used in (1.12) have to be considered in the different deformation directions. Depending on the electrical field application and the deformation of interest, piezoelectric actuators can be employed using different modes: \u2022 Longitudinal mode d33. See Figure 1.12(a). Expression (1.13) turns into: S3 = 6 \u2211 i=1 (s3iTi)+d33E3 (1.15) \u2022 Transverse mode d31. See Figure 1.12(b). Expression (1.13) turns into: S1 = 6 \u2211 i=1 (s1iTi)+d31E3 (1.16) 16 1 Actuator Principles and Classification \u2022 Shear mode d15. See Figure 1.12(c). Expression (1.13) turns into: S5 = 6 \u2211 i=1 (s5iTi)+d15E1 (1.17)"
        ]
    },
    {
        "image_filename": "designv10_8_0003119_1.2044787-Figure15-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003119_1.2044787-Figure15-1.png",
        "caption": "Fig. 15 Some 3-DOF PPR-equivalent PMs of family 13: \u201ea\u2026 2-\u201eR RR\u2026N\u201eRR\u2026I-R A\u201eRRR\u2026BRA, and \u201eb\u2026 2-\u201eR R\u2026N\u201eRRR\u2026I -R A\u201eRRR\u2026BRA",
        "texts": [],
        "surrounding_texts": [
            "Virtual chains have been introduced to represent the motion patterns of 3-DOF motions. A procedure for the type synthesis of 3-DOF PPR-equivalent PMs has also been proposed. Using the 1120 / Vol. 127, NOVEMBER 2005 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 05/06/201 proposed procedure, 3-DOF PPR-equivalent PMs are synthesized in three steps: a type synthesis of legs, b type synthesis of 3-DOF parallel kinematic chains, and c selection of actuated joints. In addition to all the 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs proposed in the literature, a number of new 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs have also been identified. It has also been found that there are no 3-DOF PPRequivalent PMs with identical types of legs. Due to the introduction of the virtual chains, the type synthesis of legs for an f-DOF parallel kinematic chain or PM generating a specified motion pattern is reduced to the type synthesis of f-DOF single-loop kinematic chains. Therefore, the proposed method is more straightforward and efficient. In order to compare the proposed approach with other approaches for the type synthesis of PMs, it has been applied to the type synthesis of translational PMs 26 the type synthesis of which have also been dealt with by different approaches. It has been shown that the proposed approach is superior to other approaches at their current state of the art. The characteristics of the proposed method are: a Fewer derivations are needed than in 5\u20137,11\u201313 . b It is easier to understand than the method proposed in 6,14 . c More types of PMs are obtained than in 4,8,9 . The proposed approach is also applicable to the type synthesis of PMs generating other 3-, 4-, and 5-DOF motion patterns. However, the classification of motion patterns is still an open issue."
        ]
    },
    {
        "image_filename": "designv10_8_0003285_015107-Figure4-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003285_015107-Figure4-1.png",
        "caption": "Figure 4. (a) Virtual model of the measuring arm, and (b) schematic view of the system with embedded frames and geometry.",
        "texts": [
            " By defining the following 4 \u00d7 4 elementary transformation matrices [29] trans (x, \u00b7) = \u23a1 \u23a2\u23a2\u23a2\u23a3 1 0 0 \u00b7 0 1 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 , trans (y, \u00b7) = \u23a1 \u23a2\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 \u00b7 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 , trans (z, \u00b7) = \u23a1 \u23a2\u23a2\u23a2\u23a3 1 0 0 0 0 1 0 \u00b7 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 , rot (x, \u00b7) = \u23a1 \u23a2\u23a2\u23a2\u23a3 1 0 0 0 0 cos(\u00b7) \u2212sin(\u00b7) 0 0 sin(\u00b7) cos(\u00b7) 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 , rot (y, \u00b7) = \u23a1 \u23a2\u23a2\u23a2\u23a3 cos(\u00b7) 0 sin(\u00b7) 0 0 1 0 0 \u2212sin(\u00b7) 0 cos(\u00b7) 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 , rot (z, \u00b7) = \u23a1 \u23a2\u23a2\u23a2\u23a3 cos(\u00b7) \u2212sin(\u00b7) 0 0 sin(\u00b7) cos(\u00b7) 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a5\u23a6 and, with reference to figure 4(b), which also shows the nominal kinematics of the structure, transformation matrices in equation (15) are defined as follows. Non-parallelism between the z-axes of frame {B} and {0} and relative position errors between their origins is described by TB 0 = trans (x, \u03b4k1) \u00b7 trans (y, \u03b4k2) \u00b7 rot (x, \u03b4k3) \u00b7 rot (y, \u03b4k4). The transformation matrix between frame {0} and {1} involves orthogonal joint axes; hence, a four-parameter D\u2013H convention is used to give T0 1 = rot (z, q1 + \u03b4k5) \u00b7 trans (z, d0 + \u03b4k6) \u00b7 trans (x, L1 + \u03b4k7) \u00b7rot (x, \u03c0/2 + \u03b4k8)",
            " No rotational parameter is involved, since the orientation may not be measured by the calibrating system (i.e. the Perspex plate). Thus T5 E = rot (z, q6) \u00b7 trans (x, a6 + \u03b4k25) \u00b7 trans (y, \u03b4k26) \u00b7trans (z, L5 + c6 + \u03b4k27). 4.3.4. Nominal kinematics. Linear dimensions of the nominal kinematics for the actual measuring arm are given below and expressed in millimetres: d0 = 66, L1 = 60, L2 = 160, L3 = 160, L4 = 60, L5 = 100, a6 = 50, c6 = 75. For a joint coordinates vector q = [0, 0, 0, 0, 0, 0]T and nominal kinematics, the system assumes the configuration shown in figure 4(b), i.e. the zero-reference configuration. Table 1 gives a list of the structural D\u2013H parameters describing the nominal kinematics of the measuring arm. An inverse kinematic model q = G(p, k0) is also derived in an analytical form for the nominal geometry of the measuring robot. The Newton\u2013Raphson method [34] is then used to solve numerically the inverse kinematic model for the error-corrupted kinematics, i.e. q = G(p, k0 + \u03b4k). Neither model is reported in this paper. In order to characterize the static performance of the actual measuring robot, resolution of the system is computed based on the nominal kinematics, while repeatability and accuracy are estimated based on experimental data, according to what is described in section 3. For the fully-extended robot configuration, as shown in figure 4(b), equation (11) gives an estimate of the theoretical worst resolution for the endeffector\u2019s endpoint. In that configuration, expressions for distances di in equation (11) are given below as d1 = \u221a (L1 + L2 + L3 + L4 + L5 + c6)2 + a2 6 d2 = L2 + L3 + L4 + L5 + c6 d3 = L3 + L4 + L5 + c6 d4 = L4 + L5 + c6 d5 = \u221a (L5 + c6)2 + a2 6 d6 = a6 . Hence, for the encoder resolution given in section 4.1, equation (11) gives RSmax \u2248 1.56 mm. A better estimate of the theoretical end-effector\u2019s endpoint resolution, in a defined portion of the operating workspace, is calculated using equation (12)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.12-1.png",
        "caption": "Figure 8.12 Stress tensor components in the xy-plane.",
        "texts": [
            "6 x 10-3 These results indicate that the dimensions of the block in the x and y directions decrease, while its dimension in the z direction increases. The deformed dimensions of the block can be deter mined in a similar manner as employed for Case (a). 8.3 Stress Transformation Consider the rectangular bar shown in Figure 8.11. The bar is subjected to externally applied forces that cause various modes of deformation within the bar. Let P be a point within the struc ture. Assume that a small cubical material element at point P with sides parallel to the sides of the bar is cut out and analyzed. As illustrated in Figure 8.12, this material element is subjected to a combination of normal (o-x and o-y) and shear (rxy) stresses in the xy-plane. Now, consider a second element at the same mate rial point but with a different orientation than the first element (Figure 8.13). One can assume that the second material element is obtained simply by rotating the first in the counterclockwise direction through an angle (). Let x' and y' be two mutually per pendicular directions representing the normals to the surfaces of the transformed material element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003800_1.2970058-Figure9-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003800_1.2970058-Figure9-1.png",
        "caption": "Fig. 9 Simulation results for zdi,2 in DS and zs,2 in SS over one gait cycle using the full model and the low-dimensional model. The error between the traces is on the order of the integrator \u22125",
        "texts": [],
        "surrounding_texts": [
            "N d r\n5\ni c t c w\nd m\nU b s I\nN b E fi\nd o m\nA H i a\nN\nc\nt\nM g\nU\nS t\nJ\nDownloaded Fr\note that the dimensions of X\u0304s and X\u0304di are each two whereas the imension of their counterparts, Xs and Xdi , are 2ns and 2ndi\n, espectively.\nStability Properties of the Model The low-dimensional model for one complete step 38 allows nvestigation of the stability properties of the motion in the limit ycle. The method of Poincar\u00e9 is used to examine the stability of he periodic gait. Based on the methodology of Refs. 2,38 , the omplete Poincar\u00e9 map is composed of the mappings associated ith SS and DS.\n5.1 Mapping for the Single Support Phase. The lowimensional model for SS is given in Proposition 2. Since zs,1 is onotonic during SS, i.e., dzs,1 /dt 0, it follows that\ndzs,2 dzs,1 = s,2 zs,1,zs,2 s,1 zs,1 zs,2\n39\nnlike the model in Ref. 2 , s,2 depends on both zs,1 and zs,2 ecause of the presence of the rolling foot. Hence, it is not posible to derive a closed form for Eq. 39 by integration along Zs. ntegration from s \u2212 to s + can be expressed as\nzs,2 \u2212 \u2212 zs,2 + = Vs zs,2 + 40\note that the integral Vs is a function of both zs,1 + and zs,2 + , but can e expressed as Vs zs,2 + since zs,1 + is a constant. With zs,2\n+ given by q. 36 , the map for the SS phase s :Sdi s Zdi \u2192Ss\ndi Zs is dened as\ns zdi,2 \u2212 = di s zdi,2 \u2212 + Vs di s zdi,2 \u2212 41\n5.2 Mapping for the Double Support Phase. The lowimensional model for DS is given in Proposition 3. The develpment of the mapping for DS follows that for SS. Since zdi,1\nis onotonic,\ndzdi,2 dzdi,1 = di,2 zdi,1 ,zdi,2 di,1 zdi,1 zdi,2 42\ns before, the second state, di,2 , depends on both zdi,1 and zdi,2 .\nence, it is not possible to derive a closed form for Eq. 42 by ntegration along Zdi . Integration from d \u2212 to d\n+ can be expressed s\nzdi,2 \u2212 \u2212 zdi,2 + = Vdi zdi,2 + 43\note that the integral Vdi is a function of both zdi,1 + and zdi,2 + , but\nan be expressed as Vdi zdi,2 + since zdi,1 + is a constant.\nSubstituting for zdi,2 + using Eqs. 35a and 35b , which give the ransition map from SS to DS, the map for the DS phase\ndi :Ss di Zs\u2192Sdi s Zdi is defined as\ndi zs,2 \u2212 = s dizs,2 \u2212 + Vdi s dizs,2 \u2212 44\n5.3 Overall Poincar\u00e9 Mapping for the Low-Dimensional odel. The Poincar\u00e9 map for the step :Ss di Zs\u2192Ss di Zs is\niven by\n= s di 45\nsing Eqs. 41 and 44 , the overall Poincar\u00e9 map is given by\nzs,2 \u2212 = di s s dizs,2 \u2212 + Vdi s dizs,2 \u2212 + Vs di s s dizs,2 \u2212 + Vdi s dizs,2 \u2212\n46 ection 6.4 presents the derivation of a linear approximation for\nhe overall Poincar\u00e9 map.\nournal of Biomechanical Engineering\nom: http://biomechanical.asmedigitalcollection.asme.org/ on 08/22/2013 T\n6 Example: Application to Normal Human Walking The analysis presented in this example is based on a minimal anthropomorphic model see Fig. 2 . The data and parameters for the model are taken from Ref. 23 . In SS, this model consists of links representing two shanks, two thighs, and a HAT segment and has 5 DOF. In DS, the model has an additional link representing the trailing foot pivoting about the ground and has 4 DOF.\nThe input to the model are the anthropometric parameters, the joint angles over a step for the actuated joints, and the ROS parameters. The anthropometric parameters for the gait analysis subject are given in Table 1. The other parameters, namely, the masses of the individual links, the locations of the link centers of mass, and moments of inertia, are derived using the anthropometric formulas provided in Ref. 23 . The parameters of the ROS are obtained using the angles of the actuated joints and reported COP data.\nAll the symbolic computations are performed using MAPLE\u00ae, and MATLAB\u00ae is used for numerical computations. In simulation, the initial posture and initial forward progression rate are specified, the joint torques required to enforce the posture are applied, and the equations of motion EOMs are integrated to obtain the resultant evolution of the gait.\n6.1 Single Support Model. In the SS model, qs = q1 ,q2 ,q3 ,q4 ,qa T= qrel,s ,qa T represent the generalized coordinates that specify the configuration. The joint torques us are computed using Eq. 24 with v x taken to be a PD proportionalderivative controller. The function hd,s is chosen to be a vector of polynomials of degree 9. The polynomial functions are parametrized by s=csqs with cs= \u22122,0 ,\u22121 ,0 ,\u22122 ; see Fig. 2. The polynomial coefficients are chosen by a least-squares fit to the gait data with invariance of output 20 ensured, as discussed in Sec. 4.3.\n6.2 Double Support Model. Since the dynamics are constrained in DS by virtue of both feet being on the ground, two coordinates are dependent on the remaining coordinates. As a result, in DS, only three joints are regulated to establish the desired shape posture of the body. The independent coordinates are chosen to be qdi = q1 ,q2 ,q3 ,qa T= qrel,di ,qa T. The joint torques ud are computed using Eq. 24 with v x taking to be a PD controller. The function hd,di\nis chosen to be a vector of polynomials of degree 9. The polynomial functions are parametrized by d =cdqdi\nwith cd= \u22122,0 ,\u22121 ,\u22122 ; see Fig. 2. The polynomial coefficients are chosen by a least-squares fit to the gait data with invariance of the output ensured.\n6.3 Simulation Results. Models 19a and 19b were simulated for one step on the limit cycle i.e., at steady state . Figure 4 gives frames of a stick animation of the simulation result. Figure 5 gives the joint trajectories from the gait data 23 and the corresponding trajectory of the model. Recall that the joint motions q1 to q4 in SS and q1 to q3 in DS were constrained with respect to forward progression and not time. Figure 6 is a comparison of the evolution of the c.m. as determined from the gait data and models 19a and 19b . Figure 7 gives the joint velocities.\nThe simulation verifies that the evolution of the unactuated co-\nordinate qa, and therefore the evolution of the c.m., closely match\nOCTOBER 2008, Vol. 130 / 051017-7\nerms of Use: http://asme.org/terms",
            "t d s c\nd m\nF m i\nF v s t\nF t v s\n0\nDownloaded Fr\nhe data in both SS and DS. This finding confirms that the lowimensional model 38 captures the essence of walking in the agittal plane: the progression of the c.m. over the complete gait ycle.\nFigures 8 and 9 compare the evolution of full- and lowimensional models\u2019 coordinates over one gait cycle. The close atch validates the derivation of the low-dimensional model. The step length of 0.64 m predicted by the model is less than\nig. 4 Stick figure animation over one step of the example odel. Note the rolling motion of the stance foot. The swing leg\ns shown with dashed lines.\nig. 5 Joint motions from the gait data in Ref. \u202023\u2021 \u201edashed\u2026 ersus models \u201e19a\u2026 and \u201e19b\u2026 \u201esolid\u2026 on the limit cycle \u201ei.e., at teady state\u2026 for one step. Note that the HAT angle, qa, is unacuated, and, therefore, its evolution is not directly controlled.\nig. 6 Comparison of the angle between the line connecting he c.m. and the ground for the gait data in Ref. \u202023\u2021 \u201edashed\u2026 ersus models \u201e19a\u2026 and \u201e19b\u2026 \u201esolid\u2026 on the limit cycle \u201ei.e., at teady state\u2026 for one step. The plot indicates a close match.\n51017-8 / Vol. 130, OCTOBER 2008\nom: http://biomechanical.asmedigitalcollection.asme.org/ on 08/22/2013 T\nthe 0.7 m calculated from the data 23 . The discrepancy can be attributed to the swiveling movement of the hips that happens in the transverse plane during human walking. This movement is not taken into account in the planar model. Winter 23 reported a\ntolerance, which was set to 1\u00c310 .\nTransactions of the ASME\nerms of Use: http://asme.org/terms",
            "w w f t i c m\nd 1 e t = p d fi f\na\ns\nm\nF i\nF \u201e p i\nJ\nDownloaded Fr\nalking rate of 1.4 m/s while the model predicts a steady-state alking rate of 1.3 m/s. Since the data in Ref. 23 are reported or only one complete gait cycle, it is difficult to ascertain whether he walking rate reported is the steady-state walking rate. A walkng rate of 1.2 m/s, which is the rate typically used to establish rossing times at traffic intersections, is generally considered noral for adults 39 .\n6.4 Stability Analysis. The Poincar\u00e9 analysis using the lowimensional model shows the existence of a fixed point see Fig. 0 . Simulation of the dynamics for multiple steps confirms the xistence of a limit cycle see Fig. 11 . The simulation reveals that he integrals Vdi and Vs can be expressed by linear relations, Vdi\ndzdi,2 + + d, and Vs= szs,2 + + s in a neighborhood of the fixed oint. As a result, the Poincar\u00e9 map for the overall lowimensional model is linear in the same neighborhood about the xed point. Approximation of Eq. 46 as a linear map proceeds as ollows. First, identify that\nzs,2 \u2212 = zs,2 + + Vs zs,2 + 1 + s zs,2 + + s 47 nd\nzdi,2 \u2212 = zdi,2 + + Vdi zdi,2 + 1 + d s dizs,2 \u2212 + d 48\no that\nzs,2 + = di s zdi,2 \u2212 di s 1 + d s dizs,2 \u2212 + d 49\nTherefore, the Poincar\u00e9 map 46 for the step may be approxiated by\nig. 10 The Poincar\u00e9 map of the full hybrid model \u201e45\u2026 versus ts linear approximation \u201e50\u2026\nig. 11 Simulation of the full hybrid model, Eqs. \u201e19a\u2026 and 19b\u2026, for 35 steps illustrating convergence to a limit cycle as redicted by the fixed point in the Poincar\u00e9 map. The triangles ndicate HC, the beginning of DS, and the transition to SS.\nournal of Biomechanical Engineering\nom: http://biomechanical.asmedigitalcollection.asme.org/ on 08/22/2013 T\n\u0303 zs,2 \u2212 \u00aa \u0303zs,2 \u2212 + V\u0303 50 where\n\u0303 \u00aa 1 + s 1 + d di\ns s di 51\nV\u0303 \u00aa 1 + s di\ns d + s 52\nThe fixed point predicted by the empirically linearized Poincar\u00e9 map 50 is within 0.02% of the value achieved in the limit cycle.\nThe slope \u0303 eigenvalue of Eq. 46 for the gait data used in the simulation is 0.77. The magnitude of the slope being less than unity indicates that the gait cycle is asymptotically stable.\n7 Discussion The approach to human walking taken in this work seeks to exploit the inherent parsimony in human gait to develop a true low-dimensional forward-dynamic model that is analytically tractable, and that captures the essence of walking dynamics in the sagittal plane over a complete gait cycle. The hypothesis is that a human uses his joint torques to control his posture. Controlling the posture changes the angular momentum about the point of contact of the stance foot with the ground. By controlling the inertia about the center of mass in a specific manner, a human uses gravity to progress forward. The developed low-dimensional model captures the dynamics of this action.\nThe approach uses input-output linearization to compute the joint torques for the coordinates that specify the posture. Since only position data from the gait analysis are required to determine the joint motions, the errors from differentiating the position signals to determine velocities and accelerations are not introduced into the model, as is the case with inverse-dynamics analyses.\nTypical forward-dynamic models based on static and dynamic optimizations are limited to simulation of a step or two due to the computational complexity involved. The approach presented in this paper enables the simulation of multiple steps, thus enabling making predictions about the stability of the gait. The slope of the Poincar\u00e9 map used is equivalent to the Floquet multipliers used for the analysis of the dynamic stability of human gait in Refs. 40\u201342 , and the value of the slope compares well with the values reported there.\nThis paper demonstrates the approach for the case of normal walking. To make the approach clinically useful, the model has been extended to model asymmetric gait 43,44 . The asymmetric model takes into account the fact that the anthropometric parameters and joint motions of the left and right legs may vary. This extension enables the study of pathological gait as in the case of a person with a leg length discrepancy or a person walking with a lower-limb prosthesis.\nThe choice of the ROS approach of Ref. 31 to model the foot-ground interface allows the incorporation of actual human gait data in the analytical models since the ROS approach is based on the center of pressure data from gait studies. The advantage of using the effective rocker shape is that it simultaneously captures the motions of the foot and ankle, and the deformations of the shoe. In addition, for normal human walking, ROS has been found to be invariant with changes in walking speed 31 , with using shoes of different heel heights within a reasonable range 45 , and with carrying loads 46 . In the application of this work to study the gait of transtibial prosthesis users, the use of the ROS enables representation of different prosthetic feet and varying alignments 44 . In robotics, the modeling approach has been extended to incorporate flat feet and ankle joint actuation 47 .\nThe model presented in this paper was simulated for different initial values of the forward progression rate and, hence, different initial walking speeds to test the convergence to a limit cycle. To model walking at a steady-state walking rate that is different from the one of the example requires calculation of new holonomic constraints, Eq. 20 . The constraints may be calculated\nOCTOBER 2008, Vol. 130 / 051017-9\nerms of Use: http://asme.org/terms"
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure11.32-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure11.32-1.png",
        "caption": "Figure 11.32 Problem 11.5.",
        "texts": [
            " Neglecting air resistance (the effect of which may be quite signi ficant), determine the takeoff speed vo, landing speed VI, and the total time t}, that the ski jumper was airborne if the skier touched down at a distance d = 50 m from the ramp measured parallel to the slope. Answers: vo = 13.2 mis, VI =29.6 mis, tI =2.7 s Problem 11.5 Assume that in another trial, the ski jumper in the previous problem manages to maintain the takeoff speed at Vo = 13.2 ml s, but leaves the ramp at an angle e = 10\u00b0 with the horizontal (Figure 11.32). How far from the ramp would the ski jumper land on the slope? Discuss whether the ski jumper improved his/her performance as compared to the trial in Problem 11.4. If yes, by how much? Answers: d =57 m, 14% improvement Problem 11.6 Figure 11.33 illustrates the trajectory of a cannon ball. Assume that the cannonball was fired into the air with an initial speed of Vo = 100 ml s at position O. The cannonball landed at position 2 that is at a horizontal distance l = 1000 m measured from position o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure8.8-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure8.8-1.png",
        "caption": "Figure 8.8. A lymphocyte attaches to an infected cell, owing to adhesive domains",
        "texts": [
            " Studies of these binding forces can aid in the development of medicine, as it helps to understand the activation processes of immune cells. It may also be possible to block harmful cells or viruses from docking to healthy ones. The binding forces lie in a range of some pN, requiring very sensitive and noise\u2013free measurement methods. Binding forces between proteins are also responsible for adhesion between cells. These adhesion forces in cell\u2013to\u2013cell contact play a major role in biological processes, for instance in the immune system, when white blood cells attach to infected cells (Figure 8.8). The trapping centers needed for attachment build up or decompose in seconds. This is an effect which is also of interest in self\u2013assembly tasks, in biological manipulation, and in characterization setups [21]. 254 Saskia Hagemann This section gives an overview of the state\u2013of\u2013the\u2013art in AFM\u2013based biological research. Its versatility, as well as an insight into the areas which benefit from the newly available measurement methods, is presented, ranging from purely imaging tasks, over the characterization of different physical, chemical, or electrical properties, to the use of the AFM as a manipulator as well as the cooperation with other end\u2013effectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.64-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.64-1.png",
        "caption": "Figure 8.64 Analyses of the element in Figure 8.63b.",
        "texts": [
            " Using Mohr's circle, determine the principal stresses and maxi mum shear stresses occurring in the beam for the states of stress shown in Figures 8.63b and 8.63c. Solution: At a given section, magnitude F of the externally ap plied force and parameters defining the geometry of the beam, the normal (flexural) stress CTx and the shear stress rxy distribu tions can be determined in a manner similar to that described in Example 8.6. Once the state of stress at a material point is known, Mohr's circle can be used for further analyses of the stresses involved. Mohr's circle in Figure 8.64a is drawn by using the plane stress element of Figure 8.63b. There is a negative normal stress with magnitude CTx and a negative shear stress with magnitude rxy on surface A of the stress element in Figure 8.63b. Therefore, point A on Mohr's circle has coordinates -CTx and -rxy. Surface B on the stress element has only a negative shear stress with magnitude rxy. Therefore, point B on the r-CT diagram lies along the r-axis, rxy distance above the origin. The center C of Mohr's circle can be determined as the point of intersection of the line connecting A and B with the CT-axis",
            " y Lx - ~ A ~a\" -- Tyx - __ Tyx 188 Fundamentals of Biomechanics Once the radius of the Mohr's circle is established, principal stresses and maximum shear stress can be determined as 0\"1 = r O\"x/2 (tensile), 0\"2 =r + O\"x/2 (compressive),and rmax =r. To deter mine the angle of rotation, (h, of the plane for which the stresses are maximum and minimum, we need to read the angle between lines CA and CD (in this case, it is 21h counterclockwise), divide it by two, and rotate the stress element in Figure 8.63b in the clockwise direction through an angle {h. This is illustrated in Figure 8.64b. Analyses of the material element in Figure 8.63c are illustrated graphically in Figure 8.65 . Example 8.8 Figure 8.66 illustrates a bench test that may be used to subject bones to bending. In the case shown, the distal end of a human femur is firmly clamped to the bench and a horizontal force with magnitude F = 500 N is applied to the head of the femur at point P. Determine the maximum normal and shear stresses generated at section aa of the femur that is located at a vertical distance h = 16 cm measured from point P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003273_978-1-84628-978-1-Figure10.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003273_978-1-84628-978-1-Figure10.3-1.png",
        "caption": "Figure 10.3. Interaction between primary electrons (PE) and substrate, which leads to electron radiation (secondary electrons (SE), backscattered electrons (BSE), Auger electrons (AE), and X-rays (X))",
        "texts": [
            " Depending on the substrate\u2019s material parameters such as composition, density, and geometry, the penetration depth of the PEs vary. When penetrating the substrate, the electrons are scattered elastically and inelastically, which leads to a characteristic energy distribution within the substrate and on its surface. During this scattering process of the PEs in the substrate, the PEs lose their energy. The lost energy is used for the generation of electrons, electromagnetic radiation, and heat. In Figure 10.3 [24], an overview of the emitted radiation is given and the electrons with their characteristic energies are described. Backscattered and low-loss electrons: Due to elastic and inelastic scattering of the primary electrons on the substrate atoms, the electrons lose part of their energy and change their direction until their energy is lost completely or until they escape at the substrate\u2019s surface. A distinction is made regarding the electrons\u2019 energy when they leave the substrate. Electrons with energies higher than 50 eV are referred to as backscattered electrons, whereas low-loss electrons are defined as electrons with an energy close to that of the primary electrons",
            " Especially with regard to EBiD, not only is their energy of considerable interest, but also their spatial distribution when emitted from the substrate. The generation of SEs is attributed to the inelastic scattering of the highenergy electrons. Secondary electrons generated due to inelastic scattering of the primary electrons on the substrate atoms are called secondary electrons 1 (SE1). However, due to the elastic scattering of primary electrons (backscattered electrons and low-loss electrons), these electrons can diffuse several \u03bcm away from the impact spot of the primary beam (Figure 10.3). During their travel, these highenergy BSE can generate secondary electrons as well, which are then called SE2. In Figure 10.5, an overview over the different generation spots for secondary electrons is given. Furthermore, the backscattered electrons can again leave the substrate and generate secondary electrons (SE3) far away from the first impact (e.g., on the vacuum chamber). However, this effect will be neglected here, as it does not contribute to the deposition on the substrate. 306 Thomas Wich Spatial distribution of the SE1: Secondary electrons are limited by their low energy, and they can, therefore, only leave the substrate when they are generated within a depth of the surface [24, 29]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002890_00006123-200110000-00003-Figure10-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002890_00006123-200110000-00003-Figure10-1.png",
        "caption": "FIGURE 10. Schematic depiction of surface micromachining of a cantilever beam. (a) blank section of Si wafer. (b) SiO2 is grown on the wafer. (c) a well is patterned in the SiO2 by photolithography and etching to expose the underlying Si. The well will form the anchor for the final device. (d) polycrystalline silicon is deposited and patterned on the wafer. The polycrystalline silicon deposited in the well is in direct",
        "texts": [
            " Electrostatic (or anodic) bonding of Si to glass substrates is performed with the application of pressure and a high voltage, whereas in Si fusion bonding two Si wafers are bonded at high temperatures in an oxygen or nitrogen ambient environment. Surface micromachining In surface micromachining, the substrate is used primarily as a mechanical support on which multiple alternating layers of structural and sacrificial material are deposited and patterned to build micromechanical structures (16, 19, 47). Sur- Neurosurgery, Vol. 49, No. 4, October 2001 face micromachining relies on the encasing of specific structural parts of a device in layers of a sacrificial material during the fabrication process. Figure 10 shows the key processing steps in the fabrication of a cantilever beam by surface micromachining. The sacrificial material is dissolved in a chemical etchant that does not attack the structural parts to leave behind the final component. Surface micromachining is highly compatible with microelectronic manufacturing processes and equipment. Consequently, it enables the fabrication of complex, multicomponent, integrated micromechanical structures that would be impossible to manufacture with traditional bulk micromachining techniques"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure12.14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure12.14-1.png",
        "caption": "Figure 12.14 A ski jumper.",
        "texts": [
            " If we choose position 2 to be the datum from which heights are measured, then the mass is located at a height hI = l(1 - cos () at position 1, and the height of the mass at position 2 is zero. Applying the conservation of energy principle between positions 1 and 2: \u00a3KI + \u00a3PI = \u00a3K2 + \u00a3P2 1 2 1 2 2\" m VI + m g hI = 2\" m V2 + m g h2 Substituting VI = 0, hI = l(1 - cos(), and h2=0 into this equa tion and solving it for the speed of the mass at position 2 will yield: V2 = )2 g l (1 - cos() Example 12.4 As illustrated in Figure 12.14, consider a ski jum per moving down a track to acquire sufficient speed to accom plish the ski jumping task. The length of the track is l = 25 m and the track makes an angle () = 45\u00b0 with the horizontal. If the skier starts at the top of the track with zero initial speed, determine the takeoff speed of the skier at the bottom of the track using (a) the work-energy theorem, (b) the conservation of energy principle, and (c) the equation of motion along with the kinematic relationships. Assume that the effects of friction and air resistance are negligible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002453_978-3-662-05271-6-Figure3.3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002453_978-3-662-05271-6-Figure3.3-1.png",
        "caption": "Fig. 3.3 Distribution of normal stress, and neutral axis",
        "texts": [],
        "surrounding_texts": [
            "Since the y and z axes are no principal axes, the given bending moment is to be resolved into components of the 1 (y) and 2 (2) axes M y = My cos cp = 18.974, Mz = -My sincp = 6.325. Introducing these values into Eq. (3.16) yields M- MO\"xx = J 1 Y 2 - J2 z fi = 3.5582 - 4.743 fi\u00b7 The neutral axis of this stress distribution is described with (0\" xx = 0)"
        ]
    },
    {
        "image_filename": "designv10_8_0003912_s0022112073001849-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003912_s0022112073001849-Figure1-1.png",
        "caption": "FIGURE 1. The two-dimensional drop. The thickness DE is greatly exaggerated.",
        "texts": [
            " For this reasonit appeared prudent to make a preliminary study of a simpler example, for which the equilibrium drop profiles can be expressed in known functions and which can also be realized experimentally. The features revealed in this case are in fact helpful in understanding the behaviour of axially symmetric drops, which will be described in a later paper. We shall consider a 'two-dimensional' drop which hangs below a horizontal surface with which it maintains a given contact angle, and which is sandwiched between two vertical parallel glass plates which are very close to each other (see figure 1, in which the separation of the plates is greatly exaggerated). Since the separation is very small the profile of the meniscus across the gap between the walls will generally be very close to a circular arc, of constant curvature, which will not affect the profile in the vertical plane; indeed if the angle of contact of the liquid and the vertical wall is exactly go\", the meniscus will be a cylindrical surface through DOPC. We shall study the behaviour of such a meniscus assuming that the gap is so narrow that the surface cannot be disturbed along the direction perpendicular to the vertical plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003304_j.mcm.2004.10.028-Figure12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003304_j.mcm.2004.10.028-Figure12-1.png",
        "caption": "Figure 12. F in i te -e lcmcnt modcl wi th th ree pairs of tee th .",
        "texts": [
            " Topology of Modified Surfaces 1075 4. S T R E S S A N A L Y S I S This section covers stress analysis and investigation of formation of bearing contact. The performed stress analysis is based on the finite-element method [8] and application of a general computer program [9]. The development of finite-element models of helical gears has been accomplished according to the ideas presented in previous papers [3,4]. 1076 F . L . LITVlN et al. A model of three teeth has been considered as it is shown in Figure 12. This model is generated automatical ly as a function of number of elements in profile and longitudinal direction. Setting of boundary conditions is accomplished automatical ly and are shown in Figure 13. The following ideas are applied, (i) Nodes on the two sides and bo t tom part of the portion of the gear rim are considered as fixed (Figure 13a). (ii) Nodes on the two sides and the bo t tom part of the pinion rim form a rigid surface (Figures 13a and 13b). (iii) A reference node N (Figure 13b) located on the axis of the pinion is used as the reference point of the previously defined rigid surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002797_s0045-7825(02)00235-9-Figure19-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002797_s0045-7825(02)00235-9-Figure19-1.png",
        "caption": "Fig. 19. Face-gear drive with conical worm: finite element model of five teeth in mesh.",
        "texts": [
            " Step 6: The definition of the contact surfaces necessary for the finite element analysis is accomplished automatically, identifying all the elements of the model required for the formation of such surfaces. A symmetric master-slave method has been applied. This method causes the algorithm to treat each surface as a master surface. The finite element analysis has been performed for a face-worm gear drive with conical worm of common design parameters represented in Table 1. For the analysis the model of the whole worm (Fig. 17) and the whole face-gear (Fig. 18) have been substituted by a model of five-pair of teeth in meshing (Fig. 19) in order to save computational time. Elements C3D8I of first order have been used for the finite element mesh. The total number of elements is 55 672 with 68 671 nodes. The material used is steel with Young\u2019s modulus E \u00bc 206800 N/mm2 and Poisson\u2019s ratio 0.29. The torque applied to the face-gear is 50 Nm. Figs. 20\u201322 show how the bearing contact looks at the beginning, at the middle, and at the end of a cycle of meshing. The results obtained by finite element analysis confirm the longitudinal path of contact and the avoidance of edge contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003980_978-1-84882-614-4-Figure6.12-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003980_978-1-84882-614-4-Figure6.12-1.png",
        "caption": "Fig. 6.12 (a) Actuator characteristic curves for different values of the induced strain. (b) Activation boundary. The shaded area represents the operation domain of the actuator when coupled with a passive structure without pre-stress",
        "texts": [
            "7) while taking into account the above mentioned change in sign for the force. It results: 166 6 Design Principles for Linear, Axial Solid-State Actuators 6.3 Theory of Single-Stroke Linear Solid-State Actuators 167 u = ka ks + ka ui (6.11) F = kska ks + ka ui (6.12) The above reported considerations about free stroke, blocking force and coupling with a linear elastic structure can be repeated for each single value of the induced stroke, while a change in the induced stroke corresponds to a translation of the actuator\u2019s characteristic (see Figure 6.12(a)) in the Fu-plane. The minimum and maximum allowed value of the induced stroke identify the activation boundary of the actuator. In general, and without considering other restrictions, every point of the (infinitely long) strip delimited by the activation boundary can be reached by proper loading. If only coupling with passive structures without pre-stress is considered, however (like in the case of Figure 6.9) the operation domain of the actuator restrict to the regions in the first and third quadrant (Figure 6.12(b)). 168 6 Design Principles for Linear, Axial Solid-State Actuators Besides the activation boundary, the actuator force and/or stroke can be limited by strength or stability consideration . For instance, a piezoelectric stack actuator cannot be significantly loaded in tension (see Figure 6.13 a), and a thin wire actuator (e.g. SMA wire) is not able to produce significant positive force (compression load). Together with the activation boundary, the strength boundary defines the operation domain of the actuator (Figure 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002466_s004220050558-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002466_s004220050558-Figure1-1.png",
        "caption": "Fig. 1. Geometry of the bipedal model. The feet are assumed to be curved with foot radius R. Both legs can vary in length, with the mass assumed to be situated in the upper part of the legs. The describing state variables are stance leg angle uSL, trailing leg angle uTL, and stance leg length LSL",
        "texts": [
            " A two-dimensional bipedal model will be de\u00aened by its mechanical structure and muscle properties. A simple re\u00afex-like scheme is applied. The system parameters will be varied and analyzed on periodic behavior with return map analysis. The describing state space of a walking cycle can be separated into two periods: stance phase dynamics and transition. The stance phase describes the dynamic behavior of the bipedal structure when standing on one foot. The transition describes the support transfer between two stance phases. The geometry of the biped is de\u00aened according to Fig. 1. In this model, three degrees of freedom are represented: stance leg angle (ush), trailing leg angle (uTI) and stance leg length LSL . This simple representation of two legs with linear joints connected by a hip joint decouples the hip rotation from the leg extension. The mass of the upper body MH is a point mass and assumed to be located between the hips, so no e ort needs to be made to stabilize it on the stance leg. The legs have mass m located at a distance p from the hip joint. The lower parts of the legs are assumed to be massless",
            " With the model de\u00aened, we can gradually extend the mechanical structure by initially setting the sti ness and damping terms of the muscles to zero. However, no cycle will then be found, since there is no energy input on level ground. Therefore, the leg extension muscles will be added \u00aerst. When energy losses in the hip joint are introduced, the hip muscles will be activated also. For the values of mass and geometry parameters an equivalence to humanoid data is made. A translation of an anthropomorphic structure to the simpli\u00aeed model of Fig. 1 needs to be made in order to convert known anatomical data to values of model parameters. For the anatomical data, the regression equations of Chandler et al. (1975) are used. The proportions of the limbs in relation to the body length are given by Winter (1990). Here a human male person of 75 kg with a total height h of 1.80 m is simulated. The inertia, mass and geometry of the body segments can be calculated. Assuming the knee and ankle are locked, the equivalent mass, inertia and COG position can be calculated (Table 1)",
            " Also involved in the project is the University of Twente, Institute for BioMedical Technology. The equations of motion where derived using Lagrange's equation: d dt @} @ _x \u00ff @} @x Xi k 1 ~Fk @~sk @x ; A1 where } UKIN \u00ff UPOT (the Lagrange operator). For the kinetic energy (UKIN) and the potential energy (UPOT) we can write, UKIN 1=2MHkVHk2 1=2mkVSLk2 1=2mkVTLk2 1=2ILk _uSLk2 1=2ILk _uTLk2 A2 UPOT lga cosuSL \u00ff mgp cosuTL MTRg USPRING A3 with l MH 1 b=a m. where Vn = speed vector of mass n, g = gravitation constant, U0 = pre-tension, USPRING = spring energy. Choosing a coordinate frame (Fig. 1), expressing speeds (V) in state vector x, substitute the result in (A2) and (A3), evaluating (A1) gives: M x x N x; _x _x G x C x \u00ffD _x 0 : A4 where, G x \u00fflag sinuSL mgp sinuTL MTg cosuSL 24 35 with b LSL \u00ff p \u00ff R, a LSL \u00ff R, MT MH 2m, k MH 1 b2=a2 m; a uSL \u00ff uTL, The total spring energy (USPRING) yields: USPRING 1 2 CTL FL \u00ff U0 \u00ff 1 2 RHIP a 2 1 2 CTL EX \u00ff U0 1 2 RHIP a 2 1 2 CSL FL \u00ff U0 \u00ff 1 2 RHIP a 2 1 2 CSL EX \u00ff U0 1 2 RHIP a 2 1 2 CLEG PFL \u00ff U0 LSL \u00ff L0 2 1 2 CLEG DFL \u00ff U0 \u00ff LSL L0 2 : A5 where the index `EX' stands for extensor, `FL' stands for \u00afexor, `PFL' stands for plantar \u00afexor, `DFL' stands for dorsi \u00afexor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003124_j.ijar.2006.08.002-Figure3-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003124_j.ijar.2006.08.002-Figure3-1.png",
        "caption": "Fig. 3. Structure of a single-inverted pendulum system.",
        "texts": [
            " The adaptive learning algorithms in the DSMFNNC system are derived by Lyapunov stability analysis, so that system stability can be guaranteed in the closed-loop system. The effectiveness of the proposed control system will be verified by simulation results in Section 4. In this section, we apply the DSMFNNC to a single-inverted pendulum system, a ballbeam system [9], a TORA system [25] and a practical seesaw system to demonstrate the theoretical development to verify the theoretical development. The structure of a single-inverted pendulum is illustrated in Fig. 3 and its dynamic is described below _x1 \u00bc x2 _x2 \u00bc mtg sin x1 mpL sin x1 cos x1x2 2 \u00fe cos x1 u L 4 3 mt mp cos2 x1 \u00fe d _x3 \u00bc x4 _x4 \u00bc 4 3 mpLx2 2 sin x1 \u00fe mpg sin x1 cos x1 4 3 mt mp cos2 x1 \u00fe 4 3 4 3 mt mp cos2 x1 u\u00fe d \u00f036\u00de where x1 = h, the angle of the pole with respect to the vertical axis; x2 \u00bc _h, the angle velocity of the pole with respect to the vertical axis; x3 = x, the position of the cart; x4 \u00bc _x, the velocity of the cart; mt = mc + mp In what follows, we define the following variables: s1 \u00bc c1\u00f0h z\u00de \u00fe _h \u00bc c1\u00f0x1 z\u00de \u00fe x2 \u00f037\u00de s2 \u00bc c2x\u00fe _x \u00bc c2x3 \u00fe x4 \u00f038\u00de and z \u00bc sat\u00f0s2=Uz\u00de Zupper; 0 < Zupper < 1 \u00f039\u00de In the simulation, the following specifications are used: mp \u00bc 0:05 kg; mc \u00bc 1 kg; L \u00bc 0:5 m; g \u00bc 9:8 m=s2 ; c1 \u00bc 5; c2 \u00bc 0:5; Uz \u00bc 15; Zupper \u00bc 0:9425; jdj 6 0:0873; 11 \u00bc 0:5; 12 \u00bc 0:5; U1 \u00bc 0:5 initial values are h \u00bc 60 ; _h \u00bc 0; x \u00bc 0; _x \u00bc 0 To avoid the situation where the cart never stops, must be properly chosen c2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure14.2-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure14.2-1.png",
        "caption": "Figure 14.2 A gymnast on the high bar.",
        "texts": [
            "4) Note that v = rwanddvjdt = ra. Therefore, ifthe angularveloc ity and acceleration are known, then the kinetic characteristics of the problem can be analyzed using: LFn = mr w2 (14.5) L Ft = m r a (14.6) Note that for rotational motion there is always a normal compo nent of the acceleration vector, and therefore, a force acting in Angular Kinetics 297 298 Fundamentals of Biomechanics the normal direction, but the tangential components of the force and acceleration vectors mayor may not exist. Example 14.1 Figure 14.2 illustrates a 60 kg gymnast swinging on a high bar. The rotational motion of the gymnast may be simplified by modeling the gymnast as a particle attached to a string such that the mass of the particle is equal to the mass of the gymnast and the length of the string is equal to the distance between the high bar and the center of gravity of the gymnast. As the gymnast moves, the center of gravity undergoes a circular motion. Assume that the center of gravity of the gymnast is located at a distance r = 1 m from the high bar, the speed of the center of gravity at position 1 is almost zero, and that the effects of air resistance are negligible. Position 1 is directly above the high bar and it represents the highest elevation reached by the center of gravity of the gymnast (a) By using the conservation of energy principle, calculate the speeds of the gymnast's center of gravity at positions 2, 3, 4, and 5. As shown in Figure 14.2, positions 2 and 4 make an angle () = 45\u00b0 with the horizontal, position 3 is along the same horizontal line as the high bar, and position 5 is directly under the high bar. (b) Calculate the angular velocities of the gymnast at positions 1,2,3,4, and 5. (c) Calculate the normal component of the linear accelerations of the gymnast's center of gravity at positions 1,2,3,4, and 5. (d) Calculate the forces applied on gymnast's arms at positions 1,2,3,4, and 5. (e) Calculate the tangential component of the linear accelera tions of the gymnast's center of gravity at positions 1,2,3,4, and 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure4.25-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure4.25-1.png",
        "caption": "Figure 4.25 Example 4.4.",
        "texts": [
            " For such de vices to be effective, they must be designed to transmit forces properly to the body part in terms of force direction and magni tude. Different arrangements of cables and pulleys can transmit different magnitudes of forces and in different directions. For example, the traction in Figure 4.23 applies a horizontal force to the leg with magnitude equal to the weight in the weight pan. On the other hand, the traction in Figure 4.24 applies a horizon tal force to the leg with magnitude twice as great as the weight in the weight pan. Example 4.4 Using three different cable-pulley arrangements shown in Figure 4.25, a block of weight W is elevated to a certain height. For each system, determine how much force is applied to the person holding the cable. Solutions: The necessary free-body diagrams to analyze each system in Figure 4.25 are shown in Figure 4.26. For the analysis Statics: Analyses of Systems in Equilibrium 65 of the system in Figure 4.25a, all we need is the free-body di agram of the block (Figure 4.26a). For the vertical equilibrium of the block, tension in the cable must be Tl = W. Therefore, a force with magnitude equal to the weight of the block is applied to the person holding the cable. For the analysis of the system in Figure 4.25b, we need to ex amine the free-body diagram of the pulley closest to the block (Figure 4.26b). For the vertical equilibrium of the pulley, the tens ion in the cable must be T2 = Wj2. T2 is the tension in the ca ble that is wrapped around the two pulleys and is held by the person. Therefore, a force with magnitude equal to half of the weight of the block is applied to the person holding the cable. For the analysis of the system in Figure 4.25c, we again need to examine the free-body diagram of the pulley closest to the block (Figure 4.26c). For the vertical equilibrium of the pulley, the tension in the cable must be T3 = Wj3. T3 is the tension in the cable that is wrapped around the three pulleys and is held by the person. Therefore, a force with a magnitude equal to one third of the weight of the block is applied to the person holding the cable. 4.10 Built-in Structures The beam shown in Figure 4.27 is built-in or welded to a wall and is called a cantilever beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.33-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.33-1.png",
        "caption": "Figure 3.33 A cantilever beam.",
        "texts": [
            " The proximal arm (AB) of the nail has a length a and makes an angle () with BC As illustrated in Figure 3.32, the intertrochanteric nail is sub jected to three experiments by applying forces F 1 (horizontal, toward the right), F 2 (aligned with AB, toward A), and L (vertically downward). Determine expressions for the moment Moment and Torque 45 generated at B by the three forces in terms of force magnitudes and geometric parameters a and (). Answers: Ml=aF1sin()(cw) M2 =0 Ma=aF3cos()(Ccw) Problem 3.4 The simple structure shown in Figure 3.33 is called a cantilever beam and is one of the fundamental mechanical ele ments in engineering. A cantilever beam is fixed at one end and free at the other. In Figure 3.33, the fixed and free ends of the beam are identified as A and C, respectively. Point B corresponds to the center of gravity of the beam. Assume that the beam shown has a weight W = 100 N and a length l = 1 m. A force with magnitude F = 150 N is applied at the free-end of the beam in a direction that makes an angle () = 45\u00b0 with the horizontal. Determine the magnitude and direction of the net moment de veloped at the fixed-end of the beam. Answer: MA = 56 N-m (ccw) Problem 3.5 Consider the L-shaped beam illustrated in Figure 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002641_5.301681-Figure18-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002641_5.301681-Figure18-1.png",
        "caption": "Fig. 18. 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 since its flux can circulate in and out the pole face. Many structural variants of buried-magnet machines have been proposed [5 1]-[541. Some of these are well suited for high-speed applications. IX. SWITCHED-RELUCTANCE MOTORS The switched-reluctance (SR) motor has a doubly salient structure [55]. The machine shown in cross section in Fig. 18 has 6 stator poles and 4 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. If supply current is switched through the coils of phase a, there will be a counterclockwise torque acting to align a 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 Fig. 18, the rotor moves x 16 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 by reversing the sequence of the currents to a, c, b. Many other pole choices are useful, particularly 8/6 (4- phase) and 10/8 (5-phase) [ S I , [56]. 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",
            " Torque In practice, many switched reluctance motors are operated so that the poles are significantly saturated when aligned and energized. The average torque which these motors can produce may be assessed from the magnetizing characteristics relating the phase flux linkage X to the coil current i when in the aligned and unaligned positions [l]. A typical set of relations for the 6/4 motor is shown in Fig. 19. It can be shown that the average torque is equal to the shaded area between the unaligned and aligned curves measured in joules (or Wb.A),divided by the rotational angle between these positions (i.e., 7r/6 rad in Fig. 18). To optimize this torque, the slope of the linear part of the aligned characteristic can be increased by reduction of the air gap between the aligned poles while the unaligned slope can be adjusted by changing the relative widths of the stator and rotor poles [57]-[59]. When the poles are aligned, the stored energy in the magnetic field is represented by the shaded area between the aligned curve and the vertical axis. The power converter is usually designed to retum this energy to the supply as efficiently as possible"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0003669_bf03256551-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0003669_bf03256551-Figure1-1.png",
        "caption": "FIG. 1. Spacecraft Body with the i th VSCMG.",
        "texts": [
            " Recently, Chang [15] provided an adaptive, robust tracking control algorithm for nonlinear MIMO systems. His work is based on the \u201csmooth projection algorithm,\u201d which has also been used in references [16] and [17] for adaptive control of SISO systems. This algorithm plays a key role in our developments by keeping the parameter estimates inside a properly defined convex set, so that the estimates neither drift into a region where the control law may become singular nor diverge to very large values. Consider a spacecraft with a VSCMG cluster of N flywheels, as shown in Fig. 1. The definition of the axes in Figure 1 is as follows ( ):i 1, . . . , N \u2022 : VSCMG gimbal axis unit vector \u2022 : VSCMG spin axis unit vector \u2022 : VSCMG transverse axis unit vector (torque vector) given as . The equations of motion of a spacecraft with a cluster of VSCMGs are rather complicated [8, 11, 18]. Thus, in this paper a set of simplified (but still nonlinear) equations will be used to assist with the control law design. The final controller will nonetheless be validated against the complete, nonlinear model in the numerical simulations later on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002960_tfuzz.2004.836087-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002960_tfuzz.2004.836087-Figure1-1.png",
        "caption": "Fig. 1. Cart with an inverted pendulum as a testbed for the proposed controllers\u2019 performance.",
        "texts": [
            " The tradeoff between the steady-state tracking error and the control effort is expressed by the radius of the uncertainty ball (28) This expression is obtained from ii). We call the above set uncertainty ball because the tracking error is guaranteed to enter the ball after finite time and reside within this ball thereafter. Note that the expression of the ball given by (28) can be obtained from (26) by letting and using the relationship . We consider an inverted pendulum on a cart system that is depicted in Fig. 1. The dynamics of the inverted pendulum can be described as (29) where is the angular position of the pendulum, is the mass of the pendulum, is the mass of the cart, is is the half the length of the pendulum. Their values are given in Table I. For details of the modeling of the above system, we refer to any of the references: [17], [19], [20], or [21]. It is easy to verify that takes positive value and is bounded away from zero for all , which is the required assumption on . Also the denominator of is strictly positive for all and by assuming that is bounded, we have bounded "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002729_cp:19951052-Figure1-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002729_cp:19951052-Figure1-1.png",
        "caption": "Figure 1 : Sliding region \u20acor a robust system",
        "texts": [],
        "surrounding_texts": [
            "220\nnetic ~ ~ ~ ~ ~ ~ t ~ ~ s Applied to Fuzzy Sliding Mode Controller Design\nK.C. Ng , Y. Li, D.3. Munay-Smith and K.C. Shaman\nUniversity of Glasgow, UK\nb a i l address: K.Ng@elec.gla.ac.uk, Y.Li@elec.gla.ac.uk\n- The drawbacks of sliding 1 in terms of high control gains\nare overcome by or~orating fuzzy control to the switching\nsystem increases the n and, at present, there design tools due to the ieJ and numerical\npaper develops an design approach to this design\ntournament and rank-based ms to replace the trial-andThe metbod is illustrated ign of a newoptimal fuzzy-\node controller for a nonlinear 1 control system. The control ves a reiatively low overshoots tb control action and retains\ning mode approach.\nmodeling imprecision and bounded It achieves robust control by\ncontrol signal across atisfying the sliding\ndue bs the non-liear compensation and can P from the effects d actuator chattering to the switching and imperfect\nhas excelled in dealing with systems that are complex, iildefined, non- l ia r , or time-varying. p;LC is relatively easy to implement, as it usually needs no mathematical model of the controlled system. This is achieved by Gonverting the linguistic control strategy d human experience OE experts' howledge into an autmatic control strategy. Fuzzy logic control\nThe feature of a smooth control action of FZC can be used to overcome the disadvantages of the SMC systems. This is achieved by merging of the FLC with the variable structure of the SMC to form afuzzysliding mode controller (p;SMC)2\"5. In this hybrid control system. the strength of the slidiug mode control lies in its ability to account for modeling imprecision and external disturbances while the K C provides better damping and reduced chattering.\nHowever, the major drawback of fuzzy control is the lack of design techniques. Most of the fuzzy rules are hman knowledge oriented and hence rules will deviate from person to person in spite of the same performance of the system. The selection d suitable membership functions and their de f~ t ions along the universe of disc~urse always involve a painstaking trid-and-error process.\nThis paper develops genetic algorithms (GAS) for the automatic design of I fuzzysliding mode control systm. In this GA based approach, a near-optimal fuzzy sliding mode controller has been achieved, fulfilling the robustness criteria spsifikd in the sliding mode contro.ol and yielding a high performance in implementation. Section II shows the deve!opment d soft-swikhd sliding mode centroller design based on the synhsis of conventional control technique. In subsequent, a fuzzy sliding mode control is being designed in which the switching gain is being fuzzified. Section Ill has provided the material in genetic algorithm and its application to FSMC design. Implemented results in this section have demonstrated a superior perfomance of FSMC in terms of chattering or smoother control action as compared with the normal SMC design. Finally, conclusion is highlighted in section IV.\nGenetic Algorithms in Engineering Systems: Innovations and Applications 12-14 September 1995, Conference Publication No. 414, Q IEE, 1995",
            "22 1\nII. FUZZY-SLIDING MODE CONTROL\nA. Soft-Switching SMC\nSuppose a non-linear system to be controlled is defmed by the general statespace equation:\n(1) x = f( x, U, t )\nwhere x \u20ac R n is the state vector, u\u20acMm the input vector, n the order of the system and m the number of inputs. Then the sliding surfacebw8 hyperplane, s(e, t) , is given by :\n(2) s (e , t )= e : H T e = o }\nwhere HERn represents the coefficients, or slope, of the sliding surface. Here\nis the negative tracking error vector. Usually a time-varying sliding surface, s(t), is simply defined in the state-space Rn by the scalar equation, given by\ns(e;t)=(-$+h) e = O n-1\n(4) where h is a strictly positive constant that can also be interpreted as the slope of the sliding surface. For instant, if n=2 (for a secondordenxi system ) ,\ns = e + h e and hence. s is simply a weighted sum d the position and velocity error.\nFrom (4). the #-order tracking problem is now behg replaced by a lS'-order stabilization problem in which the scalar s is to be kept at zero by a governing condition1 given by:\nI d --s2 2 0 2 dt (5) ss s 0\nIt can be seen that, when operating ita the sliding mode, the system response is chattering along the SO hyperplane. From (51, the existence and convergence condition can thus be re-written as5:\nsi S -qIsl (6) to permit a non-switching region. Here q is a strictly positive constant, the value of which is usually chosen based on some knowledge of disturbances or system dynamics in terms of some known amplitudes. Therefore, the condition (6) implies that some disturbances or dynamic uncertainties can be tollerated\nwhile still moving along the sliding surface. For a known maximum value of s i , say -a, the switching surface s can be transformed into a sliding hyper-region, given by\nA soft-switching control law9 in fulfilling the robust criteria (6) with a sliding hyperregion defined by <. is given by:\nu=u$ - (k ,Jedt ) - (k2e) - (k ,$) (8)\n= U, + %lnc\n4, i f ' 4 w h e k l = klb if %<s<; f\nk,, if s < -4 40 i f e s > 5\nk,, if e s < - t\nk3a i f e s > {\nI 1 k, = k2b i f < < e s < {\nk3 = k3b i f -4 S eS <( 1 k3c i f i ~ < - 4 and\nU , =-K,tanh(f)\nrepresents the major switching action. Here A is a positive constant defining the slope of the hyperbolic-tangent function.\nNote that when the states fall within the sliding region, usmc is transformed to the control equivalent, uey. and is given by :\nde I dt Ueq = -klb edt - k&? - k3b -\nwhich is purely a conventional @'ID) proportional plus integral plus derivative action.",
            "222\nB . Fuzzy SMC\nIn the fuzzy SMC ~ c h e m e ~ - ~ , the sliding surface s(t) forms the input space of the fuzzy implications of the major switching rule. its switching gain is written in the form of fuzzy rule, given by:\nwhere j=l,..,n and n is the numder of rules. With fuzzy implications, K , is then transformed to an adjustable parameter and hence the fuzzy inference mechanism can be used as estimation mechanism for adaptive control. The inclusion of such fuzzy scheme has thus accounted for bounded uncertainties in the system2v5. The use of a fuzzy scheme for determining the values of K , improves the performance by improving the damping ratio of the control system. Ideally, it works in a such way that when s(t) is far away from the sliding surface, the control gain has a higher value and when s(t) is near to the sliding surface, the gain is adjusted to a smaller value. Hence, a soft computing approach is adopted here for such a soft-switched FSMC system.\nA one-dimensioned input space is usually adequate determining the switchmg rules and is being adopted here to reduce the computational demand of the FLC. To reflect the fuzzy nature of the seven linguistic classifications and to allow for high performance controller designs, sophisticated membership functions14 are used. These are given by :\nIf s(t) is Aj, Then K , is B .\nused for determining fuzzy control action is the centre of gravity (COG) approach.\n(9) where i E (Zero; f Small; f. Medium; +_ Big} and\np+Big =1 , vx > a+Big ' g P-sis =1 9 tJx < a-B'\nwhere ctie [-Big, +Bid is termed the position parameter which describes the centre point of the membership function along the universe d discourse; j3iEE1.5, 4.51 is the shape parameter which resembles evolutionary shapes, including triangles and trapezoids; and oiE[0.05, 5.01 is the scale parameter which modifies the base-length of the membership functions and determines the amount of overlapping. Note also that in (9), oi is not included in the power of j3; and this will allow for a gradual and consistent change in base-length. The defuzzification method\nHI. GENETIC hGORITEIMS &'PLIED TO\nFSMC DESIGN\nA. The Genetic Algorithms\nThe genetic algorithmlo,ll (GA) is based on an analogy to the genetic code in OUT own DNA (deoxyribonucleic acid) structure, where its coded chromosome is composed of many genes. The GA approach involves a population of individuals represented by strings of characters or digits. Each string is however, coded with a search point In the hyper search-space. From the evolutionary theory, only the most suited individuals in the population are likely to survive and generate off-spring that pass their genetic material to the next generation. Therefore the most promising individuals are manipulated by the GA in its search for improved performances or solutions. In CAS, three basic operators, namely, reproduction, crossover and mutation, form the core of the genetic computation. In some GAS, a further operator, gene inversion is also used.\nIn the reproduction process, the selection scheme adopted in this paper is based on the tournament selection in conjunction with a rank-based method. It is achieved by initially ranking or sorting the ~ p ~ ~ t i o n in the descendiztg order where higher fitness strings are located at the top of the population. Selection is then a ~ p r o a c h ~ by choosing the fxst parents for the parent-pairs from the top 25% of the population which have the highest fitness, whilst the second parents are randomly chosen from the string-group which consist of topbottom 50% of the entire population. Hence the first parent will be used twice in the reproduction and the second parents will be each from string-group determined from the top and bottom 50% d the entire population, respectively. This method will allow both good and poor strings to evolve in the genetic search as some good genetic materials may be distributed in the p r strings.\nThe crossover operator, which is the main dominant operator in the genetic algorithm, is used to produce off-spring that are different from their parents but inherit a portion of their parents' genetic material. Under this operator, a selected chromosome is split into two parts"
        ]
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure3.28-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure3.28-1.png",
        "caption": "Figure 3.28 Scalar method.",
        "texts": [
            " The weight applies an upward (in the y direction) force with magnitude F on the arm at point C. The lengths of the upper arm and lower arm are a = 25 em and b = 30 em, respectively, and the magnitude of the applied force is F =200N. Explain how force F can be translated to the shoulder joint at A, and determine the magnitudes and directions of moments developed at the lower and upper arms by F. Solution 1: Scalar method. The scalar method of finding the moments generated on the lower arm (BC) and upper arm (AB) is illustrated in Figure 3.28, and it utilizes the concepts of couple and couple-moment. The first step is placing a pair of forces at B with equal mag nitude (F) and opposite directions, both being parallel to the original force at C (Figure 3.28a). The upward force at C and the downward force at B form a couple. Therefore, they can be re placed by a couple-moment (shown by a double-headed arrow in Figure 3.28b). The magnitude ofthe couple-moment is b F . Ap plying the right-hand-rule, we can see that the couple-moment acts in the negative x direction. If Mx refers to the magnitude of this couple-moment, then: Mx=bF ( - x direction) The next step is to place another pair of forces at A where the shoulder joint is located (Figure 3.28c). This time, the upward force at B and the downward force at A form a couple, and again, they can be replaced by a couple-moment (Figure 3.28d). The magnitude of this couple-moment is a F, and it has a direction perpendicular to the xy-plane, or, it is acting in the positive z direction. Referring to the magnitude of this moment as Mz, then: Mz=a F (+z direction) To evaluate the magnitudes of the couple-moments, the nu merical values of a, b, and F must be substituted in the above equations: Mx = (0.30)(200) = 60 N-m Mz = (0.25)(200) = 50 N-m The effect of the force applied at C is such that at the elbow joint, the person feels an upward force with magnitude F and a mo ment with magnitude Mx that is trying to rotate the lower arm in the yz-plane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_8_0002719_978-1-4757-3067-8-Figure8.14-1.png",
        "original_path": "designv10-8/openalex_figure/designv10_8_0002719_978-1-4757-3067-8-Figure8.14-1.png",
        "caption": "Figure 8.14 Principal stresses.",
        "texts": [
            "4 Principal Stresses There are infinitely many possibilities of constructing elements around a given point within a structure. Among these possibil ities, there may be one element for which the normal stresses 162 Fundamentals of Biomechanics are maximum and minimum. These maximum and minimum normal stresses are called the principal stresses, and the planes with normals collinear with the directions of the maximum and minimum stresses are called the principal planes. On a principal plane, the shear stress is zero (Figure 8.14). This condition of zero shear stress and Eqs. (8.10) through (8.12) can be utilized to de termine the principal normal stresses and the orientation of the principal planes. This can be achieved by setting Eq. (8.12) equal to zero and solving it for angle (). If the angle thus determined is denoted as ()l, then: 1 -l( 2 i xy ) ()l = -2 tan ax -ay (8.13) Here, ()l represents the angle of orientation of the principal planes relative to the x and y axes. If() in Eqs. (8.10) and (8.11) is replaced by ()l, then the following expressions can be derived for the prin cipal stresses al and a2: al = ax +ay 2 + (ax - ay )2 2 2 + ixy (8"
        ],
        "surrounding_texts": []
    }
]